source: josm/trunk/src/org/openstreetmap/josm/tools/Geometry.java@ 13127

Last change on this file since 13127 was 12742, checked in by Don-vip, 7 years ago

see #15229 - see #15182 - remove useless dependence of Geometry on GUI now that MultipolygonCache does not need anymore a MapView
  • Property svn:eol-style set to native
File size: 40.0 KB
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1// License: GPL. For details, see LICENSE file.
2package org.openstreetmap.josm.tools;
3
4import java.awt.Rectangle;
5import java.awt.geom.Area;
6import java.awt.geom.Line2D;
7import java.awt.geom.Path2D;
8import java.math.BigDecimal;
9import java.math.MathContext;
10import java.util.ArrayList;
11import java.util.Collections;
12import java.util.Comparator;
13import java.util.EnumSet;
14import java.util.LinkedHashSet;
15import java.util.List;
16import java.util.Set;
17import java.util.function.Predicate;
18
19import org.openstreetmap.josm.Main;
20import org.openstreetmap.josm.command.AddCommand;
21import org.openstreetmap.josm.command.ChangeCommand;
22import org.openstreetmap.josm.command.Command;
23import org.openstreetmap.josm.data.coor.EastNorth;
24import org.openstreetmap.josm.data.osm.BBox;
25import org.openstreetmap.josm.data.osm.DataSet;
26import org.openstreetmap.josm.data.osm.MultipolygonBuilder;
27import org.openstreetmap.josm.data.osm.MultipolygonBuilder.JoinedPolygon;
28import org.openstreetmap.josm.data.osm.Node;
29import org.openstreetmap.josm.data.osm.NodePositionComparator;
30import org.openstreetmap.josm.data.osm.OsmPrimitive;
31import org.openstreetmap.josm.data.osm.Relation;
32import org.openstreetmap.josm.data.osm.Way;
33import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon;
34import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache;
35import org.openstreetmap.josm.data.projection.Projection;
36import org.openstreetmap.josm.data.projection.Projections;
37
38/**
39 * Some tools for geometry related tasks.
40 *
41 * @author viesturs
42 */
43public final class Geometry {
44
45 private Geometry() {
46 // Hide default constructor for utils classes
47 }
48
49 /**
50 * The result types for a {@link Geometry#polygonIntersection(Area, Area)} test
51 */
52 public enum PolygonIntersection {
53 /**
54 * The first polygon is inside the second one
55 */
56 FIRST_INSIDE_SECOND,
57 /**
58 * The second one is inside the first
59 */
60 SECOND_INSIDE_FIRST,
61 /**
62 * The polygons do not overlap
63 */
64 OUTSIDE,
65 /**
66 * The polygon borders cross each other
67 */
68 CROSSING
69 }
70
71 /**
72 * Will find all intersection and add nodes there for list of given ways.
73 * Handles self-intersections too.
74 * And makes commands to add the intersection points to ways.
75 *
76 * Prerequisite: no two nodes have the same coordinates.
77 *
78 * @param ways a list of ways to test
79 * @param test if false, do not build list of Commands, just return nodes
80 * @param cmds list of commands, typically empty when handed to this method.
81 * Will be filled with commands that add intersection nodes to
82 * the ways.
83 * @return list of new nodes
84 */
85 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
86
87 int n = ways.size();
88 @SuppressWarnings("unchecked")
89 List<Node>[] newNodes = new ArrayList[n];
90 BBox[] wayBounds = new BBox[n];
91 boolean[] changedWays = new boolean[n];
92
93 Set<Node> intersectionNodes = new LinkedHashSet<>();
94
95 //copy node arrays for local usage.
