001// License: GPL. For details, see LICENSE file.
002package org.openstreetmap.josm.tools;
003
004import java.awt.Rectangle;
005import java.awt.geom.Area;
006import java.awt.geom.Line2D;
007import java.awt.geom.Path2D;
008import java.math.BigDecimal;
009import java.math.MathContext;
010import java.util.ArrayList;
011import java.util.Collections;
012import java.util.Comparator;
013import java.util.EnumSet;
014import java.util.HashSet;
015import java.util.LinkedHashSet;
016import java.util.List;
017import java.util.Set;
018
019import org.openstreetmap.josm.Main;
020import org.openstreetmap.josm.command.AddCommand;
021import org.openstreetmap.josm.command.ChangeCommand;
022import org.openstreetmap.josm.command.Command;
023import org.openstreetmap.josm.data.coor.EastNorth;
024import org.openstreetmap.josm.data.coor.LatLon;
025import org.openstreetmap.josm.data.osm.BBox;
026import org.openstreetmap.josm.data.osm.MultipolygonBuilder;
027import org.openstreetmap.josm.data.osm.Node;
028import org.openstreetmap.josm.data.osm.NodePositionComparator;
029import org.openstreetmap.josm.data.osm.OsmPrimitiveType;
030import org.openstreetmap.josm.data.osm.Relation;
031import org.openstreetmap.josm.data.osm.RelationMember;
032import org.openstreetmap.josm.data.osm.Way;
033
034/**
035 * Some tools for geometry related tasks.
036 *
037 * @author viesturs
038 */
039public final class Geometry {
040
041    private Geometry() {
042        // Hide default constructor for utils classes
043    }
044
045    public enum PolygonIntersection {FIRST_INSIDE_SECOND, SECOND_INSIDE_FIRST, OUTSIDE, CROSSING}
046
047    /**
048     * Will find all intersection and add nodes there for list of given ways.
049     * Handles self-intersections too.
050     * And makes commands to add the intersection points to ways.
051     *
052     * Prerequisite: no two nodes have the same coordinates.
053     *
054     * @param ways  a list of ways to test
055     * @param test  if false, do not build list of Commands, just return nodes
056     * @param cmds  list of commands, typically empty when handed to this method.
057     *              Will be filled with commands that add intersection nodes to
058     *              the ways.
059     * @return list of new nodes
060     */
061    public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
062
063        int n = ways.size();
064        @SuppressWarnings("unchecked")
065        List<Node>[] newNodes = new ArrayList[n];
066        BBox[] wayBounds = new BBox[n];
067        boolean[] changedWays = new boolean[n];
068
069        Set<Node> intersectionNodes = new LinkedHashSet<>();
070
071        //copy node arrays for local usage.
072        for (int pos = 0; pos < n; pos ++) {
073            newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
074            wayBounds[pos] = getNodesBounds(newNodes[pos]);
075            changedWays[pos] = false;
076        }
077
078        //iterate over all way pairs and introduce the intersections
079        Comparator<Node> coordsComparator = new NodePositionComparator();
080        for (int seg1Way = 0; seg1Way < n; seg1Way ++) {
081            for (int seg2Way = seg1Way; seg2Way < n; seg2Way ++) {
082
083                //do not waste time on bounds that do not intersect
084                if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
085                    continue;
086                }
087
088                List<Node> way1Nodes = newNodes[seg1Way];
089                List<Node> way2Nodes = newNodes[seg2Way];
090
091                //iterate over primary segmemt
092                for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos ++) {
093
094                    //iterate over secondary segment
095                    int seg2Start = seg1Way != seg2Way ? 0: seg1Pos + 2;//skip the adjacent segment
096
097                    for (int seg2Pos = seg2Start; seg2Pos + 1< way2Nodes.size(); seg2Pos ++) {
098
099                        //need to get them again every time, because other segments may be changed
100                        Node seg1Node1 = way1Nodes.get(seg1Pos);
101                        Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
102                        Node seg2Node1 = way2Nodes.get(seg2Pos);
103                        Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
104
105                        int commonCount = 0;
106                        //test if we have common nodes to add.
