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.Comparator;
012import java.util.LinkedHashSet;
013import java.util.List;
014import java.util.Set;
015
016import org.openstreetmap.josm.Main;
017import org.openstreetmap.josm.command.AddCommand;
018import org.openstreetmap.josm.command.ChangeCommand;
019import org.openstreetmap.josm.command.Command;
020import org.openstreetmap.josm.data.coor.EastNorth;
021import org.openstreetmap.josm.data.coor.LatLon;
022import org.openstreetmap.josm.data.osm.BBox;
023import org.openstreetmap.josm.data.osm.Node;
024import org.openstreetmap.josm.data.osm.NodePositionComparator;
025import org.openstreetmap.josm.data.osm.Way;
026
027/**
028 * Some tools for geometry related tasks.
029 *
030 * @author viesturs
031 */
032public final class Geometry {
033    
034    private Geometry() {
035        // Hide default constructor for utils classes
036    }
037    
038    public enum PolygonIntersection {FIRST_INSIDE_SECOND, SECOND_INSIDE_FIRST, OUTSIDE, CROSSING}
039
040    /**
041     * Will find all intersection and add nodes there for list of given ways.
042     * Handles self-intersections too.
043     * And makes commands to add the intersection points to ways.
044     *
045     * Prerequisite: no two nodes have the same coordinates.
046     *
047     * @param ways  a list of ways to test
048     * @param test  if false, do not build list of Commands, just return nodes
049     * @param cmds  list of commands, typically empty when handed to this method.
050     *              Will be filled with commands that add intersection nodes to
051     *              the ways.
052     * @return list of new nodes
053     */
054    public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
055
056        int n = ways.size();
057        @SuppressWarnings("unchecked")
058        List<Node>[] newNodes = new ArrayList[n];
059        BBox[] wayBounds = new BBox[n];
060        boolean[] changedWays = new boolean[n];
061
062        Set<Node> intersectionNodes = new LinkedHashSet<Node>();
063
064        //copy node arrays for local usage.
065        for (int pos = 0; pos < n; pos ++) {
066            newNodes[pos] = new ArrayList<Node>(ways.get(pos).getNodes());
067            wayBounds[pos] = getNodesBounds(newNodes[pos]);
068            changedWays[pos] = false;
069        }
070
071        //iterate over all way pairs and introduce the intersections
072        Comparator<Node> coordsComparator = new NodePositionComparator();
073        for (int seg1Way = 0; seg1Way < n; seg1Way ++) {
074            for (int seg2Way = seg1Way; seg2Way < n; seg2Way ++) {
075
076                //do not waste time on bounds that do not intersect
077                if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
078                    continue;
079                }
080
081                List<Node> way1Nodes = newNodes[seg1Way];
082                List<Node> way2Nodes = newNodes[seg2Way];
083
084                //iterate over primary segmemt
085                for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos ++) {
086
087                    //iterate over secondary segment
088                    int seg2Start = seg1Way != seg2Way ? 0: seg1Pos + 2;//skip the adjacent segment
089
090                    for (int seg2Pos = seg2Start; seg2Pos + 1< way2Nodes.size(); seg2Pos ++) {
091
092                        //need to get them again every time, because other segments may be changed
093                        Node seg1Node1 = way1Nodes.get(seg1Pos);
094                        Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
095                        Node seg2Node1 = way2Nodes.get(seg2Pos);
096                        Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
097
098                        int commonCount = 0;
099                        //test if we have common nodes to add.
100                        if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
101                            commonCount ++;
102
103                            if (seg1Way == seg2Way &&
104                                    seg1Pos == 0 &&
105                                    seg2Pos == way2Nodes.size() -2) {
106                                //do not add - this is first and last segment of the same way.
