source: josm/trunk/src/org/openstreetmap/josm/tools/Geometry.java@ 7447

Last change on this file since 7447 was 7392, checked in by Don-vip, 10 years ago

code cleanup, javadoc update
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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.OsmPrimitiveType;
30import org.openstreetmap.josm.data.osm.Relation;
31import org.openstreetmap.josm.data.osm.RelationMember;
32import org.openstreetmap.josm.data.osm.Way;
33
34/**
35 * Some tools for geometry related tasks.
36 *
37 * @author viesturs
38 */
39public final class Geometry {
40
41 private Geometry() {
42 // Hide default constructor for utils classes
43 }
44
45 public enum PolygonIntersection {FIRST_INSIDE_SECOND, SECOND_INSIDE_FIRST, OUTSIDE, CROSSING}
46
47 /**
48 * Will find all intersection and add nodes there for list of given ways.
49 * Handles self-intersections too.
50 * And makes commands to add the intersection points to ways.
51 *
52 * Prerequisite: no two nodes have the same coordinates.
53 *
54 * @param ways a list of ways to test
55 * @param test if false, do not build list of Commands, just return nodes
56 * @param cmds list of commands, typically empty when handed to this method.
57 * Will be filled with commands that add intersection nodes to
58 * the ways.
59 * @return list of new nodes
60 */
61 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
62
63 int n = ways.size();
64 @SuppressWarnings("unchecked")
65 List<Node>[] newNodes = new ArrayList[n];
66 BBox[] wayBounds = new BBox[n];
67 boolean[] changedWays = new boolean[n];
68
69 Set<Node> intersectionNodes = new LinkedHashSet<>();
70
71 //copy node arrays for local usage.
72 for (int pos = 0; pos < n; pos ++) {
73 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
74 wayBounds[pos] = getNodesBounds(newNodes[pos]);
75 changedWays[pos] = false;
76 }
77
78 //iterate over all way pairs and introduce the intersections
79 Comparator<Node> coordsComparator = new NodePositionComparator();
80 for (int seg1Way = 0; seg1Way < n; seg1Way ++) {
81 for (int seg2Way = seg1Way; seg2Way < n; seg2Way ++) {
82
83 //do not waste time on bounds that do not intersect
84 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
85 continue;
86 }
87
88 List<Node> way1Nodes = newNodes[seg1Way];
89 List<Node> way2Nodes = newNodes[seg2Way];
90
91 //iterate over primary segmemt
92 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos ++) {
93
94 //iterate over secondary segment
95 int seg2Start = seg1Way != seg2Way ? 0: seg1Pos + 2;//skip the adjacent segment
96
97 for (int seg2Pos = seg2Start; seg2Pos + 1< way2Nodes.size(); seg2Pos ++) {
98
99 //need to get them again every time, because other segments may be changed
100 Node seg1Node1 = way1Nodes.get(seg1Pos);
101 Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
102 Node seg2Node1 = way2Nodes.get(seg2Pos);
103 Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
104
105 int commonCount = 0;
106 //test if we have common nodes to add.
107 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
108 commonCount ++;
109
110 if (seg1Way == seg2Way &&
111 seg1Pos == 0 &&
112 seg2Pos == way2Nodes.size() -2) {
113 //do not add - this is first and last segment of the same way.
