MathGL 2.3.5

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MathGL

This file documents the Mathematical Graphic Library (MathGL), a collection of classes and routines for scientific plotting. It corresponds to release 2.3.5 of the library. Please report any errors in this manual to mathgl.abalakin@gmail.org. More information about MathGL can be found at the project homepage, http://mathgl.sourceforge.net/.

Copyright © 2008-2012 Alexey A. Balakin.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License.”

• Overview:  
• Examples:  
• General concepts:  
• MathGL core:  
• Widget classes:  
• Data processing:  
• MGL scripts:  
• UDAV:  
• Other classes:  
• Symbols and hot-keys:  
• File formats:  
• TeX-like symbols:  
• Plotting time:  
• Copying This Manual:  
• Index:  

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1 Overview

MathGL is ...

• What is MathGL?:  
• MathGL features:  
• Installation:  
• Quick guide:  
• Changes from v.1:  
• Utilities:  
• Thanks:  

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1.1 What is MathGL?

A code for making high-quality scientific graphics under Linux and Windows. A code for the fast handling and plotting of large data arrays. A code for working in window and console regimes and for easy including into another program. A code with large and renewal set of graphics. Exactly such a code I tried to put in MathGL library.

At this version (2.3.5) MathGL has more than 50 general types of graphics for 1d, 2d and 3d data arrays. It can export graphics to bitmap and vector (EPS or SVG) files. It has OpenGL interface and can be used from console programs. It has functions for data handling and script MGL language for simplification of data plotting. It also has several types of transparency and smoothed lighting, vector fonts and TeX-like symbol parsing, arbitrary curvilinear coordinate system and many other useful things (see pictures section at homepage). Finally it is platform-independent and free (under GPL v.2.0 or later license).

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1.2 MathGL features

MathGL can plot a wide range of graphics. It includes:

In fact, I created the functions for drawing of all the types of scientific plots that I know. The list of plots is growing; if you need some special type of a plot then please email me e-mail and it will appear in the new version.

I tried to make plots as nice looking as possible: e.g., a surface can be transparent and highlighted by several (up to 10) light sources. Most of the drawing functions have 2 variants: simple one for the fast plotting of data, complex one for specifying of the exact position of the plot (including parametric representation). Resulting image can be saved in bitmap PNG, JPEG, GIF, TGA, BMP format, or in vector EPS, SVG or TeX format, or in 3D formats OBJ, OFF, STL, or in PRC format which can be converted into U3D.

All texts are drawn by vector fonts, which allows for high scalability and portability. Texts may contain commands for: some of the TeX-like symbols, changing index (upper or lower indexes) and the style of font inside the text string (see Font styles). Texts of ticks are rotated with axis rotation. It is possible to create a legend of plot and put text in an arbitrary position on the plot. Arbitrary text encoding (by the help of function setlocale()) and UTF-16 encoding are supported.

Special class mglData is used for data encapsulation (see Data processing). In addition to a safe creation and deletion of data arrays it includes functions for data processing (smoothing, differentiating, integrating, interpolating and so on) and reading of data files with automatic size determination. Class mglData can handle arrays with up to three dimensions (arrays which depend on up to 3 independent indexes a_{ijk}). Using an array with higher number of dimensions is not meaningful, because I do not know how it can be plotted. Data filling and modification may be done manually or by textual formulas.

There is fast evaluation of a textual mathematical expression (see Textual formulas). It is based on string precompilation to tree-like code at the creation of class instance. At evaluation stage code performs only fast tree-walk and returns the value of the expression. In addition to changing data values, textual formulas are also used for drawing in arbitrary curvilinear coordinates. A set of such curvilinear coordinates is limited only by user’s imagination rather than a fixed list like: polar, parabolic, spherical, and so on.

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1.3 Installation

MathGL can be installed in 4 different ways.

  1. Compile from sources. The cmake build system is useded in the library. To run it, one should execute commands: cmake . twice, after it make and make install with root/sudo rights. Sometimes after installation you may need to update the library list – just execute ldconfig with root/sudo rights.

    There are several additional options which are switched off by default. They are: enable-fltk, enable-glut, enable-qt4, enable-qt5 for ebabling FLTK, GLUT and/or Qt windows; enable-jpeg, enable-gif, enable-hdf5 and so on for enabling corresponding file formats; enable-all for enabling all additional features. For using double as base internal data type use option enable-double. For enabling language interfaces use enable-python, enable-octave or enable-all-swig for all languages. You can use WYSIWYG tool (cmake-gui) to view all of them, or type cmake -D enable-all=on -D enable-all-widgets=on -D enable-all-swig=on . in command line for enabling all features.

    There is known bug for building in MinGW – you need to manually add linker option -fopenmp (i.e. CMAKE_EXE_LINKER_FLAGS:STRING='-fopenmp' and CMAKE_SHARED_LINKER_FLAGS:STRING='-fopenmp') if you enable OpenMP support (i.e. if enable-openmp=ON).

  2. Use a precompiled binary. There are binaries for MinGW (platform Win32). For a precompiled variant one needs only to unpack the archive to the location of the compiler (i.e. mathgl/lib in mingw/lib, mathgl/include in mingw/include and so on) or in arbitrary other folder and setup paths in compiler. By default, precompiled versions include the support of GSL (www.gsl.org) and PNG. So, one needs to have these libraries installed on system (it can be found, for example, at http://gnuwin32.sourceforge.net/packages.html).
  3. Install precompiled versions from standard packages (RPM, deb, DevPak and so on).

Note, you can download the latest sources (which can be not stable) from sourceforge.net SVN by command 

svn checkout http://svn.code.sf.net/p/mathgl/code/mathgl-2x mathgl-code

IMPORTANT! MathGL use a set of defines, which were determined at configure stage and may differ if used with non-default compiler (like using MathGL binaries compiled by MinGW in VisualStudio). There are MGL_SYS_NAN, MGL_HAVE_TYPEOF, MGL_HAVE_PTHREAD, MGL_HAVE_ATTRIBUTE, MGL_HAVE_C99_COMPLEX, MGL_HAVE_RVAL. I specially set them to 0 for Borland and Microsoft compilers due to compatibility reasons. Also default setting are good for GNU (gcc, mingw) and clang compilers. However, for another compiler you may need to manually set this defines to 0 in file include/mgl2/config.h if you are using precompiled binaries.

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1.4 Quick guide

There are 3 steps to prepare the plot in MathGL: (1) prepare data to be plotted, (2) setup plot, (3) plot data. Let me show this on the example of surface plotting.

First we need the data. MathGL use its own class mglData to handle data arrays (see Data processing). This class give ability to handle data arrays by more or less format independent way. So, create it 

    int main()
    {
        mglData dat(30,40);	// data to for plotting
        for(long i=0;i<30;i++)   for(long j=0;j<40;j++)
            dat.a[i+30*j] = 1/(1+(i-15)*(i-15)/225.+(j-20)*(j-20)/400.);

Here I create matrix 30*40 and initialize it by formula. Note, that I use long type for indexes i, j because data arrays can be really large and long type will automatically provide proper indexing.

Next step is setup of the plot. The only setup I need is axis rotation and lighting. 

        mglGraph gr;		// class for plot drawing
        gr.Rotate(50,60);	// rotate axis
        gr.Light(true);		// enable lighting

Everything is ready. And surface can be plotted. 

        gr.Surf(dat);		// plot surface

Basically plot is done. But I decide to add yellow (‘y’ color, see Color styles) contour lines on the surface. To do it I can just add: 

        gr.Cont(dat,"y");	// plot yellow contour lines

This demonstrate one of base MathGL concept (see, General concepts) – “new drawing never clears things drawn already”. So, you can just consequently call different plotting functions to obtain “combined” plot. For example, if one need to draw axis then he can just call one more plotting function 

        gr.Axis();			// draw axis

Now picture is ready and we can save it in a file. 

        gr.WriteFrame("sample.png");	// save it
    }

To compile your program, you need to specify the linker option -lmgl.

This is enough for a compilation of console program or with external (non-MathGL) window library. If you want to use FLTK or Qt windows provided by MathGL then you need to add the option -lmgl-wnd.

Fortran users also should add C++ library by the option -lstdc++. If library was built with enable-double=ON (this default for v.2.1 and later) then all real numbers must be real*8. You can make it automatic if use option -fdefault-real-8.

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1.5 Changes from v.1.*

There are a lot of changes for v.2. Here I denote only main of them.

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1.6 Utilities for parsing MGL

MathGL library provides several tools for parsing MGL scripts. There is tools saving it to bitmap or vectorial images (mglconv). Tool mglview show MGL script and allow to rotate and setup the image. Another feature of mglview is loading *.mgld files (see ExportMGLD()) for quick viewing 3d pictures.

Both tools have similar set of arguments. They can be name of script file or options. You can use ‘-’ as script name for using standard input (i.e. pipes). Options are:

Additionally mglconv have following options:

Also you can create animated GIF file or a set of JPEG files with names ‘frameNNNN.jpg’ (here ‘NNNN’ is frame index). Values of the parameter $0 for making animation can be specified inside the script by comment ##a val for each value val (one comment for one value) or by option(s) ‘-A val’. Also you can specify a cycle for animation by comment ##c v1 v2 dv or by option -C v1:v2:dv. In the case of found/specified animation parameters, tool will execute script several times – once for each value of $0.

MathGL also provide another simple tool mgl.cgi which parse MGL script from CGI request and send back produced PNG file. Usually this program should be placed in /usr/lib/cgi-bin/. But you need to put this program by yourself due to possible security issues and difference of Apache server settings.

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1.7 Thanks

Javascript interface was developed with support of DATADVANCE company.

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2 MathGL examples

This chapter contain information about basic and advanced MathGL, hints and samples for all types of graphics. I recommend you read first 2 sections one after another and at least look on Hints section. Also I recommend you to look at General concepts and FAQ.

Note, that MathGL v.2.* have only 2 end-user interfaces: one for C/Fortran and similar languages which don’t support classes, another one for C++/Python/Octave and similar languages which support classes. So, most of samples placed in this chapter can be run as is (after minor changes due to different syntaxes for different languages). For example, the C++ code 

#include <mgl2/mgl.h>
int main()
{
  mglGraph gr;
  gr.FPlot("sin(pi*x)");
  gr.WriteFrame("test.png");
}

in Python will be as 

from mathgl import *
gr = mglGraph();
gr.FPlot("sin(pi*x)");
gr.WriteFrame("test.png");

in Octave will be as (you need first execute mathgl; in newer Octave versions) 

gr = mglGraph();
gr.FPlot("sin(pi*x)");
gr.WriteFrame("test.png");

in C will be as 

#include <mgl2/mgl_cf.h>
int main()
{
  HMGL gr = mgl_create_graph(600,400);
  mgl_fplot(gr,"sin(pi*x)","","");
  mgl_write_frame(gr,"test.png","");
  mgl_delete_graph(gr);
}

in Fortran will be as 

integer gr, mgl_create_graph
gr = mgl_create_graph(600,400);
call mgl_fplot(gr,'sin(pi*x)','','');
call mgl_write_frame(gr,'test.png','');
call mgl_delete_graph(gr);

and so on.

• Basic usage:  
• Advanced usage:  
• Data handling:  
• Data plotting:  
• 1D samples:  
• 2D samples:  
• 3D samples:  
• Vector field samples:  
• Hints:  
• FAQ:  

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2.1 Basic usage

MathGL library can be used by several manners. Each has positive and negative sides:

MathGL drawing can be created not only by object oriented languages (like, C++ or Python), but also by pure C or Fortran-like languages. The usage of last one is mostly identical to usage of classes (except the different function names). But there are some differences. C functions must have argument HMGL (for graphics) and/or HMDT (for data arrays) which specifies the object for drawing or manipulating (changing). Fortran users may regard these variables as integer. So, firstly the user has to create this object by function mgl_create_*() and has to delete it after the using by function mgl_delete_*().

Let me consider the aforesaid in more detail.

• Using MathGL window:  
• Drawing to file:  
• Animation:  
• Drawing in memory:  
• Draw and calculate:  
• Using QMathGL:  
• MathGL and PyQt:  
• MathGL and MPI:  

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2.1.1 Using MathGL window

The “interactive” way of drawing in MathGL consists in window creation with help of class mglQT, mglFLTK or mglGLUT (see Widget classes) and the following drawing in this window. There is a corresponding code: 

#include <mgl2/qt.h>
int sample(mglGraph *gr)
{
  gr->Rotate(60,40);
  gr->Box();
  return 0;
}
//-----------------------------------------------------
int main(int argc,char **argv)
{
  mglQT gr(sample,"MathGL examples");
  return gr.Run();
}

Here callback function sample is defined. This function does all drawing. Other function main is entry point function for console program. For compilation, just execute the command 

gcc test.cpp -lmgl-qt -lmgl

Alternatively you can create yours own class inherited from mglDraw class and re-implement the function Draw() in it: 

#include <mgl2/qt.h>
class Foo : public mglDraw
{
public:
  int Draw(mglGraph *gr);
};
//-----------------------------------------------------
int Foo::Draw(mglGraph *gr)
{
  gr->Rotate(60,40);
  gr->Box();
  return 0;
}
//-----------------------------------------------------
int main(int argc,char **argv)
{
  Foo foo;
  mglQT gr(&foo,"MathGL examples");
  return gr.Run();
}

Or use pure C-functions: 

#include <mgl2/mgl_cf.h>
int sample(HMGL gr, void *)
{
  mgl_rotate(gr,60,40,0);
  mgl_box(gr);
}
int main(int argc,char **argv)
{
  HMGL gr;
  gr = mgl_create_graph_qt(sample,"MathGL examples",0,0);
  return mgl_qt_run();
/* generally I should call mgl_delete_graph() here,
 * but I omit it in main() function. */
}

The similar code can be written for mglGLUT window (function sample() is the same): 

#include <mgl2/glut.h>
int main(int argc,char **argv)
{
  mglGLUT gr(sample,"MathGL examples");
  return 0;
}

The rotation, shift, zooming, switching on/off transparency and lighting can be done with help of tool-buttons (for mglQT, mglFLTK) or by hot-keys: ‘a’, ‘d’, ‘w’, ‘s’ for plot rotation, ‘r’ and ‘f’ switching on/off transparency and lighting. Press ‘x’ for exit (or closing the window).

In this example function sample rotates axes (Rotate(), see Subplots and rotation) and draws the bounding box (Box()). Drawing is placed in separate function since it will be used on demand when window canvas needs to be redrawn.

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2.1.2 Drawing to file

Another way of using MathGL library is the direct writing of the picture to the file. It is most usable for plot creation during long calculation or for using of small programs (like Matlab or Scilab scripts) for visualizing repetitive sets of data. But the speed of drawing is much higher in comparison with a script language.

The following code produces a bitmap PNG picture: 

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  gr.Alpha(true);   gr.Light(true);
  sample(&gr);              // The same drawing function.
  gr.WritePNG("test.png");  // Don't forget to save the result!
  return 0;
}

For compilation, you need only libmgl library not the one with widgets 

gcc test.cpp -lmgl

This can be important if you create a console program in computer/cluster where X-server (and widgets) is inaccessible.

The only difference from the previous variant (using windows) is manual switching on the transparency Alpha and lightning Light, if you need it. The usage of frames (see Animation) is not advisable since the whole image is prepared each time. If function sample contains frames then only last one will be saved to the file. In principle, one does not need to separate drawing functions in case of direct file writing in consequence of the single calling of this function for each picture. However, one may use the same drawing procedure to create a plot with changeable parameters, to export in different file types, to emphasize the drawing code and so on. So, in future I will put the drawing in the separate function.

The code for export into other formats (for example, into vector EPS file) looks the same: 

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  gr.Light(true);
  sample(&gr);              // The same drawing function.
  gr.WriteEPS("test.eps");  // Don't forget to save the result!
  return 0;
}

The difference from the previous one is using other function WriteEPS() for EPS format instead of function WritePNG(). Also, there is no switching on of the plot transparency Alpha since EPS format does not support it.

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2.1.3 Animation

Widget classes (mglWindow, mglGLUT) support a delayed drawing, when all plotting functions are called once at the beginning of writing to memory lists. Further program displays the saved lists faster. Resulting redrawing will be faster but it requires sufficient memory. Several lists (frames) can be displayed one after another (by pressing ‘,’, ‘.’) or run as cinema. To switch these feature on one needs to modify function sample: 

int sample(mglGraph *gr)
{
  gr->NewFrame();             // the first frame
  gr->Rotate(60,40);
  gr->Box();
  gr->EndFrame();             // end of the first frame
  gr->NewFrame();             // the second frame
  gr->Box();
  gr->Axis("xy");
  gr->EndFrame();             // end of the second frame
  return gr->GetNumFrame();   // returns the frame number
}

First, the function creates a frame by calling NewFrame() for rotated axes and draws the bounding box. The function EndFrame() must be called after the frame drawing! The second frame contains the bounding box and axes Axis("xy") in the initial (unrotated) coordinates. Function sample returns the number of created frames GetNumFrame().

Note, that animation can be also done as visualization of running calculations (see Draw and calculate).

Pictures with animation can be saved in file(s) as well. You can: export in animated GIF, or save each frame in separate file (usually JPEG) and convert these files into the movie (for example, by help of ImageMagic). Let me show both methods.

The simplest methods is making animated GIF. There are 3 steps: (1) open GIF file by StartGIF() function; (2) create the frames by calling NewFrame() before and EndFrame() after plotting; (3) close GIF by CloseGIF() function. So the simplest code for “running” sinusoid will look like this: 

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  mglData dat(100);
  char str[32];
  gr.StartGIF("sample.gif");
  for(int i=0;i<40;i++)
  {
    gr.NewFrame();     // start frame
    gr.Box();          // some plotting
    for(int j=0;j<dat.nx;j++)
      dat.a[j]=sin(M_PI*j/dat.nx+M_PI*0.05*i);
    gr.Plot(dat,"b");
    gr.EndFrame();     // end frame
  }
  gr.CloseGIF();
  return 0;
}

The second way is saving each frame in separate file (usually JPEG) and later make the movie from them. MathGL have special function for saving frames – it is WriteFrame(). This function save each frame with automatic name ‘frame0001.jpg, frame0002.jpg’ and so on. Here prefix ‘frame’ is defined by PlotId variable of mglGraph class. So the similar code will look like this: 

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  mglData dat(100);
  char str[32];
  for(int i=0;i<40;i++)
  {
    gr.NewFrame();     // start frame
    gr.Box();          // some plotting
    for(int j=0;j<dat.nx;j++)
      dat.a[j]=sin(M_PI*j/dat.nx+M_PI*0.05*i);
    gr.Plot(dat,"b");
    gr.EndFrame();     // end frame
    gr.WriteFrame();   // save frame
  }
  return 0;
}

Created files can be converted to movie by help of a lot of programs. For example, you can use ImageMagic (command ‘convert frame*.jpg movie.mpg’), MPEG library, GIMP and so on.

Finally, you can use mglconv tool for doing the same with MGL scripts (see Utilities).

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2.1.4 Drawing in memory

The last way of MathGL using is the drawing in memory. Class mglGraph allows one to create a bitmap picture in memory. Further this picture can be displayed in window by some window libraries (like wxWidgets, FLTK, Windows GDI and so on). For example, the code for drawing in wxWidget library looks like: 

void MyForm::OnPaint(wxPaintEvent& event)
{
  int w,h,x,y;
  GetClientSize(&w,&h);   // size of the picture
  mglGraph gr(w,h);

  gr.Alpha(true);         // draws something using MathGL
  gr.Light(true);
  sample(&gr,NULL);

  wxImage img(w,h,gr.GetRGB(),true);
  ToolBar->GetSize(&x,&y);    // gets a height of the toolbar if any
  wxPaintDC dc(this);         // and draws it
  dc.DrawBitmap(wxBitmap(img),0,y);
}

The drawing in other libraries is most the same.

For example, FLTK code will look like 

void Fl_MyWidget::draw()
{
  mglGraph gr(w(),h());
  gr.Alpha(true);         // draws something using MathGL
  gr.Light(true);
  sample(&gr,NULL);
  fl_draw_image(gr.GetRGB(), x(), y(), gr.GetWidth(), gr.GetHeight(), 3);
}

Qt code will look like 

void MyWidget::paintEvent(QPaintEvent *)
{
  mglGraph gr(w(),h());

  gr.Alpha(true);         // draws something using MathGL
  gr.Light(true);         gr.Light(0,mglPoint(1,0,-1));
  sample(&gr,NULL);

  // Qt don't support RGB format as is. So, let convert it to BGRN.
  long w=gr.GetWidth(), h=gr.GetHeight();
  unsigned char *buf = new uchar[4*w*h];
  gr.GetBGRN(buf, 4*w*h)
  QPixmap pic = QPixmap::fromImage(QImage(*buf, w, h, QImage::Format_RGB32));

  QPainter paint;
  paint.begin(this);  paint.drawPixmap(0,0,pic);  paint.end();
  delete []buf;
}

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2.1.5 Draw and calculate

MathGL can be used to draw plots in parallel with some external calculations. The simplest way for this is the usage of mglDraw class. At this you should enable pthread for widgets by setting enable-pthr-widget=ON at configure stage (it is set by default). First, you need to inherit you class from mglDraw class, define virtual members Draw() and Calc() which will draw the plot and proceed calculations. You may want to add the pointer mglWnd *wnd; to window with plot for interacting with them. Finally, you may add any other data or member functions. The sample class is shown below 

class myDraw : public mglDraw
{
	mglPoint pnt;	// some variable for changeable data
	long i;			// another variable to be shown
	mglWnd *wnd;	// external window for plotting
public:
	myDraw(mglWnd *w=0) : mglDraw()	{	wnd=w;	}
	void SetWnd(mglWnd *w)	{	wnd=w;	}
	int Draw(mglGraph *gr)
	{
		gr->Line(mglPoint(),pnt,"Ar2");
		char str[16];	snprintf(str,15,"i=%ld",i);
		gr->Puts(mglPoint(),str);
		return 0;
	}
	void Calc()
	{
		for(i=0;;i++)	// do calculation
		{
			long_calculations();// which can be very long
			Check();	// check if need pause
			pnt.Set(2*mgl_rnd()-1,2*mgl_rnd()-1);
			if(wnd)	wnd->Update();
		}
	}
} dr;

There is only one issue here. Sometimes you may want to pause calculations to view result carefully, or save state, or change something. So, you need to provide a mechanism for pausing. Class mglDraw provide function Check(); which check if toolbutton with pause is pressed and wait until it will be released. This function should be called in a "safety" places, where you can pause the calculation (for example, at the end of time step). Also you may add call exit(0); at the end of Calc(); function for closing window and exit after finishing calculations. Finally, you need to create a window itself and run calculations. 

int main(int argc,char **argv)
{
	mglFLTK gr(&dr,"Multi-threading test");	// create window
	dr.SetWnd(&gr);	// pass window pointer to yours class
	dr.Run();	// run calculations
	gr.Run();	// run event loop for window
	return 0;
}

Note, that you can reach the similar functionality without using mglDraw class (i.e. even for pure C code). 

mglFLTK *gr=NULL;	// pointer to window
void *calc(void *)	// function with calculations
{
	mglPoint pnt;	// some data for plot
	for(long i=0;;i++)		// do calculation
	{
		long_calculations();	// which can be very long
		pnt.Set(2*mgl_rnd()-1,2*mgl_rnd()-1);
		if(gr)
		{
			gr->Clf();			// make new drawing
			// draw something
			gr->Line(mglPoint(),pnt,"Ar2");
			char str[16];	snprintf(str,15,"i=%ld",i);
			gr->Puts(mglPoint(),str);
			// don't forgot to update window
			gr->Update();
		}
	}
}
int main(int argc,char **argv)
{
	static pthread_t thr;
	pthread_create(&thr,0,calc,0);	// create separate thread for calculations
	pthread_detach(thr);			// and detach it
	gr = new mglFLTK;	// now create window
	gr->Run();			// and run event loop
	return 0;
}

This sample is exactly the same as one with mglDraw class, but it don’t have functionality for pausing calculations. If you need it then you have to create global mutex (like pthread_mutex_t *mutex = pthread_mutex_init(&mutex,NULL);), set it to window (like gr->SetMutex(mutex);) and periodically check it at calculations (like pthread_mutex_lock(&mutex); pthread_mutex_unlock(&mutex);).

Finally, you can put the event-handling loop in separate instead of yours code by using RunThr() function instead of Run() one. Unfortunately, such method work well only for FLTK windows and only if pthread support was enabled. Such limitation come from the Qt requirement to be run in the primary thread only. The sample code will be: 

int main(int argc,char **argv)
{
	mglFLTK gr("test");
	gr.RunThr();	// <-- need MathGL version which use pthread for widgets
	mglPoint pnt;	// some data
	for(int i=0;i<10;i++)	// do calculation
	{
		long_calculations();// which can be very long
		pnt.Set(2*mgl_rnd()-1,2*mgl_rnd()-1);
		gr.Clf();			// make new drawing
		gr.Line(mglPoint(),pnt,"Ar2");
		char str[10] = "i=0";	str[3] = '0'+i;
		gr->Puts(mglPoint(),str);
		gr.Update();		// update window
	}
	return 0;	// finish calculations and close the window
}

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2.1.6 Using QMathGL

MathGL have several interface widgets for different widget libraries. There are QMathGL for Qt, Fl_MathGL for FLTK. These classes provide control which display MathGL graphics. Unfortunately there is no uniform interface for widget classes because all libraries have slightly different set of functions, features and so on. However the usage of MathGL widgets is rather simple. Let me show it on the example of QMathGL.

First of all you have to define the drawing function or inherit a class from mglDraw class. After it just create a window and setup QMathGL instance as any other Qt widget: 

#include <QApplication>
#include <QMainWindow>
#include <QScrollArea>
#include <mgl2/qmathgl.h>
int main(int argc,char **argv)
{
  QApplication a(argc,argv);
  QMainWindow *Wnd = new QMainWindow;
  Wnd->resize(810,610);  // for fill up the QMGL, menu and toolbars
  Wnd->setWindowTitle("QMathGL sample");
  // here I allow to scroll QMathGL -- the case
  // then user want to prepare huge picture
  QScrollArea *scroll = new QScrollArea(Wnd);

  // Create and setup QMathGL
  QMathGL *QMGL = new QMathGL(Wnd);
//QMGL->setPopup(popup); // if you want to setup popup menu for QMGL
  QMGL->setDraw(sample);
  // or use QMGL->setDraw(foo); for instance of class Foo:public mglDraw
  QMGL->update();

  // continue other setup (menu, toolbar and so on)
  scroll->setWidget(QMGL);
  Wnd->setCentralWidget(scroll);
  Wnd->show();
  return a.exec();
}

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2.1.7 MathGL and PyQt

Generally SWIG based classes (including the Python one) are the same as C++ classes. However, there are few tips for using MathGL with PyQt. Below I place a very simple python code which demonstrate how MathGL can be used with PyQt. This code is mostly written by Prof. Dr. Heino Falcke. You can just copy it to a file mgl-pyqt-test.py and execute it from python shell by command execfile("mgl-pyqt-test.py") 

from PyQt4 import QtGui,QtCore
from mathgl import *
import sys
app = QtGui.QApplication(sys.argv)
qpointf=QtCore.QPointF()

class hfQtPlot(QtGui.QWidget):
    def __init__(self, parent=None):
        QtGui.QWidget.__init__(self, parent)
        self.img=(QtGui.QImage())
    def setgraph(self,gr):
        self.buffer='\t'
        self.buffer=self.buffer.expandtabs(4*gr.GetWidth()*gr.GetHeight())
        gr.GetBGRN(self.buffer,len(self.buffer))
        self.img=QtGui.QImage(self.buffer, gr.GetWidth(),gr.GetHeight(),QtGui.QImage.Format_ARGB32)
        self.update()
    def paintEvent(self, event):
        paint = QtGui.QPainter()
        paint.begin(self)
        paint.drawImage(qpointf,self.img)
        paint.end()

BackgroundColor=[1.0,1.0,1.0]
size=100
gr=mglGraph()
y=mglData(size)
#y.Modify("((0.7*cos(2*pi*(x+.2)*500)+0.3)*(rnd*0.5+0.5)+362.135+10000.)")
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
x=mglData(size)
x.Modify("x^2");

def plotpanel(gr,x,y,n):
    gr.SubPlot(2,2,n)
    gr.SetXRange(x)
    gr.SetYRange(y)
    gr.AdjustTicks()
    gr.Axis()
    gr.Box()
    gr.Label("x","x-Axis",1)
    gr.Label("y","y-Axis",1)
    gr.ClearLegend()
    gr.AddLegend("Legend: "+str(n),"k")
    gr.Legend()
    gr.Plot(x,y)


gr.Clf(BackgroundColor[0],BackgroundColor[1],BackgroundColor[2])
gr.SetPlotFactor(1.5)
plotpanel(gr,x,y,0)
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
plotpanel(gr,x,y,1)
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
plotpanel(gr,x,y,2)
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
plotpanel(gr,x,y,3)

gr.WritePNG("test.png","Test Plot")

qw = hfQtPlot()
qw.show()
qw.setgraph(gr)
qw.raise_()

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2.1.8 MathGL and MPI

For using MathGL in MPI program you just need to: (1) plot its own part of data for each running node; (2) collect resulting graphical information in a single program (for example, at node with rank=0); (3) save it. The sample code below demonstrate this for very simple sample of surface drawing.

First you need to initialize MPI 

#include <stdio.h>
#include <mgl2/mpi.h>
#include <mpi.h>

int main(int argc, char *argv[])
{
  // initialize MPI
  int rank=0, numproc=1;
  MPI_Init(&argc, &argv);
  MPI_Comm_size(MPI_COMM_WORLD,&numproc);
  MPI_Comm_rank(MPI_COMM_WORLD,&rank);
  if(rank==0) printf("Use %d processes.\n", numproc);

Next step is data creation. For simplicity, I create data arrays with the same sizes for all nodes. At this, you have to create mglGraph object too. 

  // initialize data similarly for all nodes
  mglData a(128,256);
  mglGraphMPI gr;

Now, data should be filled by numbers. In real case, it should be some kind of calculations. But I just fill it by formula. 

  // do the same plot for its own range
  char buf[64];
  sprintf(buf,"xrange %g %g",2.*rank/numproc-1,2.*(rank+1)/numproc-1);
  gr.Fill(a,"sin(2*pi*x)",buf);

It is time to plot the data. Don’t forget to set proper axis range(s) by using parametric form or by using options (as in the sample). 

  // plot data in each node
  gr.Clf();   // clear image before making the image
  gr.Rotate(40,60);
  gr.Surf(a,"",buf);

Finally, let send graphical information to node with rank=0. 

  // collect information
  if(rank!=0) gr.MPI_Send(0);
  else for(int i=1;i<numproc;i++)  gr.MPI_Recv(i);

Now, node with rank=0 have whole image. It is time to save the image to a file. Also, you can add a kind of annotations here – I draw axis and bounding box in the sample. 

  if(rank==0)
  {
    gr.Box();   gr.Axis();   // some post processing
    gr.WritePNG("test.png"); // save result
  }

In my case the program is done, and I finalize MPI. In real program, you can repeat the loop of data calculation and data plotting as many times as you need. 

  MPI_Finalize();
  return 0;
}

You can type ‘mpic++ test.cpp -lmgl-mpi -lmgl && mpirun -np 8 ./a.out’ for compilation and running the sample program on 8 nodes. Note, that you have to set enable-mpi=ON at MathGL configure to use this feature.

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2.2 Advanced usage

Now I show several non-obvious features of MathGL: several subplots in a single picture, curvilinear coordinates, text printing and so on. Generally you may miss this section at first reading.

• Subplots:  
• Axis and ticks:  
• Curvilinear coordinates:  
• Colorbars:  
• Bounding box:  
• Ternary axis:  
• Text features:  
• Legend sample:  
• Cutting sample:  

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2.2.1 Subplots

Let me demonstrate possibilities of plot positioning and rotation. MathGL has a set of functions: subplot, inplot, title, aspect and rotate and so on (see Subplots and rotation). The order of their calling is strictly determined. First, one changes the position of plot in image area (functions subplot, inplot and multiplot). Secondly, you can add the title of plot by title function. After that one may rotate the plot (function rotate). Finally, one may change aspects of axes (function aspect). The following code illustrates the aforesaid it: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0); gr->Box();
  gr->Puts(mglPoint(-1,1.1),"Just box",":L");
  gr->InPlot(0.2,0.5,0.7,1,false);  gr->Box();
  gr->Puts(mglPoint(0,1.2),"InPlot example");
  gr->SubPlot(2,2,1); gr->Title("Rotate only");
  gr->Rotate(50,60);  gr->Box();
  gr->SubPlot(2,2,2); gr->Title("Rotate and Aspect");
  gr->Rotate(50,60);  gr->Aspect(1,1,2);  gr->Box();
  gr->SubPlot(2,2,3); gr->Title("Shear");
  gr->Box("c"); gr->Shear(0.2,0.1); gr->Box();
  return 0;
}

Here I used function Puts for printing the text in arbitrary position of picture (see Text printing). Text coordinates and size are connected with axes. However, text coordinates may be everywhere, including the outside the bounding box. I’ll show its features later in Text features.

Example of several subplots on the single picture.

More complicated sample show how to use most of positioning functions: 

int sample(mglGraph *gr)
{
  gr->SubPlot(3,2,0); gr->Title("StickPlot");
  gr->StickPlot(3, 0, 20, 30);  gr->Box("r"); gr->Puts(mglPoint(0),"0","r");
  gr->StickPlot(3, 1, 20, 30);  gr->Box("g"); gr->Puts(mglPoint(0),"1","g");
  gr->StickPlot(3, 2, 20, 30);  gr->Box("b"); gr->Puts(mglPoint(0),"2","b");
  gr->SubPlot(3,2,3,"");  gr->Title("ColumnPlot");
  gr->ColumnPlot(3, 0); gr->Box("r"); gr->Puts(mglPoint(0),"0","r");
  gr->ColumnPlot(3, 1); gr->Box("g"); gr->Puts(mglPoint(0),"1","g");
  gr->ColumnPlot(3, 2); gr->Box("b"); gr->Puts(mglPoint(0),"2","b");
  gr->SubPlot(3,2,4,"");  gr->Title("GridPlot");
  gr->GridPlot(2, 2, 0);  gr->Box("r"); gr->Puts(mglPoint(0),"0","r");
  gr->GridPlot(2, 2, 1);  gr->Box("g"); gr->Puts(mglPoint(0),"1","g");
  gr->GridPlot(2, 2, 2);  gr->Box("b"); gr->Puts(mglPoint(0),"2","b");
  gr->GridPlot(2, 2, 3);  gr->Box("m"); gr->Puts(mglPoint(0),"3","m");
  gr->SubPlot(3,2,5,"");  gr->Title("InPlot");  gr->Box();
  gr->InPlot(0.4, 1, 0.6, 1, true); gr->Box("r");
  gr->MultiPlot(3,2,1, 2, 1,"");  gr->Title("MultiPlot and ShearPlot"); gr->Box();
  gr->ShearPlot(3, 0, 0.2, 0.1);  gr->Box("r"); gr->Puts(mglPoint(0),"0","r");
  gr->ShearPlot(3, 1, 0.2, 0.1);  gr->Box("g"); gr->Puts(mglPoint(0),"1","g");
  gr->ShearPlot(3, 2, 0.2, 0.1);  gr->Box("b"); gr->Puts(mglPoint(0),"2","b");
  return 0;
}
Example for most of positioning functions.

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2.2.2 Axis and ticks

MathGL library can draw not only the bounding box but also the axes, grids, labels and so on. The ranges of axes and their origin (the point of intersection) are determined by functions SetRange(), SetRanges(), SetOrigin() (see Ranges (bounding box)). Ticks on axis are specified by function SetTicks, SetTicksVal, SetTicksTime (see Ticks). But usually

Function axis draws axes. Its textual string shows in which directions the axis or axes will be drawn (by default "xyz", function draws axes in all directions). Function grid draws grid perpendicularly to specified directions. Example of axes and grid drawing is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0); gr->Title("Axis origin, Grid"); gr->SetOrigin(0,0);
  gr->Axis(); gr->Grid(); gr->FPlot("x^3");

  gr->SubPlot(2,2,1); gr->Title("2 axis");
  gr->SetRanges(-1,1,-1,1); gr->SetOrigin(-1,-1,-1);  // first axis
  gr->Axis(); gr->Label('y',"axis 1",0);  gr->FPlot("sin(pi*x)");
  gr->SetRanges(0,1,0,1);   gr->SetOrigin(1,1,1);   // second axis
  gr->Axis(); gr->Label('y',"axis 2",0);  gr->FPlot("cos(pi*x)");

  gr->SubPlot(2,2,3); gr->Title("More axis");
  gr->SetOrigin(NAN,NAN); gr->SetRange('x',-1,1);
  gr->Axis(); gr->Label('x',"x",0); gr->Label('y',"y_1",0);
  gr->FPlot("x^2","k");
  gr->SetRanges(-1,1,-1,1); gr->SetOrigin(-1.3,-1); // second axis
  gr->Axis("y","r");  gr->Label('y',"#r{y_2}",0.2);
  gr->FPlot("x^3","r");

  gr->SubPlot(2,2,2); gr->Title("4 segments, inverted axis");
  gr->SetOrigin(0,0);
  gr->InPlot(0.5,1,0.5,1);  gr->SetRanges(0,10,0,2);  gr->Axis();
  gr->FPlot("sqrt(x/2)");   gr->Label('x',"W",1); gr->Label('y',"U",1);
  gr->InPlot(0,0.5,0.5,1);  gr->SetRanges(1,0,0,2); gr->Axis("x");
  gr->FPlot("sqrt(x)+x^3"); gr->Label('x',"\\tau",-1);
  gr->InPlot(0.5,1,0,0.5);  gr->SetRanges(0,10,4,0);  gr->Axis("y");
  gr->FPlot("x/4"); gr->Label('y',"L",-1);
  gr->InPlot(0,0.5,0,0.5);  gr->SetRanges(1,0,4,0); gr->FPlot("4*x^2");
  return 0;
}

Note, that MathGL can draw not only single axis (which is default). But also several axis on the plot (see right plots). The idea is that the change of settings does not influence on the already drawn graphics. So, for 2-axes I setup the first axis and draw everything concerning it. Then I setup the second axis and draw things for the second axis. Generally, the similar idea allows one to draw rather complicated plot of 4 axis with different ranges (see bottom left plot).

At this inverted axis can be created by 2 methods. First one is used in this sample – just specify minimal axis value to be large than maximal one. This method work well for 2D axis, but can wrongly place labels in 3D case. Second method is more general and work in 3D case too – just use aspect function with negative arguments. For example, following code will produce exactly the same result for 2D case, but 2nd variant will look better in 3D. 

// variant 1
gr->SetRanges(0,10,4,0);  gr->Axis();

// variant 2
gr->SetRanges(0,10,0,4);  gr->Aspect(1,-1);   gr->Axis();
Example of axis.

Another MathGL feature is fine ticks tunning. By default (if it is not changed by SetTicks function), MathGL try to adjust ticks positioning, so that they looks most human readable. At this, MathGL try to extract common factor for too large or too small axis ranges, as well as for too narrow ranges. Last one is non-common notation and can be disabled by SetTuneTicks function.

Also, one can specify its own ticks with arbitrary labels by help of SetTicksVal function. Or one can set ticks in time format. In last case MathGL will try to select optimal format for labels with automatic switching between years, months/days, hours/minutes/seconds or microseconds. However, you can specify its own time representation using formats described in http://www.manpagez.com/man/3/strftime/. Most common variants are ‘%X’ for national representation of time, ‘%x’ for national representation of date, ‘%Y’ for year with century.

The sample code, demonstrated ticks feature is 

int sample(mglGraph *gr)
{
  gr->SubPlot(3,3,0); gr->Title("Usual axis");  gr->Axis();
  gr->SubPlot(3,3,1); gr->Title("Too big/small range");
  gr->SetRanges(-1000,1000,0,0.001);  gr->Axis();
  gr->SubPlot(3,3,2); gr->Title("LaTeX-like labels");
  gr->Axis("F!");
  gr->SubPlot(3,3,3); gr->Title("Too narrow range");
  gr->SetRanges(100,100.1,10,10.01);  gr->Axis();
  gr->SubPlot(3,3,4); gr->Title("No tuning, manual '+'");
  // for version<2.3 you need first call gr->SetTuneTicks(0);
  gr->Axis("+!");
  gr->SubPlot(3,3,5); gr->Title("Template for ticks");
  gr->SetTickTempl('x',"xxx:%g"); gr->SetTickTempl('y',"y:%g");
  gr->Axis();
  // now switch it off for other plots
  gr->SetTickTempl('x',"");   gr->SetTickTempl('y',"");
  gr->SubPlot(3,3,6); gr->Title("No tuning, higher precision");
  gr->Axis("!4");
  gr->SubPlot(3,3,7); gr->Title("Manual ticks");  gr->SetRanges(-M_PI,M_PI, 0, 2);
  gr->SetTicks('x',M_PI,0,0,"\\pi");  gr->AddTick('x',0.886,"x^*");
  // alternatively you can use following lines
  //double val[]={-M_PI, -M_PI/2, 0, 0.886, M_PI/2, M_PI};
  //gr->SetTicksVal('x', mglData(6,val), "-\\pi\n-\\pi/2\n0\nx^*\n\\pi/2\n\\pi");
  gr->Axis();  gr->Grid();  gr->FPlot("2*cos(x^2)^2", "r2");
  gr->SubPlot(3,3,8); gr->Title("Time ticks");  gr->SetRange('x',0,3e5);
  gr->SetTicksTime('x',0);  gr->Axis();
}
Features of axis ticks.

The last sample I want to show in this subsection is Log-axis. From MathGL’s point of view, the log-axis is particular case of general curvilinear coordinates. So, we need first define new coordinates (see also Curvilinear coordinates) by help of SetFunc or SetCoor functions. At this one should wary about proper axis range. So the code looks as following: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0,"<_");  gr->Title("Semi-log axis");
  gr->SetRanges(0.01,100,-1,1); gr->SetFunc("lg(x)","");
  gr->Axis(); gr->Grid("xy","g"); gr->FPlot("sin(1/x)");
  gr->Label('x',"x",0); gr->Label('y', "y = sin 1/x",0);

  gr->SubPlot(2,2,1,"<_");  gr->Title("Log-log axis");
  gr->SetRanges(0.01,100,0.1,100);  gr->SetFunc("lg(x)","lg(y)");
  gr->Axis(); gr->Grid("!","h=");   gr->Grid();
  gr->FPlot("sqrt(1+x^2)"); gr->Label('x',"x",0);
  gr->Label('y', "y = \\sqrt{1+x^2}",0);

  gr->SubPlot(2,2,2,"<_");  gr->Title("Minus-log axis");
  gr->SetRanges(-100,-0.01,-100,-0.1);  gr->SetFunc("-lg(-x)","-lg(-y)");
  gr->Axis(); gr->FPlot("-sqrt(1+x^2)");
  gr->Label('x',"x",0); gr->Label('y', "y = -\\sqrt{1+x^2}",0);

  gr->SubPlot(2,2,3,"<_");  gr->Title("Log-ticks");
  gr->SetRanges(0.1,100,0,100); gr->SetFunc("sqrt(x)","");
  gr->Axis(); gr->FPlot("x");
  gr->Label('x',"x",1); gr->Label('y', "y = x",0);
  return 0;
}
Features of axis ticks.

You can see that MathGL automatically switch to log-ticks as we define log-axis formula (in difference from v.1.*). Moreover, it switch to log-ticks for any formula if axis range will be large enough (see right bottom plot). Another interesting feature is that you not necessary define usual log-axis (i.e. when coordinates are positive), but you can define “minus-log” axis when coordinate is negative (see left bottom plot).

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2.2.3 Curvilinear coordinates

As I noted in previous subsection, MathGL support curvilinear coordinates. In difference from other plotting programs and libraries, MathGL uses textual formulas for connection of the old (data) and new (output) coordinates. This allows one to plot in arbitrary coordinates. The following code plots the line y=0, z=0 in Cartesian, polar, parabolic and spiral coordinates: 

int sample(mglGraph *gr)
{
  gr->SetOrigin(-1,1,-1);

  gr->SubPlot(2,2,0); gr->Title("Cartesian"); gr->Rotate(50,60);
  gr->FPlot("2*t-1","0.5","0","r2");
  gr->Axis(); gr->Grid();

  gr->SetFunc("y*sin(pi*x)","y*cos(pi*x)",0);
  gr->SubPlot(2,2,1); gr->Title("Cylindrical"); gr->Rotate(50,60);
  gr->FPlot("2*t-1","0.5","0","r2");
  gr->Axis(); gr->Grid();

  gr->SetFunc("2*y*x","y*y - x*x",0);
  gr->SubPlot(2,2,2); gr->Title("Parabolic"); gr->Rotate(50,60);
  gr->FPlot("2*t-1","0.5","0","r2");
  gr->Axis(); gr->Grid();

  gr->SetFunc("y*sin(pi*x)","y*cos(pi*x)","x+z");
  gr->SubPlot(2,2,3); gr->Title("Spiral");  gr->Rotate(50,60);
  gr->FPlot("2*t-1","0.5","0","r2");
  gr->Axis(); gr->Grid();
  gr->SetFunc(0,0,0); // set to default Cartesian
  return 0;
}
Example of curvilinear coordinates

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2.2.4 Colorbars

MathGL handle colorbar as special kind of axis. So, most of functions for axis and ticks setup will work for colorbar too. Colorbars can be in log-scale, and generally as arbitrary function scale; common factor of colorbar labels can be separated; and so on.

But of course, there are differences – colorbars usually located out of bounding box. At this, colorbars can be at subplot boundaries (by default), or at bounding box (if symbol ‘I’ is specified). Colorbars can handle sharp colors. And they can be located at arbitrary position too. The sample code, which demonstrate colorbar features is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0); gr->Title("Colorbar out of box"); gr->Box();
  gr->Colorbar("<");  gr->Colorbar(">");
  gr->Colorbar("_");  gr->Colorbar("^");

  gr->SubPlot(2,2,1); gr->Title("Colorbar near box");   gr->Box();
  gr->Colorbar("<I"); gr->Colorbar(">I");
  gr->Colorbar("_I"); gr->Colorbar("^I");

  gr->SubPlot(2,2,2); gr->Title("manual colors");
  mglData a,v;  mgls_prepare2d(&a,0,&v);
  gr->Box();  gr->ContD(v,a);
  gr->Colorbar(v,"<");  gr->Colorbar(v,">");
  gr->Colorbar(v,"_");  gr->Colorbar(v,"^");

  gr->SubPlot(2,2,3);   gr->Title(" ");
  gr->Puts(mglPoint(-0.5,1.55),"Color positions",":C",-2);
  gr->Colorbar("bwr>",0.25,0);  gr->Puts(mglPoint(-0.9,1.2),"Default");
  gr->Colorbar("b{w,0.3}r>",0.5,0); gr->Puts(mglPoint(-0.1,1.2),"Manual");

  gr->Puts(mglPoint(1,1.55),"log-scale",":C",-2);
  gr->SetRange('c',0.01,1e3);
  gr->Colorbar(">",0.75,0);  gr->Puts(mglPoint(0.65,1.2),"Normal scale");
  gr->SetFunc("","","","lg(c)");
  gr->Colorbar(">");    gr->Puts(mglPoint(1.35,1.2),"Log scale");
  return 0;
}
Example of colorbars

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2.2.5 Bounding box

Box around the plot is rather useful thing because it allows one to: see the plot boundaries, and better estimate points position since box contain another set of ticks. MathGL provide special function for drawing such box – box function. By default, it draw black or white box with ticks (color depend on transparency type, see Types of transparency). However, you can change the color of box, or add drawing of rectangles at rear faces of box. Also you can disable ticks drawing, but I don’t know why anybody will want it. The sample code, which demonstrate box features is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0); gr->Title("Box (default)"); gr->Rotate(50,60);
  gr->Box();
  gr->SubPlot(2,2,1); gr->Title("colored");   gr->Rotate(50,60);
  gr->Box("r");
  gr->SubPlot(2,2,2); gr->Title("with faces");  gr->Rotate(50,60);
  gr->Box("@");
  gr->SubPlot(2,2,3); gr->Title("both");  gr->Rotate(50,60);
  gr->Box("@cm");
  return 0;
}
Example of Box()

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2.2.6 Ternary axis

There are another unusual axis types which are supported by MathGL. These are ternary and quaternary axis. Ternary axis is special axis of 3 coordinates a, b, c which satisfy relation a+b+c=1. Correspondingly, quaternary axis is special axis of 4 coordinates a, b, c, d which satisfy relation a+b+c+d=1.

Generally speaking, only 2 of coordinates (3 for quaternary) are independent. So, MathGL just introduce some special transformation formulas which treat a as ‘x’, b as ‘y’ (and c as ‘z’ for quaternary). As result, all plotting functions (curves, surfaces, contours and so on) work as usual, but in new axis. You should use ternary function for switching to ternary/quaternary coordinates. The sample code is: 

int sample(mglGraph *gr)
{
  gr->SetRanges(0,1,0,1,0,1);
  mglData x(50),y(50),z(50),rx(10),ry(10), a(20,30);
  a.Modify("30*x*y*(1-x-y)^2*(x+y<1)");
  x.Modify("0.25*(1+cos(2*pi*x))");
  y.Modify("0.25*(1+sin(2*pi*x))");
  rx.Modify("rnd"); ry.Modify("(1-v)*rnd",rx);
  z.Modify("x");

  gr->SubPlot(2,2,0); gr->Title("Ordinary axis 3D");
  gr->Rotate(50,60);    gr->Light(true);
  gr->Plot(x,y,z,"r2"); gr->Surf(a,"BbcyrR#");
  gr->Axis(); gr->Grid(); gr->Box();
  gr->Label('x',"B",1); gr->Label('y',"C",1); gr->Label('z',"Z",1);

  gr->SubPlot(2,2,1); gr->Title("Ternary axis (x+y+t=1)");
  gr->Ternary(1);
  gr->Plot(x,y,"r2"); gr->Plot(rx,ry,"q^ ");  gr->Cont(a,"BbcyrR");
  gr->Line(mglPoint(0.5,0), mglPoint(0,0.75), "g2");
  gr->Axis(); gr->Grid("xyz","B;");
  gr->Label('x',"B"); gr->Label('y',"C"); gr->Label('t',"A");

  gr->SubPlot(2,2,2); gr->Title("Quaternary axis 3D");
  gr->Rotate(50,60);    gr->Light(true);
  gr->Ternary(2);
  gr->Plot(x,y,z,"r2"); gr->Surf(a,"BbcyrR#");
  gr->Axis(); gr->Grid(); gr->Box();
  gr->Label('t',"A",1); gr->Label('x',"B",1);
  gr->Label('y',"C",1); gr->Label('z',"D",1);

  gr->SubPlot(2,2,3); gr->Title("Ternary axis 3D");
  gr->Rotate(50,60);    gr->Light(true);
  gr->Ternary(1);
  gr->Plot(x,y,z,"r2"); gr->Surf(a,"BbcyrR#");
  gr->Axis(); gr->Grid(); gr->Box();
  gr->Label('t',"A",1); gr->Label('x',"B",1);
  gr->Label('y',"C",1); gr->Label('z',"Z",1);
  return 0;
}
Example of colorbars

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2.2.7 Text features

MathGL prints text by vector font. There are functions for manual specifying of text position (like Puts) and for its automatic selection (like Label, Legend and so on). MathGL prints text always in specified position even if it lies outside the bounding box. The default size of font is specified by functions SetFontSize* (see Font settings). However, the actual size of output string depends on subplot size (depends on functions SubPlot, InPlot). The switching of the font style (italic, bold, wire and so on) can be done for the whole string (by function parameter) or inside the string. By default MathGL parses TeX-like commands for symbols and indexes (see Font styles).

Text can be printed as usual one (from left to right), along some direction (rotated text), or along a curve. Text can be printed on several lines, divided by new line symbol ‘\n’.

Example of MathGL font drawing is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0,"");
  gr->Putsw(mglPoint(0,1),L"Text can be in ASCII and in Unicode");
  gr->Puts(mglPoint(0,0.6),"It can be \\wire{wire}, \\big{big} or #r{colored}");
  gr->Puts(mglPoint(0,0.2),"One can change style in string: "
  "\\b{bold}, \\i{italic, \\b{both}}");
  gr->Puts(mglPoint(0,-0.2),"Easy to \\a{overline} or "
  "\\u{underline}");
  gr->Puts(mglPoint(0,-0.6),"Easy to change indexes ^{up} _{down} @{center}");
  gr->Puts(mglPoint(0,-1),"It parse TeX: \\int \\alpha \\cdot "
  "\\sqrt3{sin(\\pi x)^2 + \\gamma_{i_k}} dx");

  gr->SubPlot(2,2,1,"");
  gr->Puts(mglPoint(0,0.5), "\\sqrt{\\frac{\\alpha^{\\gamma^2}+\\overset 1{\\big\\infty}}{\\sqrt3{2+b}}}", "@", -4);
  gr->Puts(mglPoint(0,-0.5),"Text can be printed\non several lines");

  gr->SubPlot(2,2,2,"");
  mglData y;  mgls_prepare1d(&y);
  gr->Box();  gr->Plot(y.SubData(-1,0));
  gr->Text(y,"This is very very long string drawn along a curve",":k");
  gr->Text(y,"Another string drawn under a curve","T:r");

  gr->SubPlot(2,2,3,"");
  gr->Line(mglPoint(-1,-1),mglPoint(1,-1),"rA");
  gr->Puts(mglPoint(0,-1),mglPoint(1,-1),"Horizontal");
  gr->Line(mglPoint(-1,-1),mglPoint(1,1),"rA");
  gr->Puts(mglPoint(0,0),mglPoint(1,1),"At angle","@");
  gr->Line(mglPoint(-1,-1),mglPoint(-1,1),"rA");
  gr->Puts(mglPoint(-1,0),mglPoint(-1,1),"Vertical");
  return 0;
}
Example of text printing

You can change font faces by loading font files by function loadfont. Note, that this is long-run procedure. Font faces can be downloaded from MathGL website or from here. The sample code is: 

int sample(mglGraph *gr)
{
  double h=1.1, d=0.25;
  gr->LoadFont("STIX");     gr->Puts(mglPoint(0,h), "default font (STIX)");
  gr->LoadFont("adventor"); gr->Puts(mglPoint(0,h-d), "adventor font");
  gr->LoadFont("bonum");    gr->Puts(mglPoint(0,h-2*d), "bonum font");
  gr->LoadFont("chorus");   gr->Puts(mglPoint(0,h-3*d), "chorus font");
  gr->LoadFont("cursor");   gr->Puts(mglPoint(0,h-4*d), "cursor font");
  gr->LoadFont("heros");    gr->Puts(mglPoint(0,h-5*d), "heros font");
  gr->LoadFont("heroscn");  gr->Puts(mglPoint(0,h-6*d), "heroscn font");
  gr->LoadFont("pagella");  gr->Puts(mglPoint(0,h-7*d), "pagella font");
  gr->LoadFont("schola");   gr->Puts(mglPoint(0,h-8*d), "schola font");
  gr->LoadFont("termes");   gr->Puts(mglPoint(0,h-9*d), "termes font");
  return 0;
}
Example of font faces

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2.2.8 Legend sample

Legend is one of standard ways to show plot annotations. Basically you need to connect the plot style (line style, marker and color) with some text. In MathGL, you can do it by 2 methods: manually using addlegend function; or use ‘legend’ option (see Command options), which will use last plot style. In both cases, legend entries will be added into internal accumulator, which later used for legend drawing itself. clearlegend function allow you to remove all saved legend entries.

There are 2 features. If plot style is empty then text will be printed without indent. If you want to plot the text with indent but without plot sample then you need to use space ‘ ’ as plot style. Such style ‘ ’ will draw a plot sample (line with marker(s)) which is invisible line (i.e. nothing) and print the text with indent as usual one.

Function legend draw legend on the plot. The position of the legend can be selected automatic or manually. You can change the size and style of text labels, as well as setup the plot sample. The sample code demonstrating legend features is: 

int sample(mglGraph *gr)
{
  gr->AddLegend("sin(\\pi {x^2})","b");
  gr->AddLegend("sin(\\pi x)","g*");
  gr->AddLegend("sin(\\pi \\sqrt{x})","rd");
  gr->AddLegend("just text"," ");
  gr->AddLegend("no indent for this","");

  gr->SubPlot(2,2,0,""); gr->Title("Legend (default)");
  gr->Box();  gr->Legend();

  gr->Legend(3,"A#");
  gr->Puts(mglPoint(0.75,0.65),"Absolute position","A");

  gr->SubPlot(2,2,2,"");  gr->Title("coloring");  gr->Box();
  gr->Legend(0,"r#"); gr->Legend(1,"Wb#");  gr->Legend(2,"ygr#");

  gr->SubPlot(2,2,3,"");  gr->Title("manual position"); gr->Box();
  gr->Legend(0.5,1);  gr->Puts(mglPoint(0.5,0.55),"at x=0.5, y=1","a");
  gr->Legend(1,"#-"); gr->Puts(mglPoint(0.75,0.25),"Horizontal legend","a");
  return 0;
}
Example of legend

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2.2.9 Cutting sample

The last common thing which I want to show in this section is how one can cut off points from plot. There are 4 mechanism for that.

Below I place the code which demonstrate last 3 possibilities: 

int sample(mglGraph *gr)
{
  mglData a,c,v(1); mgls_prepare2d(&a); mgls_prepare3d(&c); v.a[0]=0.5;
  gr->SubPlot(2,2,0); gr->Title("Cut on (default)");
  gr->Rotate(50,60);  gr->Light(true);
  gr->Box();  gr->Surf(a,"","zrange -1 0.5");

  gr->SubPlot(2,2,1); gr->Title("Cut off");   gr->Rotate(50,60);
  gr->Box();  gr->Surf(a,"","zrange -1 0.5; cut off");

  gr->SubPlot(2,2,2); gr->Title("Cut in box");  gr->Rotate(50,60);
  gr->SetCutBox(mglPoint(0,-1,-1), mglPoint(1,0,1.1));
  gr->Alpha(true);  gr->Box();  gr->Surf3(c);
  gr->SetCutBox(mglPoint(0), mglPoint(0));  // switch it off

  gr->SubPlot(2,2,3); gr->Title("Cut by formula");  gr->Rotate(50,60);
  gr->CutOff("(z>(x+0.5*y-1)^2-1) & (z>(x-0.5*y-1)^2-1)");
  gr->Box();  gr->Surf3(c); gr->CutOff(""); // switch it off
  return 0;
}
Example of point cutting

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2.3 Data handling

Class mglData contains all functions for the data handling in MathGL (see Data processing). There are several matters why I use class mglData but not a single array: it does not depend on type of data (mreal or double), sizes of data arrays are kept with data, memory working is simpler and safer.

• Array creation:  
• Linking array:  
• Change data:  

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2.3.1 Array creation

There are many ways in MathGL how data arrays can be created and filled.

One can put the data in mglData instance by several ways. Let us do it for sinus function:

Creation of 2d- and 3d-arrays is mostly the same. But one should keep in mind that class mglData uses flat data representation. For example, matrix 30*40 is presented as flat (1d-) array with length 30*40=1200 (nx=30, ny=40). The element with indexes {i,j} is a[i+nx*j]. So for 2d array we have: 

  mglData z(30,40);
  for(int i=0;i<30;i++)   for(int j=0;j<40;j++)
    z.a[i+30*j] = sin(M_PI*i/29.)*sin(M_PI*j/39.);

or by using Modify() function 

  mglData z(30,40);
  z.Modify("sin(pi*x)*cos(pi*y)");

The only non-obvious thing here is using multidimensional arrays in C/C++, i.e. arrays defined like mreal dat[40][30];. Since, formally these elements dat[i] can address the memory in arbitrary place you should use the proper function to convert such arrays to mglData object. For C++ this is functions like mglData::Set(mreal **dat, int N1, int N2);. For C this is functions like mgl_data_set_mreal2(HMDT d, const mreal **dat, int N1, int N2);. At this, you should keep in mind that nx=N2 and ny=N1 after conversion.

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2.3.2 Linking array

Sometimes the data arrays are so large, that one couldn’t’ copy its values to another array (i.e. into mglData). In this case, he can define its own class derived from mglDataA (see mglDataA class) or can use Link function.

In last case, MathGL just save the link to an external data array, but not copy it. You should provide the existence of this data array for whole time during which MathGL can use it. Another point is that MathGL will automatically create new array if you’ll try to modify data values by any of mglData functions. So, you should use only function with const modifier if you want still using link to the original data array.

Creating the link is rather simple – just the same as using Set function 

  double *a = new double[50];
  for(int i=0;i<50;i++)   a[i] = sin(M_PI*i/49.);

  mglData y;
  y.Link(a,50);

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2.3.3 Change data

MathGL has functions for data processing: differentiating, integrating, smoothing and so on (for more detail, see Data processing). Let us consider some examples. The simplest ones are integration and differentiation. The direction in which operation will be performed is specified by textual string, which may contain symbols ‘x’, ‘y’ or ‘z’. For example, the call of Diff("x") will differentiate data along ‘x’ direction; the call of Integral("xy") perform the double integration of data along ‘x’ and ‘y’ directions; the call of Diff2("xyz") will apply 3d Laplace operator to data and so on. Example of this operations on 2d array a=x*y is presented in code: 

int sample(mglGraph *gr)
{
  gr->SetRanges(0,1,0,1,0,1);
  mglData a(30,40); a.Modify("x*y");
  gr->SubPlot(2,2,0); gr->Rotate(60,40);
  gr->Surf(a);    gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"a(x,y)");
  gr->SubPlot(2,2,1); gr->Rotate(60,40);
  a.Diff("x");    gr->Surf(a);  gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"da/dx");
  gr->SubPlot(2,2,2); gr->Rotate(60,40);
  a.Integral("xy"); gr->Surf(a);  gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"\\int da/dx dxdy");
  gr->SubPlot(2,2,3); gr->Rotate(60,40);
  a.Diff2("y"); gr->Surf(a);  gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"\\int {d^2}a/dxdy dx");
  return 0;
}
Example of data differentiation and integration

Data smoothing (function smooth) is more interesting and important. This function has single argument which define type of smoothing and its direction. Now 3 methods are supported: ‘3’ – linear averaging by 3 points, ‘5’ – linear averaging by 5 points, and default one – quadratic averaging by 5 points.

MathGL also have some amazing functions which is not so important for data processing as useful for data plotting. There are functions for finding envelope (useful for plotting rapidly oscillating data), for data sewing (useful to removing jumps on the phase), for data resizing (interpolation). Let me demonstrate it: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0,"");  gr->Title("Envelop sample");
  mglData d1(1000); gr->Fill(d1,"exp(-8*x^2)*sin(10*pi*x)");
  gr->Axis();     gr->Plot(d1, "b");
  d1.Envelop('x');  gr->Plot(d1, "r");

  gr->SubPlot(2,2,1,"");  gr->Title("Smooth sample");
  mglData y0(30),y1,y2,y3;
  gr->SetRanges(0,1,0,1);
  gr->Fill(y0, "0.4*sin(pi*x) + 0.3*cos(1.5*pi*x) - 0.4*sin(2*pi*x)+0.5*rnd");

  y1=y0;  y1.Smooth("x3");
  y2=y0;  y2.Smooth("x5");
  y3=y0;  y3.Smooth("x");

  gr->Plot(y0,"{m7}:s", "legend 'none'"); //gr->AddLegend("none","k");
  gr->Plot(y1,"r", "legend ''3' style'");
  gr->Plot(y2,"g", "legend ''5' style'");
  gr->Plot(y3,"b", "legend 'default'");
  gr->Legend();   gr->Box();

  gr->SubPlot(2,2,2);   gr->Title("Sew sample");
  mglData d2(100, 100); gr->Fill(d2, "mod((y^2-(1-x)^2)/2,0.1)");
  gr->Rotate(50, 60);   gr->Light(true);  gr->Alpha(true);
  gr->Box();            gr->Surf(d2, "b");
  d2.Sew("xy", 0.1);  gr->Surf(d2, "r");

  gr->SubPlot(2,2,3);   gr->Title("Resize sample (interpolation)");
  mglData x0(10), v0(10), x1, v1;
  gr->Fill(x0,"rnd");     gr->Fill(v0,"rnd");
  x1 = x0.Resize(100);    v1 = v0.Resize(100);
  gr->Plot(x0,v0,"b+ ");  gr->Plot(x1,v1,"r-");
  gr->Label(x0,v0,"%n");
  return 0;
}
Example of data manipulation

Also one can create new data arrays on base of the existing one: extract slice, row or column of data (subdata), summarize along a direction(s) (sum), find distribution of data elements (hist) and so on.

Another interesting feature of MathGL is interpolation and root-finding. There are several functions for linear and cubic spline interpolation (see Interpolation). Also there is a function evaluate which do interpolation of data array for values of each data element of index data. It look as indirect access to the data elements.

This function have inverse function solve which find array of indexes at which data array is equal to given value (i.e. work as root finding). But solve function have the issue – usually multidimensional data (2d and 3d ones) have an infinite number of indexes which give some value. This is contour lines for 2d data, or isosurface(s) for 3d data. So, solve function will return index only in given direction, assuming that other index(es) are the same as equidistant index(es) of original data. If data have multiple roots then second (and later) branches can be found by consecutive call(s) of solve function. Let me demonstrate this on the following sample. 

int sample(mglGraph *gr)
{
  gr->SetRange('z',0,1);
  mglData x(20,30), y(20,30), z(20,30), xx,yy,zz;
  gr->Fill(x,"(x+2)/3*cos(pi*y)");
  gr->Fill(y,"(x+2)/3*sin(pi*y)");
  gr->Fill(z,"exp(-6*x^2-2*sin(pi*y)^2)");

  gr->SubPlot(2,1,0); gr->Title("Cartesian space");   gr->Rotate(30,-40);
  gr->Axis("xyzU");   gr->Box();  gr->Label('x',"x"); gr->Label('y',"y");
  gr->SetOrigin(1,1); gr->Grid("xy");
  gr->Mesh(x,y,z);

  // section along 'x' direction
  mglData u = x.Solve(0.5,'x');
  mglData v(u.nx);  v.Fill(0,1);
  xx = x.Evaluate(u,v);   yy = y.Evaluate(u,v);   zz = z.Evaluate(u,v);
  gr->Plot(xx,yy,zz,"k2o");

  // 1st section along 'y' direction
  mglData u1 = x.Solve(-0.5,'y');
  mglData v1(u1.nx);  v1.Fill(0,1);
  xx = x.Evaluate(v1,u1); yy = y.Evaluate(v1,u1); zz = z.Evaluate(v1,u1);
  gr->Plot(xx,yy,zz,"b2^");

  // 2nd section along 'y' direction
  mglData u2 = x.Solve(-0.5,'y',u1);
  xx = x.Evaluate(v1,u2); yy = y.Evaluate(v1,u2); zz = z.Evaluate(v1,u2);
  gr->Plot(xx,yy,zz,"r2v");

  gr->SubPlot(2,1,1); gr->Title("Accompanied space");
  gr->SetRanges(0,1,0,1); gr->SetOrigin(0,0);
  gr->Axis(); gr->Box();  gr->Label('x',"i"); gr->Label('y',"j");
  gr->Grid(z,"h");

  gr->Plot(u,v,"k2o");    gr->Line(mglPoint(0.4,0.5),mglPoint(0.8,0.5),"kA");
  gr->Plot(v1,u1,"b2^");  gr->Line(mglPoint(0.5,0.15),mglPoint(0.5,0.3),"bA");
  gr->Plot(v1,u2,"r2v");  gr->Line(mglPoint(0.5,0.7),mglPoint(0.5,0.85),"rA");
}
Example of data interpolation and root finding

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2.4 Data plotting

Let me now show how to plot the data. Next section will give much more examples for all plotting functions. Here I just show some basics. MathGL generally has 2 types of plotting functions. Simple variant requires a single data array for plotting, other data (coordinates) are considered uniformly distributed in axis range. Second variant requires data arrays for all coordinates. It allows one to plot rather complex multivalent curves and surfaces (in case of parametric dependencies). Usually each function have one textual argument for plot style and another textual argument for options (see Command options).

Note, that the call of drawing function adds something to picture but does not clear the previous plots (as it does in Matlab). Another difference from Matlab is that all setup (like transparency, lightning, axis borders and so on) must be specified before plotting functions.

Let start for plots for 1D data. Term “1D data” means that data depend on single index (parameter) like curve in parametric form {x(i),y(i),z(i)}, i=1...n. The textual argument allow you specify styles of line and marks (see Line styles). If this parameter is NULL or empty then solid line with color from palette is used (see Palette and colors).

Below I shall show the features of 1D plotting on base of plot function. Let us start from sinus plot: 

int sample(mglGraph *gr)
{
  mglData y0(50); 	y0.Modify("sin(pi*(2*x-1))");
  gr->SubPlot(2,2,0);
  gr->Plot(y0);   	gr->Box();

Style of line is not specified in plot function. So MathGL uses the solid line with first color of palette (this is blue). Next subplot shows array y1 with 2 rows: 

  gr->SubPlot(2,2,1);
  mglData y1(50,2);
  y1.Modify("sin(pi*2*x-pi)");
  y1.Modify("cos(pi*2*x-pi)/2",1);
  gr->Plot(y1);   	gr->Box();

As previously I did not specify the style of lines. As a result, MathGL again uses solid line with next colors in palette (there are green and red). Now let us plot a circle on the same subplot. The circle is parametric curve x=cos(\pi t), y=sin(\pi t). I will set the color of the circle (dark yellow, ‘Y’) and put marks ‘+’ at point position: 

  mglData x(50);  	x.Modify("cos(pi*2*x-pi)");
  gr->Plot(x,y0,"Y+");

Note that solid line is used because I did not specify the type of line. The same picture can be achieved by plot and subdata functions. Let us draw ellipse by orange dash line: 

  gr->Plot(y1.SubData(-1,0),y1.SubData(-1,1),"q|");

Drawing in 3D space is mostly the same. Let us draw spiral with default line style. Now its color is 4-th color from palette (this is cyan): 

  gr->SubPlot(2,2,2);	gr->Rotate(60,40);
  mglData z(50);  	z.Modify("2*x-1");
  gr->Plot(x,y0,z);	gr->Box();

Functions plot and subdata make 3D curve plot but for single array. Use it to put circle marks on the previous plot: 

  mglData y2(10,3);	y2.Modify("cos(pi*(2*x-1+y))");
  y2.Modify("2*x-1",2);
  gr->Plot(y2.SubData(-1,0),y2.SubData(-1,1),y2.SubData(-1,2),"bo ");

Note that line style is empty ‘ ’ here. Usage of other 1D plotting functions looks similar: 

  gr->SubPlot(2,2,3);	gr->Rotate(60,40);
  gr->Bars(x,y0,z,"r");	gr->Box();
  return 0;
}

Surfaces surf and other 2D plots (see 2D plotting) are drown the same simpler as 1D one. The difference is that the string parameter specifies not the line style but the color scheme of the plot (see Color scheme). Here I draw attention on 4 most interesting color schemes. There is gray scheme where color is changed from black to white (string ‘kw’) or from white to black (string ‘wk’). Another scheme is useful for accentuation of negative (by blue color) and positive (by red color) regions on plot (string ‘"BbwrR"’). Last one is the popular “jet” scheme (string ‘"BbcyrR"’).

Now I shall show the example of a surface drawing. At first let us switch lightning on 

int sample(mglGraph *gr)
{
  gr->Light(true);	gr->Light(0,mglPoint(0,0,1));

and draw the surface, considering coordinates x,y to be uniformly distributed in axis range 

  mglData a0(50,40);
  a0.Modify("0.6*sin(2*pi*x)*sin(3*pi*y)+0.4*cos(3*pi*(x*y))");
  gr->SubPlot(2,2,0);	gr->Rotate(60,40);
  gr->Surf(a0);		gr->Box();

Color scheme was not specified. So previous color scheme is used. In this case it is default color scheme (“jet”) for the first plot. Next example is a sphere. The sphere is parametrically specified surface: 

  mglData x(50,40),y(50,40),z(50,40);
  x.Modify("0.8*sin(2*pi*x)*sin(pi*y)");
  y.Modify("0.8*cos(2*pi*x)*sin(pi*y)");
  z.Modify("0.8*cos(pi*y)");
  gr->SubPlot(2,2,1);	gr->Rotate(60,40);
  gr->Surf(x,y,z,"BbwrR");gr->Box();

I set color scheme to "BbwrR" that corresponds to red top and blue bottom of the sphere.