107                            } else {
108                                intersectionNodes.add(seg1Node1);
109                            }
110                        }
111
112                        if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
113                            commonCount ++;
114
115                            intersectionNodes.add(seg1Node2);
116                        }
117
118                        //no common nodes - find intersection
119                        if (commonCount == 0) {
120                            EastNorth intersection = getSegmentSegmentIntersection(
121                                    seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
122                                    seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
123
124                            if (intersection != null) {
125                                if (test) {
126                                    intersectionNodes.add(seg2Node1);
127                                    return intersectionNodes;
128                                }
129
130                                Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
131                                Node intNode = newNode;
132                                boolean insertInSeg1 = false;
133                                boolean insertInSeg2 = false;
134                                //find if the intersection point is at end point of one of the segments, if so use that point
135
136                                //segment 1
137                                if (coordsComparator.compare(newNode, seg1Node1) == 0) {
138                                    intNode = seg1Node1;
139                                } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
140                                    intNode = seg1Node2;
141                                } else {
142                                    insertInSeg1 = true;
143                                }
144
145                                //segment 2
146                                if (coordsComparator.compare(newNode, seg2Node1) == 0) {
147                                    intNode = seg2Node1;
148                                } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
149                                    intNode = seg2Node2;
150                                } else {
151                                    insertInSeg2 = true;
152                                }
153
154                                if (insertInSeg1) {
155                                    way1Nodes.add(seg1Pos +1, intNode);
156                                    changedWays[seg1Way] = true;
157
158                                    //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
159                                    if (seg2Way == seg1Way) {
160                                        seg2Pos ++;
161                                    }
162                                }
163
164                                if (insertInSeg2) {
165                                    way2Nodes.add(seg2Pos +1, intNode);
166                                    changedWays[seg2Way] = true;
167
168                                    //Do not need to compare again to already split segment
169                                    seg2Pos ++;
170                                }
171
172                                intersectionNodes.add(intNode);
173
174                                if (intNode == newNode) {
175                                    cmds.add(new AddCommand(intNode));
176                                }
177                            }
178                        }
179                        else if (test && !intersectionNodes.isEmpty())
180                            return intersectionNodes;
181                    }
182                }
183            }
184        }
185
186
187        for (int pos = 0; pos < ways.size(); pos ++) {
188            if (!changedWays[pos]) {
189                continue;
190            }
191
192            Way way = ways.get(pos);
193            Way newWay = new Way(way);
194            newWay.setNodes(newNodes[pos]);
195
196            cmds.add(new ChangeCommand(way, newWay));
197        }
198
199        return intersectionNodes;
200    }
201
202    private static BBox getNodesBounds(List<Node> nodes) {
203
204        BBox bounds = new BBox(nodes.get(0));
205        for (Node n: nodes) {
206            bounds.add(n.getCoor());
207        }
208        return bounds;
209    }
210
211    /**
212     * Tests if given point is to the right side of path consisting of 3 points.
213     *
214     * (Imagine the path is continued beyond the endpoints, so you get two rays
215     * starting from lineP2 and going through lineP1 and lineP3 respectively
216     * which divide the plane into two parts. The test returns true, if testPoint
217     * lies in the part that is to the right when traveling in the direction
218     * lineP1, lineP2, lineP3.)
219     *
220     * @param lineP1 first point in path
221     * @param lineP2 second point in path
222     * @param lineP3 third point in path
223     * @param testPoint
224     * @return true if to the right side, false otherwise
225     */
226    public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
227        boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
228        boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
229        boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
230
231        if (pathBendToRight)
232            return rightOfSeg1 && rightOfSeg2;
233        else
234            return !(!rightOfSeg1 && !rightOfSeg2);
235    }
236
237    /**
238     * This method tests if secondNode is clockwise to first node.
239     * @param commonNode starting point for both vectors
240     * @param firstNode first vector end node
241     * @param secondNode second vector end node
242     * @return true if first vector is clockwise before second vector.
243     */
244    public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
245        return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
246    }
247
248    /**
249     * Finds the intersection of two line segments
250     * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
251     */
252    public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
253
254        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
255        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
256        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
257        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
258
259        double x1 = p1.getX();
260        double y1 = p1.getY();
261        double x2 = p2.getX();
262        double y2 = p2.getY();
263        double x3 = p3.getX();
264        double y3 = p3.getY();
265        double x4 = p4.getX();
266        double y4 = p4.getY();
267
268        //TODO: do this locally.
269        //TODO: remove this check after careful testing
270        if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
271
272        // solve line-line intersection in parametric form:
273        // (x1,y1) + (x2-x1,y2-y1)* u  = (x3,y3) + (x4-x3,y4-y3)* v
274        // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
275        // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
276
277        double a1 = x2 - x1;
278        double b1 = x3 - x4;
279        double c1 = x3 - x1;
280
281        double a2 = y2 - y1;
282        double b2 = y3 - y4;
283        double c2 = y3 - y1;
284
285        // Solve the equations
286        double det = a1*b2 - a2*b1;
287
288        double uu = b2*c1 - b1*c2 ;
289        double vv = a1*c2 - a2*c1;
290        double mag = Math.abs(uu)+Math.abs(vv);
291
292        if (Math.abs(det) > 1e-12 * mag) {
293            double u = uu/det, v = vv/det;
294            if (u>-1e-8 && u < 1+1e-8 && v>-1e-8 && v < 1+1e-8 ) {
295                if (u<0) u=0;
296                if (u>1) u=1.0;
297                return new EastNorth(x1+a1*u, y1+a2*u);
298            } else {
299                return null;
300            }
301        } else {
302            // parallel lines
303            return null;
304        }
305    }
306
307    /**
308     * Finds the intersection of two lines of infinite length.