114 } else {
115 intersectionNodes.add(seg1Node1);
116 }
117 }
118
119 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
120 commonCount ++;
121
122 intersectionNodes.add(seg1Node2);
123 }
124
125 //no common nodes - find intersection
126 if (commonCount == 0) {
127 EastNorth intersection = getSegmentSegmentIntersection(
128 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
129 seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
130
131 if (intersection != null) {
132 if (test) {
133 intersectionNodes.add(seg2Node1);
134 return intersectionNodes;
135 }
136
137 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
138 Node intNode = newNode;
139 boolean insertInSeg1 = false;
140 boolean insertInSeg2 = false;
141 //find if the intersection point is at end point of one of the segments, if so use that point
142
143 //segment 1
144 if (coordsComparator.compare(newNode, seg1Node1) == 0) {
145 intNode = seg1Node1;
146 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
147 intNode = seg1Node2;
148 } else {
149 insertInSeg1 = true;
150 }
151
152 //segment 2
153 if (coordsComparator.compare(newNode, seg2Node1) == 0) {
154 intNode = seg2Node1;
155 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
156 intNode = seg2Node2;
157 } else {
158 insertInSeg2 = true;
159 }
160
161 if (insertInSeg1) {
162 way1Nodes.add(seg1Pos +1, intNode);
163 changedWays[seg1Way] = true;
164
165 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
166 if (seg2Way == seg1Way) {
167 seg2Pos ++;
168 }
169 }
170
171 if (insertInSeg2) {
172 way2Nodes.add(seg2Pos +1, intNode);
173 changedWays[seg2Way] = true;
174
175 //Do not need to compare again to already split segment
176 seg2Pos ++;
177 }
178
179 intersectionNodes.add(intNode);
180
181 if (intNode == newNode) {
182 cmds.add(new AddCommand(intNode));
183 }
184 }
185 }
186 else if (test && !intersectionNodes.isEmpty())
187 return intersectionNodes;
188 }
189 }
190 }
191 }
192
193
194 for (int pos = 0; pos < ways.size(); pos ++) {
195 if (!changedWays[pos]) {
196 continue;
197 }
198
199 Way way = ways.get(pos);
200 Way newWay = new Way(way);
201 newWay.setNodes(newNodes[pos]);
202
203 cmds.add(new ChangeCommand(way, newWay));
204 }
205
206 return intersectionNodes;
207 }
208
209 private static BBox getNodesBounds(List<Node> nodes) {
210
211 BBox bounds = new BBox(nodes.get(0));
212 for (Node n: nodes) {
213 bounds.add(n.getCoor());
214 }
215 return bounds;
216 }
217
218 /**
219 * Tests if given point is to the right side of path consisting of 3 points.
220 *
221 * (Imagine the path is continued beyond the endpoints, so you get two rays
222 * starting from lineP2 and going through lineP1 and lineP3 respectively
223 * which divide the plane into two parts. The test returns true, if testPoint
224 * lies in the part that is to the right when traveling in the direction
225 * lineP1, lineP2, lineP3.)
226 *
227 * @param lineP1 first point in path
228 * @param lineP2 second point in path
229 * @param lineP3 third point in path
230 * @param testPoint
231 * @return true if to the right side, false otherwise
232 */
233 public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
234 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
235 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
236 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
237
238 if (pathBendToRight)
239 return rightOfSeg1 && rightOfSeg2;
240 else
241 return !(!rightOfSeg1 && !rightOfSeg2);
242 }
243
244 /**
245 * This method tests if secondNode is clockwise to first node.
246 * @param commonNode starting point for both vectors
247 * @param firstNode first vector end node
248 * @param secondNode second vector end node
249 * @return true if first vector is clockwise before second vector.
250 */
251 public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
252 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
253 }
254
255 /**
256 * Finds the intersection of two line segments
257 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
258 */
259 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
260
261 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
262 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
263 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
264 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
265
266 double x1 = p1.getX();
267 double y1 = p1.getY();
268 double x2 = p2.getX();
269 double y2 = p2.getY();
270 double x3 = p3.getX();
271 double y3 = p3.getY();
272 double x4 = p4.getX();
273 double y4 = p4.getY();
274
275 //TODO: do this locally.
276 //TODO: remove this check after careful testing
277 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
278
279 // solve line-line intersection in parametric form:
280 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v
281 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
282 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
283
284 double a1 = x2 - x1;
285 double b1 = x3 - x4;
286 double c1 = x3 - x1;
287
288 double a2 = y2 - y1;
289 double b2 = y3 - y4;
290 double c2 = y3 - y1;
291
292 // Solve the equations
293 double det = a1*b2 - a2*b1;
294
295 double uu = b2*c1 - b1*c2 ;
296 double vv = a1*c2 - a2*c1;
297 double mag = Math.abs(uu)+Math.abs(vv);
298
299 if (Math.abs(det) > 1e-12 * mag) {
300 double u = uu/det, v = vv/det;
301 if (u>-1e-8 && u < 1+1e-8 && v>-1e-8 && v < 1+1e-8 ) {
302 if (u<0) u=0;
303 if (u>1) u=1.0;
304 return new EastNorth(x1+a1*u, y1+a2*u);
305 } else {
306 return null;
307 }
308 } else {
309 // parallel lines
310 return null;
311 }
312 }
313
314 /**
315 * Finds the intersection of two lines of infinite length.