Surfaces will be plotted for each of slice of the data if nz>1. Next example draws surfaces for data arrays with nz=3: 

  mglData a1(50,40,3);
  a1.Modify("0.6*sin(2*pi*x)*sin(3*pi*y)+0.4*cos(3*pi*(x*y))");
  a1.Modify("0.6*cos(2*pi*x)*cos(3*pi*y)+0.4*sin(3*pi*(x*y))",1);
  a1.Modify("0.6*cos(2*pi*x)*cos(3*pi*y)+0.4*cos(3*pi*(x*y))",2);
  gr->SubPlot(2,2,2);	gr->Rotate(60,40);
  gr->Alpha(true);
  gr->Surf(a1);		gr->Box();

Note, that it may entail a confusion. However, if one will use density plot then the picture will look better: 

  gr->SubPlot(2,2,3);	gr->Rotate(60,40);
  gr->Dens(a1);		gr->Box();
  return 0;
}

Drawing of other 2D plots is analogous. The only peculiarity is the usage of flag ‘#’. By default this flag switches on the drawing of a grid on plot (grid or mesh for plots in plain or in volume). However, for isosurfaces (including surfaces of rotation axial) this flag switches the face drawing off and figure becomes wired. The following code gives example of flag ‘#’ using (compare with normal function drawing as in its description): 

int sample(mglGraph *gr)
{
  gr->Alpha(true);	gr->Light(true);	gr->Light(0,mglPoint(0,0,1));
  mglData a(30,20);
  a.Modify("0.6*sin(2*pi*x)*sin(3*pi*y) + 0.4*cos(3*pi*(x*y))");

  gr->SubPlot(2,2,0);	gr->Rotate(40,60);
  gr->Surf(a,"BbcyrR#");		gr->Box();
  gr->SubPlot(2,2,1);	gr->Rotate(40,60);
  gr->Dens(a,"BbcyrR#");		gr->Box();
  gr->SubPlot(2,2,2);	gr->Rotate(40,60);
  gr->Cont(a,"BbcyrR#");		gr->Box();
  gr->SubPlot(2,2,3);	gr->Rotate(40,60);
  gr->Axial(a,"BbcyrR#");		gr->Box();
  return 0;
}

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2.5 1D samples

This section is devoted to visualization of 1D data arrays. 1D means the data which depend on single index (parameter) like curve in parametric form {x(i),y(i),z(i)}, i=1...n. Most of samples will use the same data for plotting. So, I put its initialization in separate function 

void mgls_prepare1d(mglData *y, mglData *y1=0, mglData *y2=0, mglData *x1=0, mglData *x2=0)
{
  register long i,n=50;
  if(y) y->Create(n,3);
  if(x1)  x1->Create(n);    if(x2)  x2->Create(n);
  if(y1)  y1->Create(n);    if(y2)  y2->Create(n);
  mreal xx;
  for(i=0;i<n;i++)
  {
    xx = i/(n-1.);
    if(y)
    {
      y->a[i] = 0.7*sin(2*M_PI*xx) + 0.5*cos(3*M_PI*xx) + 0.2*sin(M_PI*xx);
      y->a[i+n] = sin(2*M_PI*xx);
      y->a[i+2*n] = cos(2*M_PI*xx);
    }
    if(y1)  y1->a[i] = 0.5+0.3*cos(2*M_PI*xx);
    if(y2)  y2->a[i] = 0.3*sin(2*M_PI*xx);
    if(x1)  x1->a[i] = xx*2-1;
    if(x2)  x2->a[i] = 0.05+0.03*cos(2*M_PI*xx);
  }
}

or using C functions 

void mgls_prepare1d(HMDT y, HMDT y1=0, HMDT y2=0, HMDT x1=0, HMDT x2=0)
{
  register long i,n=50;
  if(y)   mgl_data_create(y,n,3,1);
  if(x1)  mgl_data_create(x1,n,1,1);
  if(x2)  mgl_data_create(x2,n,1,1);
  if(y1)  mgl_data_create(y1,n,1,1);
  if(y2)  mgl_data_create(y2,n,1,1);
  mreal xx;
  for(i=0;i<n;i++)
  {
    xx = i/(n-1.);
    if(y)
    {
      mgl_data_set_value(y, 0.7*sin(2*M_PI*xx) + 0.5*cos(3*M_PI*xx) + 0.2*sin(M_PI*xx), i,0,0);
      mgl_data_set_value(y, sin(2*M_PI*xx), i,1,0);
      mgl_data_set_value(y, cos(2*M_PI*xx), i,2,0);
    }
    if(y1)  mgl_data_set_value(y1, 0.5+0.3*cos(2*M_PI*xx), i,0,0);
    if(y2)  mgl_data_set_value(y2, 0.3*sin(2*M_PI*xx), i,0,0);
    if(x1)  mgl_data_set_value(x1, xx*2-1, i,0,0);
    if(x2)  mgl_data_set_value(x2, 0.05+0.03*cos(2*M_PI*xx), i,0,0);
  }
}
• Plot sample:  
• Radar sample:  
• Step sample:  
• Tens sample:  
• Area sample:  
• Region sample:  
• Stem sample:  
• Bars sample:  
• Barh sample:  
• Cones sample:  
• Chart sample:  
• BoxPlot sample:  
• Candle sample:  
• OHLC sample:  
• Error sample:  
• Mark sample:  
• TextMark sample:  
• Label sample:  
• Table sample:  
• Tube sample:  
• Tape sample:  
• Torus sample:  
• Lamerey sample:  
• Bifurcation sample:  
• Pmap sample:  

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2.5.1 Plot sample

Function plot is most standard way to visualize 1D data array. By default, Plot use colors from palette. However, you can specify manual color/palette, and even set to use new color for each points by using ‘!’ style. Another feature is ‘ ’ style which draw only markers without line between points. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y); gr->SetOrigin(0,0,0);
  gr->SubPlot(2,2,0,"");  gr->Title("Plot plot (default)");
  gr->Box();  gr->Plot(y);

  gr->SubPlot(2,2,2,"");  gr->Title("'!' style; 'rgb' palette");
  gr->Box();  gr->Plot(y,"o!rgb");

  gr->SubPlot(2,2,3,"");  gr->Title("just markers");
  gr->Box();  gr->Plot(y," +");

  gr->SubPlot(2,2,1); gr->Title("3d variant");
  gr->Rotate(50,60);  gr->Box();
  mglData yc(30), xc(30), z(30);  z.Modify("2*x-1");
  yc.Modify("sin(pi*(2*x-1))"); xc.Modify("cos(pi*2*x-pi)");
  gr->Plot(xc,yc,z,"rs");
  return 0;
}
Example of Plot()

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2.5.2 Radar sample

Function radar plot is variant of Plot one, which make plot in polar coordinates and draw radial rays in point directions. If you just need a plot in polar coordinates then I recommend to use Curvilinear coordinates or Plot in parabolic form with x=r*cos(fi); y=r*sin(fi);. The sample code is: 

int sample(mglGraph *gr)
{
  mglData yr(10,3); yr.Modify("0.4*sin(pi*(2*x+y))+0.1*rnd");
  gr->SubPlot(1,1,0,"");  gr->Title("Radar plot (with grid, '\\#')");
  gr->Radar(yr,"#");
  return 0;
}
Example of Radar()

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2.5.3 Step sample

Function step plot data as stairs. It have the same options as Plot. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y); gr->SetOrigin(0,0,0);
  mglData yc(30), xc(30), z(30);  z.Modify("2*x-1");
  yc.Modify("sin(pi*(2*x-1))"); xc.Modify("cos(pi*2*x-pi)");

  gr->SubPlot(2,2,0,"");  gr->Title("Step plot (default)");
  gr->Box();  gr->Step(y);

  gr->SubPlot(2,2,1); gr->Title("3d variant");  gr->Rotate(50,60);
  gr->Box();  gr->Step(xc,yc,z,"r");

  gr->SubPlot(2,2,2,"");  gr->Title("'!' style");
  gr->Box();  gr->Step(y,"s!rgb");
  return 0;
}
Example of Step()

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2.5.4 Tens sample

Function tens is variant of plot with smooth coloring along the curves. At this, color is determined as for surfaces (see Color scheme). The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y); gr->SetOrigin(0,0,0);
  gr->SubPlot(2,2,0,"");  gr->Title("Tens plot (default)");
  gr->Box();  gr->Tens(y.SubData(-1,0), y.SubData(-1,1));

  gr->SubPlot(2,2,2,"");  gr->Title("' ' style");
  gr->Box();  gr->Tens(y.SubData(-1,0), y.SubData(-1,1),"o ");

  gr->SubPlot(2,2,1); gr->Title("3d variant");  gr->Rotate(50,60);  gr->Box();
  mglData yc(30), xc(30), z(30);  z.Modify("2*x-1");
  yc.Modify("sin(pi*(2*x-1))"); xc.Modify("cos(pi*2*x-pi)");
  gr->Tens(xc,yc,z,z,"s");
  return 0;
}
Example of Tens()

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2.5.5 Area sample

Function area fill the area between curve and axis plane. It support gradient filling if 2 colors per curve is specified. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y); gr->SetOrigin(0,0,0);
  gr->SubPlot(2,2,0,"");  gr->Title("Area plot (default)");
  gr->Box();  gr->Area(y);

  gr->SubPlot(2,2,1,"");  gr->Title("2 colors");
  gr->Box();  gr->Area(y,"cbgGyr");

  gr->SubPlot(2,2,2,"");  gr->Title("'!' style");
  gr->Box();  gr->Area(y,"!");

  gr->SubPlot(2,2,3); gr->Title("3d variant");
  gr->Rotate(50,60);  gr->Box();
  mglData yc(30), xc(30), z(30);  z.Modify("2*x-1");
  yc.Modify("sin(pi*(2*x-1))"); xc.Modify("cos(pi*2*x-pi)");
  gr->Area(xc,yc,z,"r");
  yc.Modify("-sin(pi*(2*x-1))");  gr->Area(xc,yc,z,"b#");
  return 0;
}
Example of Area()

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2.5.6 Region sample

Function region fill the area between 2 curves. It support gradient filling if 2 colors per curve is specified. Also it can fill only the region y1<y<y2 if style ‘i’ is used. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y);
  mglData y1 = y.SubData(-1,1), y2 = y.SubData(-1,2);  gr->SetOrigin(0,0,0);

  gr->SubPlot(2,2,0,"");  gr->Title("Region plot (default)"); gr->Box();
  gr->Region(y1,y2);  gr->Plot(y1,"k2");  gr->Plot(y2,"k2");

  gr->SubPlot(2,2,1,"");  gr->Title("2 colors");  gr->Box();
  gr->Region(y1,y2,"yr"); gr->Plot(y1,"k2");  gr->Plot(y2,"k2");

  gr->SubPlot(2,2,2,"");  gr->Title("'i' style");  gr->Box();
  gr->Region(y1,y2,"ir"); gr->Plot(y1,"k2");  gr->Plot(y2,"k2");

  gr->SubPlot(2,2,3,"^_");  gr->Title("3d variant");  gr->Rotate(40,60);  gr->Box();
  gr->Fill(y1,"cos(pi*x)"); gr->Fill(y2,"cos(pi*x+pi/3)");
  mglData x1(y1.nx), x2(y1.nx), z(y1.nx);
  gr->Fill(x1,"sin(pi*x)"); gr->Fill(x2,"sin(pi*x+pi/3)");  gr->Fill(z,"x");
  gr->Plot(x1,y1,z,"r2");   gr->Plot(x2,y2,z,"b2");
  gr->Region(x1,y1,z,x2,y2,z,"cmy!");
  return 0;
}
Example of Region()

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2.5.7 Stem sample

Function stem draw vertical bars. It is most attractive if markers are drawn too. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y); gr->SetOrigin(0,0,0);
  mglData yc(30), xc(30), z(30);  z.Modify("2*x-1");
  yc.Modify("sin(pi*(2*x-1))"); xc.Modify("cos(pi*2*x-pi)");
  gr->SubPlot(2,2,0,"");  gr->Title("Stem plot (default)");
  gr->Box();  gr->Stem(y);

  gr->SubPlot(2,2,1); gr->Title("3d variant");  gr->Rotate(50,60);
  gr->Box();  gr->Stem(xc,yc,z,"rx");

  gr->SubPlot(2,2,2,"");  gr->Title("'!' style");
  gr->Box();  gr->Stem(y,"o!rgb");
  return 0;
}
Example of Stem()

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2.5.8 Bars sample

Function bars draw vertical bars. It have a lot of options: bar-above-bar (‘a’ style), fall like (‘f’ style), 2 colors for positive and negative values, wired bars (‘#’ style), 3D variant. The sample code is: 

int sample(mglGraph *gr)
{
  mglData ys(10,3); ys.Modify("0.8*sin(pi*(2*x+y/2))+0.2*rnd");
  gr->SetOrigin(0,0,0);
  gr->SubPlot(3,2,0,"");  gr->Title("Bars plot (default)");
  gr->Box();  gr->Bars(ys);

  gr->SubPlot(3,2,1,"");  gr->Title("2 colors");
  gr->Box();  gr->Bars(ys,"cbgGyr");

  gr->SubPlot(3,2,4,"");  gr->Title("'\\#' style");
  gr->Box();  gr->Bars(ys,"#");

  gr->SubPlot(3,2,5); gr->Title("3d variant");
  gr->Rotate(50,60);  gr->Box();
  mglData yc(30), xc(30), z(30);  z.Modify("2*x-1");
  yc.Modify("sin(pi*(2*x-1))"); xc.Modify("cos(pi*2*x-pi)");
  gr->Bars(xc,yc,z,"r");

  gr->SetRanges(-1,1,-3,3);
  gr->SubPlot(3,2,2,"");  gr->Title("'a' style");
  gr->Box();  gr->Bars(ys,"a");

  gr->SubPlot(3,2,3,"");  gr->Title("'f' style");
  gr->Box();  gr->Bars(ys,"f");
  return 0;
}
Example of Bars()

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2.5.9 Barh sample

Function barh is the similar to Bars but draw horizontal bars. The sample code is: 

int sample(mglGraph *gr)
{
  mglData ys(10,3); ys.Modify("0.8*sin(pi*(2*x+y/2))+0.2*rnd");
  gr->SetOrigin(0,0,0);
  gr->SubPlot(2,2,0,"");  gr->Title("Barh plot (default)");
  gr->Box();  gr->Barh(ys);

  gr->SubPlot(2,2,1,"");  gr->Title("2 colors");
  gr->Box();  gr->Barh(ys,"cbgGyr");

  gr->SetRanges(-3,3,-1,1);
  gr->SubPlot(2,2,2,"");  gr->Title("'a' style");
  gr->Box();  gr->Barh(ys,"a");

  gr->SubPlot(2,2,3,"");  gr->Title("'f' style");
  gr->Box();  gr->Barh(ys,"f");
  return 0;
}
Example of Barh()

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2.5.10 Cones sample

Function cones is similar to Bars but draw cones. The sample code is: 

int sample(mglGraph *gr)
{
  mglData ys(10,3);   ys.Modify("0.8*sin(pi*(2*x+y/2))+0.2*rnd");
  gr->Light(true);    gr->SetOrigin(0,0,0);
  gr->SubPlot(3,2,0); gr->Title("Cones plot");
  gr->Rotate(50,60);  gr->Box();  gr->Cones(ys);

  gr->SubPlot(3,2,1); gr->Title("2 colors");
  gr->Rotate(50,60);  gr->Box();  gr->Cones(ys,"cbgGyr");

  gr->SubPlot(3,2,2); gr->Title("'#' style");
  gr->Rotate(50,60);  gr->Box();  gr->Cones(ys,"#");

  gr->SubPlot(3,2,3); gr->Title("'a' style");
  gr->SetRange('z',-2,2); // increase range since summation can exceed [-1,1]
  gr->Rotate(50,60);  gr->Box();  gr->Cones(ys,"a");

  gr->SubPlot(3,2,4); gr->Title("'t' style");
  gr->Rotate(50,60);  gr->Box();  gr->Cones(ys,"t");

  gr->SubPlot(3,2,5); gr->Title("'4' style");
  gr->Rotate(50,60);  gr->Box();  gr->Cones(ys,"4");
  return 0;
}
Example of Cones()

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2.5.11 Chart sample

Function chart draw colored boxes with width proportional to data values. Use ‘ ’ for empty box. Plot looks most attractive in polar coordinates – well known pie chart. The sample code is: 

int sample(mglGraph *gr)
{
  mglData ch(7,2);  for(int i=0;i<7*2;i++)  ch.a[i]=mgl_rnd()+0.1;
  gr->SubPlot(2,2,0); gr->Title("Chart plot (default)");
  gr->Light(true);  gr->Rotate(50,60);  gr->Box();  gr->Chart(ch);

  gr->SubPlot(2,2,1); gr->Title("'\\#' style");
  gr->Rotate(50,60);  gr->Box();  gr->Chart(ch,"#");

  gr->SubPlot(2,2,2); gr->Title("Pie chart; ' ' color");
  gr->SetFunc("(y+1)/2*cos(pi*x)","(y+1)/2*sin(pi*x)","");
  gr->Rotate(50,60);  gr->Box();  gr->Chart(ch,"bgr cmy#");

  gr->SubPlot(2,2,3); gr->Title("Ring chart; ' ' color");
  gr->SetFunc("(y+2)/3*cos(pi*x)","(y+2)/3*sin(pi*x)","");
  gr->Rotate(50,60);  gr->Box();  gr->Chart(ch,"bgr cmy#");
  return 0;
}
Example of Chart()

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2.5.12 BoxPlot sample

Function boxplot draw box-and-whisker diagram. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a(10,7);  a.Modify("(2*rnd-1)^3/2");
  gr->SubPlot(1,1,0,"");  gr->Title("Boxplot plot");
  gr->Box();  gr->BoxPlot(a);
  return 0;
}
Example of BoxPlot()

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2.5.13 Candle sample

Function candle draw candlestick chart. This is a combination of a line-chart and a bar-chart, in that each bar represents the range of price movement over a given time interval. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y(30);  gr->Fill(y,"sin(pi*x/2)^2");
  mglData y1(30); gr->Fill(y1,"v/2",y);
  mglData y2(30); gr->Fill(y2,"(1+v)/2",y);
  gr->SubPlot(1,1,0,"");  gr->Title("Candle plot (default)");
  gr->SetRange('y',0,1);  gr->Box();  gr->Candle(y,y1,y2);
  return 0;
}
Example of Candle()

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2.5.14 OHLC sample

Function ohlc draw Open-High-Low-Close diagram. This diagram show vertical line for between maximal(high) and minimal(low) values, as well as horizontal lines before/after vertical line for initial(open)/final(close) values of some process. The sample code is: 

int sample(mglGraph *gr)
{
  mglData o(10), h(10), l(10), c(10);
  gr->Fill(o,"0.5*sin(pi*x)");  gr->Fill(c,"0.5*sin(pi*(x+2/9))");
  gr->Fill(l,"0.3*rnd-0.8");    gr->Fill(h,"0.3*rnd+0.5");
  gr->SubPlot(1,1,0,"");  gr->Title("OHLC plot");
  gr->Box();  gr->OHLC(o,h,l,c);
  return 0;
}
Example of OHLC()

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2.5.15 Error sample

Function error draw error boxes around the points. You can draw default boxes or semi-transparent symbol (like marker, see Line styles). Also you can set individual color for each box. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y);
  mglData x0(10), y0(10), ex0(10), ey0(10);
  mreal x;
  for(int i=0;i<10;i++)
  {
    x = i/9.;
    x0.a[i] = 2*x-1 + 0.1*mgl_rnd()-0.05;
    y0.a[i] = 0.7*sin(2*M_PI*x)+0.5*cos(3*M_PI*x)+0.2*sin(M_PI*x)+0.2*mgl_rnd()-0.1;
    ey0.a[i]=0.2; ex0.a[i]=0.1;
  }

  gr->SubPlot(2,2,0,"");  gr->Title("Error plot (default)");
  gr->Box();  gr->Plot(y.SubData(-1,0));  gr->Error(x0,y0,ex0,ey0,"ko");

  gr->SubPlot(2,2,1,"");  gr->Title("'!' style; no e_x");
  gr->Box();  gr->Plot(y.SubData(-1,0));  gr->Error(x0,y0,ey0,"o!rgb");

  gr->SubPlot(2,2,2,"");  gr->Title("'\\@' style");
  gr->Box();  gr->Plot(y.SubData(-1,0));  gr->Error(x0,y0,ex0,ey0,"@","alpha 0.5");

  gr->SubPlot(2,2,3); gr->Title("3d variant");  gr->Rotate(50,60);
  for(int i=0;i<10;i++)
    gr->Error(mglPoint(2*mgl_rnd()-1,2*mgl_rnd()-1,2*mgl_rnd()-1),
              mglPoint(0.2,0.2,0.2),"bo");
  gr->Axis();
  return 0;
}
Example of Error()

Additionally, you can use solid large "marks" instead of error boxes by selecting proper style. 

int sample(mglGraph *gr)
{
  mglData x0(10), y0(10), ex(10), ey(10);
  for(int i=0;i<10;i++)
  {  x0.a[i] = mgl_rnd(); y0.a[i] = mgl_rnd(); ey.a[i] = ex.a[i] = 0.1; }
  gr->SetRanges(0,1,0,1); gr->Alpha(true);
  gr->SubPlot(4,3,0,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"#+@");
  gr->SubPlot(4,3,1,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"#x@");
  gr->SubPlot(4,3,2,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"#s@","alpha 0.5");
  gr->SubPlot(4,3,3,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"s@");
  gr->SubPlot(4,3,4,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"d@");
  gr->SubPlot(4,3,5,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"#d@","alpha 0.5");
  gr->SubPlot(4,3,6,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"+@");
  gr->SubPlot(4,3,7,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"x@");
  gr->SubPlot(4,3,8,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"o@");
  gr->SubPlot(4,3,9,"");  gr->Box(); gr->Error(x0,y0,ex,ey,"#o@","alpha 0.5");
  gr->SubPlot(4,3,10,""); gr->Box(); gr->Error(x0,y0,ex,ey,"#.@");
  gr->SubPlot(4,3,11,""); gr->Box(); gr->Error(x0,y0,ex,ey);
}
Example of Error() with marks

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2.5.16 Mark sample

Function mark draw markers at points. It is mostly the same as Plot but marker size can be variable. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y,y1; mgls_prepare1d(&y,&y1);
  gr->SubPlot(1,1,0,"");  gr->Title("Mark plot (default)");
  gr->Box();  gr->Mark(y,y1,"s");
  return 0;
}
Example of Mark()

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2.5.17 TextMark sample

Function textmark like Mark but draw text instead of markers. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y,y1; mgls_prepare1d(&y,&y1);
  gr->SubPlot(1,1,0,"");  gr->Title("TextMark plot (default)");
  gr->Box();  gr->TextMark(y,y1,"\\gamma","r");
  return 0;
}
Example of TextMark()

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2.5.18 Label sample

Function label print text at data points. The string may contain ‘%x’, ‘%y’, ‘%z’ for x-, y-, z-coordinates of points, ‘%n’ for point index. The sample code is: 

int sample(mglGraph *gr)
{
  mglData ys(10); ys.Modify("0.8*sin(pi*2*x)+0.2*rnd");
  gr->SubPlot(1,1,0,"");  gr->Title("Label plot");
  gr->Box();  gr->Plot(ys," *");  gr->Label(ys,"y=%y");
  return 0;
}
Example of Label()

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2.5.19 Table sample

Function table draw table with data values. The sample code is: 

int sample(mglGraph *gr)
{
  mglData ys(10,3); ys.Modify("0.8*sin(pi*(2*x+y/2))+0.2*rnd");
  gr->SubPlot(2,2,0);  gr->Title("Table plot");
  gr->Table(ys,"y_1\ny_2\ny_3");   gr->Box();
  gr->SubPlot(2,2,1);  gr->Title("no borders, colored");
  gr->Table(ys,"y_1\ny_2\ny_3","r|");
  gr->SubPlot(2,2,2);  gr->Title("no font decrease");
  gr->Table(ys,"y_1\ny_2\ny_3","#");
  gr->SubPlot(2,2,3);  gr->Title("manual width, position");
  gr->Table(0.5, 0.95, ys,"y_1\ny_2\ny_3","#", "value 0.7");  gr->Box();
  return 0;
}
Example of Table()

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2.5.20 Tube sample

Function tube draw tube with variable radius. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y,y1,y2;  mgls_prepare1d(&y,&y1,&y2); y1/=20;
  gr->SubPlot(2,2,0,"");  gr->Title("Tube plot (default)");
  gr->Light(true);  gr->Box();  gr->Tube(y,0.05);

  gr->SubPlot(2,2,1,"");  gr->Title("variable radius");
  gr->Box();  gr->Tube(y,y1);

  gr->SubPlot(2,2,2,"");  gr->Title("'\\#' style");
  gr->Box();  gr->Tube(y,0.05,"#");
  mglData yc(50), xc(50), z(50);  z.Modify("2*x-1");
  yc.Modify("sin(pi*(2*x-1))"); xc.Modify("cos(pi*2*x-pi)");

  gr->SubPlot(2,2,3); gr->Title("3d variant");  gr->Rotate(50,60);
  gr->Box();  gr->Tube(xc,yc,z,y2,"r");
  return 0;
}
Example of Tube()

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2.5.21 Tape sample

Function tape draw tapes which rotate around the curve as normal and binormal. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y;  mgls_prepare1d(&y);
  mglData xc(50), yc(50), z(50);
  yc.Modify("sin(pi*(2*x-1))");
  xc.Modify("cos(pi*2*x-pi)");  z.Fill(-1,1);
  gr->SubPlot(2,2,0,"");  gr->Title("Tape plot (default)");
  gr->Box();  gr->Tape(y);  gr->Plot(y,"k");

  gr->SubPlot(2,2,1); gr->Title("3d variant, 2 colors");
  gr->Rotate(50,60);  gr->Light(true);
  gr->Box();  gr->Plot(xc,yc,z,"k");  gr->Tape(xc,yc,z,"rg");

  gr->SubPlot(2,2,2); gr->Title("3d variant, x only");  gr->Rotate(50,60);
  gr->Box();  gr->Plot(xc,yc,z,"k");
  gr->Tape(xc,yc,z,"xr"); gr->Tape(xc,yc,z,"xr#");

  gr->SubPlot(2,2,3); gr->Title("3d variant, z only");  gr->Rotate(50,60);
  gr->Box();  gr->Plot(xc,yc,z,"k");
  gr->Tape(xc,yc,z,"zg"); gr->Tape(xc,yc,z,"zg#");
  return 0;
}
Example of Tape()

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2.5.22 Torus sample

Function torus draw surface of the curve rotation. The sample code is: 

int sample(mglGraph *gr)
{
  mglData y1,y2;  mgls_prepare1d(0,&y1,&y2);
  gr->SubPlot(2,2,0); gr->Title("Torus plot (default)");
  gr->Light(true);  gr->Rotate(50,60);  gr->Box();  gr->Torus(y1,y2);
  if(mini)  return;

  gr->SubPlot(2,2,1); gr->Title("'x' style"); gr->Rotate(50,60);
  gr->Box();  gr->Torus(y1,y2,"x");

  gr->SubPlot(2,2,2); gr->Title("'z' style"); gr->Rotate(50,60);
  gr->Box();  gr->Torus(y1,y2,"z");

  gr->SubPlot(2,2,3); gr->Title("'\\#' style"); gr->Rotate(50,60);
  gr->Box();  gr->Torus(y1,y2,"#");
  return 0;
}
Example of Torus()

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2.5.23 Lamerey sample

Function lamerey draw Lamerey diagram. The sample code is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(1,1,0,"<_");
  gr->Title("Lamerey sample");
  gr->Axis(); gr->Label('x',"\\i x");
  gr->Label('y',"\\bar{\\i x} = 2 \\i{x}");
  gr->FPlot("x","k=");  gr->FPlot("2*x","b");
  gr->Lamerey( 0.00097,"2*x","rv~");
  gr->Lamerey(-0.00097,"2*x","rv~");
}
Example of Lamerey()

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2.5.24 Bifurcation sample

Function bifurcation draw Bifurcation diagram for logistic map. The sample code is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(1,1,0,"<_");
  gr->Title("Bifurcation sample");
  gr->SetRanges(0,4,0,1);   gr->Axis();
  gr->Bifurcation(0.005,"x*y*(1-y)","r");
}
Example of Bifurcation()

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2.5.25 Pmap sample

Function pmap draw Poincare map – show intersections of the curve and the surface. The sample code is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(1,1,0,"<_^");
  gr->Title("Poincare map sample");
  mglData ini(3);	ini[0]=0.1;
  mglData r(mglODE("cos(y)+sin(z);cos(z)+sin(x);cos(x)+sin(y)","xyz",ini,0.1,100));
  mglData x(r.SubData(0)),y(r.SubData(1)), z(r.SubData(2));
  gr->Rotate(40,60);  gr->SetRanges(x,y,z);
  gr->Axis(); gr->FSurf("0"); gr->Plot(x,y,z,"b");
  gr->Label('x',"\\i x",0);   gr->Label('y',"\\i y",0);   gr->Label('z',"\\i z",0);
  gr->Pmap(x,y,z,z, "b#o");
}
Example of Pmap()

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2.6 2D samples

This section is devoted to visualization of 2D data arrays. 2D means the data which depend on 2 indexes (parameters) like matrix z(i,j)=z(x(i),y(j)), i=1...n, j=1...m or in parametric form {x(i,j),y(i,j),z(i,j)}. Most of samples will use the same data for plotting. So, I put its initialization in separate function 

void mgls_prepare2d(mglData *a, mglData *b=0, mglData *v=0)
{
  register long i,j,n=50,m=40,i0;
  if(a) a->Create(n,m);   if(b) b->Create(n,m);
  if(v) { v->Create(9); v->Fill(-1,1);  }
  mreal x,y;
  for(i=0;i<n;i++)  for(j=0;j<m;j++)
  {
    x = i/(n-1.); y = j/(m-1.); i0 = i+n*j;
    if(a) a->a[i0] = 0.6*sin(2*M_PI*x)*sin(3*M_PI*y)+0.4*cos(3*M_PI*x*y);
    if(b) b->a[i0] = 0.6*cos(2*M_PI*x)*cos(3*M_PI*y)+0.4*cos(3*M_PI*x*y);
  }
}

or using C functions 

void mgls_prepare2d(HMDT a, HMDT b=0, HMDT v=0)
{
  register long i,j,n=50,m=40,i0;
  if(a) mgl_data_create(a,n,m,1);
  if(b) mgl_data_create(b,n,m,1);
  if(v) { mgl_data_create(v,9,1,1); mgl_data_fill(v,-1,1,'x');  }
  mreal x,y;
  for(i=0;i<n;i++)  for(j=0;j<m;j++)
  {
    x = i/(n-1.); y = j/(m-1.); i0 = i+n*j;
    if(a) mgl_data_set_value(a, 0.6*sin(2*M_PI*x)*sin(3*M_PI*y)+0.4*cos(3*M_PI*x*y), i,j,0);
    if(b) mgl_data_set_value(b, 0.6*cos(2*M_PI*x)*cos(3*M_PI*y)+0.4*cos(3*M_PI*x*y), i,j,0);
  }
}
• Surf sample:  
• SurfC sample:  
• SurfA sample:  
• SurfCA sample:  
• Mesh sample:  
• Fall sample:  
• Belt sample:  
• Boxs sample:  
• Tile sample:  
• TileS sample:  
• Dens sample:  
• Cont sample:  
• ContF sample:  
• ContD sample:  
• ContV sample:  
• Axial sample:  
• Grad sample:  

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2.6.1 Surf sample

Function surf is most standard way to visualize 2D data array. Surf use color scheme for coloring (see Color scheme). You can use ‘#’ style for drawing black meshes on the surface. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->SubPlot(2,2,0); gr->Title("Surf plot (default)");
  gr->Light(true);  gr->Rotate(50,60);  gr->Box();  gr->Surf(a);

  gr->SubPlot(2,2,1); gr->Title("'\\#' style; meshnum 10");
  gr->Rotate(50,60);  gr->Box();  gr->Surf(a,"#","meshnum 10");

  gr->SubPlot(2,2,2); gr->Title("'.' style");
  gr->Rotate(50,60);  gr->Box();  gr->Surf(a,".");

  gr->SubPlot(2,2,3); gr->Title("parametric form");
  mglData x(50,40),y(50,40),z(50,40);
  gr->Fill(x,"0.8*sin(pi*x)*sin(pi*(y+1)/2)");
  gr->Fill(y,"0.8*cos(pi*x)*sin(pi*(y+1)/2)");
  gr->Fill(z,"0.8*cos(pi*(y+1)/2)");
  gr->Rotate(50,60);  gr->Box();  gr->Surf(x,y,z,"BbwrR");
  return 0;
}
Example of Surf()

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2.6.2 SurfC sample

Function surfc is similar to surf but its coloring is determined by another data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2d(&a,&b);
  gr->Title("SurfC plot");  gr->Rotate(50,60);
  gr->Light(true);  gr->Box();  gr->SurfC(a,b);
  return 0;
}
Example of SurfC()

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2.6.3 SurfA sample

Function surfa is similar to surf but its transparency is determined by another data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2d(&a,&b);
  gr->Title("SurfA plot");  gr->Rotate(50,60);
  gr->Alpha(true);  gr->Light(true);
  gr->Box();  gr->SurfA(a,b);
  return 0;
}
Example of SurfA()

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2.6.4 SurfCA sample

Function surfca is similar to surf but its color and transparency is determined by another data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2d(&a,&b);
  gr->Title("SurfCA plot");  gr->Rotate(50,60);
  gr->Alpha(true);  gr->Light(true);
  gr->Box();  gr->SurfCA(a,b,a);
  return 0;
}
Example of SurfCA()

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2.6.5 Mesh sample

Function mesh draw wired surface. You can use meshnum for changing number of lines to be drawn. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->Title("Mesh plot"); gr->Rotate(50,60);
  gr->Box();  gr->Mesh(a);
  return 0;
}
Example of Mesh()

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2.6.6 Fall sample

Function fall draw waterfall surface. You can use meshnum for changing number of lines to be drawn. Also you can use ‘x’ style for drawing lines in other direction. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->Title("Fall plot"); gr->Rotate(50,60);
  gr->Box();  gr->Fall(a);
  return 0;
}
Example of Fall()

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2.6.7 Belt sample

Function belt draw surface by belts. You can use ‘x’ style for drawing lines in other direction. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->Title("Belt plot"); gr->Rotate(50,60);
  gr->Box();  gr->Belt(a);
  return 0;
}
Example of Belt()

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2.6.8 Boxs sample

Function boxs draw surface by boxes. You can use ‘#’ for drawing wire plot. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->SetOrigin(0,0,0); gr->Light(true);
  gr->SubPlot(2,2,0);  gr->Title("Boxs plot (default)");
  gr->Rotate(40,60);  gr->Box();  gr->Boxs(a);

  gr->SubPlot(2,2,1); gr->Title("'\\@' style");
  gr->Rotate(50,60);  gr->Box();  gr->Boxs(a,"@");

  gr->SubPlot(2,2,2); gr->Title("'\\#' style");
  gr->Rotate(50,60);  gr->Box();  gr->Boxs(a,"#");

  gr->SubPlot(2,2,3); gr->Title("compare with Tile");
  gr->Rotate(50,60);  gr->Box();  gr->Tile(a);
  return 0;
}
Example of Boxs()

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2.6.9 Tile sample

Function tile draw surface by tiles. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->Title("Tile plot");
  gr->Rotate(40,60);  gr->Box();  gr->Tile(a);
  return 0;
}
Example of Tile()

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2.6.10 TileS sample

Function tiles is similar to tile but tile sizes is determined by another data. This allows one to simulate transparency of the plot. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2d(&a,&b);
  gr->SubPlot(1,1,0,""); gr->Title("TileS plot");
  gr->Box();  gr->TileS(a,b);
  return 0;
}
Example of TileS()

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2.6.11 Dens sample

Function dens draw density plot for surface. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,a1(30,40,3);  mgls_prepare2d(&a);
  gr->Fill(a1,"0.6*sin(2*pi*x+pi*(z+1)/2)*sin(3*pi*y+pi*z) + 0.4*cos(3*pi*(x*y)+pi*(z+1)^2/2)");
  gr->SubPlot(2,2,0,""); gr->Title("Dens plot (default)");
  gr->Box();  gr->Dens(a);

  gr->SubPlot(2,2,1); gr->Title("3d variant");
  gr->Rotate(50,60);  gr->Box();  gr->Dens(a);

  gr->SubPlot(2,2,2,"");  gr->Title("'\\#' style; meshnum 10");
  gr->Box();  gr->Dens(a,"#","meshnum 10");

  gr->SubPlot(2,2,3); gr->Title("several slices");
  gr->Rotate(50,60);    gr->Box();  gr->Dens(a1);
  return 0;
}
Example of Dens()

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2.6.12 Cont sample

Function cont draw contour lines for surface. You can select automatic (default) or manual levels for contours, print contour labels, draw it on the surface (default) or at plane (as Dens). The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,v(5); mgls_prepare2d(&a); v.a[0]=-0.5;  v.a[1]=-0.15; v.a[2]=0; v.a[3]=0.15;  v.a[4]=0.5;
  gr->SubPlot(2,2,0); gr->Title("Cont plot (default)");
  gr->Rotate(50,60);  gr->Box();  gr->Cont(a);

  gr->SubPlot(2,2,1); gr->Title("manual levels");
  gr->Rotate(50,60);  gr->Box();  gr->Cont(v,a);

  gr->SubPlot(2,2,2); gr->Title("'\\_' style");
  gr->Rotate(50,60);  gr->Box();  gr->Cont(a,"_");

  gr->SubPlot(2,2,3,"");  gr->Title("'t' style");
  gr->Box();  gr->Cont(a,"t");
  return 0;
}
Example of Cont()

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2.6.13 ContF sample

Function contf draw filled contours. You can select automatic (default) or manual levels for contours. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,v(5),a1(30,40,3); mgls_prepare2d(&a); v.a[0]=-0.5;
  v.a[1]=-0.15; v.a[2]=0; v.a[3]=0.15;  v.a[4]=0.5;
  gr->SubPlot(2,2,0); gr->Title("ContF plot (default)");
  gr->Rotate(50,60);  gr->Box();  gr->ContF(a);

  gr->SubPlot(2,2,1); gr->Title("manual levels");
  gr->Rotate(50,60);  gr->Box();  gr->ContF(v,a);

  gr->SubPlot(2,2,2); gr->Title("'\\_' style");
  gr->Rotate(50,60);  gr->Box();  gr->ContF(a,"_");

  gr->Fill(a1,"0.6*sin(2*pi*x+pi*(z+1)/2)*sin(3*pi*y+pi*z) +
               0.4*cos(3*pi*(x*y)+pi*(z+1)^2/2)");
  gr->SubPlot(2,2,3); gr->Title("several slices");
  gr->Rotate(50,60);  gr->Box();  gr->ContF(a1);
  return 0;
}
Example of ContF()

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2.6.14 ContD sample

Function contd is similar to ContF but with manual contour colors. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,v(5),a1(30,40,3); mgls_prepare2d(&a); v.a[0]=-0.5;
  v.a[1]=-0.15; v.a[2]=0; v.a[3]=0.15;  v.a[4]=0.5;
  gr->SubPlot(2,2,0); gr->Title("ContD plot (default)");
  gr->Rotate(50,60);  gr->Box();  gr->ContD(a);

  gr->SubPlot(2,2,1); gr->Title("manual levels");
  gr->Rotate(50,60);  gr->Box();  gr->ContD(v,a);

  gr->SubPlot(2,2,2); gr->Title("'\\_' style");
  gr->Rotate(50,60);  gr->Box();  gr->ContD(a,"_");

  gr->Fill(a1,"0.6*sin(2*pi*x+pi*(z+1)/2)*sin(3*pi*y+pi*z) + 0.4*cos(3*pi*(x*y)+pi*(z+1)^2/2)");
  gr->SubPlot(2,2,3); gr->Title("several slices");
  gr->Rotate(50,60);  gr->Box();  gr->ContD(a1);
  return 0;
}
Example of ContD()

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2.6.15 ContV sample

Function contv draw vertical cylinders (belts) at contour lines. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,v(5); mgls_prepare2d(&a); v.a[0]=-0.5;
  v.a[1]=-0.15; v.a[2]=0; v.a[3]=0.15;  v.a[4]=0.5;
  gr->SubPlot(2,2,0); gr->Title("ContV plot (default)");
  gr->Rotate(50,60);  gr->Box();  gr->ContV(a);

  gr->SubPlot(2,2,1); gr->Title("manual levels");
  gr->Rotate(50,60);  gr->Box();  gr->ContV(v,a);

  gr->SubPlot(2,2,2); gr->Title("'\\_' style");
  gr->Rotate(50,60);  gr->Box();  gr->ContV(a,"_");

  gr->SubPlot(2,2,3); gr->Title("ContV and ContF");
  gr->Rotate(50,60);  gr->Box();  gr->Light(true);
  gr->ContV(a); gr->ContF(a); gr->Cont(a,"k");
  return 0;
}
Example of ContV()

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2.6.16 Axial sample

Function axial draw surfaces of rotation for contour lines. You can draw wire surfaces (‘#’ style) or ones rotated in other directions (‘x’, ‘z’ styles). The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->SubPlot(2,2,0); gr->Title("Axial plot (default)");
  gr->Light(true);  gr->Alpha(true);  gr->Rotate(50,60);
  gr->Box();  gr->Axial(a);

  gr->SubPlot(2,2,1); gr->Title("'x' style;'.' style"); gr->Rotate(50,60);
  gr->Box();  gr->Axial(a,"x.");

  gr->SubPlot(2,2,2); gr->Title("'z' style"); gr->Rotate(50,60);
  gr->Box();  gr->Axial(a,"z");

  gr->SubPlot(2,2,3); gr->Title("'\\#' style"); gr->Rotate(50,60);
  gr->Box();  gr->Axial(a,"#");
  return 0;
}
Example of Axial()

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2.6.17 Grad sample

Function grad draw gradient lines for matrix. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->SubPlot(1,1,0,""); gr->Title("Grad plot");
  gr->Box();  gr->Grad(a);  gr->Dens(a,"{u8}w{q8}");
  return 0;
}
Example of Grad()

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2.7 3D samples

This section is devoted to visualization of 3D data arrays. 3D means the data which depend on 3 indexes (parameters) like tensor a(i,j,k)=a(x(i),y(j),x(k)), i=1...n, j=1...m, k=1...l or in parametric form {x(i,j,k),y(i,j,k),z(i,j,k),a(i,j,k)}. Most of samples will use the same data for plotting. So, I put its initialization in separate function 

void mgls_prepare3d(mglData *a, mglData *b=0)
{
  register long i,j,k,n=61,m=50,l=40,i0;
  if(a) a->Create(n,m,l);   if(b) b->Create(n,m,l);
  mreal x,y,z;
  for(i=0;i<n;i++)  for(j=0;j<m;j++)  for(k=0;k<l;k++)
  {
    x=2*i/(n-1.)-1; y=2*j/(m-1.)-1; z=2*k/(l-1.)-1; i0 = i+n*(j+m*k);
    if(a) a->a[i0] = -2*(x*x + y*y + z*z*z*z - z*z - 0.1);
    if(b) b->a[i0] = 1-2*tanh((x+y)*(x+y));
  }
}

or using C functions 

void mgls_prepare3d(HMDT a, HMDT b=0)
{
  register long i,j,k,n=61,m=50,l=40,i0;
  if(a) mgl_data_create(a,n,m,l);
  if(b) mgl_data_create(b,n,m,l);
  mreal x,y,z;
  for(i=0;i<n;i++)  for(j=0;j<m;j++)  for(k=0;k<l;k++)
  {
    x=2*i/(n-1.)-1; y=2*j/(m-1.)-1; z=2*k/(l-1.)-1; i0 = i+n*(j+m*k);
    if(a) mgl_data_set_value(a, -2*(x*x + y*y + z*z*z*z - z*z - 0.1), i,j,k);
    if(b) mgl_data_set_value(b, 1-2*tanh((x+y)*(x+y)), i,j,k);
  }
}
• Surf3 sample:  
• Surf3C sample:  
• Surf3A sample:  
• Surf3CA sample:  
• Cloud sample:  
• Dens3 sample:  
• Cont3 sample:  
• ContF3 sample:  
• Dens projection sample:  
• Cont projection sample:  
• ContF projection sample:  
• TriPlot and QuadPlot:  
• Dots sample:  
• IFS sample:  

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2.7.1 Surf3 sample

Function surf3 is one of most suitable (for my opinion) functions to visualize 3D data. It draw the isosurface(s) – surface(s) of constant amplitude (3D analogue of contour lines). You can draw wired isosurfaces if specify ‘#’ style. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->Light(true);    gr->Alpha(true);
  gr->SubPlot(2,2,0); gr->Title("Surf3 plot (default)");
  gr->Rotate(50,60);  gr->Box();  gr->Surf3(c);

  gr->SubPlot(2,2,1); gr->Title("'\\#' style");
  gr->Rotate(50,60);  gr->Box();  gr->Surf3(c,"#");

  gr->SubPlot(2,2,2); gr->Title("'.' style");
  gr->Rotate(50,60);  gr->Box();  gr->Surf3(c,".");
  return 0;
}
Example of Surf3()

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2.7.2 Surf3C sample

Function surf3c is similar to surf3 but its coloring is determined by another data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c,d;  mgls_prepare3d(&c,&d);
  gr->Title("Surf3C plot"); gr->Rotate(50,60);
  gr->Light(true);  gr->Alpha(true);
  gr->Box();  gr->Surf3C(c,d);
  return 0;
}
Example of Surf3C()

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2.7.3 Surf3A sample

Function surf3a is similar to surf3 but its transparency is determined by another data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c,d;  mgls_prepare3d(&c,&d);
  gr->Title("Surf3A plot"); gr->Rotate(50,60);
  gr->Light(true);  gr->Alpha(true);
  gr->Box();  gr->Surf3A(c,d);
  return 0;
}
Example of Surf3A()

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2.7.4 Surf3CA sample

Function surf3ca is similar to surf3 but its color and transparency is determined by another data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c,d;  mgls_prepare3d(&c,&d);
  gr->Title("Surf3CA plot"); gr->Rotate(50,60);
  gr->Light(true);  gr->Alpha(true);
  gr->Box();  gr->Surf3CA(c,d,c);
  return 0;
}
Example of Surf3CA()

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2.7.5 Cloud sample

Function cloud draw cloud-like object which is less transparent for higher data values. Similar plot can be created using many (about 10-20) Surf3A(a,a) isosurfaces. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->SubPlot(2,2,0); gr->Title("Cloud plot");
  gr->Rotate(50,60);  gr->Alpha(true);
  gr->Box();  gr->Cloud(c,"wyrRk");

  gr->SubPlot(2,2,1); gr->Title("'i' style");
  gr->Rotate(50,60);  gr->Box();  gr->Cloud(c,"iwyrRk");

  gr->SubPlot(2,2,2); gr->Title("'.' style");
  gr->Rotate(50,60);  gr->Box();  gr->Cloud(c,".wyrRk");

  gr->SubPlot(2,2,3); gr->Title("meshnum 10");
  gr->Rotate(50,60);  gr->Box();  gr->Cloud(c,"wyrRk","meshnum 10");
  return 0;
}
Example of Cloud()

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2.7.6 Dens3 sample

Function dens3 draw just usual density plot but at slices of 3D data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->Title("Dens3 sample");  gr->Rotate(50,60);
  gr->Alpha(true);  gr->SetAlphaDef(0.7);
  gr->SetOrigin(0,0,0); gr->Axis("_xyz"); gr->Box();
  gr->Dens3(c,"x"); gr->Dens3(c); gr->Dens3(c,"z");
  return 0;
}
Example of Dens3()

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2.7.7 Cont3 sample

Function cont3 draw just usual contour lines but at slices of 3D data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->Title("Cont3 sample");  gr->Rotate(50,60);
  gr->Alpha(true);  gr->SetAlphaDef(0.7);
  gr->SetOrigin(0,0,0); gr->Axis("_xyz"); gr->Box();
  gr->Cont3(c,"x"); gr->Cont3(c); gr->Cont3(c,"z");
  return 0;
}
Example of Cont3()

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2.7.8 ContF3 sample

Function contf3 draw just usual filled contours but at slices of 3D data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->Title("ContF3 sample");  gr->Rotate(50,60);
  gr->Alpha(true);  gr->SetAlphaDef(0.7);
  gr->SetOrigin(0,0,0); gr->Axis("_xyz"); gr->Box();
  gr->ContF3(c,"x");  gr->ContF3(c);    gr->ContF3(c,"z");
  gr->Cont3(c,"kx");  gr->Cont3(c,"k"); gr->Cont3(c,"kz");
  return 0;
}
Example of ContF3()

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2.7.9 Dens projection sample

Functions densz, densy, densx draw density plot on plane perpendicular to corresponding axis. One of possible application is drawing projections of 3D field. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->Title("Dens[XYZ] sample");  gr->Rotate(50,60);
  gr->Box();  gr->DensX(c.Sum("x"),0,-1);
  gr->DensY(c.Sum("y"),0,1);  gr->DensZ(c.Sum("z"),0,-1);
  return 0;
}
Example of DensX() DensY() DensZ()

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2.7.10 Cont projection sample

Functions contz, conty, contx draw contour lines on plane perpendicular to corresponding axis. One of possible application is drawing projections of 3D field. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->Title("Cont[XYZ] sample");  gr->Rotate(50,60);
  gr->Box();  gr->ContX(c.Sum("x"),"",-1);
  gr->ContY(c.Sum("y"),"",1); gr->ContZ(c.Sum("z"),"",-1);
  return 0;
}
Example of ContX() ContY() ContZ()

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2.7.11 ContF projection sample

Functions contfz, contfy, contfx, draw filled contours on plane perpendicular to corresponding axis. One of possible application is drawing projections of 3D field. The sample code is: 

int sample(mglGraph *gr)
{
  mglData c;  mgls_prepare3d(&c);
  gr->Title("Cont[XYZ] sample");  gr->Rotate(50,60);
  gr->Box();  gr->ContFX(c.Sum("x"),"",-1);
  gr->ContFY(c.Sum("y"),"",1);  gr->ContFZ(c.Sum("z"),"",-1);
  return 0;
}
Example of ContFX() ContFY() ContFZ()

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2.7.12 TriPlot and QuadPlot

Function triplot and quadplot draw set of triangles (or quadrangles for QuadPlot) for irregular data arrays. Note, that you have to provide not only vertexes, but also the indexes of triangles or quadrangles. I.e. perform triangulation by some other library. The sample code is: 

int sample(mglGraph *gr)
{
  mreal q[] = {0,1,2,3, 4,5,6,7, 0,2,4,6, 1,3,5,7, 0,4,1,5, 2,6,3,7};
  mreal xc[] = {-1,1,-1,1,-1,1,-1,1}, yc[] = {-1,-1,1,1,-1,-1,1,1}, zc[] = {-1,-1,-1,-1,1,1,1,1};
  mglData qq(6,4,q), xx(8,xc), yy(8,yc), zz(8,zc);
  gr->Light(true);  //gr->Alpha(true);
  gr->SubPlot(2,2,0); gr->Title("QuadPlot sample"); gr->Rotate(50,60);
  gr->QuadPlot(qq,xx,yy,zz,"yr");
  gr->QuadPlot(qq,xx,yy,zz,"k#");
  gr->SubPlot(2,2,2); gr->Title("QuadPlot coloring"); gr->Rotate(50,60);
  gr->QuadPlot(qq,xx,yy,zz,yy,"yr");
  gr->QuadPlot(qq,xx,yy,zz,"k#");

  mreal t[] = {0,1,2, 0,1,3, 0,2,3, 1,2,3};
  mreal xt[] = {-1,1,0,0}, yt[] = {-1,-1,1,0}, zt[] = {-1,-1,-1,1};
  mglData tt(4,3,t), uu(4,xt), vv(4,yt), ww(4,zt);
  gr->SubPlot(2,2,1); gr->Title("TriPlot sample");  gr->Rotate(50,60);
  gr->TriPlot(tt,uu,vv,ww,"b");
  gr->TriPlot(tt,uu,vv,ww,"k#");
  gr->SubPlot(2,2,3); gr->Title("TriPlot coloring");  gr->Rotate(50,60);
  gr->TriPlot(tt,uu,vv,ww,vv,"cb");
  gr->TriPlot(tt,uu,vv,ww,"k#");
  gr->TriCont(tt,uu,vv,ww,"B");
  return 0;
}
Example of TriPlot() and QuadPlot()

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2.7.13 Dots sample

Function dots is another way to draw irregular points. Dots use color scheme for coloring (see Color scheme). The sample code is: 

int sample(mglGraph *gr)
{
  int i, n=2000;
  mglData x(n),y(n),z(n),c(n);
  for(i=0;i<n;i++)
  {
    mreal t=M_PI*(mgl_rnd()-0.5), f=2*M_PI*mgl_rnd();
    x.a[i] = 0.9*cos(t)*cos(f);
    y.a[i] = 0.9*cos(t)*sin(f);
    z.a[i] = 0.6*sin(t);
    c.a[i] = cos(2*t);
  }
  gr->SubPlot(2,2,0); gr->Title("Dots sample");  gr->Rotate(50,60);
  gr->Box();  gr->Dots(x,y,z);
  gr->Alpha(true);
  gr->SubPlot(2,2,1); gr->Title("add transparency"); gr->Rotate(50,60);
  gr->Box();  gr->Dots(x,y,z,c);
  gr->SubPlot(2,2,2); gr->Title("add coloring"); gr->Rotate(50,60);
  gr->Box();  gr->Dots(x,y,z,x,c);
  gr->SubPlot(2,2,3); gr->Title("Only coloring");gr->Rotate(50,60);
  gr->Box();  gr->Tens(x,y,z,x," .");
  return 0;
}
Example of Dots()

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2.7.14 IFS sample

Commands ifs2d and ifs3d generate points for fractals using iterated function system in 2d and 3d cases correspondingly. The sample codes are: 

int sample(mglGraph *gr)
{
  mglData A;
  A.SetList(35, 0.33,0.,0.,0.33,0.,0.,0.2, 0.33,0.,0.,0.33,0.67,0.,0.2, 0.33,0.,0.,0.33,0.33,0.33,0.2,
                0.33,0.,0.,0.33,0.,0.67,0.2, 0.33,0.,0.,0.33,0.67,0.67,0.2);
  A.Rearrange(7);
  mglData f(mglIFS2d(A,100000));
  gr->SubPlot(1,1,0,"<_");
  gr->Title("IFS 2d sample");
  gr->SetRanges(f.SubData(0), f.SubData(1));
  gr->Axis(); gr->Plot(f.SubData(0), f.SubData(1),"r#o ","size 0.05");
}
Example of IFS fractal (2d case). 
int sample(mglGraph *gr)
{
  mglData A;
  A.SetList(52, 0.,0.,0.,0.,.18,0.,0.,0.,0.,0.,0.,0.,.01, .85,0.,0.,0.,.85,.1,0.,-0.1,0.85,0.,1.6,0.,.85,
                .2,-.2,0.,.2,.2,0.,0.,0.,0.3,0.,0.8,0.,.07, -.2,.2,0.,.2,.2,0.,0.,0.,0.3,0.,0.8,0.,.07);
  A.Rearrange(13);
  mglData f(mglIFS3d(A,100000));
  gr->Title("IFS 3d sample");
  gr->SetRanges(f.SubData(0), f.SubData(1), f.SubData(2));
  gr->Rotate(50,60);  gr->Axis(); gr->Box();
  gr->Dots(f.SubData(0), f.SubData(1), f.SubData(2),"G#o","size 0.05");
}
Example of IFS fractal (3d case).

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2.8 Vector field samples

Vector field visualization (especially in 3d case) is more or less complex task. MathGL provides 3 general types of plots: vector field itself (Vect), flow threads (Flow), and flow pipes with radius proportional to field amplitude (Pipe).

However, the plot may look tangly – there are too many overlapping lines. I may suggest 2 ways to solve this problem. The first one is to change SetMeshNum for decreasing the number of hachures. The second way is to use the flow thread chart Flow, or possible many flow thread from manual position (FlowP). Unfortunately, I don’t know any other methods to visualize 3d vector field. If you know any, e-mail me and I shall add it to MathGL.

Most of samples will use the same data for plotting. So, I put its initialization in separate function 

void mgls_prepare2v(mglData *a, mglData *b)
{
  register long i,j,n=20,m=30,i0;
  if(a) a->Create(n,m);   if(b) b->Create(n,m);
  mreal x,y;
  for(i=0;i<n;i++)  for(j=0;j<m;j++)
  {
    x=i/(n-1.); y=j/(m-1.); i0 = i+n*j;
    if(a) a->a[i0] = 0.6*sin(2*M_PI*x)*sin(3*M_PI*y)+0.4*cos(3*M_PI*x*y);
    if(b) b->a[i0] = 0.6*cos(2*M_PI*x)*cos(3*M_PI*y)+0.4*cos(3*M_PI*x*y);
  }
}
void mgls_prepare3v(mglData *ex, mglData *ey, mglData *ez)
{
  register long i,j,k,n=10,i0;
  if(!ex || !ey || !ez) return;
  ex->Create(n,n,n);  ey->Create(n,n,n);  ez->Create(n,n,n);
  mreal x,y,z, r1,r2;
  for(i=0;i<n;i++)  for(j=0;j<n;j++)  for(k=0;k<n;k++)
  {
    x=2*i/(n-1.)-1; y=2*j/(n-1.)-1; z=2*k/(n-1.)-1; i0 = i+n*(j+k*n);
    r1 = pow(x*x+y*y+(z-0.3)*(z-0.3)+0.03,1.5);
    r2 = pow(x*x+y*y+(z+0.3)*(z+0.3)+0.03,1.5);
    ex->a[i0]=0.2*x/r1 - 0.2*x/r2;
    ey->a[i0]=0.2*y/r1 - 0.2*y/r2;
    ez->a[i0]=0.2*(z-0.3)/r1 - 0.2*(z+0.3)/r2;
  }
}

or using C functions 

void mgls_prepare2v(HMDT a, HMDT b)
{
  register long i,j,n=20,m=30,i0;
  if(a) mgl_data_create(a,n,m,1);
  if(b) mgl_data_create(b,n,m,1);
  mreal x,y;
  for(i=0;i<n;i++)  for(j=0;j<m;j++)
  {
    x=i/(n-1.); y=j/(m-1.); i0 = i+n*j;
    if(a) mgl_data_set_value(a, 0.6*sin(2*M_PI*x)*sin(3*M_PI*y)+0.4*cos(3*M_PI*x*y), i,j,0);
    if(b) mgl_data_set_value(b, 0.6*cos(2*M_PI*x)*cos(3*M_PI*y)+0.4*cos(3*M_PI*x*y), i,j,0);
  }
}
void mgls_prepare3v(HMDT ex, HMDT ey, HMDT ez)
{
  register long i,j,k,n=10,i0;
  if(!ex || !ey || !ez) return;
  mgl_data_create(ex,n,n,n);
  mgl_data_create(ey,n,n,n);
  mgl_data_create(ez,n,n,n);
  mreal x,y,z, r1,r2;
  for(i=0;i<n;i++)  for(j=0;j<n;j++)  for(k=0;k<n;k++)
  {
    x=2*i/(n-1.)-1; y=2*j/(n-1.)-1; z=2*k/(n-1.)-1; i0 = i+n*(j+k*n);
    r1 = pow(x*x+y*y+(z-0.3)*(z-0.3)+0.03,1.5);
    r2 = pow(x*x+y*y+(z+0.3)*(z+0.3)+0.03,1.5);
    mgl_data_set_value(ex, 0.2*x/r1 - 0.2*x/r2, i,j,k);
    mgl_data_set_value(ey, 0.2*y/r1 - 0.2*y/r2, i,j,k);
    mgl_data_set_value(ez, 0.2*(z-0.3)/r1 - 0.2*(z+0.3)/r2, i,j,k);
  }
}
• Vect sample:  
• Vect3 sample:  
• Traj sample:  
• Flow sample:  
• Pipe sample:  
• Dew sample:  

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2.8.1 Vect sample

Function vect is most standard way to visualize vector fields – it draw a lot of arrows or hachures for each data cell. It have a lot of options which can be seen on the figure (and in the sample code). Vect use color scheme for coloring (see Color scheme). The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2v(&a,&b);
  gr->SubPlot(3,2,0,""); gr->Title("Vect plot (default)");
  gr->Box();  gr->Vect(a,b);

  gr->SubPlot(3,2,1,"");  gr->Title("'.' style; '=' style");
  gr->Box();  gr->Vect(a,b,"=.");

  gr->SubPlot(3,2,2,"");  gr->Title("'f' style");
  gr->Box();  gr->Vect(a,b,"f");

  gr->SubPlot(3,2,3,"");  gr->Title("'>' style");
  gr->Box();  gr->Vect(a,b,">");

  gr->SubPlot(3,2,4,"");  gr->Title("'<' style");
  gr->Box();  gr->Vect(a,b,"<");

  mglData ex,ey,ez; mgls_prepare3v(&ex,&ey,&ez);
  gr->SubPlot(3,2,5); gr->Title("3d variant");  gr->Rotate(50,60);
  gr->Box();  gr->Vect(ex,ey,ez);
  return 0;
}
Example of Vect()

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2.8.2 Vect3 sample

Function vect3 draw just usual vector field plot but at slices of 3D data. The sample code is: 

int sample(mglGraph *gr)
{
  mglData ex,ey,ez; mgls_prepare3v(&ex,&ey,&ez);
  gr->SubPlot(2,1,0); gr->Title("Vect3 sample");    gr->SetOrigin(0,0,0);
  gr->Rotate(50,60);    gr->Axis("_xyz");   gr->Box();
  gr->Vect3(ex,ey,ez,"x");  gr->Vect3(ex,ey,ez);    gr->Vect3(ex,ey,ez,"z");

  gr->SubPlot(2,1,1);   gr->Title("'f' style");
  gr->Rotate(50,60);    gr->Axis("_xyz");   gr->Box();
  gr->Vect3(ex,ey,ez,"fx"); gr->Vect3(ex,ey,ez,"f");gr->Vect3(ex,ey,ez,"fz");
  gr->Grid3(ex,"Wx");   gr->Grid3(ex,"W");  gr->Grid3(ex,"Wz");
  return 0;
}
Example of Vect3()

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2.8.3 Traj sample

Function traj is 1D analogue of Vect. It draw vectors from specified points. The sample code is: 

int sample(mglGraph *gr)
{
  mglData x,y,y1,y2;  mgls_prepare1d(&y,&y1,&y2,&x);
  gr->SubPlot(1,1,0,""); gr->Title("Traj plot");
  gr->Box();  gr->Plot(x,y);  gr->Traj(x,y,y1,y2);
  return 0;
}
Example of Traj()

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2.8.4 Flow sample

Function flow is another standard way to visualize vector fields – it draw lines (threads) which is tangent to local vector field direction. MathGL draw threads from edges of bounding box and from central slices. Sometimes it is not most appropriate variant – you may want to use FlowP to specify manual position of threads. Flow use color scheme for coloring (see Color scheme). At this warm color corresponds to normal flow (like attractor), cold one corresponds to inverse flow (like source). The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2v(&a,&b);
  gr->SubPlot(2,2,0,""); gr->Title("Flow plot (default)");
  gr->Box();  gr->Flow(a,b);

  gr->SubPlot(2,2,1,"");  gr->Title("'v' style");
  gr->Box();  gr->Flow(a,b,"v");

  gr->SubPlot(2,2,2,"");  gr->Title("'\\#' style");
  gr->Box();  gr->Flow(a,b,"#");

  mglData ex,ey,ez; mgls_prepare3v(&ex,&ey,&ez);
  gr->SubPlot(2,2,3); gr->Title("3d variant");  gr->Rotate(50,60);
  gr->Box();  gr->Flow(ex,ey,ez);
  return 0;
}
Example of Flow()

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2.8.5 Pipe sample

Function pipe is similar to flow but draw pipes (tubes) which radius is proportional to the amplitude of vector field. Pipe use color scheme for coloring (see Color scheme). At this warm color corresponds to normal flow (like attractor), cold one corresponds to inverse flow (like source). The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2v(&a,&b);
  gr->SubPlot(2,2,0,""); gr->Title("Pipe plot (default)");
  gr->Light(true);  gr->Box();  gr->Pipe(a,b);

  gr->SubPlot(2,2,1,"");  gr->Title("'i' style");
  gr->Box();  gr->Pipe(a,b,"i");

  gr->SubPlot(2,2,2,"");  gr->Title("'\\#' style");
  gr->Box();  gr->Pipe(a,b,"#");

  mglData ex,ey,ez; mgls_prepare3v(&ex,&ey,&ez);
  gr->SubPlot(2,2,3); gr->Title("3d variant");  gr->Rotate(50,60);
  gr->Box();  gr->Pipe(ex,ey,ez,"",0.1);
  return 0;
}
Example of Pipe()

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2.8.6 Dew sample

Function dew is similar to Vect but use drops instead of arrows. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a,b;  mgls_prepare2v(&a,&b);
  gr->SubPlot(1,1,0,""); gr->Title("Dew plot");
  gr->Box();  gr->Light(true);  gr->Dew(a,b);
  return 0;
}
Example of Dew()

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2.9 Hints

In this section I’ve included some small hints and advices for the improving of the quality of plots and for the demonstration of some non-trivial features of MathGL library. In contrast to previous examples I showed mostly the idea but not the whole drawing function.

• ``Compound'' graphics:  
• Transparency and lighting:  
• Types of transparency:  
• Axis projection:  
• Adding fog:  
• Lighting sample:  
• Using primitives:  
• STFA sample:  
• Mapping visualization:  
• Data interpolation:  
• Making regular data:  
• Making histogram:  
• Nonlinear fitting hints:  
• PDE solving hints:  
• Drawing phase plain:  
• Pulse properties:  
• Using MGL parser:  
• Using options:  
• ``Templates'':  
• Stereo image:  
• Reduce memory usage:  
• Saving and scanning file:  

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2.9.1 “Compound” graphics

As I noted above, MathGL functions (except the special one, like Clf()) do not erase the previous plotting but just add the new one. It allows one to draw “compound” plots easily. For example, popular Matlab command surfc can be emulated in MathGL by 2 calls: 

  Surf(a);
  Cont(a, "_");     // draw contours at bottom

Here a is 2-dimensional data for the plotting, -1 is the value of z-coordinate at which the contour should be plotted (at the bottom in this example). Analogously, one can draw density plot instead of contour lines and so on.

Another nice plot is contour lines plotted directly on the surface: 

  Light(true);       // switch on light for the surface
  Surf(a, "BbcyrR"); // select 'jet' colormap for the surface
  Cont(a, "y");      // and yellow color for contours

The possible difficulties arise in black&white case, when the color of the surface can be close to the color of a contour line. In that case I may suggest the following code: 

  Light(true);   // switch on light for the surface
  Surf(a, "kw"); // select 'gray' colormap for the surface
  CAxis(-1,0);   // first draw for darker surface colors
  Cont(a, "w");  // white contours
  CAxis(0,1);    // now draw for brighter surface colors
  Cont(a, "k");  // black contours
  CAxis(-1,1);   // return color range to original state

The idea is to divide the color range on 2 parts (dark and bright) and to select the contrasting color for contour lines for each of part.

Similarly, one can plot flow thread over density plot of vector field amplitude (this is another amusing plot from Matlab) and so on. The list of compound graphics can be prolonged but I hope that the general idea is clear.

Just for illustration I put here following sample code: 

int sample(mglGraph *gr)
{
  mglData a,b,d;  mgls_prepare2v(&a,&b);  d = a;
  for(int i=0;i<a.nx*a.ny;i++)  d.a[i] = hypot(a.a[i],b.a[i]);
  mglData c;  mgls_prepare3d(&c);
  mglData v(10);  v.Fill(-0.5,1);

  gr->SubPlot(2,2,1,"");  gr->Title("Flow + Dens");
  gr->Flow(a,b,"br"); gr->Dens(d,"BbcyrR"); gr->Box();

  gr->SubPlot(2,2,0); gr->Title("Surf + Cont"); gr->Rotate(50,60);
  gr->Light(true);  gr->Surf(a);  gr->Cont(a,"y");  gr->Box();

  gr->SubPlot(2,2,2); gr->Title("Mesh + Cont"); gr->Rotate(50,60);
  gr->Box();  gr->Mesh(a);  gr->Cont(a,"_");

  gr->SubPlot(2,2,3); gr->Title("Surf3 + ContF3");gr->Rotate(50,60);
  gr->Box();  gr->ContF3(v,c,"z",0);  gr->ContF3(v,c,"x");  gr->ContF3(v,c);
  gr->SetCutBox(mglPoint(0,-1,-1), mglPoint(1,0,1.1));
  gr->ContF3(v,c,"z",c.nz-1); gr->Surf3(-0.5,c);
  return 0;
}
Example of “combined” plots

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2.9.2 Transparency and lighting

Here I want to show how transparency and lighting both and separately change the look of a surface. So, there is code and picture for that: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->SubPlot(2,2,0); gr->Title("default"); gr->Rotate(50,60);
  gr->Box();  gr->Surf(a);

  gr->SubPlot(2,2,1); gr->Title("light on");  gr->Rotate(50,60);
  gr->Box();  gr->Light(true);  gr->Surf(a);

  gr->SubPlot(2,2,3); gr->Title("alpha on; light on");  gr->Rotate(50,60);
  gr->Box();  gr->Alpha(true);  gr->Surf(a);

  gr->SubPlot(2,2,2); gr->Title("alpha on");  gr->Rotate(50,60);
  gr->Box();  gr->Light(false); gr->Surf(a);
  return 0;
}
Example of transparency and lightings

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2.9.3 Types of transparency

MathGL library has advanced features for setting and handling the surface transparency. The simplest way to add transparency is the using of function alpha. As a result, all further surfaces (and isosurfaces, density plots and so on) become transparent. However, their look can be additionally improved.

The value of transparency can be different from surface to surface. To do it just use SetAlphaDef before the drawing of the surface, or use option alpha (see Command options). If its value is close to 0 then the surface becomes more and more transparent. Contrary, if its value is close to 1 then the surface becomes practically non-transparent.

Also you can change the way how the light goes through overlapped surfaces. The function SetTranspType defines it. By default the usual transparency is used (‘0’) – surfaces below is less visible than the upper ones. A “glass-like” transparency (‘1’) has a different look – each surface just decreases the background light (the surfaces are commutable in this case).

A “neon-like” transparency (‘2’) has more interesting look. In this case a surface is the light source (like a lamp on the dark background) and just adds some intensity to the color. At this, the library sets automatically the black color for the background and changes the default line color to white.

As example I shall show several plots for different types of transparency. The code is the same except the values of SetTranspType function: 

int sample(mglGraph *gr)
{
  gr->Alpha(true);  gr->Light(true);
  mglData a;  mgls_prepare2d(&a);
  gr->SetTranspType(0); gr->Clf();
  gr->SubPlot(2,2,0); gr->Rotate(50,60);  gr->Surf(a);  gr->Box();
  gr->SubPlot(2,2,1); gr->Rotate(50,60);  gr->Dens(a);  gr->Box();
  gr->SubPlot(2,2,2); gr->Rotate(50,60);  gr->Cont(a);  gr->Box();
  gr->SubPlot(2,2,3); gr->Rotate(50,60);  gr->Axial(a); gr->Box();
  return 0;
}
Example of SetTranspType(0).
Example of SetTranspType(1).
Example of SetTranspType(2).

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2.9.4 Axis projection

You can easily make 3D plot and draw its x-,y-,z-projections (like in CAD) by using ternary function with arguments: 4 for Cartesian, 5 for Ternary and 6 for Quaternary coordinates. The sample code is: 

int sample(mglGraph *gr)
{
  gr->SetRanges(0,1,0,1,0,1);
  mglData x(50),y(50),z(50),rx(10),ry(10), a(20,30);
  a.Modify("30*x*y*(1-x-y)^2*(x+y<1)");
  x.Modify("0.25*(1+cos(2*pi*x))");
  y.Modify("0.25*(1+sin(2*pi*x))");
  rx.Modify("rnd"); ry.Modify("(1-v)*rnd",rx);
  z.Modify("x");

  gr->Title("Projection sample");
  gr->Ternary(4);
  gr->Rotate(50,60);      gr->Light(true);
  gr->Plot(x,y,z,"r2");   gr->Surf(a,"#");
  gr->Axis(); gr->Grid(); gr->Box();
  gr->Label('x',"X",1);   gr->Label('y',"Y",1);   gr->Label('z',"Z",1);
}
Example of axis projections
Example of ternary axis projections

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2.9.5 Adding fog

MathGL can add a fog to the image. Its switching on is rather simple – just use fog function. There is the only feature – fog is applied for whole image. Not to particular subplot. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->Title("Fog sample");
  gr->Light(true);  gr->Rotate(50,60);  gr->Fog(1); gr->Box();
  gr->Surf(a);  gr->Cont(a,"y");
  return 0;
}
Example of Fog().

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2.9.6 Lighting sample

In contrast to the most of other programs, MathGL supports several (up to 10) light sources. Moreover, the color each of them can be different: white (this is usual), yellow, red, cyan, green and so on. The use of several light sources may be interesting for the highlighting of some peculiarities of the plot or just to make an amusing picture. Note, each light source can be switched on/off individually. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->Title("Several light sources");
  gr->Rotate(50,60);  gr->Light(true);
  gr->AddLight(1,mglPoint(0,1,0),'c');
  gr->AddLight(2,mglPoint(1,0,0),'y');
  gr->AddLight(3,mglPoint(0,-1,0),'m');
  gr->Box();  gr->Surf(a,"h");
  return 0;
}
Example of several light sources.

Additionally, you can use local light sources and set to use diffuse reflection instead of specular one (by default) or both kinds. Note, I use attachlight command to keep light settings relative to subplot. 

int sample(mglGraph *gr)
{
  gr->Light(true);  gr->AttachLight(true);
  gr->SubPlot(2,2,0); gr->Title("Default"); gr->Rotate(50,60);
  gr->Line(mglPoint(-1,-0.7,1.7),mglPoint(-1,-0.7,0.7),"BA"); gr->Box();  gr->Surf(a);

  gr->SubPlot(2,2,1); gr->Title("Local");   gr->Rotate(50,60);
  gr->AddLight(0,mglPoint(1,0,1),mglPoint(-2,-1,-1));
  gr->Line(mglPoint(1,0,1),mglPoint(-1,-1,0),"BAO");  gr->Box();  gr->Surf(a);

  gr->SubPlot(2,2,2); gr->Title("no diffuse"); gr->Rotate(50,60);
  gr->SetDiffuse(0);
  gr->Line(mglPoint(1,0,1),mglPoint(-1,-1,0),"BAO");  gr->Box();  gr->Surf(a);

  gr->SubPlot(2,2,3); gr->Title("diffusive only");  gr->Rotate(50,60);
  gr->SetDiffuse(0.5);
  gr->AddLight(0,mglPoint(1,0,1),mglPoint(-2,-1,-1),'w',0);
  gr->Line(mglPoint(1,0,1),mglPoint(-1,-1,0),"BAO");  gr->Box();  gr->Surf(a);
}
Example of different types of lighting.

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2.9.7 Using primitives

MathGL provide a set of functions for drawing primitives (see Primitives). Primitives are low level object, which used by most of plotting functions. Picture below demonstrate some of commonly used primitives.

Primitives in MathGL.

Generally, you can create arbitrary new kind of plot using primitives. For example, MathGL don’t provide any special functions for drawing molecules. However, you can do it using only one type of primitives drop. The sample code is: 

int sample(mglGraph *gr)
{
  gr->Alpha(true);  gr->Light(true);

  gr->SubPlot(2,2,0,"");  gr->Title("Methane, CH_4");
  gr->StartGroup("Methane");
  gr->Rotate(60,120);
  gr->Sphere(mglPoint(0,0,0),0.25,"k");
  gr->Drop(mglPoint(0,0,0),mglPoint(0,0,1),0.35,"h",1,2);
  gr->Sphere(mglPoint(0,0,0.7),0.25,"g");
  gr->Drop(mglPoint(0,0,0),mglPoint(-0.94,0,-0.33),0.35,"h",1,2);
  gr->Sphere(mglPoint(-0.66,0,-0.23),0.25,"g");
  gr->Drop(mglPoint(0,0,0),mglPoint(0.47,0.82,-0.33),0.35,"h",1,2);
  gr->Sphere(mglPoint(0.33,0.57,-0.23),0.25,"g");
  gr->Drop(mglPoint(0,0,0),mglPoint(0.47,-0.82,-0.33),0.35,"h",1,2);
  gr->Sphere(mglPoint(0.33,-0.57,-0.23),0.25,"g");
  gr->EndGroup();

  gr->SubPlot(2,2,1,"");  gr->Title("Water, H_{2}O");
  gr->StartGroup("Water");
  gr->Rotate(60,100);
  gr->StartGroup("Water_O");
  gr->Sphere(mglPoint(0,0,0),0.25,"r");
  gr->EndGroup();
  gr->StartGroup("Water_Bond_1");
  gr->Drop(mglPoint(0,0,0),mglPoint(0.3,0.5,0),0.3,"m",1,2);
  gr->EndGroup();
  gr->StartGroup("Water_H_1");
  gr->Sphere(mglPoint(0.3,0.5,0),0.25,"g");
  gr->EndGroup();
  gr->StartGroup("Water_Bond_2");
  gr->Drop(mglPoint(0,0,0),mglPoint(0.3,-0.5,0),0.3,"m",1,2);
  gr->EndGroup();
  gr->StartGroup("Water_H_2");
  gr->Sphere(mglPoint(0.3,-0.5,0),0.25,"g");
  gr->EndGroup();
  gr->EndGroup();

  gr->SubPlot(2,2,2,"");  gr->Title("Oxygen, O_2");
  gr->StartGroup("Oxygen");
  gr->Rotate(60,120);
  gr->Drop(mglPoint(0,0.5,0),mglPoint(0,-0.3,0),0.3,"m",1,2);
  gr->Sphere(mglPoint(0,0.5,0),0.25,"r");
  gr->Drop(mglPoint(0,-0.5,0),mglPoint(0,0.3,0),0.3,"m",1,2);
  gr->Sphere(mglPoint(0,-0.5,0),0.25,"r");
  gr->EndGroup();

  gr->SubPlot(2,2,3,"");  gr->Title("Ammonia, NH_3");
  gr->StartGroup("Ammonia");
  gr->Rotate(60,120);
  gr->Sphere(mglPoint(0,0,0),0.25,"b");
  gr->Drop(mglPoint(0,0,0),mglPoint(0.33,0.57,0),0.32,"n",1,2);
  gr->Sphere(mglPoint(0.33,0.57,0),0.25,"g");
  gr->Drop(mglPoint(0,0,0),mglPoint(0.33,-0.57,0),0.32,"n",1,2);
  gr->Sphere(mglPoint(0.33,-0.57,0),0.25,"g");
  gr->Drop(mglPoint(0,0,0),mglPoint(-0.65,0,0),0.32,"n",1,2);
  gr->Sphere(mglPoint(-0.65,0,0),0.25,"g");
  gr->EndGroup();
  return 0;
}
Example of molecules drawing.

Moreover, some of special plots can be more easily produced by primitives rather than by specialized function. For example, Venn diagram can be produced by Error plot: 

int sample(mglGraph *gr)
{
  double xx[3]={-0.3,0,0.3}, yy[3]={0.3,-0.3,0.3}, ee[3]={0.7,0.7,0.7};
  mglData x(3,xx), y(3,yy), e(3,ee);
  gr->Title("Venn-like diagram"); gr->Alpha(true);
  gr->Error(x,y,e,e,"!rgb@#o");
  return 0;
}

You see that you have to specify and fill 3 data arrays. The same picture can be produced by just 3 calls of circle function: 

int sample(mglGraph *gr)
{
  gr->Title("Venn-like diagram"); gr->Alpha(true);
  gr->Circle(mglPoint(-0.3,0.3),0.7,"rr@");
  gr->Circle(mglPoint(0,-0.3),0.7,"gg@");
  gr->Circle(mglPoint( 0.3,0.3),0.7,"bb@");
  return 0;
}

Of course, the first variant is more suitable if you need to plot a lot of circles. But for few ones the usage of primitives looks easy.

Example of Venn diagram.

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2.9.8 STFA sample

Short-time Fourier Analysis (stfa) is one of informative method for analyzing long rapidly oscillating 1D data arrays. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time.

MathGL can find and draw STFA result. Just to show this feature I give following sample. Initial data arrays is 1D arrays with step-like frequency. Exactly this you can see at bottom on the STFA plot. The sample code is: 

int sample(mglGraph *gr)
{
  mglData a(2000), b(2000);
  gr->Fill(a,"cos(50*pi*x)*(x<-.5)+cos(100*pi*x)*(x<0)*(x>-.5)+\
  cos(200*pi*x)*(x<.5)*(x>0)+cos(400*pi*x)*(x>.5)");
  gr->SubPlot(1, 2, 0,"<_");  gr->Title("Initial signal");
  gr->Plot(a);
  gr->Axis();
  gr->Label('x', "\\i t");

  gr->SubPlot(1, 2, 1,"<_");  gr->Title("STFA plot");
  gr->STFA(a, b, 64);
  gr->Axis();
  gr->Label('x', "\\i t");
  gr->Label('y', "\\omega", 0);
  return 0;
}
Example of STFA().

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2.9.9 Mapping visualization

Sometime ago I worked with mapping and have a question about its visualization. Let me remember you that mapping is some transformation rule for one set of number to another one. The 1d mapping is just an ordinary function – it takes a number and transforms it to another one. The 2d mapping (which I used) is a pair of functions which take 2 numbers and transform them to another 2 ones. Except general plots (like surfc, surfa) there is a special plot – Arnold diagram. It shows the area which is the result of mapping of some initial area (usually square).

I tried to make such plot in map. It shows the set of points or set of faces, which final position is the result of mapping. At this, the color gives information about their initial position and the height describes Jacobian value of the transformation. Unfortunately, it looks good only for the simplest mapping but for the real multivalent quasi-chaotic mapping it produces a confusion. So, use it if you like :).

The sample code for mapping visualization is: 

int sample(mglGraph *gr)
{
  mglData a(50, 40), b(50, 40);
  gr->Puts(mglPoint(0, 0), "\\to", ":C", -1.4);
  gr->SetRanges(-1,1,-1,1,-2,2);

  gr->SubPlot(2, 1, 0);
  gr->Fill(a,"x");  gr->Fill(b,"y");
  gr->Puts(mglPoint(0, 1.1), "\\{x, y\\}", ":C", -2);   gr->Box();
  gr->Map(a, b, "brgk");

  gr->SubPlot(2, 1, 1);
  gr->Fill(a,"(x^3+y^3)/2");  gr->Fill(b,"(x-y)/2");
  gr->Puts(mglPoint(0, 1.1), "\\{\\frac{x^3+y^3}{2}, \\frac{x-y}{2}\\}", ":C", -2);
  gr->Box();
  gr->Map(a, b, "brgk");
  return 0;
}
Example of Map().

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2.9.10 Data interpolation

There are many functions to get interpolated values of a data array. Basically all of them can be divided by 3 categories:

  1. functions which return single value at given point (see Interpolation and mglGSpline() in Global functions);
  2. functions subdata and evaluate for indirect access to data elements;
  3. functions refill, gspline and datagrid which fill regular (rectangular) data array by interpolated values.

The usage of first category is rather straightforward and don’t need any special comments.

There is difference in indirect access functions. Function subdata use use step-like interpolation to handle correctly single nan values in the data array. Contrary, function evaluate use local spline interpolation, which give smoother output but spread nan values. So, subdata should be used for specific data elements (for example, for given column), and evaluate should be used for distributed elements (i.e. consider data array as some field). Following sample illustrates this difference: 

int sample(mglGraph *gr)
{
  gr->SubPlot(1,1,0,"");  gr->Title("SubData vs Evaluate");
  mglData in(9), arg(99), e, s;
  gr->Fill(in,"x^3/1.1"); gr->Fill(arg,"4*x+4");
  gr->Plot(in,"ko ");     gr->Box();
  e = in.Evaluate(arg,false); gr->Plot(e,"b.","legend 'Evaluate'");
  s = in.SubData(arg);    gr->Plot(s,"r.","legend 'SubData'");
  gr->Legend(2);
}
Example of indirect data access.

Example of datagrid usage is done in Making regular data. Here I want to show the peculiarities of refill and gspline functions. Both functions require argument(s) which provide coordinates of the data values, and return rectangular data array which equidistantly distributed in axis range. So, in opposite to evaluate function, refill and gspline can interpolate non-equidistantly distributed data. At this both functions refill and gspline provide continuity of 2nd derivatives along coordinate(s). However, refill is slower but give better (from human point of view) result than global spline gspline due to more advanced algorithm. Following sample illustrates this difference: 

int sample(mglGraph *gr)
{
  mglData x(10), y(10), r(100);
  x.Modify("0.5+rnd");  x.CumSum("x");  x.Norm(-1,1);
  y.Modify("sin(pi*v)/1.5",x);
  gr->SubPlot(2,2,0,"<_");  gr->Title("Refill sample");
  gr->Axis();  gr->Box(); gr->Plot(x,y,"o ");
  gr->Refill(r,x,y);  // or you can use r.Refill(x,y,-1,1);
  gr->Plot(r,"r");  gr->FPlot("sin(pi*x)/1.5","B:");
  gr->SubPlot(2,2,1,"<_");gr->Title("Global spline");
  gr->Axis();  gr->Box(); gr->Plot(x,y,"o ");
  r.RefillGS(x,y,-1,1);   gr->Plot(r,"r");
  gr->FPlot("sin(pi*x)/1.5","B:");

  gr->Alpha(true);  gr->Light(true);
  mglData z(10,10), xx(10,10), yy(10,10), rr(100,100);
  y.Modify("0.5+rnd");  y.CumSum("x");  y.Norm(-1,1);
  for(int i=0;i<10;i++) for(int j=0;j<10;j++)
    z.a[i+10*j] = sin(M_PI*x.a[i]*y.a[j])/1.5;
  gr->SubPlot(2,2,2); gr->Title("2d regular");  gr->Rotate(40,60);
  gr->Axis();  gr->Box(); gr->Mesh(x,y,z,"k");
  gr->Refill(rr,x,y,z); gr->Surf(rr);

  gr->Fill(xx,"(x+1)/2*cos(y*pi/2-1)");
  gr->Fill(yy,"(x+1)/2*sin(y*pi/2-1)");
  for(int i=0;i<10*10;i++)
    z.a[i] = sin(M_PI*xx.a[i]*yy.a[i])/1.5;
  gr->SubPlot(2,2,3); gr->Title("2d non-regular");  gr->Rotate(40,60);
  gr->Axis();  gr->Box();  gr->Plot(xx,yy,z,"ko ");
  gr->Refill(rr,xx,yy,z);  gr->Surf(rr);
}
Example of non-equidistant data interpolation.

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2.9.11 Making regular data

Sometimes, one have only unregular data, like as data on triangular grids, or experimental results and so on. Such kind of data cannot be used as simple as regular data (like matrices). Only few functions, like dots, can handle unregular data as is.

However, one can use built in triangulation functions for interpolating unregular data points to a regular data grids. There are 2 ways. First way, one can use triangulation function to obtain list of vertexes for triangles. Later this list can be used in functions like triplot or tricont. Second way consist in usage of datagrid function, which fill regular data grid by interpolated values, assuming that coordinates of the data grid is equidistantly distributed in axis range. Note, you can use options (see Command options) to change default axis range as well as in other plotting functions. 

int sample(mglGraph *gr)
{
  mglData x(100), y(100), z(100);
  gr->Fill(x,"2*rnd-1"); gr->Fill(y,"2*rnd-1"); gr->Fill(z,"v^2-w^2",x,y);
  // first way - plot triangular surface for points
  mglData d = mglTriangulation(x,y);
  gr->Title("Triangulation");
  gr->Rotate(40,60);	gr->Box();	gr->Light(true);
  gr->TriPlot(d,x,y,z);	gr->TriPlot(d,x,y,z,"#k");
  // second way - make regular data and plot it
  mglData g(30,30);
  gr->DataGrid(g,x,y,z);	gr->Mesh(g,"m");
}
Example of triangulation.

