001// License: GPL. For details, see LICENSE file.
002package org.openstreetmap.josm.tools;
003
004import java.awt.geom.Area;
005import java.awt.geom.Line2D;
006import java.awt.geom.Path2D;
007import java.awt.geom.PathIterator;
008import java.awt.geom.Rectangle2D;
009import java.math.BigDecimal;
010import java.math.MathContext;
011import java.util.ArrayList;
012import java.util.Collections;
013import java.util.Comparator;
014import java.util.LinkedHashSet;
015import java.util.List;
016import java.util.Set;
017import java.util.function.Predicate;
018import java.util.stream.Collectors;
019
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.ILatLon;
025import org.openstreetmap.josm.data.osm.BBox;
026import org.openstreetmap.josm.data.osm.DataSet;
027import org.openstreetmap.josm.data.osm.INode;
028import org.openstreetmap.josm.data.osm.IPrimitive;
029import org.openstreetmap.josm.data.osm.MultipolygonBuilder;
030import org.openstreetmap.josm.data.osm.MultipolygonBuilder.JoinedPolygon;
031import org.openstreetmap.josm.data.osm.Node;
032import org.openstreetmap.josm.data.osm.NodePositionComparator;
033import org.openstreetmap.josm.data.osm.Relation;
034import org.openstreetmap.josm.data.osm.Way;
035import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon;
036import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache;
037import org.openstreetmap.josm.data.projection.Projection;
038import org.openstreetmap.josm.data.projection.ProjectionRegistry;
039import org.openstreetmap.josm.data.projection.Projections;
040
041/**
042 * Some tools for geometry related tasks.
043 *
044 * @author viesturs
045 */
046public final class Geometry {
047
048    private Geometry() {
049        // Hide default constructor for utils classes
050    }
051
052    /**
053     * The result types for a {@link Geometry#polygonIntersection(Area, Area)} test
054     */
055    public enum PolygonIntersection {
056        /**
057         * The first polygon is inside the second one
058         */
059        FIRST_INSIDE_SECOND,
060        /**
061         * The second one is inside the first
062         */
063        SECOND_INSIDE_FIRST,
064        /**
065         * The polygons do not overlap
066         */
067        OUTSIDE,
068        /**
069         * The polygon borders cross each other
070         */
071        CROSSING
072    }
073
074    /** threshold value for size of intersection area given in east/north space */
075    public static final double INTERSECTION_EPS_EAST_NORTH = 1e-4;
076
077    /**
078     * Will find all intersection and add nodes there for list of given ways.
079     * Handles self-intersections too.
080     * And makes commands to add the intersection points to ways.
081     *
082     * Prerequisite: no two nodes have the same coordinates.
083     *
084     * @param ways  a list of ways to test
085     * @param test  if false, do not build list of Commands, just return nodes
086     * @param cmds  list of commands, typically empty when handed to this method.
087     *              Will be filled with commands that add intersection nodes to
088     *              the ways.
089     * @return list of new nodes
090     */
091    public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
092
093        int n = ways.size();
094        @SuppressWarnings("unchecked")
095        List<Node>[] newNodes = new ArrayList[n];
096        BBox[] wayBounds = new BBox[n];
097        boolean[] changedWays = new boolean[n];
098
099        Set<Node> intersectionNodes = new LinkedHashSet<>();
100
101        //copy node arrays for local usage.
102        for (int pos = 0; pos < n; pos++) {
103            newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
104            wayBounds[pos] = getNodesBounds(newNodes[pos]);
105            changedWays[pos] = false;
106        }
107
108        DataSet dataset = ways.get(0).getDataSet();
109
110        //iterate over all way pairs and introduce the intersections
111        Comparator<Node> coordsComparator = new NodePositionComparator();
112        for (int seg1Way = 0; seg1Way < n; seg1Way++) {
113            for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
114
115                //do not waste time on bounds that do not intersect
116                if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
117                    continue;
118                }
119
120                List<Node> way1Nodes = newNodes[seg1Way];
121                List<Node> way2Nodes = newNodes[seg2Way];
122
123                //iterate over primary segmemt
124                for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
125
126                    //iterate over secondary segment
127                    int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
128
129                    for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
130
131                        //need to get them again every time, because other segments may be changed
132                        Node seg1Node1 = way1Nodes.get(seg1Pos);
133                        Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
134                        Node seg2Node1 = way2Nodes.get(seg2Pos);
135                        Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
136
137                        int commonCount = 0;
138                        //test if we have common nodes to add.