107                        if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
108                            commonCount ++;
109
110                            if (seg1Way == seg2Way &&
111                                    seg1Pos == 0 &&
112                                    seg2Pos == way2Nodes.size() -2) {
113                                //do not add - this is first and last segment of the same way.
114                            } else {
115                                intersectionNodes.add(seg1Node1);
116                            }
117                        }
118
119                        if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
120                            commonCount ++;
121
122                            intersectionNodes.add(seg1Node2);
123                        }
124
125                        //no common nodes - find intersection
126                        if (commonCount == 0) {
127                            EastNorth intersection = getSegmentSegmentIntersection(
128                                    seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
129                                    seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
130
131                            if (intersection != null) {
132                                if (test) {
133                                    intersectionNodes.add(seg2Node1);
134                                    return intersectionNodes;
135                                }
136
137                                Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
138                                Node intNode = newNode;
139                                boolean insertInSeg1 = false;
140                                boolean insertInSeg2 = false;
141                                //find if the intersection point is at end point of one of the segments, if so use that point
142
143                                //segment 1
144                                if (coordsComparator.compare(newNode, seg1Node1) == 0) {
145                                    intNode = seg1Node1;
146                                } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
147                                    intNode = seg1Node2;
148                                } else {
149                                    insertInSeg1 = true;
150                                }
151
152                                //segment 2
153                                if (coordsComparator.compare(newNode, seg2Node1) == 0) {
154                                    intNode = seg2Node1;
155                                } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
156                                    intNode = seg2Node2;
157                                } else {
158                                    insertInSeg2 = true;
159                                }
160
161                                if (insertInSeg1) {
162                                    way1Nodes.add(seg1Pos +1, intNode);
163                                    changedWays[seg1Way] = true;
164
165                                    //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
166                                    if (seg2Way == seg1Way) {
167                                        seg2Pos ++;
168                                    }
169                                }
170
171                                if (insertInSeg2) {
172                                    way2Nodes.add(seg2Pos +1, intNode);
173                                    changedWays[seg2Way] = true;
174
175                                    //Do not need to compare again to already split segment
176                                    seg2Pos ++;
177                                }
178
179                                intersectionNodes.add(intNode);
180
181                                if (intNode == newNode) {
182                                    cmds.add(new AddCommand(intNode));
183                                }
184                            }
185                        }
186                        else if (test && !intersectionNodes.isEmpty())
187                            return intersectionNodes;
188                    }
189                }
190            }
191        }
192
193
194        for (int pos = 0; pos < ways.size(); pos ++) {
195            if (!changedWays[pos]) {
196                continue;
197            }
198
199            Way way = ways.get(pos);
200            Way newWay = new Way(way);
201            newWay.setNodes(newNodes[pos]);
202
203            cmds.add(new ChangeCommand(way, newWay));
204        }
205
206        return intersectionNodes;
207    }
208
209    private static BBox getNodesBounds(List<Node> nodes) {
210
211        BBox bounds = new BBox(nodes.get(0));
212        for (Node n: nodes) {
213            bounds.add(n.getCoor());
214        }
215        return bounds;
216    }
217
218    /**
219     * Tests if given point is to the right side of path consisting of 3 points.
220     *
221     * (Imagine the path is continued beyond the endpoints, so you get two rays
222     * starting from lineP2 and going through lineP1 and lineP3 respectively
223     * which divide the plane into two parts. The test returns true, if testPoint
224     * lies in the part that is to the right when traveling in the direction
225     * lineP1, lineP2, lineP3.)
226     *
227     * @param lineP1 first point in path
228     * @param lineP2 second point in path
229     * @param lineP3 third point in path
230     * @param testPoint
231     * @return true if to the right side, false otherwise
232     */
233    public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
234        boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
235        boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
236        boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
237
238        if (pathBendToRight)
239            return rightOfSeg1 && rightOfSeg2;
240        else
241            return !(!rightOfSeg1 && !rightOfSeg2);
242    }
243
244    /**
245     * This method tests if secondNode is clockwise to first node.