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2.9.12 Making histogram

Using the hist function(s) for making regular distributions is one of useful fast methods to process and plot irregular data. Hist can be used to find some momentum of set of points by specifying weight function. It is possible to create not only 1D distributions but also 2D and 3D ones. Below I place the simplest sample code which demonstrate hist usage: 

int sample(mglGraph *gr)
{
  mglData x(10000), y(10000), z(10000);  gr->Fill(x,"2*rnd-1");
  gr->Fill(y,"2*rnd-1"); gr->Fill(z,"exp(-6*(v^2+w^2))",x,y);
  mglData xx=gr->Hist(x,z), yy=gr->Hist(y,z);	xx.Norm(0,1);
  yy.Norm(0,1);
  gr->MultiPlot(3,3,3,2,2,"");   gr->SetRanges(-1,1,-1,1,0,1);
  gr->Box();  gr->Dots(x,y,z,"wyrRk");
  gr->MultiPlot(3,3,0,2,1,"");   gr->SetRanges(-1,1,0,1);
  gr->Box();  gr->Bars(xx);
  gr->MultiPlot(3,3,5,1,2,"");   gr->SetRanges(0,1,-1,1);
  gr->Box();  gr->Barh(yy);
  gr->SubPlot(3,3,2);
  gr->Puts(mglPoint(0.5,0.5),"Hist and\nMultiPlot\nsample","a",-6);
  return 0;
}
Example of Hist().

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2.9.13 Nonlinear fitting hints

Nonlinear fitting is rather simple. All that you need is the data to fit, the approximation formula and the list of coefficients to fit (better with its initial guess values). Let me demonstrate it on the following simple example. First, let us use sin function with some random noise: 

  mglData dat(100), in(100); //data to be fitted and ideal data
  gr->Fill(dat,"0.4*rnd+0.1+sin(2*pi*x)");
  gr->Fill(in,"0.3+sin(2*pi*x)");

and plot it to see that data we will fit 

  gr->Title("Fitting sample");
  gr->SetRange('y',-2,2); gr->Box();  gr->Plot(dat, "k. ");
  gr->Axis(); gr->Plot(in, "b");
  gr->Puts(mglPoint(0, 2.2), "initial: y = 0.3+sin(2\\pi x)", "b");

The next step is the fitting itself. For that let me specify an initial values ini for coefficients ‘abc’ and do the fitting for approximation formula ‘a+b*sin(c*x)’ 

  mreal ini[3] = {1,1,3};
  mglData Ini(3,ini);
  mglData res = gr->Fit(dat, "a+b*sin(c*x)", "abc", Ini);

Now display it 

  gr->Plot(res, "r");
  gr->Puts(mglPoint(-0.9, -1.3), "fitted:", "r:L");
  gr->PutsFit(mglPoint(0, -1.8), "y = ", "r");

NOTE! the fitting results may have strong dependence on initial values for coefficients due to algorithm features. The problem is that in general case there are several local "optimums" for coefficients and the program returns only first found one! There are no guaranties that it will be the best. Try for example to set ini[3] = {0, 0, 0} in the code above.

The full sample code for nonlinear fitting is: 

int sample(mglGraph *gr)
{
  mglData dat(100), in(100);
  gr->Fill(dat,"0.4*rnd+0.1+sin(2*pi*x)");
  gr->Fill(in,"0.3+sin(2*pi*x)");
  mreal ini[3] = {1,1,3};
  mglData Ini(3,ini);

  mglData res = gr->Fit(dat, "a+b*sin(c*x)", "abc", Ini);

  gr->Title("Fitting sample");
  gr->SetRange('y',-2,2); gr->Box();  gr->Plot(dat, "k. ");
  gr->Axis();   gr->Plot(res, "r"); gr->Plot(in, "b");
  gr->Puts(mglPoint(-0.9, -1.3), "fitted:", "r:L");
  gr->PutsFit(mglPoint(0, -1.8), "y = ", "r");
  gr->Puts(mglPoint(0, 2.2), "initial: y = 0.3+sin(2\\pi x)", "b");
  return 0;
}
Example of nonlinear fitting.

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2.9.14 PDE solving hints

Solving of Partial Differential Equations (PDE, including beam tracing) and ray tracing (or finding particle trajectory) are more or less common task. So, MathGL have several functions for that. There are ray for ray tracing, pde for PDE solving, qo2d for beam tracing in 2D case (see Global functions). Note, that these functions take “Hamiltonian” or equations as string values. And I don’t plan now to allow one to use user-defined functions. There are 2 reasons: the complexity of corresponding interface; and the basic nature of used methods which are good for samples but may not good for serious scientific calculations.

The ray tracing can be done by ray function. Really ray tracing equation is Hamiltonian equation for 3D space. So, the function can be also used for finding a particle trajectory (i.e. solve Hamiltonian ODE) for 1D, 2D or 3D cases. The function have a set of arguments. First of all, it is Hamiltonian which defined the media (or the equation) you are planning to use. The Hamiltonian is defined by string which may depend on coordinates ‘x’, ‘y’, ‘z’, time ‘t’ (for particle dynamics) and momentums ‘p’=p_x, ‘q’=p_y, ‘v’=p_z. Next, you have to define the initial conditions for coordinates and momentums at ‘t’=0 and set the integrations step (default is 0.1) and its duration (default is 10). The Runge-Kutta method of 4-th order is used for integration. 

  const char *ham = "p^2+q^2-x-1+i*0.5*(y+x)*(y>-x)";
  mglData r = mglRay(ham, mglPoint(-0.7, -1), mglPoint(0, 0.5), 0.02, 2);

This example calculate the reflection from linear layer (media with Hamiltonian ‘p^2+q^2-x-1’=p_x^2+p_y^2-x-1). This is parabolic curve. The resulting array have 7 columns which contain data for {x,y,z,p,q,v,t}.

The solution of PDE is a bit more complicated. As previous you have to specify the equation as pseudo-differential operator \hat H(x, \nabla) which is called sometime as “Hamiltonian” (for example, in beam tracing). As previously, it is defined by string which may depend on coordinates ‘x’, ‘y’, ‘z’ (but not time!), momentums ‘p’=(d/dx)/i k_0, ‘q’=(d/dy)/i k_0 and field amplitude ‘u’=|u|. The evolutionary coordinate is ‘z’ in all cases. So that, the equation look like du/dz = ik_0 H(x,y,\hat p, \hat q, |u|)[u]. Dependence on field amplitude ‘u’=|u| allows one to solve nonlinear problems too. For example, for nonlinear Shrodinger equation you may set ham="p^2 + q^2 - u^2". Also you may specify imaginary part for wave absorption, like ham = "p^2 + i*x*(x>0)" or ham = "p^2 + i1*x*(x>0)".

Next step is specifying the initial conditions at ‘z’ equal to minimal z-axis value. The function need 2 arrays for real and for imaginary part. Note, that coordinates x,y,z are supposed to be in specified axis range. So, the data arrays should have corresponding scales. Finally, you may set the integration step and parameter k0=k_0. Also keep in mind, that internally the 2 times large box is used (for suppressing numerical reflection from boundaries) and the equation should well defined even in this extended range.

Final comment is concerning the possible form of pseudo-differential operator H. At this moment, simplified form of operator H is supported – all “mixed” terms (like ‘x*p’->x*d/dx) are excluded. For example, in 2D case this operator is effectively H = f(p,z) + g(x,z,u). However commutable combinations (like ‘x*q’->x*d/dy) are allowed for 3D case.

So, for example let solve the equation for beam deflected from linear layer and absorbed later. The operator will have the form ‘"p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)"’ that correspond to equation 1/ik_0 * du/dz + d^2 u/dx^2 + d^2 u/dy^2 + x * u + i (x+z)/2 * u = 0. This is typical equation for Electron Cyclotron (EC) absorption in magnetized plasmas. For initial conditions let me select the beam with plane phase front exp(-48*(x+0.7)^2). The corresponding code looks like this: 

int sample(mglGraph *gr)
{
  mglData a,re(128),im(128);
  gr->Fill(re,"exp(-48*(x+0.7)^2)");
  a = gr->PDE("p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)", re, im, 0.01, 30);
  a.Transpose("yxz");
  gr->SubPlot(1,1,0,"<_"); gr->Title("PDE solver");
  gr->SetRange('c',0,1);  gr->Dens(a,"wyrRk");
  gr->Axis(); gr->Label('x', "\\i x");  gr->Label('y', "\\i z");
  gr->FPlot("-x", "k|");
  gr->Puts(mglPoint(0, 0.85), "absorption: (x+z)/2 for x+z>0");
  gr->Puts(mglPoint(0,1.1),"Equation: ik_0\\partial_zu + \\Delta u + x\\cdot u + i \\frac{x+z}{2}\\cdot u = 0");
  return 0;
}
Example of PDE solving.

The last example is example of beam tracing. Beam tracing equation is special kind of PDE equation written in coordinates accompanied to a ray. Generally this is the same parameters and limitation as for PDE solving but the coordinates are defined by the ray and by parameter of grid width w in direction transverse the ray. So, you don’t need to specify the range of coordinates. BUT there is limitation. The accompanied coordinates are well defined only for smooth enough rays, i.e. then the ray curvature K (which is defined as 1/K^2 = (|r''|^2 |r'|^2 - (r'', r'')^2)/|r'|^6) is much large then the grid width: K>>w. So, you may receive incorrect results if this condition will be broken.

You may use following code for obtaining the same solution as in previous example: 

int sample(mglGraph *gr)
{
  mglData r, xx, yy, a, im(128), re(128);
  const char *ham = "p^2+q^2-x-1+i*0.5*(y+x)*(y>-x)";
  r = mglRay(ham, mglPoint(-0.7, -1), mglPoint(0, 0.5), 0.02, 2);
  gr->SubPlot(1,1,0,"<_"); gr->Title("Beam and ray tracing");
  gr->Plot(r.SubData(0), r.SubData(1), "k");
  gr->Axis(); gr->Label('x', "\\i x");  gr->Label('y', "\\i z");

  // now start beam tracing
  gr->Fill(re,"exp(-48*x^2)");
  a = mglQO2d(ham, re, im, r, xx, yy, 1, 30);
  gr->SetRange('c',0, 1);
  gr->Dens(xx, yy, a, "wyrRk");
  gr->FPlot("-x", "k|");
  gr->Puts(mglPoint(0, 0.85), "absorption: (x+y)/2 for x+y>0");
  gr->Puts(mglPoint(0.7, -0.05), "central ray");
  return 0;
}
Example of beam tracing.

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2.9.15 Drawing phase plain

Here I want say a few words of plotting phase plains. Phase plain is name for system of coordinates x, x', i.e. a variable and its time derivative. Plot in phase plain is very useful for qualitative analysis of an ODE, because such plot is rude (it topologically the same for a range of ODE parameters). Most often the phase plain {x, x'} is used (due to its simplicity), that allows to analyze up to the 2nd order ODE (i.e. x''+f(x,x')=0).

The simplest way to draw phase plain in MathGL is using flow function(s), which automatically select several points and draw flow threads. If the ODE have an integral of motion (like Hamiltonian H(x,x')=const for dissipation-free case) then you can use cont function for plotting isolines (contours). In fact. isolines are the same as flow threads, but without arrows on it. Finally, you can directly solve ODE using ode function and plot its numerical solution.

Let demonstrate this for ODE equation x''-x+3*x^2=0. This is nonlinear oscillator with square nonlinearity. It has integral H=y^2+2*x^3-x^2=Const. Also it have 2 typical stationary points: saddle at {x=0, y=0} and center at {x=1/3, y=0}. Motion at vicinity of center is just simple oscillations, and is stable to small variation of parameters. In opposite, motion around saddle point is non-stable to small variation of parameters, and is very slow. So, calculation around saddle points are more difficult, but more important. Saddle points are responsible for solitons, stochasticity and so on.

So, let draw this phase plain by 3 different methods. First, draw isolines for H=y^2+2*x^3-x^2=Const – this is simplest for ODE without dissipation. Next, draw flow threads – this is straightforward way, but the automatic choice of starting points is not always optimal. Finally, use ode to check the above plots. At this we need to run ode in both direction of time (in future and in the past) to draw whole plain. Alternatively, one can put starting points far from (or at the bounding box as done in flow) the plot, but this is a more complicated. The sample code is: 

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0,"<_");  gr->Title("Cont");  gr->Box();
  gr->Axis();  gr->Label('x',"x");  gr->Label('y',"\\dot{x}");
  mglData f(100,100);   gr->Fill(f,"y^2+2*x^3-x^2-0.5");
  gr->Cont(f);
  gr->SubPlot(2,2,1,"<_");  gr->Title("Flow");  gr->Box();
  gr->Axis();  gr->Label('x',"x");  gr->Label('y',"\\dot{x}");
  mglData fx(100,100), fy(100,100);
  gr->Fill(fx,"x-3*x^2");  gr->Fill(fy,"y");
  gr->Flow(fy,fx,"v","value 7");
  gr->SubPlot(2,2,2,"<_");  gr->Title("ODE");   gr->Box();
  gr->Axis();  gr->Label('x',"x");  gr->Label('y',"\\dot{x}");
  for(double x=-1;x<1;x+=0.1)
  {
    mglData in(2), r;   in.a[0]=x;
    r = mglODE("y;x-3*x^2","xy",in);
    gr->Plot(r.SubData(0), r.SubData(1));
    r = mglODE("-y;-x+3*x^2","xy",in);
    gr->Plot(r.SubData(0), r.SubData(1));
  }
}
Example of ODE solving and phase plain drawing.

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2.9.16 Pulse properties

There is common task in optics to determine properties of wave pulses or wave beams. MathGL provide special function pulse which return the pulse properties (maximal value, center of mass, width and so on). Its usage is rather simple. Here I just illustrate it on the example of Gaussian pulse, where all parameters are obvious. 

void sample(mglGraph *gr)
{
  gr->SubPlot(1,1,0,"<_");  gr->Title("Pulse sample");
  // first prepare pulse itself
  mglData a(100); gr->Fill(a,"exp(-6*x^2)");
  // get pulse parameters
  mglData b(a.Pulse('x'));
  // positions and widths are normalized on the number of points. So, set proper axis scale.
  gr->SetRanges(0, a.nx-1, 0, 1);
  gr->Axis(); gr->Plot(a);  // draw pulse and axis
  // now visualize found pulse properties
  double m = b[0];  // maximal amplitude
  // approximate position of maximum
  gr->Line(mglPoint(b[1],0), mglPoint(b[1],m),"r=");
  // width at half-maximum (so called FWHM)
  gr->Line(mglPoint(b[1]-b[3]/2,0), mglPoint(b[1]-b[3]/2,m),"m|");
  gr->Line(mglPoint(b[1]+b[3]/2,0), mglPoint(b[1]+b[3]/2,m),"m|");
  gr->Line(mglPoint(0,m/2), mglPoint(a.nx-1,m/2),"h");
  // parabolic approximation near maximum
  char func[128];	sprintf(func,"%g*(1-((x-%g)/%g)^2)",b[0],b[1],b[2]);
  gr->FPlot(func,"g");
}
Example of determining of pulse properties.

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2.9.17 Using MGL parser

Sometimes you may prefer to use MGL scripts in yours code. It is simpler (especially in comparison with C/Fortran interfaces) and provide faster way to plot the data with annotations, labels and so on. Class mglParse (see mglParse class parse MGL scripts in C++. It have also the corresponding interface for C/Fortran.

The key function here is mglParse::Parse() (or mgl_parse() for C/Fortran) which execute one command per string. At this the detailed information about the possible errors or warnings is passed as function value. Or you may execute the whole script as long string with lines separated by ‘\n’. Functions mglParse::Execute() and mgl_parse_text() perform it. Also you may set the values of parameters ‘$0’...‘$9’ for the script by functions mglParse::AddParam() or mgl_add_param(), allow/disable picture resizing, check “once” status and so on. The usage is rather straight-forward.

The only non-obvious thing is data transition between script and yours program. There are 2 stages: add or find variable; and set data to variable. In C++ you may use functions mglParse::AddVar() and mglParse::FindVar() which return pointer to mglData. In C/Fortran the corresponding functions are mgl_add_var(), mgl_find_var(). This data pointer is valid until next Parse() or Execute() call. Note, you must not delete or free the data obtained from these functions!

So, some simple example at the end. Here I define a data array, create variable, put data into it and plot it. The C++ code looks like this: 

int sample(mglGraph *gr)
{
  gr->Title("MGL parser sample");
  mreal a[100];   // let a_i = sin(4*pi*x), x=0...1
  for(int i=0;i<100;i++)a[i]=sin(4*M_PI*i/99);
  mglParse *parser = new mglParse;
  mglData *d = parser->AddVar("dat");
  d->Set(a,100); // set data to variable
  parser->Execute(gr, "plot dat; xrange 0 1\nbox\naxis");
  // you may break script at any line do something
  // and continue after that
  parser->Execute(gr, "xlabel 'x'\nylabel 'y'\nbox");
  // also you may use cycles or conditions in script
  parser->Execute(gr, "for $0 -1 1 0.1\nif $0<0\n"
    "line 0 0 -1 $0 'r':else:line 0 0 -1 $0 'g'\n"
    "endif\nnext");
  delete parser;
  return 0;
}

The code in C/Fortran looks practically the same: 

int sample(HMGL gr)
{
  mgl_title(gr, "MGL parser sample", "", -2);
  double a[100];   // let a_i = sin(4*pi*x), x=0...1
  int i;
  for(i=0;i<100;i++)  a[i]=sin(4*M_PI*i/99);
  HMPR parser = mgl_create_parser();
  HMDT d = mgl_parser_add_var(parser, "dat");
  mgl_data_set_double(d,a,100,1,1);    // set data to variable
  mgl_parse_text(gr, parser, "plot dat; xrange 0 1\nbox\naxis");
  // you may break script at any line do something
  // and continue after that
  mgl_parse_text(gr, parser, "xlabel 'x'\nylabel 'y'");
  // also you may use cycles or conditions in script
  mgl_parse_text(gr, parser, "for $0 -1 1 0.1\nif $0<0\n"
    "line 0 0 -1 $0 'r':else:line 0 0 -1 $0 'g'\n"
    "endif\nnext");
  mgl_write_png(gr, "test.png", "");  // don't forgot to save picture
  return 0;
}
Example of MGL script parsing.

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2.9.18 Using options

Command options allow the easy setup of the selected plot by changing global settings only for this plot. Often, options are used for specifying the range of automatic variables (coordinates). However, options allows easily change plot transparency, numbers of line or faces to be drawn, or add legend entries. The sample function for options usage is: 

void template(mglGraph *gr)
{
  mglData a(31,41);
  gr->Fill(a,"-pi*x*exp(-(y+1)^2-4*x^2)");

  gr->SubPlot(2,2,0);	gr->Title("Options for coordinates");
  gr->Alpha(true);	gr->Light(true);
  gr->Rotate(40,60);    gr->Box();
  gr->Surf(a,"r","yrange 0 1"); gr->Surf(a,"b","yrange 0 -1");
  if(mini)	return;
  gr->SubPlot(2,2,1);   gr->Title("Option 'meshnum'");
  gr->Rotate(40,60);    gr->Box();
  gr->Mesh(a,"r","yrange 0 1"); gr->Mesh(a,"b","yrange 0 -1; meshnum 5");
  gr->SubPlot(2,2,2);   gr->Title("Option 'alpha'");
  gr->Rotate(40,60);    gr->Box();
  gr->Surf(a,"r","yrange 0 1; alpha 0.7");
  gr->Surf(a,"b","yrange 0 -1; alpha 0.3");
  gr->SubPlot(2,2,3,"<_");  gr->Title("Option 'legend'");
  gr->FPlot("x^3","r","legend 'y = x^3'");
  gr->FPlot("cos(pi*x)","b","legend 'y = cos \\pi x'");
  gr->Box();    gr->Axis(); gr->Legend(2,"");
}
Example of options usage.

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2.9.19 “Templates”

As I have noted before, the change of settings will influence only for the further plotting commands. This allows one to create “template” function which will contain settings and primitive drawing for often used plots. Correspondingly one may call this template-function for drawing simplification.

For example, let one has a set of points (experimental or numerical) and wants to compare it with theoretical law (for example, with exponent law \exp(-x/2), x \in [0, 20]). The template-function for this task is: 

void template(mglGraph *gr)
{
  mglData  law(100);      // create the law
  law.Modify("exp(-10*x)");
  gr->SetRanges(0,20, 0.0001,1);
  gr->SetFunc(0,"lg(y)",0);
  gr->Plot(law,"r2");
  gr->Puts(mglPoint(10,0.2),"Theoretical law: e^x","r:L");
  gr->Label('x',"x val."); gr->Label('y',"y val.");
  gr->Axis(); gr->Grid("xy","g;"); gr->Box();
}

At this, one will only write a few lines for data drawing: 

  template(gr);     // apply settings and default drawing from template
  mglData dat("fname.dat"); // load the data
  // and draw it (suppose that data file have 2 columns)
  gr->Plot(dat.SubData(0),dat.SubData(1),"bx ");

A template-function can also contain settings for font, transparency, lightning, color scheme and so on.

I understand that this is obvious thing for any professional programmer, but I several times receive suggestion about “templates” ... So, I decide to point out it here.

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2.9.20 Stereo image

One can easily create stereo image in MathGL. Stereo image can be produced by making two subplots with slightly different rotation angles. The corresponding code looks like this: 

int sample(mglGraph *gr)
{
  mglData a;  mgls_prepare2d(&a);
  gr->Light(true);

  gr->SubPlot(2,1,0); gr->Rotate(50,60+1);
  gr->Box();  gr->Surf(a);

  gr->SubPlot(2,1,1); gr->Rotate(50,60-1);
  gr->Box();  gr->Surf(a);
  return 0;
}
Example of stereo image.

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2.9.21 Reduce memory usage

By default MathGL save all primitives in memory, rearrange it and only later draw them on bitmaps. Usually, this speed up drawing, but may require a lot of memory for plots which contain a lot of faces (like cloud, dew). You can use quality function for setting to use direct drawing on bitmap and bypassing keeping any primitives in memory. This function also allow you to decrease the quality of the resulting image but increase the speed of the drawing.

The code for lowest memory usage looks like this: 

int sample(mglGraph *gr)
{
  gr->SetQuality(6);   // firstly, set to draw directly on bitmap
  for(i=0;i<1000;i++)
    gr->Sphere(mglPoint(mgl_rnd()*2-1,mgl_rnd()*2-1),0.05);
  return 0;
}

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2.9.22 Scanning file

MathGL have possibilities to write textual information into file with variable values. In MGL script you can use save command for that. However, the usual printf(); is simple in C/C++ code. For example, lets create some textual file 

FILE *fp=fopen("test.txt","w");
fprintf(fp,"This is test: 0 -> 1 q\n");
fprintf(fp,"This is test: 1 -> -1 q\n");
fprintf(fp,"This is test: 2 -> 0 q\n");
fclose(fp);

It contents look like 

This is test: 0 -> 1 q
This is test: 1 -> -1 q
This is test: 2 -> 0 q

Let assume now that you want to read this values (i.e. [[0,1],[1,-1],[2,0]]) from the file. You can use scanfile for that. The desired values was written using template "This is test: %g -> %g q\n". So, just use 

mglData a;
a.ScanFile("test.txt","This is test: %g -> %g");

and plot it to for assurance 

gr->SetRanges(a.SubData(0), a.SubData(1));
gr->Axis();	gr->Plot(a.SubData(0),a.SubData(1),"o");

Note, I keep only the leading part of template (i.e. "This is test: %g -> %g" instead of "This is test: %g -> %g q\n"), because there is no important for us information after the second number in the line.

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2.10 FAQ

The plot does not appear

Check that points of the plot are located inside the bounding box and resize the bounding box using ranges function. Check that the data have correct dimensions for selected type of plot. Be sure that Finish() is called after the plotting functions (or be sure that the plot is saved to a file). Sometimes the light reflection from flat surfaces (like, dens) can look as if the plot were absent.

I can not find some special kind of plot.

Most “new” types of plots can be created by using the existing drawing functions. For example, the surface of curve rotation can be created by a special function torus, or as a parametrically specified surface by surf. See also, Hints. If you can not find a specific type of plot, please e-mail me and this plot will appear in the next version of MathGL library.

Should I know some graphical libraries (like OpenGL) before using the MathGL library?

No. The MathGL library is self-contained and does not require the knowledge of external libraries.

In which language is the library written? For which languages does it have an interface?

The core of the MathGL library is written in C++. But there are interfaces for: pure C, Fortran, Pascal, Forth, and its own command language MGL. Also there is a large set of interpreted languages, which are supported (Python, Java, ALLEGROCL, CHICKEN, Lisp, CFFI, C#, Guile, Lua, Modula 3, Mzscheme, Ocaml, Octave, Perl, PHP, Pike, R, Ruby, Tcl). These interfaces are written using SWIG (both pure C functions and classes) but only the interface for Python and Octave is included in the build system. The reason is that I don’t know any other interpreted languages :(. Note that most other languages can use (link to) the pure C functions.

How can I use MathGL with Fortran?

You can use MathGL as is with gfortran because it uses by default the AT&T notation for external functions. For other compilers (like Visual Fortran) you have to switch on the AT&T notation manually. The AT&T notation requires that the symbol ‘_’ is added at the end of each function name, function argument(s) is passed by pointers and the string length(s) is passed at the end of the argument list. For example:

C function – void mgl_fplot(HMGL graph, const char *fy, const char *stl, int n);

AT&T function – void mgl_fplot_(uintptr_t *graph, const char *fy, const char *stl, int *n, int ly, int ls);

Fortran users also should add C++ library by the option -lstdc++. If library was built with enable-double=ON (this default for v.2.1 and later) then all real numbers must be real*8. You can make it automatic if use option -fdefault-real-8.

How can I print in Russian/Spanish/Arabic/Japanese, and so on?

The standard way is to use Unicode encoding for the text output. But the MathGL library also has interface for 8-bit (char *) strings with internal conversion to Unicode. This conversion depends on the current locale OS. You may change it by setlocale() function. For example, for Russian text in CP1251 encoding you may use setlocale(LC_CTYPE, "ru_RU.cp1251"); (under MS Windows the name of locale may differ – setlocale(LC_CTYPE, "russian_russia.1251")). I strongly recommend not to use the constant LC_ALL in the conversion. Since it also changes the number format, it may lead to mistakes in formula writing and reading of the text in data files. For example, the program will await a ‘,’ as a decimal point but the user will enter ‘.’.

How can I exclude a point or a region of plot from the drawing?

There are 3 general ways. First, the point with NAN value as one of the coordinates (including color/alpha range) will never be plotted. Second, special functions SetCutBox() and CutOff() define the condition when the points should be omitted (see Cutting). Last, you may change the transparency of a part of the plot by the help of functions surfa, surf3a (see Dual plotting). In last case the transparency is switched on smoothly.

I use VisualStudio, CBuilder or some other compiler (not MinGW/gcc). How can I link the MathGL library?

In version 2.0, main classes (mglGraph and mglData) contains only inline functions and are acceptable for any compiler with the same binary files. However, if you plan to use widget classes (QMathGL, Fl_MathGL, ...) or to access low-level features (mglBase, mglCanvas, ...) then you have to recompile MathGL by yours compiler.

Note, that you have to make import library(-ies) *.lib for provided binary *.dll. This procedure depend on used compiler – please read documentation for yours compiler. For VisualStudio, it can be done by command lib.exe /DEF:libmgl.def /OUT:libmgl.lib.

How make FLTK/GLUT/Qt window which will display result of my calculations?

You need to put yours calculations or main event-handling loop in the separate thread. For static image you can give NULL as drawing function and call Update() function when you need to redraw it. For more details see Animation.

How I can build MathGL under Windows?

Generally, it is the same procedure as for Linux or MacOS – see section Installation. The simplest way is using the combination CMake+MinGW. Also you may need some extra libraries like GSL, PNG, JPEG and so on. All of them can be found at http://gnuwin32.sourceforge.net/packages.html. After installing all components, just run cmake-gui configurator and build the MathGL itself.

How many people write this library?

Most of the library was written by one person. This is a result of nearly a year of work (mostly in the evening and on holidays): I spent half a year to write the kernel and half a year to a year on extending, improving the library and writing documentation. This process continues now :). The build system (cmake files) was written mostly by D.Kulagin, and the export to PRC/PDF was written mostly by M.Vidassov.

How can I display a bitmap on the figure?

You can import data into a mglData instance by function import and display it by dens function. For example, for black-and-white bitmap you can use the code: mglData bmp; bmp.Import("fname.png","wk"); gr->Dens(bmp,"wk");.

How can I use MathGL in Qt, FLTK, wxWidgets etc.?

There are special classes (widgets) for these libraries: QMathGL for Qt, Fl_MathGL for FLTK and so on. If you don’t find the appropriate class then you can create your own widget that displays a bitmap using mglCanvas::GetRGB().

How can I create 3D in PDF?

Just use WritePRC() method which also create PDF file if enable-pdf=ON at MathGL configure.

How can I create TeX figure?

Just use WriteTEX() method which create LaTeX files with figure itself ‘fname.tex’, with MathGL colors ‘mglcolors.tex’ and main file ‘mglmain.tex’. Last one can be used for viewing image by command like pdflatex mglmain.tex.

Can I use MathGL in JavaScript?

Yes, sample JavaScript file is located in texinfo/ folder of sources. You should provide JSON data with 3d image for it (can be created by WriteJSON() method). Script allows basic manipulation with plot: zoom, rotation, shift. Sample of JavaScript pictures can be found in http://mathgl.sf.net/json.html.

How I can change the font family?

First, you should download new font files from here or from here. Next, you should load the font files into mglGraph class instance gr by the following command: gr->LoadFont(fontname,path);. Here fontname is the base font name like ‘STIX’ and path sets the location of font files. Use gr->RestoreFont(); to start using the default font.

How can I draw tick out of a bounding box?

Just set a negative value in ticklen. For example, use gr->SetTickLen(-0.1);.

How can I prevent text rotation?

Just use SetRotatedText(false). Also you can use axis style ‘U’ for disable only tick labels rotation.

What is *.so? What is gcc? How I can use make?

They are standard GNU tools. There is special FAQ about its usage under Windows – http://www.mingw.org/wiki/FAQ.

How can I draw equal axis range even for rectangular image?

Just use Aspect(NAN,NAN) for each subplot, or at the beginning of the drawing.

How I can set transparent background?

Just use code like Clf("r{A5}"); or prepare PNG file and set it as background image by call LoadBackground("fname.png");.

How I can reduce "white" edges around bounding box?

The simplest way is to use subplot style. However, you should be careful if you plan to add colorbar or rotate plot – part of plot can be invisible if you will use non-default subplot style.

Can I combine bitmap and vector output in EPS?

Yes. Sometimes you may have huge surface and a small set of curves and/or text on the plot. You can use function rasterize just after making surface plot. This will put all plot to bitmap background. At this later plotting will be in vector format. For example, you can do something like following: 

gr->Surf(x, y, z);
gr->Rasterize(); // make surface as bitmap
gr->Axis();
gr->WriteFrame("fname.eps");
Why I couldn’t use name ‘I’ for variable?

MathGL support C99 standard, where ‘I’ is reserved for imaginary unit. If you still need this name, then just use 

#undef I

after including MathGL header files.

How I can create MPEG video from plots?

You can save each frame into JPEG with names like ‘frame0001.jpg’, ‘frame0002.jpg’, ... Later you can use ImageMagic to convert them into MPEG video by command convert frame*.jpg movie.mpg. See also MPEG.

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3 General concepts

The set of MathGL features is rather rich – just the number of basic graphics types is larger than 50. Also there are functions for data handling, plot setup and so on. In spite of it I tried to keep a similar style in function names and in the order of arguments. Mostly it is used for different drawing functions.

There are six most general (base) concepts:

  1. Any picture is created in memory first. The internal (memory) representation can be different: bitmap picture (for SetQuality(MGL_DRAW_LMEM) or quality 6) or the list of vector primitives (default). After that the user may decide what he/she want: save to file, display on the screen, run animation, do additional editing and so on. This approach assures a high portability of the program – the source code will produce exactly the same picture in any OS. Another big positive consequence is the ability to create the picture in the console program (using command line, without creating a window)!
  2. Every plot settings (style of lines, font, color scheme) are specified by a string. It provides convenience for user/programmer – short string with parameters is more comprehensible than a large set of parameters. Also it provides portability – the strings are the same in any OS so that it is not necessary to think about argument types.
  3. All functions have “simplified” and “advanced” forms. It is done for user’s convenience. One needs to specify only one data array in the “simplified” form in order to see the result. But one may set parametric dependence of coordinates and produce rather complex curves and surfaces in the “advanced” form. In both cases the order of function arguments is the same: first data arrays, second the string with style, and later string with options for additional plot tuning.
  4. All data arrays for plotting are encapsulated in mglData(A) class. This reduces the number of errors while working with memory and provides a uniform interface for data of different types (mreal, double and so on) or for formula plotting.
  5. All plots are vector plots. The MathGL library is intended for handling scientific data which have vector nature (lines, faces, matrices and so on). As a result, vector representation is used in all cases! In addition, the vector representation allows one to scale the plot easily – change the canvas size by a factor of 2, and the picture will be proportionally scaled.
  6. New drawing never clears things drawn already. This, in some sense, unexpected, idea allows to create a lot of “combined” graphics. For example, to make a surface with contour lines one needs to call the function for surface plotting and the function for contour lines plotting (in any order). Thus the special functions for making this “combined” plots (as it is done in Matlab and some other plotting systems) are superfluous.

In addition to the general concepts I want to comment on some non-trivial or less commonly used general ideas – plot positioning, axis specification and curvilinear coordinates, styles for lines, text and color scheme.

• Coordinate axes:  
• Color styles:  
• Line styles:  
• Color scheme:  
• Font styles:  
• Textual formulas:  
• Command options:  
• Interfaces:  

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3.1 Coordinate axes

Two axis representations are used in MathGL. The first one consists of normalizing coordinates of data points in axis range (see Axis settings). If SetCut() is true then the outlier points are omitted, otherwise they are projected to the bounding box (see Cutting). Also, the point will be omitted if it lies inside the box defined by SetCutBox() or if the value of formula CutOff() is nonzero for its coordinates. After that, transformation formulas defined by SetFunc() or SetCoor() are applied to the data point (see Curved coordinates). Finally, the data point is plotted by one of the functions.

The range of x, y, z-axis can be specified by SetRange() or ranges functions. Its origin is specified by origin function. At this you can you can use NAN values for selecting axis origin automatically.

There is 4-th axis c (color axis or colorbar) in addition to the usual axes x, y, z. It sets the range of values for the surface coloring. Its borders are automatically set to values of z-range during the call of ranges function. Also, one can directly set it by call SetRange('c', ...). Use colorbar function for drawing the colorbar.

The form (appearence) of tick labels is controlled by SetTicks() function (see Ticks). Function SetTuneTicks switches on/off tick enhancing by factoring out acommon multiplier (for small coordinate values, like 0.001 to 0.002, or large, like from 1000 to 2000) or common component (for narrow range, like from 0.999 to 1.000). Finally, you may use functions SetTickTempl() for setting templates for tick labels (it supports TeX symbols). Also, there is a possibility to print arbitrary text as tick labels the by help of SetTicksVal() function.

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3.2 Color styles

Base colors are defined by one of symbol ‘wkrgbcymhRGBCYMHWlenupqLENUPQ’.

The color types are: ‘k’ – black, ‘r’ – red, ‘R’ – dark red, ‘g’ – green, ‘G’ – dark green, ‘b’ – blue, ‘B’ – dark blue, ‘c’ – cyan, ‘C’ – dark cyan, ‘m’ – magenta, ‘M’ – dark magenta, ‘y’ – yellow, ‘Y’ – dark yellow (gold), ‘h’ – gray, ‘H’ – dark gray, ‘w’ – white, ‘W’ – bright gray, ‘l’ – green-blue, ‘L’ – dark green-blue, ‘e’ – green-yellow, ‘E’ – dark green-yellow, ‘n’ – sky-blue, ‘N’ – dark sky-blue, ‘u’ – blue-violet, ‘U’ – dark blue-violet, ‘p’ – purple, ‘P’ – dark purple, ‘q’ – orange, ‘Q’ – dark orange (brown).

You can also use “bright” colors. The “bright” color contain 2 symbols in brackets ‘{cN}’: first one is the usual symbol for color id, the second one is a digit for its brightness. The digit can be in range ‘1’...‘9’. Number ‘5’ corresponds to a normal color, ‘1’ is a very dark version of the color (practically black), and ‘9’ is a very bright version of the color (practically white). For example, the colors can be ‘{b2}’ ‘{b7}’ ‘{r7}’ and so on.

Finally, you can specify RGB or RGBA values of a color using format ‘{xRRGGBB}’ or ‘{xRRGGBBAA}’ correspondingly. For example, ‘{xFF9966}’ give you melone color.

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3.3 Line styles

The line style is defined by the string which may contain specifications for color (‘wkrgbcymhRGBCYMHWlenupqLENUPQ’), dashing style (‘-|;:ji=’ or space), width (‘123456789’) and marks (‘*o+xsd.^v<>’ and ‘#’ modifier). If one of the type of information is omitted then default values used with next color from palette (see Palette and colors). Note, that internal color counter will be nullified by any change of palette. This includes even hidden change (for example, by box or axis functions). By default palette contain following colors: dark gray ‘H’, blue ‘b’, green ‘g’, red ‘r’, cyan ‘c’, magenta ‘m’, yellow ‘y’, gray ‘h’, green-blue ‘l’, sky-blue ‘n’, orange ‘q’, green-yellow ‘e’, blue-violet ‘u’, purple ‘p’.

Dashing style has the following meaning: space – no line (usable for plotting only marks), ‘-’ – solid line (■■■■■■■■■■■■■■■■), ‘|’ – long dashed line (■■■■■■■■□□□□□□□□), ‘;’ – dashed line (■■■■□□□□■■■■□□□□), ‘=’ – small dashed line (■■□□■■□□■■□□■■□□), ‘:’ – dotted line (■□□□■□□□■□□□■□□□), ‘j’ – dash-dotted line (■■■■■■■□□□□■□□□□), ‘i’ – small dash-dotted line (■■■□□■□□■■■□□■□□), ‘{dNNNN}’ – manual mask style (for v.2.3 and later, like ‘{df090}’ for (■■■■□□□□■□□■□□□□)).

Marker types are: ‘o’ – circle, ‘+’ – cross, ‘x’ – skew cross, ‘s’ - square, ‘d’ - rhomb (or diamond), ‘.’ – dot (point), ‘^’ – triangle up, ‘v’ – triangle down, ‘<’ – triangle left, ‘>’ – triangle right, ‘#*’ – Y sign, ‘#+’ – squared cross, ‘#x’ – squared skew cross, ‘#.’ – circled dot. If string contain symbol ‘#’ then the solid versions of markers are used.

One may specify to draw a special symbol (an arrow) at the beginning and at the end of line. This is done if the specification string contains one of the following symbols: ‘A’ – outer arrow, ‘V’ – inner arrow, ‘I’ – transverse hatches, ‘K’ – arrow with hatches, ‘T’ – triangle, ‘S’ – square, ‘D’ – rhombus, ‘O’ – circle, ‘X’ – skew cross, ‘_’ – nothing (the default). The following rule applies: the first symbol specifies the arrow at the end of line, the second specifies the arrow at the beginning of the line. For example, ‘r-A’ defines a red solid line with usual arrow at the end, ‘b|AI’ defines a blue dash line with an arrow at the end and with hatches at the beginning, ‘_O’ defines a line with the current style and with a circle at the beginning. These styles are applicable during the graphics plotting as well (for example, 1D plotting).

Color and line styles.

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3.4 Color scheme

The color scheme is used for determining the color of surfaces, isolines, isosurfaces and so on. The color scheme is defined by the string, which may contain several characters that are color id (see Line styles) or characters ‘#:|’. Symbol ‘#’ switches to mesh drawing or to a wire plot. Symbol ‘|’ disables color interpolation in color scheme, which can be useful, for example, for sharp colors during matrix plotting. Symbol ‘:’ terminate the color scheme parsing. Following it, the user may put styles for the text, rotation axis for curves/isocontours, and so on. Color scheme may contain up to 32 color values.

The final color is a linear interpolation of color array. The color array is constructed from the string ids (including “bright” colors, see Color styles). The argument is the amplitude normalized in color range (see Axis settings). For example, string containing 4 characters ‘bcyr’ corresponds to a colorbar from blue (lowest value) through cyan (next value) through yellow (next value) to the red (highest value). String ‘kw’ corresponds to a colorbar from black (lowest value) to white (highest value). String ‘m’ corresponds to a simple magenta color.

The special 2-axis color scheme (like in map plot) can be used if it contain symbol ‘%’. In this case the second direction (alpha channel) is used as second coordinate for colors. At this, up to 4 colors can be specified for corners: {c1,a1}, {c2,a1}, {c1,a2}, {c2,a2}. Here color and alpha ranges are {c1,c2} and {a1,a2} correspondingly. If one specify less than 4 colors then black color is used for corner {c1,a1}. If only 2 colors are specified then the color of their sum is used for corner {c2,a2}.

There are several useful combinations. String ‘kw’ corresponds to the simplest gray color scheme where higher values are brighter. String ‘wk’ presents the inverse gray color scheme where higher value is darker. Strings ‘kRryw’, ‘kGgw’, ‘kBbcw’ present the well-known hot, summer and winter color schemes. Strings ‘BbwrR’ and ‘bBkRr’ allow to view bi-color figure on white or black background, where negative values are blue and positive values are red. String ‘BbcyrR’ gives a color scheme similar to the well-known jet color scheme.

For more precise coloring, you can change default (equidistant) position of colors in color scheme. The format is ‘{CN,pos}’, ‘{CN,pos}’ or ‘{xRRGGBB,pos}’. The position value pos should be in range [0, 1]. Note, that alternative method for fine tuning of the color scheme is using the formula for coloring (see Curved coordinates).

Most popular color schemes.

When coloring by coordinate (used in map), the final color is determined by the position of the point in 3d space and is calculated from formula c=x*c[1] + y*c[2]. Here, c[1], c[2] are the first two elements of color array; x, y are normalized to axis range coordinates of the point.

Additionally, MathGL can apply mask to face filling at bitmap rendering. The kind of mask is specified by one of symbols ‘-+=;oOsS~<>jdD*^’ in color scheme. Mask can be rotated by arbitrary angle by command mask or by three predefined values +45, -45 and 90 degree by symbols ‘\/I’ correspondingly. Examples of predefined masks are shown on the figure below.

Example of masks for face coloring.

However, you can redefine mask for one symbol by specifying new matrix of size 8*8 as second argument for mask command. For example, the right-down subplot on the figure above is produced by code
gr->SetMask('+', "ff00182424f800"); gr->Dens(a,"3+");
or just use manual mask style (for v.2.3 and later)
gr->Dens(a,"3{s00ff00182424f800}");

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3.5 Font styles

Text style is specified by the string which may contain: color id characters ‘wkrgbcymhRGBCYMHW’ (see Color styles), and font style (‘ribwou’) and/or alignment (‘LRC’) specifications. At this, font style and alignment begin after the separator ‘:’. For example, ‘r:iCb’ sets the bold (‘b’) italic (‘i’) font text aligned at the center (‘C’) and with red color (‘r’). Starting from MathGL v.2.3, you can set not single color for whole text, but use color gradient for printed text (see Color scheme).

The font styles are: ‘r’ – roman (or regular) font, ‘i’ – italic style, ‘b’ – bold style. By default roman roman font is used. The align types are: ‘L’ – align left (default), ‘C’ – align center, ‘R’ – align right, ‘T’ – align under, ‘V’ – align center vertical. Additional font effects are: ‘w’ – wired, ‘o’ – over-lined, ‘u’ – underlined.

Also a parsing of the LaTeX-like syntax is provided. There are commands for the font style changing inside the string (for example, use \b for bold font): \a or \overline – over-lined, \b or \textbf – bold, \i or \textit – italic, \r or \textrm – roman (disable bold and italic attributes), \u or \underline – underlined, \w or \wire – wired, \big – bigger size, @ – smaller size. The lower and upper indexes are specified by ‘_’ and ‘^’ symbols. At this the changed font style is applied only on next symbol or symbols in braces {}. The text in braces {} are treated as single symbol that allow one to print the index of index. For example, compare the strings ‘sin (x^{2^3})’ and ‘sin (x^2^3)’. You may also change text color inside string by command #? or by \color? where ‘?’ is symbolic id of the color (see Color styles). For example, words ‘blue’ and ‘red’ will be colored in the string ‘#b{blue} and \colorr{red} text’. The most of functions understand the newline symbol ‘\n’ and allows to print multi-line text. Finally, you can use arbitrary (if it was defined in font-face) UTF codes by command \utf0x????. For example, \utf0x3b1 will produce α symbol.

The most of commands for special TeX or AMSTeX symbols, the commands for font style changing (\textrm, \textbf, \textit, \textsc, \overline, \underline), accents (\hat, \tilde, \dot, \ddot, \acute, \check, \grave, \bar, \breve) and roots (\sqrt, \sqrt3, \sqrt4) are recognized. The full list contain approximately 2000 commands. Note that first space symbol after the command is ignored, but second one is printed as normal symbol (space). For example, the following strings produce the same result \tilde a: ‘\tilde{a}’; ‘\tilde a’; ‘\tilde{}a’.

In particular, the Greek letters are recognizable special symbols: α – \alpha, β – \beta, γ – \gamma, δ – \delta, ε – \epsilon, η – \eta, ι – \iota, χ – \chi, κ – \kappa, λ – \lambda, μ – \mu, ν – \nu, o – \o, ω – \omega, ϕ – \phi, π – \pi, ψ – \psi, ρ – \rho, σ – \sigma, θ – \theta, τ – \tau, υ – \upsilon, ξ – \xi, ζ – \zeta, ς – \varsigma, ɛ – \varepsilon, ϑ – \vartheta, φ – \varphi, ϰ – \varkappa; A – \Alpha, B – \Beta, Γ – \Gamma, Δ – \Delta, E – \Epsilon, H – \Eta, I – \Iota, C – \Chi, K – \Kappa, Λ – \Lambda, M – \Mu, N – \Nu, O – \O, Ω – \Omega, Φ – \Phi, Π – \Pi, Ψ – \Psi, R – \Rho, Σ – \Sigma, Θ – \Theta, T – \Tau, Υ – \Upsilon, Ξ – \Xi, Z – \Zeta.

The small part of most common special TeX symbols are: ∠ – \angle, ⋅ – \cdot, ♣ – \clubsuit, ✓ – \checkmark, ∪ – \cup, ∩ – \cap, ♢ – \diamondsuit, ◇ – \diamond, ÷ – \div, ↓ – \downarrow, † – \dag, ‡ – \ddag, ≡ – \equiv, ∃ – \exists, ⌢ – \frown, ♭ – \flat, ≥ – \ge, ≥ – \geq, ≧ – \geqq, ← – \gets, ♡ – \heartsuit, ∞ – \infty, ∫ – \int, \Int, ℑ – \Im, ♢ – \lozenge, ⟨ – \langle, ≤ – \le, ≤ – \leq, ≦ – \leqq, ← – \leftarrow, ∓ – \mp, ∇ – \nabla, ≠ – \ne, ≠ – \neq, ♮ – \natural, ∮ – \oint, ⊙ – \odot, ⊕ – \oplus, ∂ – \partial, ∥ – \parallel, ⊥ –\perp, ± – \pm, ∝ – \propto, ∏ – \prod, ℜ – \Re, → – \rightarrow, ⟩ – \rangle, ♠ – \spadesuit, ~ – \sim, ⌣ – \smile, ⊂ – \subset, ⊃ – \supset, √ – \sqrt or \surd, § – \S, ♯ – \sharp, ∑ – \sum, × – \times, → – \to, ∴ – \therefore, ↑ – \uparrow, ℘ – \wp.

The font size can be defined explicitly (if size>0) or relatively to a base font size as |size|*FontSize (if size<0). The value size=0 specifies that the string will not be printed. The base font size is measured in internal “MathGL” units. Special functions SetFontSizePT(), SetFontSizeCM(), SetFontSizeIN() (see Font settings) allow one to set it in more “common” variables for a given dpi value of the picture.

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3.6 Textual formulas

MathGL have the fast variant of textual formula evaluation (see Evaluate expression) . There are a lot of functions and operators available. The operators are: ‘+’ – addition, ‘-’ – subtraction, ‘*’ – multiplication, ‘/’ – division, ‘^’ – integer power. Also there are logical “operators”: ‘<’ – true if x<y, ‘>’ – true if x>y, ‘=’ – true if x=y, ‘&’ – true if x and y both nonzero, ‘|’ – true if x or y nonzero. These logical operators have lowest priority and return 1 if true or 0 if false.

The basic functions are: ‘sqrt(x)’ – square root of x, ‘pow(x,y)’ – power x in y, ‘ln(x)’ – natural logarithm of x, ‘lg(x)’ – decimal logarithm of x, ‘log(a,x)’ – logarithm base a of x, ‘abs(x)’ – absolute value of x, ‘sign(x)’ – sign of x, ‘mod(x,y)’ – x modulo y, ‘step(x)’ – step function, ‘int(x)’ – integer part of x, ‘rnd’ – random number, ‘random(x)’ – random data of size as in x, ‘pi’ – number π = 3.1415926…, inf=∞

Functions for complex numbers ‘real(x)’, ‘imag(x)’, ‘abs(x)’, ‘arg(x)’, ‘conj(x)’.

Trigonometric functions are: ‘sin(x)’, ‘cos(x)’, ‘tan(x)’ (or ‘tg(x)’). Inverse trigonometric functions are: ‘asin(x)’, ‘acos(x)’, ‘atan(x)’. Hyperbolic functions are: ‘sinh(x)’ (or ‘sh(x)’), ‘cosh(x)’ (or ‘ch(x)’), ‘tanh(x)’ (or ‘th(x)’). Inverse hyperbolic functions are: ‘asinh(x)’, ‘acosh(x)’, ‘atanh(x)’.

There are a set of special functions: ‘gamma(x)’ – Gamma function Γ(x) = ∫0∞ tx-1 exp(-t) dt, ‘gamma_inc(x,y)’ – incomplete Gamma function Γ(x,y) = ∫y∞ tx-1 exp(-t) dt, ‘psi(x)’ – digamma function ψ(x) = Γ′(x)/Γ(x) for x≠0, ‘ai(x)’ – Airy function Ai(x), ‘bi(x)’ – Airy function Bi(x), ‘cl(x)’ – Clausen function, ‘li2(x)’ (or ‘dilog(x)’) – dilogarithm Li2(x) = -ℜ∫0xds log(1-s)/s, ‘sinc(x)’ – compute sinc(x) = sin(πx)/(πx) for any value of x, ‘zeta(x)’ – Riemann zeta function ζ(s) = ∑k=1∞k-s for arbitrary s≠1, ‘eta(x)’ – eta function η(s) = (1 - 21-s)ζ(s) for arbitrary s, ‘lp(l,x)’ – Legendre polynomial Pl(x), (|x|≤1, l≥0), ‘w0(x)’ – principal branch of the Lambert W function, ‘w1(x)’ – principal branch of the Lambert W function. Function W(x) is defined to be solution of the equation: W exp(W) = x.

The exponent integrals are: ‘ci(x)’ – Cosine integral Ci(x) = ∫0xdt cos(t)/t, ‘si(x)’ – Sine integral Si(x) = ∫0xdt sin(t)/t, ‘erf(x)’ – error function erf(x) = (2/√π) ∫0xdt exp(-t2) , ‘ei(x)’ – exponential integral Ei(x) = -PV(∫-x∞dt exp(-t)/t) (where PV denotes the principal value of the integral), ‘e1(x)’ – exponential integral E1(x) = ℜ∫1∞dt exp(-xt)/t, ‘e2(x)’ – exponential integral E2(x) = ℜ∫1∞dt exp(-xt)/t2, ‘ei3(x)’ – exponential integral Ei3(x) = ∫0xdt exp(-t3) for x≥0.

Bessel functions are: ‘j(nu,x)’ – regular cylindrical Bessel function of fractional order nu, ‘y(nu,x)’ – irregular cylindrical Bessel function of fractional order nu, ‘i(nu,x)’ – regular modified Bessel function of fractional order nu, ‘k(nu,x)’ – irregular modified Bessel function of fractional order nu.

Elliptic integrals are: ‘ee(k)’ – complete elliptic integral is denoted by E(k) = E(π/2,k), ‘ek(k)’ – complete elliptic integral is denoted by K(k) = F(π/2,k), ‘e(phi,k)’ – elliptic integral E(φ,k) = ∫0φdt √(1 - k2sin2(t)), ‘f(phi,k)’ – elliptic integral F(φ,k) = ∫0φdt 1/√(1 - k2sin2(t))

Jacobi elliptic functions are: ‘sn(u,m)’, ‘cn(u,m)’, ‘dn(u,m)’, ‘sc(u,m)’, ‘sd(u,m)’, ‘ns(u,m)’, ‘cs(u,m)’, ‘cd(u,m)’, ‘nc(u,m)’, ‘ds(u,m)’, ‘dc(u,m)’, ‘nd(u,m)’.

Note, some of these functions are unavailable if MathGL was compiled without GSL support.

There is no difference between lower or upper case in formulas. If argument value lie outside the range of function definition then function returns NaN.

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3.7 Command options

Command options allow the easy setup of the selected plot by changing global settings only for this plot. Each option start from symbol ‘;’. Options work so that MathGL remember the current settings, change settings as it being set in the option, execute function and return the original settings back. So, the options are most usable for plotting functions.

The most useful options are xrange, yrange, zrange. They sets the boundaries for data change. This boundaries are used for automatically filled variables. So, these options allow one to change the position of some plots. For example, in command Plot(y,"","xrange 0.1 0.9"); or plot y; xrange 0.1 0.9 the x coordinate will be equidistantly distributed in range 0.1 ... 0.9. See Using options, for sample code and picture.

The full list of options are:

MGL option: alpha val

Sets alpha value (transparency) of the plot. The value should be in range [0, 1]. See also alphadef.

MGL option: xrange val1 val2

Sets boundaries of x coordinate change for the plot. See also xrange.

MGL option: yrange val1 val2

Sets boundaries of y coordinate change for the plot. See also yrange.

MGL option: zrange val1 val2

Sets boundaries of z coordinate change for the plot. See also zrange.

MGL option: cut val

Sets whether to cut or to project the plot points lying outside the bounding box. See also cut.

MGL option: size val

Sets the size of text, marks and arrows. See also font, marksize, arrowsize.

MGL option: meshnum val

Work like meshnum command.

MGL option: legend 'txt'

Adds string ’txt’ to internal legend accumulator. The style of described line and mark is taken from arguments of the last 1D plotting command. See also legend.

MGL option: value val

Set the value to be used as additional numeric parameter in plotting command.

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3.8 Interfaces

The MathGL library has interfaces for a set of languages. Most of them are based on the C interface via SWIG tool. There are Python, Java, Octave, Lisp, C#, Guile, Lua, Modula 3, Ocaml, Perl, PHP, Pike, R, Ruby, and Tcl interfaces. Also there is a Fortran interface which has a similar set of functions, but slightly different types of arguments (integers instead of pointers). These functions are marked as [C function].

Some of the languages listed above support classes (like C++ or Python). The name of functions for them is the same as in C++ (see MathGL core and Data processing) and marked like [Method on mglGraph].

Finally, a special command language MGL (see MGL scripts) was written for a faster access to plotting functions. Corresponding scripts can be executed separately (by UDAV, mglconv, mglview and so on) or from the C/C++/Python/... code (see mglParse class).

• C interface:  
• C++ interface:  

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3.8.1 C/Fortran interface

The C interface is a base for many other interfaces. It contains the pure C functions for most of the methods of MathGL classes. In distinction to C++ classes, C functions must have an argument HMGL (for graphics) and/or HMDT (for data arrays), which specifies the object for drawing or manipulating (changing). So, firstly, the user has to create this object by the function mgl_create_*() and has to delete it after the use by function mgl_delete_*().

All C functions are described in the header file #include <mgl2/mgl_cf.h> and use variables of the following types:

These variables contain identifiers for graphics drawing objects and for the data objects.

Fortran functions/subroutines have the same names as C functions. However, there is a difference. Variable of type HMGL, HMDT must be an integer with sufficient size (integer*4 in the 32-bit operating system or integer*8 in the 64-bit operating system). All C functions of type void are subroutines in Fortran, which are called by operator call. The exceptions are functions, which return variables of types HMGL or HMDT. These functions should be declared as integer in Fortran code. Also, one should keep in mind that strings in Fortran are denoted by ' symbol, not the " symbol.

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3.8.2 C++/Python interface

MathGL provides the interface to a set of languages via SWIG library. Some of these languages support classes. The typical example is Python – which is named in this chapter’s title. Exactly the same classes are used for high-level C++ API. Its feature is using only inline member-functions what make high-level API to be independent on compiler even for binary build.

There are 3 main classes in:

To use Python classes just execute ‘import mathgl’. The simplest example will be: 

import mathgl
a=mathgl.mglGraph()
a.Box()
a.WritePNG("test.png")

Alternatively you can import all classes from mathgl module and easily access MathGL classes like this: 

from mathgl import *
a=mglGraph()
a.Box()
a.WritePNG("test.png")

This becomes useful if you create many mglData objects, for example.

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4 MathGL core

The core of MathGL is mglGraph class defined in #include <mgl2/mgl.h>. It contains a lot of plotting functions for 1D, 2D and 3D data. It also encapsulates parameters for axes drawing. Moreover an arbitrary coordinate transformation can be used for each axis. All plotting functions use data encapsulated in mglData class (see Data processing) that allows to check sizes of used arrays easily. Also it have many functions for data handling: modify it by formulas, find momentums and distribution (histogram), apply operator (differentiate, integrate, transpose, Fourier and so on), change data sizes (interpolate, squeeze, crop and so on). Additional information about colors, fonts, formula parsing can be found in General concepts and Other classes.

Some of MathGL features will appear only in novel versions. To test used MathGL version you can use following function.

MGL command: version 'ver'
Method on mglGraph: bool CheckVersion (const char *ver) static
C function: int mgl_check_version (const char *ver)

Return zero if MathGL version is appropriate for required by ver, i.e. if major version is the same and minor version is greater or equal to one in ver.

• Constructor:  
• Graphics setup:  
• Axis settings:  
• Subplots and rotation:  
• Export picture:  
• Background:  
• Primitives:  
• Text printing:  
• Axis and Colorbar:  
• Legend:  
• 1D plotting:  
• 2D plotting:  
• 3D plotting:  
• Dual plotting:  
• Vector fields:  
• Other plotting:  
• Nonlinear fitting:  
• Data manipulation:  

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4.1 Create and delete objects

Constructor on mglGraph: mglGraph (int kind=0, int width=600, int height=400)
Constructor on mglGraph: mglGraph (const mglGraph &gr)
Constructor on mglGraph: mglGraph (HMGL gr)
C function: HMGL mgl_create_graph (int width, int height)
C function: HMGL mgl_create_graph_gl ()

Creates the instance of class mglGraph with specified sizes width and height. Parameter kind may have following values: ‘0’ – use default plotter, ‘1’ – use OpenGL plotter.

Destructor on mglGraph: ~mglGraph ()
C function: HMGL mgl_delete_graph (HMGL gr)

Deletes the instance of class mglGraph.

Method on mglGraph: HMGL Self ()

Returns the pointer to internal object of type HMGL.

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4.2 Graphics setup

Functions and variables in this group influences on overall graphics appearance. So all of them should be placed before any actual plotting function calls.

MGL command: reset
Method on mglGraph: void DefaultPlotParam ()
C function: void mgl_set_def_param (HMGL gr)

Restore initial values for all of parameters and clear the image.

• Transparency:  
• Lighting:  
• Fog:  
• Default sizes:  
• Cutting:  
• Font settings:  
• Palette and colors:  
• Masks:  
• Error handling:  
• Stop drawing:  

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4.2.1 Transparency

There are several functions and variables for setup transparency. The general function is alpha which switch on/off the transparency for overall plot. It influence only for graphics which created after alpha call (with one exception, OpenGL). Function alphadef specify the default value of alpha-channel. Finally, function transptype set the kind of transparency. See Transparency and lighting, for sample code and picture.

MGL command: alpha [val=on]
Method on mglGraph: void Alpha (bool enable)
C function: void mgl_set_alpha (HMGL gr, int enable)

Sets the transparency on/off and returns previous value of transparency. It is recommended to call this function before any plotting command. Default value is transparency off.

MGL command: alphadef val
Method on mglGraph: void SetAlphaDef (mreal val)
C function: void mgl_set_alpha_default (HMGL gr, mreal alpha)

Sets default value of alpha channel (transparency) for all plotting functions. Initial value is 0.5.

MGL command: transptype val
Method on mglGraph: void SetTranspType (int type)
C function: void mgl_set_transp_type (HMGL gr, int type)

Set the type of transparency. Possible values are:

See Types of transparency, for sample code and picture..

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4.2.2 Lighting

There are several functions for setup lighting. The general function is light which switch on/off the lighting for overall plot. It influence only for graphics which created after light call (with one exception, OpenGL). Generally MathGL support up to 10 independent light sources. But in OpenGL mode only 8 of light sources is used due to OpenGL limitations. The position, color, brightness of each light source can be set separately. By default only one light source is active. It is source number 0 with white color, located at top of the plot. See Lighting sample, for sample code and picture.

MGL command: light [val=on]
Method on mglGraph: bool Light (bool enable)
C function: void mgl_set_light (HMGL gr, int enable)

Sets the using of light on/off for overall plot. Function returns previous value of lighting. Default value is lightning off.

MGL command: light num val
Method on mglGraph: void Light (int n, bool enable)
C function: void mgl_set_light_n (HMGL gr, int n, int enable)

Switch on/off n-th light source separately.

MGL command: light num xdir ydir zdir ['col'='w' br=0.5]
MGL command: light num xdir ydir zdir xpos ypos zpos ['col'='w' br=0.5]
Method on mglGraph: void AddLight (int n, mglPoint d, char c='w', mreal bright=0.5, mreal ap=0)
Method on mglGraph: void AddLight (int n, mglPoint r, mglPoint d, char c='w', mreal bright=0.5, mreal ap=0)
C function: void mgl_add_light (HMGL gr, int n, mreal dx, mreal dy, mreal dz)
C function: void mgl_add_light_ext (HMGL gr, int n, mreal dx, mreal dy, mreal dz, char c, mreal bright, mreal ap)
C function: void mgl_add_light_loc (HMGL gr, int n, mreal rx, mreal ry, mreal rz, mreal dx, mreal dy, mreal dz, char c, mreal bright, mreal ap)

The function adds a light source with identification n in direction d with color c and with brightness bright (which must be in range [0,1]). If position r is specified and isn’t NAN then light source is supposed to be local otherwise light source is supposed to be placed at infinity.

MGL command: diffuse val
Method on mglGraph: void SetDiffuse (mreal bright)
C function: void mgl_set_difbr (HMGL gr, mreal bright)

Set brightness of diffusive light (only for local light sources).

MGL command: ambient val
Method on mglGraph: void SetAmbient (mreal bright=0.5)
C function: void mgl_set_ambbr (HMGL gr, mreal bright)

Sets the brightness of ambient light. The value should be in range [0,1].

MGL command: attachlight val
Method on mglGraph: void AttachLight (bool val)
C function: void mgl_set_attach_light (HMGL gr, int val)

Set to attach light settings to inplot/subplot. Note, OpenGL and some output formats don’t support this feature.

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4.2.3 Fog

MGL command: fog val [dz=0.25]
Method on mglGraph: void Fog (mreal d, mreal dz=0.25)
C function: void mgl_set_fog (HMGL gr, mreal d, mreal dz)

Function imitate a fog in the plot. Fog start from relative distance dz from view point and its density growths exponentially in depth. So that the fog influence is determined by law ~ 1-exp(-d*z). Here z is normalized to 1 depth of the plot. If value d=0 then the fog is absent. Note, that fog was applied at stage of image creation, not at stage of drawing. See Adding fog, for sample code and picture.

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4.2.4 Default sizes

These variables control the default (initial) values for most graphics parameters including sizes of markers, arrows, line width and so on. As any other settings these ones will influence only on plots created after the settings change.

MGL command: barwidth val
Method on mglGraph: void SetBarWidth ( mreal val)
C function: void mgl_set_bar_width (HMGL gr, mreal val)

Sets relative width of rectangles in bars, barh, boxplot, candle, ohlc. Default value is 0.7.

MGL command: marksize val
Method on mglGraph: void SetMarkSize (mreal val)
C function: void mgl_set_mark_size (HMGL gr, mreal val)

Sets size of marks for 1D plotting. Default value is 1.

MGL command: arrowsize val
Method on mglGraph: void SetArrowSize (mreal val)
C function: void mgl_set_arrow_size (HMGL gr, mreal val)

Sets size of arrows for 1D plotting, lines and curves (see Primitives). Default value is 1.

MGL command: meshnum val
Method on mglGraph: void SetMeshNum (int val)
C function: void mgl_set_meshnum (HMGL gr, int num)

Sets approximate number of lines in mesh, fall, grid2 and also the number of hachures in vect, dew and the number of cells in cloud. By default (=0) it draws all lines/hachures/cells.

MGL command: facenum val
Method on mglGraph: void SetFaceNum (int val)
C function: void mgl_set_facenum (HMGL gr, int num)

Sets approximate number of visible faces. Can be used for speeding up drawing by cost of lower quality. By default (=0) it draws all of them.

MGL command: plotid 'id'
Method on mglGraph: void SetPlotId (const char *id)
C function: void mgl_set_plotid (HMGL gr, const char *id)

Sets default name id as filename for saving (in FLTK window for example).

Method on mglGraph: const char * GetPlotId ()
C function only: const char * mgl_get_plotid (HMGL gr)
Fortran subroutine: mgl_get_plotid (long gr, char *out, int len)

Gets default name id as filename for saving (in FLTK window for example).

MGL command: pendelta val
Method on mglGraph: void SetPenDelta (double val)
C function: void mgl_pen_delta (HMGL gr, double val)

Changes the blur around lines and text (default is 1). For val>1 the text and lines are more sharped. For val<1 the text and lines are more blurred.

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4.2.5 Cutting

These variables and functions set the condition when the points are excluded (cutted) from the drawing. Note, that a point with NAN value(s) of coordinate or amplitude will be automatically excluded from the drawing. See Cutting sample, for sample code and picture.

MGL command: cut val
Method on mglGraph: void SetCut (bool val)
C function: void mgl_set_cut (HMGL gr, int val)

Flag which determines how points outside bounding box are drawn. If it is true then points are excluded from plot (it is default) otherwise the points are projected to edges of bounding box.

MGL command: cut x1 y1 z1 x2 y2 z2
Method on mglGraph: void SetCutBox (mglPoint p1, mglPoint p1)
C function: void mgl_set_cut_box (HMGL gr, mreal x1, mreal y1, mreal z1, mreal x2, mreal y2, mreal z2)

Lower and upper edge of the box in which never points are drawn. If both edges are the same (the variables are equal) then the cutting box is empty.

MGL command: cut 'cond'
Method on mglGraph: void CutOff (const char *cond)
C function: void mgl_set_cutoff (HMGL gr, const char *cond)

Sets the cutting off condition by formula cond. This condition determine will point be plotted or not. If value of formula is nonzero then point is omitted, otherwise it plotted. Set argument as "" to disable cutting off condition.

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4.2.6 Font settings

MGL command: font 'fnt' [val=6]

Font style for text and labels (see text). Initial style is ’fnt’=’:rC’ give Roman font with centering. Parameter val sets the size of font for tick and axis labels. Default font size of axis labels is 1.4 times large than for tick labels. For more detail, see Font styles.

MGL command: rotatetext val
Method on mglGraph: void SetRotatedText (bool val)
C function: void mgl_set_rotated_text (HMGL gr, int val)

Sets to use or not text rotation.

MGL command: loadfont ['name'='']
Method on mglGraph: void LoadFont (const char *name, const char *path="")
C function: void mgl_load_font (HMGL gr, const char *name, const char *path)

Load font typeface from path/name. Empty name will load default font.

Method on mglGraph: void SetFontDef (const char *fnt)
C function: void mgl_set_font_def (HMGL gr, const char * val)

Sets the font specification (see Text printing). Default is ‘rC’ – Roman font centering.

Method on mglGraph: void SetFontSize (mreal val)
C function: void mgl_set_font_size (HMGL gr, mreal val)

Sets the size of font for tick and axis labels. Default font size of axis labels is 1.4 times large than for tick labels.

Method on mglGraph: void SetFontSizePT (mreal cm, int dpi=72)

Set FontSize by size in pt and picture DPI (default is 16 pt for dpi=72).

Method on mglGraph: inline void SetFontSizeCM (mreal cm, int dpi=72)

Set FontSize by size in centimeters and picture DPI (default is 0.56 cm = 16 pt).

Method on mglGraph: inline void SetFontSizeIN (mreal cm, int dpi=72)

Set FontSize by size in inch and picture DPI (default is 0.22 in = 16 pt).

Method on mglGraph: void LoadFont (const char *name, const char *path="")
C function: void mgl_load_font (HMGL gr, const char *name, const char *path)

Load font typeface from path/name.

Method on mglGraph: void CopyFont (mglGraph * from)
C function: void mgl_copy_font (HMGL gr, HMGL gr_from)

Copy font data from another mglGraph object.

Method on mglGraph: void RestoreFont ()
C function: void mgl_restore_font (HMGL gr)

Restore font data to default typeface.

Method on mglGraph: void SetDefFont (const char *name, const char *path="") static
C function: void mgl_def_font (const char *name, const char *path)

Load default font typeface (for all newly created HMGL/mglGraph objects) from path/name.

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4.2.7 Palette and colors

MGL command: palette 'colors'
Method on mglGraph: void SetPalette (const char *colors)
C function: void mgl_set_palette (HMGL gr, const char *colors)

Sets the palette as selected colors. Default value is "Hbgrcmyhlnqeup" that corresponds to colors: dark gray ‘H’, blue ‘b’, green ‘g’, red ‘r’, cyan ‘c’, magenta ‘m’, yellow ‘y’, gray ‘h’, blue-green ‘l’, sky-blue ‘n’, orange ‘q’, yellow-green ‘e’, blue-violet ‘u’, purple ‘p’. The palette is used mostly in 1D plots (see 1D plotting) for curves which styles are not specified. Internal color counter will be nullified by any change of palette. This includes even hidden change (for example, by box or axis functions).

Method on mglGraph: void SetDefScheme (const char *sch)
C function: void mgl_set_def_sch (HMGL gr, const char *sch)

Sets the sch as default color scheme. Default value is "BbcyrR".

Method on mglGraph: void SetColor (char id, mreal r, mreal g, mreal b) static
C function: void mgl_set_color (char id, mreal r, mreal g, mreal b)

Sets RGB values for color with given id. This is global setting which influence on any later usage of symbol id.

MGL command: gray val
Method on mglGraph: void Gray (bool enable)
C function: void mgl_set_gray (HMGL gr, int enable)

Sets the gray-scale mode on/off.

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4.2.8 Masks

MGL command: mask 'id' 'hex'
Method on mglGraph: void SetMask (char id, const char *hex)
Method on mglGraph: void SetMask (char id, uint64_t hex)
C function: void mgl_set_mask (HMGL gr, const char *hex)
C function: void mgl_set_mask_val (HMGL gr, uint64_t hex)

Sets new bit matrix hex of size 8*8 for mask with given id. This is global setting which influence on any later usage of symbol id. The predefined masks are (see Color scheme): ‘-’ is 000000FF00000000, ‘+’ is 080808FF08080808, ‘=’ is 0000FF00FF000000, ‘;’ is 0000007700000000, ‘o’ is 0000182424180000, ‘O’ is 0000183C3C180000, ‘s’ is 00003C24243C0000, ‘S’ is 00003C3C3C3C0000, ‘~’ is 0000060990600000, ‘<’ is 0060584658600000, ‘>’ is 00061A621A060000, ‘j’ is 0000005F00000000, ‘d’ is 0008142214080000, ‘D’ is 00081C3E1C080000, ‘*’ is 8142241818244281, ‘^’ is 0000001824420000.

MGL command: mask angle
Method on mglGraph: void SetMaskAngle (int angle)
C function: void mgl_set_mask_angle (HMGL gr, int angle)

Sets the default rotation angle (in degrees) for masks. Note, you can use symbols ‘\’, ‘/’, ‘I’ in color scheme for setting rotation angles as 45, -45 and 90 degrees correspondingly.

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4.2.9 Error handling

Normally user should set it to zero by SetWarn(0); before plotting and check if GetWarn() or Message() return non zero after plotting. Only last warning will be saved. All warnings/errors produced by MathGL is not critical – the plot just will not be drawn. By default, all warnings are printed in stderr. You can disable it by using mgl_suppress_warn(true);.

Method on mglGraph: void SetWarn (int code, const char *info="")
C function: void mgl_set_warn (HMGL gr, int code, const char *info)

Set warning code. Normally you should call this function only for clearing the warning state, i.e. call SetWarn(0);. Text info will be printed as is if code<0.

Method on mglGraph: const char *Message ()
C function only: const char *mgl_get_mess (HMGL gr)
Fortran subroutine: mgl_get_mess (long gr, char *out, int len)

Return messages about matters why some plot are not drawn. If returned string is empty then there are no messages.

Method on mglGraph: int GetWarn ()
C function: int mgl_get_warn (HMGL gr)

Return the numerical ID of warning about the not drawn plot. Possible values are:

mglWarnNone=0

Everything OK

mglWarnDim

Data dimension(s) is incompatible

mglWarnLow

Data dimension(s) is too small

mglWarnNeg

Minimal data value is negative

mglWarnFile

No file or wrong data dimensions

mglWarnMem

Not enough memory

mglWarnZero

Data values are zero

mglWarnLeg

No legend entries

mglWarnSlc

Slice value is out of range

mglWarnCnt

Number of contours is zero or negative

mglWarnOpen

Couldn’t open file

mglWarnLId

Light: ID is out of range

mglWarnSize

Setsize: size(s) is zero or negative

mglWarnFmt

Format is not supported for that build

mglWarnTern

Axis ranges are incompatible

mglWarnNull

Pointer is NULL

mglWarnSpc

Not enough space for plot

mglScrArg

Wrong argument(s) of a command in MGL script

mglScrCmd

Wrong command in MGL script

mglScrLong

Too long line in MGL script

mglScrStr

Unbalanced ’ in MGL script

mglScrTemp

Change temporary data in MGL script

Method on mglGraph: void SuppressWarn (bool state) static
C function: void mgl_suppress_warn (int state)

Disable printing warnings to stderr if state is nonzero.

Method on mglGraph: void SetGlobalWarn (const char *info) static
C function: void mgl_set_global_warn (const char *info)

Set warning message info for global scope.

Method on mglGraph: const char * GlobalWarn () static
C function: const char * mgl_get_global_warn ()

Get warning message(s) for global scope.

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4.2.10 Stop drawing

Method on mglGraph: void Stop (bool stop=true)
C function only: void mgl_ask_stop (HMGL gr, int stop)

Ask to stop drawing if stop is non-zero, otherwise reset stop flag.

Method on mglGraph: bool NeedStop ()
C function only: void mgl_need_stop (HMGL gr)

Return true if drawing should be terminated. Also it process all events in GUI. User should call this function from time to time inside a long calculation to allow processing events for GUI.

Method on mglGraph: bool SetEventFunc (void (*func)(void *), void *par=NULL)
C function only: void mgl_set_event_func (HMGL gr, void (*func)(void *), void *par)

Set callback function which will be called to process events of GUI library.

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4.3 Axis settings

These large set of variables and functions control how the axis and ticks will be drawn. Note that there is 3-step transformation of data coordinates are performed. Firstly, coordinates are projected if Cut=true (see Cutting), after it transformation formulas are applied, and finally the data was normalized in bounding box. Note, that MathGL will produce warning if axis range and transformation formulas are not compatible.

• Ranges (bounding box):  
• Curved coordinates:  
• Ticks:  

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4.3.1 Ranges (bounding box)

MGL command: xrange v1 v2 [add=off]
MGL command: yrange v1 v2 [add=off]
MGL command: zrange v1 v2 [add=off]
MGL command: crange v1 v2 [add=off]
Method on mglGraph: void SetRange (char dir, mreal v1, mreal v2)
Method on mglGraph: void AddRange (char dir, mreal v1, mreal v2)
C function: void mgl_set_range_val (HMGL gr, char dir, mreal v1, mreal v2)
C function: void mgl_add_range_val (HMGL gr, char dir, mreal v1, mreal v2)

Sets or adds the range for ‘x’-,‘y’-,‘z’- coordinate or coloring (‘c’). If one of values is NAN then it is ignored. See also ranges.

MGL command: xrange dat [add=off]
MGL command: yrange dat [add=off]
MGL command: zrange dat [add=off]
MGL command: crange dat [add=off]
Method on mglGraph: void SetRange (char dir, const mglDataA &dat, bool add=false)
C function: void mgl_set_range_dat (HMGL gr, char dir, const HCDT a, int add)

Sets the range for ‘x’-,‘y’-,‘z’- coordinate or coloring (‘c’) as minimal and maximal values of data dat. Parameter add=on shows that the new range will be joined to existed one (not replace it).

MGL command: ranges x1 x2 y1 y2 [z1=0 z2=0]
Method on mglGraph: void SetRanges (mglPoint p1, mglPoint p2)
Method on mglGraph: void SetRanges (double x1, double x2, double y1, double y2, double z1=0, double z2=0)
C function: void mgl_set_ranges (HMGL gr, double x1, double x2, double y1, double y2, double z1, double z2)

Sets the ranges of coordinates. If minimal and maximal values of the coordinate are the same then they are ignored. Also it sets the range for coloring (analogous to crange z1 z2). This is default color range for 2d plots. Initial ranges are [-1, 1].

Method on mglGraph: void SetRanges (const mglDataA &xx, const mglDataA &yy)
Method on mglGraph: void SetRanges (const mglDataA &xx, const mglDataA &yy, const mglDataA &zz)
Method on mglGraph: void SetRanges (const mglDataA &xx, const mglDataA &yy, const mglDataA &zz, const mglDataA &cc)

Sets the ranges of ‘x’-,‘y’-,‘z’-coordinates and coloring as minimal and maximal values of data xx, yy, zz, cc correspondingly.

Method on mglGraph: void SetAutoRanges (mglPoint p1, mglPoint p2)
Method on mglGraph: void SetAutoRanges (double x1, double x2, double y1, double y2, double z1=0, double z2=0, double c1=0, double c2=0)
C function: void mgl_set_auto_ranges (HMGL gr, double x1, double x2, double y1, double y2, double z1, double z2, double z1, double z2)

Sets the ranges for automatic coordinates. If minimal and maximal values of the coordinate are the same then they are ignored.

MGL command: origin x0 y0 [z0=nan]
Method on mglGraph: void SetOrigin (mglPoint p0)
Method on mglGraph: void SetOrigin (mreal x0, mreal y0, mreal z0=NAN)
C function: void mgl_set_origin (HMGL gr, mreal x0, mreal y0, mreal z0)

Sets center of axis cross section. If one of values is NAN then MathGL try to select optimal axis position.

MGL command: zoomaxis x1 x2
MGL command: zoomaxis x1 y1 x2 y2
MGL command: zoomaxis x1 y1 z1 x2 y2 z2
MGL command: zoomaxis x1 y1 z1 c1 x2 y2 z2 c2
Method on mglGraph: void ZoomAxis (mglPoint p1, mglPoint p2)
C function: void mgl_zoom_axis (HMGL gr, mreal x1, mreal y1, mreal z1, mreal c1, mreal x2, mreal y2, mreal z2, mreal c2)

Additionally extend axis range for any settings made by SetRange or SetRanges functions according the formula min += (max-min)*p1 and max += (max-min)*p1 (or min *= (max/min)^p1 and max *= (max/min)^p1 for log-axis range when inf>max/min>100 or 0<max/min<0.01). Initial ranges are [0, 1]. Attention! this settings can not be overwritten by any other functions, including DefaultPlotParam().

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4.3.2 Curved coordinates

MGL command: axis 'fx' 'fy' 'fz' ['fa'='']
Method on mglGraph: void SetFunc (const char *EqX, const char *EqY, const char *EqZ="", const char *EqA="")
C function: void mgl_set_func (HMGL gr, const char *EqX, const char *EqY, const char *EqZ, const char *EqA)

Sets transformation formulas for curvilinear coordinate. Each string should contain mathematical expression for real coordinate depending on internal coordinates ‘x’, ‘y’, ‘z’ and ‘a’ or ‘c’ for colorbar. For example, the cylindrical coordinates are introduced as SetFunc("x*cos(y)", "x*sin(y)", "z");. For removing of formulas the corresponding parameter should be empty or NULL. Using transformation formulas will slightly slowing the program. Parameter EqA set the similar transformation formula for color scheme. See Textual formulas.