139                        if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
140                            commonCount++;
141
142                            if (seg1Way == seg2Way &&
143                                    seg1Pos == 0 &&
144                                    seg2Pos == way2Nodes.size() -2) {
145                                //do not add - this is first and last segment of the same way.
146                            } else {
147                                intersectionNodes.add(seg1Node1);
148                            }
149                        }
150
151                        if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
152                            commonCount++;
153
154                            intersectionNodes.add(seg1Node2);
155                        }
156
157                        //no common nodes - find intersection
158                        if (commonCount == 0) {
159                            EastNorth intersection = getSegmentSegmentIntersection(
160                                    seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
161                                    seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
162
163                            if (intersection != null) {
164                                if (test) {
165                                    intersectionNodes.add(seg2Node1);
166                                    return intersectionNodes;
167                                }
168
169                                Node newNode = new Node(ProjectionRegistry.getProjection().eastNorth2latlon(intersection));
170                                Node intNode = newNode;
171                                boolean insertInSeg1 = false;
172                                boolean insertInSeg2 = false;
173                                //find if the intersection point is at end point of one of the segments, if so use that point
174
175                                //segment 1
176                                if (coordsComparator.compare(newNode, seg1Node1) == 0) {
177                                    intNode = seg1Node1;
178                                } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
179                                    intNode = seg1Node2;
180                                } else {
181                                    insertInSeg1 = true;
182                                }
183
184                                //segment 2
185                                if (coordsComparator.compare(newNode, seg2Node1) == 0) {
186                                    intNode = seg2Node1;
187                                } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
188                                    intNode = seg2Node2;
189                                } else {
190                                    insertInSeg2 = true;
191                                }
192
193                                if (insertInSeg1) {
194                                    way1Nodes.add(seg1Pos +1, intNode);
195                                    changedWays[seg1Way] = true;
196
197                                    //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
198                                    if (seg2Way == seg1Way) {
199                                        seg2Pos++;
200                                    }
201                                }
202
203                                if (insertInSeg2) {
204                                    way2Nodes.add(seg2Pos +1, intNode);
205                                    changedWays[seg2Way] = true;
206
207                                    //Do not need to compare again to already split segment
208                                    seg2Pos++;
209                                }
210
211                                intersectionNodes.add(intNode);
212
213                                if (intNode == newNode) {
214                                    cmds.add(new AddCommand(dataset, intNode));
215                                }
216                            }
217                        } else if (test && !intersectionNodes.isEmpty())
218                            return intersectionNodes;
219                    }
220                }
221            }
222        }
223
224
225        for (int pos = 0; pos < ways.size(); pos++) {
226            if (!changedWays[pos]) {
227                continue;
228            }
229
230            Way way = ways.get(pos);
231            Way newWay = new Way(way);
232            newWay.setNodes(newNodes[pos]);
233
234            cmds.add(new ChangeCommand(dataset, way, newWay));
235        }
236
237        return intersectionNodes;
238    }
239
240    private static BBox getNodesBounds(List<Node> nodes) {
241
242        BBox bounds = new BBox(nodes.get(0));
243        for (Node n: nodes) {
244            bounds.add(n);
245        }
246        return bounds;
247    }
248
249    /**
250     * Tests if given point is to the right side of path consisting of 3 points.
251     *
252     * (Imagine the path is continued beyond the endpoints, so you get two rays
253     * starting from lineP2 and going through lineP1 and lineP3 respectively
254     * which divide the plane into two parts. The test returns true, if testPoint
255     * lies in the part that is to the right when traveling in the direction
256     * lineP1, lineP2, lineP3.)
257     *
258     * @param <N> type of node
259     * @param lineP1 first point in path
260     * @param lineP2 second point in path
261     * @param lineP3 third point in path
262     * @param testPoint point to test
263     * @return true if to the right side, false otherwise
264     */
265    public static <N extends INode> boolean isToTheRightSideOfLine(N lineP1, N lineP2, N lineP3, N testPoint) {
266        boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
267        boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
268        boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
269
270        if (pathBendToRight)
271            return rightOfSeg1 && rightOfSeg2;
272        else
273            return !(!rightOfSeg1 && !rightOfSeg2);
274    }
275
276    /**
277     * This method tests if secondNode is clockwise to first node.
278     * @param <N> type of node
279     * @param commonNode starting point for both vectors
280     * @param firstNode first vector end node
281     * @param secondNode second vector end node
282     * @return true if first vector is clockwise before second vector.
283     */
284    public static <N extends INode> boolean angleIsClockwise(N commonNode, N firstNode, N secondNode) {
285        return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
286    }
287
288    /**
289     * Finds the intersection of two line segments.
290     * @param p1 the coordinates of the start point of the first specified line segment
291     * @param p2 the coordinates of the end point of the first specified line segment
292     * @param p3 the coordinates of the start point of the second specified line segment
293     * @param p4 the coordinates of the end point of the second specified line segment
294     * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
295     */
296    public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
297
298        CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
299        CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
300        CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
301        CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid);
302
303        double x1 = p1.getX();
304        double y1 = p1.getY();
305        double x2 = p2.getX();
306        double y2 = p2.getY();
307        double x3 = p3.getX();
308        double y3 = p3.getY();
309        double x4 = p4.getX();
310        double y4 = p4.getY();
311
312        //TODO: do this locally.
313        //TODO: remove this check after careful testing
314        if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
315
316        // solve line-line intersection in parametric form:
317        // (x1,y1) + (x2-x1,y2-y1)* u  = (x3,y3) + (x4-x3,y4-y3)* v
318        // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
319        // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
320
321        double a1 = x2 - x1;
322        double b1 = x3 - x4;
323        double c1 = x3 - x1;
324
325        double a2 = y2 - y1;
326        double b2 = y3 - y4;
327        double c2 = y3 - y1;
328
329        // Solve the equations
330        double det = a1*b2 - a2*b1;
331
332        double uu = b2*c1 - b1*c2;
333        double vv = a1*c2 - a2*c1;
334        double mag = Math.abs(uu)+Math.abs(vv);
335
336        if (Math.abs(det) > 1e-12 * mag) {
337            double u = uu/det, v = vv/det;
338            if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
339                if (u < 0) u = 0;
340                if (u > 1) u = 1.0;
341                return new EastNorth(x1+a1*u, y1+a2*u);
342            } else {
343                return null;
344            }
345        } else {
346            // parallel lines
347            return null;
348        }
349    }
350
351    /**
352     * Finds the intersection of two lines of infinite length.
353     *
354     * @param p1 first point on first line
355     * @param p2 second point on first line
356     * @param p3 first point on second line
357     * @param p4 second point on second line
358     * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
359     * @throws IllegalArgumentException if a parameter is null or without valid coordinates
360     */
361    public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
362
363        CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
364        CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
365        CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
366        CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid);
367
368        // Basically, the formula from wikipedia is used:
369        //  https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
370        // However, large numbers lead to rounding errors (see #10286).
371        // To avoid this, p1 is first subtracted from each of the points:
372        //  p1' = 0
373        //  p2' = p2 - p1
374        //  p3' = p3 - p1
375        //  p4' = p4 - p1
376        // In the end, p1 is added to the intersection point of segment p1'/p2'
377        // and segment p3'/p4'.
378
379        // Convert line from (point, point) form to ax+by=c
380        double a1 = p2.getY() - p1.getY();
381        double b1 = p1.getX() - p2.getX();
382
383        double a2 = p4.getY() - p3.getY();
384        double b2 = p3.getX() - p4.getX();
385
386        // Solve the equations
387        double det = a1 * b2 - a2 * b1;
388        if (det == 0)
389            return null; // Lines are parallel
390
391        double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
392
393        return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
394    }
395
396    /**
397     * Check if the segment p1 - p2 is parallel to p3 - p4
398     * @param p1 First point for first segment
399     * @param p2 Second point for first segment
400     * @param p3 First point for second segment
401     * @param p4 Second point for second segment
402     * @return <code>true</code> if they are parallel or close to parallel
403     */
404    public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
405
406        CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
407        CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
408        CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
409        CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid);
410
411        // Convert line from (point, point) form to ax+by=c
412        double a1 = p2.getY() - p1.getY();
413        double b1 = p1.getX() - p2.getX();
414
415        double a2 = p4.getY() - p3.getY();
416        double b2 = p3.getX() - p4.getX();
417
418        // Solve the equations
419        double det = a1 * b2 - a2 * b1;
420        // remove influence of of scaling factor
421        det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
422        return Math.abs(det) < 1e-3;
423    }
424
425    private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
426        CheckParameterUtil.ensureParameterNotNull(p1, "p1");
427        CheckParameterUtil.ensureParameterNotNull(p2, "p2");
428        CheckParameterUtil.ensureParameterNotNull(point, "point");
429
430        double ldx = p2.getX() - p1.getX();
431        double ldy = p2.getY() - p1.getY();
432
433        //segment zero length
434        if (ldx == 0 && ldy == 0)
435            return p1;
436
437        double pdx = point.getX() - p1.getX();
438        double pdy = point.getY() - p1.getY();
439
440        double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
441
442        if (segmentOnly && offset <= 0)
443            return p1;
444        else if (segmentOnly && offset >= 1)
445            return p2;
446        else
447            return p1.interpolate(p2, offset);
448    }
449
450    /**
451     * Calculates closest point to a line segment.