246     * @param commonNode starting point for both vectors
247     * @param firstNode first vector end node
248     * @param secondNode second vector end node
249     * @return true if first vector is clockwise before second vector.
250     */
251    public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
252        return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
253    }
254
255    /**
256     * Finds the intersection of two line segments
257     * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
258     */
259    public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
260
261        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
262        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
263        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
264        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
265
266        double x1 = p1.getX();
267        double y1 = p1.getY();
268        double x2 = p2.getX();
269        double y2 = p2.getY();
270        double x3 = p3.getX();
271        double y3 = p3.getY();
272        double x4 = p4.getX();
273        double y4 = p4.getY();
274
275        //TODO: do this locally.
276        //TODO: remove this check after careful testing
277        if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
278
279        // solve line-line intersection in parametric form:
280        // (x1,y1) + (x2-x1,y2-y1)* u  = (x3,y3) + (x4-x3,y4-y3)* v
281        // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
282        // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
283
284        double a1 = x2 - x1;
285        double b1 = x3 - x4;
286        double c1 = x3 - x1;
287
288        double a2 = y2 - y1;
289        double b2 = y3 - y4;
290        double c2 = y3 - y1;
291
292        // Solve the equations
293        double det = a1*b2 - a2*b1;
294
295        double uu = b2*c1 - b1*c2 ;
296        double vv = a1*c2 - a2*c1;
297        double mag = Math.abs(uu)+Math.abs(vv);
298
299        if (Math.abs(det) > 1e-12 * mag) {
300            double u = uu/det, v = vv/det;
301            if (u>-1e-8 && u < 1+1e-8 && v>-1e-8 && v < 1+1e-8 ) {
302                if (u<0) u=0;
303                if (u>1) u=1.0;
304                return new EastNorth(x1+a1*u, y1+a2*u);
305            } else {
306                return null;
307            }
308        } else {
309            // parallel lines
310            return null;
311        }
312    }
313
314    /**
315     * Finds the intersection of two lines of infinite length.
316     *
317     * @param p1 first point on first line
318     * @param p2 second point on first line
319     * @param p3 first point on second line
320     * @param p4 second point on second line
321     * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
322     * @throws IllegalArgumentException if a parameter is null or without valid coordinates
323     */
324    public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
325
326        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
327        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
328        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
329        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
330
331        if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
332
333        // Basically, the formula from wikipedia is used:
334        //  https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
335        // However, large numbers lead to rounding errors (see #10286).
336        // To avoid this, p1 is first substracted from each of the points:
337        //  p1' = 0
338        //  p2' = p2 - p1
339        //  p3' = p3 - p1
340        //  p4' = p4 - p1
341        // In the end, p1 is added to the intersection point of segment p1'/p2'
342        // and segment p3'/p4'.
343
344        // Convert line from (point, point) form to ax+by=c
345        double a1 = p2.getY() - p1.getY();
346        double b1 = p1.getX() - p2.getX();
347        // double c1 = 0;
348
349        double a2 = p4.getY() - p3.getY();
350        double b2 = p3.getX() - p4.getX();
351        double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
352
353        // Solve the equations
354        double det = a1 * b2 - a2 * b1;
355        if (det == 0)
356            return null; // Lines are parallel
357
358        return new EastNorth(b1 * c2 / det + p1.getX(),  - a1 * c2 / det + p1.getY());
359    }
360
361    public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
362
363        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
364        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
365        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
366        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
367
368        // Convert line from (point, point) form to ax+by=c
369        double a1 = p2.getY() - p1.getY();
370        double b1 = p1.getX() - p2.getX();
371
372        double a2 = p4.getY() - p3.getY();
373        double b2 = p3.getX() - p4.getX();
374
375        // Solve the equations
376        double det = a1 * b2 - a2 * b1;
377        // remove influence of of scaling factor
378        det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
379        return Math.abs(det) < 1e-3;
380    }
381
382    private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
383        CheckParameterUtil.ensureParameterNotNull(p1, "p1");
384        CheckParameterUtil.ensureParameterNotNull(p2, "p2");
385        CheckParameterUtil.ensureParameterNotNull(point, "point");
386
387        double ldx = p2.getX() - p1.getX();
388        double ldy = p2.getY() - p1.getY();
389
390        if (ldx == 0 && ldy == 0) //segment zero length
391            return p1;
392
393        double pdx = point.getX() - p1.getX();
394        double pdy = point.getY() - p1.getY();
395
396        double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
397
398        if (segmentOnly && offset <= 0)
399            return p1;
400        else if (segmentOnly && offset >= 1)
401            return p2;
402        else
403            return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
404    }
405
406    /**
407     * Calculates closest point to a line segment.