MGL command: axis how
Method on mglGraph: void SetCoor (int how)
C function: void mgl_set_coor (HMGL gr, int how)

Sets one of the predefined transformation formulas for curvilinear coordinate. Parameter how define the coordinates: mglCartesian=0 – Cartesian coordinates (no transformation); mglPolar=1 – Polar coordinates x_n=x*cos(y),y_n=x*sin(y), z_n=z; mglSpherical=2 – Sperical coordinates x_n=x*sin(y)*cos(z), y_n=x*sin(y)*sin(z), z_n=x*cos(y); mglParabolic=3 – Parabolic coordinates x_n=x*y, y_n=(x*x-y*y)/2, z_n=z; mglParaboloidal=4 – Paraboloidal coordinates x_n=(x*x-y*y)*cos(z)/2, y_n=(x*x-y*y)*sin(z)/2, z_n=x*y; mglOblate=5 – Oblate coordinates x_n=cosh(x)*cos(y)*cos(z), y_n=cosh(x)*cos(y)*sin(z), z_n=sinh(x)*sin(y); mglProlate=6 – Prolate coordinates x_n=sinh(x)*sin(y)*cos(z), y_n=sinh(x)*sin(y)*sin(z), z_n=cosh(x)*cos(y); mglElliptic=7 – Elliptic coordinates x_n=cosh(x)*cos(y), y_n=sinh(x)*sin(y), z_n=z; mglToroidal=8 – Toroidal coordinates x_n=sinh(x)*cos(z)/(cosh(x)-cos(y)), y_n=sinh(x)*sin(z)/(cosh(x)-cos(y)), z_n=sin(y)/(cosh(x)-cos(y)); mglBispherical=9 – Bispherical coordinates x_n=sin(y)*cos(z)/(cosh(x)-cos(y)), y_n=sin(y)*sin(z)/(cosh(x)-cos(y)), z_n=sinh(x)/(cosh(x)-cos(y)); mglBipolar=10 – Bipolar coordinates x_n=sinh(x)/(cosh(x)-cos(y)), y_n=sin(y)/(cosh(x)-cos(y)), z_n=z; mglLogLog=11 – log-log coordinates x_n=lg(x), y_n=lg(y), z_n=lg(z); mglLogX=12 – log-x coordinates x_n=lg(x), y_n=y, z_n=z; mglLogY=13 – log-y coordinates x_n=x, y_n=lg(y), z_n=z.

MGL command: ternary val
Method on mglGraph: void Ternary (int tern)
C function: void mgl_set_ternary (HMGL gr, int tern)

The function sets to draws Ternary (tern=1), Quaternary (tern=2) plot or projections (tern=4,5,6).

Ternary plot is special plot for 3 dependent coordinates (components) a, b, c so that a+b+c=1. MathGL uses only 2 independent coordinates a=x and b=y since it is enough to plot everything. At this third coordinate z act as another parameter to produce contour lines, surfaces and so on.

Correspondingly, Quaternary plot is plot for 4 dependent coordinates a, b, c and d so that a+b+c+d=1. MathGL uses only 3 independent coordinates a=x, b=y and d=z since it is enough to plot everything.

Projections can be obtained by adding value 4 to tern argument. So, that tern=4 will draw projections in Cartesian coordinates, tern=5 will draw projections in Ternary coordinates, tern=6 will draw projections in Quaternary coordinates. If you add 8 instead of 4 then all text labels will not be printed on projections.

Use Ternary(0) for returning to usual axis. See Ternary axis, for sample code and picture. See Axis projection, for sample code and picture.

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4.3.3 Ticks

MGL command: adjust ['dir'='xyzc']
Method on mglGraph: void Adjust (const char *dir="xyzc")
C function: void mgl_adjust_ticks (HMGL gr, const char *dir)

Set the ticks step, number of sub-ticks and initial ticks position to be the most human readable for the axis along direction(s) dir. Also set SetTuneTicks(true). Usually you don’t need to call this function except the case of returning to default settings.

MGL command: xtick val [sub=0 org=nan]
MGL command: ytick val [sub=0 org=nan]
MGL command: ztick val [sub=0 org=nan]
MGL command: ctick val [sub=0 org=nan]
Method on mglGraph: void SetTicks (char dir, mreal d=0, int ns=0, mreal org=NAN, const char *fact="")
Method on mglGraph: void SetTicks (char dir, mreal d, int ns, mreal org, const wchar_t *fact)
C function: void mgl_set_ticks (HMGL gr, char dir, mreal d, int ns, mreal org)
C function: void mgl_set_ticks_fact (HMGL gr, char dir, mreal d, int ns, mreal org, const char *fact)
C function: void mgl_set_ticks_factw (HMGL gr, char dir, mreal d, int ns, mreal org, const wchar_t *fact)

Set the ticks step d, number of sub-ticks ns (used for positive d) and initial ticks position org for the axis along direction dir (use ’c’ for colorbar ticks). Variable d set step for axis ticks (if positive) or it’s number on the axis range (if negative). Zero value set automatic ticks. If org value is NAN then axis origin is used. Parameter fact set text which will be printed after tick label (like "\pi" for d=M_PI).

MGL command: xtick val1 'lbl1' [val2 'lbl2' ...]
MGL command: ytick val1 'lbl1' [val2 'lbl2' ...]
MGL command: ztick val1 'lbl1' [val2 'lbl2' ...]
MGL command: xtick vdat 'lbls' [add=off]
MGL command: ytick vdat 'lbls' [add=off]
MGL command: ztick vdat 'lbls' [add=off]
Method on mglGraph: void SetTicksVal (char dir, const char *lbl, bool add=false)
Method on mglGraph: void SetTicksVal (char dir, const wchar_t *lbl, bool add=false)
Method on mglGraph: void SetTicksVal (char dir, const mglDataA &val, const char *lbl, bool add=false)
Method on mglGraph: void SetTicksVal (char dir, const mglDataA &val, const wchar_t *lbl, bool add=false)
C function: void mgl_set_ticks_str (HMGL gr, char dir, const char *lbl, bool add)
C function: void mgl_set_ticks_wcs (HMGL gr, char dir, const wchar_t *lbl, bool add)
C function: void mgl_set_ticks_val (HMGL gr, char dir, HCDT val, const char *lbl, bool add)
C function: void mgl_set_ticks_valw (HMGL gr, char dir, HCDT val, const wchar_t *lbl, bool add)

Set the manual positions val and its labels lbl for ticks along axis dir. If array val is absent then values equidistantly distributed in x-axis range are used. Labels are separated by ‘\n’ symbol. Use SetTicks() to restore automatic ticks.

Method on mglGraph: void AddTick (char dir, double val, const char *lbl)
Method on mglGraph: void AddTick (char dir, double val, const wchar_t *lbl)
C function: void mgl_add_tick (HMGL gr, char dir, double val, const char *lbl)
C function: void mgl_set_tickw (HMGL gr, char dir, double val, const wchar_t *lbl)

The same as previous but add single tick label lbl at position val to the lest of existed ones.

MGL command: xtick 'templ'
MGL command: ytick 'templ'
MGL command: ztick 'templ'
MGL command: ctick 'templ'
Method on mglGraph: void SetTickTempl (char dir, const char *templ)
Method on mglGraph: void SetTickTempl (char dir, const wchar_t *templ)
C function: void mgl_set_tick_templ (HMGL gr, const char *templ)
C function: void mgl_set_tick_templw (HMGL gr, const wchar_t *templ)

Set template templ for x-,y-,z-axis ticks or colorbar ticks. It may contain TeX symbols also. If templ="" then default template is used (in simplest case it is ‘%.2g’). If template start with ‘&’ symbol then long integer value will be passed instead of default type double. Setting on template switch off automatic ticks tuning.

MGL command: ticktime 'dir' [dv 'tmpl']
Method on mglGraph: void SetTicksTime (char dir, mreal val, const char *templ)
C function: void mgl_set_ticks_time (HMGL gr, mreal val, const char *templ)

Sets time labels with step val and template templ for x-,y-,z-axis ticks or colorbar ticks. It may contain TeX symbols also. The format of template templ is the same as described in http://www.manpagez.com/man/3/strftime/. Most common variants are ‘%X’ for national representation of time, ‘%x’ for national representation of date, ‘%Y’ for year with century. If val=0 and/or templ="" then automatic tick step and/or template will be selected. You can use mgl_get_time() function for obtaining number of second for given date/time string. Note, that MS Visual Studio couldn’t handle date before 1970.

C function: double mgl_get_time (const char*str, const char *templ)

Gets number of seconds from 1970 year to specified date/time str. The format of string is specified by templ, which is the same as described in http://www.manpagez.com/man/3/strftime/. Most common variants are ‘%X’ for national representation of time, ‘%x’ for national representation of date, ‘%Y’ for year with century. Note, that MS Visual Studio couldn’t handle date before 1970.

MGL command: tuneticks val [pos=1.15]
Method on mglGraph: void SetTuneTicks (int tune, mreal pos=1.15)
C function: void mgl_tune_ticks (HMGL gr, int tune, mreal pos)

Switch on/off ticks enhancing by factoring common multiplier (for small, like from 0.001 to 0.002, or large, like from 1000 to 2000, coordinate values – enabled if tune&1 is nonzero) or common component (for narrow range, like from 0.999 to 1.000 – enabled if tune&2 is nonzero). Also set the position pos of common multiplier/component on the axis: =0 at minimal axis value, =1 at maximal axis value. Default value is 1.15.

MGL command: tickshift dx [dy=0 dz=0 dc=0]
Method on mglGraph: void SetTickShift (mglPoint d)
C function: void mgl_set_tick_shift (HMGL gr, mreal dx, mreal dy, mreal dz, mreal dc)

Set value of additional shift for ticks labels.

Method on mglGraph: void SetTickRotate (bool val)
C function: void mgl_set_tick_rotate (HMGL gr, bool val)

Enable/disable ticks rotation if there are too many ticks or ticks labels are too long.

Method on mglGraph: void SetTickSkip (bool val)
C function: void mgl_set_tick_skip (HMGL gr, bool val)

Enable/disable ticks skipping if there are too many ticks or ticks labels are too long.

Method on mglGraph: void SetTimeUTC (bool val)

Enable/disable using UTC time for ticks labels. In C/Fortran you can use mgl_set_flag(gr,val, MGL_USE_GMTIME);.

MGL command: origintick val
Method on mglGraph: void SetOriginTick (bool val=true)

Enable/disable drawing of ticks labels at axis origin. In C/Fortran you can use mgl_set_flag(gr,val, MGL_NO_ORIGIN);.

MGL command: ticklen val [stt=1]
Method on mglGraph: void SetTickLen (mreal val, mreal stt=1)
C function: void mgl_set_tick_len (HMGL gr, mreal val, mreal stt)

The relative length of axis ticks. Default value is 0.1. Parameter stt>0 set relative length of subticks which is in sqrt(1+stt) times smaller.

MGL command: axisstl 'stl' ['tck'='' 'sub'='']
Method on mglGraph: void SetAxisStl (const char *stl="k", const char *tck=0, const char *sub=0)
C function: void mgl_set_axis_stl (HMGL gr, const char *stl, const char *tck, const char *sub)

The line style of axis (stl), ticks (tck) and subticks (sub). If stl is empty then default style is used (‘k’ or ‘w’ depending on transparency type). If tck or sub is empty then axis style is used (i.e. stl).

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4.4 Subplots and rotation

These functions control how and where further plotting will be placed. There is a certain calling order of these functions for the better plot appearance. First one should be subplot, multiplot or inplot for specifying the place. Second one can be title for adding title for the subplot. After it a rotate, shear and aspect. And finally any other plotting functions may be called. Alternatively you can use columnplot, gridplot, stickplot, shearplot or relative inplot for positioning plots in the column (or grid, or stick) one by another without gap between plot axis (bounding boxes). See Subplots, for sample code and picture.

MGL command: subplot nx ny m ['stl'='<>_^' dx=0 dy=0]
Method on mglGraph: void SubPlot (int nx, int ny, int m, const char *stl="<>_^", mreal dx=0, mreal dy=0)
C function: void mgl_subplot (HMGL gr, int nx, int ny, int m, const char *stl)
C function: void mgl_subplot_d (HMGL gr, int nx, int ny, int m, const char *stl, mreal dx, mreal dy)

Puts further plotting in a m-th cell of nx*ny grid of the whole frame area. This function set off any aspects or rotations. So it should be used first for creating the subplot. Extra space will be reserved for axis/colorbar if stl contain:

From the aesthetical point of view it is not recommended to use this function with different matrices in the same frame. The position of the cell can be shifted from its default position by relative size dx, dy. Note, colorbar can be invisible (be out of image borders) if you set empty style ‘’.

MGL command: multiplot nx ny m dx dy ['style'='<>_^']
Method on mglGraph: void MultiPlot (int nx, int ny, int m, int dx, int dy, const char *stl="<>_^")
C function: void mgl_multiplot (HMGL gr, int nx, int ny, int m, int dx, int dy, const char *stl)

Puts further plotting in a rectangle of dx*dy cells starting from m-th cell of nx*ny grid of the whole frame area. This function set off any aspects or rotations. So it should be used first for creating subplot. Extra space will be reserved for axis/colorbar if stl contain:

MGL command: inplot x1 x2 y1 y2 [rel=on]
Method on mglGraph: void InPlot (mreal x1, mreal x2, mreal y1, mreal y2, bool rel=true)
C function: void mgl_inplot (HMGL gr, mreal x1, mreal x2, mreal y1, mreal y2)
C function: void mgl_relplot (HMGL gr, mreal x1, mreal x2, mreal y1, mreal y2)

Puts further plotting in some region of the whole frame surface. This function allows one to create a plot in arbitrary place of the screen. The position is defined by rectangular coordinates [x1, x2]*[y1, y2]. The coordinates x1, x2, y1, y2 are normalized to interval [0, 1]. If parameter rel=true then the relative position to current subplot (or inplot with rel=false) is used. This function set off any aspects or rotations. So it should be used first for creating subplot.

MGL command: columnplot num ind [d=0]
Method on mglGraph: void ColumnPlot (int num, int ind, mreal d=0)
C function: void mgl_columnplot (HMGL gr, int num, int ind)
C function: void mgl_columnplot_d (HMGL gr, int num, int ind, mreal d)

Puts further plotting in ind-th cell of column with num cells. The position is relative to previous subplot (or inplot with rel=false). Parameter d set extra gap between cells.

MGL command: gridplot nx ny ind [d=0]
Method on mglGraph: void GridPlot (int nx, int ny, int ind, mreal d=0)
C function: void mgl_gridplot (HMGL gr, int nx, int ny, int ind)
C function: void mgl_gridplot_d (HMGL gr, int nx, int ny, int ind, mreal d)

Puts further plotting in ind-th cell of nx*ny grid. The position is relative to previous subplot (or inplot with rel=false). Parameter d set extra gap between cells.

MGL command: stickplot num ind tet phi
Method on mglGraph: void StickPlot (int num, int ind, mreal tet, mreal phi)
C function: void mgl_stickplot (HMGL gr, int num, int ind, mreal tet, mreal phi)

Puts further plotting in ind-th cell of stick with num cells. At this, stick is rotated on angles tet, phi. The position is relative to previous subplot (or inplot with rel=false).

MGL command: shearplot num ind sx sy [xd yd]
Method on mglGraph: void ShearPlot (int num, int ind, mreal sx, mreal sy, mreal xd=1, mreal yd=0)
C function: void mgl_shearplot (HMGL gr, int num, int ind, mreal sx, mreal sy, mreal xd, mreal yd)

Puts further plotting in ind-th cell of stick with num cells. At this, cell is sheared on values sx, sy. Stick direction is specified be xd and yd. The position is relative to previous subplot (or inplot with rel=false).

MGL command: title 'title' ['stl'='' size=-2]
Method on mglGraph: void Title (const char *txt, const char *stl="", mreal size=-2)
Method on mglGraph: void Title (const wchar_t *txt, const char *stl="", mreal size=-2)
C function: void mgl_title (HMGL gr, const char *txt, const char *stl, mreal size)
C function: void mgl_titlew (HMGL gr, const wchar_t *txt, const char *stl, mreal size)

Add text title for current subplot/inplot. Parameter stl can contain:

Parameter size set font size. This function set off any aspects or rotations. So it should be used just after creating subplot.

MGL command: rotate tetx tetz [tety=0]
Method on mglGraph: void Rotate (mreal TetX, mreal TetZ, mreal TetY=0)
C function: void mgl_rotate (HMGL gr, mreal TetX, mreal TetZ, mreal TetY)

Rotates a further plotting relative to each axis {x, z, y} consecutively on angles TetX, TetZ, TetY.

MGL command: rotate tet x y z
Method on mglGraph: void RotateN (mreal Tet, mreal x, mreal y, mreal z)
C function: void mgl_rotate_vector (HMGL gr, mreal Tet, mreal x, mreal y, mreal z)

Rotates a further plotting around vector {x, y, z} on angle Tet.

MGL command: shear sx sy
Method on mglGraph: void Shear (mreal sx, mreal sy)
C function: void mgl_shear (HMGL gr, mreal sx, mreal sy)

Shears a further plotting on values sx, sy.

MGL command: aspect ax ay [az=1]
Method on mglGraph: void Aspect (mreal Ax, mreal Ay, mreal Az=1)
C function: void mgl_aspect (HMGL gr, mreal Ax, mreal Ay, mreal Az)

Defines aspect ratio for the plot. The viewable axes will be related one to another as the ratio Ax:Ay:Az. For the best effect it should be used after rotate function. If Ax is NAN then function try to select optimal aspect ratio to keep equal ranges for x-y axis. At this, Ay will specify proportionality factor, or set to use automatic one if Ay=NAN.

Method on mglGraph: void Push ()
C function: void mgl_mat_push (HMGL gr)

Push transformation matrix into stack. Later you can restore its current state by Pop() function.

Method on mglGraph: void Pop ()
C function: void mgl_mat_pop (HMGL gr)

Pop (restore last ’pushed’) transformation matrix into stack.

Method on mglGraph: void SetPlotFactor (mreal val)
C function: void mgl_set_plotfactor (HMGL gr, mreal val)

Sets the factor of plot size. It is not recommended to set it lower then 1.5. This is some analogue of function Zoom() but applied not to overall image but for each InPlot. Use negative value or zero to enable automatic selection.

There are 3 functions View(), Zoom() and Perspective() which transform whole image. I.e. they act as secondary transformation matrix. They were introduced for rotating/zooming the whole plot by mouse. It is not recommended to call them for picture drawing.

MGL command: perspective val
Method on mglGraph: void Perspective (mreal a)
C function: void mgl_perspective (HMGL gr, mreal a)

Add (switch on) the perspective to plot. The parameter a = Depth/(Depth+dz) \in [0,1). By default (a=0) the perspective is off.

MGL command: view tetx tetz [tety=0]
Method on mglGraph: void View (mreal TetX, mreal TetZ, mreal TetY=0)
C function: void mgl_view (HMGL gr, mreal TetX, mreal TetZ, mreal TetY)

Rotates a further plotting relative to each axis {x, z, y} consecutively on angles TetX, TetZ, TetY. Rotation is done independently on rotate. Attention! this settings can not be overwritten by DefaultPlotParam(). Use Zoom(0,0,1,1) to return default view.

MGL command: zoom x1 y1 x2 y2
Method on mglGraph (C++, Python): void Zoom (mreal x1, mreal y1, mreal x2, mreal y2)
C function: void mgl_set_zoom (HMGL gr, mreal x1, mreal y1, mreal x2, mreal y2)

The function changes the scale of graphics that correspond to zoom in/out of the picture. After function call the current plot will be cleared and further the picture will contain plotting from its part [x1,x2]*[y1,y2]. Here picture coordinates x1, x2, y1, y2 changes from 0 to 1. Attention! this settings can not be overwritten by any other functions, including DefaultPlotParam(). Use Zoom(0,0,1,1) to return default view.

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4.5 Export picture

Functions in this group save or give access to produced picture. So, usually they should be called after plotting is done.

MGL command: setsize w h
Method on mglGraph: void SetSize (int width, int height, bool clear=true)
C function: void mgl_set_size (HMGL gr, int width, int height)
C function: void mgl_scale_size (HMGL gr, int width, int height)

Sets size of picture in pixels. This function should be called before any other plotting because it completely remove picture contents if clear=true. Function just clear pixels and scale all primitives if clear=false.

MGL command: setsizescl factor
Method on mglGraph: void SetSizeScl (double factor)
C function: void mgl_set_size_scl (HMGL gr, double factor)

Set factor for width and height in all further calls of setsize.

MGL command: quality [val=2]
Method on mglGraph: void SetQuality (int val=MGL_DRAW_NORM)
C function: void mgl_set_quality (HMGL gr, int val)

Sets quality of the plot depending on value val: MGL_DRAW_WIRE=0 – no face drawing (fastest), MGL_DRAW_FAST=1 – no color interpolation (fast), MGL_DRAW_NORM=2 – high quality (normal), MGL_DRAW_HIGH=3 – high quality with 3d primitives (arrows and marks); MGL_DRAW_LMEM=0x4 – direct bitmap drawing (low memory usage); MGL_DRAW_DOTS=0x8 – for dots drawing instead of primitives (extremely fast).

Method on mglGraph: int GetQuality ()
C function: int mgl_get_quality (HMGL gr)

Gets quality of the plot: MGL_DRAW_WIRE=0 – no face drawing (fastest), MGL_DRAW_FAST=1 – no color interpolation (fast), MGL_DRAW_NORM=2 – high quality (normal), MGL_DRAW_HIGH=3 – high quality with 3d primitives (arrows and marks); MGL_DRAW_LMEM=0x4 – direct bitmap drawing (low memory usage); MGL_DRAW_DOTS=0x8 – for dots drawing instead of primitives (extremely fast).

Method on mglGraph: void StartGroup (const char *name)
C function: void mgl_start_group (HMGL gr, const char *name)

Starts group definition. Groups contain objects and other groups, they are used to select a part of a model to zoom to or to make invisible or to make semitransparent and so on.

Method on mglGraph: void EndGroup ()
C function: void mgl_end_group (HMGL gr)

Ends group definition.

• Export to file:  
• Frames/Animation:  
• Bitmap in memory:  
• Parallelization:  

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4.5.1 Export to file

These functions export current view to a graphic file. The filename fname should have appropriate extension. Parameter descr gives the short description of the picture. Just now the transparency is supported in PNG, SVG, OBJ and PRC files.

MGL command: write ['fname'='']
Method on mglGraph: void WriteFrame (const char *fname="", const char *descr="")
C function: void mgl_write_frame (HMGL gr, const char *fname, const char *descr)

Exports current frame to a file fname which type is determined by the extension. Parameter descr adds description to file (can be ""). If fname="" then the file ‘frame####.jpg’ is used, where ‘####’ is current frame id and name ‘frame’ is defined by plotid class property.

Method on mglGraph: void WritePNG (const char *fname, const char *descr="", int compr="", bool alpha=true)
C function: void mgl_write_png (HMGL gr, const char *fname, const char *descr)
C function: void mgl_write_png_solid (HMGL gr, const char *fname, const char *descr)

Exports current frame to PNG file. Parameter fname specifies the file name, descr adds description to file, alpha gives the transparency type. By default there are no description added and semitransparent image used. This function does nothing if HAVE_PNG isn’t defined during compilation of MathGL library.

Method on mglGraph: void WriteJPEG (const char *fname, const char *descr="")
C function: void mgl_write_jpg (HMGL gr, const char *fname, const char *descr)

Exports current frame to JPEG file. Parameter fname specifies the file name, descr adds description to file. By default there is no description added. This function does nothing if HAVE_JPEG isn’t defined during compilation of MathGL library.

Method on mglGraph: void WriteGIF (const char *fname, const char *descr="")
C function: void mgl_write_gif (HMGL gr, const char *fname, const char *descr)

Exports current frame to GIF file. Parameter fname specifies the file name, descr adds description to file. By default there is no description added. This function does nothing if HAVE_GIF isn’t defined during compilation of MathGL library.

Method on mglGraph: void WriteBMP (const char *fname, const char *descr="")
C function: void mgl_write_bmp (HMGL gr, const char *fname, const char *descr)

Exports current frame to BMP file. Parameter fname specifies the file name, descr adds description to file. There is no compression used.

Method on mglGraph: void WriteTGA (const char *fname, const char *descr="")
C function: void mgl_write_tga (HMGL gr, const char *fname, const char *descr)

Exports current frame to TGA file. Parameter fname specifies the file name, descr adds description to file. There is no compression used.

Method on mglGraph: void WriteEPS (const char *fname, const char *descr="")
C function: void mgl_write_eps (HMGL gr, const char *fname, const char *descr)

Exports current frame to EPS file using vector representation. So it is not recommended for the export of large data plot. It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file. By default there is no description added. If file name is terminated by ‘z’ (for example, ‘fname.eps.gz’) then file will be compressed in gzip format. Note, that EPS format don’t support color interpolation, and the resulting plot will look as you use quality=1 for plotting.

Method on mglGraph: void WriteBPS (const char *fname, const char *descr="")
C function: void mgl_write_eps (HMGL gr, const char *fname, const char *descr)

Exports current frame to EPS file using bitmap representation. Parameter fname specifies the file name, descr adds description to file. By default there is no description added. If file name is terminated by ‘z’ (for example, ‘fname.eps.gz’) then file will be compressed in gzip format.

Method on mglGraph: void WriteSVG (const char *fname, const char *descr="")
C function: void mgl_write_svg (HMGL gr, const char *fname, const char *descr)

Exports current frame to SVG (Scalable Vector Graphics) file using vector representation. In difference of EPS format, SVG format support transparency that allows to correctly draw semitransparent plot (like surfa, surf3a or cloud). Note, the output file may be too large for graphic of large data array (especially for surfaces). It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file (default is file name). If file name is terminated by ‘z’ (for example, ‘fname.svgz’) then file will be compressed in gzip format. Note, that SVG format don’t support color interpolation, and the resulting plot will look as you use quality=1 for plotting.

Method on mglGraph: void WriteTEX (const char *fname, const char *descr="")
C function: void mgl_write_tex (HMGL gr, const char *fname, const char *descr)

Exports current frame to LaTeX (package Tikz/PGF) file using vector representation. Note, the output file may be too large for graphic of large data array (especially for surfaces). It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file (default is file name). Note, there is no text scaling now (for example, in subplots), what may produce miss-aligned labels.

Method on mglGraph: void WritePRC (const char *fname, const char *descr="", bool make_pdf=true)
C function: void mgl_write_prc (HMGL gr, const char *fname, const char *descr, int make_pdf)

Exports current frame to PRC file using vector representation (see http://en.wikipedia.org/wiki/PRC_%28file_format%29). Note, the output file may be too large for graphic of large data array (especially for surfaces). It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file (default is file name). If parameter make_pdf=true and PDF was enabled at MathGL configure then corresponding PDF file with 3D image will be created.

Method on mglGraph: void WriteOBJ (const char *fname, const char *descr="")
C function: void mgl_write_obj (HMGL gr, const char *fname, const char *descr)

Exports current frame to OBJ/MTL file using vector representation (see OBJ format for details). Note, the output file may be too large for graphic of large data array (especially for surfaces). It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file (default is file name).

Method on mglGraph: void WriteXYZ (const char *fname, const char *descr="")
C function: void mgl_write_xyz (HMGL gr, const char *fname, const char *descr)

Exports current frame to XYZ/XYZL/XYZF files using vector representation (see XYZ format for details). Note, the output file may be too large for graphic of large data array (especially for surfaces). It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file (default is file name).

Method on mglGraph: void WriteSTL (const char *fname, const char *descr="")
C function: void mgl_write_stl (HMGL gr, const char *fname, const char *descr)

Exports current frame to STL file using vector representation (see STL format for details). Note, the output file may be too large for graphic of large data array (especially for surfaces). It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file (default is file name.

Method on mglGraph: void WriteOFF (const char *fname, const char *descr="", bool colored=false)
C function: void mgl_write_off (HMGL gr, const char *fname, const char *descr, bool colored)

Exports current frame to OFF file using vector representation (see OFF format for details). Note, the output file may be too large for graphic of large data array (especially for surfaces). It is better to use bitmap format (for example PNG or JPEG). However, program has no internal limitations for size of output file. Parameter fname specifies the file name, descr adds description to file (default is file name).

Method on mglGraph: void ShowImage (const char *viewer, bool nowait=false)
C function: void mgl_show_image (const char *viewer, int nowait)

Displays the current picture using external program viewer for viewing. The function save the picture to temporary file and call viewer to display it. If nowait=true then the function return immediately (it will not wait while window will be closed).

Method on mglGraph: void WriteJSON (const char *fname, const char *descr="")
C function: void mgl_write_json (HMGL gr, const char *fname, const char *descr)

Exports current frame to textual file using JSON format. Later this file can be used for faster loading and viewing by JavaScript script. Parameter fname specifies the file name, descr adds description to file.

Method on mglGraph: void ExportMGLD (const char *fname, const char *descr="")
C function: void mgl_export_mgld (HMGL gr, const char *fname, const char *descr)

Exports points and primitives in file using MGLD format. Later this file can be used for faster loading and viewing by mglview utility. Parameter fname specifies the file name, descr adds description to file (default is file name).

Method on mglGraph: void ImportMGLD (const char *fname, bool add=false)
C function: void mgl_import_mgld (HMGL gr, const char *fname, int add)

Imports points and primitives in file using MGLD format. Later this file can be used for faster loading and viewing by mglview utility. Parameter fname specifies the file name, add sets to append or replace primitives to existed ones.

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4.5.2 Frames/Animation

These functions provide ability to create several pictures simultaneously. For most of cases it is useless but for widget classes (see Widget classes) they can provide a way to show animation. Also you can write several frames into animated GIF file.

Method on mglGraph: void NewFrame ()
C function: void mgl_new_frame (HMGL gr)

Creates new frame. Function returns current frame id. This is not thread safe function in OpenGL mode! Use direct list creation in multi-threading drawing. The function EndFrame() must be call after the finishing of the frame drawing for each call of this function.

Method on mglGraph: void EndFrame ()
C function: void mgl_end_frame (HMGL gr)

Finishes the frame drawing.

Method on mglGraph: int GetNumFrame ()
C function: int mgl_get_num_frame (HMGL gr)

Gets the number of created frames.

Method on mglGraph: void SetFrame (int i)
C function: void mgl_set_frame (HMGL gr, int i)

Finishes the frame drawing and sets drawing data to frame i, which should be in range [0, GetNumFrame()-1]. This function is similar to EndFrame() but don’t add frame to the GIF image.

Method on mglGraph: void GetFrame (int i)
C function: void mgl_get_frame (HMGL gr, int i)

Replaces drawing data by one from frame i. Function work if MGL_VECT_FRAME is set on (by default).

Method on mglGraph: void ShowFrame (int i)
C function: void mgl_show_frame (HMGL gr, int i)

Appends drawing data from frame i to current one. Function work if MGL_VECT_FRAME is set on (by default).

Method on mglGraph: void DelFrame (int i)
C function: void mgl_del_frame (HMGL gr, int i)

Deletes drawing data for frame i and shift all later frame indexes. Function work if MGL_VECT_FRAME is set on (by default). Do nothing in OpenGL mode.

Method on mglGraph: void ResetFrames ()
C function: void mgl_reset_frames (HMGL gr)

Reset frames counter (start it from zero).

Method on mglGraph: void ClearFrame (int i)
C function: void mgl_clear_frame (HMGL gr, int i)

Clear list of primitives for current drawing.

Method on mglGraph: void StartGIF (const char *fname, int ms=100)
C function: void mgl_start_gif (HMGL gr, const char *fname, int ms)

Start writing frames into animated GIF file fname. Parameter ms set the delay between frames in milliseconds. You should not change the picture size during writing the cinema. Use CloseGIF() to finalize writing. Note, that this function is disabled in OpenGL mode.

Method on mglGraph: void CloseGIF ()
C function: void mgl_close_gif (HMGL gr)

Finish writing animated GIF and close connected pointers.

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4.5.3 Bitmap in memory

These functions return the created picture (bitmap), its width and height. You may display it by yourself in any graphical library (see also, Widget classes) or save in file (see also, Export to file).

Method on mglGraph: const unsigned char * GetRGB ()
Method on mglGraph: void GetRGB (char *buf, int size)
Method on mglGraph: void GetBGRN (char *buf, int size)
C function: const unsigned char * mgl_get_rgb (HMGL gr)

Gets RGB bitmap of the current state of the image. Format of each element of bits is: {red, green, blue}. Number of elements is Width*Height. Position of element {i,j} is [3*i + 3*Width*j] (or is [4*i + 4*Width*j] for GetBGRN()). You have to provide the proper size of the buffer, buf, i.e. the code for Python should look like 

from mathgl import *
gr = mglGraph();
bits='\t';
bits=bits.expandtabs(4*gr.GetWidth()*gr.GetHeight());
gr.GetBGRN(bits, len(bits));
Method on mglGraph: const unsigned char * GetRGBA ()
Method on mglGraph: void GetRGBA (char *buf, int size)
C function: const unsigned char * mgl_get_rgba (HMGL gr)

Gets RGBA bitmap of the current state of the image. Format of each element of bits is: {red, green, blue, alpha}. Number of elements is Width*Height. Position of element {i,j} is [4*i + 4*Width*j].

Method on mglGraph: int GetWidth ()
Method on mglGraph: int GetHeight ()
C function: int mgl_get_width (HMGL gr)
C function: int mgl_get_height (HMGL gr)

Gets width and height of the image.

Method on mglGraph: mglPoint CalcXYZ (int xs, int ys)
C function: void mgl_calc_xyz (HMGL gr, int xs, int ys, mreal *x, mreal *y, mreal *z)

Calculate 3D coordinate {x,y,z} for screen point {xs,ys}. At this moment it ignore perspective and transformation formulas (curvilinear coordinates). The calculation are done for the last used InPlot (see Subplots and rotation).

Method on mglGraph: mglPoint CalcScr (mglPoint p)
C function: void mgl_calc_scr (HMGL gr, mreal x, mreal y, mreal z, int *xs, int *ys)

Calculate screen point {xs,ys} for 3D coordinate {x,y,z}. The calculation are done for the last used InPlot (see Subplots and rotation).

Method on mglGraph: void SetObjId (int id)
C function: void mgl_set_obj_id (HMGL gr, int id)

Set the numeric id for object or subplot/inplot.

Method on mglGraph: int GetObjId (int xs, int ys)
C function: int mgl_get_obj_id (HMGL gr, int xs, int ys)

Get the numeric id for most upper object at pixel {xs, ys} of the picture.

Method on mglGraph: int GetSplId (int xs, int ys)
C function: int mgl_get_spl_id (HMGL gr, int xs, int ys)

Get the numeric id for most subplot/inplot at pixel {xs, ys} of the picture.

Method on mglGraph: void Highlight (int id)
C function: void mgl_highlight (HMGL gr, int id)

Highlight the object with given id.

Method on mglGraph: long IsActive (int xs, int ys, int d=1)
C function: long mgl_is_active (HMGL gr, int xs, int ys, int d)

Checks if point {xs, ys} is close to one of active point (i.e. mglBase::Act) with accuracy d and return its index or -1 if not found. Active points are special points which characterize primitives (like edges and so on). This function for advanced users only.

Method on mglGraph: long SetDrawReg (int nx=1, int ny=1, int m=0)
C function: long mgl_set_draw_reg (HMGL gr, int nx, int ny, int m)

Limits drawing region by rectangular area of m-th cell of matrix with sizes nx*ny (like in subplot). This function can be used to update only small region of the image for purposes of higher speed. This function for advanced users only.

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4.5.4 Parallelization

Many of things MathGL do in parallel by default (if MathGL was built with pthread). However, there is function which set the number of threads to be used.

C function: int mgl_set_num_thr (int n)

Set the number of threads to be used by MathGL. If n<1 then the number of threads is set as maximal number of processors (cores). If n=1 then single thread will be used (this is default if pthread was disabled).

Another option is combining bitmap image (taking into account Z-ordering) from different instances of mglGraph. This method is most appropriate for computer clusters when the data size is so large that it exceed the memory of single computer node.

Method on mglGraph: int Combine (const mglGraph *g)
C function: int mgl_combine_gr (HMGL gr, HMGL g)

Combine drawing from instance g with gr (or with this) taking into account Z-ordering of pixels. The width and height of both instances must be the same.

Method on mglGraph: int MPI_Send (int id)
C function: int mgl_mpi_send (HMGL gr, int id)

Send graphical information from node id using MPI. The width and height in both nodes must be the same.

Method on mglGraph: int MPI_Recv (int id)
C function: int mgl_mpi_send (HMGL gr, int id)

Receive graphical information from node id using MPI. The width and height in both nodes must be the same.

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4.6 Background

These functions change background image.

MGL command: clf ['col']
Method on mglGraph: void Clf ()
Method on mglGraph: void Clf (const char * col)
Method on mglGraph: void Clf (char col)
Method on mglGraph: void Clf (mreal r, mreal g, mreal b)
C function: void mgl_clf (HMGL gr)
C function: void mgl_clf_str (HMGL gr, const char * col)
C function: void mgl_clf_chr (HMGL gr, char col)
C function: void mgl_clf_rgb (HMGL gr, mreal r, mreal g, mreal b)

Clear the picture and fill background by specified color.

MGL command: rasterize
Method on mglGraph: void Rasterize ()
C function: void mgl_rasterize (HMGL gr)

Force drawing the plot and use it as background. After it, function clear the list of primitives, like clf. This function is useful if you want save part of plot as bitmap one (for example, large surfaces, isosurfaces or vector fields) and keep some parts as vector one (like annotation, curves, axis and so on).

MGL command: background 'fname' [alpha=1]
Method on mglGraph: void LoadBackground (const char * fname, double alpha=1)
C function: void mgl_load_background (HMGL gr, const char * fname, double alpha)

Load PNG or JPEG file fname as background for the plot. Parameter alpha manually set transparency of the background.

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4.7 Primitives

These functions draw some simple objects like line, point, sphere, drop, cone and so on. See Using primitives, for sample code and picture.

MGL command: ball x y ['col'='r.']
MGL command: ball x y z ['col'='r.']
Method on mglGraph: void Ball (mglPoint p, char col='r')
Method on mglGraph: void Mark (mglPoint p, const char *mark)
C function: void mgl_mark (HMGL gr, mreal x, mreal y, mreal z, const char *mark)

Draws a mark (point ‘.’ by default) at position p={x, y, z} with color col.

MGL command: errbox x y ex ey ['stl'='']
MGL command: errbox x y z ex ey ez ['stl'='']
Method on mglGraph: void Error (mglPoint p, mglPoint e, char *stl="")
C function: void mgl_error_box (HMGL gr, mreal x, mreal y, mreal z, mreal ex, mreal ey, mreal ez, char *stl)

Draws a 3d error box at position p={x, y, z} with sizes e={ex, ey, ez} and style stl. Use NAN for component of e to reduce number of drawn elements.

MGL command: line x1 y1 x2 y2 ['stl'='']
MGL command: line x1 y1 z1 x2 y2 z2 ['stl'='']
Method on mglGraph: void Line (mglPoint p1, mglPoint p2, char *stl="B", int num=2)
C function: void mgl_line (HMGL gr, mreal x1, mreal y1, mreal z1, mreal x2, mreal y2, mreal z2, char *stl, int num)

Draws a geodesic line (straight line in Cartesian coordinates) from point p1 to p2 using line style stl. Parameter num define the “quality” of the line. If num=2 then the stright line will be drawn in all coordinate system (independently on transformation formulas (see Curved coordinates). Contrary, for large values (for example, =100) the geodesic line will be drawn in corresponding coordinate system (straight line in Cartesian coordinates, circle in polar coordinates and so on). Line will be drawn even if it lies out of bounding box.

MGL command: curve x1 y1 dx1 dy1 x2 y2 dx2 dy2 ['stl'='']
MGL command: curve x1 y1 z1 dx1 dy1 dz1 x2 y2 z2 dx2 dy2 dz2 ['stl'='']
Method on mglGraph: void Curve (mglPoint p1, mglPoint d1, mglPoint p2, mglPoint d2, const char *stl="B", int num=100)
C function: void mgl_curve (HMGL gr, mreal x1, mreal y1, mreal z1, mreal dx1, mreal dy1, mreal dz1, mreal x2, mreal y2, mreal z2, mreal dx2, mreal dy2, mreal dz2, const char *stl, int num)

Draws Bezier-like curve from point p1 to p2 using line style stl. At this tangent is codirected with d1, d2 and proportional to its amplitude. Parameter num define the “quality” of the curve. If num=2 then the straight line will be drawn in all coordinate system (independently on transformation formulas, see Curved coordinates). Contrary, for large values (for example, =100) the spline like Bezier curve will be drawn in corresponding coordinate system. Curve will be drawn even if it lies out of bounding box.

MGL command: face x1 y1 x2 y2 x3 y3 x4 y4 ['stl'='']
MGL command: face x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4 ['stl'='']
Method on mglGraph: void Face (mglPoint p1, mglPoint p2, mglPoint p3, mglPoint p4, const char *stl="w")
C function: void mgl_face (HMGL gr, mreal x1, mreal y1, mreal z1, mreal x2, mreal y2, mreal z2, mreal x3, mreal y3, mreal z3, mreal x4, mreal y4, mreal z4, const char *stl)

Draws the solid quadrangle (face) with vertexes p1, p2, p3, p4 and with color(s) stl. At this colors can be the same for all vertexes or different if all 4 colors are specified for each vertex. Face will be drawn even if it lies out of bounding box.

MGL command: rect x1 y1 x2 y2 ['stl'='']
MGL command: rect x1 y1 z1 x2 y2 z2 ['stl'='']

Draws the solid rectangle (face) with vertexes {x1, y1, z1} and {x2, y2, z2} with color stl. At this colors can be the same for all vertexes or separately if all 4 colors are specified for each vertex. Face will be drawn even if it lies out of bounding box.

MGL command: facex x0 y0 z0 wy wz ['stl'='' d1=0 d2=0]
MGL command: facey x0 y0 z0 wx wz ['stl'='' d1=0 d2=0]
MGL command: facez x0 y0 z0 wx wy ['stl'='' d1=0 d2=0]
Method on mglGraph: void FaceX (mreal x0, mreal y0, mreal z0, mreal wy, mreal wz, const char *stl="w", mreal d1=0, mreal d2=0)
Method on mglGraph: void FaceY (mreal x0, mreal y0, mreal z0, mreal wx, mreal wz, const char *stl="w", mreal d1=0, mreal d2=0)
Method on mglGraph: void FaceZ (mreal x0, mreal y0, mreal z0, mreal wx, mreal wy, const char *stl="w", mreal d1=0, mreal d2=0)
C function: void mgl_facex (HMGL gr, mreal x0, mreal y0, mreal z0, mreal wy, mreal wz, const char *stl, mreal d1, mreal d2)
C function: void mgl_facey (HMGL gr, mreal x0, mreal y0, mreal z0, mreal wx, mreal wz, const char *stl, mreal d1, mreal d2)
C function: void mgl_facez (HMGL gr, mreal x0, mreal y0, mreal z0, mreal wx, mreal wy, const char *stl, mreal d1, mreal d2)

Draws the solid rectangle (face) perpendicular to [x,y,z]-axis correspondingly at position {x0, y0, z0} with color stl and with widths wx, wy, wz along corresponding directions. At this colors can be the same for all vertexes or separately if all 4 colors are specified for each vertex. Parameters d1!=0, d2!=0 set additional shift of the last vertex (i.e. to draw quadrangle). Face will be drawn even if it lies out of bounding box.

MGL command: sphere x0 y0 r ['col'='r']
MGL command: sphere x0 y0 z0 r ['col'='r']
Method on mglGraph: void Sphere (mglPoint p, mreal r, const char *stl="r")
C function: void mgl_sphere (HMGL gr, mreal x0, mreal y0, mreal z0, mreal r, const char *stl)

Draw the sphere with radius r and center at point p={x0, y0, z0} and color stl.

MGL command: drop x0 y0 dx dy r ['col'='r' sh=1 asp=1]
MGL command: drop x0 y0 z0 dx dy dz r ['col'='r' sh=1 asp=1]
Method on mglGraph: void Drop (mglPoint p, mglPoint d, mreal r, const char *col="r", mreal shift=1, mreal ap=1)
C function: void mgl_drop (HMGL gr, mreal x0, mreal y0, mreal z0, mreal dx, mreal dy, mreal dz, mreal r, const char *col, mreal shift, mreal ap)

Draw the drop with radius r at point p elongated in direction d and with color col. Parameter shift set the degree of drop oblongness: ‘0’ is sphere, ‘1’ is maximally oblongness drop. Parameter ap set relative width of the drop (this is analogue of “ellipticity” for the sphere).

MGL command: cone x1 y1 z1 x2 y2 z2 r1 [r2=-1 'stl'='']
Method on mglGraph: void Cone (mglPoint p1, mglPoint p2, mreal r1, mreal r2=-1, const char *stl="B")
C function: void mgl_cone (HMGL gr, mreal x1, mreal y1, mreal z1, mreal x2, mreal y2, mreal z2, mreal r1, mreal r2, const char *stl)

Draw tube (or truncated cone if edge=false) between points p1, p2 with radius at the edges r1, r2. If r2<0 then it is supposed that r2=r1. The cone color is defined by string stl. Parameter stl can contain:

MGL command: circle x0 y0 r ['col'='r']
MGL command: circle x0 y0 z0 r ['col'='r']
Method on mglGraph: void Circle (mglPoint p, mreal r, const char *stl="r")

Draw the circle with radius r and center at point p={x0, y0, z0}. Parameter col may contain

MGL command: ellipse x1 y1 x2 y2 r ['col'='r']
MGL command: ellipse x1 y1 z1 x2 y2 z2 r ['col'='r']
Method on mglGraph: void Ellipse (mglPoint p1, mglPoint p2, mreal r, const char *col="r")
C function: void mgl_ellipse (HMGL gr, mreal x1, mreal y1, mreal z1, mreal x2, mreal y2, mreal z2, mreal r, const char *col)

Draw the ellipse with radius r and focal points p1, p2. Parameter col may contain

MGL command: rhomb x1 y1 x2 y2 r ['col'='r']
MGL command: rhomb x1 y1 z1 x2 y2 z2 r ['col'='r']
Method on mglGraph: void Rhomb (mglPoint p1, mglPoint p2, mreal r, const char *col="r")
C function: void mgl_rhomb (HMGL gr, mreal x1, mreal y1, mreal z1, mreal x2, mreal y2, mreal z2, mreal r, const char *col)

Draw the rhombus with width r and edge points p1, p2. Parameter col may contain

MGL command: arc x0 y0 x1 y1 a ['col'='r']
MGL command: arc x0 y0 z0 x1 y1 a ['col'='r']
MGL command: arc x0 y0 z0 xa ya za x1 y1 z1 a ['col'='r']
Method on mglGraph: void Arc (mglPoint p0, mglPoint p1, mreal a, const char *col="r")
Method on mglGraph: void Arc (mglPoint p0, mglPoint pa, mglPoint p1, mreal a, const char *col="r")
C function: void mgl_arc (HMGL gr, mreal x0, mreal y0, mreal x1, mreal y1, mreal a, const char *col)
C function: void mgl_arc_ext (HMGL gr, mreal x0, mreal y0, mreal z0, mreal xa, mreal ya, mreal za, mreal x1, mreal y1, mreal z1, mreal a, const char *col)

Draw the arc around axis pa (default is z-axis pa={0,0,1}) with center at p0 and starting from point p1. Parameter a set the angle of arc in degree. Parameter col may contain color of the arc and arrow style for arc edges.

MGL command: polygon x0 y0 x1 y1 num ['col'='r']
MGL command: polygon x0 y0 z0 x1 y1 z1 num ['col'='r']
Method on mglGraph: void Polygon (mglPoint p0, mglPoint p1, int num, const char *col="r")
C function: void mgl_polygon (HMGL gr, mreal x0, mreal y0, mreal z0, mreal x1, mreal y1, mreal z1, int num, const char *col)

Draw the polygon with num edges starting from p1. The center of polygon is located in p0. Parameter col may contain

MGL command: logo 'fname' [smooth=off]
Method on mglGraph: void Logo (const char *fname, bool smooth=false, const char *opt="")
Method on mglGraph: void Logo (long w, long h, const unsigned char *rgba, bool smooth=false, const char *opt="")
C function only: void mgl_logo (HMGL gr, long w, long h, const unsigned char *rgba, bool smooth, const char *opt)
C function: void mgl_logo_file (HMGL gr, const char *fname, bool smooth, const char *opt)

Draw bitmap (logo) along whole axis range, which can be changed by Command options. Bitmap can be loaded from file or specified as RGBA values for pixels. Parameter smooth set to draw bitmap without or with color interpolation.

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4.8 Text printing

These functions draw the text. There are functions for drawing text in arbitrary place, in arbitrary direction and along arbitrary curve. MathGL can use arbitrary font-faces and parse many TeX commands (for more details see Font styles). All these functions have 2 variant: for printing 8-bit text (char *) and for printing Unicode text (wchar_t *). In first case the conversion into the current locale is used. So sometimes you need to specify it by setlocale() function. The size argument control the size of text: if positive it give the value, if negative it give the value relative to SetFontSize(). The font type (STIX, arial, courier, times and so on) can be selected by function LoadFont(). See Font settings.

The font parameters are described by string. This string may set the text color ‘wkrgbcymhRGBCYMHW’ (see Color styles). Starting from MathGL v.2.3, you can set color gradient for text (see Color scheme). Also, after delimiter symbol ‘:’, it can contain characters of font type (‘rbiwou’) and/or align (‘LRCTV’) specification. The font types are: ‘r’ – roman (or regular) font, ‘i’ – italic style, ‘b’ – bold style, ‘w’ – wired style, ‘o’ – over-lined text, ‘u’ – underlined text. By default roman font is used. The align types are: ‘L’ – align left (default), ‘C’ – align center, ‘R’ – align right, ‘T’ – align under, ‘V’ – align center vertical. For example, string ‘b:iC’ correspond to italic font style for centered text which printed by blue color.

If string contains symbols ‘aA’ then text is printed at absolute position {x, y} (supposed to be in range [0,1]) of picture (for ‘A’) or subplot/inplot (for ‘a’). If string contains symbol ‘@’ then box around text is drawn.

See Text features, for sample code and picture.

MGL command: text x y 'text' ['fnt'='' size=-1]
MGL command: text x y z 'text' ['fnt'='' size=-1]
Method on mglGraph: void Puts (mglPoint p, const char *text, const char *fnt=":C", mreal size=-1)
Method on mglGraph: void Putsw (mglPoint p, const wchar_t *text, const char *fnt=":C", mreal size=-1)
Method on mglGraph: void Puts (mreal x, mreal y, const char *text, const char *fnt=":AC", mreal size=-1)
Method on mglGraph: void Putsw (mreal x, mreal y, const wchar_t *text, const char *fnt=":AC", mreal size=-1)
C function: void mgl_puts (HMGL gr, mreal x, mreal y, mreal z, const char *text, const char *fnt, mreal size)
C function: void mgl_putsw (HMGL gr, mreal x, mreal y, mreal z, const wchar_t *text, const char *fnt, mreal size)

The function plots the string text at position p with fonts specifying by the criteria fnt. The size of font is set by size parameter (default is -1).

MGL command: text x y dx dy 'text' ['fnt'=':L' size=-1]
MGL command: text x y z dx dy dz 'text' ['fnt'=':L' size=-1]
Method on mglGraph: void Puts (mglPoint p, mglPoint d, const char *text, const char *fnt=":L", mreal size=-1)
Method on mglGraph: void Putsw (mglPoint p, mglPoint d, const wchar_t *text, const char *fnt=":L", mreal size=-1)
C function: void mgl_puts_dir (HMGL gr, mreal x, mreal y, mreal z, mreal dx, mreal dy, mreal dz, const char *text, const char *fnt, mreal size)
C function: void mgl_putsw_dir (HMGL gr, mreal x, mreal y, mreal z, mreal dx, mreal dy, mreal dz, const wchar_t *text, const char *fnt, mreal size)

The function plots the string text at position p along direction d with specified size. Parameter fnt set text style and text position: under (‘T’) or above (‘t’) the line.

MGL command: fgets x y 'fname' [n=0 'fnt'='' size=-1.4]
MGL command: fgets x y z 'fname' [n=0 'fnt'='' size=-1.4]

Draws unrotated n-th line of file fname at position {x,y,z} with specified size. By default parameters from font command are used.

MGL command: text ydat 'text' ['fnt'='']
MGL command: text xdat ydat 'text' ['fnt'='']
MGL command: text xdat ydat zdat 'text' ['fnt'='']
Method on mglGraph: void Text (const mglDataA &y, const char *text, const char *fnt="", const char *opt="")
Method on mglGraph: void Text (const mglDataA &y, const wchar_t *text, const char *fnt="", const char *opt="")
Method on mglGraph: void Text (const mglDataA &x, const mglDataA &y, const char *text, const char *fnt="", const char *opt="")
Method on mglGraph: void Text (const mglDataA &x, const mglDataA &y, const wchar_t *text, const char *fnt="", const char *opt="")
Method on mglGraph: void Text (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *text, const char *fnt="", const char *opt="")
Method on mglGraph: void Text (const mglDataA &x, const mglDataA &y, const mglDataA &z, const wchar_t *text, const char *fnt="", const char *opt="")
C function: void mgl_text_y (HMGL gr, HCDT y, const char *text, const char *fnt, const char *opt)
C function: void mgl_textw_y (HMGL gr, HCDT y, const wchar_t *text, const char *fnt, const char *opt)
C function: void mgl_text_xy (HCDT x, HCDT y, const char *text, const char *fnt, const char *opt)
C function: void mgl_textw_xy (HCDT x, HCDT y, const wchar_t *text, const char *fnt, const char *opt)
C function: void mgl_text_xyz (HCDT x, HCDT y, HCDT z, const char *text, const char *fnt, const char *opt)
C function: void mgl_textw_xyz (HCDT x, HCDT y, HCDT z, const wchar_t *text, const char *fnt, const char *opt)

The function draws text along the curve between points {x[i], y[i], z[i]} by font style fnt. The string fnt may contain symbols ‘t’ for printing the text under the curve (default), or ‘T’ for printing the text under the curve. The sizes of 1st dimension must be equal for all arrays x.nx=y.nx=z.nx. If array x is not specified then its an automatic array is used with values equidistantly distributed in x-axis range (see Ranges (bounding box)). If array z is not specified then z[i] equal to minimal z-axis value is used. String opt contain command options (see Command options).

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4.9 Axis and Colorbar

These functions draw the “things for measuring”, like axis with ticks, colorbar with ticks, grid along axis, bounding box and labels for axis. For more information see Axis settings.

MGL command: axis ['dir'='xyz' 'stl'='']
Method on mglGraph: void Axis (const char *dir="xyz", const char *stl="", const char *opt="")
C function: void mgl_axis (HMGL gr, const char *dir, const char *stl, const char *opt)

Draws axes with ticks (see Axis settings). Parameter dir may contain:

Styles of ticks and axis can be overrided by using stl string. Option value set the manual rotation angle for the ticks. See Axis and ticks, for sample code and picture.

MGL command: colorbar ['sch'='']
Method on mglGraph: void Colorbar (const char *sch="")
C function: void mgl_colorbar (HMGL gr, const char *sch)

Draws colorbar. Parameter sch may contain:

See Colorbars, for sample code and picture.

MGL command: colorbar vdat ['sch'='']
Method on mglGraph: void Colorbar (const mglDataA &v, const char *sch="")
C function: void mgl_colorbar_val (HMGL gr, HCDT v, const char *sch)

The same as previous but with sharp colors sch (current palette if sch="") for values v. See ContD sample, for sample code and picture.

MGL command: colorbar 'sch' x y [w=1 h=1]
Method on mglGraph: void Colorbar (const char *sch, mreal x, mreal y, mreal w=1, mreal h=1)
C function: void mgl_colorbar_ext (HMGL gr, const char *sch, mreal x, mreal y, mreal w, mreal h)

The same as first one but at arbitrary position of subplot {x, y} (supposed to be in range [0,1]). Parameters w, h set the relative width and height of the colorbar.

MGL command: colorbar vdat 'sch' x y [w=1 h=1]
Method on mglGraph: void Colorbar (const mglDataA &v, const char *sch, mreal x, mreal y, mreal w=1, mreal h=1)
C function: void mgl_colorbar_val_ext (HMGL gr, HCDT v, const char *sch, mreal x, mreal y, mreal w, mreal h)

The same as previous but with sharp colors sch (current palette if sch="") for values v. See ContD sample, for sample code and picture.

MGL command: grid ['dir'='xyz' 'pen'='B']
Method on mglGraph: void Grid (const char *dir="xyz", const char *pen="B", const char *opt="")
C function: void mgl_axis_grid (HMGL gr, const char *dir, const char *pen, const char *opt)

Draws grid lines perpendicular to direction determined by string parameter dir. If dir contain ‘!’ then grid lines will be drawn at coordinates of subticks also. The step of grid lines is the same as tick step for axis. The style of lines is determined by pen parameter (default value is dark blue solid line ‘B-’).

MGL command: box ['stl'='k' ticks=on]
Method on mglGraph: void Box (const char *col="", bool ticks=true)
C function: void mgl_box (HMGL gr, int ticks)
C function: void mgl_box_str (HMGL gr, const char *col, int ticks)

Draws bounding box outside the plotting volume with color col. If col contain ‘@’ then filled faces are drawn. At this first color is used for faces (default is light yellow), last one for edges. See Bounding box, for sample code and picture.

MGL command: xlabel 'text' [pos=1]
MGL command: ylabel 'text' [pos=1]
MGL command: zlabel 'text' [pos=1]
MGL command: tlabel 'text' [pos=1]
Method on mglGraph: void Label (char dir, const char *text, mreal pos=1, const char *opt="")
Method on mglGraph: void Label (char dir, const wchar_t *text, mreal pos=1, const char *opt="")
C function: void mgl_label (HMGL gr, char dir, const char *text, mreal pos, const char *opt)
C function: void mgl_labelw (HMGL gr, char dir, const wchar_t *text, mreal pos, const char *opt)

Prints the label text for axis dir=‘x’,‘y’,‘z’,‘t’ (here ‘t’ is “ternary” axis t=1-x-y). The position of label is determined by pos parameter. If pos=0 then label is printed at the center of axis. If pos>0 then label is printed at the maximum of axis. If pos<0 then label is printed at the minimum of axis. Option value set additional shifting of the label. See Text printing.

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4.10 Legend

These functions draw legend to the graph (useful for 1D plotting). Legend entry is a pair of strings: one for style of the line, another one with description text (with included TeX parsing). The arrays of strings may be used directly or by accumulating first to the internal arrays (by function addlegend) and further plotting it. The position of the legend can be selected automatic or manually (even out of bounding box). Parameters fnt and size specify the font style and size (see Font settings). Parameter llen set the relative width of the line sample and the text indent. If line style string for entry is empty then the corresponding text is printed without indent. Parameter fnt may contain:

See Legend sample, for sample code and picture.

MGL command: legend [pos=3 'fnt'='#']
Method on mglGraph: void Legend (int pos=0x3, const char *fnt="#", const char *opt="")
C function: void mgl_legend (HMGL gr, int pos, const char *fnt, const char *opt)

Draws legend of accumulated legend entries by font fnt with size. Parameter pos sets the position of the legend: ‘0’ is bottom left corner, ‘1’ is bottom right corner, ‘2’ is top left corner, ‘3’ is top right corner (is default). Option value set the space between line samples and text (default is 0.1).

MGL command: legend x y ['fnt'='#']
Method on mglGraph: void Legend (mreal x, mreal y, const char *fnt="#", const char *opt="")
C function: void mgl_legend_pos (HMGL gr, mreal x, mreal y, const char *fnt, const char *opt)

Draws legend of accumulated legend entries by font fnt with size. Position of legend is determined by parameter x, y which supposed to be normalized to interval [0,1]. Option value set the space between line samples and text (default is 0.1).

MGL command: addlegend 'text' 'stl'
Method on mglGraph: void AddLegend (const char *text, const char *style)
Method on mglGraph: void AddLegend (const wchar_t *text, const char *style)
C function: void mgl_add_legend (HMGL gr, const char *text, const char *style)
C function: void mgl_add_legendw (HMGL gr, const wchar_t *text, const char *style)

Adds string text to internal legend accumulator. The style of described line and mark is specified in string style (see Line styles).

MGL command: clearlegend
Method on mglGraph: void ClearLegend ()
C function: void mgl_clear_legend (HMGL gr)

Clears saved legend strings.

MGL command: legendmarks val
Method on mglGraph: void SetLegendMarks (int num)
C function: void mgl_set_legend_marks (HMGL gr, int num)

Set the number of marks in the legend. By default 1 mark is used.

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4.11 1D plotting

These functions perform plotting of 1D data. 1D means that data depended from only 1 parameter like parametric curve {x[i],y[i],z[i]}, i=1...n. By default (if absent) values of x[i] are equidistantly distributed in axis range, and z[i] equal to minimal z-axis value. The plots are drawn for each row if one of the data is the matrix. By any case the sizes of 1st dimension must be equal for all arrays x.nx=y.nx=z.nx.

String pen specifies the color and style of line and marks (see Line styles). By default (pen="") solid line with color from palette is used (see Palette and colors). Symbol ‘!’ set to use new color from palette for each point (not for each curve, as default). String opt contain command options (see Command options). See 1D samples, for sample code and picture.

MGL command: plot ydat ['stl'='']
MGL command: plot xdat ydat ['stl'='']
MGL command: plot xdat ydat zdat ['stl'='']
Method on mglGraph: void Plot (const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Plot (const mglDataA &x, const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Plot (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_plot (HMGL gr, HCDT y, const char *pen, const char *opt)
C function: void mgl_plot_xy (HMGL gr, HCDT x, HCDT y, const char *pen, const char *opt)
C function: void mgl_plot_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *pen, const char *opt)

These functions draw continuous lines between points {x[i], y[i], z[i]}. See also area, step, stem, tube, mark, error, belt, tens, tape. See Plot sample, for sample code and picture.

MGL command: radar adat ['stl'='']
Method on mglGraph: void Radar (const mglDataA &a, const char *pen="", const char *opt="")
C function: void mgl_radar (HMGL gr, HCDT a, const char *pen, const char *opt)

This functions draws radar chart which is continuous lines between points located on an radial lines (like plot in Polar coordinates). Option value set the additional shift of data (i.e. the data a+value is used instead of a). If value<0 then r=max(0, -min(value). If pen containt ‘#’ symbol then "grid" (radial lines and circle for r) is drawn. See also plot. See Radar sample, for sample code and picture.

MGL command: step ydat ['stl'='']
MGL command: step xdat ydat ['stl'='']
MGL command: step xdat ydat zdat ['stl'='']
Method on mglGraph: void Step (const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Step (const mglDataA &x, const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Step (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_step (HMGL gr, HCDT y, const char *pen, const char *opt)
C function: void mgl_step_xy (HMGL gr, HCDT x, HCDT y, const char *pen, const char *opt)
C function: void mgl_step_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *pen, const char *opt)

These functions draw continuous stairs for points to axis plane. See also plot, stem, tile, boxs. See Step sample, for sample code and picture.

MGL command: tens ydat cdat ['stl'='']
MGL command: tens xdat ydat cdat ['stl'='']
MGL command: tens xdat ydat zdat cdat ['stl'='']
Method on mglGraph: void Tens (const mglDataA &y, const mglDataA &c, const char *pen="", const char *opt="")
Method on mglGraph: void Tens (const mglDataA &x, const mglDataA &y, const mglDataA &c, const char *pen="", const char *opt="")
Method on mglGraph: void Tens (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const char *pen="", const char *opt="")
C function: void mgl_tens (HMGL gr, HCDT y, HCDT c, const char *pen, const char *opt)
C function: void mgl_tens_xy (HMGL gr, HCDT x, HCDT y, HCDT c, const char *pen, const char *opt)
C function: void mgl_tens_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT c, const char *pen, const char *opt)

These functions draw continuous lines between points {x[i], y[i], z[i]} with color defined by the special array c[i] (look like tension plot). String pen specifies the color scheme (see Color scheme) and style and/or width of line (see Line styles). See also plot, mesh, fall. See Tens sample, for sample code and picture.

MGL command: tape ydat ['stl'='']
MGL command: tape xdat ydat ['stl'='']
MGL command: tape xdat ydat zdat ['stl'='']
Method on mglGraph: void Tape (const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Tape (const mglDataA &x, const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Tape (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_tape (HMGL gr, HCDT y, const char *pen, const char *opt)
C function: void mgl_tape_xy (HMGL gr, HCDT x, HCDT y, const char *pen, const char *opt)
C function: void mgl_tape_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *pen, const char *opt)

These functions draw tapes of normals for curve between points {x[i], y[i], z[i]}. Initial tape(s) was selected in x-y plane (for ‘x’ in pen) and/or y-z plane (for ‘x’ in pen). The width of tape is proportional to barwidth and can be changed by option value. See also plot, flow, barwidth. See Tape sample, for sample code and picture.

MGL command: area ydat ['stl'='']
MGL command: area xdat ydat ['stl'='']
MGL command: area xdat ydat zdat ['stl'='']
Method on mglGraph: void Area (const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Area (const mglDataA &x, const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Area (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_area (HMGL gr, HCDT y, const char *pen, const char *opt)
C function: void mgl_area_xy (HMGL gr, HCDT x, HCDT y, const char *pen, const char *opt)
C function: void mgl_area_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *pen, const char *opt)

These functions draw continuous lines between points and fills it to axis plane. Also you can use gradient filling if number of specified colors is equal to 2*number of curves. See also plot, bars, stem, region. See Area sample, for sample code and picture.

MGL command: region ydat1 ydat2 ['stl'='']
MGL command: region xdat ydat1 ydat2 ['stl'='']
MGL command: region xdat1 ydat1 xdat2 ydat2 ['stl'='']
MGL command: region xdat1 ydat1 zdat1 xdat2 ydat2 zdat2 ['stl'='']
Method on mglGraph: void Region (const mglDataA &y1, const mglDataA &y2, const char *pen="", const char *opt="")
Method on mglGraph: void Region (const mglDataA &x, const mglDataA &y1, const mglDataA &y2, const char *pen="", const char *opt="")
Method on mglGraph: void Region (const mglDataA &x1, const mglDataA &y1, const mglDataA &x2, const mglDataA &y2, const char *pen="", const char *opt="")
Method on mglGraph: void Region (const mglDataA &x1, const mglDataA &y1, const mglDataA &z1, const mglDataA &x2, const mglDataA &y2, const mglDataA &z2, const char *pen="", const char *opt="")
C function: void mgl_region (HMGL gr, HCDT y1, HCDT y2, const char *pen, const char *opt)
C function: void mgl_region_xy (HMGL gr, HCDT x, HCDT y1, HCDT y2, const char *pen, const char *opt)
C function: void mgl_region_3d (HMGL gr, HCDT x1, HCDT y1, HCDT z1, HCDT x2, HCDT y2, HCDT z2, const char *pen, const char *opt)

These functions fill area between 2 curves. Dimensions of arrays y1 and y2 must be equal. Also you can use gradient filling if number of specified colors is equal to 2*number of curves. If for 2D version pen contain symbol ‘i’ then only area with y1<y<y2 will be filled else the area with y2<y<y1 will be filled too. See also area, bars, stem. See Region sample, for sample code and picture.

MGL command: stem ydat ['stl'='']
MGL command: stem xdat ydat ['stl'='']
MGL command: stem xdat ydat zdat ['stl'='']
Method on mglGraph: void Stem (const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Stem (const mglDataA &x, const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Stem (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_stem (HMGL gr, HCDT y, const char *pen, const char *opt)
C function: void mgl_stem_xy (HMGL gr, HCDT x, HCDT y, const char *pen, const char *opt)
C function: void mgl_stem_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *pen, const char *opt)

These functions draw vertical lines from points to axis plane. See also area, bars, plot, mark. See Stem sample, for sample code and picture.

MGL command: bars ydat ['stl'='']
MGL command: bars xdat ydat ['stl'='']
MGL command: bars xdat ydat zdat ['stl'='']
Method on mglGraph: void Bars (const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Bars (const mglDataA &x, const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Bars (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_bars (HMGL gr, HCDT y, const char *pen, const char *opt)
C function: void mgl_bars_xy (HMGL gr, HCDT x, HCDT y, const char *pen, const char *opt)
C function: void mgl_bars_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *pen, const char *opt)

These functions draw vertical bars from points to axis plane. If string pen contain symbol ‘a’ then lines are drawn one above another (like summation). If string contain symbol ‘f’ then waterfall chart is drawn for determining the cumulative effect of sequentially introduced positive or negative values. You can give different colors for positive and negative values if number of specified colors is equal to 2*number of curves. If pen contain ‘<’, ‘^’ or ‘>’ then boxes will be aligned left, right or centered at its x-coordinates. See also barh, cones, area, stem, chart, barwidth. See Bars sample, for sample code and picture.

MGL command: barh vdat ['stl'='']
MGL command: barh ydat vdat ['stl'='']
Method on mglGraph: void Barh (const mglDataA &v, const char *pen="", const char *opt="")
Method on mglGraph: void Barh (const mglDataA &y, const mglDataA &v, const char *pen="", const char *opt="")
C function: void mgl_barh (HMGL gr, HCDT v, const char *pen, const char *opt)
C function: void mgl_barh_xy (HMGL gr, HCDT y, HCDT v, const char *pen, const char *opt)

These functions draw horizontal bars from points to axis plane. If string contain symbol ‘a’ then lines are drawn one above another (like summation). If string contain symbol ‘f’ then waterfall chart is drawn for determining the cumulative effect of sequentially introduced positive or negative values. You can give different colors for positive and negative values if number of specified colors is equal to 2*number of curves. If pen contain ‘<’, ‘^’ or ‘>’ then boxes will be aligned left, right or centered at its x-coordinates. See also bars, barwidth. See Barh sample, for sample code and picture.

MGL command: cones ydat ['stl'='']
MGL command: cones xdat ydat ['stl'='']
MGL command: cones xdat ydat zdat ['stl'='']
Method on mglGraph: void Cones (const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Cones (const mglDataA &x, const mglDataA &y, const char *pen="", const char *opt="")
Method on mglGraph: void Cones (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_cones (HMGL gr, HCDT y, const char *pen, const char *opt)
C function: void mgl_cones_xy (HMGL gr, HCDT x, HCDT y, const char *pen, const char *opt)
C function: void mgl_cones_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *pen, const char *opt)

These functions draw cones from points to axis plane. If string contain symbol ‘a’ then cones are drawn one above another (like summation). You can give different colors for positive and negative values if number of specified colors is equal to 2*number of curves. Parameter pen can contain:

See also bars, cone, barwidth. See Cones sample, for sample code and picture.

MGL command: chart adat ['col'='']
Method on mglGraph: void Chart (const mglDataA &a, const char *col="", const char *opt="")
C function: void mgl_chart (HMGL gr, HCDT a, const char *col, const char *opt)

The function draws colored stripes (boxes) for data in array a. The number of stripes is equal to the number of rows in a (equal to a.ny). The color of each next stripe is cyclically changed from colors specified in string col or in palette Pal (see Palette and colors). Spaces in colors denote transparent “color” (i.e. corresponding stripe(s) are not drawn). The stripe width is proportional to value of element in a. Chart is plotted only for data with non-negative elements. If string col have symbol ‘#’ then black border lines are drawn. The most nice form the chart have in 3d (after rotation of coordinates) or in cylindrical coordinates (becomes so called Pie chart). See Chart sample, for sample code and picture.

MGL command: boxplot adat ['stl'='']
MGL command: boxplot xdat adat ['stl'='']
Method on mglGraph: void BoxPlot (const mglDataA &a, const char *pen="", const char *opt="")
Method on mglGraph: void BoxPlot (const mglDataA &x, const mglDataA &a, const char *pen="", const char *opt="")
C function: void mgl_boxplot (HMGL gr, HCDT a, const char *pen, const char *opt)
C function: void mgl_boxplot_xy (HMGL gr, HCDT x, HCDT a, const char *pen, const char *opt)

These functions draw boxplot (also known as a box-and-whisker diagram) at points x[i]. This is five-number summaries of data a[i,j] (minimum, lower quartile (Q1), median (Q2), upper quartile (Q3) and maximum) along second (j-th) direction. If pen contain ‘<’, ‘^’ or ‘>’ then boxes will be aligned left, right or centered at its x-coordinates. See also plot, error, bars, barwidth. See BoxPlot sample, for sample code and picture.

MGL command: candle vdat1 ['stl'='']
MGL command: candle vdat1 vdat2 ['stl'='']
MGL command: candle vdat1 ydat1 ydat2 ['stl'='']
MGL command: candle vdat1 vdat2 ydat1 ydat2 ['stl'='']
MGL command: candle xdat vdat1 vdat2 ydat1 ydat2 ['stl'='']
Method on mglGraph: void Candle (const mglDataA &v1, const char *pen="", const char *opt="")
Method on mglGraph: void Candle (const mglDataA &v1, const mglDataA &v2, const char *pen="", const char *opt="")
Method on mglGraph: void Candle (const mglDataA &v1, const mglDataA &y1, const mglDataA &y2, const char *pen="", const char *opt="")
Method on mglGraph: void Candle (const mglDataA &v1, const mglDataA &v2, const mglDataA &y1, const mglDataA &y2, const char *pen="", const char *opt="")
Method on mglGraph: void Candle (const mglDataA &x, const mglDataA &v1, const mglDataA &v2, const mglDataA &y1, const mglDataA &y2, const char *pen="", const char *opt="")
C function: void mgl_candle (HMGL gr, HCDT v1, HCDT y1, HCDT y2, const char *pen, const char *opt)
C function: void mgl_candle_yv (HMGL gr, HCDT v1, HCDT v2, HCDT y1, HCDT y2, const char *pen, const char *opt)
C function: void mgl_candle_xyv (HMGL gr, HCDT x, HCDT v1, HCDT v2, HCDT y1, HCDT y2, const char *pen, const char *opt)

These functions draw candlestick chart at points x[i]. This is a combination of a line-chart and a bar-chart, in that each bar represents the range of price movement over a given time interval. Wire (or white) candle correspond to price growth v1[i]<v2[i], opposite case – solid (or dark) candle. You can give different colors for growth and decrease values if number of specified colors is equal to 2. If pen contain ‘#’ then the wire candle will be used even for 2-color scheme. "Shadows" show the minimal y1 and maximal y2 prices. If v2 is absent then it is determined as v2[i]=v1[i+1]. See also plot, bars, ohlc, barwidth. See Candle sample, for sample code and picture.

MGL command: ohlc odat hdat ldat cdat ['stl'='']
MGL command: ohlc xdat odat hdat ldat cdat ['stl'='']
Method on mglGraph: void OHLC (const mglDataA &o, const mglDataA &h, const mglDataA &l, const mglDataA &c, const char *pen="", const char *opt="")
Method on mglGraph: void OHLC (const mglDataA &x, const mglDataA &o, const mglDataA &h, const mglDataA &l, const mglDataA &c, const char *pen="", const char *opt="")
C function: void mgl_ohlc (HMGL gr, HCDT o, HCDT h, HCDT l, HCDT c, const char *pen, const char *opt)
C function: void mgl_ohlc_x (HMGL gr, HCDT x, HCDT o, HCDT h, HCDT l, HCDT c, const char *pen, const char *opt)

These functions draw Open-High-Low-Close diagram. This diagram show vertical line for between maximal(high h) and minimal(low l) values, as well as horizontal lines before/after vertical line for initial(open o)/final(close c) values of some process (usually price). You can give different colors for up and down values (when closing values higher or not as in previous point) if number of specified colors is equal to 2*number of curves. See also candle, plot, barwidth. See OHLC sample, for sample code and picture.

MGL command: error ydat yerr ['stl'='']
MGL command: error xdat ydat yerr ['stl'='']
MGL command: error xdat ydat xerr yerr ['stl'='']
Method on mglGraph: void Error (const mglDataA &y, const mglDataA &ey, const char *pen="", const char *opt="")
Method on mglGraph: void Error (const mglDataA &x, const mglDataA &y, const mglDataA &ey, const char *pen="", const char *opt="")
Method on mglGraph: void Error (const mglDataA &x, const mglDataA &y, const mglDataA &ex, const mglDataA &ey, const char *pen="", const char *opt="")
C function: void mgl_error (HMGL gr, HCDT y, HCDT ey, const char *pen, const char *opt)
C function: void mgl_error_xy (HMGL gr, HCDT x, HCDT y, HCDT ey, const char *pen, const char *opt)
C function: void mgl_error_exy (HMGL gr, HCDT x, HCDT y, HCDT ex, HCDT ey, const char *pen, const char *opt)

These functions draw error boxes {ex[i], ey[i]} at points {x[i], y[i]}. This can be useful, for example, in experimental points, or to show numeric error or some estimations and so on. If string pen contain symbol ‘@’ than large semitransparent mark is used instead of error box. See also plot, mark. See Error sample, for sample code and picture.

MGL command: mark ydat rdat ['stl'='']
MGL command: mark xdat ydat rdat ['stl'='']
MGL command: mark xdat ydat zdat rdat ['stl'='']
Method on mglGraph: void Mark (const mglDataA &y, const mglDataA &r, const char *pen="", const char *opt="")
Method on mglGraph: void Mark (const mglDataA &x, const mglDataA &y, const mglDataA &r, const char *pen="", const char *opt="")
Method on mglGraph: void Mark (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &r, const char *pen="", const char *opt="")
C function: void mgl_mark_y (HMGL gr, HCDT y, HCDT r, const char *pen, const char *opt)
C function: void mgl_mark_xy (HMGL gr, HCDT x, HCDT y, HCDT r, const char *pen, const char *opt)
C function: void mgl_mark_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT r, const char *pen, const char *opt)

These functions draw marks with size r[i]*marksize at points {x[i], y[i], z[i]}. If you need to draw markers of the same size then you can use plot function with empty line style ‘ ’. For markers with size in axis range use error with style ‘@’. See also plot, textmark, error, stem. See Mark sample, for sample code and picture.

MGL command: textmark ydat 'txt' ['stl'='']
MGL command: textmark ydat rdat 'txt' ['stl'='']
MGL command: textmark xdat ydat rdat 'txt' ['stl'='']
MGL command: textmark xdat ydat zdat rdat 'txt' ['stl'='']
Method on mglGraph: void TextMark (const mglDataA &y, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void TextMark (const mglDataA &y, const wchar_t *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void TextMark (const mglDataA &y, const mglDataA &r, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void TextMark (const mglDataA &y, const mglDataA &r, const wchar_t *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void TextMark (const mglDataA &x, const mglDataA &y, const mglDataA &r, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void TextMark (const mglDataA &x, const mglDataA &y, const mglDataA &r, const wchar_t *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void TextMark (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &r, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void TextMark (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &r, const wchar_t *txt, const char *fnt="", const char *opt="")
C function: void mgl_textmark (HMGL gr, HCDT y, const char *txt, const char *fnt, const char *opt)
C function: void mgl_textmarkw (HMGL gr, HCDT y, const wchar_t *txt, const char *fnt, const char *opt)
C function: void mgl_textmark_yr (HMGL gr, HCDT y, HCDT r, const char *txt, const char *fnt, const char *opt)
C function: void mgl_textmarkw_yr (HMGL gr, HCDT y, HCDT r, const wchar_t *txt, const char *fnt, const char *opt)
C function: void mgl_textmark_xyr (HMGL gr, HCDT x, HCDT y, HCDT r, const char *txt, const char *fnt, const char *opt)
C function: void mgl_textmarkw_xyr (HMGL gr, HCDT x, HCDT y, HCDT r, const wchar_t *txt, const char *fnt, const char *opt)
C function: void mgl_textmark_xyzr (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT r, const char *txt, const char *fnt, const char *opt)
C function: void mgl_textmarkw_xyzr (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT r, const wchar_t *txt, const char *fnt, const char *opt)

These functions draw string txt as marks with size proportional to r[i]*marksize at points {x[i], y[i], z[i]}. By default (if omitted) r[i]=1. See also plot, mark, stem. See TextMark sample, for sample code and picture.