452     * @param segmentP1 First point determining line segment
453     * @param segmentP2 Second point determining line segment
454     * @param point Point for which a closest point is searched on line segment [P1,P2]
455     * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
456     * a new point if closest point is between segmentP1 and segmentP2.
457     * @see #closestPointToLine
458     * @since 3650
459     */
460    public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
461        return closestPointTo(segmentP1, segmentP2, point, true);
462    }
463
464    /**
465     * Calculates closest point to a line.
466     * @param lineP1 First point determining line
467     * @param lineP2 Second point determining line
468     * @param point Point for which a closest point is searched on line (P1,P2)
469     * @return The closest point found on line. It may be outside the segment [P1,P2].
470     * @see #closestPointToSegment
471     * @since 4134
472     */
473    public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
474        return closestPointTo(lineP1, lineP2, point, false);
475    }
476
477    /**
478     * This method tests if secondNode is clockwise to first node.
479     *
480     * The line through the two points commonNode and firstNode divides the
481     * plane into two parts. The test returns true, if secondNode lies in
482     * the part that is to the right when traveling in the direction from
483     * commonNode to firstNode.
484     *
485     * @param commonNode starting point for both vectors
486     * @param firstNode first vector end node
487     * @param secondNode second vector end node
488     * @return true if first vector is clockwise before second vector.
489     */
490    public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
491
492        CheckParameterUtil.ensure(commonNode, "commonNode", EastNorth::isValid);
493        CheckParameterUtil.ensure(firstNode, "firstNode", EastNorth::isValid);
494        CheckParameterUtil.ensure(secondNode, "secondNode", EastNorth::isValid);
495
496        double dy1 = firstNode.getY() - commonNode.getY();
497        double dy2 = secondNode.getY() - commonNode.getY();
498        double dx1 = firstNode.getX() - commonNode.getX();
499        double dx2 = secondNode.getX() - commonNode.getX();
500
501        return dy1 * dx2 - dx1 * dy2 > 0;
502    }
503
504    /**
505     * Returns the Area of a polygon, from its list of nodes.
506     * @param polygon List of nodes forming polygon
507     * @return Area for the given list of nodes  (EastNorth coordinates)
508     * @since 6841
509     */
510    public static Area getArea(List<? extends INode> polygon) {
511        Path2D path = new Path2D.Double();
512
513        boolean begin = true;
514        for (INode n : polygon) {
515            EastNorth en = n.getEastNorth();
516            if (en != null) {
517                if (begin) {
518                    path.moveTo(en.getX(), en.getY());
519                    begin = false;
520                } else {
521                    path.lineTo(en.getX(), en.getY());
522                }
523            }
524        }
525        if (!begin) {
526            path.closePath();
527        }
528
529        return new Area(path);
530    }
531
532    /**
533     * Builds a path from a list of nodes
534     * @param polygon Nodes, forming a closed polygon
535     * @param path2d path to add to; can be null, then a new path is created
536     * @return the path (LatLon coordinates)
537     * @since 13638 (signature)
538     */
539    public static Path2D buildPath2DLatLon(List<? extends ILatLon> polygon, Path2D path2d) {
540        Path2D path = path2d != null ? path2d : new Path2D.Double();
541        boolean begin = true;
542        for (ILatLon n : polygon) {
543            if (begin) {
544                path.moveTo(n.lon(), n.lat());
545                begin = false;
546            } else {
547                path.lineTo(n.lon(), n.lat());
548            }
549        }
550        if (!begin) {
551            path.closePath();
552        }
553        return path;
554    }
555
556    /**
557     * Returns the Area of a polygon, from the multipolygon relation.
558     * @param multipolygon the multipolygon relation
559     * @return Area for the multipolygon (LatLon coordinates)
560     */
561    public static Area getAreaLatLon(Relation multipolygon) {
562        final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon);
563        Path2D path = new Path2D.Double();
564        path.setWindingRule(Path2D.WIND_EVEN_ODD);
565        for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) {
566            buildPath2DLatLon(pd.getNodes(), path);
567            for (Multipolygon.PolyData pdInner : pd.getInners()) {
568                buildPath2DLatLon(pdInner.getNodes(), path);
569            }
570        }
571        return new Area(path);
572    }
573
574    /**
575     * Tests if two polygons intersect.
