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AngleAxis< _Scalar > Class Template Reference

Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...

List of all members.

Public Types

enum  { Dim }
typedef Matrix< Scalar, 3, 3 > Matrix3
typedef Quaternion< ScalarQuaternionType
typedef _Scalar Scalar
typedef Matrix< Scalar, 3, 1 > Vector3

Public Member Functions

Scalar angle () const
Scalarangle ()
 AngleAxis ()
template<typename Derived >
 AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
 AngleAxis (const QuaternionType &q)
template<typename Derived >
 AngleAxis (const MatrixBase< Derived > &m)
template<typename OtherScalarType >
 AngleAxis (const AngleAxis< OtherScalarType > &other)
const Vector3axis () const
Vector3axis ()
template<typename NewScalarType >
ei_cast_return_type< AngleAxis,
AngleAxis< NewScalarType >
>::type 
cast () const
template<typename Derived >
AngleAxisfromRotationMatrix (const MatrixBase< Derived > &m)
AngleAxis inverse () const
bool isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
QuaternionType operator* (const AngleAxis &other) const
QuaternionType operator* (const QuaternionType &other) const
Matrix3 operator* (const Matrix3 &other) const
Vector3 operator* (const Vector3 &other) const
AngleAxisoperator= (const QuaternionType &q)
template<typename Derived >
AngleAxisoperator= (const MatrixBase< Derived > &m)
Matrix3 toRotationMatrix (void) const

Protected Attributes

Scalar m_angle
Vector3 m_axis

Friends

QuaternionType operator* (const QuaternionType &a, const AngleAxis &b)
Matrix3 operator* (const Matrix3 &a, const AngleAxis &b)

Detailed Description

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >

Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.

This is defined in the Geometry module.

 #include <Eigen/Geometry> 
Parameters:
_Scalarthe scalar type, i.e., the type of the coefficients.

The following two typedefs are provided for convenience:

Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily mimic Euler-angles. Here is an example:

Matrix3f m;
m = AngleAxisf(0.25*M_PI, Vector3f::UnitX())
  * AngleAxisf(0.5*M_PI,  Vector3f::UnitY())
  * AngleAxisf(0.33*M_PI, Vector3f::UnitZ());
cout << m << endl << "is unitary: " << m.isUnitary() << endl;

Output:

 8.67e-08         0         1
    0.969    -0.249 -5.36e-09
    0.249     0.969  1.13e-07
is unitary: 1
Note:
This class is not aimed to be used to store a rotation transformation, but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) and transformation objects.
See also:
class Quaternion, class Transform, MatrixBase::UnitX()

Member Typedef Documentation

typedef _Scalar Scalar

the scalar type of the coefficients

Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.


Constructor & Destructor Documentation

AngleAxis ( ) [inline]

Default constructor without initialization.

AngleAxis ( Scalar  angle,
const MatrixBase< Derived > &  axis 
) [inline]

Constructs and initialize the angle-axis rotation from an angle in radian and an axis which must be normalized.

AngleAxis ( const QuaternionType q) [inline]

Constructs and initialize the angle-axis rotation from a quaternion q.

AngleAxis ( const MatrixBase< Derived > &  m) [inline, explicit]

Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.

AngleAxis ( const AngleAxis< OtherScalarType > &  other) [inline, explicit]

Copy constructor with scalar type conversion


Member Function Documentation

ei_cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast ( ) const [inline]
Returns:
*this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

AngleAxis inverse ( void  ) const [inline]
Returns:
the inverse rotation, i.e., an angle-axis with opposite rotation angle

Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.

bool isApprox ( const AngleAxis< _Scalar > &  other,
typename NumTraits< Scalar >::Real  prec = precision<Scalar>() 
) const [inline]
Returns:
true if *this is approximately equal to other, within the precision determined by prec.
See also:
MatrixBase::isApprox()
QuaternionType operator* ( const AngleAxis< _Scalar > &  other) const [inline]

Concatenates two rotations

QuaternionType operator* ( const QuaternionType other) const [inline]

Concatenates two rotations

Matrix3 operator* ( const Matrix3 other) const [inline]

Concatenates two rotations

Vector3 operator* ( const Vector3 other) const [inline]

Applies rotation to vector

AngleAxis< Scalar > & operator= ( const QuaternionType q)

Set *this from a quaternion. The axis is normalized.

AngleAxis< Scalar > & operator= ( const MatrixBase< Derived > &  mat)

Set *this from a 3x3 rotation matrix mat.

AngleAxis< Scalar >::Matrix3 toRotationMatrix ( void  ) const

Constructs and

Returns:
an equivalent 3x3 rotation matrix.

Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.


Friends And Related Function Documentation

QuaternionType operator* ( const QuaternionType a,
const AngleAxis< _Scalar > &  b 
) [friend]

Concatenates two rotations

Matrix3 operator* ( const Matrix3 a,
const AngleAxis< _Scalar > &  b 
) [friend]

Concatenates two rotations


The documentation for this class was generated from the following file: