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.LinkedHashSet;
015import java.util.List;
016import java.util.Set;
017import java.util.function.Predicate;
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.MultipolygonBuilder.JoinedPolygon;
028import org.openstreetmap.josm.data.osm.Node;
029import org.openstreetmap.josm.data.osm.NodePositionComparator;
030import org.openstreetmap.josm.data.osm.OsmPrimitive;
031import org.openstreetmap.josm.data.osm.Relation;
032import org.openstreetmap.josm.data.osm.Way;
033import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon;
034import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache;
035import org.openstreetmap.josm.data.projection.Projection;
036import org.openstreetmap.josm.data.projection.Projections;
037
038/**
039 * Some tools for geometry related tasks.
040 *
041 * @author viesturs
042 */
043public final class Geometry {
044
045    private Geometry() {
046        // Hide default constructor for utils classes
047    }
048
049    public enum PolygonIntersection {
050        FIRST_INSIDE_SECOND,
051        SECOND_INSIDE_FIRST,
052        OUTSIDE,
053        CROSSING
054    }
055
056    /**
057     * Will find all intersection and add nodes there for list of given ways.
058     * Handles self-intersections too.
059     * And makes commands to add the intersection points to ways.
060     *
061     * Prerequisite: no two nodes have the same coordinates.
062     *
063     * @param ways  a list of ways to test
064     * @param test  if false, do not build list of Commands, just return nodes
065     * @param cmds  list of commands, typically empty when handed to this method.
066     *              Will be filled with commands that add intersection nodes to
067     *              the ways.
068     * @return list of new nodes
069     */
070    public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
071
072        int n = ways.size();
073        @SuppressWarnings("unchecked")
074        List<Node>[] newNodes = new ArrayList[n];
075        BBox[] wayBounds = new BBox[n];
076        boolean[] changedWays = new boolean[n];
077
078        Set<Node> intersectionNodes = new LinkedHashSet<>();
079
080        //copy node arrays for local usage.
081        for (int pos = 0; pos < n; pos++) {
082            newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
083            wayBounds[pos] = getNodesBounds(newNodes[pos]);
084            changedWays[pos] = false;
085        }
086
087        //iterate over all way pairs and introduce the intersections
088        Comparator<Node> coordsComparator = new NodePositionComparator();
089        for (int seg1Way = 0; seg1Way < n; seg1Way++) {
090            for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
091
092                //do not waste time on bounds that do not intersect
093                if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
094                    continue;
095                }
096
097                List<Node> way1Nodes = newNodes[seg1Way];
098                List<Node> way2Nodes = newNodes[seg2Way];
099
100                //iterate over primary segmemt
101                for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
102
103                    //iterate over secondary segment
104                    int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
105
106                    for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
107
108                        //need to get them again every time, because other segments may be changed
109                        Node seg1Node1 = way1Nodes.get(seg1Pos);
110                        Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
111                        Node seg2Node1 = way2Nodes.get(seg2Pos);
112                        Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
113
114                        int commonCount = 0;
115                        //test if we have common nodes to add.
116                        if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
117                            commonCount++;
118
119                            if (seg1Way == seg2Way &&
120                                    seg1Pos == 0 &&
121                                    seg2Pos == way2Nodes.size() -2) {
122                                //do not add - this is first and last segment of the same way.
123                            } else {
124                                intersectionNodes.add(seg1Node1);
125                            }
126                        }
127
128                        if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
129                            commonCount++;
130
131                            intersectionNodes.add(seg1Node2);
132                        }
133
134                        //no common nodes - find intersection
135                        if (commonCount == 0) {
136                            EastNorth intersection = getSegmentSegmentIntersection(
137                                    seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
138                                    seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
139
140                            if (intersection != null) {
141                                if (test) {
142                                    intersectionNodes.add(seg2Node1);
143                                    return intersectionNodes;
144                                }
145
146                                Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
147                                Node intNode = newNode;
148                                boolean insertInSeg1 = false;
149                                boolean insertInSeg2 = false;
150                                //find if the intersection point is at end point of one of the segments, if so use that point
151
152                                //segment 1
153                                if (coordsComparator.compare(newNode, seg1Node1) == 0) {
154                                    intNode = seg1Node1;
155                                } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
156                                    intNode = seg1Node2;
157                                } else {
158                                    insertInSeg1 = true;
159                                }
160
161                                //segment 2
162                                if (coordsComparator.compare(newNode, seg2Node1) == 0) {
163                                    intNode = seg2Node1;
164                                } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
165                                    intNode = seg2Node2;
166                                } else {
167                                    insertInSeg2 = true;
168                                }
169
170                                if (insertInSeg1) {
171                                    way1Nodes.add(seg1Pos +1, intNode);
172                                    changedWays[seg1Way] = true;
173
174                                    //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
175                                    if (seg2Way == seg1Way) {
176                                        seg2Pos++;
177                                    }
178                                }
179
180                                if (insertInSeg2) {
181                                    way2Nodes.add(seg2Pos +1, intNode);
182                                    changedWays[seg2Way] = true;
183
184                                    //Do not need to compare again to already split segment
185                                    seg2Pos++;
186                                }
187
188                                intersectionNodes.add(intNode);
189
190                                if (intNode == newNode) {
191                                    cmds.add(new AddCommand(intNode));
192                                }
193                            }
194                        } else if (test && !intersectionNodes.isEmpty())
195                            return intersectionNodes;
196                    }
197                }
198            }
199        }
200
201
202        for (int pos = 0; pos < ways.size(); pos++) {
203            if (!changedWays[pos]) {
204                continue;
205            }
206
207            Way way = ways.get(pos);
208            Way newWay = new Way(way);
209            newWay.setNodes(newNodes[pos]);
210
211            cmds.add(new ChangeCommand(way, newWay));
212        }
213
214        return intersectionNodes;
215    }
216
217    private static BBox getNodesBounds(List<Node> nodes) {
218
219        BBox bounds = new BBox(nodes.get(0));
220        for (Node n: nodes) {
221            bounds.add(n.getCoor());
222        }
223        return bounds;
224    }
225
226    /**
227     * Tests if given point is to the right side of path consisting of 3 points.
228     *
229     * (Imagine the path is continued beyond the endpoints, so you get two rays
230     * starting from lineP2 and going through lineP1 and lineP3 respectively
231     * which divide the plane into two parts. The test returns true, if testPoint
232     * lies in the part that is to the right when traveling in the direction
233     * lineP1, lineP2, lineP3.)
234     *
235     * @param lineP1 first point in path
236     * @param lineP2 second point in path
237     * @param lineP3 third point in path
238     * @param testPoint point to test
239     * @return true if to the right side, false otherwise
240     */
241    public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
242        boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
243        boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
244        boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
245
246        if (pathBendToRight)
247            return rightOfSeg1 && rightOfSeg2;
248        else
249            return !(!rightOfSeg1 && !rightOfSeg2);
250    }
251
252    /**
253     * This method tests if secondNode is clockwise to first node.
254     * @param commonNode starting point for both vectors
255     * @param firstNode first vector end node
256     * @param secondNode second vector end node
257     * @return true if first vector is clockwise before second vector.
258     */
259    public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
260        return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
261    }
262
263    /**
264     * Finds the intersection of two line segments.
265     * @param p1 the coordinates of the start point of the first specified line segment
266     * @param p2 the coordinates of the end point of the first specified line segment
267     * @param p3 the coordinates of the start point of the second specified line segment
268     * @param p4 the coordinates of the end point of the second specified line segment
269     * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
270     */
271    public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
272
273        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
274        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
275        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
276        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
277
278        double x1 = p1.getX();
279        double y1 = p1.getY();
280        double x2 = p2.getX();
281        double y2 = p2.getY();
282        double x3 = p3.getX();
283        double y3 = p3.getY();
284        double x4 = p4.getX();
285        double y4 = p4.getY();
286
287        //TODO: do this locally.
288        //TODO: remove this check after careful testing
289        if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
290
291        // solve line-line intersection in parametric form:
292        // (x1,y1) + (x2-x1,y2-y1)* u  = (x3,y3) + (x4-x3,y4-y3)* v
293        // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
294        // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
295
296        double a1 = x2 - x1;
297        double b1 = x3 - x4;
298        double c1 = x3 - x1;
299
300        double a2 = y2 - y1;
301        double b2 = y3 - y4;
302        double c2 = y3 - y1;
303
304        // Solve the equations
305        double det = a1*b2 - a2*b1;
306
307        double uu = b2*c1 - b1*c2;
308        double vv = a1*c2 - a2*c1;
309        double mag = Math.abs(uu)+Math.abs(vv);
310
311        if (Math.abs(det) > 1e-12 * mag) {
312            double u = uu/det, v = vv/det;
313            if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
314                if (u < 0) u = 0;
315                if (u > 1) u = 1.0;
316                return new EastNorth(x1+a1*u, y1+a2*u);
317            } else {
318                return null;
319            }
320        } else {
321            // parallel lines
322            return null;
323        }
324    }
325
326    /**
327     * Finds the intersection of two lines of infinite length.
328     *
329     * @param p1 first point on first line
330     * @param p2 second point on first line
331     * @param p3 first point on second line
332     * @param p4 second point on second line
333     * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
334     * @throws IllegalArgumentException if a parameter is null or without valid coordinates
335     */
336    public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
337
338        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
339        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
340        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
341        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
342
343        if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
344
345        // Basically, the formula from wikipedia is used:
346        //  https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
347        // However, large numbers lead to rounding errors (see #10286).
348        // To avoid this, p1 is first substracted from each of the points:
349        //  p1' = 0
350        //  p2' = p2 - p1
351        //  p3' = p3 - p1
352        //  p4' = p4 - p1
353        // In the end, p1 is added to the intersection point of segment p1'/p2'
354        // and segment p3'/p4'.
355
356        // Convert line from (point, point) form to ax+by=c
357        double a1 = p2.getY() - p1.getY();
358        double b1 = p1.getX() - p2.getX();
359
360        double a2 = p4.getY() - p3.getY();
361        double b2 = p3.getX() - p4.getX();
362
363        // Solve the equations
364        double det = a1 * b2 - a2 * b1;
365        if (det == 0)
366            return null; // Lines are parallel
367
368        double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
369
370        return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
371    }
372
373    public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
374
375        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
376        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
377        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
378        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
379
380        // Convert line from (point, point) form to ax+by=c
381        double a1 = p2.getY() - p1.getY();
382        double b1 = p1.getX() - p2.getX();
383
384        double a2 = p4.getY() - p3.getY();
385        double b2 = p3.getX() - p4.getX();
386
387        // Solve the equations
388        double det = a1 * b2 - a2 * b1;
389        // remove influence of of scaling factor
390        det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
391        return Math.abs(det) < 1e-3;
392    }
393
394    private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
395        CheckParameterUtil.ensureParameterNotNull(p1, "p1");
396        CheckParameterUtil.ensureParameterNotNull(p2, "p2");
397        CheckParameterUtil.ensureParameterNotNull(point, "point");
398
399        double ldx = p2.getX() - p1.getX();
400        double ldy = p2.getY() - p1.getY();
401
402        //segment zero length
403        if (ldx == 0 && ldy == 0)
404            return p1;
405
406        double pdx = point.getX() - p1.getX();
407        double pdy = point.getY() - p1.getY();
408
409        double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
410
411        if (segmentOnly && offset <= 0)
412            return p1;
413        else if (segmentOnly && offset >= 1)
414            return p2;
415        else
416            return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
417    }
418
419    /**
420     * Calculates closest point to a line segment.
421     * @param segmentP1 First point determining line segment
422     * @param segmentP2 Second point determining line segment
423     * @param point Point for which a closest point is searched on line segment [P1,P2]
424     * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
425     * a new point if closest point is between segmentP1 and segmentP2.
426     * @see #closestPointToLine
427     * @since 3650
428     */
429    public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
430        return closestPointTo(segmentP1, segmentP2, point, true);
431    }
432
433    /**
434     * Calculates closest point to a line.