576     * @param first List of nodes forming first polygon
577     * @param second List of nodes forming second polygon
578     * @return intersection kind
579     */
580    public static PolygonIntersection polygonIntersection(List<? extends INode> first, List<? extends INode> second) {
581        Area a1 = getArea(first);
582        Area a2 = getArea(second);
583        return polygonIntersection(a1, a2, INTERSECTION_EPS_EAST_NORTH);
584    }
585
586    /**
587     * Tests if two polygons intersect. It is assumed that the area is given in East North points.
588     * @param a1 Area of first polygon
589     * @param a2 Area of second polygon
590     * @return intersection kind
591     * @since 6841
592     */
593    public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
594        return polygonIntersection(a1, a2, INTERSECTION_EPS_EAST_NORTH);
595    }
596
597    /**
598     * Tests if two polygons intersect.
599     * @param a1 Area of first polygon
600     * @param a2 Area of second polygon
601     * @param eps an area threshold, everything below is considered an empty intersection
602     * @return intersection kind
603     */
604    public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
605
606        Area inter = new Area(a1);
607        inter.intersect(a2);
608
609        if (inter.isEmpty() || !checkIntersection(inter, eps)) {
610            return PolygonIntersection.OUTSIDE;
611        } else if (a2.getBounds2D().contains(a1.getBounds2D()) && inter.equals(a1)) {
612            return PolygonIntersection.FIRST_INSIDE_SECOND;
613        } else if (a1.getBounds2D().contains(a2.getBounds2D()) && inter.equals(a2)) {
614            return PolygonIntersection.SECOND_INSIDE_FIRST;
615        } else {
616            return PolygonIntersection.CROSSING;
617        }
618    }
619
620    /**
621     * Check an intersection area which might describe multiple small polygons.
622     * Return true if any of the polygons is bigger than the given threshold.
623     * @param inter the intersection area
624     * @param eps an area threshold, everything below is considered an empty intersection
625     * @return true if any of the polygons is bigger than the given threshold
626     */
627    private static boolean checkIntersection(Area inter, double eps) {
628        PathIterator pit = inter.getPathIterator(null);
629        double[] res = new double[6];
630        Rectangle2D r = new Rectangle2D.Double();
631        while (!pit.isDone()) {
632            int type = pit.currentSegment(res);
633            switch (type) {
634            case PathIterator.SEG_MOVETO:
635                r = new Rectangle2D.Double(res[0], res[1], 0, 0);
636                break;
637            case PathIterator.SEG_LINETO:
638                r.add(res[0], res[1]);
639                break;
640            case PathIterator.SEG_CLOSE:
641                if (r.getWidth() > eps || r.getHeight() > eps)
642                    return true;
643                break;
644            default:
645                break;
646            }
647            pit.next();
648        }
649        return false;
650    }
651
652    /**
653     * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
654     * @param polygonNodes list of nodes from polygon path.
655     * @param point the point to test
656     * @return true if the point is inside polygon.
657     */
658    public static boolean nodeInsidePolygon(INode point, List<? extends INode> polygonNodes) {
659        if (polygonNodes.size() < 2)
660            return false;
661
662        //iterate each side of the polygon, start with the last segment
663        INode oldPoint = polygonNodes.get(polygonNodes.size() - 1);
664
665        if (!oldPoint.isLatLonKnown()) {
666            return false;
667        }
668
669        boolean inside = false;
670        INode p1, p2;
671
672        for (INode newPoint : polygonNodes) {
673            //skip duplicate points
674            if (newPoint.equals(oldPoint)) {
675                continue;
676            }
677
678            if (!newPoint.isLatLonKnown()) {
679                return false;
680            }
681
682            //order points so p1.lat <= p2.lat
683            if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
684                p1 = oldPoint;
685                p2 = newPoint;
686            } else {
687                p1 = newPoint;
688                p2 = oldPoint;
689            }
690
691            EastNorth pEN = point.getEastNorth();
692            EastNorth opEN = oldPoint.getEastNorth();
693            EastNorth npEN = newPoint.getEastNorth();
694            EastNorth p1EN = p1.getEastNorth();
695            EastNorth p2EN = p2.getEastNorth();
696
697            if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
698                //test if the line is crossed and if so invert the inside flag.