96 for (int pos = 0; pos < n; pos++) {
97 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
98 wayBounds[pos] = getNodesBounds(newNodes[pos]);
99 changedWays[pos] = false;
100 }
101
102 DataSet dataset = ways.get(0).getDataSet();
103
104 //iterate over all way pairs and introduce the intersections
105 Comparator<Node> coordsComparator = new NodePositionComparator();
106 for (int seg1Way = 0; seg1Way < n; seg1Way++) {
107 for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
108
109 //do not waste time on bounds that do not intersect
110 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
111 continue;
112 }
113
114 List<Node> way1Nodes = newNodes[seg1Way];
115 List<Node> way2Nodes = newNodes[seg2Way];
116
117 //iterate over primary segmemt
118 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
119
120 //iterate over secondary segment
121 int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
122
123 for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
124
125 //need to get them again every time, because other segments may be changed
126 Node seg1Node1 = way1Nodes.get(seg1Pos);
127 Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
128 Node seg2Node1 = way2Nodes.get(seg2Pos);
129 Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
130
131 int commonCount = 0;
132 //test if we have common nodes to add.
133 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
134 commonCount++;
135
136 if (seg1Way == seg2Way &&
137 seg1Pos == 0 &&
138 seg2Pos == way2Nodes.size() -2) {
139 //do not add - this is first and last segment of the same way.
140 } else {
141 intersectionNodes.add(seg1Node1);
142 }
143 }
144
145 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
146 commonCount++;
147
148 intersectionNodes.add(seg1Node2);
149 }
150
151 //no common nodes - find intersection
152 if (commonCount == 0) {
153 EastNorth intersection = getSegmentSegmentIntersection(
154 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
155 seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
156
157 if (intersection != null) {
158 if (test) {
159 intersectionNodes.add(seg2Node1);
160 return intersectionNodes;
161 }
162
163 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
164 Node intNode = newNode;
165 boolean insertInSeg1 = false;
166 boolean insertInSeg2 = false;
167 //find if the intersection point is at end point of one of the segments, if so use that point
168
169 //segment 1
170 if (coordsComparator.compare(newNode, seg1Node1) == 0) {
171 intNode = seg1Node1;
172 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
173 intNode = seg1Node2;
174 } else {
175 insertInSeg1 = true;
176 }
177
178 //segment 2
179 if (coordsComparator.compare(newNode, seg2Node1) == 0) {
180 intNode = seg2Node1;
181 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
182 intNode = seg2Node2;
183 } else {
184 insertInSeg2 = true;
185 }
186
187 if (insertInSeg1) {
188 way1Nodes.add(seg1Pos +1, intNode);
189 changedWays[seg1Way] = true;
190
191 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
192 if (seg2Way == seg1Way) {
193 seg2Pos++;
194 }
195 }
196
197 if (insertInSeg2) {
198 way2Nodes.add(seg2Pos +1, intNode);
199 changedWays[seg2Way] = true;
200
201 //Do not need to compare again to already split segment
202 seg2Pos++;
203 }
204
205 intersectionNodes.add(intNode);
206
207 if (intNode == newNode) {
208 cmds.add(new AddCommand(dataset, intNode));
209 }
210 }
211 } else if (test && !intersectionNodes.isEmpty())
212 return intersectionNodes;
213 }
214 }
215 }
216 }
217
218
219 for (int pos = 0; pos < ways.size(); pos++) {
220 if (!changedWays[pos]) {
221 continue;
222 }
223
224 Way way = ways.get(pos);
225 Way newWay = new Way(way);
226 newWay.setNodes(newNodes[pos]);
227
228 cmds.add(new ChangeCommand(dataset, way, newWay));
229 }
230
231 return intersectionNodes;
232 }
233
234 private static BBox getNodesBounds(List<Node> nodes) {
235
236 BBox bounds = new BBox(nodes.get(0));
237 for (Node n: nodes) {
238 bounds.add(n);
239 }
240 return bounds;
241 }
242
243 /**
244 * Tests if given point is to the right side of path consisting of 3 points.
245 *
246 * (Imagine the path is continued beyond the endpoints, so you get two rays
247 * starting from lineP2 and going through lineP1 and lineP3 respectively
248 * which divide the plane into two parts. The test returns true, if testPoint
249 * lies in the part that is to the right when traveling in the direction
250 * lineP1, lineP2, lineP3.)
