source: josm/trunk/src/org/openstreetmap/josm/tools/Geometry.java@ 10570

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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.HashSet;
15import java.util.LinkedHashSet;
16import java.util.List;
17import java.util.Set;
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.coor.LatLon;
25import org.openstreetmap.josm.data.osm.BBox;
26import org.openstreetmap.josm.data.osm.MultipolygonBuilder;
27import org.openstreetmap.josm.data.osm.Node;
28import org.openstreetmap.josm.data.osm.NodePositionComparator;
29import org.openstreetmap.josm.data.osm.OsmPrimitive;
30import org.openstreetmap.josm.data.osm.OsmPrimitiveType;
31import org.openstreetmap.josm.data.osm.Relation;
32import org.openstreetmap.josm.data.osm.RelationMember;
33import org.openstreetmap.josm.data.osm.Way;
34import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon;
35import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache;
36import org.openstreetmap.josm.data.projection.Projection;
37import org.openstreetmap.josm.data.projection.Projections;
38
39/**
40 * Some tools for geometry related tasks.
41 *
42 * @author viesturs
43 */
44public final class Geometry {
45
46 private Geometry() {
47 // Hide default constructor for utils classes
48 }
49
50 public enum PolygonIntersection {
51 FIRST_INSIDE_SECOND,
52 SECOND_INSIDE_FIRST,
53 OUTSIDE,
54 CROSSING
55 }
56
57 /**
58 * Will find all intersection and add nodes there for list of given ways.
59 * Handles self-intersections too.
60 * And makes commands to add the intersection points to ways.
61 *
62 * Prerequisite: no two nodes have the same coordinates.
63 *
64 * @param ways a list of ways to test
65 * @param test if false, do not build list of Commands, just return nodes
66 * @param cmds list of commands, typically empty when handed to this method.
67 * Will be filled with commands that add intersection nodes to
68 * the ways.
69 * @return list of new nodes
70 */
71 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
72
73 int n = ways.size();
74 @SuppressWarnings("unchecked")
75 List<Node>[] newNodes = new ArrayList[n];
76 BBox[] wayBounds = new BBox[n];
77 boolean[] changedWays = new boolean[n];
78
79 Set<Node> intersectionNodes = new LinkedHashSet<>();
80
81 //copy node arrays for local usage.
82 for (int pos = 0; pos < n; pos++) {
83 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
84 wayBounds[pos] = getNodesBounds(newNodes[pos]);
85 changedWays[pos] = false;
86 }
87
88 //iterate over all way pairs and introduce the intersections
89 Comparator<Node> coordsComparator = new NodePositionComparator();
90 for (int seg1Way = 0; seg1Way < n; seg1Way++) {
91 for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
92
93 //do not waste time on bounds that do not intersect
94 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
95 continue;
96 }
97
98 List<Node> way1Nodes = newNodes[seg1Way];
99 List<Node> way2Nodes = newNodes[seg2Way];
100
101 //iterate over primary segmemt
102 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
103
104 //iterate over secondary segment
105 int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
106
107 for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
108
109 //need to get them again every time, because other segments may be changed
110 Node seg1Node1 = way1Nodes.get(seg1Pos);
111 Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
112 Node seg2Node1 = way2Nodes.get(seg2Pos);
113 Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
114
115 int commonCount = 0;
116 //test if we have common nodes to add.
117 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
118 commonCount++;
119
120 if (seg1Way == seg2Way &&
121 seg1Pos == 0 &&
122 seg2Pos == way2Nodes.size() -2) {
123 //do not add - this is first and last segment of the same way.