699                if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
700                        && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
701                        < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
702                    inside = !inside;
703                }
704            }
705
706            oldPoint = newPoint;
707        }
708
709        return inside;
710    }
711
712    /**
713     * Returns area of a closed way in square meters.
714     *
715     * @param way Way to measure, should be closed (first node is the same as last node)
716     * @return area of the closed way.
717     */
718    public static double closedWayArea(Way way) {
719        return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea();
720    }
721
722    /**
723     * Returns area of a multipolygon in square meters.
724     *
725     * @param multipolygon the multipolygon to measure
726     * @return area of the multipolygon.
727     */
728    public static double multipolygonArea(Relation multipolygon) {
729        double area = 0.0;
730        final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon);
731        for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) {
732            area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea();
733        }
734        return area;
735    }
736
737    /**
738     * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives
739     *
740     * @param osm the primitive to measure
741     * @return area of the primitive, or {@code null}
742     * @since 13638 (signature)
743     */
744    public static Double computeArea(IPrimitive osm) {
745        if (osm instanceof Way && ((Way) osm).isClosed()) {
746            return closedWayArea((Way) osm);
747        } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) {
748            return multipolygonArea((Relation) osm);
749        } else {
750            return null;
751        }
752    }
753
754    /**
755     * Determines whether a way is oriented clockwise.
756     *
757     * Internals: Assuming a closed non-looping way, compute twice the area
758     * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
759     * If the area is negative the way is ordered in a clockwise direction.
760     *
761     * See http://paulbourke.net/geometry/polyarea/
762     *
763     * @param w the way to be checked.
764     * @return true if and only if way is oriented clockwise.
765     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
766     */
767    public static boolean isClockwise(Way w) {
768        return isClockwise(w.getNodes());
769    }
770
771    /**
772     * Determines whether path from nodes list is oriented clockwise.
773     * @param nodes Nodes list to be checked.
774     * @return true if and only if way is oriented clockwise.
775     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
776     * @see #isClockwise(Way)
777     */
778    public static boolean isClockwise(List<? extends INode> nodes) {
779        int nodesCount = nodes.size();
780        if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
781            throw new IllegalArgumentException("Way must be closed to check orientation.");
782        }
783        double area2 = 0.;
784
785        for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
786            INode coorPrev = nodes.get(node - 1);
787            INode coorCurr = nodes.get(node % nodesCount);
788            area2 += coorPrev.lon() * coorCurr.lat();
789            area2 -= coorCurr.lon() * coorPrev.lat();
790        }
791        return area2 < 0;
792    }
793
794    /**
795     * Returns angle of a segment defined with 2 point coordinates.
796     *
797     * @param p1 first point
798     * @param p2 second point
799     * @return Angle in radians (-pi, pi]
800     */
801    public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
802
803        CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
804        CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
805
806        return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
807    }
808
809    /**
810     * Returns angle of a corner defined with 3 point coordinates.
811     *
812     * @param p1 first point
813     * @param common Common end point
814     * @param p3 third point
815     * @return Angle in radians (-pi, pi]
816     */
817    public static double getCornerAngle(EastNorth p1, EastNorth common, EastNorth p3) {
818
819        CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
820        CheckParameterUtil.ensure(common, "p2", EastNorth::isValid);
821        CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
822
823        double result = getSegmentAngle(common, p1) - getSegmentAngle(common, p3);
824        if (result <= -Math.PI) {
825            result += 2 * Math.PI;
826        }
827
828        if (result > Math.PI) {
829            result -= 2 * Math.PI;
830        }
831
832        return result;
833    }
834
835    /**
836     * Get angles in radians and return it's value in range [0, 180].