316 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
317 * @throws IllegalArgumentException if a parameter is null or without valid coordinates
318 */
319 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
320
321 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
322 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
323 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
324 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
325
326 if (!p1.isValid()) throw new IllegalArgumentException();
327
328 // Convert line from (point, point) form to ax+by=c
329 double a1 = p2.getY() - p1.getY();
330 double b1 = p1.getX() - p2.getX();
331 double c1 = p2.getX() * p1.getY() - p1.getX() * p2.getY();
332
333 double a2 = p4.getY() - p3.getY();
334 double b2 = p3.getX() - p4.getX();
335 double c2 = p4.getX() * p3.getY() - p3.getX() * p4.getY();
336
337 // Solve the equations
338 double det = a1 * b2 - a2 * b1;
339 if (det == 0)
340 return null; // Lines are parallel
341
342 return new EastNorth((b1 * c2 - b2 * c1) / det, (a2 * c1 - a1 * c2) / det);
343 }
344
345 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
346
347 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
348 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
349 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
350 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
351
352 // Convert line from (point, point) form to ax+by=c
353 double a1 = p2.getY() - p1.getY();
354 double b1 = p1.getX() - p2.getX();
355
356 double a2 = p4.getY() - p3.getY();
357 double b2 = p3.getX() - p4.getX();
358
359 // Solve the equations
360 double det = a1 * b2 - a2 * b1;
361 // remove influence of of scaling factor
362 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
363 return Math.abs(det) < 1e-3;
364 }
365
366 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
367 CheckParameterUtil.ensureParameterNotNull(p1, "p1");
368 CheckParameterUtil.ensureParameterNotNull(p2, "p2");
369 CheckParameterUtil.ensureParameterNotNull(point, "point");
370
371 double ldx = p2.getX() - p1.getX();
372 double ldy = p2.getY() - p1.getY();
373
374 if (ldx == 0 && ldy == 0) //segment zero length
375 return p1;
376
377 double pdx = point.getX() - p1.getX();
378 double pdy = point.getY() - p1.getY();
379
380 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
381
382 if (segmentOnly && offset <= 0)
383 return p1;
384 else if (segmentOnly && offset >= 1)
385 return p2;
386 else
387 return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
388 }
389
390 /**
391 * Calculates closest point to a line segment.
392 * @param segmentP1 First point determining line segment
393 * @param segmentP2 Second point determining line segment
394 * @param point Point for which a closest point is searched on line segment [P1,P2]
395 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
396 * a new point if closest point is between segmentP1 and segmentP2.
397 * @since 3650
398 * @see #closestPointToLine
399 */
400 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
401 return closestPointTo(segmentP1, segmentP2, point, true);
402 }
403
404 /**
405 * Calculates closest point to a line.
406 * @param lineP1 First point determining line
407 * @param lineP2 Second point determining line
408 * @param point Point for which a closest point is searched on line (P1,P2)
409 * @return The closest point found on line. It may be outside the segment [P1,P2].
410 * @since 4134
411 * @see #closestPointToSegment
412 */
413 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
414 return closestPointTo(lineP1, lineP2, point, false);
415 }
416
417 /**
418 * This method tests if secondNode is clockwise to first node.
419 *
420 * The line through the two points commonNode and firstNode divides the
421 * plane into two parts. The test returns true, if secondNode lies in
422 * the part that is to the right when traveling in the direction from
423 * commonNode to firstNode.
424 *
425 * @param commonNode starting point for both vectors
426 * @param firstNode first vector end node
427 * @param secondNode second vector end node
428 * @return true if first vector is clockwise before second vector.
429 */
430 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
431
432 CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
433 CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
434 CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
435
436 double dy1 = (firstNode.getY() - commonNode.getY());
437 double dy2 = (secondNode.getY() - commonNode.getY());
438 double dx1 = (firstNode.getX() - commonNode.getX());
439 double dx2 = (secondNode.getX() - commonNode.getX());
440
441 return dy1 * dx2 - dx1 * dy2 > 0;
442 }
443
444 /**
445 * Returns the Area of a polygon, from its list of nodes.