251 *
252 * @param lineP1 first point in path
253 * @param lineP2 second point in path
254 * @param lineP3 third point in path
255 * @param testPoint point to test
256 * @return true if to the right side, false otherwise
257 */
258 public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
259 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
260 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
261 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
262
263 if (pathBendToRight)
264 return rightOfSeg1 && rightOfSeg2;
265 else
266 return !(!rightOfSeg1 && !rightOfSeg2);
267 }
268
269 /**
270 * This method tests if secondNode is clockwise to first node.
271 * @param commonNode starting point for both vectors
272 * @param firstNode first vector end node
273 * @param secondNode second vector end node
274 * @return true if first vector is clockwise before second vector.
275 */
276 public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
277 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
278 }
279
280 /**
281 * Finds the intersection of two line segments.
282 * @param p1 the coordinates of the start point of the first specified line segment
283 * @param p2 the coordinates of the end point of the first specified line segment
284 * @param p3 the coordinates of the start point of the second specified line segment
285 * @param p4 the coordinates of the end point of the second specified line segment
286 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
287 */
288 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
289
290 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
291 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
292 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
293 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid);
294
295 double x1 = p1.getX();
296 double y1 = p1.getY();
297 double x2 = p2.getX();
298 double y2 = p2.getY();
299 double x3 = p3.getX();
300 double y3 = p3.getY();
301 double x4 = p4.getX();
302 double y4 = p4.getY();
303
304 //TODO: do this locally.
305 //TODO: remove this check after careful testing
306 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
307
308 // solve line-line intersection in parametric form:
309 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v
310 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
311 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
312
313 double a1 = x2 - x1;
314 double b1 = x3 - x4;
315 double c1 = x3 - x1;
316
317 double a2 = y2 - y1;
318 double b2 = y3 - y4;
319 double c2 = y3 - y1;
320
321 // Solve the equations
322 double det = a1*b2 - a2*b1;
323
324 double uu = b2*c1 - b1*c2;
325 double vv = a1*c2 - a2*c1;
326 double mag = Math.abs(uu)+Math.abs(vv);
327
328 if (Math.abs(det) > 1e-12 * mag) {
329 double u = uu/det, v = vv/det;
330 if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
331 if (u < 0) u = 0;
332 if (u > 1) u = 1.0;
333 return new EastNorth(x1+a1*u, y1+a2*u);
334 } else {
335 return null;
336 }
337 } else {
338 // parallel lines
339 return null;
340 }
341 }
342
343 /**
344 * Finds the intersection of two lines of infinite length.
345 *
346 * @param p1 first point on first line
347 * @param p2 second point on first line
348 * @param p3 first point on second line
349 * @param p4 second point on second line
350 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
351 * @throws IllegalArgumentException if a parameter is null or without valid coordinates
352 */
353 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
354
355 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
356 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
357 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
358 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid);
359
360 // Basically, the formula from wikipedia is used:
361 // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
362 // However, large numbers lead to rounding errors (see #10286).
363 // To avoid this, p1 is first substracted from each of the points:
364 // p1' = 0
365 // p2' = p2 - p1
366 // p3' = p3 - p1
367 // p4' = p4 - p1
368 // In the end, p1 is added to the intersection point of segment p1'/p2'
369 // and segment p3'/p4'.