837     *
838     * @param angle the angle in radians
839     * @return normalized angle in degrees
840     * @since 13670
841     */
842    public static double getNormalizedAngleInDegrees(double angle) {
843        return Math.abs(180 * angle / Math.PI);
844    }
845
846    /**
847     * Compute the centroid/barycenter of nodes
848     * @param nodes Nodes for which the centroid is wanted
849     * @return the centroid of nodes
850     * @see Geometry#getCenter
851     */
852    public static EastNorth getCentroid(List<? extends INode> nodes) {
853        return getCentroidEN(nodes.stream().map(INode::getEastNorth).collect(Collectors.toList()));
854    }
855
856    /**
857     * Compute the centroid/barycenter of nodes
858     * @param nodes Coordinates for which the centroid is wanted
859     * @return the centroid of nodes
860     * @since 13712
861     */
862    public static EastNorth getCentroidEN(List<EastNorth> nodes) {
863
864        final int size = nodes.size();
865        if (size == 1) {
866            return nodes.get(0);
867        } else if (size == 2) {
868            return nodes.get(0).getCenter(nodes.get(1));
869        }
870
871        BigDecimal area = BigDecimal.ZERO;
872        BigDecimal north = BigDecimal.ZERO;
873        BigDecimal east = BigDecimal.ZERO;
874
875        // See https://en.wikipedia.org/wiki/Centroid#Of_a_polygon for the equation used here
876        for (int i = 0; i < size; i++) {
877            EastNorth n0 = nodes.get(i);
878            EastNorth n1 = nodes.get((i+1) % size);
879
880            if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
881                BigDecimal x0 = BigDecimal.valueOf(n0.east());
882                BigDecimal y0 = BigDecimal.valueOf(n0.north());
883                BigDecimal x1 = BigDecimal.valueOf(n1.east());
884                BigDecimal y1 = BigDecimal.valueOf(n1.north());
885
886                BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
887
888                area = area.add(k, MathContext.DECIMAL128);
889                east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
890                north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
891            }
892        }
893
894        BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
895        area = area.multiply(d, MathContext.DECIMAL128);
896        if (area.compareTo(BigDecimal.ZERO) != 0) {
897            north = north.divide(area, MathContext.DECIMAL128);
898            east = east.divide(area, MathContext.DECIMAL128);
899        }
900
901        return new EastNorth(east.doubleValue(), north.doubleValue());
902    }
903
904    /**
905     * Compute center of the circle closest to different nodes.
906     *
907     * Ensure exact center computation in case nodes are already aligned in circle.
908     * This is done by least square method.
909     * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
910     * Center must be intersection of all bisectors.
911     * <pre>
912     *          [ a1  b1  ]         [ -c1 ]
913     * With A = [ ... ... ] and Y = [ ... ]
914     *          [ an  bn  ]         [ -cn ]
915     * </pre>
916     * An approximation of center of circle is (At.A)^-1.At.Y
917     * @param nodes Nodes parts of the circle (at least 3)
918     * @return An approximation of the center, of null if there is no solution.
919     * @see Geometry#getCentroid
920     * @since 6934
921     */
922    public static EastNorth getCenter(List<? extends INode> nodes) {
923        int nc = nodes.size();
924        if (nc < 3) return null;
925        /**
926         * Equation of each bisector ax + by + c = 0
927         */
928        double[] a = new double[nc];
929        double[] b = new double[nc];
930        double[] c = new double[nc];
931        // Compute equation of bisector
932        for (int i = 0; i < nc; i++) {
933            EastNorth pt1 = nodes.get(i).getEastNorth();
934            EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
935            a[i] = pt1.east() - pt2.east();
936            b[i] = pt1.north() - pt2.north();
937            double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
938            if (d == 0) return null;
939            a[i] /= d;
940            b[i] /= d;
941            double xC = (pt1.east() + pt2.east()) / 2;
942            double yC = (pt1.north() + pt2.north()) / 2;
943            c[i] = -(a[i]*xC + b[i]*yC);
944        }
945        // At.A = [aij]
946        double a11 = 0, a12 = 0, a22 = 0;
947        // At.Y = [bi]
948        double b1 = 0, b2 = 0;
949        for (int i = 0; i < nc; i++) {
950            a11 += a[i]*a[i];
951            a12 += a[i]*b[i];
952            a22 += b[i]*b[i];
953            b1 -= a[i]*c[i];
954            b2 -= b[i]*c[i];
955        }
956        // (At.A)^-1 = [invij]
957        double det = a11*a22 - a12*a12;
958        if (Math.abs(det) < 1e-5) return null;
959        double inv11 = a22/det;
960        double inv12 = -a12/det;
961        double inv22 = a11/det;
962        // center (xC, yC) = (At.A)^-1.At.y
963        double xC = inv11*b1 + inv12*b2;
964        double yC = inv12*b1 + inv22*b2;
965        return new EastNorth(xC, yC);
966    }
967
968    /**
969     * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
970     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
971     * @param node node
972     * @param multiPolygon multipolygon
973     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
974     * @return {@code true} if the node is inside the multipolygon
975     */
976    public static boolean isNodeInsideMultiPolygon(INode node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