435     * @param lineP1 First point determining line
436     * @param lineP2 Second point determining line
437     * @param point Point for which a closest point is searched on line (P1,P2)
438     * @return The closest point found on line. It may be outside the segment [P1,P2].
439     * @see #closestPointToSegment
440     * @since 4134
441     */
442    public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
443        return closestPointTo(lineP1, lineP2, point, false);
444    }
445
446    /**
447     * This method tests if secondNode is clockwise to first node.
448     *
449     * The line through the two points commonNode and firstNode divides the
450     * plane into two parts. The test returns true, if secondNode lies in
451     * the part that is to the right when traveling in the direction from
452     * commonNode to firstNode.
453     *
454     * @param commonNode starting point for both vectors
455     * @param firstNode first vector end node
456     * @param secondNode second vector end node
457     * @return true if first vector is clockwise before second vector.
458     */
459    public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
460
461        CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
462        CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
463        CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
464
465        double dy1 = firstNode.getY() - commonNode.getY();
466        double dy2 = secondNode.getY() - commonNode.getY();
467        double dx1 = firstNode.getX() - commonNode.getX();
468        double dx2 = secondNode.getX() - commonNode.getX();
469
470        return dy1 * dx2 - dx1 * dy2 > 0;
471    }
472
473    /**
474     * Returns the Area of a polygon, from its list of nodes.
475     * @param polygon List of nodes forming polygon (EastNorth coordinates)
476     * @return Area for the given list of nodes
477     * @since 6841
478     */
479    public static Area getArea(List<Node> polygon) {
480        Path2D path = new Path2D.Double();
481
482        boolean begin = true;
483        for (Node n : polygon) {
484            EastNorth en = n.getEastNorth();
485            if (en != null) {
486                if (begin) {
487                    path.moveTo(en.getX(), en.getY());
488                    begin = false;
489                } else {
490                    path.lineTo(en.getX(), en.getY());
491                }
492            }
493        }
494        if (!begin) {
495            path.closePath();
496        }
497
498        return new Area(path);
499    }
500
501    /**
502     * Returns the Area of a polygon, from its list of nodes.
503     * @param polygon List of nodes forming polygon (LatLon coordinates)
504     * @return Area for the given list of nodes
505     * @since 6841
506     */
507    public static Area getAreaLatLon(List<Node> polygon) {
508        Path2D path = new Path2D.Double();
509
510        boolean begin = true;
511        for (Node n : polygon) {
512            if (begin) {
513                path.moveTo(n.getCoor().lon(), n.getCoor().lat());
514                begin = false;
515            } else {
516                path.lineTo(n.getCoor().lon(), n.getCoor().lat());
517            }
518        }
519        if (!begin) {
520            path.closePath();
521        }
522
523        return new Area(path);
524    }
525
526    /**
527     * Tests if two polygons intersect.
528     * @param first List of nodes forming first polygon
529     * @param second List of nodes forming second polygon
530     * @return intersection kind
531     */
532    public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
533        Area a1 = getArea(first);
534        Area a2 = getArea(second);
535        return polygonIntersection(a1, a2);
536    }
537
538    /**
539     * Tests if two polygons intersect.
540     * @param a1 Area of first polygon
541     * @param a2 Area of second polygon
542     * @return intersection kind
543     * @since 6841
544     */
545    public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
546        return polygonIntersection(a1, a2, 1.0);
547    }
548
549    /**
550     * Tests if two polygons intersect.
551     * @param a1 Area of first polygon
552     * @param a2 Area of second polygon
553     * @param eps an area threshold, everything below is considered an empty intersection
554     * @return intersection kind
555     */
556    public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
557
558        Area inter = new Area(a1);
559        inter.intersect(a2);
560
561        Rectangle bounds = inter.getBounds();
562
563        if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
564            return PolygonIntersection.OUTSIDE;
565        } else if (a2.getBounds2D().contains(a1.getBounds2D()) && inter.equals(a1)) {
566            return PolygonIntersection.FIRST_INSIDE_SECOND;
567        } else if (a1.getBounds2D().contains(a2.getBounds2D()) && inter.equals(a2)) {
568            return PolygonIntersection.SECOND_INSIDE_FIRST;
569        } else {
570            return PolygonIntersection.CROSSING;
571        }
572    }
573
574    /**
575     * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
576     * @param polygonNodes list of nodes from polygon path.