124 } else {
125 intersectionNodes.add(seg1Node1);
126 }
127 }
128
129 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
130 commonCount++;
131
132 intersectionNodes.add(seg1Node2);
133 }
134
135 //no common nodes - find intersection
136 if (commonCount == 0) {
137 EastNorth intersection = getSegmentSegmentIntersection(
138 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
139 seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
140
141 if (intersection != null) {
142 if (test) {
143 intersectionNodes.add(seg2Node1);
144 return intersectionNodes;
145 }
146
147 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
148 Node intNode = newNode;
149 boolean insertInSeg1 = false;
150 boolean insertInSeg2 = false;
151 //find if the intersection point is at end point of one of the segments, if so use that point
152
153 //segment 1
154 if (coordsComparator.compare(newNode, seg1Node1) == 0) {
155 intNode = seg1Node1;
156 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
157 intNode = seg1Node2;
158 } else {
159 insertInSeg1 = true;
160 }
161
162 //segment 2
163 if (coordsComparator.compare(newNode, seg2Node1) == 0) {
164 intNode = seg2Node1;
165 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
166 intNode = seg2Node2;
167 } else {
168 insertInSeg2 = true;
169 }
170
171 if (insertInSeg1) {
172 way1Nodes.add(seg1Pos +1, intNode);
173 changedWays[seg1Way] = true;
174
175 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
176 if (seg2Way == seg1Way) {
177 seg2Pos++;
178 }
179 }
180
181 if (insertInSeg2) {
182 way2Nodes.add(seg2Pos +1, intNode);
183 changedWays[seg2Way] = true;
184
185 //Do not need to compare again to already split segment
186 seg2Pos++;
187 }
188
189 intersectionNodes.add(intNode);
190
191 if (intNode == newNode) {
192 cmds.add(new AddCommand(intNode));
193 }
194 }
195 } else if (test && !intersectionNodes.isEmpty())
196 return intersectionNodes;
197 }
198 }
199 }
200 }
201
202
203 for (int pos = 0; pos < ways.size(); pos++) {
204 if (!changedWays[pos]) {
205 continue;
206 }
207
208 Way way = ways.get(pos);
209 Way newWay = new Way(way);
210 newWay.setNodes(newNodes[pos]);
211
212 cmds.add(new ChangeCommand(way, newWay));
213 }
214
215 return intersectionNodes;
216 }
217
218 private static BBox getNodesBounds(List<Node> nodes) {
219
220 BBox bounds = new BBox(nodes.get(0));
221 for (Node n: nodes) {
222 bounds.add(n.getCoor());
223 }
224 return bounds;
225 }
226
227 /**
228 * Tests if given point is to the right side of path consisting of 3 points.
229 *
230 * (Imagine the path is continued beyond the endpoints, so you get two rays
231 * starting from lineP2 and going through lineP1 and lineP3 respectively
232 * which divide the plane into two parts. The test returns true, if testPoint
233 * lies in the part that is to the right when traveling in the direction
234 * lineP1, lineP2, lineP3.)
235 *
236 * @param lineP1 first point in path
237 * @param lineP2 second point in path
238 * @param lineP3 third point in path
239 * @param testPoint point to test
240 * @return true if to the right side, false otherwise
241 */
242 public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
243 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
244 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
245 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
246
247 if (pathBendToRight)
248 return rightOfSeg1 && rightOfSeg2;
249 else
250 return !(!rightOfSeg1 && !rightOfSeg2);
251 }
252
253 /**
254 * This method tests if secondNode is clockwise to first node.
255 * @param commonNode starting point for both vectors
256 * @param firstNode first vector end node
257 * @param secondNode second vector end node
258 * @return true if first vector is clockwise before second vector.
259 */
260 public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
261 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
262 }
263
264 /**
265 * Finds the intersection of two line segments.
266 * @param p1 the coordinates of the start point of the first specified line segment
267 * @param p2 the coordinates of the end point of the first specified line segment
268 * @param p3 the coordinates of the start point of the second specified line segment
269 * @param p4 the coordinates of the end point of the second specified line segment
270 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
271 */
272 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
273
274 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
275 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
276 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
277 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
278
279 double x1 = p1.getX();
280 double y1 = p1.getY();
281 double x2 = p2.getX();
282 double y2 = p2.getY();
283 double x3 = p3.getX();
284 double y3 = p3.getY();
285 double x4 = p4.getX();
286 double y4 = p4.getY();
287
288 //TODO: do this locally.