309     * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
310     * @throws IllegalArgumentException if a parameter is null or without valid coordinates
311     */
312    public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
313
314        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
315        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
316        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
317        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
318
319        if (!p1.isValid()) throw new IllegalArgumentException();
320
321        // Convert line from (point, point) form to ax+by=c
322        double a1 = p2.getY() - p1.getY();
323        double b1 = p1.getX() - p2.getX();
324        double c1 = p2.getX() * p1.getY() - p1.getX() * p2.getY();
325
326        double a2 = p4.getY() - p3.getY();
327        double b2 = p3.getX() - p4.getX();
328        double c2 = p4.getX() * p3.getY() - p3.getX() * p4.getY();
329
330        // Solve the equations
331        double det = a1 * b2 - a2 * b1;
332        if (det == 0)
333            return null; // Lines are parallel
334
335        return new EastNorth((b1 * c2 - b2 * c1) / det, (a2 * c1 - a1 * c2) / det);
336    }
337
338    public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
339
340        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
341        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
342        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
343        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
344
345        // Convert line from (point, point) form to ax+by=c
346        double a1 = p2.getY() - p1.getY();
347        double b1 = p1.getX() - p2.getX();
348
349        double a2 = p4.getY() - p3.getY();
350        double b2 = p3.getX() - p4.getX();
351
352        // Solve the equations
353        double det = a1 * b2 - a2 * b1;
354        // remove influence of of scaling factor
355        det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
356        return Math.abs(det) < 1e-3;
357    }
358
359    private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
360        CheckParameterUtil.ensureParameterNotNull(p1, "p1");
361        CheckParameterUtil.ensureParameterNotNull(p2, "p2");
362        CheckParameterUtil.ensureParameterNotNull(point, "point");
363
364        double ldx = p2.getX() - p1.getX();
365        double ldy = p2.getY() - p1.getY();
366
367        if (ldx == 0 && ldy == 0) //segment zero length
368            return p1;
369
370        double pdx = point.getX() - p1.getX();
371        double pdy = point.getY() - p1.getY();
372
373        double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
374
375        if (segmentOnly && offset <= 0)
376            return p1;
377        else if (segmentOnly && offset >= 1)
378            return p2;
379        else
380            return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
381    }
382
383    /**
384     * Calculates closest point to a line segment.
385     * @param segmentP1 First point determining line segment
386     * @param segmentP2 Second point determining line segment
387     * @param point Point for which a closest point is searched on line segment [P1,P2]
388     * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
389     * a new point if closest point is between segmentP1 and segmentP2.
390     * @since 3650
391     * @see #closestPointToLine
392     */
393    public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
394        return closestPointTo(segmentP1, segmentP2, point, true);
395    }
396
397    /**
398     * Calculates closest point to a line.
399     * @param lineP1 First point determining line
400     * @param lineP2 Second point determining line
401     * @param point Point for which a closest point is searched on line (P1,P2)
402     * @return The closest point found on line. It may be outside the segment [P1,P2].
403     * @since 4134
404     * @see #closestPointToSegment
405     */
406    public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
407        return closestPointTo(lineP1, lineP2, point, false);
408    }
409
410    /**
411     * This method tests if secondNode is clockwise to first node.
412     *
413     * The line through the two points commonNode and firstNode divides the
414     * plane into two parts. The test returns true, if secondNode lies in
415     * the part that is to the right when traveling in the direction from
416     * commonNode to firstNode.
417     *
418     * @param commonNode starting point for both vectors
419     * @param firstNode first vector end node
420     * @param secondNode second vector end node
421     * @return true if first vector is clockwise before second vector.
422     */
423    public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
424
425        CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
426        CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
427        CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
428
429        double dy1 = (firstNode.getY() - commonNode.getY());
430        double dy2 = (secondNode.getY() - commonNode.getY());
431        double dx1 = (firstNode.getX() - commonNode.getX());
432        double dx2 = (secondNode.getX() - commonNode.getX());
433
434        return dy1 * dx2 - dx1 * dy2 > 0;
435    }
436
437    private static Area getArea(List<Node> polygon) {
438        Path2D path = new Path2D.Double();
439
440        boolean begin = true;
441        for (Node n : polygon) {
442            if (begin) {
443                path.moveTo(n.getEastNorth().getX(), n.getEastNorth().getY());
444                begin = false;
445            } else {
446                path.lineTo(n.getEastNorth().getX(), n.getEastNorth().getY());
447            }
448        }
449        if (!begin) {
450            path.closePath();
451        }
452
453        return new Area(path);
454    }
455
456    /**
457     * Tests if two polygons intersect.