577     * @param point the point to test
578     * @return true if the point is inside polygon.
579     */
580    public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
581        if (polygonNodes.size() < 2)
582            return false;
583
584        //iterate each side of the polygon, start with the last segment
585        Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
586
587        if (!oldPoint.isLatLonKnown()) {
588            return false;
589        }
590
591        boolean inside = false;
592        Node p1, p2;
593
594        for (Node newPoint : polygonNodes) {
595            //skip duplicate points
596            if (newPoint.equals(oldPoint)) {
597                continue;
598            }
599
600            if (!newPoint.isLatLonKnown()) {
601                return false;
602            }
603
604            //order points so p1.lat <= p2.lat
605            if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
606                p1 = oldPoint;
607                p2 = newPoint;
608            } else {
609                p1 = newPoint;
610                p2 = oldPoint;
611            }
612
613            EastNorth pEN = point.getEastNorth();
614            EastNorth opEN = oldPoint.getEastNorth();
615            EastNorth npEN = newPoint.getEastNorth();
616            EastNorth p1EN = p1.getEastNorth();
617            EastNorth p2EN = p2.getEastNorth();
618
619            if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
620                //test if the line is crossed and if so invert the inside flag.
621                if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
622                        && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
623                        < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
624                    inside = !inside;
625                }
626            }
627
628            oldPoint = newPoint;
629        }
630
631        return inside;
632    }
633
634    /**
635     * Returns area of a closed way in square meters.
636     *
637     * @param way Way to measure, should be closed (first node is the same as last node)
638     * @return area of the closed way.
639     */
640    public static double closedWayArea(Way way) {
641        return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea();
642    }
643
644    /**
645     * Returns area of a multipolygon in square meters.
646     *
647     * @param multipolygon the multipolygon to measure
648     * @return area of the multipolygon.
649     */
650    public static double multipolygonArea(Relation multipolygon) {
651        double area = 0.0;
652        final Multipolygon mp = Main.map == null || Main.map.mapView == null
653                ? new Multipolygon(multipolygon)
654                : MultipolygonCache.getInstance().get(Main.map.mapView, multipolygon);
655        for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) {
656            area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea();
657        }
658        return area;
659    }
660
661    /**
662     * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives
663     *
664     * @param osm the primitive to measure
665     * @return area of the primitive, or {@code null}
666     */
667    public static Double computeArea(OsmPrimitive osm) {
668        if (osm instanceof Way && ((Way) osm).isClosed()) {
669            return closedWayArea((Way) osm);
670        } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) {
671            return multipolygonArea((Relation) osm);
672        } else {
673            return null;
674        }
675    }
676
677    /**
678     * Determines whether a way is oriented clockwise.
679     *
680     * Internals: Assuming a closed non-looping way, compute twice the area
681     * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
682     * If the area is negative the way is ordered in a clockwise direction.
683     *
684     * See http://paulbourke.net/geometry/polyarea/
685     *
686     * @param w the way to be checked.
687     * @return true if and only if way is oriented clockwise.
688     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
689     */
690    public static boolean isClockwise(Way w) {
691        return isClockwise(w.getNodes());
692    }
693
694    /**
695     * Determines whether path from nodes list is oriented clockwise.
696     * @param nodes Nodes list to be checked.
697     * @return true if and only if way is oriented clockwise.
698     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
699     * @see #isClockwise(Way)
700     */
701    public static boolean isClockwise(List<Node> nodes) {
702        int nodesCount = nodes.size();
703        if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
704            throw new IllegalArgumentException("Way must be closed to check orientation.");
705        }
706        double area2 = 0.;
707
708        for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
709            LatLon coorPrev = nodes.get(node - 1).getCoor();
710            LatLon coorCurr = nodes.get(node % nodesCount).getCoor();
711            area2 += coorPrev.lon() * coorCurr.lat();
712            area2 -= coorCurr.lon() * coorPrev.lat();
713        }
714        return area2 < 0;
715    }
716
717    /**
718     * Returns angle of a segment defined with 2 point coordinates.