370
371 // Convert line from (point, point) form to ax+by=c
372 double a1 = p2.getY() - p1.getY();
373 double b1 = p1.getX() - p2.getX();
374
375 double a2 = p4.getY() - p3.getY();
376 double b2 = p3.getX() - p4.getX();
377
378 // Solve the equations
379 double det = a1 * b2 - a2 * b1;
380 if (det == 0)
381 return null; // Lines are parallel
382
383 double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
384
385 return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
386 }
387
388 /**
389 * Check if the segment p1 - p2 is parallel to p3 - p4
390 * @param p1 First point for first segment
391 * @param p2 Second point for first segment
392 * @param p3 First point for second segment
393 * @param p4 Second point for second segment
394 * @return <code>true</code> if they are parallel or close to parallel
395 */
396 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
397
398 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
399 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
400 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
401 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid);
402
403 // Convert line from (point, point) form to ax+by=c
404 double a1 = p2.getY() - p1.getY();
405 double b1 = p1.getX() - p2.getX();
406
407 double a2 = p4.getY() - p3.getY();
408 double b2 = p3.getX() - p4.getX();
409
410 // Solve the equations
411 double det = a1 * b2 - a2 * b1;
412 // remove influence of of scaling factor
413 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
414 return Math.abs(det) < 1e-3;
415 }
416
417 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
418 CheckParameterUtil.ensureParameterNotNull(p1, "p1");
419 CheckParameterUtil.ensureParameterNotNull(p2, "p2");
420 CheckParameterUtil.ensureParameterNotNull(point, "point");
421
422 double ldx = p2.getX() - p1.getX();
423 double ldy = p2.getY() - p1.getY();
424
425 //segment zero length
426 if (ldx == 0 && ldy == 0)
427 return p1;
428
429 double pdx = point.getX() - p1.getX();
430 double pdy = point.getY() - p1.getY();
431
432 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
433
434 if (segmentOnly && offset <= 0)
435 return p1;
436 else if (segmentOnly && offset >= 1)
437 return p2;
438 else
439 return p1.interpolate(p2, offset);
440 }
441
442 /**
443 * Calculates closest point to a line segment.
444 * @param segmentP1 First point determining line segment
445 * @param segmentP2 Second point determining line segment
446 * @param point Point for which a closest point is searched on line segment [P1,P2]
447 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
448 * a new point if closest point is between segmentP1 and segmentP2.
449 * @see #closestPointToLine
450 * @since 3650
451 */
452 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
453 return closestPointTo(segmentP1, segmentP2, point, true);
454 }
455
456 /**
457 * Calculates closest point to a line.
458 * @param lineP1 First point determining line
459 * @param lineP2 Second point determining line
460 * @param point Point for which a closest point is searched on line (P1,P2)
461 * @return The closest point found on line. It may be outside the segment [P1,P2].
462 * @see #closestPointToSegment
463 * @since 4134
464 */
465 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
466 return closestPointTo(lineP1, lineP2, point, false);
467 }
468
469 /**
470 * This method tests if secondNode is clockwise to first node.
471 *
472 * The line through the two points commonNode and firstNode divides the
473 * plane into two parts. The test returns true, if secondNode lies in
474 * the part that is to the right when traveling in the direction from
475 * commonNode to firstNode.
476 *
477 * @param commonNode starting point for both vectors
478 * @param firstNode first vector end node
479 * @param secondNode second vector end node
480 * @return true if first vector is clockwise before second vector.
481 */
482 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
483
484 CheckParameterUtil.ensure(commonNode, "commonNode", EastNorth::isValid);
485 CheckParameterUtil.ensure(firstNode, "firstNode", EastNorth::isValid);
486 CheckParameterUtil.ensure(secondNode, "secondNode", EastNorth::isValid);
487
488 double dy1 = firstNode.getY() - commonNode.getY();
489 double dy2 = secondNode.getY() - commonNode.getY();
490 double dx1 = firstNode.getX() - commonNode.getX();
491 double dx2 = secondNode.getX() - commonNode.getX();
492
493 return dy1 * dx2 - dx1 * dy2 > 0;
494 }
495
496 /**
497 * Returns the Area of a polygon, from its list of nodes.