408     * @param segmentP1 First point determining line segment
409     * @param segmentP2 Second point determining line segment
410     * @param point Point for which a closest point is searched on line segment [P1,P2]
411     * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
412     * a new point if closest point is between segmentP1 and segmentP2.
413     * @since 3650
414     * @see #closestPointToLine
415     */
416    public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
417        return closestPointTo(segmentP1, segmentP2, point, true);
418    }
419
420    /**
421     * Calculates closest point to a line.
422     * @param lineP1 First point determining line
423     * @param lineP2 Second point determining line
424     * @param point Point for which a closest point is searched on line (P1,P2)
425     * @return The closest point found on line. It may be outside the segment [P1,P2].
426     * @since 4134
427     * @see #closestPointToSegment
428     */
429    public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
430        return closestPointTo(lineP1, lineP2, point, false);
431    }
432
433    /**
434     * This method tests if secondNode is clockwise to first node.
435     *
436     * The line through the two points commonNode and firstNode divides the
437     * plane into two parts. The test returns true, if secondNode lies in
438     * the part that is to the right when traveling in the direction from
439     * commonNode to firstNode.
440     *
441     * @param commonNode starting point for both vectors
442     * @param firstNode first vector end node
443     * @param secondNode second vector end node
444     * @return true if first vector is clockwise before second vector.
445     */
446    public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
447
448        CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
449        CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
450        CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
451
452        double dy1 = (firstNode.getY() - commonNode.getY());
453        double dy2 = (secondNode.getY() - commonNode.getY());
454        double dx1 = (firstNode.getX() - commonNode.getX());
455        double dx2 = (secondNode.getX() - commonNode.getX());
456
457        return dy1 * dx2 - dx1 * dy2 > 0;
458    }
459
460    /**
461     * Returns the Area of a polygon, from its list of nodes.
462     * @param polygon List of nodes forming polygon (EastNorth coordinates)
463     * @return Area for the given list of nodes
464     * @since 6841
465     */
466    public static Area getArea(List<Node> polygon) {
467        Path2D path = new Path2D.Double();
468
469        boolean begin = true;
470        for (Node n : polygon) {
471            EastNorth en = n.getEastNorth();
472            if (en != null) {
473                if (begin) {
474                    path.moveTo(en.getX(), en.getY());
475                    begin = false;
476                } else {
477                    path.lineTo(en.getX(), en.getY());
478                }
479            }
480        }
481        if (!begin) {
482            path.closePath();
483        }
484
485        return new Area(path);
486    }
487
488    /**
489     * Returns the Area of a polygon, from its list of nodes.
490     * @param polygon List of nodes forming polygon (LatLon coordinates)
491     * @return Area for the given list of nodes
492     * @since 6841
493     */
494    public static Area getAreaLatLon(List<Node> polygon) {
495        Path2D path = new Path2D.Double();
496
497        boolean begin = true;
498        for (Node n : polygon) {
499            if (begin) {
500                path.moveTo(n.getCoor().lon(), n.getCoor().lat());
501                begin = false;
502            } else {
503                path.lineTo(n.getCoor().lon(), n.getCoor().lat());
504            }
505        }
506        if (!begin) {
507            path.closePath();
508        }
509
510        return new Area(path);
511    }
512
513    /**
514     * Tests if two polygons intersect.
515     * @param first List of nodes forming first polygon
516     * @param second List of nodes forming second polygon
517     * @return intersection kind
518     */
519    public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
520        Area a1 = getArea(first);
521        Area a2 = getArea(second);
522        return polygonIntersection(a1, a2);
523    }
524
525    /**
526     * Tests if two polygons intersect.