446 * @param polygon List of nodes forming polygon (EastNorth coordinates)
447 * @return Area for the given list of nodes
448 * @since 6841
449 */
450 public static Area getArea(List<Node> polygon) {
451 Path2D path = new Path2D.Double();
452
453 boolean begin = true;
454 for (Node n : polygon) {
455 EastNorth en = n.getEastNorth();
456 if (en != null) {
457 if (begin) {
458 path.moveTo(en.getX(), en.getY());
459 begin = false;
460 } else {
461 path.lineTo(en.getX(), en.getY());
462 }
463 }
464 }
465 if (!begin) {
466 path.closePath();
467 }
468
469 return new Area(path);
470 }
471
472 /**
473 * Returns the Area of a polygon, from its list of nodes.
474 * @param polygon List of nodes forming polygon (LatLon coordinates)
475 * @return Area for the given list of nodes
476 * @since 6841
477 */
478 public static Area getAreaLatLon(List<Node> polygon) {
479 Path2D path = new Path2D.Double();
480
481 boolean begin = true;
482 for (Node n : polygon) {
483 if (begin) {
484 path.moveTo(n.getCoor().lon(), n.getCoor().lat());
485 begin = false;
486 } else {
487 path.lineTo(n.getCoor().lon(), n.getCoor().lat());
488 }
489 }
490 if (!begin) {
491 path.closePath();
492 }
493
494 return new Area(path);
495 }
496
497 /**
498 * Tests if two polygons intersect.
499 * @param first List of nodes forming first polygon
500 * @param second List of nodes forming second polygon
501 * @return intersection kind
502 */
503 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
504 Area a1 = getArea(first);
505 Area a2 = getArea(second);
506 return polygonIntersection(a1, a2);
507 }
508
509 /**
510 * Tests if two polygons intersect.
511 * @param a1 Area of first polygon
512 * @param a2 Area of second polygon
513 * @return intersection kind
514 * @since 6841
515 */
516 public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
517 return polygonIntersection(a1, a2, 1.0);
518 }
519
520 /**
521 * Tests if two polygons intersect.
522 * @param a1 Area of first polygon
523 * @param a2 Area of second polygon
524 * @param eps an area threshold, everything below is considered an empty intersection
525 * @return intersection kind
526 */
527 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
528
529 Area inter = new Area(a1);
530 inter.intersect(a2);
531
532 Rectangle bounds = inter.getBounds();
533
534 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
535 return PolygonIntersection.OUTSIDE;
536 } else if (inter.equals(a1)) {
537 return PolygonIntersection.FIRST_INSIDE_SECOND;
538 } else if (inter.equals(a2)) {
539 return PolygonIntersection.SECOND_INSIDE_FIRST;
540 } else {
541 return PolygonIntersection.CROSSING;
542 }
543 }
544
545 /**
546 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
547 * @param polygonNodes list of nodes from polygon path.
548 * @param point the point to test
549 * @return true if the point is inside polygon.
550 */
551 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
552 if (polygonNodes.size() < 2)
553 return false;
554
555 boolean inside = false;
556 Node p1, p2;
557
558 //iterate each side of the polygon, start with the last segment
559 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
560
561 for (Node newPoint : polygonNodes) {
562 //skip duplicate points
563 if (newPoint.equals(oldPoint)) {
564 continue;
565 }
566
567 //order points so p1.lat <= p2.lat
568 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
569 p1 = oldPoint;
570 p2 = newPoint;
571 } else {
572 p1 = newPoint;
573 p2 = oldPoint;
574 }
575
576 //test if the line is crossed and if so invert the inside flag.
577 if ((newPoint.getEastNorth().getY() < point.getEastNorth().getY()) == (point.getEastNorth().getY() <= oldPoint.getEastNorth().getY())
578 && (point.getEastNorth().getX() - p1.getEastNorth().getX()) * (p2.getEastNorth().getY() - p1.getEastNorth().getY())
579 < (p2.getEastNorth().getX() - p1.getEastNorth().getX()) * (point.getEastNorth().getY() - p1.getEastNorth().getY()))
580 {
581 inside = !inside;
582 }
583
584 oldPoint = newPoint;
585 }
586
587 return inside;
588 }
589
590 /**
591 * Returns area of a closed way in square meters.
592 * (approximate(?), but should be OK for small areas)
593 *
594 * Relies on the current projection: Works correctly, when
595 * one unit in projected coordinates corresponds to one meter.
596 * This is true for most projections, but not for WGS84 and
597 * Mercator (EPSG:3857).
598 *
599 * @param way Way to measure, should be closed (first node is the same as last node)
600 * @return area of the closed way.