977        return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
978    }
979
980    /**
981     * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
982     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
983     * <p>
984     * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
985     * @param nodes nodes forming the polygon
986     * @param multiPolygon multipolygon
987     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
988     * @return {@code true} if the polygon formed by nodes is inside the multipolygon
989     */
990    public static boolean isPolygonInsideMultiPolygon(List<? extends INode> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
991        // Extract outer/inner members from multipolygon
992        final Pair<List<JoinedPolygon>, List<JoinedPolygon>> outerInner;
993        try {
994            outerInner = MultipolygonBuilder.joinWays(multiPolygon);
995        } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
996            Logging.trace(ex);
997            Logging.debug("Invalid multipolygon " + multiPolygon);
998            return false;
999        }
1000        // Test if object is inside an outer member
1001        for (JoinedPolygon out : outerInner.a) {
1002            if (nodes.size() == 1
1003                    ? nodeInsidePolygon(nodes.get(0), out.getNodes())
1004                    : PolygonIntersection.FIRST_INSIDE_SECOND == polygonIntersection(nodes, out.getNodes())) {
1005                boolean insideInner = false;
1006                // If inside an outer, check it is not inside an inner
1007                for (JoinedPolygon in : outerInner.b) {
1008                    if (nodes.size() == 1 ? nodeInsidePolygon(nodes.get(0), in.getNodes())
1009                            : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
1010                                    && polygonIntersection(in.getNodes(),
1011                                            out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND) {
1012                        insideInner = true;
1013                        break;
1014                    }
1015                }
1016                // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
1017                if (!insideInner) {
1018                    // Final check using predicate
1019                    if (isOuterWayAMatch == null || isOuterWayAMatch.test(out.ways.get(0)
1020                            /* TODO give a better representation of the outer ring to the predicate */)) {
1021                        return true;
1022                    }
1023                }
1024            }
1025        }
1026        return false;
1027    }
1028
1029    /**
1030     * Data class to hold two double values (area and perimeter of a polygon).
1031     */
1032    public static class AreaAndPerimeter {
1033        private final double area;
1034        private final double perimeter;
1035
1036        /**
1037         * Create a new {@link AreaAndPerimeter}
1038         * @param area The area
1039         * @param perimeter The perimeter
1040         */
1041        public AreaAndPerimeter(double area, double perimeter) {
1042            this.area = area;
1043            this.perimeter = perimeter;
1044        }
1045
1046        /**
1047         * Gets the area
1048         * @return The area size
1049         */
1050        public double getArea() {
1051            return area;
1052        }
1053
1054        /**
1055         * Gets the perimeter
1056         * @return The perimeter length
1057         */
1058        public double getPerimeter() {
1059            return perimeter;
1060        }
1061    }
1062
1063    /**
1064     * Calculate area and perimeter length of a polygon.
1065     *
1066     * Uses current projection; units are that of the projected coordinates.
1067     *
1068     * @param nodes the list of nodes representing the polygon
1069     * @return area and perimeter
1070     */
1071    public static AreaAndPerimeter getAreaAndPerimeter(List<? extends ILatLon> nodes) {
1072        return getAreaAndPerimeter(nodes, null);
1073    }
1074
1075    /**
1076     * Calculate area and perimeter length of a polygon in the given projection.
1077     *
1078     * @param nodes the list of nodes representing the polygon
1079     * @param projection the projection to use for the calculation, {@code null} defaults to {@link ProjectionRegistry#getProjection()}
1080     * @return area and perimeter
1081     * @since 13638 (signature)
1082     */
1083    public static AreaAndPerimeter getAreaAndPerimeter(List<? extends ILatLon> nodes, Projection projection) {
1084        CheckParameterUtil.ensureParameterNotNull(nodes, "nodes");
1085        double area = 0;
1086        double perimeter = 0;
1087        Projection useProjection = projection == null ? ProjectionRegistry.getProjection() : projection;
1088
1089        if (!nodes.isEmpty()) {
1090            boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1);
1091            int numSegments = closed ? nodes.size() - 1 : nodes.size();
1092            EastNorth p1 = nodes.get(0).getEastNorth(useProjection);
1093            for (int i = 1; i <= numSegments; i++) {
1094                final ILatLon node = nodes.get(i == numSegments ? 0 : i);
1095                final EastNorth p2 = node.getEastNorth(useProjection);
1096                if (p1 != null && p2 != null) {
1097                    area += p1.east() * p2.north() - p2.east() * p1.north();
1098                    perimeter += p1.distance(p2);
1099                }
1100                p1 = p2;
1101            }
1102        }
1103        return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
1104    }
1105}