527     * @param a1 Area of first polygon
528     * @param a2 Area of second polygon
529     * @return intersection kind
530     * @since 6841
531     */
532    public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
533        return polygonIntersection(a1, a2, 1.0);
534    }
535
536    /**
537     * Tests if two polygons intersect.
538     * @param a1 Area of first polygon
539     * @param a2 Area of second polygon
540     * @param eps an area threshold, everything below is considered an empty intersection
541     * @return intersection kind
542     */
543    public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
544
545        Area inter = new Area(a1);
546        inter.intersect(a2);
547
548        Rectangle bounds = inter.getBounds();
549
550        if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
551            return PolygonIntersection.OUTSIDE;
552        } else if (inter.equals(a1)) {
553            return PolygonIntersection.FIRST_INSIDE_SECOND;
554        } else if (inter.equals(a2)) {
555            return PolygonIntersection.SECOND_INSIDE_FIRST;
556        } else {
557            return PolygonIntersection.CROSSING;
558        }
559    }
560
561    /**
562     * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
563     * @param polygonNodes list of nodes from polygon path.
564     * @param point the point to test
565     * @return true if the point is inside polygon.
566     */
567    public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
568        if (polygonNodes.size() < 2)
569            return false;
570
571        boolean inside = false;
572        Node p1, p2;
573
574        //iterate each side of the polygon, start with the last segment
575        Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
576
577        if (!oldPoint.isLatLonKnown()) {
578            return false;
579        }
580
581        for (Node newPoint : polygonNodes) {
582            //skip duplicate points
583            if (newPoint.equals(oldPoint)) {
584                continue;
585            }
586
587            if (!newPoint.isLatLonKnown()) {
588                return false;
589            }
590
591            //order points so p1.lat <= p2.lat
592            if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
593                p1 = oldPoint;
594                p2 = newPoint;
595            } else {
596                p1 = newPoint;
597                p2 = oldPoint;
598            }
599
600            //test if the line is crossed and if so invert the inside flag.
601            if ((newPoint.getEastNorth().getY() < point.getEastNorth().getY()) == (point.getEastNorth().getY() <= oldPoint.getEastNorth().getY())
602                    && (point.getEastNorth().getX() - p1.getEastNorth().getX()) * (p2.getEastNorth().getY() - p1.getEastNorth().getY())
603                    < (p2.getEastNorth().getX() - p1.getEastNorth().getX()) * (point.getEastNorth().getY() - p1.getEastNorth().getY()))
604            {
605                inside = !inside;
606            }
607
608            oldPoint = newPoint;
609        }
610
611        return inside;
612    }
613
614    /**
615     * Returns area of a closed way in square meters.
616     * (approximate(?), but should be OK for small areas)
617     *
618     * Relies on the current projection: Works correctly, when
619     * one unit in projected coordinates corresponds to one meter.
620     * This is true for most projections, but not for WGS84 and
621     * Mercator (EPSG:3857).
622     *
623     * @param way Way to measure, should be closed (first node is the same as last node)
624     * @return area of the closed way.
625     */
626    public static double closedWayArea(Way way) {
627
628        //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
629        double area = 0;
630        Node lastN = null;
631        for (Node n : way.getNodes()) {
632            if (lastN != null) {
633                n.getEastNorth().getX();
634
635                area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
636            }
637            lastN = n;
638        }
639        return Math.abs(area/2);
640    }
641
642    protected static double calcX(Node p1){
643        double lat1, lon1, lat2, lon2;
644        double dlon, dlat;
645
646        lat1 = p1.getCoor().lat() * Math.PI / 180.0;
647        lon1 = p1.getCoor().lon() * Math.PI / 180.0;
648        lat2 = lat1;
649        lon2 = 0;
650
651        dlon = lon2 - lon1;
652        dlat = lat2 - lat1;
653
654        double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
655        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
656        return 6367000 * c;
657    }
658
659    protected static double calcY(Node p1){
660        double lat1, lon1, lat2, lon2;
661        double dlon, dlat;
662
663        lat1 = p1.getCoor().lat() * Math.PI / 180.0;
664        lon1 = p1.getCoor().lon() * Math.PI / 180.0;
665        lat2 = 0;
666        lon2 = lon1;
667
668        dlon = lon2 - lon1;
669        dlat = lat2 - lat1;
670
671        double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
672        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
673        return 6367000 * c;
674    }
675
676    /**
677     * Determines whether a way is oriented clockwise.