289 //TODO: remove this check after careful testing
290 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
291
292 // solve line-line intersection in parametric form:
293 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v
294 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
295 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
296
297 double a1 = x2 - x1;
298 double b1 = x3 - x4;
299 double c1 = x3 - x1;
300
301 double a2 = y2 - y1;
302 double b2 = y3 - y4;
303 double c2 = y3 - y1;
304
305 // Solve the equations
306 double det = a1*b2 - a2*b1;
307
308 double uu = b2*c1 - b1*c2;
309 double vv = a1*c2 - a2*c1;
310 double mag = Math.abs(uu)+Math.abs(vv);
311
312 if (Math.abs(det) > 1e-12 * mag) {
313 double u = uu/det, v = vv/det;
314 if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
315 if (u < 0) u = 0;
316 if (u > 1) u = 1.0;
317 return new EastNorth(x1+a1*u, y1+a2*u);
318 } else {
319 return null;
320 }
321 } else {
322 // parallel lines
323 return null;
324 }
325 }
326
327 /**
328 * Finds the intersection of two lines of infinite length.
329 *
330 * @param p1 first point on first line
331 * @param p2 second point on first line
332 * @param p3 first point on second line
333 * @param p4 second point on second line
334 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
335 * @throws IllegalArgumentException if a parameter is null or without valid coordinates
336 */
337 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
338
339 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
340 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
341 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
342 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
343
344 if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
345
346 // Basically, the formula from wikipedia is used:
347 // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
348 // However, large numbers lead to rounding errors (see #10286).
349 // To avoid this, p1 is first substracted from each of the points:
350 // p1' = 0
351 // p2' = p2 - p1
352 // p3' = p3 - p1
353 // p4' = p4 - p1
354 // In the end, p1 is added to the intersection point of segment p1'/p2'
355 // and segment p3'/p4'.
356
357 // Convert line from (point, point) form to ax+by=c
358 double a1 = p2.getY() - p1.getY();
359 double b1 = p1.getX() - p2.getX();
360
361 double a2 = p4.getY() - p3.getY();
362 double b2 = p3.getX() - p4.getX();
363
364 // Solve the equations
365 double det = a1 * b2 - a2 * b1;
366 if (det == 0)
367 return null; // Lines are parallel
368
369 double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
370
371 return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
372 }
373
374 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
375
376 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
377 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
378 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
379 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
380
381 // Convert line from (point, point) form to ax+by=c
382 double a1 = p2.getY() - p1.getY();
383 double b1 = p1.getX() - p2.getX();
384
385 double a2 = p4.getY() - p3.getY();
386 double b2 = p3.getX() - p4.getX();
387
388 // Solve the equations
389 double det = a1 * b2 - a2 * b1;
390 // remove influence of of scaling factor
391 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
392 return Math.abs(det) < 1e-3;
393 }
394
395 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
396 CheckParameterUtil.ensureParameterNotNull(p1, "p1");
397 CheckParameterUtil.ensureParameterNotNull(p2, "p2");
398 CheckParameterUtil.ensureParameterNotNull(point, "point");
399
400 double ldx = p2.getX() - p1.getX();
401 double ldy = p2.getY() - p1.getY();
402
403 //segment zero length
404 if (ldx == 0 && ldy == 0)
405 return p1;
406
407 double pdx = point.getX() - p1.getX();
408 double pdy = point.getY() - p1.getY();
409
410 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
411
412 if (segmentOnly && offset <= 0)
413 return p1;
414 else if (segmentOnly && offset >= 1)
415 return p2;
416 else
417 return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
418 }
419
420 /**
421 * Calculates closest point to a line segment.
422 * @param segmentP1 First point determining line segment
423 * @param segmentP2 Second point determining line segment
424 * @param point Point for which a closest point is searched on line segment [P1,P2]
425 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
426 * a new point if closest point is between segmentP1 and segmentP2.
427 * @see #closestPointToLine
428 * @since 3650
429 */
430 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
431 return closestPointTo(segmentP1, segmentP2, point, true);
432 }
433
434 /**
435 * Calculates closest point to a line.
436 * @param lineP1 First point determining line
437 * @param lineP2 Second point determining line
438 * @param point Point for which a closest point is searched on line (P1,P2)
439 * @return The closest point found on line. It may be outside the segment [P1,P2].
440 * @see #closestPointToSegment
441 * @since 4134
442 */
443 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
444 return closestPointTo(lineP1, lineP2, point, false);
445 }
446
447 /**
448 * This method tests if secondNode is clockwise to first node.