458     * @param first
459     * @param second
460     * @return intersection kind
461     */
462    public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
463
464        Area a1 = getArea(first);
465        Area a2 = getArea(second);
466
467        Area inter = new Area(a1);
468        inter.intersect(a2);
469
470        Rectangle bounds = inter.getBounds();
471
472        if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= 1.0) {
473            return PolygonIntersection.OUTSIDE;
474        } else if (inter.equals(a1)) {
475            return PolygonIntersection.FIRST_INSIDE_SECOND;
476        } else if (inter.equals(a2)) {
477            return PolygonIntersection.SECOND_INSIDE_FIRST;
478        } else {
479            return PolygonIntersection.CROSSING;
480        }
481    }
482
483    /**
484     * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
485     * @param polygonNodes list of nodes from polygon path.
486     * @param point the point to test
487     * @return true if the point is inside polygon.
488     */
489    public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
490        if (polygonNodes.size() < 2)
491            return false;
492
493        boolean inside = false;
494        Node p1, p2;
495
496        //iterate each side of the polygon, start with the last segment
497        Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
498
499        for (Node newPoint : polygonNodes) {
500            //skip duplicate points
501            if (newPoint.equals(oldPoint)) {
502                continue;
503            }
504
505            //order points so p1.lat <= p2.lat
506            if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
507                p1 = oldPoint;
508                p2 = newPoint;
509            } else {
510                p1 = newPoint;
511                p2 = oldPoint;
512            }
513
514            //test if the line is crossed and if so invert the inside flag.
515            if ((newPoint.getEastNorth().getY() < point.getEastNorth().getY()) == (point.getEastNorth().getY() <= oldPoint.getEastNorth().getY())
516                    && (point.getEastNorth().getX() - p1.getEastNorth().getX()) * (p2.getEastNorth().getY() - p1.getEastNorth().getY())
517                    < (p2.getEastNorth().getX() - p1.getEastNorth().getX()) * (point.getEastNorth().getY() - p1.getEastNorth().getY()))
518            {
519                inside = !inside;
520            }
521
522            oldPoint = newPoint;
523        }
524
525        return inside;
526    }
527
528    /**
529     * Returns area of a closed way in square meters.
530     * (approximate(?), but should be OK for small areas)
531     *
532     * Relies on the current projection: Works correctly, when
533     * one unit in projected coordinates corresponds to one meter.
534     * This is true for most projections, but not for WGS84 and
535     * Mercator (EPSG:3857).
536     *
537     * @param way Way to measure, should be closed (first node is the same as last node)
538     * @return area of the closed way.
539     */
540    public static double closedWayArea(Way way) {
541
542        //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
543        double area = 0;
544        Node lastN = null;
545        for (Node n : way.getNodes()) {
546            if (lastN != null) {
547                n.getEastNorth().getX();
548
549                area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
550            }
551            lastN = n;
552        }
553        return Math.abs(area/2);
554    }
555
556    protected static double calcX(Node p1){
557        double lat1, lon1, lat2, lon2;
558        double dlon, dlat;
559
560        lat1 = p1.getCoor().lat() * Math.PI / 180.0;
561        lon1 = p1.getCoor().lon() * Math.PI / 180.0;
562        lat2 = lat1;
563        lon2 = 0;
564
565        dlon = lon2 - lon1;
566        dlat = lat2 - lat1;
567
568        double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
569        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
570        return 6367000 * c;
571    }
572
573    protected static double calcY(Node p1){
574        double lat1, lon1, lat2, lon2;
575        double dlon, dlat;
576
577        lat1 = p1.getCoor().lat() * Math.PI / 180.0;
578        lon1 = p1.getCoor().lon() * Math.PI / 180.0;
579        lat2 = 0;
580        lon2 = lon1;
581
582        dlon = lon2 - lon1;
583        dlat = lat2 - lat1;
584
585        double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
586        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
587        return 6367000 * c;
588    }
589
590    /**
591     * Determines whether a way is oriented clockwise.
592     *
593     * Internals: Assuming a closed non-looping way, compute twice the area
594     * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
595     * If the area is negative the way is ordered in a clockwise direction.
596     *
597     * See http://paulbourke.net/geometry/polyarea/
598     *
599     * @param w the way to be checked.