678     *
679     * Internals: Assuming a closed non-looping way, compute twice the area
680     * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
681     * If the area is negative the way is ordered in a clockwise direction.
682     *
683     * See http://paulbourke.net/geometry/polyarea/
684     *
685     * @param w the way to be checked.
686     * @return true if and only if way is oriented clockwise.
687     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
688     */
689    public static boolean isClockwise(Way w) {
690        if (!w.isClosed()) {
691            throw new IllegalArgumentException("Way must be closed to check orientation.");
692        }
693
694        double area2 = 0.;
695        int nodesCount = w.getNodesCount();
696
697        for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
698            LatLon coorPrev = w.getNode(node - 1).getCoor();
699            LatLon coorCurr = w.getNode(node % nodesCount).getCoor();
700            area2 += coorPrev.lon() * coorCurr.lat();
701            area2 -= coorCurr.lon() * coorPrev.lat();
702        }
703        return area2 < 0;
704    }
705
706    /**
707     * Returns angle of a segment defined with 2 point coordinates.
708     *
709     * @param p1
710     * @param p2
711     * @return Angle in radians (-pi, pi]
712     */
713    public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
714
715        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
716        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
717
718        return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
719    }
720
721    /**
722     * Returns angle of a corner defined with 3 point coordinates.
723     *
724     * @param p1
725     * @param p2 Common endpoint
726     * @param p3
727     * @return Angle in radians (-pi, pi]
728     */
729    public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
730
731        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
732        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
733        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
734
735        Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
736        if (result <= -Math.PI) {
737            result += 2 * Math.PI;
738        }
739
740        if (result > Math.PI) {
741            result -= 2 * Math.PI;
742        }
743
744        return result;
745    }
746
747    /**
748     * Compute the centroid/barycenter of nodes
749     * @param nodes Nodes for which the centroid is wanted
750     * @return the centroid of nodes
751     * @see Geometry#getCenter
752     */
753    public static EastNorth getCentroid(List<Node> nodes) {
754
755        BigDecimal area = BigDecimal.ZERO;
756        BigDecimal north = BigDecimal.ZERO;
757        BigDecimal east = BigDecimal.ZERO;
758
759        // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
760        for (int i = 0; i < nodes.size(); i++) {
761            EastNorth n0 = nodes.get(i).getEastNorth();
762            EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
763
764            if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
765                BigDecimal x0 = new BigDecimal(n0.east());
766                BigDecimal y0 = new BigDecimal(n0.north());
767                BigDecimal x1 = new BigDecimal(n1.east());
768                BigDecimal y1 = new BigDecimal(n1.north());
769
770                BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
771
772                area = area.add(k, MathContext.DECIMAL128);
773                east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
774                north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
775            }
776        }
777
778        BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
779        area  = area.multiply(d, MathContext.DECIMAL128);
780        if (area.compareTo(BigDecimal.ZERO) != 0) {
781            north = north.divide(area, MathContext.DECIMAL128);
782            east = east.divide(area, MathContext.DECIMAL128);
783        }
784
785        return new EastNorth(east.doubleValue(), north.doubleValue());
786    }
787
788    /**
789     * Compute center of the circle closest to different nodes.
790     *
791     * Ensure exact center computation in case nodes are already aligned in circle.
792     * This is done by least square method.
793     * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
794     * Center must be intersection of all bisectors.
795     * <pre>
796     *          [ a1  b1  ]         [ -c1 ]
797     * With A = [ ... ... ] and Y = [ ... ]
798     *          [ an  bn  ]         [ -cn ]
799     * </pre>
800     * An approximation of center of circle is (At.A)^-1.At.Y
801     * @param nodes Nodes parts of the circle (at least 3)
802     * @return An approximation of the center, of null if there is no solution.