498 * @param polygon List of nodes forming polygon
499 * @return Area for the given list of nodes (EastNorth coordinates)
500 * @since 6841
501 */
502 public static Area getArea(List<Node> polygon) {
503 Path2D path = new Path2D.Double();
504
505 boolean begin = true;
506 for (Node n : polygon) {
507 EastNorth en = n.getEastNorth();
508 if (en != null) {
509 if (begin) {
510 path.moveTo(en.getX(), en.getY());
511 begin = false;
512 } else {
513 path.lineTo(en.getX(), en.getY());
514 }
515 }
516 }
517 if (!begin) {
518 path.closePath();
519 }
520
521 return new Area(path);
522 }
523
524 /**
525 * Builds a path from a list of nodes
526 * @param polygon Nodes, forming a closed polygon
527 * @param path2d path to add to; can be null, then a new path is created
528 * @return the path (LatLon coordinates)
529 */
530 public static Path2D buildPath2DLatLon(List<Node> polygon, Path2D path2d) {
531 Path2D path = path2d != null ? path2d : new Path2D.Double();
532 boolean begin = true;
533 for (Node n : polygon) {
534 if (begin) {
535 path.moveTo(n.lon(), n.lat());
536 begin = false;
537 } else {
538 path.lineTo(n.lon(), n.lat());
539 }
540 }
541 if (!begin) {
542 path.closePath();
543 }
544 return path;
545 }
546
547 /**
548 * Returns the Area of a polygon, from the multipolygon relation.
549 * @param multipolygon the multipolygon relation
550 * @return Area for the multipolygon (LatLon coordinates)
551 */
552 public static Area getAreaLatLon(Relation multipolygon) {
553 final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon);
554 Path2D path = new Path2D.Double();
555 path.setWindingRule(Path2D.WIND_EVEN_ODD);
556 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) {
557 buildPath2DLatLon(pd.getNodes(), path);
558 for (Multipolygon.PolyData pdInner : pd.getInners()) {
559 buildPath2DLatLon(pdInner.getNodes(), path);
560 }
561 }
562 return new Area(path);
563 }
564
565 /**
566 * Tests if two polygons intersect.
567 * @param first List of nodes forming first polygon
568 * @param second List of nodes forming second polygon
569 * @return intersection kind
570 */
571 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
572 Area a1 = getArea(first);
573 Area a2 = getArea(second);
574 return polygonIntersection(a1, a2);
575 }
576
577 /**
578 * Tests if two polygons intersect.
579 * @param a1 Area of first polygon
580 * @param a2 Area of second polygon
581 * @return intersection kind
582 * @since 6841
583 */
584 public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
585 return polygonIntersection(a1, a2, 1.0);
586 }
587
588 /**
589 * Tests if two polygons intersect.
590 * @param a1 Area of first polygon
591 * @param a2 Area of second polygon
592 * @param eps an area threshold, everything below is considered an empty intersection
593 * @return intersection kind
594 */
595 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
596
597 Area inter = new Area(a1);
598 inter.intersect(a2);
599
600 Rectangle bounds = inter.getBounds();
601
602 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
603 return PolygonIntersection.OUTSIDE;
604 } else if (a2.getBounds2D().contains(a1.getBounds2D()) && inter.equals(a1)) {
605 return PolygonIntersection.FIRST_INSIDE_SECOND;
606 } else if (a1.getBounds2D().contains(a2.getBounds2D()) && inter.equals(a2)) {
607 return PolygonIntersection.SECOND_INSIDE_FIRST;
608 } else {
609 return PolygonIntersection.CROSSING;
610 }
611 }
612
613 /**
614 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
615 * @param polygonNodes list of nodes from polygon path.
616 * @param point the point to test
617 * @return true if the point is inside polygon.