719     *
720     * @param p1 first point
721     * @param p2 second point
722     * @return Angle in radians (-pi, pi]
723     */
724    public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
725
726        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
727        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
728
729        return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
730    }
731
732    /**
733     * Returns angle of a corner defined with 3 point coordinates.
734     *
735     * @param p1 first point
736     * @param p2 Common endpoint
737     * @param p3 third point
738     * @return Angle in radians (-pi, pi]
739     */
740    public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
741
742        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
743        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
744        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
745
746        Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
747        if (result <= -Math.PI) {
748            result += 2 * Math.PI;
749        }
750
751        if (result > Math.PI) {
752            result -= 2 * Math.PI;
753        }
754
755        return result;
756    }
757
758    /**
759     * Compute the centroid/barycenter of nodes
760     * @param nodes Nodes for which the centroid is wanted
761     * @return the centroid of nodes
762     * @see Geometry#getCenter
763     */
764    public static EastNorth getCentroid(List<Node> nodes) {
765
766        BigDecimal area = BigDecimal.ZERO;
767        BigDecimal north = BigDecimal.ZERO;
768        BigDecimal east = BigDecimal.ZERO;
769
770        // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
771        for (int i = 0; i < nodes.size(); i++) {
772            EastNorth n0 = nodes.get(i).getEastNorth();
773            EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
774
775            if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
776                BigDecimal x0 = BigDecimal.valueOf(n0.east());
777                BigDecimal y0 = BigDecimal.valueOf(n0.north());
778                BigDecimal x1 = BigDecimal.valueOf(n1.east());
779                BigDecimal y1 = BigDecimal.valueOf(n1.north());
780
781                BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
782
783                area = area.add(k, MathContext.DECIMAL128);
784                east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
785                north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
786            }
787        }
788
789        BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
790        area = area.multiply(d, MathContext.DECIMAL128);
791        if (area.compareTo(BigDecimal.ZERO) != 0) {
792            north = north.divide(area, MathContext.DECIMAL128);
793            east = east.divide(area, MathContext.DECIMAL128);
794        }
795
796        return new EastNorth(east.doubleValue(), north.doubleValue());
797    }
798
799    /**
800     * Compute center of the circle closest to different nodes.
801     *
802     * Ensure exact center computation in case nodes are already aligned in circle.
803     * This is done by least square method.
804     * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
805     * Center must be intersection of all bisectors.
806     * <pre>
807     *          [ a1  b1  ]         [ -c1 ]
808     * With A = [ ... ... ] and Y = [ ... ]
809     *          [ an  bn  ]         [ -cn ]
810     * </pre>
811     * An approximation of center of circle is (At.A)^-1.At.Y
812     * @param nodes Nodes parts of the circle (at least 3)
813     * @return An approximation of the center, of null if there is no solution.