449 *
450 * The line through the two points commonNode and firstNode divides the
451 * plane into two parts. The test returns true, if secondNode lies in
452 * the part that is to the right when traveling in the direction from
453 * commonNode to firstNode.
454 *
455 * @param commonNode starting point for both vectors
456 * @param firstNode first vector end node
457 * @param secondNode second vector end node
458 * @return true if first vector is clockwise before second vector.
459 */
460 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
461
462 CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
463 CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
464 CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
465
466 double dy1 = firstNode.getY() - commonNode.getY();
467 double dy2 = secondNode.getY() - commonNode.getY();
468 double dx1 = firstNode.getX() - commonNode.getX();
469 double dx2 = secondNode.getX() - commonNode.getX();
470
471 return dy1 * dx2 - dx1 * dy2 > 0;
472 }
473
474 /**
475 * Returns the Area of a polygon, from its list of nodes.
476 * @param polygon List of nodes forming polygon (EastNorth coordinates)
477 * @return Area for the given list of nodes
478 * @since 6841
479 */
480 public static Area getArea(List<Node> polygon) {
481 Path2D path = new Path2D.Double();
482
483 boolean begin = true;
484 for (Node n : polygon) {
485 EastNorth en = n.getEastNorth();
486 if (en != null) {
487 if (begin) {
488 path.moveTo(en.getX(), en.getY());
489 begin = false;
490 } else {
491 path.lineTo(en.getX(), en.getY());
492 }
493 }
494 }
495 if (!begin) {
496 path.closePath();
497 }
498
499 return new Area(path);
500 }
501
502 /**
503 * Returns the Area of a polygon, from its list of nodes.
504 * @param polygon List of nodes forming polygon (LatLon coordinates)
505 * @return Area for the given list of nodes
506 * @since 6841
507 */
508 public static Area getAreaLatLon(List<Node> polygon) {
509 Path2D path = new Path2D.Double();
510
511 boolean begin = true;
512 for (Node n : polygon) {
513 if (begin) {
514 path.moveTo(n.getCoor().lon(), n.getCoor().lat());
515 begin = false;
516 } else {
517 path.lineTo(n.getCoor().lon(), n.getCoor().lat());
518 }
519 }
520 if (!begin) {
521 path.closePath();
522 }
523
524 return new Area(path);
525 }
526
527 /**
528 * Tests if two polygons intersect.
529 * @param first List of nodes forming first polygon
530 * @param second List of nodes forming second polygon
531 * @return intersection kind
532 */
533 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
534 Area a1 = getArea(first);
535 Area a2 = getArea(second);
536 return polygonIntersection(a1, a2);
537 }
538
539 /**
540 * Tests if two polygons intersect.
541 * @param a1 Area of first polygon
542 * @param a2 Area of second polygon
543 * @return intersection kind
544 * @since 6841
545 */
546 public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
547 return polygonIntersection(a1, a2, 1.0);
548 }
549
550 /**
551 * Tests if two polygons intersect.
552 * @param a1 Area of first polygon
553 * @param a2 Area of second polygon
554 * @param eps an area threshold, everything below is considered an empty intersection
555 * @return intersection kind
556 */
557 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
558
559 Area inter = new Area(a1);
560 inter.intersect(a2);
561
562 Rectangle bounds = inter.getBounds();
563
564 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
565 return PolygonIntersection.OUTSIDE;
566 } else if (inter.equals(a1)) {
567 return PolygonIntersection.FIRST_INSIDE_SECOND;
568 } else if (inter.equals(a2)) {
569 return PolygonIntersection.SECOND_INSIDE_FIRST;
570 } else {
571 return PolygonIntersection.CROSSING;
572 }
573 }
574
575 /**
576 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
577 * @param polygonNodes list of nodes from polygon path.
578 * @param point the point to test
579 * @return true if the point is inside polygon.