618 */
619 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
620 if (polygonNodes.size() < 2)
621 return false;
622
623 //iterate each side of the polygon, start with the last segment
624 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
625
626 if (!oldPoint.isLatLonKnown()) {
627 return false;
628 }
629
630 boolean inside = false;
631 Node p1, p2;
632
633 for (Node newPoint : polygonNodes) {
634 //skip duplicate points
635 if (newPoint.equals(oldPoint)) {
636 continue;
637 }
638
639 if (!newPoint.isLatLonKnown()) {
640 return false;
641 }
642
643 //order points so p1.lat <= p2.lat
644 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
645 p1 = oldPoint;
646 p2 = newPoint;
647 } else {
648 p1 = newPoint;
649 p2 = oldPoint;
650 }
651
652 EastNorth pEN = point.getEastNorth();
653 EastNorth opEN = oldPoint.getEastNorth();
654 EastNorth npEN = newPoint.getEastNorth();
655 EastNorth p1EN = p1.getEastNorth();
656 EastNorth p2EN = p2.getEastNorth();
657
658 if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
659 //test if the line is crossed and if so invert the inside flag.
660 if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
661 && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
662 < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
663 inside = !inside;
664 }
665 }
666
667 oldPoint = newPoint;
668 }
669
670 return inside;
671 }
672
673 /**
674 * Returns area of a closed way in square meters.
675 *
676 * @param way Way to measure, should be closed (first node is the same as last node)
677 * @return area of the closed way.
678 */
679 public static double closedWayArea(Way way) {
680 return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea();
681 }
682
683 /**
684 * Returns area of a multipolygon in square meters.
685 *
686 * @param multipolygon the multipolygon to measure
687 * @return area of the multipolygon.
688 */
689 public static double multipolygonArea(Relation multipolygon) {
690 double area = 0.0;
691 final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon);
692 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) {
693 area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea();
694 }
695 return area;
696 }
697
698 /**
699 * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives
700 *
701 * @param osm the primitive to measure
702 * @return area of the primitive, or {@code null}
703 */
704 public static Double computeArea(OsmPrimitive osm) {
705 if (osm instanceof Way && ((Way) osm).isClosed()) {
706 return closedWayArea((Way) osm);
707 } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) {
708 return multipolygonArea((Relation) osm);
709 } else {
710 return null;
711 }
712 }
713
714 /**
715 * Determines whether a way is oriented clockwise.
716 *
717 * Internals: Assuming a closed non-looping way, compute twice the area
718 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
719 * If the area is negative the way is ordered in a clockwise direction.
720 *
721 * See http://paulbourke.net/geometry/polyarea/
722 *
723 * @param w the way to be checked.
724 * @return true if and only if way is oriented clockwise.
725 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
726 */
727 public static boolean isClockwise(Way w) {
728 return isClockwise(w.getNodes());
729 }
730
731 /**
732 * Determines whether path from nodes list is oriented clockwise.
733 * @param nodes Nodes list to be checked.
734 * @return true if and only if way is oriented clockwise.
735 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
736 * @see #isClockwise(Way)
737 */
738 public static boolean isClockwise(List<Node> nodes) {
739 int nodesCount = nodes.size();
740 if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
741 throw new IllegalArgumentException("Way must be closed to check orientation.");
742 }
743 double area2 = 0.;
744
745 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
746 Node coorPrev = nodes.get(node - 1);
747 Node coorCurr = nodes.get(node % nodesCount);
748 area2 += coorPrev.lon() * coorCurr.lat();
749 area2 -= coorCurr.lon() * coorPrev.lat();
750 }
751 return area2 < 0;
752 }
753
754 /**
755 * Returns angle of a segment defined with 2 point coordinates.
756 *
757 * @param p1 first point
758 * @param p2 second point
759 * @return Angle in radians (-pi, pi]
760 */
761 public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
762
763 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
764 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
765
766 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
767 }
768
769 /**
770 * Returns angle of a corner defined with 3 point coordinates.