MGL command: label ydat 'txt' ['stl'='']
MGL command: label xdat ydat 'txt' ['stl'='']
MGL command: label xdat ydat zdat 'txt' ['stl'='']
Method on mglGraph: void Label (const mglDataA &y, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Label (const mglDataA &y, const wchar_t *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Label (const mglDataA &x, const mglDataA &y, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Label (const mglDataA &x, const mglDataA &y, const wchar_t *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Label (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Label (const mglDataA &x, const mglDataA &y, const mglDataA &z, const wchar_t *txt, const char *fnt="", const char *opt="")
C function: void mgl_label (HMGL gr, HCDT y, const char *txt, const char *fnt, const char *opt)
C function: void mgl_labelw (HMGL gr, HCDT y, const wchar_t *txt, const char *fnt, const char *opt)
C function: void mgl_label_xy (HMGL gr, HCDT x, HCDT y, const char *txt, const char *fnt, const char *opt)
C function: void mgl_labelw_xy (HMGL gr, HCDT x, HCDT y, const wchar_t *txt, const char *fnt, const char *opt)
C function: void mgl_label_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const char *txt, const char *fnt, const char *opt)
C function: void mgl_labelw_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, const wchar_t *txt, const char *fnt, const char *opt)

These functions draw string txt at points {x[i], y[i], z[i]}. If string txt contain ‘%x’, ‘%y’, ‘%z’ or ‘%n’ then it will be replaced by the value of x-,y-,z-coordinate of the point or its index. String fnt may contain:

See also plot, mark, textmark, table. See Label sample, for sample code and picture.

MGL command: table vdat 'txt' ['stl'='#']
MGL command: table x y vdat 'txt' ['stl'='#']
Method on mglGraph: void Table (const mglDataA &val, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Table (const mglDataA &val, const wchar_t *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Table (mreal x, mreal y, const mglDataA &val, const char *txt, const char *fnt="", const char *opt="")
Method on mglGraph: void Table (mreal x, mreal y, const mglDataA &val, const wchar_t *txt, const char *fnt="", const char *opt="")
C function: void mgl_table (HMGL gr, mreal x, mreal y, HCDT val, const char *txt, const char *fnt, const char *opt)
C function: void mgl_tablew (HMGL gr, mreal x, mreal y, HCDT val, const wchar_t *txt, const char *fnt, const char *opt)

These functions draw table with values of val and captions from string txt (separated by newline symbol ‘\n’) at points {x, y} (default at {0,0}) related to current subplot. String fnt may contain:

Option value set the width of the table (default is 1). See also plot, label. See Table sample, for sample code and picture.

MGL command: tube ydat rdat ['stl'='']
MGL command: tube ydat rval ['stl'='']
MGL command: tube xdat ydat rdat ['stl'='']
MGL command: tube xdat ydat rval ['stl'='']
MGL command: tube xdat ydat zdat rdat ['stl'='']
MGL command: tube xdat ydat zdat rval ['stl'='']
Method on mglGraph: void Tube (const mglDataA &y, const mglDataA &r, const char *pen="", const char *opt="")
Method on mglGraph: void Tube (const mglDataA &y, mreal r, const char *pen="", const char *opt="")
Method on mglGraph: void Tube (const mglDataA &x, const mglDataA &y, const mglDataA &r, const char *pen="", const char *opt="")
Method on mglGraph: void Tube (const mglDataA &x, const mglDataA &y, mreal r, const char *pen="", const char *opt="")
Method on mglGraph: void Tube (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &r, const char *pen="", const char *opt="")
Method on mglGraph: void Tube (const mglDataA &x, const mglDataA &y, const mglDataA &z, mreal r, const char *pen="", const char *opt="")
C function: void mgl_tube_r (HMGL gr, HCDT y, HCDT r, const char *pen, const char *opt)
C function: void mgl_tube (HMGL gr, HCDT y, mreal r, const char *pen, const char *opt)
C function: void mgl_tube_xyr (HMGL gr, HCDT x, HCDT y, HCDT r, const char *pen, const char *opt)
C function: void mgl_tube_xy (HMGL gr, HCDT x, HCDT y, mreal r, const char *pen, const char *opt)
C function: void mgl_tube_xyzr (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT r, const char *pen, const char *opt)
C function: void mgl_tube_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, mreal r, const char *pen, const char *opt)

These functions draw the tube with variable radius r[i] along the curve between points {x[i], y[i], z[i]}. See also plot. See Tube sample, for sample code and picture.

MGL command: torus rdat zdat ['stl'='']
Method on mglGraph: void Torus (const mglDataA &r, const mglDataA &z, const char *pen="", const char *opt="")
C function: void mgl_torus (HMGL gr, HCDT r, HCDT z, const char *pen, const char *opt)

These functions draw surface which is result of curve {r, z} rotation around axis. If string pen contain symbols ‘x’ or ‘z’ then rotation axis will be set to specified direction (default is ‘y’). If string pen have symbol ‘#’ then wire plot is produced. If string pen have symbol ‘.’ then plot by dots is produced. See also plot, axial. See Torus sample, for sample code and picture.

MGL command: lamerey x0 ydat ['stl'='']
MGL command: lamerey x0 'y(x)' ['stl'='']
Method on mglGraph: void Lamerey (double x0, const mglDataA &y, const char *stl="", const char *opt="")
Method on mglGraph: void Lamerey (double x0, const char *y, const char *stl="", const char *opt="")
C function: void mgl_lamerey_dat (HMGL gr, double x0, HCDT y, const char *stl, const char *opt)
C function: void mgl_lamerey_str (HMGL gr, double x0, const char *y, const char *stl, const char *opt)

These functions draw Lamerey diagram for mapping x_new = y(x_old) starting from point x0. String stl may contain line style, symbol ‘v’ for drawing arrows, symbol ‘~’ for disabling first segment. Option value set the number of segments to be drawn (default is 20). See also plot, fplot, bifurcation, pmap. See Lamerey sample, for sample code and picture.

MGL command: bifurcation dx ydat ['stl'='']
MGL command: bifurcation dx 'y(x)' ['stl'='']
Method on mglGraph: void Bifurcation (double dx, const mglDataA &y, const char *stl="", const char *opt="")
Method on mglGraph: void Bifurcation (double dx, const char *y, const char *stl="", const char *opt="")
C function: void mgl_bifurcation_dat (HMGL gr, double dx, HCDT y, const char *stl, const char *opt)
C function: void mgl_bifurcation_str (HMGL gr, double dx, const char *y, const char *stl, const char *opt)

These functions draw bifurcation diagram for mapping x_new = y(x_old). Parameter dx set the accuracy along x-direction. String stl set color. Option value set the number of stationary points (default is 1024). See also plot, fplot, lamerey. See Bifurcation sample, for sample code and picture.

MGL command: pmap ydat sdat ['stl'='']
MGL command: pmap xdat ydat sdat ['stl'='']
MGL command: pmap xdat ydat zdat sdat ['stl'='']
Method on mglGraph: void Pmap (const mglDataA &y, const mglDataA &s, const char *stl="", const char *opt="")
Method on mglGraph: void Pmap (const mglDataA &x, const mglDataA &y, const mglDataA &s, const char *stl="", const char *opt="")
Method on mglGraph: void Pmap (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &s, const char *stl="", const char *opt="")
C function: void mgl_pmap (HMGL gr, HMDT y, HCDT s, const char *stl, const char *opt)
C function: void mgl_pmap_xy (HMGL gr, HCDT x, HMDT y, HCDT s, const char *stl, const char *opt)
C function: void mgl_pmap_xyz (HMGL gr, HCDT x, HMDT y, HCDT z, HCDT s, const char *stl, const char *opt)

These functions draw Poincare map for curve {x, y, z} at surface s=0. Basically, it show intersections of the curve and the surface. String stl set the style of marks. See also plot, mark, lamerey. See Pmap sample, for sample code and picture.

Next: , Previous: , Up: MathGL core   [Contents][Index]

4.12 2D plotting

These functions perform plotting of 2D data. 2D means that data depend from 2 independent parameters like matrix f(x_i,y_j), i=1...n, j=1...m. By default (if absent) values of x, y are equidistantly distributed in axis range. The plots are drawn for each z slice of the data. The minor dimensions of arrays x, y, z should be equal x.nx=z.nx && y.nx=z.ny or x.nx=y.nx=z.nx && x.ny=y.ny=z.ny. Arrays x and y can be vectors (not matrices as z). String sch sets the color scheme (see Color scheme) for plot. String opt contain command options (see Command options). See 2D samples, for sample code and picture.

MGL command: surf zdat ['sch'='']
MGL command: surf xdat ydat zdat ['sch'='']
Method on mglGraph: void Surf (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Surf (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_surf (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_surf_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws surface specified parametrically {x[i,j], y[i,j], z[i,j]}. If string sch have symbol ‘#’ then grid lines are drawn. If string sch have symbol ‘.’ then plot by dots is produced. See also mesh, dens, belt, tile, boxs, surfc, surfa. See Surf sample, for sample code and picture.

MGL command: mesh zdat ['sch'='']
MGL command: mesh xdat ydat zdat ['sch'='']
Method on mglGraph: void Mesh (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Mesh (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_mesh (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_mesh_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws mesh lines for surface specified parametrically {x[i,j], y[i,j], z[i,j]}. See also surf, fall, meshnum, cont, tens. See Mesh sample, for sample code and picture.

MGL command: fall zdat ['sch'='']
MGL command: fall xdat ydat zdat ['sch'='']
Method on mglGraph: void Fall (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Fall (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_fall (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_fall_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws fall lines for surface specified parametrically {x[i,j], y[i,j], z[i,j]}. This plot can be used for plotting several curves shifted in depth one from another. If sch contain ‘x’ then lines are drawn along x-direction else (by default) lines are drawn along y-direction. See also belt, mesh, tens, meshnum. See Fall sample, for sample code and picture.

MGL command: belt zdat ['sch'='']
MGL command: belt xdat ydat zdat ['sch'='']
Method on mglGraph: void Belt (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Belt (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_belt (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_belt_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws belts for surface specified parametrically {x[i,j], y[i,j], z[i,j]}. This plot can be used as 3d generalization of plot). If sch contain ‘x’ then belts are drawn along x-direction else (by default) belts are drawn along y-direction. See also fall, surf, plot, meshnum. See Belt sample, for sample code and picture.

MGL command: boxs zdat ['sch'='']
MGL command: boxs xdat ydat zdat ['sch'='']
Method on mglGraph: void Boxs (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Boxs (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_boxs (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_boxs_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws vertical boxes for surface specified parametrically {x[i,j], y[i,j], z[i,j]}. Symbol ‘@’ in sch set to draw filled boxes. See also surf, dens, tile, step. See Boxs sample, for sample code and picture.

MGL command: tile zdat ['sch'='']
MGL command: tile xdat ydat zdat ['sch'='']
Method on mglGraph: void Tile (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Tile (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_tile (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_tile_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws horizontal tiles for surface specified parametrically {x[i,j], y[i,j], z[i,j]}. Such plot can be used as 3d generalization of step. See also surf, boxs, step, tiles. See Tile sample, for sample code and picture.

MGL command: dens zdat ['sch'='']
MGL command: dens xdat ydat zdat ['sch'='']
Method on mglGraph: void Dens (const mglDataA &z, const char *sch="", const char *opt="", mreal zVal=NAN)
Method on mglGraph: void Dens (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="", mreal zVal=NAN)
C function: void mgl_dens (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_dens_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws density plot for surface specified parametrically {x[i,j], y[i,j], z[i,j]} at z equal to minimal z-axis value. If string sch have symbol ‘#’ then grid lines are drawn. If string sch have symbol ‘.’ then plot by dots is produced. See also surf, cont, contf, boxs, tile, dens[xyz]. See Dens sample, for sample code and picture.

MGL command: cont vdat zdat ['sch'='']
MGL command: cont vdat xdat ydat zdat ['sch'='']
Method on mglGraph: void Cont (const mglDataA &v, const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Cont (const mglDataA &v, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_cont__val (HMGL gr, HCDT v, HCDT z, const char *sch, const char *opt)
C function: void mgl_cont_xy_val (HMGL gr, HCDT v, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws contour lines for surface specified parametrically {x[i,j], y[i,j], z[i,j]} at z=v[k], or at z equal to minimal z-axis value if sch contain symbol ‘_’. Contours are plotted for z[i,j]=v[k] where v[k] are values of data array v. If string sch have symbol ‘t’ or ‘T’ then contour labels v[k] will be drawn below (or above) the contours. See also dens, contf, contd, axial, cont[xyz]. See Cont sample, for sample code and picture.

MGL command: cont zdat ['sch'='']
MGL command: cont xdat ydat zdat ['sch'='']
Method on mglGraph: void Cont (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Cont (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_cont (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_cont_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The same as previous with vector v of num-th elements equidistantly distributed in color range. Here num is equal to parameter value in options opt (default is 7).

MGL command: contf vdat zdat ['sch'='']
MGL command: contf vdat xdat ydat zdat ['sch'='']
Method on mglGraph: void ContF (const mglDataA &v, const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void ContF (const mglDataA &v, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_contf_val (HMGL gr, HCDT v, HCDT z, const char *sch, const char *opt)
C function: void mgl_contf_xy_val (HMGL gr, HCDT v, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws solid (or filled) contour lines for surface specified parametrically {x[i,j], y[i,j], z[i,j]} at z=v[k], or at z equal to minimal z-axis value if sch contain symbol ‘_’. Contours are plotted for z[i,j]=v[k] where v[k] are values of data array v (must be v.nx>2). See also dens, cont, contd, contf[xyz]. See ContF sample, for sample code and picture.

MGL command: contf zdat ['sch'='']
MGL command: contf xdat ydat zdat ['sch'='']
Method on mglGraph: void ContF (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void ContF (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_contf (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_contf_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The same as previous with vector v of num-th elements equidistantly distributed in color range. Here num is equal to parameter value in options opt (default is 7).

MGL command: contd vdat zdat ['sch'='']
MGL command: contd vdat xdat ydat zdat ['sch'='']
Method on mglGraph: void ContD (const mglDataA &v, const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void ContD (const mglDataA &v, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_contd_val (HMGL gr, HCDT v, HCDT z, const char *sch, const char *opt)
C function: void mgl_contd_xy_val (HMGL gr, HCDT v, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws solid (or filled) contour lines for surface specified parametrically {x[i,j], y[i,j], z[i,j]} at z=v[k] (or at z equal to minimal z-axis value if sch contain symbol ‘_’) with manual colors. Contours are plotted for z[i,j]=v[k] where v[k] are values of data array v (must be v.nx>2). String sch sets the contour colors: the color of k-th contour is determined by character sch[k%strlen(sch)]. See also dens, cont, contf. See ContD sample, for sample code and picture.

MGL command: contd zdat ['sch'='']
MGL command: contd xdat ydat zdat ['sch'='']
Method on mglGraph: void ContD (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void ContD (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_contd (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_contd_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The same as previous with vector v of num-th elements equidistantly distributed in color range. Here num is equal to parameter value in options opt (default is 7).

MGL command: contv vdat zdat ['sch'='']
MGL command: contv vdat xdat ydat zdat ['sch'='']
Method on mglGraph: void ContV (const mglDataA &v, const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void ContV (const mglDataA &v, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_contv_val (HMGL gr, HCDT v, HCDT z, const char *sch, const char *opt)
C function: void mgl_contv_xy_val (HMGL gr, HCDT v, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws vertical cylinder (tube) at contour lines for surface specified parametrically {x[i,j], y[i,j], z[i,j]} at z=v[k], or at z equal to minimal z-axis value if sch contain symbol ‘_’. Contours are plotted for z[i,j]=v[k] where v[k] are values of data array v. See also cont, contf. See ContV sample, for sample code and picture.

MGL command: contv zdat ['sch'='']
MGL command: contv xdat ydat zdat ['sch'='']
Method on mglGraph: void ContV (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void ContV (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_contv (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_contv_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The same as previous with vector v of num-th elements equidistantly distributed in color range. Here num is equal to parameter value in options opt (default is 7).

MGL command: axial vdat zdat ['sch'='']
MGL command: axial vdat xdat ydat zdat ['sch'='']
Method on mglGraph: void Axial (const mglDataA &v, const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Axial (const mglDataA &v, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_axial_val (HMGL gr, HCDT v, HCDT z, const char *sch, const char *opt)
C function: void mgl_axial_xy_val (HMGL gr, HCDT v, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws surface which is result of contour plot rotation for surface specified parametrically {x[i,j], y[i,j], z[i,j]}. Contours are plotted for z[i,j]=v[k] where v[k] are values of data array v. If string sch have symbol ‘#’ then wire plot is produced. If string sch have symbol ‘.’ then plot by dots is produced. If string contain symbols ‘x’ or ‘z’ then rotation axis will be set to specified direction (default is ‘y’). See also cont, contf, torus, surf3. See Axial sample, for sample code and picture.

MGL command: axial zdat ['sch'='']
MGL command: axial xdat ydat zdat ['sch'='']
Method on mglGraph: void Axial (const mglDataA &z, const char *sch="", const char *opt="", int num=3)
Method on mglGraph: void Axial (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="", int num=3)
C function: void mgl_axial (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_axial_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The same as previous with vector v of num-th elements equidistantly distributed in color range. Here num is equal to parameter value in options opt (default is 3).

MGL command: grid2 zdat ['sch'='']
MGL command: grid2 xdat ydat zdat ['sch'='']
Method on mglGraph: void Grid (const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Grid (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_grid (HMGL gr, HCDT z, const char *sch, const char *opt)
C function: void mgl_grid_xy (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws grid lines for density plot of surface specified parametrically {x[i,j], y[i,j], z[i,j]} at z equal to minimal z-axis value. See also dens, cont, contf, grid3, meshnum.

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4.13 3D plotting

These functions perform plotting of 3D data. 3D means that data depend from 3 independent parameters like matrix f(x_i,y_j,z_k), i=1...n, j=1...m, k=1...l. By default (if absent) values of x, y, z are equidistantly distributed in axis range. The minor dimensions of arrays x, y, z, a should be equal x.nx=a.nx && y.nx=a.ny && z.nz=a.nz or x.nx=y.nx=z.nx=a.nx && x.ny=y.ny=z.ny=a.ny && x.nz=y.nz=z.nz=a.nz. Arrays x, y and z can be vectors (not matrices as a). String sch sets the color scheme (see Color scheme) for plot. String opt contain command options (see Command options). See 3D samples, for sample code and picture.

MGL command: surf3 adat val ['sch'='']
MGL command: surf3 xdat ydat zdat adat val ['sch'='']
Method on mglGraph: void Surf3 (mreal val, const mglDataA &a, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3 (mreal val, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", const char *opt="")
C function: void mgl_surf3_val (HMGL gr, mreal val, HCDT a, const char *sch, const char *opt)
C function: void mgl_surf3_xyz_val (HMGL gr, mreal val, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, const char *opt)

The function draws isosurface plot for 3d array specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]) at a(x,y,z)=val. If string contain ‘#’ then wire plot is produced. If string sch have symbol ‘.’ then plot by dots is produced. Note, that there is possibility of incorrect plotting due to uncertainty of cross-section defining if there are two or more isosurface intersections inside one cell. See also cloud, dens3, surf3c, surf3a, axial. See Surf3 sample, for sample code and picture.

MGL command: surf3 adat ['sch'='']
MGL command: surf3 xdat ydat zdat adat ['sch'='']
Method on mglGraph: void Surf3 (const mglDataA &a, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3 (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", const char *opt="")
C function: void mgl_surf3 (HMGL gr, HCDT a, const char *sch, const char *opt)
C function: void mgl_surf3_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, const char *opt)

Draws num-th uniformly distributed in color range isosurfaces for 3d data. Here num is equal to parameter value in options opt (default is 3).

MGL command: cloud adat ['sch'='']
MGL command: cloud xdat ydat zdat adat ['sch'='']
Method on mglGraph: void Cloud (const mglDataA &a, const char *sch="", const char *opt="")
Method on mglGraph: void Cloud (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", const char *opt="")
C function: void mgl_cloud (HMGL gr, HCDT a, const char *sch, const char *opt)
C function: void mgl_cloud_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, const char *opt)

The function draws cloud plot for 3d data specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]). This plot is a set of cubes with color and transparency proportional to value of a. The resulting plot is like cloud – low value is transparent but higher ones are not. The number of plotting cells depend on meshnum. If string sch contain symbol ‘.’ then lower quality plot will produced with much low memory usage. If string sch contain symbol ‘i’ then transparency will be inversed, i.e. higher become transparent and lower become not transparent. See also surf3, meshnum. See Cloud sample, for sample code and picture.

MGL command: dens3 adat ['sch'='' sval=-1]
MGL command: dens3 xdat ydat zdat adat ['sch'='' sval=-1]
Method on mglGraph: void Dens3 (const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
Method on mglGraph: void Dens3 (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
C function: void mgl_dens3 (HMGL gr, HCDT a, const char *sch, mreal sVal, const char *opt)
C function: void mgl_dens3_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, mreal sVal, const char *opt)

The function draws density plot for 3d data specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]). Density is plotted at slice sVal in direction {‘x’, ‘y’, ‘z’} if sch contain corresponding symbol (by default, ‘y’ direction is used). If string stl have symbol ‘#’ then grid lines are drawn. See also cont3, contf3, dens, grid3. See Dens3 sample, for sample code and picture.

MGL command: cont3 vdat adat ['sch'='' sval=-1]
MGL command: cont3 vdat xdat ydat zdat adat ['sch'='' sval=-1]
Method on mglGraph: void Cont3 (const mglDataA &v, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
Method on mglGraph: void Cont3 (const mglDataA &v, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
C function: void mgl_cont3_val (HMGL gr, HCDT v, HCDT a, const char *sch, mreal sVal, const char *opt)
C function: void mgl_cont3_xyz_val (HMGL gr, HCDT v, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, mreal sVal, const char *opt)

The function draws contour plot for 3d data specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]). Contours are plotted for values specified in array v at slice sVal in direction {‘x’, ‘y’, ‘z’} if sch contain corresponding symbol (by default, ‘y’ direction is used). If string sch have symbol ‘#’ then grid lines are drawn. If string sch have symbol ‘t’ or ‘T’ then contour labels will be drawn below (or above) the contours. See also dens3, contf3, cont, grid3. See Cont3 sample, for sample code and picture.

MGL command: cont3 adat ['sch'='' sval=-1]
MGL command: cont3 xdat ydat zdat adat ['sch'='' sval=-1]
Method on mglGraph: void Cont3 (const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="", const char *opt="")
Method on mglGraph: void Cont3 (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
C function: void mgl_cont3 (HMGL gr, HCDT a, const char *sch, mreal sVal, const char *opt)
C function: void mgl_cont3_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, mreal sVal, const char *opt)

The same as previous with vector v of num-th elements equidistantly distributed in color range. Here num is equal to parameter value in options opt (default is 7).

MGL command: contf3 vdat adat ['sch'='' sval=-1]
MGL command: contf3 vdat xdat ydat zdat adat ['sch'='' sval=-1]
Method on mglGraph: void Contf3 (const mglDataA &v, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
Method on mglGraph: void Contf3 (const mglDataA &v, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
C function: void mgl_contf3_val (HMGL gr, HCDT v, HCDT a, const char *sch, mreal sVal, const char *opt)
C function: void mgl_contf3_xyz_val (HMGL gr, HCDT v, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, mreal sVal, const char *opt)

The function draws solid (or filled) contour plot for 3d data specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]). Contours are plotted for values specified in array v at slice sVal in direction {‘x’, ‘y’, ‘z’} if sch contain corresponding symbol (by default, ‘y’ direction is used). If string sch have symbol ‘#’ then grid lines are drawn. See also dens3, cont3, contf, grid3. See ContF3 sample, for sample code and picture.

MGL command: contf3 adat ['sch'='' sval=-1]
MGL command: contf3 xdat ydat zdat adat ['sch'='' sval=-1]
Method on mglGraph: void Contf3 (const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="", const char *opt="")
Method on mglGraph: void Contf3 (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
C function: void mgl_contf3 (HMGL gr, HCDT a, const char *sch, mreal sVal, const char *opt)
C function: void mgl_contf3_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, mreal sVal, const char *opt)

The same as previous with vector v of num-th elements equidistantly distributed in color range. Here num is equal to parameter value in options opt (default is 7).

MGL command: grid3 adat ['sch'='' sval=-1]
MGL command: grid3 xdat ydat zdat adat ['sch'='' sval=-1]
Method on mglGraph: void Grid3 (const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
Method on mglGraph: void Grid3 (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", mreal sVal=-1, const char *opt="")
C function: void mgl_grid3 (HMGL gr, HCDT a, const char *sch, mreal sVal, const char *opt)
C function: void mgl_grid3_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, mreal sVal, const char *opt)

The function draws grid for 3d data specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]). Grid is plotted at slice sVal in direction {‘x’, ‘y’, ‘z’} if sch contain corresponding symbol (by default, ‘y’ direction is used). See also cont3, contf3, dens3, grid2, meshnum.

MGL command: beam tr g1 g2 adat rval ['sch'='' flag=0 num=3]
Method on mglGraph: void Beam (const mglDataA &tr, const mglDataA &g1, const mglDataA &g2, const mglDataA &a, mreal r, const char *stl="", int flag=0, int num=3)
Method on mglGraph: void Beam (mreal val, const mglDataA &tr, const mglDataA &g1, const mglDataA &g2, const mglDataA &a, mreal r, const char *stl="", int flag=0)
C function: void mgl_beam (HMGL gr, HCDT tr, HCDT g1, HCDT g2, HCDT a, mreal r, const char *stl, int flag, int num)
C function: void mgl_beam_val (HMGL gr, mreal val, HCDT tr, HCDT g1, HCDT g2, HCDT a, mreal r, const char *stl, int flag)

Draws the isosurface for 3d array a at constant values of a=val. This is special kind of plot for a specified in accompanied coordinates along curve tr with orts g1, g2 and with transverse scale r. Variable flag is bitwise: ‘0x1’ - draw in accompanied (not laboratory) coordinates; ‘0x2’ - draw projection to \rho-z plane; ‘0x4’ - draw normalized in each slice field. The x-size of data arrays tr, g1, g2 must be nx>2. The y-size of data arrays tr, g1, g2 and z-size of the data array a must be equal. See also surf3.

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4.14 Dual plotting

These plotting functions draw two matrix simultaneously. There are 5 generally different types of data representations: surface or isosurface colored by other data (SurfC, Surf3C), surface or isosurface transpared by other data (SurfA, Surf3A), tiles with variable size (TileS), mapping diagram (Map), STFA diagram (STFA). By default (if absent) values of x, y, z are equidistantly distributed in axis range. The minor dimensions of arrays x, y, z, c should be equal. Arrays x, y (and z for Surf3C, Surf3A) can be vectors (not matrices as c). String sch sets the color scheme (see Color scheme) for plot. String opt contain command options (see Command options).

MGL command: surfc zdat cdat ['sch'='']
MGL command: surfc xdat ydat zdat cdat ['sch'='']
Method on mglGraph: void SurfC (const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void SurfC (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
C function: void mgl_surfc (HMGL gr, HCDT z, HCDT c, const char *sch, const char *opt)
C function: void mgl_surfc_xy (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT c, const char *sch, const char *opt)

The function draws surface specified parametrically {x[i,j], y[i,j], z[i,j]} and color it by matrix c[i,j]. If string sch have symbol ‘#’ then grid lines are drawn. If string sch have symbol ‘.’ then plot by dots is produced. All dimensions of arrays z and c must be equal. Surface is plotted for each z slice of the data. See also surf, surfa, surfca, surf3c. See SurfC sample, for sample code and picture.

MGL command: surf3c adat cdat val ['sch'='']
MGL command: surf3c xdat ydat zdat adat cdat val ['sch'='']
Method on mglGraph: void Surf3C (mreal val, const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3C (mreal val, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
C function: void mgl_surf3c_val (HMGL gr, mreal val, HCDT a, HCDT c, const char *sch, const char *opt)
C function: void mgl_surf3c_xyz_val (HMGL gr, mreal val, HCDT x, HCDT y, HCDT z, HCDT a, HCDT c, const char *sch, const char *opt)

The function draws isosurface plot for 3d array specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]) at a(x,y,z)=val. It is mostly the same as surf3 function but the color of isosurface depends on values of array c. If string sch contain ‘#’ then wire plot is produced. If string sch have symbol ‘.’ then plot by dots is produced. See also surf3, surfc, surf3a, surf3ca. See Surf3C sample, for sample code and picture.

MGL command: surf3c adat cdat ['sch'='']
MGL command: surf3c xdat ydat zdat adat cdat ['sch'='']
Method on mglGraph: void Surf3C (const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3C (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
C function: void mgl_surf3c (HMGL gr, HCDT a, HCDT c, const char *sch, const char *opt)
C function: void mgl_surf3c_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, HCDT c, const char *sch, const char *opt)

Draws num-th uniformly distributed in color range isosurfaces for 3d data. Here num is equal to parameter value in options opt (default is 3).

MGL command: surfa zdat cdat ['sch'='']
MGL command: surfa xdat ydat zdat cdat ['sch'='']
Method on mglGraph: void SurfA (const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void SurfA (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
C function: void mgl_surfa (HMGL gr, HCDT z, HCDT c, const char *sch, const char *opt)
C function: void mgl_surfa_xy (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT c, const char *sch, const char *opt)

The function draws surface specified parametrically {x[i,j], y[i,j], z[i,j]} and transparent it by matrix c[i,j]. If string sch have symbol ‘#’ then grid lines are drawn. If string sch have symbol ‘.’ then plot by dots is produced. All dimensions of arrays z and c must be equal. Surface is plotted for each z slice of the data. See also surf, surfc, surfca, surf3a. See SurfA sample, for sample code and picture.

MGL command: surf3a adat cdat val ['sch'='']
MGL command: surf3a xdat ydat zdat adat cdat val ['sch'='']
Method on mglGraph: void Surf3A (mreal val, const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3A (mreal val, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
C function: void mgl_surf3a_val (HMGL gr, mreal val, HCDT a, HCDT c, const char *sch, const char *opt)
C function: void mgl_surf3a_xyz_val (HMGL gr, mreal val, HCDT x, HCDT y, HCDT z, HCDT a, HCDT c, const char *sch, const char *opt)

The function draws isosurface plot for 3d array specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]) at a(x,y,z)=val. It is mostly the same as surf3 function but the transparency of isosurface depends on values of array c. If string sch contain ‘#’ then wire plot is produced. If string sch have symbol ‘.’ then plot by dots is produced. See also surf3, surfc, surf3a, surf3ca. See Surf3A sample, for sample code and picture.

MGL command: surf3a adat cdat ['sch'='']
MGL command: surf3a xdat ydat zdat adat cdat ['sch'='']
Method on mglGraph: void Surf3A (const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3A (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &c, const char *sch="", const char *opt="")
C function: void mgl_surf3a (HMGL gr, HCDT a, HCDT c, const char *sch, const char *opt)
C function: void mgl_surf3a_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, HCDT c, const char *sch, const char *opt)

Draws num-th uniformly distributed in color range isosurfaces for 3d data. At this array c can be vector with values of transparency and num=c.nx. In opposite case num is equal to parameter value in options opt (default is 3).

MGL command: surfca zdat cdat adat ['sch'='']
MGL command: surfca xdat ydat zdat cdat adat ['sch'='']
Method on mglGraph: void SurfCA (const mglDataA &z, const mglDataA &c, const mglDataA &a, const char *sch="", const char *opt="")
Method on mglGraph: void SurfCA (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const mglDataA &a, const char *sch="", const char *opt="")
C function: void mgl_surfca (HMGL gr, HCDT z, HCDT c, HCDT a, const char *sch, const char *opt)
C function: void mgl_surfca_xy (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT c, HCDT a, const char *sch, const char *opt)

The function draws surface specified parametrically {x[i,j], y[i,j], z[i,j]}, color it by matrix c[i,j] and transparent it by matrix a[i,j]. If string sch have symbol ‘#’ then grid lines are drawn. If string sch have symbol ‘.’ then plot by dots is produced. All dimensions of arrays z and c must be equal. Surface is plotted for each z slice of the data. Note, you can use map-like coloring if use ‘%’ in color scheme. See also surf, surfc, surfa, surf3ca. See SurfCA sample, for sample code and picture.

MGL command: surf3ca adat cdat bdat val ['sch'='']
MGL command: surf3ca xdat ydat zdat adat cdat bdat val ['sch'='']
Method on mglGraph: void Surf3CA (mreal val, const mglDataA &a, const mglDataA &c, const mglDataA &b, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3CA (mreal val, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &c, const mglDataA &b, const char *sch="", const char *opt="")
C function: void mgl_surf3ca_val (HMGL gr, mreal val, HCDT a, HCDT c, HCDT b, const char *sch, const char *opt)
C function: void mgl_surf3ca_xyz_val (HMGL gr, mreal val, HCDT x, HCDT y, HCDT z, HCDT a, HCDT c, HCDT b,const char *sch, const char *opt)

The function draws isosurface plot for 3d array specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]) at a(x,y,z)=val. It is mostly the same as surf3 function but the color and the transparency of isosurface depends on values of array c and b correspondingly. If string sch contain ‘#’ then wire plot is produced. If string sch have symbol ‘.’ then plot by dots is produced. Note, you can use map-like coloring if use ‘%’ in color scheme. See also surf3, surfca, surf3c, surf3a. See Surf3CA sample, for sample code and picture.

MGL command: surf3ca adat cdat bdat ['sch'='']
MGL command: surf3ca xdat ydat zdat adat cdat bdat ['sch'='']
Method on mglGraph: void Surf3CA (const mglDataA &a, const mglDataA &c, const mglDataA &b, const char *sch="", const char *opt="")
Method on mglGraph: void Surf3CA (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &c, const mglDataA &b, const char *sch="", const char *opt="")
C function: void mgl_surf3ca (HMGL gr, HCDT a, HCDT c, HCDT b, const char *sch, const char *opt)
C function: void mgl_surf3ca_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, HCDT c, HCDT b, const char *sch, const char *opt)

Draws num-th uniformly distributed in color range isosurfaces for 3d data. Here parameter num is equal to parameter value in options opt (default is 3).

MGL command: tiles zdat rdat ['sch'='']
MGL command: tiles xdat ydat zdat rdat ['sch'='']
Method on mglGraph: void TileS (const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void TileS (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &r, const char *sch="", const char *opt="")
C function: void mgl_tiles (HMGL gr, HCDT z, HCDT c, const char *sch, const char *opt)
C function: void mgl_tiles_xy (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT r, const char *sch, const char *opt)

The function draws horizontal tiles for surface specified parametrically {x[i,j], y[i,j], z[i,j]}. It is mostly the same as tile but the size of tiles is determined by r array. This is some kind of “transparency” useful for exporting to EPS files. Tiles is plotted for each z slice of the data. See also surfa, tile. See TileS sample, for sample code and picture.

MGL command: map udat vdat ['sch'='']
MGL command: map xdat ydat udat vdat ['sch'='']
Method on mglGraph: void Map (const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
Method on mglGraph: void Map (const mglDataA &x, const mglDataA &y, const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
C function: void mgl_map (HMGL gr, HCDT ax, HCDT ay, const char *sch, const char *opt)
C function: void mgl_map_xy (HMGL gr, HCDT x, HCDT y, HCDT ax, HCDT ay, const char *sch, const char *opt)

The function draws mapping plot for matrices {ax, ay } which parametrically depend on coordinates x, y. The initial position of the cell (point) is marked by color. Height is proportional to Jacobian(ax,ay). This plot is like Arnold diagram ??? If string sch contain symbol ‘.’ then the color ball at matrix knots are drawn otherwise face is drawn. See Mapping visualization, for sample code and picture.

MGL command: stfa re im dn ['sch'='']
MGL command: stfa xdat ydat re im dn ['sch'='']
Method on mglGraph: void STFA (const mglDataA &re, const mglDataA &im, int dn, const char *sch="", const char *opt="")
Method on mglGraph: void STFA (const mglDataA &x, const mglDataA &y, const mglDataA &re, const mglDataA &im, int dn, const char *sch="", const char *opt="")
C function: void mgl_stfa (HMGL gr, HCDT re, HCDT im, int dn, const char *sch, const char *opt)
C function: void mgl_stfa_xy (HMGL gr, HCDT x, HCDT y, HCDT re, HCDT im, int dn, const char *sch, const char *opt)

Draws spectrogram of complex array re+i*im for Fourier size of dn points at plane z equal to minimal z-axis value. For example in 1D case, result is density plot of data res[i,j]=|\sum_d^dn exp(I*j*d)*(re[i*dn+d]+I*im[i*dn+d])|/dn with size {int(nx/dn), dn, ny}. At this array re, im parametrically depend on coordinates x, y. The size of re and im must be the same. The minor dimensions of arrays x, y, re should be equal. Arrays x, y can be vectors (not matrix as re). See STFA sample, for sample code and picture.

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4.15 Vector fields

These functions perform plotting of 2D and 3D vector fields. There are 5 generally different types of vector fields representations: simple vector field (Vect), vectors along the curve (Traj), vector field by dew-drops (Dew), flow threads (Flow, FlowP), flow pipes (Pipe). By default (if absent) values of x, y, z are equidistantly distributed in axis range. The minor dimensions of arrays x, y, z, ax should be equal. The size of ax, ay and az must be equal. Arrays x, y, z can be vectors (not matrices as ax). String sch sets the color scheme (see Color scheme) for plot. String opt contain command options (see Command options).

MGL command: traj xdat ydat udat vdat ['sch'='']
MGL command: traj xdat ydat zdat udat vdat wdat ['sch'='']
Method on mglGraph: void Traj (const mglDataA &x, const mglDataA &y, const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
Method on mglGraph: void Traj (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", const char *opt="")
C function: void mgl_traj_xyz (HMGL gr, HCDTx, HCDTy, HCDTz, HCDTax, HCDTay, HCDTaz, const char *sch, const char *opt)
C function: void mgl_traj_xy (HMGL gr, HCDTx, HCDTy, HCDTax, HCDTay, const char *sch, const char *opt)

The function draws vectors {ax, ay, az} along a curve {x, y, z}. The length of arrows are proportional to \sqrt{ax^2+ay^2+az^2}. String pen specifies the color (see Line styles). By default (pen="") color from palette is used (see Palette and colors). Option value set the vector length factor (if non-zero) or vector length to be proportional the distance between curve points (if value=0). The minor sizes of all arrays must be equal and large 2. The plots are drawn for each row if one of the data is the matrix. See also vect. See Traj sample, for sample code and picture.

MGL command: vect udat vdat ['sch'='']
MGL command: vect xdat ydat udat vdat ['sch'='']
Method on mglGraph: void Vect (const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
Method on mglGraph: void Vect (const mglDataA &x, const mglDataA &y, const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
C function: void mgl_vect_2d (HMGL gr, HCDT ax, HCDT ay, const char *sch, const char *opt)
C function: void mgl_vect_xy (HMGL gr, HCDT x, HCDT y, HCDT ax, HCDT ay, const char *sch, const char *opt)

The function draws plane vector field plot for the field {ax, ay} depending parametrically on coordinates x, y at level z equal to minimal z-axis value. The length and color of arrows are proportional to \sqrt{ax^2+ay^2}. The number of arrows depend on meshnum. The appearance of the hachures (arrows) can be changed by symbols:

See also flow, dew. See Vect sample, for sample code and picture.

MGL command: vect udat vdat wdat ['sch'='']
MGL command: vect xdat ydat zdat udat vdat wdat ['sch'='']
Method on mglGraph: void Vect (const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", const char *opt="")
Method on mglGraph: void Vect (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", const char *opt="")
C function: void mgl_vect_3d (HMGL gr, HCDT ax, HCDT ay, HCDT az, const char *sch, const char *opt)
C function: void mgl_vect_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT ax, HCDT ay, HCDT az, const char *sch, const char *opt)

This is 3D version of the first functions. Here arrays ax, ay, az must be 3-ranged tensors with equal sizes and the length and color of arrows is proportional to \sqrt{ax^2+ay^2+az^2}.

MGL command: vect3 udat vdat wdat ['sch'='' sval]
MGL command: vect3 xdat ydat zdat udat vdat wdat ['sch'='' sval]
Method on mglGraph: void Vect3 (const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", mreal sVal=-1, const char *opt="")
Method on mglGraph: void Vect3 (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", mreal sVal=-1, const char *opt="")
C function: void mgl_vect3 (HMGL gr, HCDT ax, HCDT ay, HCDT az, const char *sch, mreal sVal, const char *opt)
C function: void mgl_vect3_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT ax, HCDT ay, HCDT az, const char *sch, mreal sVal, const char *opt)

The function draws 3D vector field plot for the field {ax, ay, az} depending parametrically on coordinates x, y, z. Vector field is drawn at slice sVal in direction {‘x’, ‘y’, ‘z’} if sch contain corresponding symbol (by default, ‘y’ direction is used). The length and color of arrows are proportional to \sqrt{ax^2+ay^2+az^2}. The number of arrows depend on meshnum. The appearance of the hachures (arrows) can be changed by symbols:

See also vect, flow, dew. See Vect3 sample, for sample code and picture.

MGL command: dew udat vdat ['sch'='']
MGL command: dew xdat ydat udat vdat ['sch'='']
Method on mglGraph: void Dew (const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
Method on mglGraph: void Dew (const mglDataA &x, const mglDataA &y, const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
C function: void mgl_dew (HMGL gr, HCDT ax, HCDT ay, const char *sch, const char *opt)
C function: void mgl_dew_xy (HMGL gr, HCDT x, HCDT y, HCDT ax, HCDT ay, const char *sch, const char *opt)

The function draws dew-drops for plane vector field {ax, ay} depending parametrically on coordinates x, y at level z equal to minimal z-axis value. Note that this is very expensive plot in memory usage and creation time! The color of drops is proportional to \sqrt{ax^2+ay^2}. The number of drops depend on meshnum. See also vect. See Dew sample, for sample code and picture.

MGL command: flow udat vdat ['sch'='']
MGL command: flow xdat ydat udat vdat ['sch'='']
Method on mglGraph: void Flow (const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
Method on mglGraph: void Flow (const mglDataA &x, const mglDataA &y, const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
C function: void mgl_flow_2d (HMGL gr, HCDT ax, HCDT ay, const char *sch, const char *opt)
C function: void mgl_flow_xy (HMGL gr, HCDT x, HCDT y, HCDT ax, HCDT ay, const char *sch, const char *opt)

The function draws flow threads for the plane vector field {ax, ay} parametrically depending on coordinates x, y at level z equal to minimal z-axis value. Number of threads is proportional to value option (default is 5). String sch may contain:

See also pipe, vect, tape, barwidth. See Flow sample, for sample code and picture.

MGL command: flow udat vdat wdat ['sch'='']
MGL command: flow xdat ydat zdat udat vdat wdat ['sch'='']
Method on mglGraph: void Flow (const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", const char *opt="")
Method on mglGraph: void Flow (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", const char *opt="")
C function: void mgl_flow_3d (HMGL gr, HCDT ax, HCDT ay, HCDT az, const char *sch, const char *opt)
C function: void mgl_flow_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT ax, HCDT ay, HCDT az, const char *sch, const char *opt)

This is 3D version of the first functions. Here arrays ax, ay, az must be 3-ranged tensors with equal sizes and the color of line is proportional to \sqrt{ax^2+ay^2+az^2}.

MGL command: flow x0 y0 udat vdat ['sch'='']
MGL command: flow x0 y0 xdat ydat udat vdat ['sch'='']
Method on mglGraph: void FlowP (mglPoint p0, const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
Method on mglGraph: void FlowP (mglPoint p0, const mglDataA &x, const mglDataA &y, const mglDataA &ax, const mglDataA &ay, const char *sch="", const char *opt="")
C function: void mgl_flowp_2d (HMGL gr, mreal x0, mreal y0, mreal z0, HCDT ax, HCDT ay, const char *sch, const char *opt)
C function: void mgl_flowp_xy (HMGL gr, mreal x0, mreal y0, mreal z0, HCDT x, HCDT y, HCDT ax, HCDT ay, const char *sch, const char *opt)

The same as first one (flow) but draws single flow thread starting from point p0={x0,y0,z0}.

MGL command: flow x0 y0 z0 udat vdat wdat ['sch'='']
MGL command: flow x0 y0 z0 xdat ydat zdat udat vdat wdat ['sch'='']
Method on mglGraph: void FlowP (mglPoint p0, const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", const char *opt="")
Method on mglGraph: void FlowP (mglPoint p0, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", const char *opt="")
C function: void mgl_flowp_3d (HMGL gr, mreal x0, mreal y0, mreal z0, HCDT ax, HCDT ay, HCDT az, const char *sch, const char *opt)
C function: void mgl_flowp_xyz (HMGL gr, mreal x0, mreal y0, mreal z0, HCDT x, HCDT y, HCDT z, HCDT ax, HCDT ay, HCDT az, const char *sch, const char *opt)

This is 3D version of the previous functions.

MGL command: grad pdat ['sch'='']
MGL command: grad xdat ydat pdat ['sch'='']
MGL command: grad xdat ydat zdat pdat ['sch'='']
Method on mglGraph: void Grad (const mglDataA &phi, const char *sch="", const char *opt="")
Method on mglGraph: void Grad (const mglDataA &x, const mglDataA &y, const mglDataA &phi, const char *sch="", const char *opt="")
Method on mglGraph: void Grad (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &phi, const char *sch="", const char *opt="")
C function: void mgl_grad (HMGL gr, HCDT phi, const char *sch, const char *opt)
C function: void mgl_grad_xy (HMGL gr, HCDT x, HCDT y, HCDT phi, const char *sch, const char *opt)
C function: void mgl_grad_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT phi, const char *sch, const char *opt)

The function draws gradient lines for scalar field phi[i,j] (or phi[i,j,k] in 3d case) specified parametrically {x[i,j,k], y[i,j,k], z[i,j,k]}. Number of lines is proportional to value option (default is 5). See also dens, cont, flow.

MGL command: pipe udat vdat ['sch'='' r0=0.05]
MGL command: pipe xdat ydat udat vdat ['sch'='' r0=0.05]
Method on mglGraph: void Pipe (const mglDataA &ax, const mglDataA &ay, const char *sch="", mreal r0=0.05, const char *opt="")
Method on mglGraph: void Pipe (const mglDataA &x, const mglDataA &y, const mglDataA &ax, const mglDataA &ay, const char *sch="", mreal r0=0.05, const char *opt="")
C function: void mgl_pipe_2d (HMGL gr, HCDT ax, HCDT ay, const char *sch, mreal r0, const char *opt)
C function: void mgl_pipe_xy (HMGL gr, HCDT x, HCDT y, HCDT ax, HCDT ay, const char *sch, mreal r0, const char *opt)

The function draws flow pipes for the plane vector field {ax, ay} parametrically depending on coordinates x, y at level z equal to minimal z-axis value. Number of pipes is proportional to value option (default is 5). If ‘#’ symbol is specified then pipes start only from edges of axis range. The color of lines is proportional to \sqrt{ax^2+ay^2}. Warm color corresponds to normal flow (like attractor). Cold one corresponds to inverse flow (like source). Parameter r0 set the base pipe radius. If r0<0 or symbol ‘i’ is specified then pipe radius is inverse proportional to amplitude. The vector field is plotted for each z slice of ax, ay. See also flow, vect. See Pipe sample, for sample code and picture.

MGL command: pipe udat vdat wdat ['sch'='' r0=0.05]
MGL command: pipe xdat ydat zdat udat vdat wdat ['sch'='' r0=0.05]
Method on mglGraph: void Pipe (const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", mreal r0=0.05, const char *opt="")
Method on mglGraph: void Pipe (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &ax, const mglDataA &ay, const mglDataA &az, const char *sch="", mreal r0=0.05, const char *opt="")
C function: void mgl_pipe_3d (HMGL gr, HCDT ax, HCDT ay, HCDT az, const char *sch, mreal r0, const char *opt)
C function: void mgl_pipe_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT ax, HCDT ay, HCDT az, const char *sch, mreal r0, const char *opt)

This is 3D version of the first functions. Here arrays ax, ay, az must be 3-ranged tensors with equal sizes and the color of line is proportional to \sqrt{ax^2+ay^2+az^2}.

Next: , Previous: , Up: MathGL core   [Contents][Index]

4.16 Other plotting

These functions perform miscellaneous plotting. There is unstructured data points plots (Dots), surface reconstruction (Crust), surfaces on the triangular or quadrangular mesh (TriPlot, TriCont, QuadPlot), textual formula plotting (Plots by formula), data plots at edges (Dens[XYZ], Cont[XYZ], ContF[XYZ]). Each type of plotting has similar interface. There are 2 kind of versions which handle the arrays of data and coordinates or only single data array. Parameters of color scheme are specified by the string argument. See Color scheme.

MGL command: densx dat ['sch'='' sval=nan]
MGL command: densy dat ['sch'='' sval=nan]
MGL command: densz dat ['sch'='' sval=nan]
Method on mglGraph: void DensX (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void DensY (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void DensZ (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
C function: void mgl_dens_x (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_dens_y (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_dens_z (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)

These plotting functions draw density plot in x, y, or z plain. If a is a tensor (3-dimensional data) then interpolation to a given sVal is performed. These functions are useful for creating projections of the 3D data array to the bounding box. See also ContXYZ, ContFXYZ, dens, Data manipulation. See Dens projection sample, for sample code and picture.

MGL command: contx dat ['sch'='' sval=nan]
MGL command: conty dat ['sch'='' sval=nan]
MGL command: contz dat ['sch'='' sval=nan]
Method on mglGraph: void ContX (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContY (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContZ (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
C function: void mgl_cont_x (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_cont_y (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_cont_z (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)

These plotting functions draw contour lines in x, y, or z plain. If a is a tensor (3-dimensional data) then interpolation to a given sVal is performed. These functions are useful for creating projections of the 3D data array to the bounding box. Option value set the number of contours. See also ContFXYZ, DensXYZ, cont, Data manipulation. See Cont projection sample, for sample code and picture.

Method on mglGraph: void ContX (const mglDataA &v, const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContY (const mglDataA &v, const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContZ (const mglDataA &v, const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
C function: void mgl_cont_x_val (HMGL gr, HCDT v, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_cont_y_val (HMGL gr, HCDT v, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_cont_z_val (HMGL gr, HCDT v, HCDT a, const char *stl, mreal sVal, const char *opt)

The same as previous with manual contour levels.

MGL command: contfx dat ['sch'='' sval=nan]
MGL command: contfy dat ['sch'='' sval=nan]
MGL command: contfz dat ['sch'='' sval=nan]
Method on mglGraph: void ContFX (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContFY (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContFZ (const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
C function: void mgl_contf_x (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_contf_y (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_contf_z (HMGL gr, HCDT a, const char *stl, mreal sVal, const char *opt)

These plotting functions draw solid contours in x, y, or z plain. If a is a tensor (3-dimensional data) then interpolation to a given sVal is performed. These functions are useful for creating projections of the 3D data array to the bounding box. Option value set the number of contours. See also ContFXYZ, DensXYZ, cont, Data manipulation. See ContF projection sample, for sample code and picture.

Method on mglGraph: void ContFX (const mglDataA &v, const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContFY (const mglDataA &v, const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
Method on mglGraph: void ContFZ (const mglDataA &v, const mglDataA &a, const char *stl="", mreal sVal=NAN, const char *opt="")
C function: void mgl_contf_x_val (HMGL gr, HCDT v, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_contf_y_val (HMGL gr, HCDT v, HCDT a, const char *stl, mreal sVal, const char *opt)
C function: void mgl_contf_z_val (HMGL gr, HCDT v, HCDT a, const char *stl, mreal sVal, const char *opt)

The same as previous with manual contour levels.

MGL command: fplot 'y(x)' ['pen'='']
Method on mglGraph: void FPlot (const char *eqY, const char *pen="", const char *opt="")
C function: void mgl_fplot (HMGL gr, const char *eqY, const char *pen, const char *opt)

Draws command function ‘y(x)’ at plane z equal to minimal z-axis value, where ‘x’ variable is changed in xrange. You do not need to create the data arrays to plot it. Option value set initial number of points. See also plot.

MGL command: fplot 'x(t)' 'y(t)' 'z(t)' ['pen'='']
Method on mglGraph: void FPlot (const char *eqX, const char *eqY, const char *eqZ, const char *pen, const char *opt="")
C function: void mgl_fplot_xyz (HMGL gr, const char *eqX, const char *eqY, const char *eqZ, const char *pen, const char *opt)

Draws command parametrical curve {‘x(t)’, ‘y(t)’, ‘z(t)’} where ‘t’ variable is changed in range [0, 1]. You do not need to create the data arrays to plot it. Option value set number of points. See also plot.

MGL command: fsurf 'z(x,y)' ['sch'='']
Method on mglGraph: void FSurf (const char *eqZ, const char *sch="", const char *opt="");
C function: void mgl_fsurf (HMGL gr, const char *eqZ, const char *sch, const char *opt);

Draws command surface for function ‘z(x,y)’ where ‘x’, ‘y’ variable are changed in xrange, yrange. You do not need to create the data arrays to plot it. Option value set number of points. See also surf.

MGL command: fsurf 'x(u,v)' 'y(u,v)' 'z(u,v)' ['sch'='']
Method on mglGraph: void FSurf (const char *eqX, const char *eqY, const char *eqZ, const char *sch="", const char *opt="")
C function: void mgl_fsurf_xyz (HMGL gr, const char *eqX, const char *eqY, const char *eqZ, const char *sch, const char *opt)

Draws command parametrical surface {‘x(u,v)’, ‘y(u,v)’, ‘z(u,v)’} where ‘u’, ‘v’ variable are changed in range [0, 1]. You do not need to create the data arrays to plot it. Option value set number of points. See also surf.

MGL command: triplot idat xdat ydat ['sch'='']
MGL command: triplot idat xdat ydat zdat ['sch'='']
MGL command: triplot idat xdat ydat zdat cdat ['sch'='']
Method on mglGraph: void TriPlot (const mglDataA &id, const mglDataA &x, const mglDataA &y, const char *sch="", const char *opt="")
Method on mglGraph: void TriPlot (const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void TriPlot (const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_triplot_xy (HMGL gr, HCDT id, HCDT x, HCDT y, const char *sch, const char *opt)
C function: void mgl_triplot_xyz (HMGL gr, HCDT id, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)
C function: void mgl_triplot_xyzc (HMGL gr, HCDT id, HCDT x, HCDT y, HCDT z, HCDT c, const char *sch, const char *opt)

The function draws the surface of triangles. Triangle vertexes are set by indexes id of data points {x[i], y[i], z[i]}. String sch sets the color scheme. If string contain ‘#’ then wire plot is produced. First dimensions of id must be 3 or greater. Arrays x, y, z must have equal sizes. Parameter c set the colors of triangles (if id.ny=c.nx) or colors of vertexes (if x.nx=c.nx). See also dots, crust, quadplot, triangulation. See TriPlot and QuadPlot, for sample code and picture.

MGL command: tricont vdat idat xdat ydat zdat cdat ['sch'='']
MGL command: tricont vdat idat xdat ydat zdat ['sch'='']
MGL command: tricont idat xdat ydat zdat ['sch'='']
Method on mglGraph: void TriCont (const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void TriCont (const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void TriContV (const mglDataA &v, const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void TriContV (const mglDataA &v, const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_tricont_xyzc (HMGL gr, HCDT id, HCDT x, HCDT y, HCDT z, HCDT c, const char *sch, const char *opt)
C function: void mgl_tricont_xyz (HMGL gr, HCDT id, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)
C function: void mgl_tricont_xyzcv (HMGL gr, HCDT v, HCDT id, HCDT x, HCDT y, HCDT z, HCDT c, const char *sch, const char *opt)
C function: void mgl_tricont_xyzv (HMGL gr, HCDT v, HCDT id, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function draws contour lines for surface of triangles at z=v[k] (or at z equal to minimal z-axis value if sch contain symbol ‘_’). Triangle vertexes are set by indexes id of data points {x[i], y[i], z[i]}. Contours are plotted for z[i,j]=v[k] where v[k] are values of data array v. If v is absent then arrays of option value elements equidistantly distributed in color range is used. String sch sets the color scheme. Array c (if specified) is used for contour coloring. First dimensions of id must be 3 or greater. Arrays x, y, z must have equal sizes. Parameter c set the colors of triangles (if id.ny=c.nx) or colors of vertexes (if x.nx=c.nx). See also triplot, cont, triangulation.

MGL command: quadplot idat xdat ydat ['sch'='']
MGL command: quadplot idat xdat ydat zdat ['sch'='']
MGL command: quadplot idat xdat ydat zdat cdat ['sch'='']
Method on mglGraph: void QuadPlot (const mglDataA &id, const mglDataA &x, const mglDataA &y, const char *sch="", const char *opt="")
Method on mglGraph: void QuadPlot (const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const char *sch="", const char *opt="")
Method on mglGraph: void QuadPlot (const mglDataA &id, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_quadplot_xy (HMGL gr, HCDT id, HCDT x, HCDT y, const char *sch, const char *opt)
C function: void mgl_quadplot_xyz (HMGL gr, HCDT id, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)
C function: void mgl_quadplot_xyzc (HMGL gr, HCDT id, HCDT x, HCDT y, HCDT z, HCDT c, const char *sch, const char *opt)

The function draws the surface of quadrangles. Quadrangles vertexes are set by indexes id of data points {x[i], y[i], z[i]}. String sch sets the color scheme. If string contain ‘#’ then wire plot is produced. First dimensions of id must be 4 or greater. Arrays x, y, z must have equal sizes. Parameter c set the colors of quadrangles (if id.ny=c.nx) or colors of vertexes (if x.nx=c.nx). See also triplot. See TriPlot and QuadPlot, for sample code and picture.

MGL command: dots xdat ydat zdat ['sch'='']
MGL command: dots xdat ydat zdat adat ['sch'='']
Method on mglGraph: void Dots (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
Method on mglGraph: void Dots (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *sch="", const char *opt="")
Method on mglGraph: void Dots (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &c, const mglDataA &a, const char *sch="", const char *opt="")
C function: void mgl_dots (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)
C function: void mgl_dots_a (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *sch, const char *opt)
C function: void mgl_dots_ca (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT c, HCDT a, const char *sch, const char *opt)

The function draws the arbitrary placed points {x[i], y[i], z[i]}. String sch sets the color scheme and kind of marks. If arrays c, a are specified then they define colors and transparencies of dots. You can use tens plot with style ‘ .’ to draw non-transparent dots with specified colors. Arrays x, y, z, a must have equal sizes. See also crust, tens, mark, plot. See Dots sample, for sample code and picture.

MGL command: crust xdat ydat zdat ['sch'='']
Method on mglGraph: void Crust (const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *sch="", const char *opt="")
C function: void mgl_crust (HMGL gr, HCDT x, HCDT y, HCDT z, const char *sch, const char *opt)

The function reconstruct and draws the surface for arbitrary placed points {x[i], y[i], z[i]}. String sch sets the color scheme. If string contain ‘#’ then wire plot is produced. Arrays x, y, z must have equal sizes. See also dots, triplot.

Next: , Previous: , Up: MathGL core   [Contents][Index]

4.17 Nonlinear fitting

These functions fit data to formula. Fitting goal is to find formula parameters for the best fit the data points, i.e. to minimize the sum \sum_i (f(x_i, y_i, z_i) - a_i)^2/s_i^2. At this, approximation function ‘f’ can depend only on one argument ‘x’ (1D case), on two arguments ‘x,y’ (2D case) and on three arguments ‘x,y,z’ (3D case). The function ‘f’ also may depend on parameters. Normally the list of fitted parameters is specified by var string (like, ‘abcd’). Usually user should supply initial values for fitted parameters by ini variable. But if he/she don’t supply it then the zeros are used. Parameter print=true switch on printing the found coefficients to Message (see Error handling).

Functions Fit() and FitS() do not draw the obtained data themselves. They fill the data fit by formula ‘f’ with found coefficients and return it. At this, the ‘x,y,z’ coordinates are equidistantly distributed in the axis range. Number of points in fit is defined by option value (default is mglFitPnts=100). Note, that this functions use GSL library and do something only if MathGL was compiled with GSL support. See Nonlinear fitting hints, for sample code and picture.

MGL command: fits res adat sdat 'func' 'var' [ini=0]
MGL command: fits res xdat adat sdat 'func' 'var' [ini=0]
MGL command: fits res xdat ydat adat sdat 'func' 'var' [ini=0]
MGL command: fits res xdat ydat zdat adat sdat 'func' 'var' [ini=0]
Method on mglGraph: mglData FitS (const mglDataA &a, const mglDataA &s, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData FitS (const mglDataA &a, const mglDataA &s, const char *func, const char *var, mglData &ini, const char *opt="")
Method on mglGraph: mglData FitS (const mglDataA &x, const mglDataA &a, const mglDataA &s, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData FitS (const mglDataA &x, const mglDataA &a, const mglDataA &s, const char *func, const char *var, mglData &ini, const char *opt="")
Method on mglGraph: mglData FitS (const mglDataA &x, const mglDataA &y, const mglDataA &a, const mglDataA &s, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData FitS (const mglDataA &x, const mglDataA &y, const mglDataA &a, const mglDataA &s, const char *func, const char *var, mglData &ini, const char *opt="")
Method on mglGraph: mglData FitS (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &s, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData FitS (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const mglDataA &s, const char *func, const char *var, mglData &ini, const char *opt="")
C function: HMDT mgl_fit_ys (HMGL gr, HCDT a, HCDT s, const char *func, const char *var, HMDT ini, const char *opt)
C function: HMDT mgl_fit_xys (HMGL gr, HCDT x, HCDT a, HCDT s, const char *func, const char *var, HMDT ini, const char *opt)
C function: HMDT mgl_fit_xyzs (HMGL gr, HCDT x, HCDT y, HCDT a, HCDT s, const char *func, const char *var, HMDT ini, const char *opt)
C function: HMDT mgl_fit_xyzas (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, HCDT s, const char *func, const char *var, HMDT ini, const char *opt)

Fit data along x-, y- and z-directions for array specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]) with weight factor s[i,j,k].

MGL command: fit res adat 'func' 'var' [ini=0]
MGL command: fit res xdat adat 'func' 'var' [ini=0]
MGL command: fit res xdat ydat adat 'func' 'var' [ini=0]
MGL command: fit res xdat ydat zdat adat 'func' 'var' [ini=0]
Method on mglGraph: mglData Fit (const mglDataA &a, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData Fit (const mglDataA &a, const char *func, const char *var, mglData &ini, const char *opt="")
Method on mglGraph: mglData Fit (const mglDataA &x, const mglDataA &a, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData Fit (const mglDataA &x, const mglDataA &a, const char *func, const char *var, mglData &ini, const char *opt="")
Method on mglGraph: mglData Fit (const mglDataA &x, const mglDataA &y, const mglDataA &a, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData Fit (const mglDataA &x, const mglDataA &y, const mglDataA &a, const char *func, const char *var, mglData &ini, const char *opt="")
Method on mglGraph: mglData Fit (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData Fit (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *func, const char *var, mglData &ini, const char *opt="")
C function: HMDT mgl_fit_y (HMGL gr, HCDT a, const char *func, const char *var, HMDT ini, const char *opt)
C function: HMDT mgl_fit_xy (HMGL gr, HCDT x, HCDT a, const char *func, const char *var, HMDT ini, const char *opt)
C function: HMDT mgl_fit_xyz (HMGL gr, HCDT x, HCDT y, HCDT a, const char *func, const char *var, HMDT ini, const char *opt)
C function: HMDT mgl_fit_xyza (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *func, const char *var, HMDT ini, const char *opt)

Fit data along x-, y- and z-directions for array specified parametrically a[i,j,k](x[i,j,k], y[i,j,k], z[i,j,k]) with weight factor 1.

Method on mglGraph: mglData Fit2 (const mglDataA &a, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData Fit2 (mglData &fit, const mglDataA &a, const char *func, const char *var, mglData &ini, const char *opt="")
Method on mglGraph: mglData Fit3 (mglData &fit, const mglDataA &a, const char *func, const char *var, const char *opt="")
Method on mglGraph: mglData Fit3 (mglData &fit, const mglDataA &a, const char *func, const char *var, mglData &ini, const char *opt="")
C function: HMDT mgl_fit_2 (HMGL gr, HCDT a, const char *func, const char *var, HMDT ini, const char *opt)
C function: HMDT mgl_fit_3 (HMGL gr, HCDT a, const char *func, const char *var, HMDT ini, const char *opt)

Fit data along all directions for 2d or 3d arrays a with s=1 and x, y, z equidistantly distributed in axis range.

MGL command: putsfit x y ['pre'='' 'fnt'='' size=-1]
Method on mglGraph: void PutsFit (mglPoint p, const char *prefix="", const char *font="", mreal size=-1)
C function: void mgl_puts_fit (HMGL gr, mreal x, mreal y, mreal z, const char *prefix, const char *font, mreal size)

Print last fitted formula with found coefficients (as numbers) at position p0. The string prefix will be printed before formula. All other parameters are the same as in Text printing.

Method on mglGraph: const char *GetFit ()
C function only: const char * mgl_get_fit (HMGL gr)
Fortran subroutine: mgl_get_fit (long gr, char *out, int len)

Get last fitted formula with found coefficients (as numbers).

Method on mglGraph: mreal GetFitChi ()
C function: mreal mgl_get_fit_chi ()

Get \chi for last fitted formula.

Method on mglGraph: mreal GetFitCovar ()
C function: mreal mgl_get_fit_covar ()

Get covariance matrix for last fitted formula.

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4.18 Data manipulation

MGL command: hist RES xdat adat
MGL command: hist RES xdat ydat adat
MGL command: hist RES xdat ydat zdat adat
Method on mglGraph: mglData Hist (const mglDataA &x, const mglDataA &a, const char *opt="")
Method on mglGraph: mglData Hist (const mglDataA &x, const mglDataA &y, const mglDataA &a, const char *opt="")
Method on mglGraph: mglData Hist (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &a, const char *opt="")
C function: HMDT mgl_hist_x (HMGL gr, HCDT x, HCDT a, const char *opt)
C function: HMDT mgl_hist_xy (HMGL gr, HCDT x, HCDT y, HCDT a, const char *opt)
C function: HMDT mgl_hist_xyz (HMGL gr, HCDT x, HCDT y, HCDT z, HCDT a, const char *opt)

These functions make distribution (histogram) of data. They do not draw the obtained data themselves. These functions can be useful if user have data defined for random points (for example, after PIC simulation) and he want to produce a plot which require regular data (defined on grid(s)). The range for grids is always selected as axis range. Arrays x, y, z define the positions (coordinates) of random points. Array a define the data value. Number of points in output array res is defined by option value (default is mglFitPnts=100).

MGL command: fill dat 'eq'
MGL command: fill dat 'eq' vdat
MGL command: fill dat 'eq' vdat wdat
Method on mglGraph: void Fill (mglData &u, const char *eq, const char *opt="")
Method on mglGraph: void Fill (mglData &u, const char *eq, const mglDataA &v, const char *opt="")
Method on mglGraph: void Fill (mglData &u, const char *eq, const mglDataA &v, const mglDataA &w, const char *opt="")
C function: void mgl_data_fill_eq (HMGL gr, HMDT u, const char *eq, HCDTv, HCDTw, const char *opt)

Fills the value of array ‘u’ according to the formula in string eq. Formula is an arbitrary expression depending on variables ‘x’, ‘y’, ‘z’, ‘u’, ‘v’, ‘w’. Coordinates ‘x’, ‘y’, ‘z’ are supposed to be normalized in axis range. Variable ‘u’ is the original value of the array. Variables ‘v’ and ‘w’ are values of arrays v, w which can be NULL (i.e. can be omitted).

MGL command: datagrid dat xdat ydat zdat
Method on mglGraph: void DataGrid (mglData &u, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *opt="")
C function: void mgl_data_grid (HMGL gr, HMDT u, HCDT x, HCDT y, HCDT z, const char *opt)

Fills the value of array ‘u’ according to the linear interpolation of triangulated surface, found for arbitrary placed points ‘x’, ‘y’, ‘z’. Interpolation is done at points equidistantly distributed in axis range. NAN value is used for grid points placed outside of triangulated surface. See Making regular data, for sample code and picture.

MGL command: refill dat xdat vdat [sl=-1]
MGL command: refill dat xdat ydat vdat [sl=-1]
MGL command: refill dat xdat ydat zdat vdat
Method on mglData: void Refill (mglDataA &dat, const mglDataA &x, const mglDataA &v, long sl=-1, const char *opt="")
Method on mglData: void Refill (mglDataA &dat, const mglDataA &x, const mglDataA &y, const mglDataA &v, long sl=-1, const char *opt="")
Method on mglData: void Refill (mglDataA &dat, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &v, const char *opt="")
C function: void mgl_data_refill_gr (HMGL gr, HMDT a, HCDT x, HCDT y, HCDT z, HCDT v, long sl, const char *opt)

Fills by interpolated values of array v at the point {x, y, z}={X[i], Y[j], Z[k]} (or {x, y, z}={X[i,j,k], Y[i,j,k], Z[i,j,k]} if x, y, z are not 1d arrays), where X,Y,Z are equidistantly distributed in axis range and have the same sizes as array dat. If parameter sl is 0 or positive then changes will be applied only for slice sl.

MGL command: pde RES 'ham' ini_re ini_im [dz=0.1 k0=100]
Method on mglGraph: mglData PDE (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, mreal dz=0.1, mreal k0=100, const char *opt="")
C function: HMDT mgl_pde_solve (HMGL gr, const char *ham, HCDT ini_re, HCDT ini_im, mreal dz, mreal k0, const char *opt)

Solves equation du/dz = i*k0*ham(p,q,x,y,z,|u|)[u], where p=-i/k0*d/dx, q=-i/k0*d/dy are pseudo-differential operators. Parameters ini_re, ini_im specify real and imaginary part of initial field distribution. Coordinates ‘x’, ‘y’, ‘z’ are supposed to be normalized in axis range. Note, that really this ranges are increased by factor 3/2 for purpose of reducing reflection from boundaries. Parameter dz set the step along evolutionary coordinate z. At this moment, simplified form of function ham is supported – all “mixed” terms (like ‘x*p’->x*d/dx) are excluded. For example, in 2D case this function is effectively ham = f(p,z) + g(x,z,u). However commutable combinations (like ‘x*q’->x*d/dy) are allowed. Here variable ‘u’ is used for field amplitude |u|. This allow one solve nonlinear problems – for example, for nonlinear Shrodinger equation you may set ham="p^2 + q^2 - u^2". You may specify imaginary part for wave absorption, like ham = "p^2 + i*x*(x>0)", but only if dependence on variable ‘i’ is linear (i.e. ham = hre+i*him). See PDE solving hints, for sample code and picture.

Next: , Previous: , Up: Top   [Contents][Index]

5 Widget classes

There are set of “window” classes for making a window with MathGL graphics: mglWindow, mglFLTK, mglQT and mglGLUT for whole window, Fl_MathGL and QMathGL as widgets. All these classes allow user to show, rotate, export, and change view of the plot using keyboard. Most of them (except mglGLUT) also have toolbar and menu for simplifying plot manipulation. All window classes have mostly the same set of functions derived from mglWnd class.

For drawing you can use: NULL pointer if you’ll update plot manually, global callback function of type int draw(HMGL gr, void *p) or int draw(mglGraph *gr), or instance of class derived from mglDraw class. Basically, this class have 2 main virtual methods: 

class mglDraw
{
public:
    virtual int Draw(mglGraph *) { return 0; };
    virtual void Reload() {};
};

You should inherit yours class from mglDraw and re-implement one or both functions for drawing.

The window can be constructed using one of following classes (see Using MathGL window for examples).

Constructor on mglFLTK: mglFLTK (const char *title="MathGL")
Constructor on mglFLTK: mglFLTK (int (*draw)(HMGL gr, void *p), const char *title="MathGL", void *par=NULL, void (*reload)(HMGL gr, void *p)=0)
Constructor on mglFLTK: mglFLTK (int (*draw)(mglGraph *gr), const char *title="MathGL")
Constructor on mglFLTK: mglFLTK (mglDraw *draw, const char *title="MathGL")
C function: HMGL mgl_create_graph_fltk (int (*draw)(HMGL gr, void *p), const char *title, void *par, void (*reload)(HMGL gr, void *p))

Creates a FLTK-based window for plotting. Parameter draw sets a pointer to drawing function (this is the name of function) or instance of mglDraw class. There is support of a list of plots (frames). So as one can prepare a set of frames at first and redraw it fast later (but it requires more memory). Function should return positive number of frames for the list or zero if it will plot directly. Note, that draw can be NULL for displaying static bitmaps only (no animation or slides). Parameter title sets the title of the window. Parameter par contains pointer to data for the plotting function draw. FLTK-based windows is a bit faster than Qt ones, and provide better support of multi-threading.

Method on mglFLTK: int RunThr ()
C function: int mgl_fltk_thr ()

Run main loop for event handling in separate thread. Note, right now it work for FLTK windows only.

Constructor on mglQT: mglQT (const char *title="MathGL")
Constructor on mglQT: mglQT (int (*draw)(HMGL gr, void *p), const char *title="MathGL", void *par=NULL, void (*reload)(HMGL gr, void *p)=0)
Constructor on mglQT: mglQT (int (*draw)(mglGraph *gr), const char *title="MathGL")
Constructor on mglQT: mglQT (mglDraw *draw, const char *title="MathGL")
C function: HMGL mgl_create_graph_qt (int (*draw)(HMGL gr, void *p), const char *title, void *par, void (*reload)(HMGL gr, void *p))

Creates a FLTK-based window for plotting. Parameter draw sets a pointer to drawing function (this is the name of function) or instance of mglDraw class. There is support of a list of plots (frames). So as one can prepare a set of frames at first and redraw it fast later (but it requires more memory). Function should return positive number of frames for the list or zero if it will plot directly. Note, that draw can be NULL for displaying static bitmaps only (no animation or slides). Parameter title sets the title of the window. Parameter par contains pointer to data for the plotting function draw.

Constructor on mglGLUT: mglGLUT (const char *title="MathGL")
Constructor on mglGLUT: mglGLUT (int (*draw)(HMGL gr, void *p), const char *title="MathGL", void *par=NULL, void (*reload)(HMGL gr, void *p)=0)
Constructor on mglGLUT: mglGLUT (int (*draw)(mglGraph *gr), const char *title="MathGL")
Constructor on mglGLUT: mglGLUT (mglDraw *draw, const char *title="MathGL")
C function: HMGL mgl_create_graph_glut (int (*draw)(HMGL gr, void *p), const char *title, void *par, void (*reload)(HMGL gr, void *p))

Creates a GLUT-based window for plotting. Parameter draw sets a pointer to drawing function (this is the name of function) or instance of mglDraw class. There is support of a list of plots (frames). So as one can prepare a set of frames at first and redraw it fast later (but it requires more memory). Function should return positive number of frames for the list or zero if it will plot directly. Note, that draw can be NULL for displaying static bitmaps only (no animation or slides). Parameter title sets the title of the window. Parameter par contains pointer to data for the plotting function draw. GLUT-based windows are fastest one but there is no toolbar, and plot have some issues due to OpenGL limitations.

There are some keys handles for manipulating by the plot: ’a’, ’d’, ’w’, ’s’ for the rotating; ’,’, ’.’ for viewing of the previous or next frames in the list; ’r’ for the switching of transparency; ’f’ for the switching of lightning; ’x’ for hiding (closing) the window.

• mglWnd class:  
• mglDraw class:  
• Fl_MathGL class:  
• QMathGL class:  
• wxMathGL class:  

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5.1 mglWnd class

This class is abstract class derived from mglGraph class (see MathGL core). It is defined in #include <mgl2/wnd.h> and provide base methods for handling window with MathGL graphics. Inherited classes are exist for QT and FLTK widget libraries: mglQT in #include <mgl2/qt.h>, mglFLTK in #include <mgl2/fltk.h>.

Method on mglWnd: int Run ()
C function: int mgl_qt_run ()
C function: int mgl_fltk_run ()

Run main loop for event handling. Usually it should be called in a separate thread or as last function call in main().

Method on mglWnd: void SetDrawFunc (int (*draw)(HMGL gr, void *p), void *par=NULL, void (*reload)(void *p)=NULL)
Method on mglWnd: void SetDrawFunc (int (*draw)(mglGraph *gr))
Method on mglWnd: void SetDrawFunc (mglDraw *obj)
C function: void mgl_wnd_set_func (HMGL gr, int (*draw)(HMGL gr, void *p), void *par, void (*reload)(void *p))

Set callback functions for drawing (draw) and data reloading (reload), or instance obj of a class derived from mglDraw.

Method on mglWnd: void SetClickFunc (void (*func)(HMGL gr, void *p))
C function: void mgl_set_click_func (void (*func)(HMGL gr, void *p))

Set callback function func which will be called on mouse click.

Method on mglWnd: void SetMutex(pthread_mutex_t *mutex)
C function: void mgl_wnd_set_mutex(HMGL gr, pthread_mutex_t *mutex)

Set external mutex for lock/unlock external calculations by widget. This functions is called automatically at using mglDraw class.

Method on mglWnd: void ToggleAlpha ()
C function: void mgl_wnd_toggle_alpha (HMGL gr)

Switch on/off transparency but do not overwrite switches in user drawing function.

Method on mglWnd: void ToggleLight ()
C function: void mgl_wnd_toggle_light (HMGL gr)

Switch on/off lighting but do not overwrite switches in user drawing function.

Method on mglWnd: void ToggleRotate ()
C function: void mgl_wnd_toggle_rotate (HMGL gr)

Switch on/off rotation by mouse. Usually, left button is used for rotation, middle button for shift, right button for zoom/perspective.

Method on mglWnd: void ToggleZoom ()
C function: void mgl_wnd_toggle_zoom (HMGL gr)

Switch on/off zooming by mouse. Just select rectangular region by mouse and it will be zoomed in.

Method on mglWnd: void ToggleNo ()
C function: void mgl_wnd_toggle_no (HMGL gr)

Switch off all zooming and rotation and restore initial state.

Method on mglWnd: void Update ()
C function: void mgl_wnd_update (HMGL gr)

Update window contents. This is very useful function for manual updating the plot while long calculation was running in parallel thread.

Method on mglWnd: void ReLoad ()
C function: void mgl_wnd_reload (HMGL gr)

Reload user data and update picture. This function also update number of frames which drawing function can create.

Method on mglWnd: void Adjust ()
C function: void mgl_wnd_adjust (HMGL gr)

Adjust size of bitmap to window size.

Method on mglWnd: void NextFrame ()
C function: void mgl_wnd_next_frame (HMGL gr)

Show next frame if one.

Method on mglWnd: void PrevFrame ()
C function: void mgl_wnd_prev_frame (HMGL gr)

Show previous frame if one.

Method on mglWnd: void Animation ()
C function: void mgl_wnd_animation (HMGL gr)

Run/stop slideshow (animation) of frames.

Method on mglWnd: void SetDelay (double dt)
C function: void mgl_wnd_set_delay (HMGL gr, double dt)

Sets delay for animation in seconds. Default value is 1 sec.

Method on mglWnd: double GetDelay ()
C function: double mgl_wnd_get_delay (HMGL gr)

Gets delay for animation in seconds.

Method on mglWnd: void Setup (bool clfupd=true, bool showpos=false)
C function: void mgl_setup_window (HMGL gr, bool clfupd, bool showpos)

Enable/disable flags for:

Method on mglWnd: mglPoint LastMousePos ()
C function: void mgl_get_last_mouse_pos (HMGL gr, mreal *x, mreal *y, mreal *z)

Gets last position of mouse click.

Method on mglWnd: void * Widget ()
C function: void * mgl_fltk_widget (HMGL gr)
C function: void * mgl_qt_widget (HMGL gr)

Return pointer to widget (Fl_MathGL class or QMathGL class) used for plotting.

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5.2 mglDraw class

This class provide base functionality for callback drawing and running calculation in separate thread. It is defined in #include <mgl2/wnd.h>. You should make inherited class and implement virtual functions if you need it.

Virtual method on mglDraw: int Draw (mglGraph *gr)

This is callback drawing function, which will be called when any redrawing is required for the window. There is support of a list of plots (frames). So as one can prepare a set of frames at first and redraw it fast later (but it requires more memory). Function should return positive number of frames for the list or zero if it will plot directly.

Virtual method on mglDraw: void Reload ()

This is callback function, which will be called if user press menu or toolbutton to reload data.

Virtual method on mglDraw: void Click ()

This is callback function, which will be called if user click mouse.