803     * @see Geometry#getCentroid
804     * @since 6934
805     */
806    public static EastNorth getCenter(List<Node> nodes) {
807        int nc = nodes.size();
808        if(nc < 3) return null;
809        /**
810         * Equation of each bisector ax + by + c = 0
811         */
812        double[] a = new double[nc];
813        double[] b = new double[nc];
814        double[] c = new double[nc];
815        // Compute equation of bisector
816        for(int i = 0; i < nc; i++) {
817            EastNorth pt1 = nodes.get(i).getEastNorth();
818            EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
819            a[i] = pt1.east() - pt2.east();
820            b[i] = pt1.north() - pt2.north();
821            double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
822            if(d == 0) return null;
823            a[i] /= d;
824            b[i] /= d;
825            double xC = (pt1.east() + pt2.east()) / 2;
826            double yC = (pt1.north() + pt2.north()) / 2;
827            c[i] = -(a[i]*xC + b[i]*yC);
828        }
829        // At.A = [aij]
830        double a11 = 0, a12 = 0, a22 = 0;
831        // At.Y = [bi]
832        double b1 = 0, b2 = 0;
833        for(int i = 0; i < nc; i++) {
834            a11 += a[i]*a[i];
835            a12 += a[i]*b[i];
836            a22 += b[i]*b[i];
837            b1 -= a[i]*c[i];
838            b2 -= b[i]*c[i];
839        }
840        // (At.A)^-1 = [invij]
841        double det = a11*a22 - a12*a12;
842        if(Math.abs(det) < 1e-5) return null;
843        double inv11 = a22/det;
844        double inv12 = -a12/det;
845        double inv22 = a11/det;
846        // center (xC, yC) = (At.A)^-1.At.y
847        double xC = inv11*b1 + inv12*b2;
848        double yC = inv12*b1 + inv22*b2;
849        return new EastNorth(xC, yC);
850    }
851
852    public static class MultiPolygonMembers {
853        public final Set<Way> outers = new HashSet<>();
854        public final Set<Way> inners = new HashSet<>();
855
856        public MultiPolygonMembers(Relation multiPolygon) {
857            for (RelationMember m : multiPolygon.getMembers()) {
858                if (m.getType().equals(OsmPrimitiveType.WAY)) {
859                    if ("outer".equals(m.getRole())) {
860                        outers.add(m.getWay());
861                    } else if ("inner".equals(m.getRole())) {
862                        inners.add(m.getWay());
863                    }
864                }
865            }
866        }
867    }
868
869    /**
870     * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
871     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
872     */
873    public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
874        return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
875    }
876
877    /**
878     * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
879     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
880     * <p>
881     * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
882     */
883    public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
884        // Extract outer/inner members from multipolygon
885        final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
886        // Construct complete rings for the inner/outer members
887        final List<MultipolygonBuilder.JoinedPolygon> outerRings;
888        final List<MultipolygonBuilder.JoinedPolygon> innerRings;
889        try {
890            outerRings = MultipolygonBuilder.joinWays(mpm.outers);
891            innerRings = MultipolygonBuilder.joinWays(mpm.inners);
892        } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
893            Main.debug("Invalid multipolygon " + multiPolygon);
894            return false;
895        }
896        // Test if object is inside an outer member
897        for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
898            if (nodes.size() == 1
899                    ? nodeInsidePolygon(nodes.get(0), out.getNodes())
900                    : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(polygonIntersection(nodes, out.getNodes()))) {
901                boolean insideInner = false;
902                // If inside an outer, check it is not inside an inner
903                for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
904                    if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
905                            && (nodes.size() == 1
906                            ? nodeInsidePolygon(nodes.get(0), in.getNodes())
907                            : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
908                        insideInner = true;
909                        break;
910                    }
911                }
912                // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
913                if (!insideInner) {
914                    // Final check using predicate
915                    if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0) /* TODO give a better representation of the outer ring to the predicate */)) {
916                        return true;
917                    }
918                }
919            }
920        }
921        return false;
922    }
923}