771 *
772 * @param p1 first point
773 * @param p2 Common endpoint
774 * @param p3 third point
775 * @return Angle in radians (-pi, pi]
776 */
777 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
778
779 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid);
780 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid);
781 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid);
782
783 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
784 if (result <= -Math.PI) {
785 result += 2 * Math.PI;
786 }
787
788 if (result > Math.PI) {
789 result -= 2 * Math.PI;
790 }
791
792 return result;
793 }
794
795 /**
796 * Compute the centroid/barycenter of nodes
797 * @param nodes Nodes for which the centroid is wanted
798 * @return the centroid of nodes
799 * @see Geometry#getCenter
800 */
801 public static EastNorth getCentroid(List<Node> nodes) {
802
803 BigDecimal area = BigDecimal.ZERO;
804 BigDecimal north = BigDecimal.ZERO;
805 BigDecimal east = BigDecimal.ZERO;
806
807 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
808 for (int i = 0; i < nodes.size(); i++) {
809 EastNorth n0 = nodes.get(i).getEastNorth();
810 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
811
812 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
813 BigDecimal x0 = BigDecimal.valueOf(n0.east());
814 BigDecimal y0 = BigDecimal.valueOf(n0.north());
815 BigDecimal x1 = BigDecimal.valueOf(n1.east());
816 BigDecimal y1 = BigDecimal.valueOf(n1.north());
817
818 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
819
820 area = area.add(k, MathContext.DECIMAL128);
821 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
822 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
823 }
824 }
825
826 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
827 area = area.multiply(d, MathContext.DECIMAL128);
828 if (area.compareTo(BigDecimal.ZERO) != 0) {
829 north = north.divide(area, MathContext.DECIMAL128);
830 east = east.divide(area, MathContext.DECIMAL128);
831 }
832
833 return new EastNorth(east.doubleValue(), north.doubleValue());
834 }
835
836 /**
837 * Compute center of the circle closest to different nodes.
838 *
839 * Ensure exact center computation in case nodes are already aligned in circle.
840 * This is done by least square method.
841 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
842 * Center must be intersection of all bisectors.
843 * <pre>
844 * [ a1 b1 ] [ -c1 ]
845 * With A = [ ... ... ] and Y = [ ... ]
846 * [ an bn ] [ -cn ]
847 * </pre>
848 * An approximation of center of circle is (At.A)^-1.At.Y
849 * @param nodes Nodes parts of the circle (at least 3)
850 * @return An approximation of the center, of null if there is no solution.
851 * @see Geometry#getCentroid
852 * @since 6934
853 */
854 public static EastNorth getCenter(List<Node> nodes) {
855 int nc = nodes.size();
856 if (nc < 3) return null;
857 /**
858 * Equation of each bisector ax + by + c = 0
859 */
860 double[] a = new double[nc];
861 double[] b = new double[nc];
862 double[] c = new double[nc];
863 // Compute equation of bisector
864 for (int i = 0; i < nc; i++) {
865 EastNorth pt1 = nodes.get(i).getEastNorth();
866 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
867 a[i] = pt1.east() - pt2.east();
868 b[i] = pt1.north() - pt2.north();
869 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
870 if (d == 0) return null;
871 a[i] /= d;
872 b[i] /= d;
873 double xC = (pt1.east() + pt2.east()) / 2;
874 double yC = (pt1.north() + pt2.north()) / 2;
875 c[i] = -(a[i]*xC + b[i]*yC);
876 }
877 // At.A = [aij]
878 double a11 = 0, a12 = 0, a22 = 0;
879 // At.Y = [bi]
880 double b1 = 0, b2 = 0;
881 for (int i = 0; i < nc; i++) {
882 a11 += a[i]*a[i];
883 a12 += a[i]*b[i];
884 a22 += b[i]*b[i];
885 b1 -= a[i]*c[i];
886 b2 -= b[i]*c[i];
887 }
888 // (At.A)^-1 = [invij]
889 double det = a11*a22 - a12*a12;
890 if (Math.abs(det) < 1e-5) return null;
891 double inv11 = a22/det;
892 double inv12 = -a12/det;
893 double inv22 = a11/det;
894 // center (xC, yC) = (At.A)^-1.At.y
895 double xC = inv11*b1 + inv12*b2;
896 double yC = inv12*b1 + inv22*b2;
897 return new EastNorth(xC, yC);
898 }
899
900 /**
901 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
902 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
903 * @param node node
904 * @param multiPolygon multipolygon
905 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