Virtual method on mglDraw: void Calc ()

This is callback function, which will be called if user start calculations in separate thread by calling mglDraw::Run() function. It should periodically call mglDraw::Check() function to check if calculations should be paused.

Method on mglDraw: void Run ()

Runs mglDraw::Calc() function in separate thread. It also initialize mglDraw::thr variable and unlock mglDraw::mutex. Function is present only if FLTK support for widgets was enabled.

Method on mglDraw: void Cancel ()

Cancels thread with calculations. Function is present only if FLTK support for widgets was enabled.

Method on mglDraw: void Pause ()

Pauses thread with calculations by locking mglDraw::mutex. You should call mglDraw::Continue() to continue calculations. Function is present only if FLTK support for widgets was enabled.

Method on mglDraw: void Continue ()

Continues calculations by unlocking mglDraw::mutex. Function is present only if FLTK support for widgets was enabled.

Method on mglDraw: void Continue ()

Checks if calculations should be paused and pause it. Function is present only if FLTK support for widgets was enabled.

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5.3 Fl_MathGL class

Class is FLTK widget which display MathGL graphics. It is defined in #include <mgl2/fltk.h>.

Example of FLTK window with MathGL plot.
Method on Fl_MathGL: void set_draw (int (*draw)(HMGL gr, void *p))
Method on Fl_MathGL: void set_draw (int (*draw)(mglGraph *gr))
Method on Fl_MathGL: void set_draw (mglDraw *draw)

Sets drawing function as global function or as one from a class mglDraw. There is support of a list of plots (frames). So as one can prepare a set of frames at first and redraw it fast later (but it requires more memory). Function should return positive number of frames for the list or zero if it will plot directly. Parameter par contains pointer to data for the plotting function draw.

Method on Fl_MathGL: void update ()

Update (redraw) plot.

Method on Fl_MathGL: void set_angle (mreal t, mreal p)

Set angles for additional plot rotation

Method on Fl_MathGL: void set_flag (int f)

Set bitwise flags for general state (1-Alpha, 2-Light)

Method on Fl_MathGL: void set_state (bool r, bool z)

Set flags for handling mouse: z=true allow zooming, r=true allow rotation/shifting/perspective and so on.

Method on Fl_MathGL: void set_zoom (mreal X1, mreal Y1, mreal X2, mreal Y2)

Set zoom in/out region

Method on Fl_MathGL: void get_zoom (mreal *X1, mreal *Y1, mreal *X2, mreal *Y2)

Get zoom in/out region

Method on Fl_MathGL: void set_popup (const Fl_Menu_Item *pmenu, Fl_Widget *w, void *v)

Set popup menu pointer

Method on Fl_MathGL: void set_graph (HMGL gr)
Method on Fl_MathGL: void set_graph (mglGraph *gr)

Set new grapher instead of built-in one. Note that Fl_MathGL will automatically delete this object at destruction or at new set_graph() call.

Method on Fl_MathGL: HMGL get_graph ()

Get pointer to grapher.

Method on Fl_MathGL: void adjust ()

Adjust image size to fit whole widget.

Fl_MathGL option of Fl_MathGL: Fl_Valuator * tet_val

Pointer to external tet-angle validator.

Fl_MathGL option of Fl_MathGL: Fl_Valuator * phi_val

Pointer to external phi-angle validator.

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5.4 QMathGL class

Class is Qt widget which display MathGL graphics. It is defined in #include <mgl2/qt.h>.

Example of Qt window with MathGL plot.
Method on QMathGL: void setDraw (mglDraw *dr)

Sets drawing functions from a class inherited from mglDraw.

Method on QMathGL: void setDraw (int (*draw)(mglBase *gr, void *p), void *par=NULL)
Method on QMathGL: void setDraw (int (*draw)(mglGraph *gr))

Sets the drawing function draw. There is support of a list of plots (frames). So as one can prepare a set of frames at first and redraw it fast later (but it requires more memory). Function should return positive number of frames for the list or zero if it will plot directly. Parameter par contains pointer to data for the plotting function draw.

Method on QMathGL: void setGraph (HMGL gr)
Method on QMathGL: void setGraph (mglGraph *gr)

Set pointer to external grapher (instead of built-in one). Note that QMathGL will automatically delete this object at destruction or at new setGraph() call.

Method on QMathGL: HMGL getGraph ()

Get pointer to grapher.

Method on QMathGL: void setPopup (QMenu *p)

Set popup menu pointer.

Method on QMathGL: void setSize (int w, int h)

Set widget/picture sizes

Method on QMathGL: double getRatio ()

Return aspect ratio of the picture.

Method on QMathGL: int getPer ()

Get perspective value in percents.

Method on QMathGL: int getPhi ()

Get Phi-angle value in degrees.

Method on QMathGL: int getTet ()

Get Theta-angle value in degrees.

Method on QMathGL: bool getAlpha ()

Get transparency state.

Method on QMathGL: bool getLight ()

Get lightning state.

Method on QMathGL: bool getZoom ()

Get mouse zooming state.

Method on QMathGL: bool getRotate ()

Get mouse rotation state.

Slot on QMathGL: void refresh ()

Redraw saved bitmap without executing drawing function.

Slot on QMathGL: void update ()

Update picture by executing drawing function.

Slot on QMathGL: void copy ()

Copy graphics to clipboard.

Slot on QMathGL: void copyClickCoor ()

Copy coordinates of click (as text).

Slot on QMathGL: void print ()

Print current picture.

Slot on QMathGL: void stop ()

Send signal to stop drawing.

Slot on QMathGL: void adjust ()

Adjust image size to fit whole widget.

Slot on QMathGL: void nextSlide ()

Show next slide.

Slot on QMathGL: void prevSlide ()

Show previous slide.

Slot on QMathGL: void animation (bool st=true)

Start/stop animation.

Slot on QMathGL: void setPer (int val)

Set perspective value.

Slot on QMathGL: void setPhi (int val)

Set Phi-angle value.

Slot on QMathGL: void setTet (int val)

Set Theta-angle value.

Slot on QMathGL: void setAlpha (bool val)

Switch on/off transparency.

Slot on QMathGL: void setLight (bool val)

Switch on/off lightning.

Slot on QMathGL: void setGrid (bool val)

Switch on/off drawing of grid for absolute coordinates.

Slot on QMathGL: void setZoom (bool val)

Switch on/off mouse zooming.

Slot on QMathGL: void setRotate (bool val)

Switch on/off mouse rotation.

Slot on QMathGL: void zoomIn ()

Zoom in graphics.

Slot on QMathGL: void zoomOut ()

Zoom out graphics.

Slot on QMathGL: void shiftLeft ()

Shift graphics to left direction.

Slot on QMathGL: void shiftRight ()

Shift graphics to right direction.

Slot on QMathGL: void shiftUp ()

Shift graphics to up direction.

Slot on QMathGL: void shiftDown ()

Shift graphics to down direction.

Slot on QMathGL: void restore ()

Restore zoom and rotation to default values.

Slot on QMathGL: void exportPNG (QString fname="")

Export current picture to PNG file.

Slot on QMathGL: void exportPNGs (QString fname="")

Export current picture to PNG file (no transparency).

Slot on QMathGL: void exportJPG (QString fname="")

Export current picture to JPEG file.

Slot on QMathGL: void exportBPS (QString fname="")

Export current picture to bitmap EPS file.

Slot on QMathGL: void exportEPS (QString fname="")

Export current picture to vector EPS file.

Slot on QMathGL: void exportSVG (QString fname="")

Export current picture to SVG file.

Slot on QMathGL: void exportGIF (QString fname="")

Export current picture to GIF file.

Slot on QMathGL: void exportTEX (QString fname="")

Export current picture to LaTeX/Tikz file.

Slot on QMathGL: void exportTGA (QString fname="")

Export current picture to TGA file.

Slot on QMathGL: void exportXYZ (QString fname="")

Export current picture to XYZ/XYZL/XYZF file.

Slot on QMathGL: void exportOBJ (QString fname="")

Export current picture to OBJ/MTL file.

Slot on QMathGL: void exportSTL (QString fname="")

Export current picture to STL file.

Slot on QMathGL: void exportOFF (QString fname="")

Export current picture to OFF file.

Slot on QMathGL: voidsetUsePrimitives (bool use)

Enable using list of primitives for frames. This allows frames transformation/zoom but requires much more memory. Default value is true.

Slot on QMathGL: void setMGLFont (QString path)

Restore (path="") or load font for graphics.

Slot on QMathGL: void about ()

Show about information.

Slot on QMathGL: void aboutQt ()

Show information about Qt version.

Signal on QMathGL: void phiChanged (int val)

Phi angle changed (by mouse or by toolbar).

Signal on QMathGL: void tetChanged (int val)

Tet angle changed (by mouse or by toolbar).

Signal on QMathGL: void perChanged (int val)

Perspective changed (by mouse or by toolbar).

Signal on QMathGL: void alphaChanged (bool val)

Transparency changed (by toolbar).

Signal on QMathGL: void lightChanged (bool val)

Lighting changed (by toolbar).

Signal on QMathGL: void gridChanged (bool val)

Grid drawing changed (by toolbar).

Signal on QMathGL: void zoomChanged (bool val)

Zooming changed (by toolbar).

Signal on QMathGL: void rotateChanged (bool val)

Rotation changed (by toolbar).

Signal on QMathGL: void mouseClick (mreal x, mreal y, mreal z)

Mouse click take place at position {x,y,z}.

Signal on QMathGL: void frameChanged (int val)

Need another frame to show.

Signal on QMathGL: void showWarn (QString warn)

Need to show warning.

Signal on QMathGL: void posChanged (QString pos)

Position of mouse click is changed.

Signal on QMathGL: void objChanged (int id)

Object id is changed (due to mouse click).

Signal on QMathGL: void refreshData ()

Data can be changed (drawing is finished).

QMathGL option of QMathGL: QString appName

Application name for message boxes.

QMathGL option of QMathGL: bool autoResize

Allow auto resizing (default is false).

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5.5 wxMathGL class

Class is WX widget which display MathGL graphics. It is defined in #include <mgl2/wx.h>.

Method on wxMathGL: void SetDraw (mglDraw *dr)

Sets drawing functions from a class inherited from mglDraw.

Method on wxMathGL: void SetDraw (int (*draw)(mglBase *gr, void *p), void *par=NULL)
Method on wxMathGL: void SetDraw (int (*draw)(mglGraph *gr))

Sets the drawing function draw. There is support of a list of plots (frames). So as one can prepare a set of frames at first and redraw it fast later (but it requires more memory). Function should return positive number of frames for the list or zero if it will plot directly. Parameter par contains pointer to data for the plotting function draw.

Method on wxMathGL: void SetGraph (HMGL gr)
Method on wxMathGL: void SetGraph (mglGraph *gr)

Set pointer to external grapher (instead of built-in one). Note that wxMathGL will automatically delete this object at destruction or at new setGraph() call.

Method on wxMathGL: HMGL GetGraph ()

Get pointer to grapher.

Method on wxMathGL: void SetPopup (wxMenu *p)

Set popup menu pointer.

Method on wxMathGL: void SetSize (int w, int h)

Set widget/picture sizes

Method on wxMathGL: double GetRatio ()

Return aspect ratio of the picture.

Method on wxMathGL: int GetPer ()

Get perspective value in percents.

Method on wxMathGL: int GetPhi ()

Get Phi-angle value in degrees.

Method on wxMathGL: int GetTet ()

Get Theta-angle value in degrees.

Method on wxMathGL: bool GetAlpha ()

Get transparency state.

Method on wxMathGL: bool GetLight ()

Get lightning state.

Method on wxMathGL: bool GetZoom ()

Get mouse zooming state.

Method on wxMathGL: bool GetRotate ()

Get mouse rotation state.

Method on wxMathGL: void Repaint ()

Redraw saved bitmap without executing drawing function.

Method on wxMathGL: void Update ()

Update picture by executing drawing function.

Method on wxMathGL: void Copy ()

Copy graphics to clipboard.

Method on wxMathGL: void Print ()

Print current picture.

Method on wxMathGL: void Adjust ()

Adjust image size to fit whole widget.

Method on wxMathGL: void NextSlide ()

Show next slide.

Method on wxMathGL: void PrevSlide ()

Show previous slide.

Method on wxMathGL: void Animation (bool st=true)

Start/stop animation.

Method on wxMathGL: void SetPer (int val)

Set perspective value.

Method on wxMathGL: void SetPhi (int val)

Set Phi-angle value.

Method on wxMathGL: void SetTet (int val)

Set Theta-angle value.

Method on wxMathGL: void SetAlpha (bool val)

Switch on/off transparency.

Method on wxMathGL: void SetLight (bool val)

Switch on/off lightning.

Method on wxMathGL: void SetZoom (bool val)

Switch on/off mouse zooming.

Method on wxMathGL: void SetRotate (bool val)

Switch on/off mouse rotation.

Method on wxMathGL: void ZoomIn ()

Zoom in graphics.

Method on wxMathGL: void ZoomOut ()

Zoom out graphics.

Method on wxMathGL: void ShiftLeft ()

Shift graphics to left direction.

Method on wxMathGL: void ShiftRight ()

Shift graphics to right direction.

Method on wxMathGL: void ShiftUp ()

Shift graphics to up direction.

Method on wxMathGL: void ShiftDown ()

Shift graphics to down direction.

Method on wxMathGL: void Restore ()

Restore zoom and rotation to default values.

Method on wxMathGL: void About ()

Show about information.

Method on wxMathGL: void ExportPNG (QString fname="")

Export current picture to PNG file.

Method on wxMathGL: void ExportPNGs (QString fname="")

Export current picture to PNG file (no transparency).

Method on wxMathGL: void ExportJPG (QString fname="")

Export current picture to JPEG file.

Method on wxMathGL: void ExportBPS (QString fname="")

Export current picture to bitmap EPS file.

Method on wxMathGL: void ExportEPS (QString fname="")

Export current picture to vector EPS file.

Method on wxMathGL: void ExportSVG (QString fname="")

Export current picture to SVG file.

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6 Data processing

This chapter describe classes mglData and mglDataC for working with data arrays of real and complex numbers. Both classes are derived from abstract class mglDataA, and can be used as arguments of any plotting functions (see MathGL core). These classes are defined in #include <mgl2/data.h> and #include <mgl2/datac.h> correspondingly. The classes have mostly the same set of functions for easy and safe allocation, resizing, loading, saving, modifying of data arrays. Also it can numerically differentiate and integrate data, interpolate, fill data by formula and so on. Classes support data with dimensions up to 3 (like function of 3 variables – x,y,z). The internal representation of numbers is mreal (or dual=std::complex<mreal> for mglDataC), which can be configured as float or double by selecting option --enable-double at the MathGL configuring (see Installation). Float type have smaller size in memory and usually it has enough precision in plotting purposes. However, double type provide high accuracy what can be important for time-axis, for example. Data arrays are denoted by Small Caps (like DAT) if it can be (re-)created by MGL commands.

• Public variables:  
• Data constructor:  
• Data resizing:  
• Data filling:  
• File I/O:  
• Make another data:  
• Data changing:  
• Interpolation:  
• Data information:  
• Operators:  
• Global functions:  
• Evaluate expression:  
• Special data classes:  

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6.1 Public variables

Variable of mglData: mreal * a
Variable of mglDataC: dual * a

Data array itself. The flat data representation is used. For example, matrix [nx x ny] is presented as flat (1d-) array with length nx*ny. The element with indexes {i, j, k} is a[i+nx*j+nx*ny*k] (indexes are zero based).

Variable of mglData: long nx
Variable of mglDataC: long nx

Number of points in 1st dimensions (’x’ dimension).

Variable of mglData: long ny
Variable of mglDataC: long ny

Number of points in 2nd dimensions (’y’ dimension).

Variable of mglData: long nz
Variable of mglDataC: long nz

Number of points in 3d dimensions (’z’ dimension).

Variable of mglData: std::string id
Variable of mglDataC: std::string id

Names of column (or slice if nz>1) – one character per column.

Variable of mglData: bool link
Variable of mglDataC: bool link

Flag to use external data, i.e. don’t delete it.

Variable of mglDataA: std::wstring s

Name of data. It is used in parsing of MGL scripts.

Variable of mglDataA: bool temp

Flag of temporary variable, which should be deleted.

Variable of mglDataA: void (*)(void *) func

Pointer to callback function which will be called at destroying.

Variable of mglDataA: void * o

Pointer to object for callback function.

Method on mglData: mreal GetVal (long i)
Method on mglDataC: mreal GetVal (long i)
Method on mglData: void SetVal (mreal val, long i)
Method on mglDataC: void SetVal (mreal val, long i)

Gets or sets the value in by "flat" index i without border checking. Index i should be in range [0, nx*ny*nz-1].

Method on mglDataA: long GetNx ()
Method on mglDataA: long GetNy ()
Method on mglDataA: long GetNz ()
C function: long mgl_data_get_nx (HCDT dat)
C function: long mgl_data_get_ny (HCDT dat)
C function: long mgl_data_get_nz (HCDT dat)

Gets the x-, y-, z-size of the data.

C function: mreal mgl_data_get_value (HCDT dat, int i, int j, int k)
C function: dual mgl_datac_get_value (HCDT dat, int i, int j, int k)
C function: mreal * mgl_data_value (HMDT dat, int i, int j, int k)
C function: dual * mgl_datac_value (HADT dat, int i, int j, int k)
C function: void mgl_data_set_value (HMDT dat, mreal v, int i, int j, int k)
C function: void mgl_datac_set_value (HADT dat, dual v, int i, int j, int k)

Gets or sets the value in specified cell of the data with border checking.

C function: const mreal * mgl_data_data (HCDT dat)
C function: const dual * mgl_datac_data (HCDT dat)

Returns pointer to internal data array.

C function only: void mgl_data_set_func (mglDataA *dat, void (*func)(void *), void *par)

Set pointer to callback function which will be called at destroying.

C function: void mgl_data_set_name (mglDataA *dat, const char *name)
C function: void mgl_data_set_name_w (mglDataA *dat, const wchar_t *name)

Set name of data, which used in parsing of MGL scripts.

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6.2 Data constructor

MGL command: new DAT [nx=1 'eq']
MGL command: new DAT nx ny ['eq']
MGL command: new DAT nx ny nz ['eq']
Constructor on mglData: mglData (int mx=1, int my=1, int mz=1)
Constructor on mglDataC: mglDataC (int mx=1, int my=1, int mz=1)
C function: HMDT mgl_create_data ()
C function: HMDT mgl_create_data_size (int mx, int my, int mz)
C function: HADT mgl_create_datac ()
C function: HADT mgl_create_datac_size (int mx, int my, int mz)

Default constructor. Allocates the memory for data array and initializes it by zero. If string eq is specified then data will be filled by corresponding formula as in fill.

MGL command: copy DAT dat2 ['eq'='']
MGL command: copy DAT val
Constructor on mglData: mglData (const mglDataA &dat2)
Constructor on mglData: mglData (const mglDataA *dat2)
Constructor on mglData: mglData (int size, const float *dat2)
Constructor on mglData: mglData (int size, int cols, const float *dat2)
Constructor on mglData: mglData (int size, const double *dat2)
Constructor on mglData: mglData (int size, int cols, const double *dat2)
Constructor on mglData: mglData (const double *dat2, int size)
Constructor on mglData: mglData (const double *dat2, int size, int cols)
Constructor on mglDataC: mglDataC (const mglDataA &dat2)
Constructor on mglDataC: mglDataC (const mglDataA *dat2)
Constructor on mglDataC: mglDataC (int size, const float *dat2)
Constructor on mglDataC: mglDataC (int size, int cols, const float *dat2)
Constructor on mglDataC: mglDataC (int size, const double *dat2)
Constructor on mglDataC: mglDataC (int size, int cols, const double *dat2)
Constructor on mglDataC: mglDataC (int size, const dual *dat2)
Constructor on mglDataC: mglDataC (int size, int cols, const dual *dat2)

Copy constructor. Allocates the memory for data array and copy values from other array. At this, if parameter eq is specified then the data will be modified by corresponding formula similarly to fill.

MGL command: read DAT 'fname'
Constructor on mglData: mglData (const char *fname)
Constructor on mglDataC: mglDataC (const char *fname)
C function: HMDT mgl_create_data_file (const char *fname)
C function: HADT mgl_create_datac_file (const char *fname)

Reads data from tab-separated text file with auto determining sizes of the data.

MGL command: delete dat
Destructor on mglData: ~mglData ()
C function: void mgl_delete_data (HMDT dat)
Destructor on mglDataC: ~mglDataC ()
C function: void mgl_delete_datac (HADT dat)

Deletes the instance of class mglData.

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6.3 Data resizing

MGL command: new DAT [nx=1 ny=1 nz=1]
Method on mglData: void Create (int mx, int my=1, int mz=1)
Method on mglDataC: void Create (int mx, int my=1, int mz=1)
C function: void mgl_data_create (HMDT dat, int mx, int my, int mz)
C function: void mgl_datac_create (HADT dat, int mx, int my, int mz)

Creates or recreates the array with specified size and fills it by zero. This function does nothing if one of parameters mx, my, mz is zero or negative.

MGL command: rearrange dat mx [my=0 mz=0]
Method on mglData: void Rearrange (int mx, int my=0, int mz=0)
Method on mglDataC: void Rearrange (int mx, int my=0, int mz=0)
C function: void mgl_data_rearrange (HMDT dat, int mx, int my, int mz)
C function: void mgl_datac_rearrange (HADT dat, int mx, int my, int mz)

Rearrange dimensions without changing data array so that resulting sizes should be mx*my*mz < nx*ny*nz. If some of parameter my or mz are zero then it will be selected to optimal fill of data array. For example, if my=0 then it will be change to my=nx*ny*nz/mx and mz=1.

MGL command: transpose dat ['dim'='yxz']
Method on mglData: void Transpose (const char *dim="yx")
Method on mglDataC: void Transpose (const char *dim="yx")
C function: void mgl_data_transpose (HMDT dat, const char *dim)
C function: void mgl_datac_transpose (HADT dat, const char *dim)

Transposes (shift order of) dimensions of the data. New order of dimensions is specified in string dim. This function can be useful also after reading of one-dimensional data.

MGL command: extend dat n1 [n2=0]
Method on mglData: void Extend (int n1, int n2=0)
Method on mglDataC: void Extend (int n1, int n2=0)
C function: void mgl_data_extend (HMDT dat, int n1, int n2)
C function: void mgl_datac_extend (HADT dat, int n1, int n2)

Increase the dimensions of the data by inserting new (|n1|+1)-th slices after (for n1>0) or before (for n1<0) of existed one. It is possible to insert 2 dimensions simultaneously for 1d data by using parameter n2. Data to new slices is copy from existed one. For example, for n1>0 new array will be a_ij^new = a_i^old where j=0...n1. Correspondingly, for n1<0 new array will be a_ij^new = a_j^old where i=0...|n1|.

MGL command: squeeze dat rx [ry=1 rz=1 sm=off]
Method on mglData: void Squeeze (int rx, int ry=1, int rz=1, bool smooth=false)
Method on mglDataC: void Squeeze (int rx, int ry=1, int rz=1, bool smooth=false)
C function: void mgl_data_squeeze (HMDT dat, int rx, int ry, int rz, int smooth)
C function: void mgl_datac_squeeze (HADT dat, int rx, int ry, int rz, int smooth)

Reduces the data size by excluding data elements which indexes are not divisible by rx, ry, rz correspondingly. Parameter smooth set to use smoothing (i.e. out[i]=\sum_{j=i,i+r} a[j]/r) or not (i.e. out[i]=a[j*r]).

MGL command: crop dat n1 n2 'dir'
Method on mglData: void Crop (int n1, int n2, char dir='x')
Method on mglDataC: void Crop (int n1, int n2, char dir='x')
C function: void mgl_data_crop (HMDT dat, int n1, int n2, char dir)
C function: void mgl_datac_crop (HADT dat, int n1, int n2, char dir)

Cuts off edges of the data i<n1 and i>n2 if n2>0 or i>n[xyz]-n2 if n2<=0 along direction dir.

MGL command: insert dat 'dir' [pos=off num=0]
Method on mglData: void Insert (char dir, int pos=0, int num=1)
Method on mglDataC: void Insert (char dir, int pos=0, int num=1)
C function: void mgl_data_insert (HMDT dat, char dir, int pos, char num)
C function: void mgl_datac_insert (HADT dat, char dir, int pos, char num)

Insert num slices along dir-direction at position pos and fill it by zeros.

MGL command: delete dat 'dir' [pos=off num=0]
Method on mglData: void Delete (char dir, int pos=0, int num=1)
Method on mglDataC: void Delete (char dir, int pos=0, int num=1)
C function: void mgl_data_delete (HMDT dat, char dir, int pos, char num)
C function: void mgl_datac_delete (HADT dat, char dir, int pos, char num)

Delete num slices along dir-direction at position pos.

MGL command: sort dat idx [idy=-1]
Method on mglData: void Sort (lond idx, long idy=-1)
C function: void mgl_data_sort (HMDT dat, lond idx, long idy)

Sort data rows (or slices in 3D case) by values of specified column idx (or cell {idx,idy} for 3D case). Note, this function is not thread safe!

MGL command: clean dat idx
Method on mglData: void Clean (lond idx)
C function: void mgl_data_clean (HMDT dat, lond idx)

Delete rows which values are equal to next row for given column idx.

MGL command: join dat vdat [v2dat ...]
Method on mglData: void Join (const mglDataA &vdat)
Method on mglDataC: void Join (const mglDataA &vdat)
C function: void mgl_data_join (HMDT dat, HCDT vdat)
C function: void mgl_datac_join (HADT dat, HCDT vdat)

Join data cells from vdat to dat. At this, function increase dat sizes according following: z-size for data arrays arrays with equal x-,y-sizes; or y-size for data arrays with equal x-sizes; or x-size otherwise.

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6.4 Data filling

MGL command: list DAT v1 ...

Creates new variable with name dat and fills it by numeric values of command arguments v1 .... Command can create one-dimensional and two-dimensional arrays with arbitrary values. For creating 2d array the user should use delimiter ‘|’ which means that the following values lie in next row. Array sizes are [maximal of row sizes * number of rows]. For example, command list 1 | 2 3 creates the array [1 0; 2 3]. Note, that the maximal number of arguments is 1000.

MGL command: list DAT d1 ...

Creates new variable with name dat and fills it by data values of arrays of command arguments d1 .... Command can create two-dimensional or three-dimensional (if arrays in arguments are 2d arrays) arrays with arbitrary values. Minor dimensions of all arrays in arguments should be equal to dimensions of first array d1. In the opposite case the argument will be ignored. Note, that the maximal number of arguments is 1000.

Method on mglData: void Set (const float *A, int NX, int NY=1, int NZ=1)
Method on mglData: void Set (const double *A, int NX, int NY=1, int NZ=1)
C function: void mgl_data_set_float (HMDT dat, const mreal *A, int NX, int NY, int NZ)
C function: void mgl_data_set_double (HMDT dat, const double *A, int NX, int NY, int NZ)
Method on mglDataC: void Set (const float *A, int NX, int NY=1, int NZ=1)
Method on mglDataC: void Set (const double *A, int NX, int NY=1, int NZ=1)
Method on mglDataC: void Set (const dual *A, int NX, int NY=1, int NZ=1)
C function: void mgl_datac_set_float (HADT dat, const mreal *A, int NX, int NY, int NZ)
C function: void mgl_datac_set_double (HADT dat, const double *A, int NX, int NY, int NZ)
C function: void mgl_datac_set_complex (HADT dat, const dual *A, int NX, int NY, int NZ)

Allocates memory and copies the data from the flat float* or double* array.

Method on mglData: void Set (const float **A, int N1, int N2)
Method on mglData: void Set (const double **A, int N1, int N2)
C function: void mgl_data_set_mreal2 (HMDT dat, const mreal **A, int N1, int N2)
C function: void mgl_data_set_double2 (HMDT dat, const double **A, int N1, int N2)

Allocates memory and copies the data from the float** or double** array with dimensions N1, N2, i.e. from array defined as mreal a[N1][N2];.

Method on mglData: void Set (const float ***A, int N1, int N2)
Method on mglData: void Set (const double ***A, int N1, int N2)
C function: void mgl_data_set_mreal3 (HMDT dat, const mreal ***A, int N1, int N2)
C function: void mgl_data_set_double3 (HMDT dat, const double ***A, int N1, int N2)

Allocates memory and copies the data from the float*** or double*** array with dimensions N1, N2, N3, i.e. from array defined as mreal a[N1][N2][N3];.

Method on mglData: void Set (gsl_vector *v)
Method on mglDataC: void Set (gsl_vector *v)
C function: void mgl_data_set_vector (HMDT dat, gsl_vector *v)
C function: void mgl_datac_set_vector (HADT dat, gsl_vector *v)

Allocates memory and copies the data from the gsl_vector * structure.

Method on mglData: void Set (gsl_matrix *m)
Method on mglDataC: void Set (gsl_matrix *m)
C function: void mgl_data_set_matrix (HMDT dat, gsl_matrix *m)
C function: void mgl_datac_set_matrix (HADT dat, gsl_matrix *m)

Allocates memory and copies the data from the gsl_matrix * structure.

Method on mglData: void Set (const mglDataA &from)
Method on mglData: void Set (HCDT from)
C function: void mgl_data_set (HMDT dat, HCDT from)
Method on mglDataC: void Set (const mglDataA &from)
Method on mglDataC: void Set (HCDT from)
C function: void mgl_datac_set (HADT dat, HCDT from)

Copies the data from mglData (or mglDataA) instance from.

Method on mglDataC: void Set (const mglDataA &re, const mglDataA &im)
Method on mglDataC: void Set (HCDT re, HCDT im)
Method on mglDataC: void SetAmpl (HCDT ampl, const mglDataA &phase)
C function: void mgl_datac_set_ri (HADT dat, HCDT re, HCDT im)
C function: void mgl_datac_set_ap (HADT dat, HCDT ampl, HCDT phase)

Copies the data from mglData instances for real and imaginary parts of complex data arrays.

Method on mglData: void Set (const std::vector<int> &d)
Method on mglDataC: void Set (const std::vector<int> &d)
Method on mglData: void Set (const std::vector<float> &d)
Method on mglDataC: void Set (const std::vector<float> &d)
Method on mglData: void Set (const std::vector<double> &d)
Method on mglDataC: void Set (const std::vector<double> &d)
Method on mglDataC: void Set (const std::vector<dual> &d)

Allocates memory and copies the data from the std::vector<T> array.

Method on mglData: void Set (const char *str, int NX, int NY=1, int NZ=1)
C function: void mgl_data_set_values (const char *str, int NX, int NY, int NZ)
Method on mglDataC: void Set (const char *str, int NX, int NY=1, int NZ=1)
C function: void mgl_datac_set_values (const char *str, int NX, int NY, int NZ)

Allocates memory and scanf the data from the string.

Method on mglData: void SetList (long n, ...)

Allocate memory and set data from variable argument list of double values. Note, you need to specify decimal point ‘.’ for integer values! For example, the code SetList(2,0.,1.); is correct, but the code SetList(2,0,1); is incorrect.

Method on mglData: void Link (mglData &from)
Method on mglData: void Link (mreal *A, int NX, int NY=1, int NZ=1)
C function: void mgl_data_link (HMDT dat, mreal *A, int NX, int NY, int NZ)
Method on mglDataC: void Link (mglDataC &from)
Method on mglDataC: void Link (dual *A, int NX, int NY=1, int NZ=1)
C function: void mgl_datac_link (HADT dat, dual *A, int NX, int NY, int NZ)

Links external data array, i.e. don’t delete this array at exit.

MGL command: var DAT num v1 [v2=nan]

Creates new variable with name dat for one-dimensional array of size num. Array elements are equidistantly distributed in range [v1, v2]. If v2=nan then v2=v1 is used.

MGL command: fill dat v1 v2 ['dir'='x']
Method on mglData: void Fill (mreal v1, mreal v2, char dir='x')
Method on mglDataC: void Fill (dual v1, dual v2, char dir='x')
C function: void mgl_data_fill (HMDT dat, mreal v1, mreal v2, char dir)
C function: void mgl_datac_fill (HADT dat, dual v1, dual v2, char dir)

Equidistantly fills the data values to range [v1, v2] in direction dir={‘x’,‘y’,‘z’}.

MGL command: fill dat 'eq'
MGL command: fill dat 'eq' vdat
MGL command: fill dat 'eq' vdat wdat
Method on mglData: void Fill (HMGL gr, const char *eq, const char *opt="")
Method on mglData: void Fill (HMGL gr, const char *eq, const mglDataA &vdat, const char *opt="")
Method on mglData: void Fill (HMGL gr, const char *eq, const mglDataA &vdat, const mglDataA &wdat, const char *opt="")
Method on mglDataC: void Fill (HMGL gr, const char *eq, const char *opt="")
Method on mglDataC: void Fill (HMGL gr, const char *eq, const mglDataA &vdat, const char *opt="")
Method on mglDataC: void Fill (HMGL gr, const char *eq, const mglDataA &vdat, const mglDataA &wdat, const char *opt="")
C function: void mgl_data_fill_eq (HMGL gr, HMDT dat, const char *eq, HCDT vdat, HCDT wdat, const char *opt)
C function: void mgl_datac_fill_eq (HMGL gr, HADT dat, const char *eq, HCDT vdat, HCDT wdat, const char *opt)

Fills the value of array according to the formula in string eq. Formula is an arbitrary expression depending on variables ‘x’, ‘y’, ‘z’, ‘u’, ‘v’, ‘w’. Coordinates ‘x’, ‘y’, ‘z’ are supposed to be normalized in axis range of canvas gr (in difference from Modify functions). Variable ‘u’ is the original value of the array. Variables ‘v’ and ‘w’ are values of vdat, wdat which can be NULL (i.e. can be omitted).

MGL command: modify dat 'eq' [dim=0]
MGL command: modify dat 'eq' vdat
MGL command: modify dat 'eq' vdat wdat
Method on mglData: void Modify (const char *eq, int dim=0)
Method on mglData: void Modify (const char *eq, const mglDataA &v)
Method on mglData: void Modify (const char *eq, const mglDataA &v, const mglDataA &w)
Method on mglDataC: void Modify (const char *eq, int dim=0)
Method on mglDataC: void Modify (const char *eq, const mglDataA &v)
Method on mglDataC: void Modify (const char *eq, const mglDataA &v, const mglDataA &w)
C function: void mgl_data_modify (HMDT dat, const char *eq, int dim)
C function: void mgl_data_modify_vw (HMDT dat, const char *eq, HCDT v, HCDT w)
C function: void mgl_datac_modify (HADT dat, const char *eq, int dim)
C function: void mgl_datac_modify_vw (HADT dat, const char *eq, HCDT v, HCDT w)

The same as previous ones but coordinates ‘x’, ‘y’, ‘z’ are supposed to be normalized in range [0,1]. If dim>0 is specified then modification will be fulfilled only for slices >=dim.

MGL command: fillsample dat 'how'
Method on mglData: void FillSample (const char *how)
C function: void mgl_data_fill_sample (HMDT a, const char *how)

Fills data by ’x’ or ’k’ samples for Hankel (’h’) or Fourier (’f’) transform.

MGL command: datagrid dat xdat ydat zdat
Method on mglData: mglData Grid (HMGL gr, const mglDataA &x, const mglDataA &y, const mglDataA &z, const char *opt="")
Method on mglData: mglData Grid (const mglDataA &x, const mglDataA &y, const mglDataA &z, mglPoint p1, mglPoint p2)
C function: void mgl_data_grid (HMGL gr, HMDT u, HCDT x, HCDT y, HCDT z, const char *opt)
C function: void mgl_data_grid_xy (HMDT u, HCDT x, HCDT y, HCDT z, mreal x1, mreal x2, mreal y1, mreal y2)

Fills the value of array according to the linear interpolation of triangulated surface assuming x-,y-coordinates equidistantly distributed in axis range (or in range [x1,x2]*[y1,y2]). Triangulated surface is found for arbitrary placed points ‘x’, ‘y’, ‘z’. NAN value is used for grid points placed outside of triangulated surface. See Making regular data, for sample code and picture.

MGL command: put dat val [i=: j=: k=:]
Method on mglData: void Put (mreal val, int i=-1, int j=-1, int k=-1)
Method on mglDataC: void Put (dual val, int i=-1, int j=-1, int k=-1)
C function: void mgl_data_put_val (HMDT a, mreal val, int i, int j, int k)
C function: void mgl_datac_put_val (HADT a, dual val, int i, int j, int k)

Sets value(s) of array a[i, j, k] = val. Negative indexes i, j, k=-1 set the value val to whole range in corresponding direction(s). For example, Put(val,-1,0,-1); sets a[i,0,j]=val for i=0...(nx-1), j=0...(nz-1).

MGL command: put dat vdat [i=: j=: k=:]
Method on mglData: void Put (const mglDataA &v, int i=-1, int j=-1, int k=-1)
Method on mglDataC: void Put (const mglDataA &v, int i=-1, int j=-1, int k=-1)
C function: void mgl_data_put_dat (HMDT a, HCDT v, int i, int j, int k)
C function: void mgl_datac_put_dat (HADT a, HCDT v, int i, int j, int k)

Copies value(s) from array v to the range of original array. Negative indexes i, j, k=-1 set the range in corresponding direction(s). At this minor dimensions of array v should be large than corresponding dimensions of this array. For example, Put(v,-1,0,-1); sets a[i,0,j]=v.ny>nz ? v[i,j] : v[i], where i=0...(nx-1), j=0...(nz-1) and condition v.nx>=nx is true.

MGL command: refill dat xdat vdat [sl=-1]
MGL command: refill dat xdat ydat vdat [sl=-1]
MGL command: refill dat xdat ydat zdat vdat
Method on mglData: void Refill (const mglDataA &x, const mglDataA &v, mreal x1, mreal x2, long sl=-1)
Method on mglData: void Refill (const mglDataA &x, const mglDataA &v, mglPoint p1, mglPoint p2, long sl=-1)
Method on mglData: void Refill (const mglDataA &x, const mglDataA &y, const mglDataA &v, mglPoint p1, mglPoint p2, long sl=-1)
Method on mglData: void Refill (const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &v, mglPoint p1, mglPoint p2)
Method on mglData: void Refill (HMGL gr, const mglDataA &x, const mglDataA &v, long sl=-1, const char *opt="")
Method on mglData: void Refill (HMGL gr, const mglDataA &x, const mglDataA &y, const mglDataA &v, long sl=-1, const char *opt="")
Method on mglData: void Refill (HMGL gr, const mglDataA &x, const mglDataA &y, const mglDataA &z, const mglDataA &v, const char *opt="")
C function: void mgl_data_refill_x (HMDT a, HCDT x, HCDT v, mreal x1, mreal x2, long sl)
C function: void mgl_data_refill_xy (HMDT a, HCDT x, HCDT y, HCDT v, mreal x1, mreal x2, mreal y1, mreal y2, long sl)
C function: void mgl_data_refill_xyz (HMDT a, HCDT x, HCDT y, HCDT z, HCDT v, mreal x1, mreal x2, mreal y1, mreal y2, mreal z1, mreal z2)
C function: void mgl_data_refill_gr (HMGL gr, HMDT a, HCDT x, HCDT y, HCDT z, HCDT v, long sl, const char *opt)

Fills by interpolated values of array v at the point {x, y, z}={X[i], Y[j], Z[k]} (or {x, y, z}={X[i,j,k], Y[i,j,k], Z[i,j,k]} if x, y, z are not 1d arrays), where X,Y,Z are equidistantly distributed in range [x1,x2]*[y1,y2]*[z1,z2] and have the same sizes as this array. If parameter sl is 0 or positive then changes will be applied only for slice sl.

MGL command: gspline dat xdat vdat [sl=-1]
Method on mglData: void RefillGS (const mglDataA &x, const mglDataA &v, mreal x1, mreal x2, long sl=-1)
C function: void mgl_data_refill_gs (HMDT a, HCDT x, HCDT v, mreal x1, mreal x2, long sl)

Fills by global cubic spline values of array v at the point x=X[i], where X are equidistantly distributed in range [x1,x2] and have the same sizes as this array. If parameter sl is 0 or positive then changes will be applied only for slice sl.

MGL command: idset dat 'ids'
Method on mglData: void SetColumnId (const char *ids)
Method on mglDataC: void SetColumnId (const char *ids)
C function: void mgl_data_set_id (HMDT a, const char *ids)
C function: void mgl_datac_set_id (HADT a, const char *ids)

Sets the symbol ids for data columns. The string should contain one symbol ’a’...’z’ per column. These ids are used in column.

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6.5 File I/O

MGL command: read DAT 'fname'
Method on mglData: bool Read (const char *fname)
Method on mglDataC: bool Read (const char *fname)
C function: int mgl_data_read (HMDT dat, const char *fname)
C function: int mgl_datac_read (HADT dat, const char *fname)

Reads data from tab-separated text file with auto determining sizes of the data. Double newline means the beginning of new z-slice.

MGL command: read DAT 'fname' mx [my=1 mz=1]
Method on mglData: bool Read (const char *fname, int mx, int my=1, int mz=1)
Method on mglDataC: bool Read (const char *fname, int mx, int my=1, int mz=1)
C function: int mgl_data_read_dim (HMDT dat, const char *fname, int mx, int my, int mz)
C function: int mgl_datac_read_dim (HADT dat, const char *fname, int mx, int my, int mz)

Reads data from text file with specified data sizes. This function does nothing if one of parameters mx, my or mz is zero or negative.

MGL command: readmat DAT 'fname' [dim=2]
Method on mglData: bool ReadMat (const char *fname, int dim=2)
Method on mglDataC: bool ReadMat (const char *fname, int dim=2)
C function: int mgl_data_read_mat (HMDT dat, const char *fname, int dim)
C function: int mgl_datac_read_mat (HADT dat, const char *fname, int dim)

Read data from text file with size specified at beginning of the file by first dim numbers. At this, variable dim set data dimensions.

MGL command: readall DAT 'templ' v1 v2 [dv=1 slice=off]
Method on mglData: void ReadRange (const char *templ, mreal from, mreal to, mreal step=1, bool as_slice=false)
Method on mglDataC: void ReadRange (const char *templ, mreal from, mreal to, mreal step=1, bool as_slice=false)
C function: int mgl_data_read_range (HMDT dat, const char *templ, mreal from, mreal to, mreal step, int as_slice)
C function: int mgl_datac_read_range (HADT dat, const char *templ, mreal from, mreal to, mreal step, int as_slice)

Join data arrays from several text files. The file names are determined by function call sprintf(fname,templ,val);, where val changes from from to to with step step. The data load one-by-one in the same slice if as_slice=false or as slice-by-slice if as_slice=true.

MGL command: readall DAT 'templ' [slice=off]
Method on mglData: void ReadAll (const char *templ, bool as_slice=false)
Method on mglDataC: void ReadAll (const char *templ, bool as_slice=false)
C function: int mgl_data_read_all (HMDT dat, const char *templ, int as_slice)
C function: int mgl_datac_read_all (HADT dat, const char *templ, int as_slice)

Join data arrays from several text files which filenames satisfied the template templ (for example, templ="t_*.dat"). The data load one-by-one in the same slice if as_slice=false or as slice-by-slice if as_slice=true.

MGL command: scanfile DAT 'fname' 'templ'
Method on mglData: bool ScanFile (const char *fname, const char *templ)
C function: int mgl_data_scan_file (HMDT dat, const char *fname, const char *templ)

Read file fname line-by-line and scan each line for numbers according the template templ. The numbers denoted as ‘%g’ in the template. See Saving and scanning file, for sample code and picture.

MGL command: save dat 'fname'
Method on mglDataA: void Save (const char *fname, int ns=-1) const
C function: void mgl_data_save (HCDT dat, const char *fname, int ns)
C function: void mgl_datac_save (HCDT dat, const char *fname, int ns)

Saves the whole data array (for ns=-1) or only ns-th slice to the text file fname.

MGL command: save 'str' 'fname' ['mode'='a']

Saves the string str to the text file fname. For parameter mode=‘a’ will append string to the file (default); for mode=‘w’ will overwrite the file. See Saving and scanning file, for sample code and picture.

MGL command: readhdf DAT 'fname' 'dname'
Method on mglData: void ReadHDF (const char *fname, const char *dname)
Method on mglDataC: void ReadHDF (const char *fname, const char *dname)
C function: void mgl_data_read_hdf (HMDT dat, const char *fname, const char *dname)
C function: void mgl_datac_read_hdf (HADT dat, const char *fname, const char *dname)

Reads data array named dname from HDF5 or HDF4 file. This function does nothing if HDF5|HDF4 was disabled during library compilation.

MGL command: savehdf dat 'fname' 'dname' [rewrite=off]
Method on mglDataA: void SaveHDF (const char *fname, const char *dname, bool rewrite=false) const
C function: void mgl_data_save_hdf (HCDT dat, const char *fname, const char *dname, int rewrite)
C function: void mgl_datac_save_hdf (HCDT dat, const char *fname, const char *dname, int rewrite)

Saves data array named dname to HDF5 file. This function does nothing if HDF5 was disabled during library compilation.

MGL command: datas 'fname'
Method on mglDataA: int DatasHDF (const char *fname, char *buf, long size) static
C function: int mgl_datas_hdf (const char *fname, char *buf, long size)

Put data names from HDF5 file fname into buf as ’\t’ separated fields. In MGL version the list of data names will be printed as message. This function does nothing if HDF5 was disabled during library compilation.

MGL command: import DAT 'fname' 'sch' [v1=0 v2=1]
Method on mglData: void Import (const char *fname, const char *scheme, mreal v1=0, mreal v2=1)
C function: void mgl_data_import (HMDT dat, const char *fname, const char *scheme, mreal v1, mreal v2)

Reads data from bitmap file (now support only PNG format). The RGB values of bitmap pixels are transformed to mreal values in range [v1, v2] using color scheme scheme (see Color scheme).

MGL command: export dat 'fname' 'sch' [v1=0 v2=0]
Method on mglDataA: void Export (const char *fname, const char *scheme, mreal v1=0, mreal v2=0, int ns=-1) const
C function: void mgl_data_export (HMDT dat, const char *fname, const char *scheme, mreal v1, mreal v2, int ns) const

Saves data matrix (or ns-th slice for 3d data) to bitmap file (now support only PNG format). The data values are transformed from range [v1, v2] to RGB pixels of bitmap using color scheme scheme (see Color scheme). If v1>=v2 then the values of v1, v2 are automatically determined as minimal and maximal value of the data array.

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6.6 Make another data

MGL command: subdata RES dat xx [yy=: zz=:]
Method on mglData: mglData SubData (mreal xx, mreal yy=-1, mreal zz=-1) const
Method on mglDataC: mglData SubData (mreal xx, mreal yy=-1, mreal zz=-1) const
C function: HMDT mgl_data_subdata (HCDT dat, mreal xx, mreal yy, mreal zz)

Extracts sub-array data from the original data array keeping fixed positive index. For example SubData(-1,2) extracts 3d row (indexes are zero based), SubData(4,-1) extracts 5th column, SubData(-1,-1,3) extracts 4th slice and so on. If argument(s) are non-integer then linear interpolation between slices is used. In MGL version this command usually is used as inline one dat(xx,yy,zz). Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: subdata RES dat xdat [ydat=: zdat=:]
Method on mglData: mglData SubData (const mglDataA &xx, const mglDataA &yy, const mglDataA &zz) const
Method on mglDataC: mglData SubData (const mglDataA &xx, const mglDataA &yy, const mglDataA &zz) const
Method on mglData: mglData SubData (const mglDataA &xx, const mglDataA &yy) const
Method on mglDataC: mglData SubData (const mglDataA &xx, const mglDataA &yy) const
Method on mglData: mglData SubData (const mglDataA &xx) const
Method on mglDataC: mglData SubData (const mglDataA &xx) const
C function: HMDT mgl_data_subdata_ext (HCDT dat, HCDT xx, HCDT yy, HCDT zz)
C function: HADT mgl_datac_subdata_ext (HCDT dat, HCDT xx, HCDT yy, HCDT zz)

Extracts sub-array data from the original data array for indexes specified by arrays xx, yy, zz (indirect access). This function work like previous one for 1D arguments or numbers, and resulting array dimensions are equal dimensions of 1D arrays for corresponding direction. For 2D and 3D arrays in arguments, the resulting array have the same dimensions as input arrays. The dimensions of all argument must be the same (or to be scalar 1*1*1) if they are 2D or 3D arrays. In MGL version this command usually is used as inline one dat(xx,yy,zz). Function return NULL or create empty data if data cannot be created for given arguments. In C function some of xx, yy, zz can be NULL.

MGL command: column RES dat 'eq'
Method on mglData: mglData Column (const char *eq) const
Method on mglDataC: mglData Column (const char *eq) const
C function: HMDT mgl_data_column (HCDT dat, const char *eq)

Get column (or slice) of the data filled by formula eq on column ids. For example, Column("n*w^2/exp(t)");. The column ids must be defined first by idset function or read from files. In MGL version this command usually is used as inline one dat('eq'). Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: resize RES dat mx [my=1 mz=1]
Method on mglData: mglData Resize (int mx, int my=0, int mz=0, mreal x1=0, mreal x2=1, mreal y1=0, mreal y2=1, mreal z1=0, mreal z2=1) const
Method on mglDataC: mglData Resize (int mx, int my=0, int mz=0, mreal x1=0, mreal x2=1, mreal y1=0, mreal y2=1, mreal z1=0, mreal z2=1) const
C function: HMDT mgl_data_resize (HCDT dat, int mx, int my, int mz)
C function: HMDT mgl_data_resize_box (HCDT dat, int mx, int my, int mz, mreal x1, mreal x2, mreal y1, mreal y2, mreal z1, mreal z2)

Resizes the data to new size mx, my, mz from box (part) [x1,x2] x [y1,y2] x [z1,z2] of original array. Initially x,y,z coordinates are supposed to be in [0,1]. If one of sizes mx, my or mz is 0 then initial size is used. Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: evaluate RES dat idat [norm=on]
MGL command: evaluate RES dat idat jdat [norm=on]
MGL command: evaluate RES dat idat jdat kdat [norm=on]
Method on mglData: mglData Evaluate (const mglDataA &idat, bool norm=true) const
Method on mglData: mglData Evaluate (const mglDataA &idat, const mglDataA &jdat, bool norm=true) const
Method on mglData: mglData Evaluate (const mglDataA &idat, const mglDataA &jdat, const mglDataA &kdat, bool norm=true) const
Method on mglDataC: mglData Evaluate (const mglDataA &idat, bool norm=true) const
Method on mglDataC: mglData Evaluate (const mglDataA &idat, const mglDataA &jdat, bool norm=true) const
Method on mglDataC: mglData Evaluate (const mglDataA &idat, const mglDataA &jdat, const mglDataA &kdat, bool norm=true) const
C function: HMDT mgl_data_evaluate (HCDT dat, HCDT idat, HCDT jdat, HCDT kdat, int norm)

Gets array which values is result of interpolation of original array for coordinates from other arrays. All dimensions must be the same for data idat, jdat, kdat. Coordinates from idat, jdat, kdat are supposed to be normalized in range [0,1] (if norm=true) or in ranges [0,nx], [0,ny], [0,nz] correspondingly. Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: solve RES dat val 'dir' [norm=on]
MGL command: solve RES dat val 'dir' idat [norm=on]
Method on mglData: mglData Solve (mreal val, char dir, bool norm=true) const
Method on mglData: mglData Solve (mreal val, char dir, const mglDataA &idat, bool norm=true) const
C function: HMDT mgl_data_solve (HCDT dat, mreal val, char dir, HCDT idat, int norm)

Gets array which values is indexes (roots) along given direction dir, where interpolated values of data dat are equal to val. Output data will have the sizes of dat in directions transverse to dir. If data idat is provided then its values are used as starting points. This allows to find several branches by consequentive calls. Indexes are supposed to be normalized in range [0,1] (if norm=true) or in ranges [0,nx], [0,ny], [0,nz] correspondingly. Function return NULL or create empty data if data cannot be created for given arguments. See Solve sample, for sample code and picture.

MGL command: roots RES 'func' ini ['var'='x']
MGL command: roots RES 'func' ini ['var'='x']
Method on mglData: mglData Roots (const char *func, char var) const
C function: HMDT mgl_data_roots (const char *func, HCDT ini, char var)
C function: mreal mgl_find_root_txt (const char *func, mreal ini, char var)

Find roots of equation ’func’=0 for variable var with initial guess ini. Secant method is used for root finding. Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: hist RES dat num v1 v2 [nsub=0]
MGL command: hist RES dat wdat num v1 v2 [nsub=0]
Method on mglData: mglData Hist (int n, mreal v1=0, mreal v2=1, int nsub=0) const
Method on mglData: mglData Hist (const mglDataA &w, int n, mreal v1=0, mreal v2=1, int nsub=0) const
Method on mglDataC: mglData Hist (int n, mreal v1=0, mreal v2=1, int nsub=0) const
Method on mglDataC: mglData Hist (const mglDataA &w, int n, mreal v1=0, mreal v2=1, int nsub=0) const
C function: HMDT mgl_data_hist (HCDT dat, int n, mreal v1, mreal v2, int nsub)
C function: HMDT mgl_data_hist_w (HCDT dat, HCDT w, int n, mreal v1, mreal v2, int nsub)

Creates n-th points distribution of the data values in range [v1, v2]. Array w specifies weights of the data elements (by default is 1). Parameter nsub define the number of additional interpolated points (for smoothness of histogram). Function return NULL or create empty data if data cannot be created for given arguments. See also Data manipulation

MGL command: momentum RES dat 'how' ['dir'='z']
Method on mglData: mglData Momentum (char dir, const char *how) const
Method on mglDataC: mglData Momentum (char dir, const char *how) const
C function: HMDT mgl_data_momentum (HCDT dat, char dir, const char *how)

Gets momentum (1d-array) of the data along direction dir. String how contain kind of momentum. The momentum is defined like as res_k = \sum_ij how(x_i,y_j,z_k) a_ij/ \sum_ij a_ij if dir=‘z’ and so on. Coordinates ‘x’, ‘y’, ‘z’ are data indexes normalized in range [0,1]. Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: sum RES dat 'dir'
Method on mglData: mglData Sum (const char *dir) const
Method on mglDataC: mglData Sum (const char *dir) const
C function: HMDT mgl_data_sum (HCDT dat, const char *dir)

Gets array which is the result of summation in given direction or direction(s). Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: max RES dat 'dir'
Method on mglData: mglData Max (const char *dir) const
Method on mglDataC: mglData Max (const char *dir) const
C function: HMDT mgl_data_max_dir (HCDT dat, const char *dir)

Gets array which is the maximal data values in given direction or direction(s). Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: min RES dat 'dir'
Method on mglData: mglData Min (const char *dir) const
Method on mglDataC: mglData Min (const char *dir) const
C function: HMDT mgl_data_min_dir (HCDT dat, const char *dir)

Gets array which is the maximal data values in given direction or direction(s). Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: combine RES adat bdat
Method on mglData: mglData Combine (const mglDataA &a) const
Method on mglDataC: mglData Combine (const mglDataA &a) const
C function: HMDT mgl_data_combine (HCDT dat, HCDT a)

Returns direct multiplication of arrays (like, res[i,j] = this[i]*a[j] and so on). Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: trace RES dat
Method on mglData: mglData Trace () const
Method on mglDataC: mglData Trace () const
C function: HMDT mgl_data_trace (HCDT dat)

Gets array of diagonal elements a[i,i] (for 2D case) or a[i,i,i] (for 3D case) where i=0...nx-1. Function return copy of itself for 1D case. Data array must have dimensions ny,nz >= nx or ny,nz = 1. Function return NULL or create empty data if data cannot be created for given arguments.

MGL command: correl RES adat bdat 'dir'
Method on mglData: mglData Correl (const mglDataA &b, const char *dir) const
Method on mglData: mglData AutoCorrel (const char *dir) const
Method on mglDataC: mglDataC Correl (const mglDataA &b, const char *dir) const
Method on mglDataC: mglDataC AutoCorrel (const char *dir) const
C function: HMDT mgl_data_correl (HCDT a, HCDT b, const char *dir)
C function: HADT mgl_datac_correl (HCDT a, HCDT b, const char *dir)

Find correlation between data a (or this in C++) and b along directions dir. Fourier transform is used to find the correlation. So, you may want to use functions swap or norm before plotting it. Function return NULL or create empty data if data cannot be created for given arguments.

Method on mglDataC: mglData Real () const
C function: HMDT mgl_datac_real (HCDT dat)

Gets array of real parts of the data.

Method on mglDataC: mglData Imag () const
C function: HMDT mgl_datac_imag (HCDT dat)

Gets array of imaginary parts of the data.

Method on mglDataC: mglData Abs () const
C function: HMDT mgl_datac_abs (HCDT dat)

Gets array of absolute values of the data.

Method on mglDataC: mglData Arg () const
C function: HMDT mgl_datac_arg (HCDT dat)

Gets array of arguments of the data.

MGL command: pulse RES dat 'dir'
Method on mglData: mglData Pulse (const char *dir) const
C function: HMDT mgl_data_pulse (HCDT dat, const char *dir)

Find pulse properties along direction dir: pulse maximum (in column 0) and its position (in column 1), pulse width near maximum (in column 3) and by half height (in column 2), energy in first pulse (in column 4). NAN values are used for widths if maximum is located near the edges. Note, that there is uncertainty for complex data. Usually one should use square of absolute value (i.e. |dat[i]|^2) for them. So, MathGL don’t provide this function for complex data arrays. However, C function will work even in this case but use absolute value (i.e. |dat[i]|). Function return NULL or create empty data if data cannot be created for given arguments. See also max, min, momentum, sum. See Pulse properties, for sample code and picture.

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6.7 Data changing

These functions change the data in some direction like differentiations, integrations and so on. The direction in which the change will applied is specified by the string parameter, which may contain ‘x’, ‘y’ or ‘z’ characters for 1-st, 2-nd and 3-d dimension correspondingly.

MGL command: cumsum dat 'dir'
Method on mglData: void CumSum (const char *dir)
Method on mglDataC: void CumSum (const char *dir)
C function: void mgl_data_cumsum (HMDT dat, const char *dir)
C function: void mgl_datac_cumsum (HADT dat, const char *dir)

Cumulative summation of the data in given direction or directions.

MGL command: integrate dat 'dir'
Method on mglData: void Integral (const char *dir)
Method on mglDataC: void Integral (const char *dir)
C function: void mgl_data_integral (HMDT dat, const char *dir)
C function: void mgl_datac_integral (HADT dat, const char *dir)

Integrates (like cumulative summation) the data in given direction or directions.

MGL command: diff dat 'dir'
Method on mglData: void Diff (const char *dir)
Method on mglDataC: void Diff (const char *dir)
C function: void mgl_data_diff (HMDT dat, const char *dir)
C function: void mgl_datac_diff (HADT dat, const char *dir)

Differentiates the data in given direction or directions.

MGL command: diff dat xdat ydat [zdat=0]
Method on mglData: void Diff (const mglDataA &x, const mglDataA &y)
Method on mglData: void Diff (const mglDataA &x, const mglDataA &y, const mglDataA &z)
C function: void mgl_data_diff_par (HMDT dat, HCDT x, HCDTy, HCDTz)

Differentiates the data specified parametrically in direction x with y, z=constant. Parametrical differentiation uses the formula (for 2D case): da/dx = (a_j*y_i-a_i*y_j)/(x_j*y_i-x_i*y_j) where a_i=da/di, a_j=da/dj denotes usual differentiation along 1st and 2nd dimensions. The similar formula is used for 3D case. Note, that you may change the order of arguments – for example, if you have 2D data a(i,j) which depend on coordinates {x(i,j), y(i,j)} then usual derivative along ‘x’ will be Diff(x,y); and usual derivative along ‘y’ will be Diff(y,x);.

MGL command: diff2 dat 'dir'
Method on mglData: void Diff2 (const char *dir)
Method on mglDataC: void Diff2 (const char *dir)
C function: void mgl_data_diff2 (HMDT dat, const char *dir)
C function: void mgl_datac_diff2 (HADT dat, const char *dir)

Double-differentiates (like Laplace operator) the data in given direction.

MGL command: sinfft dat 'dir'
Method on mglData: void SinFFT (const char *dir)
C function: void mgl_data_sinfft (HMDT dat, const char *dir)

Do Sine transform of the data in given direction or directions. The Sine transform is \sum a_j \sin(k j) (see http://en.wikipedia.org/wiki/Discrete_sine_transform#DST-I).

MGL command: cosfft dat 'dir'
Method on mglData: void CosFFT (const char *dir)
C function: void mgl_data_cosfft (HMDT dat, const char *dir)

Do Cosine transform of the data in given direction or directions. The Cosine transform is \sum a_j \cos(k j) (see http://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-I).

Method on mglDataC: void FFT (const char *dir)
C function: void mgl_datac_fft (HADT dat, const char *dir)

Do Fourier transform of the data in given direction or directions. If dir contain ‘i’ then inverse Fourier is used. The Fourier transform is \sum a_j \exp(i k j) (see http://en.wikipedia.org/wiki/Discrete_Fourier_transform).

MGL command: hankel dat 'dir'
Method on mglData: void Hankel (const char *dir)
Method on mglDataC: void Hankel (const char *dir)
C function: void mgl_data_hankel (HMDT dat, const char *dir)
C function: void mgl_datac_hankel (HADT dat, const char *dir)

Do Hankel transform of the data in given direction or directions. The Hankel transform is \sum a_j J_0(k j) (see http://en.wikipedia.org/wiki/Hankel_transform).

MGL command: wavelet dat 'dir' k
Method on mglData: void Wavelet (const char *dir, int k)
C function: void mgl_data_wavelet (HMDT dat, const char *dir, int k)

Apply wavelet transform of the data in given direction or directions. Parameter dir set the kind of wavelet transform: ‘d’ for daubechies, ‘D’ for centered daubechies, ‘h’ for haar, ‘H’ for centered haar, ‘b’ for bspline, ‘B’ for centered bspline. If string dir contain symbol ‘i’ then inverse wavelet transform is applied. Parameter k set the size of wavelet transform.

MGL command: swap dat 'dir'
Method on mglData: void Swap (const char *dir)
Method on mglDataC: void Swap (const char *dir)
C function: void mgl_data_swap (HMDT dat, const char *dir)
C function: void mgl_datac_swap (HADT dat, const char *dir)

Swaps the left and right part of the data in given direction (useful for Fourier spectrum).

MGL command: roll dat 'dir' num
Method on mglData: void Roll (char dir, num)
Method on mglDataC: void Roll (char dir, num)
C function: void mgl_data_roll (HMDT dat, char dir, num)
C function: void mgl_datac_roll (HADT dat, char dir, num)

Rolls the data along direction dir. Resulting array will be out[i] = ini[(i+num)%nx] if dir='x'.

MGL command: mirror dat 'dir'
Method on mglData: void Mirror (const char *dir)
Method on mglDataC: void Mirror (const char *dir)
C function: void mgl_data_mirror (HMDT dat, const char *dir)
C function: void mgl_datac_mirror (HADT dat, const char *dir)

Mirror the left-to-right part of the data in given direction. Looks like change the value index i->n-i. Note, that the similar effect in graphics you can reach by using options (see Command options), for example, surf dat; xrange 1 -1.

MGL command: sew dat ['dir'='xyz' da=2*pi]
Method on mglData: void Sew (const char *dir, mreal da=2*M_PI)
C function: void mgl_data_sew (HMDT dat, const char *dir, mreal da)

Remove value steps (like phase jumps after inverse trigonometric functions) with period da in given direction.

MGL command: smooth data type ['dir'='xyz']
Method on mglData: void Smooth (const char *dir="xyz", mreal delta=0)
Method on mglDataC: void Smooth (const char *dir="xyz", mreal delta=0)
C function: void mgl_data_smooth (HMDT dat, const char *dir, mreal delta)
C function: void mgl_datac_smooth (HADT dat, const char *dir, mreal delta)

Smooths the data on specified direction or directions. String dirs specifies the dimensions which will be smoothed. It may contain characters: ‘x’ for 1st dimension, ‘y’ for 2nd dimension, ‘z’ for 3d dimension. If string dir contain: ‘0’ then does nothing, ‘3’ – linear averaging over 3 points, ‘5’ – linear averaging over 5 points. If string dir contain ‘dN’ (where ‘N’ is digit 1,2,...,9) then linear averaging over (2*N+1)-th points is used. By default quadratic averaging over 5 points is used.

MGL command: envelop dat ['dir'='x']
Method on mglData: void Envelop (char dir='x')
C function: void mgl_data_envelop (HMDT dat, char dir)

Find envelop for data values along direction dir.

MGL command: diffract dat 'how' q
Method on mglDataC: void Diffraction (const char *how, mreal q)
C function: void mgl_datac_diffr (HADT dat, const char *how, mreal q)

Calculates one step of diffraction by finite-difference method with parameter q=\delta t/\delta x^2 using method with 3-d order of accuracy. Parameter how may contain:

MGL command: norm dat v1 v2 [sym=off dim=0]
Method on mglData: void Norm (mreal v1=0, mreal v2=1, bool sym=false, long dim=0)
C function: void mgl_data_norm (HMDT dat, mreal v1, mreal v2, int sym, long dim)

Normalizes the data to range [v1,v2]. If flag sym=true then symmetrical interval [-max(|v1|,|v2|), max(|v1|,|v2|)] is used. Modification will be applied only for slices >=dim.

MGL command: normsl dat v1 v2 ['dir'='z' keep=on sym=off]
Method on mglData: void NormSl (mreal v1=0, mreal v2=1, char dir='z', bool keep_en=true, bool sym=false)
C function: void mgl_data_norm_slice (HMDT dat, mreal v1, mreal v2, char dir, int keep_en, int sym)

Normalizes data slice-by-slice along direction dir the data in slices to range [v1,v2]. If flag sym=true then symmetrical interval [-max(|v1|,|v2|), max(|v1|,|v2|)] is used. If keep_en is set then maximal value of k-th slice will be limited by \sqrt{\sum a_ij(k)/\sum a_ij(0)}.

MGL command: limit dat val
Method on mglData: void Limit (mreal val)
Method on mglDataC: void Limit (mreal val)
C function: void mgl_data_limit (HMDT dat, mreal val)
C function: void mgl_datac_limit (HADT dat, mreal val)

Limits the data values to be inside the range [-val,val], keeping the original sign of the value (phase for complex numbers). This is equivalent to operation a[i] *= abs(a[i])<val?1.:val/abs(a[i]);.

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6.8 Interpolation

MGL scripts can use spline interpolation by evaluate or refill commands. Also you can use resize for obtaining a data array with new sizes.

However, there are much special faster functions in other modes (C/C++/Fortran/Python/...).

Method on mglData: mreal Spline (mreal x, mreal y=0, mreal z=0) const
Method on mglDataC: dual Spline (mreal x, mreal y=0, mreal z=0) const
C function: mreal mgl_data_spline (HCDT dat, mreal x, mreal y, mreal z)
C function: dual mgl_datac_spline (HCDT dat, mreal x, mreal y, mreal z)

Interpolates data by cubic spline to the given point x in [0...nx-1], y in [0...ny-1], z in [0...nz-1].

Method on mglData: mreal Spline1 (mreal x, mreal y=0, mreal z=0) const
Method on mglDataC: dual Spline1 (mreal x, mreal y=0, mreal z=0) const

Interpolates data by cubic spline to the given point x, y, z which assumed to be normalized in range [0, 1].

Method on mglData: mreal Spline (mglPoint &dif, mreal x, mreal y=0, mreal z=0) const
C function: mreal mgl_data_spline_ext (HCDT dat, mreal x, mreal y, mreal z, mreal *dx, mreal *dy, mreal *dz)
C function: dual mgl_datac_spline_ext (HCDT dat, mreal x, mreal y, mreal z, dual *dx, dual *dy, dual *dz)

Interpolates data by cubic spline to the given point x in [0...nx-1], y in [0...ny-1], z in [0...nz-1]. The values of derivatives at the point are saved in dif.

Method on mglData: mreal Spline1 (mglPoint &dif, mreal x, mreal y=0, mreal z=0) const

Interpolates data by cubic spline to the given point x, y, z which assumed to be normalized in range [0, 1]. The values of derivatives at the point are saved in dif.

Method on mglData: mreal Linear (mreal x, mreal y=0, mreal z=0) const
Method on mglDataC: dual Linear (mreal x, mreal y=0, mreal z=0) const
C function: mreal mgl_data_linear (HCDT dat, mreal x, mreal y, mreal z)
C function: dual mgl_datac_linear (HCDT dat, mreal x, mreal y, mreal z)

Interpolates data by linear function to the given point x in [0...nx-1], y in [0...ny-1], z in [0...nz-1].

Method on mglData: mreal Linear1 (mreal x, mreal y=0, mreal z=0) const
Method on mglDataC: dual Linear1 (mreal x, mreal y=0, mreal z=0) const

Interpolates data by linear function to the given point x, y, z which assumed to be normalized in range [0, 1].

Method on mglData: mreal Linear (mglPoint &dif, mreal x, mreal y=0, mreal z=0) const
Method on mglDataC: dual Linear (mglPoint &dif, mreal x, mreal y=0, mreal z=0) const
C function: mreal mgl_data_linear_ext (HCDT dat, mreal x, mreal y, mreal z, mreal *dx, mreal *dy, mreal *dz)
C function: dual mgl_datac_linear_ext (HCDT dat, mreal x, mreal y, mreal z, dual *dx, dual *dy, dual *dz)

Interpolates data by linear function to the given point x in [0...nx-1], y in [0...ny-1], z in [0...nz-1]. The values of derivatives at the point are saved in dif.

Method on mglData: mreal Linear1 (mglPoint &dif, mreal x, mreal y=0, mreal z=0) const
Method on mglDataC: dual Linear1 (mglPoint &dif, mreal x, mreal y=0, mreal z=0) const

Interpolates data by linear function to the given point x, y, z which assumed to be normalized in range [0, 1]. The values of derivatives at the point are saved in dif.

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6.9 Data information

There are a set of functions for obtaining data properties in MGL language. However most of them can be found using "suffixes". Suffix can get some numerical value of the data array (like its size, maximal or minimal value, the sum of elements and so on) as number. Later it can be used as usual number in command arguments. The suffixes start from point ‘.’ right after (without spaces) variable name or its sub-array. For example, a.nx give the x-size of data a, b(1).max give maximal value of second row of variable b, (c(:,0)^2).sum give the sum of squares of elements in the first column of c and so on.

MGL command: info dat
Method on mglDataA: const char * PrintInfo () const
Method on mglDataA: void PrintInfo (FILE *fp) const
C function only: const char * mgl_data_info (HCDT dat)
Fortran subroutine: mgl_data_info (long dat, char *out, int len)

Gets or prints to file fp or as message (in MGL) information about the data (sizes, maximum/minimum, momentums and so on).

MGL command: info 'txt'

Prints string txt as message.

MGL command: info val

Prints value of number val as message.

MGL command: print dat
MGL command: print 'txt'
MGL command: print val

The same as info but immediately print to stdout.

MGL command: echo dat

Prints all values of the data array dat as message.

MGL suffix: (dat) .nx
MGL suffix: (dat) .ny
MGL suffix: (dat) .nz
Method on mglDataA: long GetNx ()
Method on mglDataA: long GetNy ()
Method on mglDataA: long GetNz ()
C function: long mgl_data_get_nx (HCDT dat)
C function: long mgl_data_get_ny (HCDT dat)
C function: long mgl_data_get_nz (HCDT dat)

Gets the x-, y-, z-size of the data.

MGL suffix: (dat) .max
Method on mglDataA: mreal Maximal () const
C function: mreal mgl_data_max (HCDT dat)

Gets maximal value of the data.

MGL suffix: (dat) .min
Method on mglDataA: mreal Minimal () const
C function: mreal mgl_data_min (HMDT dat) const

Gets minimal value of the data.

Method on mglDataA: mreal Minimal (int &i, int &j, int &k) const
C function: mreal mgl_data_min_int (HCDT dat, int *i, int *j, int *k)

Gets position of minimum to variables i, j, k and returns the minimal value.

Method on mglDataA: mreal Maximal (int &i, int &j, int &k) const
C function: mreal mgl_data_max_int (HCDT dat, int *i, int *j, int *k)

Gets position of maximum to variables i, j, k and returns the maximal value.

Method on mglDataA: mreal Minimal (mreal &x, mreal &y, mreal &z) const
C function: mreal mgl_data_min_real (HCDT dat, mreal *x, mreal *y, mreal *z)

Gets approximated (interpolated) position of minimum to variables x, y, z and returns the minimal value.

MGL suffix: (dat) .mx
MGL suffix: (dat) .my
MGL suffix: (dat) .mz
Method on mglDataA: mreal Maximal (mreal &x, mreal &y, mreal &z) const
C function: mreal mgl_data_max_real (HCDT dat, mreal *x, mreal *y, mreal *z)

Gets approximated (interpolated) position of maximum to variables x, y, z and returns the maximal value.

MGL suffix: (dat) .sum
MGL suffix: (dat) .ax
MGL suffix: (dat) .ay
MGL suffix: (dat) .az
MGL suffix: (dat) .aa
MGL suffix: (dat) .wx
MGL suffix: (dat) .wy
MGL suffix: (dat) .wz
MGL suffix: (dat) .wa
MGL suffix: (dat) .sx
MGL suffix: (dat) .sy
MGL suffix: (dat) .sz
MGL suffix: (dat) .sa
MGL suffix: (dat) .kx
MGL suffix: (dat) .ky
MGL suffix: (dat) .kz
MGL suffix: (dat) .ka
Method on mglDataA: mreal Momentum (char dir, mreal &a, mreal &w) const
Method on mglDataA: mreal Momentum (char dir, mreal &m, mreal &w, mreal &s, mreal &k) const
C function: mreal mgl_data_momentum_val (HCDT dat, char dir, mreal *a, mreal *w, mreal *s, mreal *k)

Gets zero-momentum (energy, I=\sum dat_i) and write first momentum (median, a = \sum \xi_i dat_i/I), second momentum (width, w^2 = \sum (\xi_i-a)^2 dat_i/I), third momentum (skewness, s = \sum (\xi_i-a)^3 dat_i/ I w^3) and fourth momentum (kurtosis, k = \sum (\xi_i-a)^4 dat_i / 3 I w^4) to variables. Here \xi is corresponding coordinate if dir is ‘'x'’, ‘'y'’ or ‘'z'’. Otherwise median is a = \sum dat_i/N, width is w^2 = \sum (dat_i-a)^2/N and so on.

MGL suffix: (dat) .fst
Method on mglDataA: mreal Find (const char *cond, int &i, int &j, int &k) const
C function: mreal mgl_data_first (HCDT dat, const char *cond, int *i, int *j, int *k)

Find position (after specified in i, j, k) of first nonzero value of formula cond. Function return the data value at found position.

MGL suffix: (dat) .lst
Method on mglDataA: mreal Last (const char *cond, int &i, int &j, int &k) const
C function: mreal mgl_data_last (HCDT dat, const char *cond, int *i, int *j, int *k)

Find position (before specified in i, j, k) of last nonzero value of formula cond. Function return the data value at found position.

Method on mglDataA: int Find (const char *cond, char dir, int i=0, int j=0, int k=0) const
C function: mreal mgl_data_find (HCDT dat, const char *cond, int i, int j, int k)

Return position of first in direction dir nonzero value of formula cond. The search is started from point {i,j,k}.

Method on mglDataA: bool FindAny (const char *cond) const
C function: mreal mgl_data_find_any (HCDT dat, const char *cond)

Determines if any nonzero value of formula in the data array.

MGL suffix: (dat) .a

Give first (for .a, i.e. dat->a[0]).

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6.10 Operators

MGL command: copy DAT dat2 ['eq'='']
Method on mglData: void operator= (const mglDataA &d)

Copies data from other variable.

MGL command: copy dat val
Method on mreal: void operator= (mreal val)

Set all data values equal to val.

MGL command: multo dat dat2
MGL command: multo dat val
Method on mglData: void operator*= (const mglDataA &d)
Method on mglData: void operator*= (mreal d)
C function: void mgl_data_mul_dat (HMDT dat, HCDT d)
C function: void mgl_data_mul_num (HMDT dat, mreal d)

Multiplies data element by the other one or by value.

MGL command: divto dat dat2
MGL command: divto dat val
Method on mglData: void operator/= (const mglDataA &d)
Method on mglData: void operator/= (mreal d)
C function: void mgl_data_div_dat (HMDT dat, HCDT d)
C function: void mgl_data_div_num (HMDT dat, mreal d)

Divides each data element by the other one or by value.

MGL command: addto dat dat2
MGL command: addto dat val
Method on mglData: void operator+= (const mglDataA &d)
Method on mglData: void operator+= (mreal d)
C function: void mgl_data_add_dat (HMDT dat, HCDT d)
C function: void mgl_data_add_num (HMDT dat, mreal d)

Adds to each data element the other one or the value.

MGL command: subto dat dat2
MGL command: subto dat val
Method on mglData: void operator-= (const mglDataA &d)
Method on mglData: void operator-= (mreal d)
C function: void mgl_data_sub_dat (HMDT dat, HCDT d)
C function: void mgl_data_sub_num (HMDT dat, mreal d)

Subtracts from each data element the other one or the value.

Library Function: mglData operator+ (const mglDataA &a, const mglDataA &b)
Library Function: mglData operator+ (mreal a, const mglDataA &b)
Library Function: mglData operator+ (const mglDataA &a, mreal b)

Adds the other data or the number.

Library Function: mglData operator- (const mglDataA &a, const mglDataA &b)
Library Function: mglData operator- (mreal a, const mglDataA &b)
Library Function: mglData operator- (const mglDataA &a, mreal b)

Subtracts the other data or the number.

Library Function: mglData operator* (const mglDataA &a, const mglDataA &b)
Library Function: mglData operator* (mreal a, const mglDataA &b)
Library Function: mglData operator* (const mglDataA &a, mreal b)

Multiplies by the other data or the number.

Library Function: mglData operator/ (const mglDataA &a, const mglDataA &b)
Library Function: mglData operator/ (const mglDataA &a, mreal b)

Divides by the other data or the number.

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6.11 Global functions

These functions are not methods of mglData class. However it provide additional functionality to handle data. So I put it in this chapter.

MGL command: transform DAT 'type' real imag
Global function: mglData mglTransform (const mglDataA &real, const mglDataA &imag, const char *type)
C function: HMDT mgl_transform (HCDT real, HCDT imag, const char *type)

Does integral transformation of complex data real, imag on specified direction. The order of transformations is specified in string type: first character for x-dimension, second one for y-dimension, third one for z-dimension. The possible character are: ‘f’ is forward Fourier transformation, ‘i’ is inverse Fourier transformation, ‘s’ is Sine transform, ‘c’ is Cosine transform, ‘h’ is Hankel transform, ‘n’ or ‘ ’ is no transformation.

MGL command: transforma DAT 'type' ampl phase
Global function: mglData mglTransformA const mglDataA &ampl, const mglDataA &phase, const char *type)
C function: HMDT mgl_transform_a HCDT ampl, HCDT phase, const char *type)

The same as previous but with specified amplitude ampl and phase phase of complex numbers.

MGL command: fourier reDat imDat 'dir'
MGL command: fourier complexDat 'dir'
Global function: void mglFourier const mglDataA &re, const mglDataA &im, const char *dir)
C function: void mgl_data_fourier HCDT re, HCDT im, const char *dir)

Does Fourier transform of complex data re+i*im in directions dir. Result is placed back into re and im data arrays.

MGL command: stfad RES real imag dn ['dir'='x']
Global function: mglData mglSTFA (const mglDataA &real, const mglDataA &imag, int dn, char dir='x')
C function: HMDT mgl_data_stfa (HCDT real, HCDT imag, int dn, char dir)

Short time Fourier transformation for real and imaginary parts. Output is amplitude of partial Fourier of length dn. For example if dir=‘x’, result will have size {int(nx/dn), dn, ny} and it will contain res[i,j,k]=|\sum_d^dn exp(I*j*d)*(real[i*dn+d,k]+I*imag[i*dn+d,k])|/dn.

MGL command: tridmat RES ADAT BDAT CDAT DDAT 'how'
Global function: mglData mglTridMat (const mglDataA &A, const mglDataA &B, const mglDataA &C, const mglDataA &D, const char *how)
Global function: mglDataC mglTridMatC (const mglDataA &A, const mglDataA &B, const mglDataA &C, const mglDataA &D, const char *how)
C function: HMDT mgl_data_tridmat (HCDT A, HCDT B, HCDT C, HCDT D, const char*how)
C function: HADT mgl_datac_tridmat (HCDT A, HCDT B, HCDT C, HCDT D, const char*how)

Get array as solution of tridiagonal system of equations A[i]*x[i-1]+B[i]*x[i]+C[i]*x[i+1]=D[i]. String how may contain:

Data dimensions of arrays A, B, C should be equal. Also their dimensions need to be equal to all or to minor dimension(s) of array D. See PDE solving hints, for sample code and picture.