580 */
581 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
582 if (polygonNodes.size() < 2)
583 return false;
584
585 //iterate each side of the polygon, start with the last segment
586 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
587
588 if (!oldPoint.isLatLonKnown()) {
589 return false;
590 }
591
592 boolean inside = false;
593 Node p1, p2;
594
595 for (Node newPoint : polygonNodes) {
596 //skip duplicate points
597 if (newPoint.equals(oldPoint)) {
598 continue;
599 }
600
601 if (!newPoint.isLatLonKnown()) {
602 return false;
603 }
604
605 //order points so p1.lat <= p2.lat
606 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
607 p1 = oldPoint;
608 p2 = newPoint;
609 } else {
610 p1 = newPoint;
611 p2 = oldPoint;
612 }
613
614 EastNorth pEN = point.getEastNorth();
615 EastNorth opEN = oldPoint.getEastNorth();
616 EastNorth npEN = newPoint.getEastNorth();
617 EastNorth p1EN = p1.getEastNorth();
618 EastNorth p2EN = p2.getEastNorth();
619
620 if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
621 //test if the line is crossed and if so invert the inside flag.
622 if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
623 && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
624 < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
625 inside = !inside;
626 }
627 }
628
629 oldPoint = newPoint;
630 }
631
632 return inside;
633 }
634
635 /**
636 * Returns area of a closed way in square meters.
637 *
638 * @param way Way to measure, should be closed (first node is the same as last node)
639 * @return area of the closed way.
640 */
641 public static double closedWayArea(Way way) {
642 return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea();
643 }
644
645 /**
646 * Returns area of a multipolygon in square meters.
647 *
648 * @param multipolygon the multipolygon to measure
649 * @return area of the multipolygon.
650 */
651 public static double multipolygonArea(Relation multipolygon) {
652 double area = 0.0;
653 final Multipolygon mp = Main.map == null || Main.map.mapView == null
654 ? new Multipolygon(multipolygon)
655 : MultipolygonCache.getInstance().get(Main.map.mapView, multipolygon);
656 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) {
657 area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea();
658 }
659 return area;
660 }
661
662 /**
663 * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives
664 *
665 * @param osm the primitive to measure
666 * @return area of the primitive, or {@code null}
667 */
668 public static Double computeArea(OsmPrimitive osm) {
669 if (osm instanceof Way && ((Way) osm).isClosed()) {
670 return closedWayArea((Way) osm);
671 } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) {
672 return multipolygonArea((Relation) osm);
673 } else {
674 return null;
675 }
676 }
677
678 /**
679 * Determines whether a way is oriented clockwise.
680 *
681 * Internals: Assuming a closed non-looping way, compute twice the area
682 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
683 * If the area is negative the way is ordered in a clockwise direction.
684 *
685 * See http://paulbourke.net/geometry/polyarea/
686 *
687 * @param w the way to be checked.
688 * @return true if and only if way is oriented clockwise.
689 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
690 */
691 public static boolean isClockwise(Way w) {
692 return isClockwise(w.getNodes());
693 }
694
695 /**
696 * Determines whether path from nodes list is oriented clockwise.
697 * @param nodes Nodes list to be checked.
698 * @return true if and only if way is oriented clockwise.
699 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
700 * @see #isClockwise(Way)
701 */
702 public static boolean isClockwise(List<Node> nodes) {
703 int nodesCount = nodes.size();
704 if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
705 throw new IllegalArgumentException("Way must be closed to check orientation.");
706 }
707 double area2 = 0.;
708
709 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
710 LatLon coorPrev = nodes.get(node - 1).getCoor();
711 LatLon coorCurr = nodes.get(node % nodesCount).getCoor();
712 area2 += coorPrev.lon() * coorCurr.lat();
713 area2 -= coorCurr.lon() * coorPrev.lat();
714 }
715 return area2 < 0;
716 }
717
718 /**
719 * Returns angle of a segment defined with 2 point coordinates.
720 *
721 * @param p1 first point
722 * @param p2 second point
723 * @return Angle in radians (-pi, pi]
724 */
725 public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
726
727 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
728 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
729
730 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
731 }
732
733 /**
734 * Returns angle of a corner defined with 3 point coordinates.