600     * @return true if and only if way is oriented clockwise.
601     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
602     */
603    public static boolean isClockwise(Way w) {
604        if (!w.isClosed()) {
605            throw new IllegalArgumentException("Way must be closed to check orientation.");
606        }
607
608        double area2 = 0.;
609        int nodesCount = w.getNodesCount();
610
611        for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
612            LatLon coorPrev = w.getNode(node - 1).getCoor();
613            LatLon coorCurr = w.getNode(node % nodesCount).getCoor();
614            area2 += coorPrev.lon() * coorCurr.lat();
615            area2 -= coorCurr.lon() * coorPrev.lat();
616        }
617        return area2 < 0;
618    }
619
620    /**
621     * Returns angle of a segment defined with 2 point coordinates.
622     *
623     * @param p1
624     * @param p2
625     * @return Angle in radians (-pi, pi]
626     */
627    public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
628
629        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
630        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
631
632        return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
633    }
634
635    /**
636     * Returns angle of a corner defined with 3 point coordinates.
637     *
638     * @param p1
639     * @param p2 Common endpoint
640     * @param p3
641     * @return Angle in radians (-pi, pi]
642     */
643    public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
644
645        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
646        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
647        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
648
649        Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
650        if (result <= -Math.PI) {
651            result += 2 * Math.PI;
652        }
653
654        if (result > Math.PI) {
655            result -= 2 * Math.PI;
656        }
657
658        return result;
659    }
660
661    /**
662     * Compute the centroid of nodes
663     * @param nodes Nodes for which the centroid is wanted
664     * @return the centroid of nodes
665     */
666    public static EastNorth getCentroid(List<Node> nodes) {
667
668        BigDecimal area = BigDecimal.ZERO;
669        BigDecimal north = BigDecimal.ZERO;
670        BigDecimal east = BigDecimal.ZERO;
671
672        // See http://en.wikipedia.org/w/index.php?title=Centroid&oldid=294224857#Centroid_of_polygon for the equation used here
673        for (int i = 0; i < nodes.size(); i++) {
674            EastNorth n0 = nodes.get(i).getEastNorth();
675            EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
676
677            if (n0.isValid() && n1.isValid()) {
678                BigDecimal x0 = new BigDecimal(n0.east());
679                BigDecimal y0 = new BigDecimal(n0.north());
680                BigDecimal x1 = new BigDecimal(n1.east());
681                BigDecimal y1 = new BigDecimal(n1.north());
682
683                BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
684
685                area = area.add(k, MathContext.DECIMAL128);
686                east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
687                north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
688            }
689        }
690
691        BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
692        area  = area.multiply(d, MathContext.DECIMAL128);
693        if (area.compareTo(BigDecimal.ZERO) != 0) {
694            north = north.divide(area, MathContext.DECIMAL128);
695            east = east.divide(area, MathContext.DECIMAL128);
696        }
697
698        return new EastNorth(east.doubleValue(), north.doubleValue());
699    }
700
701    /**
702     * Returns the coordinate of intersection of segment sp1-sp2 and an altitude
703     * to it starting at point ap. If the line defined with sp1-sp2 intersects
704     * its altitude out of sp1-sp2, null is returned.
705     *
706     * @param sp1
707     * @param sp2
708     * @param ap
709     * @return Intersection coordinate or null
710     */
711    public static EastNorth getSegmentAltituteIntersection(EastNorth sp1, EastNorth sp2, EastNorth ap) {
712
713        CheckParameterUtil.ensureValidCoordinates(sp1, "sp1");
714        CheckParameterUtil.ensureValidCoordinates(sp2, "sp2");
715        CheckParameterUtil.ensureValidCoordinates(ap, "ap");
716
717        Double segmentLenght = sp1.distance(sp2);
718        Double altitudeAngle = getSegmentAngle(sp1, sp2) + Math.PI / 2;
719
720        // Taking a random point on the altitude line (angle is known).
721        EastNorth ap2 = new EastNorth(ap.east() + 1000
722                * Math.cos(altitudeAngle), ap.north() + 1000
723                * Math.sin(altitudeAngle));
724
725        // Finding the intersection of two lines
726        EastNorth resultCandidate = Geometry.getLineLineIntersection(sp1, sp2,
727                ap, ap2);
728
729        // Filtering result
730        if (resultCandidate != null
731                && resultCandidate.distance(sp1) * .999 < segmentLenght
732                && resultCandidate.distance(sp2) * .999 < segmentLenght) {
733            return resultCandidate;
734        } else {
735            return null;
736        }
737    }
738}