MGL command: pde RES 'ham' ini_re ini_im [dz=0.1 k0=100]
Global function: mglData mglPDE (HMGL gr, const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, mreal dz=0.1, mreal k0=100, const char *opt="")
Global function: mglDataC mglPDEc (HMGL gr, const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, mreal dz=0.1, mreal k0=100, const char *opt="")
C function: HMDT mgl_pde_solve (HMGL gr, const char *ham, HCDT ini_re, HCDT ini_im, mreal dz, mreal k0, const char *opt)
C function: HADT mgl_pde_solve_c (HMGL gr, const char *ham, HCDT ini_re, HCDT ini_im, mreal dz, mreal k0, const char *opt)

Solves equation du/dz = i*k0*ham(p,q,x,y,z,|u|)[u], where p=-i/k0*d/dx, q=-i/k0*d/dy are pseudo-differential operators. Parameters ini_re, ini_im specify real and imaginary part of initial field distribution. Parameters Min, Max set the bounding box for the solution. Note, that really this ranges are increased by factor 3/2 for purpose of reducing reflection from boundaries. Parameter dz set the step along evolutionary coordinate z. At this moment, simplified form of function ham is supported – all “mixed” terms (like ‘x*p’->x*d/dx) are excluded. For example, in 2D case this function is effectively ham = f(p,z) + g(x,z,u). However commutable combinations (like ‘x*q’->x*d/dy) are allowed. Here variable ‘u’ is used for field amplitude |u|. This allow one solve nonlinear problems – for example, for nonlinear Shrodinger equation you may set ham="p^2 + q^2 - u^2". You may specify imaginary part for wave absorption, like ham = "p^2 + i*x*(x>0)", but only if dependence on variable ‘i’ is linear (i.e. ham = hre+i*him). See also qo2d, qo3d. See PDE solving hints, for sample code and picture.

MGL command: ray RES 'ham' x0 y0 z0 p0 q0 v0 [dt=0.1 tmax=10]
Global function: mglData mglRay (const char *ham, mglPoint r0, mglPoint p0, mreal dt=0.1, mreal tmax=10)
C function: HMDT mgl_ray_trace (const char *ham, mreal x0, mreal y0, mreal z0, mreal px, mreal py, mreal pz, mreal dt, mreal tmax)

Solves GO ray equation like dr/dt = d ham/dp, dp/dt = -d ham/dr. This is Hamiltonian equations for particle trajectory in 3D case. Here ham is Hamiltonian which may depend on coordinates ‘x’, ‘y’, ‘z’, momentums ‘p’=px, ‘q’=py, ‘v’=pz and time ‘t’: ham = H(x,y,z,p,q,v,t). The starting point (at t=0) is defined by variables r0, p0. Parameters dt and tmax specify the integration step and maximal time for ray tracing. Result is array of {x,y,z,p,q,v,t} with dimensions {7 * int(tmax/dt+1) }.

MGL command: ode RES 'df' 'var' ini [dt=0.1 tmax=10]
Global function: mglData mglODE (const char *df, const char *var, const mglDataA &ini, mreal dt=0.1, mreal tmax=10)
C function: HMDT mgl_ode_solve_str (const char *df, const char *var, HCDT ini, mreal dt, mreal tmax)
C function: HMDT mgl_ode_solve (void (*df)(const mreal *x, mreal *dx, void *par), int n, const mreal *ini, mreal dt, mreal tmax)
C function: HMDT mgl_ode_solve_ex (void (*df)(const mreal *x, mreal *dx, void *par), int n, const mreal *ini, mreal dt, mreal tmax, void (*bord)(mreal *x, const mreal *xprev, void *par))

Solves ODE equations dx/dt = df(x). The functions df can be specified as string of ’;’-separated textual formulas (argument var set the character ids of variables x[i]) or as callback function, which fill dx array for give x’s. Parameters ini, dt, tmax set initial values, time step and maximal time of the calculation. Result is data array with dimensions {n * int(tmax/dt+1)}.

MGL command: qo2d RES 'ham' ini_re ini_im ray [r=1 k0=100 xx yy]
Global function: mglData mglQO2d (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mreal r=1, mreal k0=100)
Global function: mglData mglQO2d (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mglData &xx, mglData &yy, mreal r=1, mreal k0=100)
Global function: mglDataC mglQO2dc (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mreal r=1, mreal k0=100)
Global function: mglDataC mglQO2dc (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mglData &xx, mglData &yy, mreal r=1, mreal k0=100)
C function: HMDT mgl_qo2d_solve (const char *ham, HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy)
C function: HADT mgl_qo2d_solve_c (const char *ham, HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy)
C function: HMDT mgl_qo2d_func (dual (*ham)(mreal u, mreal x, mreal y, mreal px, mreal py, void *par), HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy)
C function: HADT mgl_qo2d_func_c (dual (*ham)(mreal u, mreal x, mreal y, mreal px, mreal py, void *par), HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy)

Solves equation du/dt = i*k0*ham(p,q,x,y,|u|)[u], where p=-i/k0*d/dx, q=-i/k0*d/dy are pseudo-differential operators (see mglPDE() for details). Parameters ini_re, ini_im specify real and imaginary part of initial field distribution. Parameters ray set the reference ray, i.e. the ray around which the accompanied coordinate system will be maked. You may use, for example, the array created by ray function. Note, that the reference ray must be smooth enough to make accompanied coodrinates unambiguity. Otherwise errors in the solution may appear. If xx and yy are non-zero then Cartesian coordinates for each point will be written into them. See also pde, qo3d. See PDE solving hints, for sample code and picture.

MGL command: qo3d RES 'ham' ini_re ini_im ray [r=1 k0=100 xx yy zz]
Global function: mglData mglQO3d (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mreal r=1, mreal k0=100)
Global function: mglData mglQO3d (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mglData &xx, mglData &yy, mglData &zz, mreal r=1, mreal k0=100)
Global function: mglDataC mglQO3dc (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mreal r=1, mreal k0=100)
Global function: mglDataC mglQO3dc (const char *ham, const mglDataA &ini_re, const mglDataA &ini_im, const mglDataA &ray, mglData &xx, mglData &yy, mglData &zz, mreal r=1, mreal k0=100)
C function: HMDT mgl_qo3d_solve (const char *ham, HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy, HMDT zz)
C function: HADT mgl_qo3d_solve_c (const char *ham, HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy, HMDT zz)
C function: HMDT mgl_qo3d_func (dual (*ham)(mreal u, mreal x, mreal y, mreal z, mreal px, mreal py, mreal pz, void *par), HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy, HMDT zz)
C function: HADT mgl_qo3d_func_c (dual (*ham)(mreal u, mreal x, mreal y, mreal z, mreal px, mreal py, mreal pz, void *par), HCDT ini_re, HCDT ini_im, HCDT ray, mreal r, mreal k0, HMDT xx, HMDT yy, HMDT zz)

Solves equation du/dt = i*k0*ham(p,q,v,x,y,z,|u|)[u], where p=-i/k0*d/dx, q=-i/k0*d/dy, v=-i/k0*d/dz are pseudo-differential operators (see mglPDE() for details). Parameters ini_re, ini_im specify real and imaginary part of initial field distribution. Parameters ray set the reference ray, i.e. the ray around which the accompanied coordinate system will be maked. You may use, for example, the array created by ray function. Note, that the reference ray must be smooth enough to make accompanied coodrinates unambiguity. Otherwise errors in the solution may appear. If xx and yy and zz are non-zero then Cartesian coordinates for each point will be written into them. See also pde, qo2d. See PDE solving hints, for sample code and picture.

MGL command: jacobian RES xdat ydat [zdat]
Global function: mglData mglJacobian (const mglDataA &x, const mglDataA &y)
Global function: mglData mglJacobian (const mglDataA &x, const mglDataA &y, const mglDataA &z)
C function: HMDT mgl_jacobian_2d (HCDT x, HCDT y)
C function: HMDT mgl_jacobian_3d (HCDT x, HCDT y, HCDT z)

Computes the Jacobian for transformation {i,j,k} to {x,y,z} where initial coordinates {i,j,k} are data indexes normalized in range [0,1]. The Jacobian is determined by formula det||dr_\alpha/d\xi_\beta|| where r={x,y,z} and \xi={i,j,k}. All dimensions must be the same for all data arrays. Data must be 3D if all 3 arrays {x,y,z} are specified or 2D if only 2 arrays {x,y} are specified.

MGL command: triangulation RES xdat ydat
Global function: mglData mglTriangulation (const mglDataA &x, const mglDataA &y)
C function: HMDT mgl_triangulation_2d (HCDT x, HCDT y)

Computes triangulation for arbitrary placed points with coordinates {x,y} (i.e. finds triangles which connect points). MathGL use s-hull code for triangulation. The sizes of 1st dimension must be equal for all arrays x.nx=y.nx. Resulting array can be used in triplot or tricont functions for visualization of reconstructed surface. See Making regular data, for sample code and picture.

Global function: mglData mglGSplineInit (const mglDataA &x, const mglDataA &y)
Global function: mglDataC mglGSplineCInit (const mglDataA &x, const mglDataA &y)
C function: HMDT mgl_gspline_init (HCDT x, HCDT y)
C function: HADT mgl_gsplinec_init (HCDT x, HCDT y)

Prepare coefficients for global cubic spline interpolation.

Global function: mreal mglGSpline (const mglDataA &coef, mreal dx, mreal *d1=0, mreal *d2=0)
Global function: dual mglGSplineC (const mglDataA &coef, mreal dx, dual *d1=0, dual *d2=0)
C function: mreal mgl_gspline (HCDT coef, mreal dx, mreal *d1, mreal *d2)
C function: dual mgl_gsplinec (HCDT coef, mreal dx, dual *d1, dual *d2)

Evaluate global cubic spline (and its 1st and 2nd derivatives d1, d2 if they are not NULL) using prepared coefficients coef at point dx+x0 (where x0 is 1st element of data x provided to mglGSpline*Init() function).

MGL command: ifs2d RES dat num [skip=20]
Global function: mglData mglIFS2d (const mglDataA &dat, long num, long skip=20)
C function: HMDT mgl_data_ifs_2d (HCDT dat, long num, long skip)

Computes num points {x[i]=res[0,i], y[i]=res[1,i]} for fractal using iterated function system. Matrix dat is used for generation according the formulas 

x[i+1] = dat[0,i]*x[i] + dat[1,i]*y[i] + dat[4,i];
y[i+1] = dat[2,i]*x[i] + dat[3,i]*y[i] + dat[5,i];

Value dat[6,i] is used as weight factor for i-th row of matrix dat. At this first skip iterations will be omitted. Data array dat must have x-size greater or equal to 7. See IFS sample, for sample code and picture.

MGL command: ifs3d RES dat num [skip=20]
Global function: mglData mglIFS3d (const mglDataA &dat, long num, long skip=20)
C function: HMDT mgl_data_ifs_3d (HCDT dat, long num, long skip)

Computes num points {x[i]=res[0,i], y[i]=res[1,i], z[i]=res[2,i]} for fractal using iterated function system. Matrix dat is used for generation according the formulas 

x[i+1] = dat[0,i]*x[i] + dat[1,i]*y[i] + dat[2,i]*z[i] + dat[9,i];
y[i+1] = dat[3,i]*x[i] + dat[4,i]*y[i] + dat[5,i]*z[i] + dat[10,i];
z[i+1] = dat[6,i]*x[i] + dat[7,i]*y[i] + dat[8,i]*z[i] + dat[10,i];

Value dat[12,i] is used as weight factor for i-th row of matrix dat. At this first skip iterations will be omitted. Data array dat must have x-size greater or equal to 13. See IFS sample, for sample code and picture.

MGL command: ifsfile RES 'fname' 'name' num [skip=20]
Global function: mglData mglIFSfile (const char *fname, const char *name, long num, long skip=20)
C function: HMDT mgl_data_ifs_file (const char *fname, const char *name, long num, long skip)

Reads parameters of IFS fractal named name from file fname and computes num points for this fractal. At this first skip iterations will be omitted. See also ifs2d, ifs3d.

IFS file may contain several records. Each record contain the name of fractal (‘binary’ in the example below) and the body of fractal, which is enclosed in curly braces {}. Symbol ‘;’ start the comment. If the name of fractal contain ‘(3D)’ or ‘(3d)’ then the 3d IFS fractal is specified. The sample below contain two fractals: ‘binary’ – usual 2d fractal, and ‘3dfern (3D)’ – 3d fractal. 

 binary
 { ; comment allowed here
  ; and here
  .5  .0 .0 .5 -2.563477 -0.000003 .333333   ; also comment allowed here
  .5  .0 .0 .5  2.436544 -0.000003 .333333
  .0 -.5 .5 .0  4.873085  7.563492 .333333
  }

 3dfern (3D) {
   .00  .00 0 .0 .18 .0 0  0.0 0.00 0 0.0 0 .01
   .85  .00 0 .0 .85 .1 0 -0.1 0.85 0 1.6 0 .85
   .20 -.20 0 .2 .20 .0 0  0.0 0.30 0 0.8 0 .07
  -.20  .20 0 .2 .20 .0 0  0.0 0.30 0 0.8 0 .07
  }

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6.12 Evaluate expression

MathGL have a special classes mglExpr and mglExprC for evaluating of formula specified by the string for real and complex numbers correspondingly. These classes are defined in #include <mgl2/data.h> and #include <mgl2/datac.h> correspondingly. It is the fast variant of formula evaluation. At creation it will be recognized and compiled to tree-like internal code. At evaluation stage only fast calculations are performed. There is no difference between lower or upper case in formulas. If argument value lie outside the range of function definition then function returns NaN. See Textual formulas.

Constructor on mglExpr: mglExpr (const char *expr)
Constructor on mglExprC: mglExprC (const char *expr)
C function: HMEX mgl_create_expr (const char *expr)
C function: HAEX mgl_create_cexpr (const char *expr)

Parses the formula expr and creates formula-tree. Constructor recursively parses the formula and creates a tree-like structure containing functions and operators for fast further evaluating by Calc() or CalcD() functions.

Destructor on mglExpr: ~mglExpr ()
Destructor on mglExprC: ~mglExprC ()
C function: void mgl_delete_expr (HMEX ex)
C function: void mgl_delete_cexpr (HAEX ex)

Deletes the instance of class mglExpr.

Method on mglExpr: mreal Eval (mreal x, mreal y, mreal z)
Method on mglExprC: dual Eval (dual x, dual y, dual z)
C function: mreal mgl_expr_eval (HMEX ex, mreal x, mreal y, mreal z)
C function: dual mgl_cexpr_eval (HAEX ex, dual x, dual y, dual z)

Evaluates the formula for 'x','r'=x, 'y','n'=y, 'z','t'=z, 'a','u'=u.

Method on mglExpr: mreal Eval (mreal var[26])
Method on mglExprC: dual Eval (dual var[26])
C function: mreal mgl_expr_eval_v (HMEX ex, mreal *var)
C function: dual mgl_expr_eval_v (HAEX ex, dual *var)

Evaluates the formula for variables in array var[0,...,’z’-’a’].

Method on mglExpr: mreal Diff (char dir, mreal x, mreal y, mreal z)
C function: mreal mgl_expr_diff (HMEX ex, char dir, mreal x, mreal y, mreal z)

Evaluates the formula derivation respect to dir for 'x','r'=x, 'y','n'=y, 'z','t'=z, 'a','u'=u.

Method on mglExpr: mreal Diff (char dir, mreal var[26])
C function: mreal mgl_expr_diff_v (HMEX ex, char dir, mreal *var)

Evaluates the formula derivation respect to dir for variables in array var[0,...,’z’-’a’].

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6.13 Special data classes

This section describe special data classes mglDataV, mglDataF, mglDataT and mglDataR which sometime can noticeable speed up drawing or data handling. These classes are defined in #include <mgl2/data.h>. Note, that all plotting and data handling routines can be done using usual mglData or mglDataC classes. Also these special classes are usable in C++ code only.

Class mglDataV

represent variable with values equidistantly distributed in given range.

Constructor on mglDataV: mglDataV (const mglDataV & d)

Copy constructor.

Constructor on mglDataV: mglDataV (long nx=1, long ny=1, long nz=1, mreal v1=0, mreal v2=NaN, char dir='x')

Create variable with "sizes" nxxnyxnz which changes from v1 to v2 (or is constant if v2=NaN) along dir direction.

Method on mglDataV: void Create (long nx=1, long ny=1, long nz=1)

Set "sizes" nxxnyxnz.

Method on mglDataV: void Fill (mreal x1, mreal x2=NaN, char dir='x')

Set ranges of the variable.

Method on mglDataV: void Freq (mreal dp, char dir='x')

Set as frequency variable with increment dp.

Class mglDataF

represent function which values are evaluated (instead of access to data array as in mglData).

Constructor on mglDataF: mglDataF (const mglDataF & d)

Copy constructor.

Constructor on mglDataF: mglDataF (long nx=1, long ny=1, long nz=1)

Create variable with "sizes" nxxnyxnz with zero function.

Method on mglDataF: void Create (long nx=1, long ny=1, long nz=1)

Set "sizes" nxxnyxnz.

Method on mglDataF: void SetRanges (mglPoint p1, mglPoint p2)

Set ranges for internal x,y,z variables.

Method on mglDataF: void SetFormula (const char *func)

Set string which will be evaluated at function calls. Note this variant is about 10 times slower than SetFunc() one.

Method on mglDataF: void SetFunc (mreal (*f)(mreal x,mreal y,mreal z,void *p), void *p=NULL)

Set pointer to function which will be used for data.

Class mglDataT

represent named reference to column of another data array.

Constructor on mglDataT: mglDataT (const mglDataT & d)

Copy constructor.

Constructor on mglDataT: mglDataT (const mglDataA & d, long col=0)

Create variable which reference col-th column of data d.

Method on mglDataT: void SetInd (long col, wchar_t name)
Method on mglDataT: void SetInd (long col, const wchar_t * name)

Set reference to another column of the same data and its name.

Class mglDataR

represent named reference to row of another data array.

Constructor on mglDataR: mglDataR (const mglDataR & d)

Copy constructor.

Constructor on mglDataR: mglDataR (const mglDataA & d, long row=0)

Create variable which reference row-th row of data d.

Method on mglDataR: void SetInd (long row, wchar_t name)
Method on mglDataR: void SetInd (long row, const wchar_t * name)

Set reference to another row of the same data and its name.

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7 MGL scripts

MathGL library supports the simplest scripts for data handling and plotting. These scripts can be used independently (with the help of UDAV, mglconv, mglview programs and others , see Utilities) or in the frame of the library using.

• MGL definition:  
• Program flow commands:  
• LaTeX package:  
• mglParse class:  

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7.1 MGL definition

MGL script language is rather simple. Each string is a command. First word of string is the name of command. Other words are command arguments. Words are separated from each other by space or tabulation symbol. The upper or lower case of words is important, i.e. variables a and A are different variables. Symbol ‘#’ starts the comment (all characters after # will be ignored). The exception is situation when ‘#’ is a part of some string. Also options can be specified after symbol ‘;’ (see Command options). Symbol ‘:’ starts new command (like new line character) if it is not placed inside a string or inside brackets.

If string contain references to external parameters (substrings ‘$0’, ‘$1’ ... ‘$9’) or definitions (substrings ‘$a’, ‘$b’ ... ‘$z’) then before execution the values of parameter/definition will be substituted instead of reference. It allows to use the same MGL script for different parameters (filenames, paths, condition and so on).

Argument can be a string, a variable (data arrays) or a number (scalars).

Before the first using all variables must be defined with the help of commands, like, new, var, list, copy, read, hist, sum and so on (see sections Data constructor, Data filling and Make another data).

Command may have several set of possible arguments (for example, plot ydat and plot xdat ydat). All command arguments for a selected set must be specified. However, some arguments can have default values. These argument are printed in [], like text ydat ['stl'=''] or text x y 'txt' ['fnt'='' size=-1]. At this, the record [arg1 arg2 arg3 ...] means [arg1 [arg2 [arg3 ...]]], i.e. you can omit only tailing arguments if you agree with its default values. For example, text x y 'txt' '' 1 or text x y 'txt' '' is correct, but text x y 'txt' 1 is incorrect (argument 'fnt' is missed).

You can provide several variants of arguments for a command by using ‘?’ symbol for separating them. The actual argument being used is set by variant. At this, the last argument is used if the value of variant is large than the number of provided variants. By default the first argument is used (i.e. as for variant 0). For example, the first plot will be drawn by blue (default is the first argument ‘b’), but the plot after variant 1 will be drawn by red dash (the second is ‘r|’): 

fplot 'x' 'b'?'r'
variant 1
fplot 'x^3' 'b'?'r|'

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7.2 Program flow commands

Below I show commands to control program flow, like, conditions, loops, define script arguments and so on. Other commands can be found in chapters MathGL core and Data processing. Note, that some of program flow commands (like define, ask, call, for, func) should be placed alone in the string.

MGL command: chdir 'path'

Changes the current directory to path.

MGL command: ask $N 'question'

Sets N-th script argument to answer which give the user on the question. Usually this show dialog with question where user can enter some text as answer. Here N is digit (0...9) or alpha (a...z).

MGL command: define $N smth

Sets N-th script argument to smth. Note, that smth is used as is (with ‘'’ symbols if present). Here N is digit (0...9) or alpha (a...z).

MGL command: define name smth

Create scalar variable name which have the numeric value of smth. Later you can use this variable as usual number.

MGL command: defchr $N smth

Sets N-th script argument to character with value evaluated from smth. Here N is digit (0...9) or alpha (a...z).

MGL command: defnum $N smth

Sets N-th script argument to number with value evaluated from smth. Here N is digit (0...9) or alpha (a...z).

MGL command: call 'funcname' [ARG1 ARG2 ... ARG9]

Executes function fname (or script if function is not found). Optional arguments will be passed to functions. See also func.

MGL command: func 'funcname' [narg=0]

Define the function fname and number of required arguments. The arguments will be placed in script parameters $1, $2, ... $9. Note, script execution is stopped at func keyword, similarly to stop command. See also return.

MGL command: return

Return from the function. See also func.

MGL command: load 'filename'

Load additional MGL command from external module (DLL or .so), located in file filename. This module have to contain array with name mgl_cmd_extra of type mglCommand, which describe provided commands.

MGL command: if dat 'cond'

Starts block which will be executed if dat satisfy to cond.

MGL command: if val

Starts block which will be executed if val is nonzero.

MGL command: elseif dat 'cond'

Starts block which will be executed if previous if or elseif is false and dat satisfy to cond.

MGL command: elseif val

Starts block which will be executed if previous if or elseif is false and val is nonzero.

MGL command: else

Starts block which will be executed if previous if or elseif is false.

MGL command: endif

Finishes if/elseif/else block.

MGL command: for $N v1 v2 [dv=1]

Starts cycle with $N-th argument changing from v1 to v2 with the step dv. Here N is digit (0...9) or alpha (a...z).

MGL command: for $N dat

Starts cycle with $N-th argument changing for dat values. Here N is digit (0...9) or alpha (a...z).

MGL command: next

Finishes for cycle.

MGL command: once val

The code between once on and once off will be executed only once. Useful for large data manipulation in programs like UDAV.

MGL command: stop

Terminate execution.

MGL command: variant val

Set variant of argument(s) separated by ‘?’ symbol to be used in further commands.

MGL command: rkstep eq1;... var1;... [dt=1]

Make one step for ordinary differential equation(s) {var1’ = eq1, ... } with time-step dt. Here variable(s) ‘var1’, ... are the ones, defined in MGL script previously. The Runge-Kutta 4-th order method is used for solution.

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7.3 LaTeX package

There is LaTeX package mgltex (was made by Diego Sejas Viscarra) which allow one to make figures directly from MGL script located in LaTeX file.

For using this package you need to specify --shell-escape option for latex/pdflatex or manually run mglconv tool with produced MGL scripts for generation of images. Don’t forgot to run latex/pdflatex second time to insert generated images into the output document. Also you need to run pdflatex third time to update converted from EPS images if you are using vector EPS output (default).

The package may have following options: draft, final — the same as in the graphicx package; on, off — to activate/deactivate the creation of scripts and graphics; comments, nocomments — to make visible/invisible commentaries contained inside mglcomment environments; jpg, jpeg, png — to export graphics as JPEG/PNG images; eps, epsz — to export to uncompressed/compressed EPS format as primitives; bps, bpsz — to export to uncompressed/compressed EPS format as bitmap (doesn’t work with pdflatex); pdf — to export to 3D PDF; tex — to export to LaTeX/tikz document.

The package defines the following environments:

‘mgl’

It writes its contents to a general script which has the same name as the LaTeX document, but its extension is .mgl. The code in this environment is compiled and the image produced is included. It takes exactly the same optional arguments as the \includegraphics command, plus an additional argument imgext, which specifies the extension to save the image.

An example of usage of ‘mgl’ environment would be: 

\begin{mglfunc}{prepare2d}
  new a 50 40 '0.6*sin(pi*(x+1))*sin(1.5*pi*(y+1))+0.4*cos(0.75*pi*(x+1)*(y+1))'
  new b 50 40 '0.6*cos(pi*(x+1))*cos(1.5*pi*(y+1))+0.4*cos(0.75*pi*(x+1)*(y+1))'
\end{mglfunc}

\begin{figure}[!ht]
  \centering
  \begin{mgl}[width=0.85\textwidth,height=7.5cm]
    fog 0.5
    call 'prepare2d'
    subplot 2 2 0 : title 'Surf plot (default)' : rotate 50 60 : light on : box : surf a

    subplot 2 2 1 : title '"\#" style; meshnum 10' : rotate 50 60 : box
    surf a '#'; meshnum 10

    subplot 2 2 2 : title 'Mesh plot' : rotate 50 60 : box
    mesh a

    new x 50 40 '0.8*sin(pi*x)*sin(pi*(y+1)/2)'
    new y 50 40 '0.8*cos(pi*x)*sin(pi*(y+1)/2)'
    new z 50 40 '0.8*cos(pi*(y+1)/2)'
    subplot 2 2 3 : title 'parametric form' : rotate 50 60 : box
    surf x y z 'BbwrR'
  \end{mgl}
\end{figure}
‘mgladdon’

It adds its contents to the general script, without producing any image.

‘mglcode’

Is exactly the same as ‘mgl’, but it writes its contents verbatim to its own file, whose name is specified as a mandatory argument.

‘mglscript’

Is exactly the same as ‘mglcode’, but it doesn’t produce any image, nor accepts optional arguments. It is useful, for example, to create a MGL script, which can later be post processed by another package like "listings".

‘mglblock’

It writes its contents verbatim to a file, specified as a mandatory argument, and to the LaTeX document, and numerates each line of code.

‘mglverbatim’

Exactly the same as ‘mglblock’, but it doesn’t write to a file. This environment doesn’t have arguments.

‘mglfunc’

Is used to define MGL functions. It takes one mandatory argument, which is the name of the function, plus one additional argument, which specifies the number of arguments of the function. The environment needs to contain only the body of the function, since the first and last lines are appended automatically, and the resulting code is written at the end of the general script, after the stop command, which is also written automatically. The warning is produced if 2 or more function with the same name is defined.

‘mglcomment’

Is used to contain multiline commentaries. This commentaries will be visible/invisible in the output document, depending on the use of the package options comments and nocomments (see above), or the \mglcomments and \mglnocomments commands (see bellow).

‘mglsetup’

If many scripts with the same code are to be written, the repetitive code can be written inside this environment only once, then this code will be used automatically every time the ‘\mglplot’ command is used (see below). It takes one optional argument, which is a name to be associated to the corresponding contents of the environment; this name can be passed to the ‘\mglplot’ command to use the corresponding block of code automatically (see below).

The package also defines the following commands:

‘\mglplot’

It takes one mandatory argument, which is MGL instructions separated by the symbol ‘:’ this argument can be more than one line long. It takes the same optional arguments as the ‘mgl’ environment, plus an additional argument setup, which indicates the name associated to a block of code inside a ‘mglsetup’ environment. The code inside the mandatory argument will be appended to the block of code specified, and the resulting code will be written to the general script.

An example of usage of ‘\mglplot’ command would be: 

\begin{mglsetup}
    box '@{W9}' : axis
\end{mglsetup}
\begin{mglsetup}[2d]
  box : axis
  grid 'xy' ';k'
\end{mglsetup}
\begin{mglsetup}[3d]
  rotate 50 60
  box : axis : grid 'xyz' ';k'
\end{mglsetup}
\begin{figure}[!ht]
  \centering
  \mglplot[scale=0.5]{new a 200 'sin(pi*x)' : plot a '2B'}
\end{figure}
\begin{figure}[!ht]
  \centering
  \mglplot[scale=0.5,setup=2d]{
    fplot 'sin(pi*x)' '2B' :
    fplot 'cos(pi*x^2)' '2R'
  }
\end{figure}
\begin{figure}[!ht]
  \centering
  \mglplot[setup=3d]{fsurf 'sin(pi*x)+cos(pi*y)'}
\end{figure}
‘\mglgraphics’

This command takes the same optional arguments as the ‘mgl’ environment, and one mandatory argument, which is the name of a MGL script. This command will compile the corresponding script and include the resulting image. It is useful when you have a script outside the LaTeX document, and you want to include the image, but you don’t want to type the script again.

‘\mglinclude’

This is like ‘\mglgraphics’ but, instead of creating/including the corresponding image, it writes the contents of the MGL script to the LaTeX document, and numerates the lines.

‘\mgldir’

This command can be used in the preamble of the document to specify a directory where LaTeX will save the MGL scripts and generate the corresponding images. This directory is also where ‘\mglgraphics’ and ‘\mglinclude’ will look for scripts.

‘\mglquality’

Adjust the quality of the MGL graphics produced similarly to quality.

‘\mgltexon, \mgltexoff’

Activate/deactivate the creation of MGL scripts and images. Notice these commands have local behavior in the sense that their effect is from the point they are called on.

‘\mglcomment, \mglnocomment’

Make visible/invisible the contents of the mglcomment environments. These commands have local effect too.

‘\mglTeX’

It just pretty prints the name of the package.

As an additional feature, when an image is not found or cannot be included, instead of issuing an error, mgltex prints a box with the word ‘MGL image not found’ in the LaTeX document.

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7.4 mglParse class

Class for parsing and executing MGL script. This class is defined in #include <mgl2/mgl.h>.

The main function of mglParse class is Execute(). Exactly this function parses and executes the script string-by-string. Also there are subservient functions for the finding and creation of a variable (object derived from mglDataA). These functions can be useful for displaying values of variables (arrays) in some external object (like, window) or for providing access to internal data. Function AllowSetSize() allows one to prevent changing the size of the picture inside the script (forbids the MGL command setsize).

Constructor on mglParse: mglParse (bool setsize=false)
Constructor on mglParse: mglParse (HMPR pr)
Constructor on mglParse: mglParse (mglParse &pr)
C function: HMPR mgl_create_parser ()

Constructor initializes all values with zero and set AllowSetSize value.

Destructor on mglParse: ~mglParse ()
C function: void mgl_delete_parser (HMPR p)

Destructor delete parser

Method on mglParse: HMPR Self ()

Returns the pointer to internal object of type HMPR.

Method on mglParse: void Execute (mglGraph *gr, const char *text)
Method on mglParse: void Execute (mglGraph *gr, const wchar_t *text)
C function: void mgl_parse_text (HMGL gr, HMPR p, const char *text)
C function: void mgl_parse_textw (HMGL gr, HMPR p, const wchar_t *text)

Main function in the class. Function parse and execute line-by-line MGL script in array text. Lines are separated by newline symbol ‘\n’ as usual.

Method on mglParse: void Execute (mglGraph *gr, FILE *fp, bool print=false)
C function: void mgl_parse_file (HMGL gr, HMPR p, FILE *fp, int print)

The same as previous but read script from the file fp. If print=true then all warnings and information will be printed in stdout.

Method on mglParse: int Parse (mglGraph *gr, const char *str, long pos=0)
Method on mglParse: int Parse (mglGraph *gr, const wchar_t *str, long pos=0)
C function: int mgl_parse_line (HMGL gr, HMPR p, const char *str, int pos)
C function: int mgl_parse_linew (HMGL gr, HMPR p, const wchar_t *str, int pos)

Function parses the string str and executes it by using gr as a graphics plotter. Returns the value depending on an error presence in the string str: 0 – no error, 1 – wrong command argument(s), 2 – unknown command, 3 – string is too long, 4 – strings is not closed. Optional argument pos allows to save the string position in the document (or file) for using for|next command.

Method on mglParse: mglData Calc (const char *formula)
Method on mglParse: mglData Calc (const wchar_t *formula)
C function: HMDT mgl_parser_calc (HMPR p, const char *formula)
C function: HMDT mgl_parser_calcw (HMPR p, const wchar_t *formula)

Function parses the string formula and return resulting data array. In difference to AddVar() or FindVar(), it is usual data array which should be deleted after usage.

Method on mglParse: mglDataC CalcComplex (const char *formula)
Method on mglParse: mglDataC CalcComplex (const wchar_t *formula)
C function: HADT mgl_parser_calc_complex (HMPR p, const char *formula)
C function: HADT mgl_parser_calc_complexw (HMPR p, const wchar_t *formula)

Function parses the string formula and return resulting data array with complex values. In difference to AddVar() or FindVar(), it is usual data array which should be deleted after usage.

Method on mglParse: void AddParam (int n, const char *str)
Method on mglParse: void AddParam (int n, const wchar_t *str)
C function: void mgl_parser_add_param (HMPR p, int id, const char *val)
C function: void mgl_parser_add_paramw (HMPR p, int id, const wchar_t *val)

Function set the value of n-th parameter as string str (n=0, 1 ... ’z’-’a’+10). String str shouldn’t contain ‘$’ symbol.

Method on mglParse: mglVar * FindVar (const char *name)
Method on mglParse: mglVar * FindVar (const wchar_t *name)
C function: HMDT mgl_parser_find_var (HMPR p, const char *name)
C function: HMDT mgl_parser_find_varw (HMPR p, const wchar_t *name)

Function returns the pointer to variable with name name or zero if variable is absent. Use this function to put external data array to the script or get the data from the script. You must not delete obtained data arrays!

Method on mglParse: mglVar * AddVar (const char *name)
Method on mglParse: mglVar * AddVar (const wchar_t *name)
C function: HMDT mgl_parser_add_var (HMPR p, const char *name)
C function: HMDT mgl_parser_add_varw (HMPR p, const wchar_t *name)

Function returns the pointer to variable with name name. If variable is absent then new variable is created with name name. Use this function to put external data array to the script or get the data from the script. You must not delete obtained data arrays!

Method on mglParse (C++): void DeleteVar (const char *name)
Method on mglParse (C++): void DeleteVar (const wchar_t *name)
C function: void mgl_parser_del_var (HMPR p, const char *name)
C function: void mgl_parser_del_varw (HMPR p, const wchar_t *name)

Function delete the variable with given name.

Method on mglParse (C++): void DeleteAll ()
C function: void mgl_parser_del_all (HMPR p)

Function delete all variables and reset list of commands to default one in this parser.

Method on mglParse: void RestoreOnce ()
C function: void mgl_parser_restore_once (HMPR p)

Restore Once flag.

Method on mglParse: void AllowSetSize (bool a)
C function: void mgl_parser_allow_setsize (HMPR p, int a)

Allow to parse setsize command or not.

Method on mglParse: void AllowFileIO (bool a)
C function: void mgl_parser_allow_file_io (HMPR p, int a)

Allow reading/saving files or not.

Method on mglParse: void AllowDllCall (bool a)
C function: void mgl_parser_allow_dll_call (HMPR p, int a)

Allow to parse load command or not.

Method on mglParse: void Stop ()
C function: void mgl_parser_stop (HMPR p)

Sends stop signal which terminate execution at next command.

Method on mglParse: void SetVariant (int var=0)
C function: void mgl_parser_variant (HMPR p, int var=0)

Sets variant of argument(s) separated by ‘?’ symbol to be used in further commands.

Method on mglParse: long GetCmdNum ()
C function: long mgl_parser_cmd_num (HMPR p)

Return the number of registered MGL commands.

Method on mglParse: const char * GetCmdName (long id)
C function: const char * mgl_parser_cmd_name (HMPR p, long id)

Return the name of command with given id.

Method on mglParse: int CmdType (const char *name)
C function: int mgl_parser_cmd_type (HMPR p, const char *name)

Return the type of MGL command name. Type of commands are: 0 – not the command, 1 - data plot, 2 - other plot, 3 - setup, 4 - data handle, 5 - data create, 6 - subplot, 7 - program, 8 - 1d plot, 9 - 2d plot, 10 - 3d plot, 11 - dd plot, 12 - vector plot, 13 - axis, 14 - primitives, 15 - axis setup, 16 - text/legend, 17 - data transform.

Method on mglParse: const char * CmdFormat (const char *name)
C function: const char * mgl_parser_cmd_frmt (HMPR p, const char *name)

Return the format of arguments for MGL command name.

Method on mglParse: const char * CmdDesc (const char *name)
C function: const char * mgl_parser_cmd_desc (HMPR p, const char *name)

Return the description of MGL command name.

Method on mglParse: void RK_Step (const char *eqs, const char *vars, mreal dt=1)
Method on mglParse: void RK_Step (const wchar_t *eqs, const wchar_t *vars, mreal dt=1)
C function: void mgl_rk_step (HMPR p, const char *eqs, const char *vars, mreal dt)
C function: void mgl_rk_step_w (HMPR p, const wchar_t *eqs, const wchar_t *vars, mreal dt)

Make one step for ordinary differential equation(s) {var1’ = eq1, ... } with time-step dt. Here strings eqs and vars contain the equations and variable names separated by symbol ‘;’. The variable(s) ‘var1’, ... are the ones, defined in MGL script previously. The Runge-Kutta 4-th order method is used.

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8 UDAV

UDAV (Universal Data Array Visualizator) is cross-platform program for data arrays visualization based on MathGL library. It support wide spectrum of graphics, simple script language and visual data handling and editing. It has window interface for data viewing, changing and plotting. Also it can execute MGL scripts, setup and rotate graphics and so on. UDAV hot-keys can be found in the appendix Hot-keys for UDAV.

• UDAV overview:  
• UDAV dialogs:  
• UDAV hints:  

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8.1 UDAV overview

UDAV have main window divided by 2 parts in general case and optional bottom panel(s). Left side contain tabs for MGL script and data arrays. Right side contain tabs with graphics itself, with list of variables and with help on MGL. Bottom side may contain the panel with MGL messages and warnings, and the panel with calculator.

Main window

Main window is shown on the figure above. You can see the script (at left) with current line highlighted by light-yellow, and result of its execution at right. Each panel have its own set of toolbuttons.

Editor toolbuttons allow: open and save script from/to file; undo and redo changes; cut, copy and paste selection; find/replace text; show dialogs for command arguments and for plot setup; show calculator at bottom.

Graphics toolbuttons allow: enable/disable additional transparency and lighting; show grid of absolute coordinates; enable mouse rotation; restore image view; refresh graphics (execute the script); stop calculation; copy graphics into clipboard; add primitives (line, curve, box, rhombus, ellipse, mark, text) to the image; change view angles manually. Vertical toolbuttons allow: shift and zoom in/out of image as whole; show next and previous frame of animation, or start animation (if one present).

Graphics panel support plot editing by mouse.

Main window - help panel

Short command description and list of its arguments are shown at the status-bar, when you move cursor to the new line of code. You can press F1 to see more detailed help on special panel.

Main window - data viewing

Also you can look the current list of variables, its dimensions and its size in the memory (right side of above figure). Toolbuttons allow: create new variable, edit variable, delete variable, preview variable plot and its properties, refresh list of variables. Pressing on any column will sort table according its contents. Double click on a variable will open panel with data cells of the variable, where you can view/edit each cell independently or apply a set of transformations.

Main window - calculator and messages

Finally, pressing F2 or F4 you can show/hide windows with messages/warnings and with calculator. Double click on a warning in message window will jump to corresponding line in editor. Calculator allow you type expression by keyboard as well as by toolbuttons. It know about all current variables, so you can use them in formulas.

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8.2 UDAV dialogs

There are a set of dialogs, which allow change/add a command, setup global plot properties, or setup UDAV itself.

New command dialog

One of most interesting dialog (hotkey Meta-C or Win-C) is dialog which help to enter new command or change arguments of existed one. It allows consequently select the category of command, command name in category and appropriate set of command arguments. At this right side show detailed command description. Required argument(s) are denoted by bold text. Strings are placed in apostrophes, like 'txt'. Buttons below table allow to call dialogs for changing style of command (if argument 'fmt' is present in the list of command arguments); to set variable or expression for argument(s); to add options for command. Note, you can click on a cell to enter value, or double-click to call corresponding dialog.

Style dialog - pen style
Style dialog - color scheme
Style dialog - text style
Style dialog - manual mask

Dialog for changing style can be called independently, but usually is called from New command dialog or by double click on primitive. It contain 3 tabs: one for pen style, one for color scheme, one for text style. You should select appropriate one. Resulting string of style and sample picture are shown at bottom of dialog. Usually it can be called from New command dialog.

Variable dialog

Dialog for entering variable allow to select variable or expression which can be used as argument of a command. Here you can select the variable name; range of indexes in each directions; operation which will be applied (like, summation, finding minimal/maximal values and so on). Usually it can be called from New command dialog.

Dialog for options of a command

Dialog for command options allow to change Command options. Usually it can be called from New command dialog.

New inplot dialog

Another interesting dialog, which help to select and properly setup a subplot, inplot, columnplot, stickplot and similar commands.

Dialog for general properties
Dialog for light properties

There is dialog for setting general plot properties, including tab for setting lighting properties. It can be called by called by hotkey ??? and put setup commands at the beginning of MGL script.

Dialog for script parameters

Also you can set or change script parameters (‘$0’ ... ‘$9’, see MGL definition).

Dialog for UDAV settings

Finally, there is dialog for UDAV settings. It allow to change most of things in UDAV appearance and working, including colors of keywords and numbers, default font and image size, and so on (see figure above).

There are also a set of dialogs for data handling, but they are too simple and clear. So, I will not put them here.

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8.3 UDAV hints

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9 Other classes

There are few end-user classes: mglGraph (see MathGL core), mglWindow and mglGLUT (see Widget classes), mglData (see Data processing), mglParse (see MGL scripts). Exactly these classes I recommend to use in most of user programs. All methods in all of these classes are inline and have exact C/Fortran analogue functions. This give compiler independent binary libraries for MathGL.

However, sometimes you may need to extend MathGL by writing yours own plotting functions or handling yours own data structures. In these cases you may need to use low-level API. This chapter describes it.

Class diagram for MathGL

The internal structure of MathGL is rather complicated. There are C++ classes mglBase, mglCanvas, ... for drawing primitives and positioning the plot (blue ones in the figure). There is a layer of C functions, which include interface for most important methods of these classes. Also most of plotting functions are implemented as C functions. After it, there are “inline” front-end classes which are created for user convenience (yellow ones in the figure). Also there are widgets for FLTK and Qt libraries (green ones in the figure).

Below I show how this internal classes can be used.

• mglBase class:  
• mglDataA class:  
• mglColor class:  
• mglPoint class:  

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9.1 Define new kind of plot (mglBase class)

Basically most of new kinds of plot can be created using just MathGL primitives (see Primitives). However the usage of mglBase methods can give you higher speed of drawing and better control of plot settings.

All plotting functions should use a pointer to mglBase class (or HMGL type in C functions) due to compatibility issues. Exactly such type of pointers are used in front-end classes (mglGraph, mglWindow) and in widgets (QMathGL, Fl_MathGL).

MathGL tries to remember all vertexes and all primitives and plot creation stage, and to use them for making final picture by demand. Basically for making plot, you need to add vertexes by AddPnt() function, which return index for new vertex, and call one of primitive drawing function (like mark_plot(), arrow_plot(), line_plot(), trig_plot(), quad_plot(), text_plot()), using vertex indexes as argument(s). AddPnt() function use 2 mreal numbers for color specification. First one is positioning in textures – integer part is texture index, fractional part is relative coordinate in the texture. Second number is like a transparency of plot (or second coordinate in the 2D texture).

I don’t want to put here detailed description of mglBase class. It was rather well documented in mgl2/base.h file. I just show and example of its usage on the base of circle drawing.

First, we should prototype new function circle() as C function. 

#ifdef __cplusplus
extern "C" {
#endif
void circle(HMGL gr, mreal x, mreal y, mreal z, mreal r, const char *stl, const char *opt);
#ifdef __cplusplus
}
#endif

This is done for generating compiler independent binary. Because only C-functions have standard naming mechanism, the same for any compilers.

Now, we create a C++ file and put the code of function. I’ll write it line by line and try to comment all important points. 

void circle(HMGL gr, mreal x, mreal y, mreal z, mreal r, const char *stl, const char *opt)
{

First, we need to check all input arguments and send warnings if something is wrong. In our case it is negative value of r argument. We just send warning, since it is not critical situation – other plot still can be drawn. 

  if(r<=0)  { gr->SetWarn(mglWarnNeg,"Circle"); return; }

Next step is creating a group. Group keep some general setting for plot (like options) and useful for export in 3d files. 

  static int cgid=1;  gr->StartGroup("Circle",cgid++);

Now let apply options. Options are rather useful things, generally, which allow one easily redefine axis range(s), transparency and other settings (see Command options). 

  gr->SaveState(opt);

I use global setting for determining the number of points in circle approximation. Note, that user can change MeshNum by options easily. 

  const int n = gr->MeshNum>1?gr->MeshNum : 41;

Let try to determine plot specific flags. MathGL functions expect that most of flags will be sent in string. In our case it is symbol ‘@’ which set to draw filled circle instead of border only (last will be default). Note, you have to handle NULL as string pointer. 

  bool fill = mglchr(stl,'@');

Now, time for coloring. I use palette mechanism because circle have few colors: one for filling and another for border. SetPenPal() function parse input string and write resulting texture index in pal. Function return the character for marker, which can be specified in string str. Marker will be plotted at the center of circle. I’ll show on next sample how you can use color schemes (smooth colors) too. 

  long pal=0;
  char mk=gr->SetPenPal(stl,&pal);

Next step, is determining colors for filling and for border. First one for filling. 

  mreal c=gr->NextColor(pal), d;

Second one for border. I use black color (call gr->AddTexture('k')) if second color is not specified. 

  mreal k=(gr->GetNumPal(pal)>1)?gr->NextColor(pal):gr->AddTexture('k');

If user want draw only border (fill=false) then I use first color for border. 

  if(!fill) k=c;

Now we should reserve space for vertexes. This functions need n for border, n+1 for filling and 1 for marker. So, maximal number of vertexes is 2*n+2. Note, that such reservation is not required for normal work but can sufficiently speed up the plotting. 

  gr->Reserve(2*n+2);

We’ve done with setup and ready to start drawing. First, we need to add vertex(es). Let define NAN as normals, since I don’t want handle lighting for this plot, 

  mglPoint q(NAN,NAN);

and start adding vertexes. First one for central point of filling. I use -1 if I don’t need this point. The arguments of AddPnt() function is: mglPoint(x,y,z) – coordinate of vertex, c – vertex color, q – normal at vertex, -1 – vertex transparency (-1 for default), 3 bitwise flag which show that coordinates will be scaled (0x1) and will not be cutted (0x2). 

  long n0,n1,n2,m1,m2,i;
  n0 = fill ? gr->AddPnt(mglPoint(x,y,z),c,q,-1,3):-1;

Similar for marker, but we use different color k. 

  n2 = mk ? gr->AddPnt(mglPoint(x,y,z),k,q,-1,3):-1;

Draw marker. 

  if(mk)  gr->mark_plot(n2,mk);

Time for drawing circle itself. I use -1 for m1, n1 as sign that primitives shouldn’t be drawn for first point i=0. 

  for(i=0,m1=n1=-1;i<n;i++)
  {

Each function should check Stop variable and return if it is non-zero. It is done for interrupting drawing for system which don’t support multi-threading. 

    if(gr->Stop)  return;

Let find coordinates of vertex. 

    mreal t = i*2*M_PI/(n-1.);
    mglPoint p(x+r*cos(t), y+r*sin(t), z);

Save previous vertex and add next one 

    n2 = n1;  n1 = gr->AddPnt(p,c,q,-1,3);

and copy it for border but with different color. Such copying is much faster than adding new vertex using AddPnt(). 

    m2 = m1;  m1 = gr->CopyNtoC(n1,k);

Now draw triangle for filling internal part 

    if(fill)  gr->trig_plot(n0,n1,n2);

and draw line for border. 

    gr->line_plot(m1,m2);
  }

Drawing is done. Let close group and return. 

  gr->EndGroup();
}

Another sample I want to show is exactly the same function but with smooth coloring using color scheme. So, I’ll add comments only in the place of difference. 

void circle_cs(HMGL gr, mreal x, mreal y, mreal z, mreal r, const char *stl, const char *opt)
{

In this case let allow negative radius too. Formally it is not the problem for plotting (formulas the same) and this allow us to handle all color range. 

//if(r<=0)  { gr->SetWarn(mglWarnNeg,"Circle"); return; }

  static int cgid=1;  gr->StartGroup("CircleCS",cgid++);
  gr->SaveState(opt);
  const int n = gr->MeshNum>1?gr->MeshNum : 41;
  bool fill = mglchr(stl,'@');

Here is main difference. We need to create texture for color scheme specified by user 

  long ss = gr->AddTexture(stl);

But we need also get marker and color for it (if filling is enabled). Let suppose that marker and color is specified after ‘:’. This is standard delimiter which stop color scheme entering. So, just lets find it and use for setting pen. 

  const char *pen=0;
  if(stl) pen = strchr(stl,':');
  if(pen) pen++;

The substring is placed in pen and it will be used as line style. 

  long pal=0;
  char mk=gr->SetPenPal(pen,&pal);

Next step, is determining colors for filling and for border. First one for filling. 

  mreal c=gr->GetC(ss,r);

Second one for border. 

  mreal k=gr->NextColor(pal);

The rest part is the same as in previous function. 

  if(!fill) k=c;

  gr->Reserve(2*n+2);
  mglPoint q(NAN,NAN);
  long n0,n1,n2,m1,m2,i;
  n0 = fill ? gr->AddPnt(mglPoint(x,y,z),c,q,-1,3):-1;
  n2 = mk ? gr->AddPnt(mglPoint(x,y,z),k,q,-1,3):-1;
  if(mk)  gr->mark_plot(n2,mk);
  for(i=0,m1=n1=-1;i<n;i++)
  {
    if(gr->Stop)  return;
    mreal t = i*2*M_PI/(n-1.);
    mglPoint p(x+r*cos(t), y+r*sin(t), z);
    n2 = n1;  n1 = gr->AddPnt(p,c,q,-1,3);
    m2 = m1;  m1 = gr->CopyNtoC(n1,k);
    if(fill)  gr->trig_plot(n0,n1,n2);
    gr->line_plot(m1,m2);
  }
  gr->EndGroup();
}

The last thing which we can do is derive our own class with new plotting functions. Good idea is to derive it from mglGraph (if you don’t need extended window), or from mglWindow (if you need to extend window). So, in our case it will be 

class MyGraph : public mglGraph
{
public:
  inline void Circle(mglPoint p, mreal r, const char *stl="", const char *opt="")
  { circle(p.x,p.y,p.z, r, stl, opt); }
  inline void CircleCS(mglPoint p, mreal r, const char *stl="", const char *opt="")
  { circle_cs(p.x,p.y,p.z, r, stl, opt); }
};

Note, that I use inline modifier for using the same binary code with different compilers.

So, the complete sample will be 

#include <mgl2/mgl.h>
//---------------------------------------------------------
#ifdef __cplusplus
extern "C" {
#endif
void circle(HMGL gr, mreal x, mreal y, mreal z, mreal r, const char *stl, const char *opt);
void circle_cs(HMGL gr, mreal x, mreal y, mreal z, mreal r, const char *stl, const char *opt);
#ifdef __cplusplus
}
#endif
//---------------------------------------------------------
class MyGraph : public mglGraph
{
public:
  inline void CircleCF(mglPoint p, mreal r, const char *stl="", const char *opt="")
  { circle(p.x,p.y,p.z, r, stl, opt); }
  inline void CircleCS(mglPoint p, mreal r, const char *stl="", const char *opt="")
  { circle_cs(p.x,p.y,p.z, r, stl, opt); }
};
//---------------------------------------------------------
void circle(HMGL gr, mreal x, mreal y, mreal z, mreal r, const char *stl, const char *opt)
{
  if(r<=0)  { gr->SetWarn(mglWarnNeg,"Circle"); return; }
  static int cgid=1;  gr->StartGroup("Circle",cgid++);
  gr->SaveState(opt);
  const int n = gr->MeshNum>1?gr->MeshNum : 41;
  bool fill = mglchr(stl,'@');
  long pal=0;
  char mk=gr->SetPenPal(stl,&pal);
  mreal c=gr->NextColor(pal), d;
  mreal k=(gr->GetNumPal(pal)>1)?gr->NextColor(pal):gr->AddTexture('k');
  if(!fill) k=c;
  gr->Reserve(2*n+2);
  mglPoint q(NAN,NAN);
  long n0,n1,n2,m1,m2,i;
  n0 = fill ? gr->AddPnt(mglPoint(x,y,z),c,q,-1,3):-1;
  n2 = mk ? gr->AddPnt(mglPoint(x,y,z),k,q,-1,3):-1;
  if(mk)  gr->mark_plot(n2,mk);
  for(i=0,m1=n1=-1;i<n;i++)
  {
    if(gr->Stop)  return;
    mreal t = i*2*M_PI/(n-1.);
    mglPoint p(x+r*cos(t), y+r*sin(t), z);
    n2 = n1;  n1 = gr->AddPnt(p,c,q,-1,3);
    m2 = m1;  m1 = gr->CopyNtoC(n1,k);
    if(fill)  gr->trig_plot(n0,n1,n2);
    gr->line_plot(m1,m2);
  }
  gr->EndGroup();
}
//---------------------------------------------------------
void circle_cs(HMGL gr, mreal x, mreal y, mreal z, mreal r, const char *stl, const char *opt)
{
  static int cgid=1;  gr->StartGroup("CircleCS",cgid++);
  gr->SaveState(opt);
  const int n = gr->MeshNum>1?gr->MeshNum : 41;
  bool fill = mglchr(stl,'@');
  long ss = gr->AddTexture(stl);
  const char *pen=0;
  if(stl) pen = strchr(stl,':');
  if(pen) pen++;
  long pal=0;
  char mk=gr->SetPenPal(pen,&pal);
  mreal c=gr->GetC(ss,r);
  mreal k=gr->NextColor(pal);
  if(!fill) k=c;

  gr->Reserve(2*n+2);
  mglPoint q(NAN,NAN);
  long n0,n1,n2,m1,m2,i;
  n0 = fill ? gr->AddPnt(mglPoint(x,y,z),c,q,-1,3):-1;
  n2 = mk ? gr->AddPnt(mglPoint(x,y,z),k,q,-1,3):-1;
  if(mk)  gr->mark_plot(n2,mk);
  for(i=0,m1=n1=-1;i<n;i++)
  {
    if(gr->Stop)  return;
    mreal t = i*2*M_PI/(n-1.);
    mglPoint p(x+r*cos(t), y+r*sin(t), z);
    n2 = n1;  n1 = gr->AddPnt(p,c,q,-1,3);
    m2 = m1;  m1 = gr->CopyNtoC(n1,k);
    if(fill)  gr->trig_plot(n0,n1,n2);
    gr->line_plot(m1,m2);
  }
  gr->EndGroup();
}
//---------------------------------------------------------
int main()
{
  MyGraph gr;
  gr.Box();
  // first let draw circles with fixed colors
  for(int i=0;i<10;i++)
    gr.CircleCF(mglPoint(2*mgl_rnd()-1, 2*mgl_rnd()-1), mgl_rnd());
  // now let draw circles with color scheme
  for(int i=0;i<10;i++)
    gr.CircleCS(mglPoint(2*mgl_rnd()-1, 2*mgl_rnd()-1), 2*mgl_rnd()-1);
}

Next: , Previous: , Up: Other classes   [Contents][Index]

9.2 User defined types (mglDataA class)

mglData class have abstract predecessor class mglDataA. Exactly the pointers to mglDataA instances are used in all plotting functions and some of data processing functions. This was done for taking possibility to define yours own class, which will handle yours own data (for example, complex numbers, or differently organized data). And this new class will be almost the same as mglData for plotting purposes.

However, the most of data processing functions will be slower as if you used mglData instance. This is more or less understandable – I don’t know how data in yours particular class will be organized, and couldn’t optimize the these functions generally.

There are few virtual functions which must be provided in derived classes. This functions give:

Let me, for example define class mglComplex which will handle complex number and draw its amplitude or phase, depending on flag use_abs: 

#include <complex>
#include <mgl2/mgl.h>
#define dual std::complex<double>
class mglComplex : public mglDataA
{
public:
  long nx;      ///< number of points in 1st dimensions ('x' dimension)
  long ny;      ///< number of points in 2nd dimensions ('y' dimension)
  long nz;      ///< number of points in 3d dimensions ('z' dimension)
  dual *a;      ///< data array
  bool use_abs; ///< flag to use abs() or arg()

  inline mglComplex(long xx=1,long yy=1,long zz=1)
  { a=0;  use_abs=true; Create(xx,yy,zz); }
  virtual ~mglComplex()  { if(a)  delete []a; }

  /// Get sizes
  inline long GetNx() const { return nx;  }
  inline long GetNy() const { return ny;  }
  inline long GetNz() const { return nz;  }
  /// Create or recreate the array with specified size and fill it by zero
  inline void Create(long mx,long my=1,long mz=1)
  { nx=mx;  ny=my;  nz=mz;  if(a) delete []a;
  a = new dual[nx*ny*nz]; }
  /// Get maximal value of the data
  inline mreal Maximal() const  { return mgl_data_max(this);  }
  /// Get minimal value of the data
  inline mreal Minimal() const  { return mgl_data_min(this);  }

protected:
  inline mreal v(long i,long j=0,long k=0) const
  { return use_abs ? abs(a[i+nx*(j+ny*k)]) : arg(a[i+nx*(j+ny*k)]);  }
  inline mreal vthr(long i) const
  { return use_abs ? abs(a[i]) : arg(a[i]);  }
  inline mreal dvx(long i,long j=0,long k=0) const
  { register long i0=i+nx*(j+ny*k);
    std::complex<double> res=i>0? (i<nx-1? (a[i0+1]-a[i0-1])/2.:a[i0]-a[i0-1]) : a[i0+1]-a[i0];
    return use_abs? abs(res) : arg(res);  }
  inline mreal dvy(long i,long j=0,long k=0) const
  { register long i0=i+nx*(j+ny*k);
    std::complex<double> res=j>0? (j<ny-1? (a[i0+nx]-a[i0-nx])/2.:a[i0]-a[i0-nx]) : a[i0+nx]-a[i0];
    return use_abs? abs(res) : arg(res);  }
  inline mreal dvz(long i,long j=0,long k=0) const
  { register long i0=i+nx*(j+ny*k), n=nx*ny;
    std::complex<double> res=k>0? (k<nz-1? (a[i0+n]-a[i0-n])/2.:a[i0]-a[i0-n]) : a[i0+n]-a[i0];
    return use_abs? abs(res) : arg(res);  }
};
int main()
{
  mglComplex dat(20);
  for(long i=0;i<20;i++)
    dat.a[i] = 3*exp(-0.05*(i-10)*(i-10))*dual(cos(M_PI*i*0.3), sin(M_PI*i*0.3));
  mglGraph gr;
  gr.SetRange('y', -M_PI, M_PI);  gr.Box();

  gr.Plot(dat,"r","legend 'abs'");
  dat.use_abs=false;
  gr.Plot(dat,"b","legend 'arg'");
  gr.Legend();
  gr.WritePNG("complex.png");
  return 0;
}

Next: , Previous: , Up: Other classes   [Contents][Index]

9.3 mglColor class

Structure for working with colors. This structure is defined in #include <mgl2/type.h>.

There are two ways to set the color in MathGL. First one is using of mreal values of red, green and blue channels for precise color definition. The second way is the using of character id. There are a set of characters specifying frequently used colors. Normally capital letter gives more dark color than lowercase one. See Line styles.

Parameter of mglColor: mreal r, g, b, a

Reg, green and blue component of color.

Method on mglColor: mglColor (mreal R, mreal G, mreal B, mreal A=1)

Constructor sets the color by mreal values of Red, Green, Blue and Alpha channels. These values should be in interval [0,1].

Method on mglColor: mglColor (char c='k', mreal bright=1)

Constructor sets the color from character id. The black color is used by default. Parameter br set additional “lightness” of color.

Method on mglColor: void Set (mreal R, mreal G, mreal B, mreal A=1)

Sets color from values of Red, Green, Blue and Alpha channels. These values should be in interval [0,1].

Method on mglColor: void Set (mglColor c, mreal bright=1)

Sets color as “lighted” version of color c.

Method on mglColor: void Set (char p, mreal bright=1)

Sets color from symbolic id.

Method on mglColor: bool Valid ()

Checks correctness of the color.

Method on mglColor: mreal Norm ()

Gets maximal of spectral component.

Method on mglColor: bool operator== (const mglColor &c)
Method on mglColor: bool operator!= (const mglColor &c)

Compare with another color

Method on mglColor: bool operator*= (mreal v)

Multiplies color components by number v.

Method on mglColor: bool operator+= (const mglColor &c)

Adds color c component by component.

Method on mglColor: bool operator-= (const mglColor &c)

Subtracts color c component by component.

Library Function: mglColor operator+ (const mglColor &a, const mglColor &b)

Adds colors by its RGB values.

Library Function: mglColor operator- (const mglColor &a, const mglColor &b)

Subtracts colors by its RGB values.

Library Function: mglColor operator* (const mglColor &a, mreal b)
Library Function: mglColor operator* (mreal a, const mglColor &b)

Multiplies color by number.

Library Function: mglColor operator/ (const mglColor &a, mreal b)

Divide color by number.

Library Function: mglColor operator! (const mglColor &a)

Return inverted color.

Previous: , Up: Other classes   [Contents][Index]

9.4 mglPoint class

Structure describes point in space. This structure is defined in #include <mgl2/type.h>

Parameter of mglPoint: mreal x, y, z, c

Point coordinates {x,y,z} and one extra value c used for amplitude, transparency and so on. By default all values are zero.

Method on mglPoint: mglPoint (mreal X=0, mreal Y=0, mreal Z=0, mreal C=0)

Constructor sets the color by mreal values of Red, Green, Blue and Alpha channels. These values should be in interval [0,1].

Method on mglPoint: bool IsNAN ()

Returns true if point contain NAN values.

Method on mglPoint: mreal norm ()

Returns the norm \sqrt{x^2+y^2+z^2} of vector.

Method on mglPoint: void Normalize ()

Normalizes vector to be unit vector.

Method on mglPoint: mreal val (int i)

Returns point component: x for i=0, y for i=1, z for i=2, c for i=3.

Library Function: mglPoint operator+ (const mglPoint &a, const mglPoint &b)

Point of summation (summation of vectors).

Library Function: mglPoint operator- (const mglPoint &a, const mglPoint &b)

Point of difference (difference of vectors).

Library Function: mglPoint operator* (mreal a, const mglPoint &b)
Library Function: mglPoint operator* (const mglPoint &a, mreal b)

Multiplies (scale) points by number.

Library Function: mglPoint operator/ (const mglPoint &a, mreal b)

Multiplies (scale) points by number 1/b.

Library Function: mreal operator* (const mglPoint &a, const mglPoint &b)

Scalar product of vectors.

Library Function: mglPoint operator/ (const mglPoint &a, const mglPoint &b)

Return vector of element-by-element product.

Library Function: mglPoint operator^ (const mglPoint &a, const mglPoint &b)

Cross-product of vectors.

Library Function: mglPoint operator& (const mglPoint &a, const mglPoint &b)

The part of a which is perpendicular to vector b.

Library Function: mglPoint operator| (const mglPoint &a, const mglPoint &b)

The part of a which is parallel to vector b.

Library Function: mglPoint operator! (const mglPoint &a)

Return vector perpendicular to vector a.

Library Function: mreal mgl_norm (const mglPoint &a)

Return the norm sqrt(|a|^2) of vector a.

Library Function: bool operator== (const mglPoint &a, const mglPoint &b)

Return true if points are the same.

Library Function: bool operator!= (const mglPoint &a, const mglPoint &b)

Return true if points are different.

Next: , Previous: , Up: Top   [Contents][Index]

Appendix A Symbols and hot-keys

This appendix contain the full list of symbols (characters) used by MathGL for setting up plot. Also it contain sections for full list of hot-keys supported by mglview tool and by UDAV program.

• Symbols for styles:  
• Hot-keys for mglview:  
• Hot-keys for UDAV:  

Next: , Up: Symbols and hot-keys   [Contents][Index]

A.1 Symbols for styles

Below is full list of all characters (symbols) which MathGL use for setting up the plot.

‘space ' '’

empty line style (see Line styles);

empty color in chart.

‘!’

set to use new color from palette for each point (not for each curve, as default) in 1D plotting;

set to disable ticks tuning in axis and colorbar;

set to draw grid lines at subticks coordinates too;

define complex variable/expression in MGL script if placed at beginning.

‘#’

set to use solid marks (see Line styles) or solid error boxes;

set to draw wired plot for axial, surf3, surf3a, surf3c, triplot, quadplot, area, bars, barh, tube, tape, cone, boxs and draw boundary only for circle, ellipse, rhomb;

set to draw also mesh lines for surf, surfc, surfa, dens, densx, densy, densz, dens3, or boundary for chart, facex, facey, facez, rect;

set to draw boundary and box for legend, title, or grid lines for table;

set to draw grid for radar;

set to start flow threads and pipes from edges only for flow, pipe;

set to use whole are for axis range in subplot, inplot;

change text color inside a string (see Font styles);

start comment in MGL scripts or in Command options.

‘$’

denote parameter of MGL scripts.

‘%’

set color scheme along 2 coordinates Color scheme.

‘&’

set to pass long integer number in tick template xtick, ytick, ztick, ctick.

operation in Textual formulas.

‘’’

denote string in MGL scripts or in Command options.

‘*’

one of marks (see Line styles);

one of mask for face filling (see Color scheme);

set to start flow threads from 2d array inside data (see flow);

operation in Textual formulas.

‘+’

one of marks (see Line styles) or kind of error boxes;

one of mask for face filling (see Color scheme);

set to print ‘+’ for positive numbers in axis, label, table;

operation in Textual formulas.

‘,’

separator for color positions (see Color styles) or items in a list.

‘-’

solid line style (see Line styles);

one of mask for face filling (see Color scheme);

place entries horizontally in legend;

set to use usual ‘-’ for negative numbers in axis, label, table;

operation in Textual formulas.

‘.’

one of marks (see Line styles) or kind of error boxes;

set to draw hachures instead of arrows for vect, vect3;

set to use dots instead of faces for cloud, torus, axial, surf3, surf3a, surf3c, surf, surfa, surfc, dens, map;

delimiter of fractional parts for numbers.

‘/’

operation in Textual formulas.

‘:’

line dashing style (see Line styles);

stop color scheme parsing (see Color scheme);

range operation in MGL scripts;

separator of commands in MGL scripts.

‘;’

line dashing style (see Line styles);

one of mask for face filling (see Color scheme);

start of an option in MGL scripts or in Command options.

‘<’

one of marks (see Line styles);

one of mask for face filling (see Color scheme);

style of subplot and inplot;

set position of colorbar;

style of vect, vect3;

align left in bars, barh, boxplot, cones, candle, ohlc;

operation in Textual formulas.

‘>’

one of marks (see Line styles);

one of mask for face filling (see Color scheme);

style of subplot and inplot;

set position of colorbar;

style of vect, vect3;

align right in bars, barh, boxplot, cones, candle, ohlc;

operation in Textual formulas.

‘=’

line dashing style (see Line styles);

one of mask for face filling (see Color scheme);

set to use equidistant columns for table;

set to use color gradient for vect, vect3;

operation in Textual formulas.

‘@’

set to draw box around text for text and similar functions;

set to draw boundary and fill it for circle, ellipse, rhomb;

set to fill faces for box;

set to draw large semitransparent mark instead of error box for error;

set to draw edges for cone;

set to draw filled boxes for boxs;

reduce text size inside a string (see Font styles);

operation in Textual formulas.

‘^’

one of marks (see Line styles);

one of mask for face filling (see Color scheme);

style of subplot and inplot;

set position of colorbar;

set outer position for legend;

inverse default position for axis;

switch to upper index inside a string (see Font styles);

align center in bars, barh, boxplot, cones, candle, ohlc;

operation in Textual formulas.

‘_’

empty arrow style (see Line styles);

disable drawing of tick labels for axis;

style of subplot and inplot;

set position of colorbar;

set to draw contours at bottom for cont, contf, contd, contv, tricont;

switch to lower index inside a string (see Font styles).

‘[]’

contain symbols excluded from color scheme parsing (see Color scheme).

‘{}’

contain extended specification of color (see Color styles), dashing (see Line styles) or mask (see Color scheme);

denote special operation in MGL scripts;

denote ’meta-symbol’ for LaTeX like string parsing (see Font styles).

‘|’

line dashing style (see Line styles);

set to use sharp color scheme (see Color scheme);

set to limit width by subplot width for table;

delimiter in list command;

operation in Textual formulas.

‘\’

string continuation symbol on next line for MGL scripts.

‘~’

disable drawing of tick labels for axis and colorbar;

disable first segment in lamerey;

one of mask for face filling (see Color scheme).

‘0,1,2,3,4,5,6,7,8,9’

line width (see Line styles);

brightness of a color (see Color styles);

precision of numbers in axis, label, table;

kind of smoothing (for digits 1,3,5) in smooth;

digits for a value.

‘4,6,8’

set to draw square, hex- or octo-pyramids instead of cones in cone, cones.

‘A,B,C,D,E,F,a,b,c,d,e,f’

can be hex-digit for color specification if placed inside {} (see Color styles).

‘A’

arrow style (see Line styles);

set to use absolute position in whole picture for text, colorbar, legend.

‘a’

set to use absolute position in subplot for text;

style of bars, barh, cones.

‘B’

dark blue color (see Color styles).

‘b’

blue color (see Color styles);

bold font face if placed after ‘:’ (see Font styles).

‘C’

dark cyan color (see Color styles);

align text to center if placed after ‘:’ (see Font styles).

‘c’

cyan color (see Color styles);

name of color axis;

cosine transform for transform.

‘D’

arrow style (see Line styles);

one of mask for face filling (see Color scheme).

‘d’

one of marks (see Line styles) or kind of error boxes;

one of mask for face filling (see Color scheme);

start hex-dash description if placed inside {} (see Line styles).

‘E’

dark green-yellow color (see Color styles).

‘e’

green-yellow color (see Color styles).

‘F’

set LaTeX-like format for numbers in axis, label, table.

‘f’

style of bars, barh;

style of vect, vect3;

set fixed format for numbers in axis, label, table;

Fourier transform for transform.

‘G’

dark green color (see Color styles).

‘g’

green color (see Color styles).

‘H’

dark gray color (see Color styles).

‘h’

gray color (see Color styles);

Hankel transform for transform.

‘I’

arrow style (see Line styles);

set colorbar position near boundary.

‘i’

line dashing style (see Line styles);

italic font face if placed after ‘:’ (see Font styles).

set to use inverse values for cloud, pipe, dew;

set to fill only area with y1<y<y2 for region;

inverse Fourier transform for transform.

‘j’

line dashing style (see Line styles);

one of mask for face filling (see Color scheme).

‘K’

arrow style (see Line styles).

‘k’

black color (see Color styles).

‘L’

dark green-blue color (see Color styles);

align text to left if placed after ‘:’ (see Font styles).

‘l’

green-blue color (see Color styles).

‘M’

dark magenta color (see Color styles).

‘m’

magenta color (see Color styles).

‘N’

dark sky-blue color (see Color styles).

‘n’

sky-blue color (see Color styles).

‘O’

arrow style (see Line styles);

one of mask for face filling (see Color scheme).

‘o’

one of marks (see Line styles) or kind of error boxes;

one of mask for face filling (see Color scheme);

over-line text if placed after ‘:’ (see Font styles).

‘P’

dark purple color (see Color styles).

‘p’

purple color (see Color styles).

‘Q’

dark orange or brown color (see Color styles).

‘q’

orange color (see Color styles).

‘R’

dark red color (see Color styles);

align text to right if placed after ‘:’ (see Font styles).

‘r’

red color (see Color styles).

‘S’

arrow style (see Line styles);

one of mask for face filling (see Color scheme).

‘s’

one of marks (see Line styles) or kind of error boxes;

one of mask for face filling (see Color scheme);

start hex-mask description if placed inside {} (see Color scheme);

sine transform for transform.

‘t’

draw tubes instead of cones in cone, cones;

‘T’

arrow style (see Line styles);

place text under the curve for text, cont, cont3.

‘t’

set to draw text labels for cont, cont3;

name of t-axis (one of ternary axis);

variable in Textual formulas, which usually is varied in range [0,1].

‘U’

dark blue-violet color (see Color styles);

disable rotation of tick labels for axis.

‘u’

blue-violet color (see Color styles);

under-line text if placed after ‘:’ (see Font styles);

name of u-axis (one of ternary axis);

variable in Textual formulas, which usually denote array itself.

‘V’

arrow style (see Line styles);

place text centering on vertical direction for text.

‘v’

one of marks (see Line styles);

set to draw vectors on flow threads for flow and on segments for lamerey.

‘W’

bright gray color (see Color styles).

‘w’

white color (see Color styles);

wired text if placed after ‘:’ (see Font styles);

name of w-axis (one of ternary axis);

‘X’

arrow style (see Line styles).

‘x’

one of marks (see Line styles) or kind of error boxes;

name of x-axis or x-direction or 1st dimension of a data array;

start hex-color description if placed inside {} (see Color styles);

style of tape.

‘Y’

dark yellow or gold color (see Color styles).

‘y’

yellow color (see Color styles);

name of y-axis or y-direction or 2nd dimension of a data array.

‘z’

name of z-axis or z-direction or 3d dimension of a data array;

style of tape.

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A.2 Hot-keys for mglview

KeyDescription
Ctrl-POpen printer dialog and print graphics.
Ctrl-WClose window.
Ctrl-TSwitch on/off transparency for the graphics.
Ctrl-LSwitch on/off additional lightning for the graphics.
Ctrl-SpaceRestore default graphics rotation, zoom and perspective.
F5Execute script and redraw graphics.
F6Change canvas size to fill whole region.
F7Stop drawing and script execution.
Ctrl-F5Run slideshow. If no parameter specified then the dialog with slideshow options will appear.
Ctrl-Comma, Ctrl-PeriodShow next/previous slide. If no parameter specified then the dialog with slideshow options will appear.
Ctrl-Shift-GCopy graphics to clipboard.
Alt-PExport as semitransparent PNG.
Alt-FExport as solid PNG.
Alt-JExport as JPEG.
Alt-EExport as vector EPS.
Alt-SExport as vector SVG.
Alt-LExport as LaTeX/Tikz image.
Alt-MExport as MGLD.
Alt-DExport as PRC/PDF.
Alt-OExport as OBJ.

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A.3 Hot-keys for UDAV

KeyDescription
Ctrl-NCreate new window with empty script. Note, all scripts share variables. So, second window can be used to see some additional information of existed variables.
Ctrl-OOpen and execute/show script or data from file. You may switch off automatic exection in UDAV properties
Ctrl-SSave script to a file.
Ctrl-POpen printer dialog and print graphics.
Ctrl-ZUndo changes in script editor.
Ctrl-Shift-ZRedo changes in script editor.
Ctrl-XCut selected text into clipboard.
Ctrl-CCopy selected text into clipboard.
Ctrl-VPaste selected text from clipboard.
Ctrl-ASelect all text in editor.
Ctrl-FShow dialog for text finding.
F3Find next occurrence of the text.
Win-C or Meta-CShow dialog for new command and put it into the script.
Win-F or Meta-FInsert last fitted formula with found coefficients.
Win-S or Meta-SShow dialog for styles and put it into the script. Styles define the plot view (color scheme, marks, dashing and so on).
Win-O or Meta-OShow dialog for options and put it into the script. Options are used for additional setup the plot.
Win-N or Meta-NReplace selected expression by its numerical value.
Win-P or Meta-PSelect file and insert its file name into the script.
Win-G or Meta-GShow dialog for plot setup and put resulting code into the script. This dialog setup axis, labels, lighting and other general things.
Ctrl-Shift-OLoad data from file. Data will be deleted only at exit but UDAV will not ask to save it.
Ctrl-Shift-SSave data to a file.
Ctrl-Shift-CCopy range of numbers to clipboard.
Ctrl-Shift-VPaste range of numbers from clipboard.
Ctrl-Shift-NRecreate the data with new sizes and fill it by zeros.
Ctrl-Shift-RResize (interpolate) the data to specified sizes.
Ctrl-Shift-TTransform data along dimension(s).
Ctrl-Shift-MMake another data.
Ctrl-Shift-HFind histogram of data.
Ctrl-TSwitch on/off transparency for the graphics.
Ctrl-LSwitch on/off additional lightning for the graphics.
Ctrl-GSwitch on/off grid of absolute coordinates.
Ctrl-SpaceRestore default graphics rotation, zoom and perspective.
F5Execute script and redraw graphics.
F6Change canvas size to fill whole region.
F7Stop script execution and drawing.
F8Show/hide tool window with list of hidden plots.
F9Restore status for ’once’ command and reload data.
Ctrl-F5Run slideshow. If no parameter specified then the dialog with slideshow options will appear.
Ctrl-Comma, Ctrl-PeriodShow next/previous slide. If no parameter specified then the dialog with slideshow options will appear.
Ctrl-WOpen dialog with slideshow options.
Ctrl-Shift-GCopy graphics to clipboard.
F1Show help on MGL commands
F2Show/hide tool window with messages and information.
F4Show/hide calculator which evaluate and help to type textual formulas. Textual formulas may contain data variables too.
Meta-Shift-Up, Meta-Shift-DownChange view angle \theta.
Meta-Shift-Left, Meta-Shift-RightChange view angle \phi.
Alt-Minus, Alt-EqualZoom in/out whole image.
Alt-Up, Alt-Down, Alt-Right, Alt-LeftShift whole image.
Alt-PExport as semitransparent PNG.
Alt-FExport as solid PNG.
Alt-JExport as JPEG.
Alt-EExport as vector EPS.
Alt-SExport as vector SVG.
Alt-LExport as LaTeX/Tikz image.
Alt-MExport as MGLD.
Alt-DExport as PRC/PDF.
Alt-OExport as OBJ.

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Appendix B File formats

This appendix contain description of file formats used by MathGL.

• Font files:  
• MGLD format:  
• JSON format:  
• IFS format:  

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B.1 Font files

Starting from v.1.6 the MathGL library uses new font files. The font is defined in 4 files with suffixes ‘*.vfm’, ‘*_b.vfm’, ‘*_i.vfm’, ‘*_bi.vfm’. These files are text files containing the data for roman font, bold font, italic font and bold italic font. The files (or some symbols in the files) for bold, italic or bold italic fonts can be absent. In this case the roman glyph will be used for them. By analogy, if the bold italic font is absent but the bold font is present then bold glyph will be used for bold italic. You may create these font files by yourself from *.ttf, *.otf files with the help of program font_tools. This program can be found at MathGL home site.

The format of font files (*.vfm – vector font for MathGL) is the following.

  1. First string contains human readable comment and is always ignored.
  2. Second string contains 3 numbers, delimited by space or tabulation. The order of numbers is the following: numg – the number of glyphs in the file (integer), fact – the factor for glyph sizing (mreal), size – the size of buffer for glyph description (integer).
  3. After it numg-th strings with glyphs description are placed. Each string contains 6 positive numbers, delimited by space of tabulation. The order of numbers is the following: Unicode glyph ID, glyph width, number of lines in glyph, position of lines coordinates in the buffer (length is 2*number of lines), number of triangles in glyph, position of triangles coordinates in the buffer (length is 6*number of triangles).
  4. The end of file contains the buffer with point coordinates at lines or triangles vertexes. The size of buffer (the number of integer) is size.

Each font file can be compressed by gzip.

Note: the closing contour line is done automatically (so the last segment may be absent). For starting new contour use a point with coordinates {0x3fff, 0x3fff}.