735 *
736 * @param p1 first point
737 * @param p2 Common endpoint
738 * @param p3 third point
739 * @return Angle in radians (-pi, pi]
740 */
741 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
742
743 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
744 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
745 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
746
747 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
748 if (result <= -Math.PI) {
749 result += 2 * Math.PI;
750 }
751
752 if (result > Math.PI) {
753 result -= 2 * Math.PI;
754 }
755
756 return result;
757 }
758
759 /**
760 * Compute the centroid/barycenter of nodes
761 * @param nodes Nodes for which the centroid is wanted
762 * @return the centroid of nodes
763 * @see Geometry#getCenter
764 */
765 public static EastNorth getCentroid(List<Node> nodes) {
766
767 BigDecimal area = BigDecimal.ZERO;
768 BigDecimal north = BigDecimal.ZERO;
769 BigDecimal east = BigDecimal.ZERO;
770
771 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
772 for (int i = 0; i < nodes.size(); i++) {
773 EastNorth n0 = nodes.get(i).getEastNorth();
774 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
775
776 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
777 BigDecimal x0 = BigDecimal.valueOf(n0.east());
778 BigDecimal y0 = BigDecimal.valueOf(n0.north());
779 BigDecimal x1 = BigDecimal.valueOf(n1.east());
780 BigDecimal y1 = BigDecimal.valueOf(n1.north());
781
782 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
783
784 area = area.add(k, MathContext.DECIMAL128);
785 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
786 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
787 }
788 }
789
790 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
791 area = area.multiply(d, MathContext.DECIMAL128);
792 if (area.compareTo(BigDecimal.ZERO) != 0) {
793 north = north.divide(area, MathContext.DECIMAL128);
794 east = east.divide(area, MathContext.DECIMAL128);
795 }
796
797 return new EastNorth(east.doubleValue(), north.doubleValue());
798 }
799
800 /**
801 * Compute center of the circle closest to different nodes.
802 *
803 * Ensure exact center computation in case nodes are already aligned in circle.
804 * This is done by least square method.
805 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
806 * Center must be intersection of all bisectors.
807 * <pre>
808 * [ a1 b1 ] [ -c1 ]
809 * With A = [ ... ... ] and Y = [ ... ]
810 * [ an bn ] [ -cn ]
811 * </pre>
812 * An approximation of center of circle is (At.A)^-1.At.Y
813 * @param nodes Nodes parts of the circle (at least 3)
814 * @return An approximation of the center, of null if there is no solution.
815 * @see Geometry#getCentroid
816 * @since 6934
817 */
818 public static EastNorth getCenter(List<Node> nodes) {
819 int nc = nodes.size();
820 if (nc < 3) return null;
821 /**
822 * Equation of each bisector ax + by + c = 0
823 */
824 double[] a = new double[nc];
825 double[] b = new double[nc];
826 double[] c = new double[nc];
827 // Compute equation of bisector
828 for (int i = 0; i < nc; i++) {
829 EastNorth pt1 = nodes.get(i).getEastNorth();
830 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
831 a[i] = pt1.east() - pt2.east();
832 b[i] = pt1.north() - pt2.north();
833 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
834 if (d == 0) return null;
835 a[i] /= d;
836 b[i] /= d;
837 double xC = (pt1.east() + pt2.east()) / 2;
838 double yC = (pt1.north() + pt2.north()) / 2;
839 c[i] = -(a[i]*xC + b[i]*yC);
840 }
841 // At.A = [aij]
842 double a11 = 0, a12 = 0, a22 = 0;
843 // At.Y = [bi]
844 double b1 = 0, b2 = 0;
845 for (int i = 0; i < nc; i++) {
846 a11 += a[i]*a[i];
847 a12 += a[i]*b[i];
848 a22 += b[i]*b[i];
849 b1 -= a[i]*c[i];
850 b2 -= b[i]*c[i];
851 }
852 // (At.A)^-1 = [invij]
853 double det = a11*a22 - a12*a12;
854 if (Math.abs(det) < 1e-5) return null;
855 double inv11 = a22/det;
856 double inv12 = -a12/det;
857 double inv22 = a11/det;
858 // center (xC, yC) = (At.A)^-1.At.y
859 double xC = inv11*b1 + inv12*b2;
860 double yC = inv12*b1 + inv22*b2;
861 return new EastNorth(xC, yC);
862 }
863
864 public static class MultiPolygonMembers {
865 public final Set<Way> outers = new HashSet<>();
866 public final Set<Way> inners = new HashSet<>();
867
868 public MultiPolygonMembers(Relation multiPolygon) {
869 for (RelationMember m : multiPolygon.getMembers()) {
870 if (m.getType().equals(OsmPrimitiveType.WAY)) {
871 if ("outer".equals(m.getRole())) {
872 outers.add(m.getWay());
873 } else if ("inner".equals(m.getRole())) {
874 inners.add(m.getWay());
875 }