814     * @see Geometry#getCentroid
815     * @since 6934
816     */
817    public static EastNorth getCenter(List<Node> nodes) {
818        int nc = nodes.size();
819        if (nc < 3) return null;
820        /**
821         * Equation of each bisector ax + by + c = 0
822         */
823        double[] a = new double[nc];
824        double[] b = new double[nc];
825        double[] c = new double[nc];
826        // Compute equation of bisector
827        for (int i = 0; i < nc; i++) {
828            EastNorth pt1 = nodes.get(i).getEastNorth();
829            EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
830            a[i] = pt1.east() - pt2.east();
831            b[i] = pt1.north() - pt2.north();
832            double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
833            if (d == 0) return null;
834            a[i] /= d;
835            b[i] /= d;
836            double xC = (pt1.east() + pt2.east()) / 2;
837            double yC = (pt1.north() + pt2.north()) / 2;
838            c[i] = -(a[i]*xC + b[i]*yC);
839        }
840        // At.A = [aij]
841        double a11 = 0, a12 = 0, a22 = 0;
842        // At.Y = [bi]
843        double b1 = 0, b2 = 0;
844        for (int i = 0; i < nc; i++) {
845            a11 += a[i]*a[i];
846            a12 += a[i]*b[i];
847            a22 += b[i]*b[i];
848            b1 -= a[i]*c[i];
849            b2 -= b[i]*c[i];
850        }
851        // (At.A)^-1 = [invij]
852        double det = a11*a22 - a12*a12;
853        if (Math.abs(det) < 1e-5) return null;
854        double inv11 = a22/det;
855        double inv12 = -a12/det;
856        double inv22 = a11/det;
857        // center (xC, yC) = (At.A)^-1.At.y
858        double xC = inv11*b1 + inv12*b2;
859        double yC = inv12*b1 + inv22*b2;
860        return new EastNorth(xC, yC);
861    }
862
863    /**
864     * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
865     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
866     * @param node node
867     * @param multiPolygon multipolygon
868     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
869     * @return {@code true} if the node is inside the multipolygon
870     */
871    public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
872        return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
873    }
874
875    /**
876     * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
877     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
878     * <p>
879     * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
880     * @param nodes nodes forming the polygon
881     * @param multiPolygon multipolygon
882     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
883     * @return {@code true} if the polygon formed by nodes is inside the multipolygon
884     */
885    public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
886        // Extract outer/inner members from multipolygon
887        final Pair<List<JoinedPolygon>, List<JoinedPolygon>> outerInner;
888        try {
889            outerInner = MultipolygonBuilder.joinWays(multiPolygon);
890        } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
891            Main.trace(ex);
892            Main.debug("Invalid multipolygon " + multiPolygon);
893            return false;
894        }
895        // Test if object is inside an outer member
896        for (JoinedPolygon out : outerInner.a) {
897            if (nodes.size() == 1
898                    ? nodeInsidePolygon(nodes.get(0), out.getNodes())
899                    : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
900                            polygonIntersection(nodes, out.getNodes()))) {
901                boolean insideInner = false;
902                // If inside an outer, check it is not inside an inner
903                for (JoinedPolygon in : outerInner.b) {
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.test(out.ways.get(0)
916                            /* TODO give a better representation of the outer ring to the predicate */)) {
917                        return true;
918                    }
919                }
920            }
921        }
922        return false;
923    }
924
925    /**
926     * Data class to hold two double values (area and perimeter of a polygon).
927     */
928    public static class AreaAndPerimeter {
929        private final double area;
930        private final double perimeter;
931
932        public AreaAndPerimeter(double area, double perimeter) {
933            this.area = area;
934            this.perimeter = perimeter;
935        }
936
937        public double getArea() {
938            return area;
939        }
940
941        public double getPerimeter() {
942            return perimeter;
943        }
944    }
945
946    /**
947     * Calculate area and perimeter length of a polygon.
948     *
949     * Uses current projection; units are that of the projected coordinates.
950     *
951     * @param nodes the list of nodes representing the polygon
952     * @return area and perimeter
953     */
954    public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) {
955        return getAreaAndPerimeter(nodes, null);
956    }
957
958    /**
959     * Calculate area and perimeter length of a polygon in the given projection.
960     *
961     * @param nodes the list of nodes representing the polygon
962     * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()}
963     * @return area and perimeter
964     */
965    public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes, Projection projection) {
966        CheckParameterUtil.ensureParameterNotNull(nodes, "nodes");
967        double area = 0;
968        double perimeter = 0;
969        if (!nodes.isEmpty()) {
970            boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1);
971            int numSegments = closed ? nodes.size() - 1 : nodes.size();
972            EastNorth p1 = projection == null ? nodes.get(0).getEastNorth() : projection.latlon2eastNorth(nodes.get(0).getCoor());
973            for (int i = 1; i <= numSegments; i++) {
974                final Node node = nodes.get(i == numSegments ? 0 : i);
975                final EastNorth p2 = projection == null ? node.getEastNorth() : projection.latlon2eastNorth(node.getCoor());
976                if (p1 != null && p2 != null) {
977                    area += p1.east() * p2.north() - p2.east() * p1.north();
978                    perimeter += p1.distance(p2);
979                }
980                p1 = p2;
981            }
982        }
983        return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
984    }
985}