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B.2 MGLD format

MGLD is textual file, which contain all required information for drawing 3D image, i.e. it contain vertexes with colors and normales, primitives with all properties, textures, and glyph descriptions. MGLD file can be imported or viewed separately, without parsing data files itself.

MGLD file start from string 

MGLD npnts nprim ntxtr nglfs # optional description

which contain signature ‘MGLD’ and number of points npnts, number of primitives nprim, number of textures ntxtr, number of glyph descriptions nglfs, and optional description. Empty strings and string with ‘#’ are ignored.

Next, file contain npnts strings with points coordinates and colors. The format of each string is 

x y z c t ta u v w r g b a

Here x, y, z are coordinates, c, t are color indexes in texture, ta is normalized t according to current alpha setting, u, v, w are coordinates of normal vector (can be NAN if disabled), r, g, b, a are RGBA color values.

Next, file contain nprim strings with properties of primitives. The format of each string is 

type n1 n2 n3 n4 id s w p

Here type is kind of primitive (0 - mark, 1 - line, 2 - triangle, 3 - quadrangle, 4 - glyph), n1...n4 is index of point for vertexes, id is primitive identification number, s and w are size and width if applicable, p is scaling factor for glyphs.

Next, file contain ntxtr strings with descriptions of textures. The format of each string is 

smooth alpha colors

Here smooth set to enable smoothing between colors, alpha set to use half-transparent texture, colors contain color scheme itself as it described in Color scheme.

Finally, file contain nglfs entries with description of each glyph used in the figure. The format of entries are 

nT nL
xA yA xB yB xC yC ...
xP yP ...

Here nT is the number of triangles; nL is the number of line vertexes; xA, yA, xB, yB, xC, yC are coordinates of triangles; and xP, yP, xQ, yQ are coordinates of lines. Line coordinate xP=0x3fff, yP=0x3fff denote line breaking.

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B.3 JSON format

MathGL can save points and primitives of 3D object. It contain a set of variables listed below.

‘width’

width of the image;

‘height’

height of the image

‘depth’

depth of the image, usually =sqrt(width*height);

‘npnts’

number of points (vertexes);

‘pnts’

array of coordinates of points (vertexes), each element is array in form [x, y, z];

‘nprim’

number of primitives;

‘prim’

array of primitives, each element is array in form [type, n1, n2, n3, n4, id, s, w, p, z, color].

Here type is kind of primitive (0 - mark, 1 - line, 2 - triangle, 3 - quadrangle, 4 - glyph), n1...n4 is index of point for vertexes and n2 can be index of glyph coordinate, s and w are size and width if applicable, z is average z-coordinate, id is primitive identification number, p is scaling factor for glyphs.

‘ncoor’

number of glyph positions

‘coor’

array of glyph positions, each element is array in form [dx,dy]

‘nglfs’

number of glyph descriptions

‘glfs’

array of glyph descriptions, each element is array in form [nL, [xP0, yP0, xP1, yP1 ...]]. Here nL is the number of line vertexes; and xP, yP, xQ, yQ are coordinates of lines. Line coordinate xP=0x3fff, yP=0x3fff denote line breaking.

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B.4 IFS format

MathGL can read IFS fractal parameters (see ifsfile) from a IFS file. Let remind IFS file format. File may contain several records. Each record contain the name of fractal (‘binary’ in the example below) and the body of fractal, which is enclosed in curly braces {}. Symbol ‘;’ start the comment. If the name of fractal contain ‘(3D)’ or ‘(3d)’ then the 3d IFS fractal is specified. The sample below contain two fractals: ‘binary’ – usual 2d fractal, and ‘3dfern (3D)’ – 3d fractal. 

 binary
 { ; comment allowed here
  ; and here
  .5  .0 .0 .5 -2.563477 -0.000003 .333333   ; also comment allowed here
  .5  .0 .0 .5  2.436544 -0.000003 .333333
  .0 -.5 .5 .0  4.873085  7.563492 .333333
  }

 3dfern (3D) {
   .00  .00 0 .0 .18 .0 0  0.0 0.00 0 0.0 0 .01
   .85  .00 0 .0 .85 .1 0 -0.1 0.85 0 1.6 0 .85
   .20 -.20 0 .2 .20 .0 0  0.0 0.30 0 0.8 0 .07
  -.20  .20 0 .2 .20 .0 0  0.0 0.30 0 0.8 0 .07
  }

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Appendix C Plotting time

Table below show plotting time in seconds for all samples in file examples/samples.cpp. The test was done in my laptop (i5-2430M) with 64-bit Debian.

Few words about the speed. Firstly, direct bitmap drawing (Quality=4,5,6) is faster than buffered one (Quality=0,1,2), but sometimes it give incorrect result (see cloud) and don’t allow to export in vector or 3d formats (like EPS, SVG, PDF ...). Secondly, lower quality is faster than high one generally, i.e. Quality=1 is faster than Quality=2, and Quality=0 is faster than Quality=1. However, if plot contain a lot of faces (like cloud, surf3, pipe, dew) then Quality=0 may become slow, especially for small images. Finally, smaller images are drawn faster than larger ones.

Results for image size 800*600 (default one).

Nameq=0q=1q=2q=4q=5q=6q=8
alpha0.09940.1060.1370.0340.05650.0680.0332
area0.08130.06660.110.03420.04260.07940.0435
aspect0.09240.1420.1180.02810.03760.06930.0246
axial0.7060.6060.9110.2430.2640.4750.0657
axis0.1360.1630.1550.02990.02930.04940.0506
barh0.08110.1050.1210.02990.03260.04540.0273
bars0.7390.1340.1340.04770.08320.06620.0641
belt0.05760.09840.09160.04290.03070.04650.0252
box0.09380.1050.1270.03120.03520.05490.0501
boxplot0.04690.1270.05340.05870.02520.0350.0152
boxs0.2420.2230.3310.05670.06830.1890.095
candle0.08420.1320.06340.05410.05090.05320.016
chart0.5060.4270.7150.1820.1990.4770.154
cloud0.09274.725.160.03081.21.640.0265
colorbar0.2660.2730.2460.1740.1820.2530.267
combined0.6030.4010.4580.3060.2760.3620.256
cones0.3080.1890.2410.1440.1320.1720.109
cont0.0790.07950.1240.03740.03740.06060.0326
cont_xyz0.140.1060.2490.330.1590.1150.152
conta0.1350.1060.1320.08220.1010.08940.083
contd0.2090.1810.20.07220.0750.1090.0666
contf0.1560.1570.1770.06450.06580.08810.0584
contf_xyz0.2140.2110.1750.09340.1110.1040.0851
contfa0.2930.2240.2590.1420.1650.1760.14
contv0.1130.1050.1350.0510.04820.0710.0386
correl0.05970.07980.07720.06170.06970.05690.0284
curvcoor0.09060.08920.1340.04340.04320.06880.0403
cut1.210.7760.7950.8430.6320.6830.62
dat_diff0.1440.1040.130.1050.07790.09540.0927
dat_extra0.4420.2790.3040.1220.2130.2570.0869
data15.134.083.723.743.453.953.35
data23.312.722.8132.982.822.61
dens0.1050.1180.1680.04560.05470.0850.0426
dens_xyz0.1580.160.230.08270.1680.1060.148
densa0.1270.1380.1590.09150.09810.110.0805
dew1.70.8310.7650.2040.1720.1820.0895
dots0.1480.1190.130.05350.05350.06740.0636
error0.1040.07240.08610.09990.1210.1110.0285
error20.06250.06720.08730.04630.03590.05580.0365
export0.1770.2210.2490.1120.1240.1540.17
fall0.1350.03460.06410.03630.04850.07970.084
fit3.110.1690.130.07340.07272.990.123
flow0.5130.3860.4970.2720.4230.3770.262
fog0.10.1130.1170.02970.0390.07120.0616
fonts2.672.633.032.742.672.882.94
grad0.1240.1190.1920.1270.06720.1090.0476
hist0.2160.2020.2260.1310.1490.1420.0786
indirect0.06020.05820.05860.08440.07920.1520.0262
inplot0.1480.1390.09640.03990.06240.04490.0495
label0.1460.05770.1690.05780.09590.0790.0289
legend0.1680.2270.230.03450.03640.0730.0382
light0.1070.08140.08210.08040.0730.07740.073
loglog0.07760.07410.1130.04510.03750.05590.0335
map0.1780.1190.1880.07670.08870.1110.0304
mark0.07850.1410.05510.0280.03110.03650.016
mask0.08540.1310.1150.02960.04120.05470.0213
mesh0.110.1120.08940.03680.05180.05080.0724
mirror0.1970.1040.1460.03630.04330.06950.0384
molecule0.1530.1070.1990.06530.06570.0860.037
ode1.490.6180.7180.620.5950.720.556
ohlc0.03470.04870.05510.04060.02810.03890.0167
param10.3160.2470.3210.1190.1550.1580.0958
param20.5050.4280.4960.1520.1380.1870.104
param33.333.593.371.821.891.941.65
paramv4.314.74.251.211.131.231.07
parser0.0740.1020.1280.09730.1540.1040.145
pde0.9430.9340.9871.010.8160.790.809
pipe4.132.982.460.5970.8480.8150.588
plot0.07020.08480.1120.04090.04090.05680.029
primitives0.09980.09580.1750.03130.03630.08150.0265
projection0.1380.140.2220.04630.0460.1570.104
projection50.1240.1320.1970.04140.04230.10.0353
qo2d0.3750.3310.3640.2440.2790.2870.244
radar0.03480.05030.05980.05820.02970.0830.0147
refill0.3910.280.2330.1610.1330.1550.0867
region0.07480.07190.1170.02910.03190.05660.0256
schemes0.1230.1020.1840.03710.03920.07170.0469
several_light0.08620.1020.1280.02840.03270.09120.0246
solve0.1260.09440.1480.060.0780.08410.0579
stem0.0610.05580.1240.03120.03150.04790.0265
step0.1320.09620.07080.03210.03220.1910.0398
stereo0.07060.08770.1370.03040.03340.06720.0394
stfa0.1770.09180.1460.05180.06570.09350.059
style0.1760.1660.2260.04080.04260.0820.0252
surf0.1910.1910.2330.06690.07040.1050.118
surf33.12.92.882.892.783.571.16
surf3a0.7540.4710.5260.3990.3940.5110.349
surf3c0.7360.4480.5020.3830.3870.4940.333
surfa0.06470.1120.09160.02980.03110.06260.025
surfc0.05880.1030.1390.03130.03110.06020.0248
table0.1940.2260.2790.03580.03610.08090.0438
tape0.10.1080.1250.03020.03260.05260.0405
tens0.09590.1090.06420.07270.09650.0740.0254
ternary0.1420.1370.2050.0410.04180.09420.0355
text0.1230.1240.1660.0450.05670.07580.025
text20.1320.1320.1670.07210.08720.0950.0467
textmark0.2240.07220.09390.1260.04740.05750.0242
ticks0.1860.1450.2070.03410.0420.06890.0609
tile0.08610.08110.110.02770.02990.04510.0618
tiles0.05580.05810.07720.02720.03030.04540.0583
torus0.1210.1160.1930.0380.04480.1040.0314
traj0.03540.03950.07890.04670.02530.03640.0173
triangulation0.06030.2140.1390.04550.07340.08450.0265
triplot0.06920.05190.1310.04970.03250.09430.0124
tube0.1510.1350.2940.04910.06010.1080.0609
type00.2510.1870.2480.1130.07850.1570.0567
type10.2490.1790.2740.07960.07860.1450.0564
type20.2460.2120.250.08680.1040.1510.0625
vect0.1660.1550.2550.130.1320.1810.174
vecta0.1210.08410.1080.07550.06720.1550.0686
venn0.01820.05270.09130.03680.03850.07060.013

Results for image size 1920*1440 (print quality)

Nameq=0q=1q=2q=4q=5q=6q=8
alpha0.160.1840.3620.08680.1050.2460.0674
area0.1020.1650.3270.07950.1240.2550.0656
aspect0.0940.09390.150.06640.06740.110.0618
axial0.9090.9852.030.3710.4641.280.105
axis0.1210.1210.1980.07050.06830.1230.0951
barh0.08860.1050.1810.0680.07950.1370.13
bars0.110.1260.2070.08680.09730.1620.0754
belt0.09440.120.2120.06740.0890.1920.0629
box0.1220.1610.250.07350.09510.1740.0641
boxplot0.06960.06990.1180.06330.06340.1060.0514
boxs0.2960.3540.7860.1110.2130.580.0872
candle0.07620.07870.1430.07890.08590.1350.0548
chart0.5720.7782.390.2440.4291.640.2
cloud0.08187.169.380.06912.434.960.063
colorbar0.2210.2480.3630.2270.2850.3780.11
combined0.5830.4640.6970.3390.3750.5860.293
cones0.2890.240.4520.1840.1910.3750.131
cont0.1240.1230.2080.07850.07780.140.0774
cont_xyz0.1340.130.1840.1130.1130.1630.108
conta0.1280.1540.2890.1120.1290.1620.177
contd0.2390.2550.3540.120.1420.2360.103
contf0.2030.2260.3340.1110.130.2260.0992
contf_xyz0.170.2150.3050.1260.1510.2360.118
contfa0.2870.3690.4930.180.2030.4010.165
contv0.1620.1760.3060.0890.1030.2120.076
correl0.0990.08940.1690.08150.08550.1290.0659
curvcoor0.1320.1310.2310.0840.08430.1510.124
cut1.250.8421.060.7430.7681.130.644
dat_diff0.1270.1630.2610.1150.1350.2160.0846
dat_extra0.3280.260.3510.170.2670.30.114
data14.983.753.983.63.523.93.29
data23.282.742.822.812.783.22.61
dens0.1530.2440.4070.10.1410.2730.0771
dens_xyz0.150.2110.3580.1230.1620.2820.0961
densa0.1830.2110.3510.120.1540.2960.0912
dew1.70.9421.030.2240.2410.3610.129
dots0.1610.1670.2170.1040.110.1480.0639
error0.1010.1090.1760.110.1130.1940.0688
error20.09310.1120.2090.07420.08080.1560.0675
export0.2870.3630.5310.1740.220.360.253
fall0.0790.07520.1570.06520.0640.1220.0868
fit0.1090.8240.1730.08940.09180.1360.0793
flow0.390.3950.5660.3130.4230.4350.3
fog0.1110.1690.3620.07160.1270.30.063
fonts33.023.142.752.572.882.66
grad0.1190.2290.4240.1030.1580.3060.0859
hist0.2940.3030.3580.2090.2170.2740.0886
indirect0.1080.09080.1470.1110.1140.160.0556
inplot0.1020.09980.1740.07470.07260.1230.0664
label0.08360.08030.1290.08080.080.120.0529
legend0.1850.1950.30.07580.08640.1710.0622
light0.2730.2710.2990.2770.2740.2990.274
loglog0.120.1230.1980.0760.07790.1330.0692
map0.1070.1590.2550.120.1490.3160.0684
mark0.0830.09370.1260.0720.07230.110.0507
mask0.120.240.2570.07230.1410.1690.0597
mesh0.08660.09060.1890.06610.09320.1560.0638
mirror0.1630.1640.3050.080.0940.2090.0679
molecule0.1550.1660.3540.07540.1110.2630.0628
ode0.6520.6540.7880.6310.6360.7930.635
ohlc0.06680.06680.1170.06750.07340.1040.053
param10.2880.2950.5180.1370.1580.3520.147
param20.5550.540.7670.5910.2320.510.151
param33.153.633.781.862.032.351.61
paramv4.554.94.71.141.191.351.11
parser0.1180.1160.1950.1150.1220.2250.0954
pde0.8830.9611.130.8340.8430.9530.781
pipe4.273.233.040.6640.8310.9930.52
plot0.1540.1190.2210.09210.09330.1430.0835
primitives0.1430.1880.430.07490.1080.3130.0879
projection0.1820.2070.4940.08780.1030.3490.0768
projection50.170.20.4270.08350.09560.3230.11
qo2d0.3250.4230.5960.2860.3410.50.26
radar0.07240.07380.1150.0760.08040.1350.0499
refill0.3290.2630.380.1970.1670.2860.114
region0.09640.2350.2650.07290.09860.1910.0663
schemes0.1580.2050.3580.09470.1160.2310.0633
several_light0.1210.1360.4940.07040.09660.4270.0609
solve0.1380.1340.2470.1080.1040.2040.0741
stem0.1030.1010.1710.0790.07450.1350.0653
step0.1140.110.1570.07820.07550.1190.0636
stereo0.120.1380.3080.07150.09960.2740.065
stfa0.1280.1680.3660.09820.1220.2730.0732
style0.1810.2020.3380.08140.09290.190.0614
surf0.2350.2330.3950.120.1370.2840.0811
surf33.333.344.023.663.315.021.18
surf3a0.8250.5810.9010.4690.6411.340.378
surf3c0.7970.5770.910.4710.6371.340.375
surfa0.09790.1410.3580.06980.09530.2640.0639
surfc0.09920.1350.30.06820.09640.2520.0619
table0.2130.2050.330.07840.07960.1590.0633
tape0.10.1170.2110.070.08080.1470.0662
tens0.08910.08650.140.1080.110.1530.181
ternary0.180.1990.3760.08670.09680.2630.07
text0.1640.1650.2530.08630.0880.1550.0635
text20.1450.1450.2110.1090.1090.1680.0717
textmark0.1150.1130.1710.08470.08150.1330.16
ticks0.180.1840.2770.07560.0740.1610.063
tile0.08260.1160.2090.06710.08390.160.0638
tiles0.08560.1340.2170.06850.09010.1570.0678
torus0.1680.2020.5210.08120.1140.3720.0758
traj0.06410.0650.130.0660.06250.1120.0529
triangulation0.08950.1270.3040.08390.1170.2710.0707
triplot0.07210.1760.5810.06390.1180.4390.0497
tube0.1510.2190.480.09220.1320.3470.0719
type00.2960.2890.6560.1350.1960.5550.117
type10.2940.2860.6610.1380.1960.5660.116
type20.3110.3040.670.1550.2150.5740.135
vect0.190.1920.310.1750.1640.2730.12
vecta0.09710.09820.1860.1080.1180.310.0698
venn0.0640.240.3970.06310.1550.3230.0474

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Appendix D TeX-like symbols

The full list of TeX-like commands recognizable by MathGL is shown below. If command is not recognized then it will be printed as is by ommitting ‘\’ symbol. For example, ‘\#’ produce “#”, ‘\\’ produce “\”, ‘\qq’ produce “qq”.

Change case: _, ^, @.

Text style: \big, \b, \textbf, \i, \textit, \bi, \r, \textrm, \a, \overline, \u, \underline, \w, \wire, #, \color[wkrgbcymhRGBCYMHWlenupqLENUPQ]

Roots: \sqrt, \sqrt3, \sqrt4

Fractions: \frac, \stack, \overset, \underset, \stackr, \stackl

Accents: \hat, \tilde, \dot, \ddot, \dddot, \ddddot, \acute, \check, \grave, \vec, \bar, \breve

Special symbols:

\# (#), \% (%), \& (&), \^ (^).

\AA (Å), \AE (Æ), \APLboxquestion (⍰), \APLboxupcaret (⍓), \APLnotbackslash (⍀), \APLnotslash (⌿), \Alpha (Α), \And (&), \Angstrom (Å), \Barv (⫧), \BbbC (ℂ), \BbbGamma (ℾ), \BbbH (ℍ), \BbbN (ℕ), \BbbP (ℙ), \BbbPi (ℿ), \BbbQ (ℚ), \BbbR (ℝ), \BbbZ (ℤ), \Bbbgamma (ℽ), \Bbbpi (ℼ), \Bbbsum (⅀), \Beta (Β), \Bumpeq (≎), \Cap (⋒), \Chi (Χ), \Colon (∷), \Coloneq (⩴), \Cup (⋓), \DDownarrow (⟱), \DH (Ð), \DJ (Đ), \DashV (⫥), \DashVDash (⟚), \Dashv (⫤), \Ddownarrow (⤋), \Delta (Δ), \Digamma (Ϝ), \Doteq (≑), \Downarrow (⇓), \Epsilon (Ε), \Equiv (≣), \Eta (Η), \Eulerconst (ℇ), \Exclam (‼), \Finv (Ⅎ), \Game (⅁), \Gamma (Γ), \Gt (⪢), \Hermaphrodite (⚥), \Im (ℑ), \Iota (Ι), \Kappa (Κ), \Koppa (Ϟ), \L (Ł), \LLeftarrow (⭅), \Lambda (Λ), \Lbrbrak (⟬), \Ldsh (↲), \Leftarrow (⇐), \Leftrightarrow (⇔), \Lleftarrow (⇚), \Longleftarrow (⟸), \Longleftrightarrow (⟺), \Longmapsfrom (⟽), \Longmapsto (⟾), \Longrightarrow (⟹), \Lparengtr (⦕), \Lsh (↰), \Lt (⪡), \Lvzigzag (⧚), \Mapsfrom (⤆), \Mapsto (⤇), \Mu (Μ), \NG (Ŋ), \Nearrow (⇗), \Not (⫬), \Nu (Ν), \Nwarrow (⇖), \O (Ø), \OE (Œ), \Ohorn (Ơ), \Omega (Ω), \Omicron (Ο), \Otimes (⨷), \P (¶), \Phi (Φ), \Pi (Π), \Planckconst (ℎ), \Prec (⪻), \PropertyLine (⅊), \Psi (Ψ), \QED (∎), \Question (⁇), \RRightarrow (⭆), \Rbrbrak (⟭), \Rdsh (↳), \Re (ℜ), \Rho (Ρ), \Rightarrow (⇒), \Rparenless (⦖), \Rrightarrow (⇛), \Rsh (↱), \Rvzigzag (⧛), \S (§), \Sc (⪼), \Searrow (⇘), \Sigma (Σ), \Sqcap (⩎), \Sqcup (⩏), \Stigma (Ϛ), \Subset (⋐), \Supset (⋑), \Swarrow (⇙), \TH (Þ), \Tau (Τ), \Theta (Θ), \UUparrow (⟰), \Uhorn (Ư), \Uparrow (⇑), \Updownarrow (⇕), \Uuparrow (⤊), \VDash (⊫), \Vbar (⫫), \Vdash (⊩), \Vee (⩔), \Vert (‖), \Vvdash (⊪), \Vvert (⦀), \Wedge (⩓), \XBox (☒), \Xi (Ξ), \Yup (⅄), \Zbar (Ƶ), \Zeta (Ζ).

\aa (å), \ac (∾), \accurrent (⏦), \acidfree (♾), \acwcirclearrow (⥀), \acwgapcirclearrow (⟲), \acwleftarcarrow (⤹), \acwopencirclearrow (↺), \acwoverarcarrow (⤺), \acwundercurvearrow (⤻), \adots (⋰), \ae (æ), \aleph (ℵ), \alpha (α), \amalg (⨿), \angdnr (⦟), \angle (∠), \angles (⦞), \angleubar (⦤), \approx (≈), \approxeq (≊), \approxeqq (⩰), \approxident (≋), \arceq (≘), \aries (♈), \assert (⊦), \ast (∗), \asteq (⩮), \astrosun (☉), \asymp (≍), \awint (⨑).

\bNot (⫭), \backcong (≌), \backdprime (‶), \backepsilon (϶), \backprime (‵), \backsim (∽), \backsimeq (⋍), \backslash (\), \backtrprime (‷), \bagmember (⋿), \barV (⫪), \barcap (⩃), \barcup (⩂), \bardownharpoonleft (⥡), \bardownharpoonright (⥝), \barleftarrow (⇤), \barleftarrowrightarrowbar (↹), \barleftharpoondown (⥖), \barleftharpoonup (⥒), \barovernorthwestarrow (↸), \barrightarrowdiamond (⤠), \barrightharpoondown (⥟), \barrightharpoonup (⥛), \baruparrow (⤒), \barupharpoonleft (⥘), \barupharpoonright (⥔), \barvee (⊽), \barwedge (⊼), \bbrktbrk (⎶), \bdHrule (═), \bdVrule (║), \bdbVbH (╬), \bdbVbh (╫), \bdbVlH (╣), \bdbVlh (╢), \bdbVrH (╠), \bdbVrh (╟), \bdbvbH (╪), \bdbvbh (┼), \bdbvlH (╡), \bdbvlh (┤), \bdbvrH (╞), \bdbvrh (├), \bddVbH (╦), \bddVbh (╥), \bddVlH (╗), \bddVlh (╖), \bddVrH (╔), \bddVrh (╓), \bddvbH (╤), \bddvbh (┬), \bddvlH (╕), \bddvlh (┐), \bddvrH (╒), \bddvrh (┌), \bdhrule (─), \bdnesw (╱), \bdnwse (╲), \bdquadhdash (┈), \bdquadvdash (┊), \bdtriplevdash (┆), \bduVbH (╩), \bduVbh (╨), \bduVlH (╝), \bduVlh (╜), \bduVrH (╚), \bduVrh (╙), \bduvbH (╧), \bduvbh (┴), \bduvlH (╛), \bduvlh (┘), \bduvrH (╘), \bduvrh (└), \bdvrule (│), \because (∵), \benzenr (⏣), \beta (β), \beth (ℶ), \between (≬), \bigblacktriangledown (▼), \bigblacktriangleup (▲), \bigbot (⟘), \bigcap (⋂), \bigcup (⋃), \bigslopedvee (⩗), \bigslopedwedge (⩘), \bigstar (★), \bigtop (⟙), \bigtriangledown (▽), \bigtriangleup (△), \bigvee (⋁), \bigwedge (⋀), \bigwhitestar (☆), \blackcircledownarrow (⧭), \blackcircledrightdot (⚈), \blackcircledsanseight (➑), \blackcircledsansfive (➎), \blackcircledsansfour (➍), \blackcircledsansnine (➒), \blackcircledsansone (➊), \blackcircledsansseven (➐), \blackcircledsanssix (➏), \blackcircledsansten (➓), \blackcircledsansthree (➌), \blackcircledsanstwo (➋), \blackcircledtwodots (⚉), \blackcircleulquadwhite (◕), \blackdiamonddownarrow (⧪), \blackhourglass (⧗), \blackinwhitediamond (◈), \blackinwhitesquare (▣), \blacklefthalfcircle (◖), \blackpointerleft (◄), \blackpointerright (►), \blackrighthalfcircle (◗), \blacksmiley (☻), \blacktriangle (▴), \blacktriangledown (▾), \blacktriangleleft (◀), \blacktriangleright (▶), \blkhorzoval (⬬), \blkvertoval (⬮), \blockfull (█), \blockhalfshaded (▒), \blocklefthalf (▌), \blocklowhalf (▄), \blockqtrshaded (░), \blockrighthalf (▐), \blockthreeqtrshaded (▓), \blockuphalf (▀), \bot (⊥), \botsemicircle (◡), \bowtie (⋈), \box (◻), \boxast (⧆), \boxbar (◫), \boxbox (⧈), \boxbslash (⧅), \boxcircle (⧇), \boxdiag (⧄), \boxdot (⊡), \boxminus (⊟), \boxonbox (⧉), \boxplus (⊞), \boxtimes (⊠), \bsimilarleftarrow (⭁), \bsimilarrightarrow (⭇), \bsolhsub (⟈), \btimes (⨲), \bullet (∙), \bullseye (◎), \bumpeq (≏), \bumpeqq (⪮).

\calB (ℬ), \calE (ℰ), \calF (ℱ), \calH (ℋ), \calM (ℳ), \calR (ℛ), \cap (∩), \capdot (⩀), \capwedge (⩄), \caretinsert (‸), \carreturn (⏎), \carriagereturn (↵), \ccwundercurvearrow (⤿), \cdot (⋅), \cdotp (·), \cdots (⋯), \cdprime (ʺ), \checkmark (✓), \chi (χ), \cirE (⧃), \cirbot (⟟), \circ (∘), \circeq (≗), \circfint (⨐), \circlebottomhalfblack (◒), \circledA (Ⓐ), \circledB (Ⓑ), \circledC (Ⓒ), \circledD (Ⓓ), \circledE (Ⓔ), \circledF (Ⓕ), \circledG (Ⓖ), \circledH (Ⓗ), \circledI (Ⓘ), \circledJ (Ⓙ), \circledK (Ⓚ), \circledL (Ⓛ), \circledM (Ⓜ), \circledN (Ⓝ), \circledO (Ⓞ), \circledP (Ⓟ), \circledQ (Ⓠ), \circledR (Ⓡ), \circledS (Ⓢ), \circledT (Ⓣ), \circledU (Ⓤ), \circledV (Ⓥ), \circledW (Ⓦ), \circledX (Ⓧ), \circledY (Ⓨ), \circledZ (Ⓩ), \circleda (ⓐ), \circledast (⊛), \circledb (ⓑ), \circledbullet (⦿), \circledc (ⓒ), \circledcirc (⊚), \circledd (ⓓ), \circleddash (⊝), \circlede (ⓔ), \circledeight (⑧), \circledequal (⊜), \circledf (ⓕ), \circledfive (⑤), \circledfour (④), \circledg (ⓖ), \circledh (ⓗ), \circledi (ⓘ), \circledj (ⓙ), \circledk (ⓚ), \circledl (ⓛ), \circledm (ⓜ), \circledn (ⓝ), \circlednine (⑨), \circledo (ⓞ), \circledone (①), \circledownarrow (⧬), \circledp (ⓟ), \circledparallel (⦷), \circledq (ⓠ), \circledr (ⓡ), \circledrightdot (⚆), \circleds (ⓢ), \circledsanseight (➇), \circledsansfive (➄), \circledsansfour (➃), \circledsansnine (➈), \circledsansone (➀), \circledsansseven (➆), \circledsanssix (➅), \circledsansten (➉), \circledsansthree (➂), \circledsanstwo (➁), \circledseven (⑦), \circledsix (⑥), \circledstar (✪), \circledt (ⓣ), \circledthree (③), \circledtwo (②), \circledtwodots (⚇), \circledu (ⓤ), \circledv (ⓥ), \circledvert (⦶), \circledw (ⓦ), \circledwhitebullet (⦾), \circledx (ⓧ), \circledy (ⓨ), \circledz (ⓩ), \circledzero (⓪), \circlehbar (⦵), \circlelefthalfblack (◐), \circlellquad (◵), \circlelrquad (◶), \circleonleftarrow (⬰), \circleonrightarrow (⇴), \circlerighthalfblack (◑), \circletophalfblack (◓), \circleulquad (◴), \circleurquad (◷), \circleurquadblack (◔), \circlevertfill (◍), \cirmid (⫯), \cirscir (⧂), \clangle (〈), \closedvarcap (⩍), \closedvarcup (⩌), \closedvarcupsmashprod (⩐), \closure (⁐), \cloverleaf (⌘), \clubsuit (♣), \colon (:), \colon (∶), \coloneq (≔), \commaminus (⨩), \complement (∁), \concavediamond (⟡), \concavediamondtickleft (⟢), \concavediamondtickright (⟣), \cong (≅), \congdot (⩭), \conictaper (⌲), \conjunction (☌), \coprod (∐), \cprime (ʹ), \crangle (〉), \csub (⫏), \csube (⫑), \csup (⫐), \csupe (⫒), \cuberoot (∛), \cup (∪), \cupdot (⊍), \cupleftarrow (⊌), \cupvee (⩅), \curlyeqprec (⋞), \curlyeqsucc (⋟), \curlyvee (⋎), \curlywedge (⋏), \curvearrowleft (↶), \curvearrowleftplus (⤽), \curvearrowright (↷), \curvearrowrightminus (⤼), \cwcirclearrow (⥁), \cwgapcirclearrow (⟳), \cwopencirclearrow (↻), \cwrightarcarrow (⤸), \cwundercurvearrow (⤾), \cylcty (⌭).

\dag (†), \dagger (†), \daleth (ℸ), \danger (☡), \dashV (⫣), \dashVdash (⟛), \dashcolon (∹), \dashleftharpoondown (⥫), \dashrightharpoondown (⥭), \dashv (⊣), \dbkarow (⤏), \ddag (‡), \ddagger (‡), \ddots (⋱), \ddotseq (⩷), \delta (δ), \dh (ð), \diameter (⌀), \diamond (◇), \diamondbotblack (⬙), \diamondcdot (⟐), \diamondleftarrow (⤝), \diamondleftarrowbar (⤟), \diamondleftblack (⬖), \diamondrightblack (⬗), \diamondsuit (♢), \diamondtopblack (⬘), \dicei (⚀), \diceii (⚁), \diceiii (⚂), \diceiv (⚃), \dicev (⚄), \dicevi (⚅), \digamma (ϝ), \dingasterisk (✽), \dircurrent (⎓), \disin (⋲), \div (÷), \divideontimes (⋇), \dj (đ), \dlcrop (⌍), \doteq (≐), \dotequiv (⩧), \dotminus (∸), \dotplus (∔), \dots (…), \dotsim (⩪), \dotsminusdots (∺), \dottedcircle (◌), \dottedsquare (⬚), \dottimes (⨰), \doublebarvee (⩢), \doublebarwedge (⩞), \doubleplus (⧺), \downarrow (↓), \downarrowbar (⤓), \downarrowbarred (⤈), \downdasharrow (⇣), \downdownarrows (⇊), \downfishtail (⥿), \downharpoonleft (⇃), \downharpoonleftbar (⥙), \downharpoonright (⇂), \downharpoonrightbar (⥕), \downharpoonsleftright (⥥), \downrightcurvedarrow (⤵), \downtriangleleftblack (⧨), \downtrianglerightblack (⧩), \downuparrows (⇵), \downupharpoonsleftright (⥯), \downwhitearrow (⇩), \downzigzagarrow (↯), \dprime (″), \draftingarrow (➛), \drbkarow (⤐), \drcrop (⌌), \dsol (⧶), \dsub (⩤), \dualmap (⧟).

\earth (♁), \egsdot (⪘), \eighthnote (♪), \elinters (⏧), \ell (ℓ), \elsdot (⪗), \emdash (—), \emptyset (∅), \emptysetoarr (⦳), \emptysetoarrl (⦴), \emptysetobar (⦱), \emptysetocirc (⦲), \endash (–), \enleadertwodots (‥), \envelope (✉), \eparsl (⧣), \epsilon (ϵ), \eqcirc (≖), \eqcolon (≕), \eqdef (≝), \eqdot (⩦), \eqeq (⩵), \eqeqeq (⩶), \eqgtr (⋝), \eqless (⋜), \eqqgtr (⪚), \eqqless (⪙), \eqqplus (⩱), \eqqsim (⩳), \eqqslantgtr (⪜), \eqqslantless (⪛), \eqsim (≂), \eqslantgtr (⪖), \eqslantless (⪕), \equalleftarrow (⭀), \equalparallel (⋕), \equalrightarrow (⥱), \equiv (≡), \equivDD (⩸), \equivVert (⩨), \equivVvert (⩩), \eqvparsl (⧥), \errbarblackcircle (⧳), \errbarblackdiamond (⧱), \errbarblacksquare (⧯), \errbarcircle (⧲), \errbardiamond (⧰), \errbarsquare (⧮), \eta (η), \euro (€), \exists (∃).

\fallingdotseq (≒), \fbowtie (⧓), \fcmp (⨾), \fdiagovnearrow (⤯), \fdiagovrdiag (⤬), \female (♀), \figdash (‒), \fint (⨏), \fisheye (◉), \flat (♭), \fltns (⏥), \forall (∀), \forks (⫝̸), \forksnot (⫝), \forkv (⫙), \fourthroot (∜), \fourvdots (⦙), \fracfiveeighths (⅝), \fracfivesixths (⅚), \fracfourfifths (⅘), \fraconeeighth (⅛), \fraconefifth (⅕), \fraconesixth (⅙), \fraconethird (⅓), \fracseveneights (⅞), \fracslash (⁄), \fracthreeeighths (⅜), \fracthreefifths (⅗), \fractwofifths (⅖), \fractwothirds (⅔), \frakC (ℭ), \frakH (ℌ), \frakZ (ℨ), \frown (⌢), \frownie (☹), \fullouterjoin (⟗).

\gamma (γ), \ge (≥), \geq (≥), \geqq (≧), \geqslant (⩾), \gescc (⪩), \gesdot (⪀), \gesdoto (⪂), \gesdotol (⪄), \gesles (⪔), \gets (←), \gg (≫), \ggg (⋙), \gggnest (⫸), \gimel (ℷ), \glE (⪒), \gla (⪥), \gleichstark (⧦), \glj (⪤), \gnapprox (⪊), \gneq (⪈), \gneqq (≩), \gnsim (⋧), \greater (>), \gsime (⪎), \gsiml (⪐), \gtcc (⪧), \gtcir (⩺), \gtlpar (⦠), \gtquest (⩼), \gtrapprox (⪆), \gtrarr (⥸), \gtrdot (⋗), \gtreqless (⋛), \gtreqqless (⪌), \gtrless (≷), \gtrsim (≳), \guillemotleft («), \guillemotright (»), \guilsinglleft (‹), \guilsinglright (›).

\harrowextender (⎯), \hatapprox (⩯), \hbar (ℏ), \heartsuit (♡), \hermitmatrix (⊹), \hexagon (⎔), \hexagonblack (⬣), \hiraganano (の), \hknearrow (⤤), \hknwarrow (⤣), \hksearow (⤥), \hkswarow (⤦), \hookleftarrow (↩), \hookrightarrow (↪), \horizbar (―), \hourglass (⧖), \house (⌂), \hrectangle (▭), \hrectangleblack (▬), \hslash (ℏ), \hyphenbullet (⁃), \hzigzag (〰).

\iiiint (⨌), \iiint (∭), \iinfin (⧜), \iint (∬), \imageof (⊷), \in (∈), \incare (℅), \increment (∆), \infty (∞), \int (∫), \intBar (⨎), \intbar (⨍), \intbottom (⌡), \intcap (⨙), \intclockwise (∱), \intcup (⨚), \intercal (⊺), \interleave (⫴), \intextender (⎮), \intlharhk (⨗), \intprod (⨼), \intprodr (⨽), \inttop (⌠), \intx (⨘), \inversebullet (◘), \inversewhitecircle (◙), \invnot (⌐), \invwhitelowerhalfcircle (◛), \invwhiteupperhalfcircle (◚), \iota (ι), \ipasupgamma (ˠ), \ipasupl (ˡ), \ipasuprerglotstpp (ˤ), \ipasups (ˢ), \ipasupx (ˣ), \ipaunaspirated (˭), \ipavoicing (ˬ), \isinE (⋹), \isindot (⋵), \isinobar (⋷), \isins (⋴), \isinvb (⋸), \itBbbD (ⅅ), \itBbbd (ⅆ), \itBbbe (ⅇ), \itBbbi (ⅈ), \itBbbj (ⅉ).

\jupiter (♃), \kappa (κ), \kernelcontraction (∻), \koppa (ϟ).

\l (ł), \lAngle (⟪), \lBrace (⦃), \lBrack (⟦), \lParen (⦅), \lambda (λ), \lambdabar (ƛ), \langle (⟨), \langledot (⦑), \laplac (⧠), \lasp (ʽ), \lat (⪫), \late (⪭), \lbag (⟅), \lblkbrbrak (⦗), \lbrace ({), \lbracelend (⎩), \lbracemid (⎨), \lbraceuend (⎧), \lbrack ([), \lbrackextender (⎢), \lbracklend (⎣), \lbracklltick (⦏), \lbrackubar (⦋), \lbrackuend (⎡), \lbrackultick (⦍), \lbrbrak (❲), \lceil (⌈), \lcurvyangle (⧼), \ldasharrhead (⇠), \le (≤), \leadsto (↝), \leftarrow (←), \leftarrowapprox (⭊), \leftarrowbackapprox (⭂), \leftarrowbsimilar (⭋), \leftarrowless (⥷), \leftarrowonoplus (⬲), \leftarrowplus (⥆), \leftarrowshortrightarrow (⥃), \leftarrowsimilar (⥳), \leftarrowsubset (⥺), \leftarrowtail (↢), \leftarrowtriangle (⇽), \leftarrowx (⬾), \leftbkarrow (⤌), \leftcurvedarrow (⬿), \leftdasharrow (⇠), \leftdasharrowhead (⇡), \leftdbkarrow (⤎), \leftdbltail (⤛), \leftdotarrow (⬸), \leftdowncurvedarrow (⤶), \leftfishtail (⥼), \leftharpoondown (↽), \leftharpoondownbar (⥞), \leftharpoonsupdown (⥢), \leftharpoonup (↼), \leftharpoonupbar (⥚), \leftharpoonupdash (⥪), \leftleftarrows (⇇), \leftmoon (☾), \leftouterjoin (⟕), \leftrightarrow (↔), \leftrightarrowcircle (⥈), \leftrightarrows (⇆), \leftrightarrowtriangle (⇿), \leftrightharpoondowndown (⥐), \leftrightharpoondownup (⥋), \leftrightharpoons (⇋), \leftrightharpoonsdown (⥧), \leftrightharpoonsup (⥦), \leftrightharpoonupdown (⥊), \leftrightharpoonupup (⥎), \leftrightsquigarrow (↭), \leftsquigarrow (↜), \leftsquigarrow (⇜), \lefttail (⤙), \leftthreearrows (⬱), \leftthreetimes (⋋), \leftwhitearrow (⇦), \leq (≤), \leqq (≦), \leqqslant (⫹), \leqqslant (⫺), \leqslant (⩽), \lescc (⪨), \lesdot (⩿), \lesdoto (⪁), \lesdotor (⪃), \lesges (⪓), \less (<), \lessapprox (⪅), \lessdot (⋖), \lesseqgtr (⋚), \lesseqqgtr (⪋), \lessgtr (≶), \lesssim (≲), \lfbowtie (⧑), \lfloor (⌊), \lftimes (⧔), \lgE (⪑), \lgblkcircle (⬤), \lgblksquare (⬛), \lgwhtcircle (◯), \lgwhtsquare (⬜), \lhd (⊲), \linefeed (↴), \ll (≪), \llangle (⦉), \llarc (◟), \llblacktriangle (◣), \llcorner (⌞), \lll (⋘), \lllnest (⫷), \llparenthesis (⦇), \lltriangle (◺), \lmoustache (⎰), \lnapprox (⪉), \lneq (⪇), \lneqq (≨), \lnsim (⋦), \longdashv (⟞), \longdivision (⟌), \longleftarrow (⟵), \longleftrightarrow (⟷), \longleftsquigarrow (⬳), \longmapsfrom (⟻), \longmapsto (⟼), \longrightarrow (⟶), \longrightsquigarrow (⟿), \looparrowleft (↫), \looparrowright (↬), \lowint (⨜), \lozenge (◊), \lozengeminus (⟠), \lparenextender (⎜), \lparenlend (⎝), \lparenless (⦓), \lparenuend (⎛), \lq (‘), \lrarc (◞), \lrblacktriangle (◢), \lrcorner (⌟), \lrtriangle (◿), \lrtriangleeq (⧡), \lsime (⪍), \lsimg (⪏), \lsqhook (⫍), \ltcc (⪦), \ltcir (⩹), \ltimes (⋉), \ltlarr (⥶), \ltquest (⩻), \ltrivb (⧏), \lvboxline (⎸), \lvzigzag (⧘).

\male (♂), \maltese (✠), \mapsdown (↧), \mapsfrom (↤), \mapsto (↦), \mapsup (↥), \mdblkdiamond (⬥), \mdblklozenge (⬧), \mdblkrcl (⚫), \mdblksquare (◼), \mdlgblkcircle (●), \mdlgblkdiamond (◆), \mdlgblklozenge (⧫), \mdlgblksquare (■), \mdlgwhtcircle (○), \mdlgwhtdiamond (◇), \mdlgwhtsquare (□), \mdsmblkcircle (⦁), \mdsmblksquare (◾), \mdsmwhtcircl (⚬), \mdsmwhtsquare (◽), \mdwhtcircl (⚪), \mdwhtdiamond (⬦), \mdwhtlozenge (⬨), \mdwhtsquare (◻), \measangledltosw (⦯), \measangledrtose (⦮), \measangleldtosw (⦫), \measanglelutonw (⦩), \measanglerdtose (⦪), \measanglerutone (⦨), \measangleultonw (⦭), \measangleurtone (⦬), \measeq (≞), \measuredangle (∡), \measuredangleleft (⦛), \measuredrightangle (⊾), \medblackstar (⭑), \medmathspace ( ), \medwhitestar (⭐), \mercury (☿), \mho (℧), \mid (∣), \midbarvee (⩝), \midbarwedge (⩜), \midcir (⫰), \minus (−), \minusdot (⨪), \minusfdots (⨫), \minusrdots (⨬), \mlcp (⫛), \models (⊧), \mp (∓), \mu (μ), \multimap (⊸), \multimapinv (⟜).

\nHdownarrow (⇟), \nHuparrow (⇞), \nLeftarrow (⇍), \nLeftrightarrow (⇎), \nRightarrow (⇏), \nVDash (⊯), \nVdash (⊮), \nVleftarrow (⇺), \nVleftarrowtail (⬺), \nVleftrightarrow (⇼), \nVrightarrow (⇻), \nVrightarrowtail (⤕), \nVtwoheadleftarrow (⬵), \nVtwoheadleftarrowtail (⬽), \nVtwoheadrightarrow (⤁), \nVtwoheadrightarrowtail (⤘), \nabla (∇), \napprox (≉), \nasymp (≭), \natural (♮), \ncong (≇), \ne (≠), \nearrow (↗), \neg (¬), \neovnwarrow (⤱), \neovsearrow (⤮), \neptune (♆), \neq (≠), \nequiv (≢), \neswarrow (⤢), \neuter (⚲), \nexists (∄), \ng (ŋ), \ngeq (≱), \ngtr (≯), \ngtrless (≹), \ngtrsim (≵), \nhVvert (⫵), \nhpar (⫲), \ni (∋), \niobar (⋾), \nis (⋼), \nisd (⋺), \nleftarrow (↚), \nleftrightarrow (↮), \nleq (≰), \nless (≮), \nlessgtr (≸), \nlesssim (≴), \nmid (∤), \nni (∌), \nobreakhyphen (‑), \notin (∉), \nparallel (∦), \npolint (⨔), \nprec (⊀), \npreccurlyeq (⋠), \nrightarrow (↛), \nsim (≁), \nsime (≄), \nsqsubseteq (⋢), \nsqsupseteq (⋣), \nsubset (⊄), \nsubseteq (⊈), \nsucc (⊁), \nsucccurlyeq (⋡), \nsupset (⊅), \nsupseteq (⊉), \ntriangleleft (⋪), \ntrianglelefteq (⋬), \ntriangleright (⋫), \ntrianglerighteq (⋭), \nu (ν), \nvDash (⊭), \nvLeftarrow (⤂), \nvLeftrightarrow (⤄), \nvRightarrow (⤃), \nvdash (⊬), \nvinfty (⧞), \nvleftarrow (⇷), \nvleftarrowtail (⬹), \nvleftrightarrow (⇹), \nvrightarrow (⇸), \nvrightarrowtail (⤔), \nvtwoheadleftarrow (⬴), \nvtwoheadleftarrowtail (⬼), \nvtwoheadrightarrow (⤀), \nvtwoheadrightarrowtail (⤗), \nwarrow (↖), \nwovnearrow (⤲), \nwsearrow (⤡).

\o (ø), \obar (⌽), \obot (⦺), \obrbrak (⏠), \obslash (⦸), \odiv (⨸), \odot (⊙), \odotslashdot (⦼), \oe (œ), \ogreaterthan (⧁), \ohorn (ơ), \oiiint (∰), \oiint (∯), \oint (∮), \ointctrclockwise (∳), \olcross (⦻), \oldKoppa (Ϙ), \oldkoppa (ϙ), \olessthan (⧀), \omega (ω), \omicron (ο), \ominus (⊖), \operp (⦹), \oplus (⊕), \opluslhrim (⨭), \oplusrhrim (⨮), \origof (⊶), \oslash (⊘), \otimes (⊗), \otimeshat (⨶), \otimeslhrim (⨴), \otimesrhrim (⨵), \overbrace (⏞), \overbracket (⎴), \overline (‾), \overparen (⏜), \owns (∋).

\parallel (∥), \parallelogram (▱), \parallelogramblack (▰), \parsim (⫳), \partial (∂), \partialmeetcontraction (⪣), \pentagon (⬠), \pentagonblack (⬟), \perp (⟂), \perps (⫡), \phi (ϕ), \phone (☎), \pi (π), \pitchfork (⋔), \plusdot (⨥), \pluseqq (⩲), \plushat (⨣), \plussim (⨦), \plussubtwo (⨧), \plustrif (⨨), \pluto (♇), \pm (±), \pointnt (⨕), \postalmark (〒), \prec (≺), \precapprox (⪷), \preccurlyeq (≼), \preceq (⪯), \preceqq (⪳), \precnapprox (⪹), \precneq (⪱), \precneqq (⪵), \precnsim (⋨), \precsim (≾), \prime (′), \prod (∏), \profalar (⌮), \profline (⌒), \profsurf (⌓), \propto (∝), \prurel (⊰), \psi (ψ), \pullback (⟓), \pushout (⟔).

\qprime (⁗), \quarternote (♩), \questeq (≟), \quotdblbase („), \quotdblright (‟), \quotsinglbase (‚), \quotsinglright (‛).

\rAngle (⟫), \rBrace (⦄), \rBrack (⟧), \rParen (⦆), \rangle (⟩), \rangledot (⦒), \rangledownzigzagarrow (⍼), \rasp (ʼ), \rbag (⟆), \rblkbrbrak (⦘), \rbrace (}), \rbracelend (⎭), \rbracemid (⎬), \rbraceuend (⎫), \rbrack (]), \rbrackextender (⎥), \rbracklend (⎦), \rbracklrtick (⦎), \rbrackubar (⦌), \rbrackuend (⎤), \rbrackurtick (⦐), \rbrbrak (❳), \rceil (⌉), \rcurvyangle (⧽), \rdiagovfdiag (⤫), \rdiagovsearrow (⤰), \recorder (⌕), \revangle (⦣), \revangleubar (⦥), \revemptyset (⦰), \revnmid (⫮), \rfbowtie (⧒), \rfloor (⌋), \rftimes (⧕), \rhd (⊳), \rho (ρ), \righarrowbsimilar (⭌), \rightangle (∟), \rightanglemdot (⦝), \rightanglesqr (⦜), \rightarrow (→), \rightarrowapprox (⥵), \rightarrowbackapprox (⭈), \rightarrowbar (⇥), \rightarrowdiamond (⤞), \rightarrowgtr (⭃), \rightarrowonoplus (⟴), \rightarrowplus (⥅), \rightarrowshortleftarrow (⥂), \rightarrowsimilar (⥴), \rightarrowsupset (⭄), \rightarrowtail (↣), \rightarrowtriangle (⇾), \rightarrowx (⥇), \rightbkarrow (⤍), \rightcurvedarrow (⤳), \rightdasharrow (⇢), \rightdbltail (⤜), \rightdotarrow (⤑), \rightdowncurvedarrow (⤷), \rightfishtail (⥽), \rightharpoondown (⇁), \rightharpoondownbar (⥗), \rightharpoonsupdown (⥤), \rightharpoonup (⇀), \rightharpoonupbar (⥓), \rightharpoonupdash (⥬), \rightimply (⥰), \rightleftarrows (⇄), \rightleftharpoons (⇌), \rightleftharpoonsdown (⥩), \rightleftharpoonsup (⥨), \rightmoon (☽), \rightouterjoin (⟖), \rightpentagon (⭔), \rightpentagonblack (⭓), \rightrightarrows (⇉), \rightsquigarrow (↝), \rightsquigarrow (⇝), \righttail (⤚), \rightthreearrows (⇶), \rightthreetimes (⋌), \rightwhitearrow (⇨), \ringplus (⨢), \risingdotseq (≓), \rmoustache (⎱), \rparenextender (⎟), \rparengtr (⦔), \rparenlend (⎠), \rparenuend (⎞), \rppolint (⨒), \rq (’), \rrangle (⦊), \rrparenthesis (⦈), \rsolbar (⧷), \rsqhook (⫎), \rsub (⩥), \rtimes (⋊), \rtriltri (⧎), \ruledelayed (⧴), \rvboxline (⎹), \rvzigzag (⧙).

\sampi (ϡ), \sansLmirrored (⅃), \sansLturned (⅂), \saturn (♄), \scissors (✂), \scpolint (⨓), \scrB (ℬ), \scrE (ℰ), \scrF (ℱ), \scrH (ℋ), \scrI (ℐ), \scrL (ℒ), \scrM (ℳ), \scrR (ℛ), \scre (ℯ), \scrg (ℊ), \scro (ℴ), \scurel (⊱), \searrow (↘), \seovnearrow (⤭), \setminus (∖), \setminus (⧵), \sharp (♯), \shortdowntack (⫟), \shortleftarrow (←), \shortlefttack (⫞), \shortrightarrow (→), \shortrightarrowleftarrow (⥄), \shortuptack (⫠), \shuffle (⧢), \sigma (σ), \silon (υ), \silon (ϒ), \sim (∼), \simeq (≃), \simgE (⪠), \simgtr (⪞), \similarleftarrow (⭉), \similarrightarrow (⥲), \simlE (⪟), \simless (⪝), \simminussim (⩬), \simneqq (≆), \simplus (⨤), \simrdots (⩫), \sinewave (∿), \slash (∕), \smallblacktriangleleft (◂), \smallblacktriangleright (▸), \smalldiamond (⋄), \smallin (∊), \smallint (∫), \smallni (∍), \smallsetminus (∖), \smalltriangleleft (◃), \smalltriangleright (▹), \smashtimes (⨳), \smblkdiamond (⬩), \smblklozenge (⬪), \smblksquare (▪), \smeparsl (⧤), \smile (⌣), \smiley (☺), \smt (⪪), \smte (⪬), \smwhitestar (⭒), \smwhtcircle (◦), \smwhtlozenge (⬫), \smwhtsquare (▫), \spadesuit (♠), \sphericalangle (∢), \sphericalangleup (⦡), \sqcap (⊓), \sqcup (⊔), \sqint (⨖), \sqlozenge (⌑), \sqrt (√), \sqrt3 (∛), \sqrt4 (∜), \sqrtbottom (⎷), \sqsubset (⊏), \sqsubseteq (⊑), \sqsubsetneq (⋤), \sqsupset (⊐), \sqsupseteq (⊒), \sqsupsetneq (⋥), \squarecrossfill (▩), \squaregrayfill (▩), \squarehfill (▤), \squarehvfill (▦), \squareleftblack (◧), \squareleftblack (◨), \squarellblack (⬕), \squarellquad (◱), \squarelrblack (◪), \squarelrquad (◲), \squareneswfill (▨), \squarenwsefill (▧), \squareulblack (◩), \squareulquad (◰), \squareurblack (⬔), \squareurquad (◳), \squarevfill (▥), \squoval (▢), \ss (ß), \star (⋆), \stareq (≛), \sterling (£), \stigma (ϛ), \strns (⏤), \subedot (⫃), \submult (⫁), \subrarr (⥹), \subset (⊂), \subsetapprox (⫉), \subsetcirc (⟃), \subsetdot (⪽), \subseteq (⊆), \subseteqq (⫅), \subsetneq (⊊), \subsetneqq (⫋), \subsetplus (⪿), \subsim (⫇), \subsub (⫕), \subsup (⫓), \succ (≻), \succapprox (⪸), \succcurlyeq (≽), \succeq (⪰), \succeqq (⪴), \succnapprox (⪺), \succneq (⪲), \succneqq (⪶), \succnsim (⋩), \succsim (≿), \sum (∑), \sumbottom (⎳), \sumint (⨋), \sumtop (⎲), \sun (☼), \supdsub (⫘), \supedot (⫄), \suphsol (⟉), \suphsub (⫗), \suplarr (⥻), \supmult (⫂), \supn (ⁿ), \supset (⊃), \supsetapprox (⫊), \supsetcirc (⟄), \supsetdot (⪾), \supseteq (⊇), \supseteqq (⫆), \supsetneq (⊋), \supsetneqq (⫌), \supsetplus (⫀), \supsim (⫈), \supsub (⫔), \supsup (⫖), \surd (√), \swarrow (↙).

\talloblong (⫾), \target (⌖), \tau (τ), \taurus (♉), \testhookx (ᶍ), \textAsterisks (⁑), \textacute (ˊ), \textadvanced (˖), \textain (ʿ), \textasciiacute (´), \textasciicircum (^), \textasciidieresis (¨), \textasciigrave (‘), \textasciimacron (¯), \textasciitilde (~), \textasterisklow (⁎), \textbackdprime (‶), \textbackprime (‵), \textbacktrprime (‷), \textbardotlessj (ɟ), \textbardotlessjvar (ʄ), \textbarglotstop (ʡ), \textbari (ɨ), \textbarl (ƚ), \textbaro (ɵ), \textbarrevglotstop (ʢ), \textbaru (ʉ), \textbeltl (ɬ), \textbenttailyogh (ƺ), \textbreve (˘), \textbrokenbar (¦), \textbullet (•), \textbullseye (ʘ), \textcent (¢), \textcircledP (℗), \textcloseepsilon (ʚ), \textcloseomega (ɷ), \textcloserevepsilon (ɞ), \textcopyright (©), \textcrb (ƀ), \textcrh (ħ), \textcrinvglotstop (ƾ), \textcrlambda (ƛ), \textcrtwo (ƻ), \textctc (ɕ), \textctd (ȡ), \textctesh (ʆ), \textctj (ʝ), \textctl (ȴ), \textctn (ȵ), \textctt (ȶ), \textctyogh (ʓ), \textctz (ʑ), \textcurrency (¤), \textdctzlig (ʥ), \textdegree (°), \textdiscount (⁒), \textdollar ($), \textdotaccent (˙), \textdotlessj (ȷ), \textdoubleacute (˝), \textdoublebarpipe (ǂ), \textdoublepipe (ǁ), \textdprime (″), \textdptr (˅), \textdyoghlig (ʤ), \textdzlig (ʣ), \textepsilon (ɛ), \textesh (ʃ), \textestimated (℮), \textexclam (ǃ), \textexclamdown (¡), \textfishhookr (ɾ), \textflorin (ƒ), \textfranc (₣), \textgamma (ɣ), \textglotstop (ʔ), \textgrave (ˋ), \texthalflength (ˑ), \texthamza (ʾ), \texthen (ꜧ), \textheng (ꜧ), \texthooks (ᶊ), \texthookz (ᶎ), \texthtb (ɓ), \texthtc (ƈ), \texthtd (ɗ), \texthtg (ɠ), \texthth (ɦ), \texththeng (ɧ), \texthtk (ƙ), \texthtp (ƥ), \texthtq (ʠ), \texthtscg (ʛ), \texthtt (ƭ), \texthvlig (ƕ), \texthyphen (‐), \textinvglotstop (ʖ), \textinvscr (ʁ), \textiota (ɩ), \textlengthmark (ː), \textlhalfring (˓), \textlhookd (ᶁ), \textlhookk (ᶄ), \textlhookl (ᶅ), \textlhookt (ƫ), \textlhti (ɿ), \textlira (₤), \textlonglegr (ɼ), \textlongy (ʮ), \textlongy (ʯ), \textlooptoprevesh (ƪ), \textlowacute (ˏ), \textlowered (˕), \textlowgrave (ˎ), \textlowmacron (ˍ), \textlptr (˂), \textltailm (ɱ), \textltailn (ɲ), \textltilde (ɫ), \textlyoghlig (ɮ), \textmacron (ˉ), \textmu (µ), \textnumero (№), \textogonek (˛), \textohm (Ω), \textonehalf (½), \textonequarter (¼), \textonesuperior (¹), \textopeno (ɔ), \textordfeminine (ª), \textordmasculine (º), \textovercross (˟), \textoz (℥), \textpertenthousand (‱), \textperthousand (‰), \textpesetas (₧), \textphi (ɸ), \textpipe (ǀ), \textprime (′), \textprimstress (ˈ), \textqprime (⁗), \textquestiondown (¿), \textquotedbl ("), \textquotedblleft (“), \textquotedblright (”), \textraised (˔), \textraiseglotstop (ˀ), \textraiserevglotstop (ˁ), \textramshorns (ɤ), \textrecipe (℞), \textreferencemark (※), \textregistered (®), \textretracted (˗), \textreve (ɘ), \textrevepsilon (ɜ), \textrevglotstop (ʕ), \textrhalfring (˒), \textrhookrevepsilon (ɝ), \textrhookschwa (ɚ), \textrhoticity (˞), \textringaccent (˚), \textrptr (˃), \textrtaild (ɖ), \textrtaill (ɭ), \textrtailn (ɳ), \textrtailr (ɽ), \textrtails (ʂ), \textrtailt (ʈ), \textrtailz (ʐ), \textsca (ᴀ), \textscb (ʙ), \textsce (ᴇ), \textscg (ɢ), \textsch (ʜ), \textschwa (ə), \textsci (ɪ), \textscl (ʟ), \textscn (ɴ), \textscoelig (ɶ), \textscr (ʀ), \textscripta (ɑ), \textscriptg (ɡ), \textscriptv (ʋ), \textscu (ᴜ), \textscy (ʏ), \textsecstress (ˌ), \textsemicolonreversed (⁏), \textsilon (Υ), \textsmalltilde (˜), \textstretchcvar (ʗ), \textsubw (w), \textsuph (ʰ), \textsuphth (ʱ), \textsupinvscr (ʶ), \textsupj (ʲ), \textsupr (ʳ), \textsupturnr (ʴ), \textsupturnrrtail (ʵ), \textsupw (ʷ), \textsupy (ʸ), \texttctctlig (ʧ), \texttctctlig (ʨ), \textthreequarters (¾), \textthreesuperior (³), \texttrademark (™), \texttrprime (‴), \texttslig (ʦ), \textturna (ɐ), \textturncomma (ʻ), \textturnh (ɥ), \textturnk (ʞ), \textturnlonglegr (ɺ), \textturnm (ɯ), \textturnmrleg (ɰ), \textturnr (ɹ), \textturnrrtail (ɻ), \textturnscripta (ɒ), \textturnt (ʇ), \textturnv (ʌ), \textturnw (ʍ), \textturny (ʎ), \texttwosuperior (²), \textupsilon (ʊ), \textuptr (˄), \textvibyi (ʅ), \textvisiblespace (␣), \textyogh (ʒ), \th (þ), \therefore (∴), \thermod (⧧), \theta (θ), \thickapprox (≈), \thicksim (∼), \threedangle (⟀), \threedotcolon (⫶), \tieconcat (⁀), \tieinfty (⧝), \times (×), \timesbar (⨱), \tminus (⧿), \to (→), \toea (⤨), \tona (⤧), \tonebarextrahigh (˥), \tonebarextralow (˩), \tonebarhigh (˦), \tonebarlow (˨), \tonebarmid (˧), \top (⊤), \topbot (⌶), \topcir (⫱), \topfork (⫚), \topsemicircle (◠), \tosa (⤩), \towa (⤪), \tplus (⧾), \trapezium (⏢), \trianglecdot (◬), \triangledown (▿), \triangleexclam (⚠), \triangleleft (◁), \triangleleftblack (◭), \trianglelefteq (⊴), \triangleminus (⨺), \triangleodot (⧊), \triangleplus (⨹), \triangleq (≜), \triangleright (▷), \trianglerightblack (◮), \trianglerighteq (⊵), \triangles (⧌), \triangleserifs (⧍), \triangletimes (⨻), \triangleubar (⧋), \tripleplus (⧻), \trprime (‴), \turnangle (⦢), \turnediota (℩), \turnednot (⌙), \twocaps (⩋), \twocups (⩊), \twoheaddownarrow (↡), \twoheadleftarrow (↞), \twoheadleftarrowtail (⬻), \twoheadleftdbkarrow (⬷), \twoheadmapsfrom (⬶), \twoheadmapsto (⤅), \twoheadrightarrow (↠), \twoheadrightarrowtail (⤖), \twoheaduparrow (↟), \twoheaduparrowcircle (⥉), \twolowline (‗), \twonotes (♫), \typecolon (⦂).

\ubrbrak (⏡), \uhorn (ư), \ularc (◜), \ulblacktriangle (◤), \ulcorner (⌜), \ulcrop (⌏), \ultriangle (◸), \uminus (⩁), \underbrace (⏟), \underbracket (⎵), \underparen (⏝), \unlhd (⊴), \unrhd (⊵), \upand (⅋), \uparrow (↑), \uparrowbarred (⤉), \uparrowoncircle (⦽), \updasharrow (⇢), \updownarrow (↕), \updownarrowbar (↨), \updownarrows (⇅), \updownharpoonleftleft (⥑), \updownharpoonleftright (⥍), \updownharpoonrightleft (⥌), \updownharpoonrightright (⥏), \updownharpoonsleftright (⥮), \upfishtail (⥾), \upharpoonleft (↿), \upharpoonleftbar (⥠), \upharpoonright (↾), \upharpoonrightbar (⥜), \upharpoonsleftright (⥣), \upin (⟒), \upint (⨛), \uplus (⊎), \uprightcurvearrow (⤴), \upuparrows (⇈), \upwhitearrow (⇧), \urarc (◝), \urblacktriangle (◥), \urcorner (⌝), \urcrop (⌎), \urtriangle (◹).

\v (ˇ), \vBar (⫨), \vBarv (⫩), \vDash (⊨), \vDdash (⫢), \varTheta (ϴ), \varVdash (⫦), \varbarwedge (⌅), \varbeta (ϐ), \varclubsuit (♧), \vardiamondsuit (♦), \vardoublebarwedge (⌆), \varepsilon (ε), \varheartsuit (♥), \varhexagon (⬡), \varhexagonblack (⬢), \varhexagonlrbonds (⌬), \varin (∈), \varisinobar (⋶), \varisins (⋳), \varkappa (ϰ), \varlrtriangle (⊿), \varni (∋), \varniobar (⋽), \varnis (⋻), \varnothing (∅), \varointclockwise (∲), \varphi (φ), \varpi (ϖ), \varpropto (∝), \varrho (ϱ), \varrowextender (⏐), \varsigma (ς), \varspadesuit (♤), \varstar (✶), \vartheta (ϑ), \vartriangle (▵), \vartriangleleft (⊲), \vartriangleright (⊳), \varveebar (⩡), \vbraceextender (⎪), \vbrtri (⧐), \vdash (⊢), \vdots (⋮), \vectimes (⨯), \vee (∨), \veebar (⊻), \veedot (⟇), \veedoublebar (⩣), \veeeq (≚), \veemidvert (⩛), \veeodot (⩒), \veeonvee (⩖), \veeonwedge (⩙), \vert (|), \viewdata (⌗), \vlongdash (⟝), \vrectangle (▯), \vrectangleblack (▮), \vysmlblksquare (⬝), \vysmlwhtsquare (⬞), \vzigzag (⦚).

\watchicon (⌚), \wedge (∧), \wedgebar (⩟), \wedgedot (⟑), \wedgedoublebar (⩠), \wedgemidvert (⩚), \wedgeodot (⩑), \wedgeonwedge (⩕), \wedgeq (≙), \whitearrowupfrombar (⇪), \whiteinwhitetriangle (⟁), \whitepointerleft (◅), \whitepointerright (▻), \whitesquaretickleft (⟤), \whitesquaretickright (⟥), \whthorzoval (⬭), \whtvertoval (⬯), \wideangledown (⦦), \wideangleup (⦧), \wp (℘), \wr (≀).

\xbsol (⧹), \xi (ξ), \xsol (⧸), \yen (¥), \zeta (ζ), \zpipe (⨠),

IF ANYBODY WILL CHECK WHETHER ALL NAMES CORRESPOND TO RIGHT TEX SYMBOLS I SHALL APPRECIATE IT GREATLY.

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Appendix E GNU Free Documentation License

Version 1.2, November 2002 
Copyright © 2000,2001,2002 Free Software Foundation, Inc.
51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
  1. PREAMBLE

    The purpose of this License is to make a manual, textbook, or other functional and useful document free in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

    This License is a kind of “copyleft”, which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

    We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

  2. APPLICABILITY AND DEFINITIONS

    This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The “Document”, below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as “you”. You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.

    A “Modified Version” of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.

    A “Secondary Section” is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document’s overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

    The “Invariant Sections” are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

    The “Cover Texts” are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

    A “Transparent” copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not “Transparent” is called “Opaque”.

    Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.

    The “Title Page” means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, “Title Page” means the text near the most prominent appearance of the work’s title, preceding the beginning of the body of the text.

    A section “Entitled XYZ” means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as “Acknowledgements”, “Dedications”, “Endorsements”, or “History”.) To “Preserve the Title” of such a section when you modify the Document means that it remains a section “Entitled XYZ” according to this definition.

    The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.

  3. VERBATIM COPYING

    You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

    You may also lend copies, under the same conditions stated above, and you may publicly display copies.

  4. COPYING IN QUANTITY

    If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document’s license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

    If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

    If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

    It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.

  5. MODIFICATIONS

    You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

    1. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
    2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
    3. State on the Title page the name of the publisher of the Modified Version, as the publisher.
    4. Preserve all the copyright notices of the Document.
    5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
    6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
    7. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document’s license notice.
    8. Include an unaltered copy of this License.
    9. Preserve the section Entitled “History”, Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled “History” in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
    10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the “History” section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
    11. For any section Entitled “Acknowledgements” or “Dedications”, Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
    12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
    13. Delete any section Entitled “Endorsements”. Such a section may not be included in the Modified Version.
    14. Do not retitle any existing section to be Entitled “Endorsements” or to conflict in title with any Invariant Section.
    15. Preserve any Warranty Disclaimers.

    If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version’s license notice. These titles must be distinct from any other section titles.

    You may add a section Entitled “Endorsements”, provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

    You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

    The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

  6. COMBINING DOCUMENTS

    You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

    The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

    In the combination, you must combine any sections Entitled “History” in the various original documents, forming one section Entitled “History”; likewise combine any sections Entitled “Acknowledgements”, and any sections Entitled “Dedications”. You must delete all sections Entitled “Endorsements.”

  7. COLLECTIONS OF DOCUMENTS

    You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

    You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

  8. AGGREGATION WITH INDEPENDENT WORKS

    A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an “aggregate” if the copyright resulting from the compilation is not used to limit the legal rights of the compilation’s users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

    If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document’s Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

  9. TRANSLATION

    Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

    If a section in the Document is Entitled “Acknowledgements”, “Dedications”, or “History”, the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

  10. TERMINATION

    You may not copy, modify, sublicense, or distribute the Document except as expressly provided for under this License. Any other attempt to copy, modify, sublicense or distribute the Document is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance.

  11. FUTURE REVISIONS OF THIS LICENSE

    The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

    Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License “or any later version” applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation.

ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page: 

  Copyright (C)  year  your name.
  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.2
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled ``GNU
  Free Documentation License''.

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the “with…Texts.” line with this: 

    with the Invariant Sections being list their titles, with
    the Front-Cover Texts being list, and with the Back-Cover Texts
    being list.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

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Index

Jump to:   A   B   C   D   E   F   G   H   I   J   L   M   N   O   P   Q   R   S   T   V   W   X   Y   Z  
Index Entry  Section
A
AddLegend: Legend
AddLight: Lighting
AddTick: Ticks
Adjust: Ticks
alpha: Command options
Alpha: Transparency
alphadef: Command options
AlphaDef: Transparency
Ambient: Lighting
Area: 1D plotting
Arrows: Line styles
ArrowSize: Default sizes
ask: Program flow commands
Aspect: Subplots and rotation
AutoCorrel: Make another data
Axial: 2D plotting
Axis: Curved coordinates
Axis: Axis and Colorbar
AxisStl: Ticks
B
Ball: Primitives
Barh: 1D plotting
Bars: 1D plotting
BarWidth: Default sizes
Beam: 3D plotting
Belt: 2D plotting
Box: Axis and Colorbar
BoxPlot: 1D plotting
Boxs: 2D plotting
C
call: Program flow commands
Candle: 1D plotting
Chart: 1D plotting
chdir: Program flow commands
Clean: Data resizing
ClearLegend: Legend
Clf: Background
CloseGIF: Frames/Animation
Cloud: 3D plotting
Color scheme: Color scheme
Colorbar: Axis and Colorbar
Column: Make another data
ColumnPlot: Subplots and rotation
Combine: Parallelization
Combine: Make another data
Cone: Primitives
Cones: 1D plotting
Cont: 2D plotting
Cont3: 3D plotting
ContD: 2D plotting
ContF: 2D plotting
ContF3: 3D plotting
ContFXYZ: Other plotting
ContXYZ: Other plotting
CopyFont: Font settings
Correl: Make another data
CosFFT: Data changing
CRange: Ranges (bounding box)
Create: Data resizing
Crop: Data resizing
Crust: Other plotting
CTick: Ticks
CumSum: Data changing
Curve: Primitives
cut: Command options
Cut: Cutting
CutOff: Cutting
D
DataGrid: Data manipulation
defchr: Program flow commands
define: Program flow commands
defnum: Program flow commands
Delete: Data resizing
Dens: 2D plotting
Dens3: 3D plotting
DensXYZ: Other plotting
Dew: Vector fields
Diff: Data changing
Diff2: Data changing
Dots: Other plotting
Drop: Primitives
E
else: Program flow commands
elseif: Program flow commands
EndFrame: Frames/Animation
endif: Program flow commands
Envelop: Data changing
Error: Primitives
Error: 1D plotting
Evaluate: Make another data
Export: File I/O
Extend: Data resizing
F
Face: Primitives
FaceX: Primitives
FaceY: Primitives
FaceZ: Primitives
Fall: 2D plotting
fgets: Text printing
Fill: Data manipulation
Fill: Data filling
Find: Data information
FindAny: Data information
Fit: Nonlinear fitting
Fit2: Nonlinear fitting
Fit3: Nonlinear fitting
FitS: Nonlinear fitting
Flow: Vector fields
FlowP: Vector fields
Fl_MathGL: Widget classes
Fl_MathGL: Fl_MathGL class
Fog: Fog
Font: Font settings
Font styles: Font styles
fontsize: Command options
for: Program flow commands
FPlot: Other plotting
FSurf: Other plotting
func: Program flow commands
G
GetNumFrame: Frames/Animation
GetNx: Data information
GetNy: Data information
GetNz: Data information
GetWarn: Error handling
Glyph: Primitives
Grad: 2D plotting
Grid: Axis and Colorbar
Grid: 2D plotting
Grid3: 3D plotting
H
Hankel: Data changing
Hist: Data manipulation
Hist: Make another data
I
if: Program flow commands
Import: File I/O
InPlot: Subplots and rotation
Insert: Data resizing
Integral: Data changing
J
Join: Data resizing
L
Label: Text printing
Label: Axis and Colorbar
Label: 1D plotting
Last: Data information
legend: Command options
Legend: Legend
Light: Lighting
Line: Primitives
Line style: Line styles
Linear: Interpolation
Linear1: Interpolation
Linear1: Interpolation
List: Data filling
load: Program flow commands
LoadBackground: Background
LoadFont: Font settings
M
Map: Dual plotting
Mark: Primitives
Mark: 1D plotting
Mark style: Line styles
MarkSize: Default sizes
MathGL overview: Overview
MathGL setup: Graphics setup
Max: Make another data
Maximal: Data information
Mesh: 2D plotting
meshnum: Command options
MeshNum: Default sizes
Message: Error handling
mglColor: mglColor class
mglData: Data constructor
mglDraw: mglDraw class
mglExpr: Evaluate expression
mglExprC: Evaluate expression
mglFitPnts: Nonlinear fitting
mglGLUT: Widget classes
mglGraph: MathGL core
mglParse: mglParse class
mglPoint: mglPoint class
mglWnd: Widget classes
mglWnd: mglWnd class
Min: Make another data
Minimal: Data information
Mirror: Data changing
Modify: Data filling
Momentum: Make another data
Momentum: Data information
MPI_Recv: Parallelization
MPI_Send: Parallelization
MultiPlot: Subplots and rotation
N
NeedStop: Stop drawing
NewFrame: Frames/Animation
next: Program flow commands
Norm: Data changing
NormSl: Data changing
O
once: Program flow commands
Origin: Ranges (bounding box)
P
Palette: Palette and colors
Perspective: Subplots and rotation
Pipe: Vector fields
Plot: 1D plotting
Pop: Subplots and rotation
PrintInfo: Data information
Push: Subplots and rotation
Puts: Text printing
PutsFit: Nonlinear fitting
Putsw: Text printing
Q
QMathGL: Widget classes
QMathGL: QMathGL class
QuadPlot: Other plotting
R
Radar: 1D plotting
Ranges: Ranges (bounding box)
Rasterize: Background
Read: File I/O
ReadAll: File I/O
ReadHDF: File I/O
ReadMat: File I/O
ReadRange: File I/O
Rearrange: Data resizing
Refill: Data filling
Region: 1D plotting
ResetFrames: Frames/Animation
Resize: Make another data
RestoreFont: Font settings
return: Program flow commands
rkstep: Program flow commands
Roll: Data changing
Roots: Make another data
Rotate: Subplots and rotation
RotateN: Subplots and rotation
RotateText: Font settings
S
Save: File I/O
SaveHDF: File I/O
Set: Data filling
SetAlphaDef: Transparency
SetAmbient: Lighting
SetArrowSize: Default sizes
SetAxisStl: Ticks
SetBarWidth: Default sizes
SetCoor: Curved coordinates
SetCut: Cutting
SetCutBox: Cutting
SetEventFunc: Stop drawing
SetFontDef: Font settings
SetFontSize: Font settings
SetFontSizeCM: Font settings
SetFontSizeIN: Font settings
SetFontSizePT: Font settings
SetFunc: Curved coordinates
SetLegendBox: Legend
SetLegendMarks: Legend
SetMarkSize: Default sizes
SetMask: Masks
SetMaskAngle: Masks
SetMeshNum: Default sizes
SetOrigin: Ranges (bounding box)
SetOriginTick: Ticks
SetPalette: Palette and colors
SetPlotId: Default sizes
SetRange: Ranges (bounding box)
SetRanges: Ranges (bounding box)
SetRotatedText: Font settings
SetSize: Export picture
SetTickLen: Ticks
SetTickRotate: Ticks
SetTicks: Ticks
SetTickSkip: Ticks
SetTicksVal: Ticks
SetTickTempl: Ticks
SetTickTime: Ticks
SetTranspType: Transparency
SetTuneTicks: Ticks
SetWarn: Error handling
Sew: Data changing
ShowImage: Export to file
SinFFT: Data changing
Smooth: Data changing
Sort: Data resizing
Sphere: Primitives
Spline: Interpolation
Spline1: Interpolation
Spline1: Interpolation
Squeeze: Data resizing
StartGIF: Frames/Animation
Stem: 1D plotting
Step: 1D plotting
STFA: Dual plotting
StickPlot: Subplots and rotation
Stop: Stop drawing
stop: Program flow commands
SubData: Make another data
SubPlot: Subplots and rotation
Sum: Make another data
Surf: 2D plotting
Surf3: 3D plotting
Surf3A: Dual plotting
Surf3C: Dual plotting
SurfA: Dual plotting
SurfC: Dual plotting
Swap: Data changing
T
Tape: 1D plotting
Tens: 1D plotting
Ternary: Curved coordinates
Text: Text printing
TextMark: 1D plotting
Textual formulas: Textual formulas
TickLen: Ticks
Tile: 2D plotting
TileS: Dual plotting
Title: Subplots and rotation
Torus: 1D plotting
Trace: Make another data
Traj: Vector fields
Transpose: Data resizing
TranspType: Transparency
TriCont: Other plotting
TriPlot: Other plotting
Tube: 1D plotting
V
value: Command options
Var: Data filling
variant: Program flow commands
Vect: Vector fields
View: Subplots and rotation
W
widgets: Using MathGL window
widgets: Widget classes
widgets: Fl_MathGL class
widgets: QMathGL class
widgets: wxMathGL class
window: Using MathGL window
window: Widget classes
window: mglWnd class
Write: Export to file
WriteBMP: Export to file
WriteBPS: Export to file
WriteEPS: Export to file
WriteFrame: Export to file
WriteGIF: Export to file
WriteJPEG: Export to file
WriteOBJ: Export to file
WritePNG: Export to file
WritePRC: Export to file
WriteSVG: Export to file
WriteTEX: Export to file
WriteTGA: Export to file
WriteWGL: Export to file
wxMathGL: wxMathGL class
X
xrange: Command options
XRange: Ranges (bounding box)
XTick: Ticks
Y
yrange: Command options
YRange: Ranges (bounding box)
YTick: Ticks
Z
zrange: Command options
ZRange: Ranges (bounding box)
ZTick: Ticks
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