876 }
877 }
878 }
879 }
880
881 /**
882 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
883 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
884 * @param node node
885 * @param multiPolygon multipolygon
886 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
887 * @return {@code true} if the node is inside the multipolygon
888 */
889 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
890 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
891 }
892
893 /**
894 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
895 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
896 * <p>
897 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
898 * @param nodes nodes forming the polygon
899 * @param multiPolygon multipolygon
900 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
901 * @return {@code true} if the polygon formed by nodes is inside the multipolygon
902 */
903 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
904 // Extract outer/inner members from multipolygon
905 final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
906 // Construct complete rings for the inner/outer members
907 final List<MultipolygonBuilder.JoinedPolygon> outerRings;
908 final List<MultipolygonBuilder.JoinedPolygon> innerRings;
909 try {
910 outerRings = MultipolygonBuilder.joinWays(mpm.outers);
911 innerRings = MultipolygonBuilder.joinWays(mpm.inners);
912 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
913 Main.debug("Invalid multipolygon " + multiPolygon);
914 return false;
915 }
916 // Test if object is inside an outer member
917 for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
918 if (nodes.size() == 1
919 ? nodeInsidePolygon(nodes.get(0), out.getNodes())
920 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
921 polygonIntersection(nodes, out.getNodes()))) {
922 boolean insideInner = false;
923 // If inside an outer, check it is not inside an inner
924 for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
925 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
926 && (nodes.size() == 1
927 ? nodeInsidePolygon(nodes.get(0), in.getNodes())
928 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
929 insideInner = true;
930 break;
931 }
932 }
933 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
934 if (!insideInner) {
935 // Final check using predicate
936 if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0)
937 /* TODO give a better representation of the outer ring to the predicate */)) {
938 return true;
939 }
940 }
941 }
942 }
943 return false;
944 }
945
946 /**
947 * Data class to hold two double values (area and perimeter of a polygon).
948 */
949 public static class AreaAndPerimeter {
950 private final double area;
951 private final double perimeter;
952
953 public AreaAndPerimeter(double area, double perimeter) {
954 this.area = area;
955 this.perimeter = perimeter;
956 }
957
958 public double getArea() {
959 return area;
960 }
961
962 public double getPerimeter() {
963 return perimeter;
964 }
965 }
966
967 /**
968 * Calculate area and perimeter length of a polygon.
969 *
970 * Uses current projection; units are that of the projected coordinates.
971 *
972 * @param nodes the list of nodes representing the polygon
973 * @return area and perimeter
974 */
975 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) {
976 return getAreaAndPerimeter(nodes, null);
977 }
978
979 /**
980 * Calculate area and perimeter length of a polygon in the given projection.
981 *
982 * @param nodes the list of nodes representing the polygon
983 * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()}
984 * @return area and perimeter
985 */
986 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes, Projection projection) {
987 CheckParameterUtil.ensureParameterNotNull(nodes, "nodes");
988 double area = 0;
989 double perimeter = 0;
990 if (!nodes.isEmpty()) {
991 boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1);
992 int numSegments = closed ? nodes.size() - 1 : nodes.size();
993 EastNorth p1 = projection == null ? nodes.get(0).getEastNorth() : projection.latlon2eastNorth(nodes.get(0).getCoor());
994 for (int i = 1; i <= numSegments; i++) {
995 final Node node = nodes.get(i == numSegments ? 0 : i);
996 final EastNorth p2 = projection == null ? node.getEastNorth() : projection.latlon2eastNorth(node.getCoor());
997 area += p1.east() * p2.north() - p2.east() * p1.north();
998 perimeter += p1.distance(p2);
999 p1 = p2;
1000 }
1001 }
1002 return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
1003 }
1004}
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