906 * @return {@code true} if the node is inside the multipolygon
907 */
908 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
909 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
910 }
911
912 /**
913 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
914 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
915 * <p>
916 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
917 * @param nodes nodes forming the polygon
918 * @param multiPolygon multipolygon
919 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
920 * @return {@code true} if the polygon formed by nodes is inside the multipolygon
921 */
922 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
923 // Extract outer/inner members from multipolygon
924 final Pair<List<JoinedPolygon>, List<JoinedPolygon>> outerInner;
925 try {
926 outerInner = MultipolygonBuilder.joinWays(multiPolygon);
927 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
928 Logging.trace(ex);
929 Logging.debug("Invalid multipolygon " + multiPolygon);
930 return false;
931 }
932 // Test if object is inside an outer member
933 for (JoinedPolygon out : outerInner.a) {
934 if (nodes.size() == 1
935 ? nodeInsidePolygon(nodes.get(0), out.getNodes())
936 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
937 polygonIntersection(nodes, out.getNodes()))) {
938 boolean insideInner = false;
939 // If inside an outer, check it is not inside an inner
940 for (JoinedPolygon in : outerInner.b) {
941 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
942 && (nodes.size() == 1
943 ? nodeInsidePolygon(nodes.get(0), in.getNodes())
944 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
945 insideInner = true;
946 break;
947 }
948 }
949 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
950 if (!insideInner) {
951 // Final check using predicate
952 if (isOuterWayAMatch == null || isOuterWayAMatch.test(out.ways.get(0)
953 /* TODO give a better representation of the outer ring to the predicate */)) {
954 return true;
955 }
956 }
957 }
958 }
959 return false;
960 }
961
962 /**
963 * Data class to hold two double values (area and perimeter of a polygon).
964 */
965 public static class AreaAndPerimeter {
966 private final double area;
967 private final double perimeter;
968
969 /**
970 * Create a new {@link AreaAndPerimeter}
971 * @param area The area
972 * @param perimeter The perimeter
973 */
974 public AreaAndPerimeter(double area, double perimeter) {
975 this.area = area;
976 this.perimeter = perimeter;
977 }
978
979 /**
980 * Gets the area
981 * @return The area size
982 */
983 public double getArea() {
984 return area;
985 }
986
987 /**
988 * Gets the perimeter
989 * @return The perimeter length
990 */
991 public double getPerimeter() {
992 return perimeter;
993 }
994 }
995
996 /**
997 * Calculate area and perimeter length of a polygon.
998 *
999 * Uses current projection; units are that of the projected coordinates.
1000 *
1001 * @param nodes the list of nodes representing the polygon
1002 * @return area and perimeter
1003 */
1004 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) {
1005 return getAreaAndPerimeter(nodes, null);
1006 }
1007
1008 /**
1009 * Calculate area and perimeter length of a polygon in the given projection.
1010 *
1011 * @param nodes the list of nodes representing the polygon
1012 * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()}
1013 * @return area and perimeter
1014 */
1015 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes, Projection projection) {
1016 CheckParameterUtil.ensureParameterNotNull(nodes, "nodes");
1017 double area = 0;
1018 double perimeter = 0;
1019 Projection useProjection = projection == null ? Main.getProjection() : projection;
1020
1021 if (!nodes.isEmpty()) {
1022 boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1);
1023 int numSegments = closed ? nodes.size() - 1 : nodes.size();
1024 EastNorth p1 = nodes.get(0).getEastNorth(useProjection);
1025 for (int i = 1; i <= numSegments; i++) {
1026 final Node node = nodes.get(i == numSegments ? 0 : i);
1027 final EastNorth p2 = node.getEastNorth(useProjection);
1028 if (p1 != null && p2 != null) {
1029 area += p1.east() * p2.north() - p2.east() * p1.north();
1030 perimeter += p1.distance(p2);
1031 }
1032 p1 = p2;
1033 }
1034 }
1035 return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
1036 }
1037}
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