601 */
602 public static double closedWayArea(Way way) {
603
604 //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
605 double area = 0;
606 Node lastN = null;
607 for (Node n : way.getNodes()) {
608 if (lastN != null) {
609 n.getEastNorth().getX();
610
611 area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
612 }
613 lastN = n;
614 }
615 return Math.abs(area/2);
616 }
617
618 protected static double calcX(Node p1){
619 double lat1, lon1, lat2, lon2;
620 double dlon, dlat;
621
622 lat1 = p1.getCoor().lat() * Math.PI / 180.0;
623 lon1 = p1.getCoor().lon() * Math.PI / 180.0;
624 lat2 = lat1;
625 lon2 = 0;
626
627 dlon = lon2 - lon1;
628 dlat = lat2 - lat1;
629
630 double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
631 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
632 return 6367000 * c;
633 }
634
635 protected static double calcY(Node p1){
636 double lat1, lon1, lat2, lon2;
637 double dlon, dlat;
638
639 lat1 = p1.getCoor().lat() * Math.PI / 180.0;
640 lon1 = p1.getCoor().lon() * Math.PI / 180.0;
641 lat2 = 0;
642 lon2 = lon1;
643
644 dlon = lon2 - lon1;
645 dlat = lat2 - lat1;
646
647 double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
648 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
649 return 6367000 * c;
650 }
651
652 /**
653 * Determines whether a way is oriented clockwise.
654 *
655 * Internals: Assuming a closed non-looping way, compute twice the area
656 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
657 * If the area is negative the way is ordered in a clockwise direction.
658 *
659 * See http://paulbourke.net/geometry/polyarea/
660 *
661 * @param w the way to be checked.
662 * @return true if and only if way is oriented clockwise.
663 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
664 */
665 public static boolean isClockwise(Way w) {
666 if (!w.isClosed()) {
667 throw new IllegalArgumentException("Way must be closed to check orientation.");
668 }
669
670 double area2 = 0.;
671 int nodesCount = w.getNodesCount();
672
673 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
674 LatLon coorPrev = w.getNode(node - 1).getCoor();
675 LatLon coorCurr = w.getNode(node % nodesCount).getCoor();
676 area2 += coorPrev.lon() * coorCurr.lat();
677 area2 -= coorCurr.lon() * coorPrev.lat();
678 }
679 return area2 < 0;
680 }
681
682 /**
683 * Returns angle of a segment defined with 2 point coordinates.
684 *
685 * @param p1
686 * @param p2
687 * @return Angle in radians (-pi, pi]
688 */
689 public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
690
691 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
692 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
693
694 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
695 }
696
697 /**
698 * Returns angle of a corner defined with 3 point coordinates.
699 *
700 * @param p1
701 * @param p2 Common endpoint
702 * @param p3
703 * @return Angle in radians (-pi, pi]
704 */
705 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
706
707 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
708 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
709 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
710
711 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
712 if (result <= -Math.PI) {
713 result += 2 * Math.PI;
714 }
715
716 if (result > Math.PI) {
717 result -= 2 * Math.PI;
718 }
719
720 return result;
721 }
722
723 /**
724 * Compute the centroid/barycenter of nodes
725 * @param nodes Nodes for which the centroid is wanted
726 * @return the centroid of nodes
727 * @see Geometry#getCenter
728 */
729 public static EastNorth getCentroid(List<Node> nodes) {
730
731 BigDecimal area = BigDecimal.ZERO;
732 BigDecimal north = BigDecimal.ZERO;
733 BigDecimal east = BigDecimal.ZERO;
734
735 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
736 for (int i = 0; i < nodes.size(); i++) {
737 EastNorth n0 = nodes.get(i).getEastNorth();
738 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
739
740 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
741 BigDecimal x0 = new BigDecimal(n0.east());
742 BigDecimal y0 = new BigDecimal(n0.north());
743 BigDecimal x1 = new BigDecimal(n1.east());
744 BigDecimal y1 = new BigDecimal(n1.north());
745
746 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
747
748 area = area.add(k, MathContext.DECIMAL128);
749 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
750 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
751 }
752 }
753
754 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
755 area = area.multiply(d, MathContext.DECIMAL128);
756 if (area.compareTo(BigDecimal.ZERO) != 0) {
757 north = north.divide(area, MathContext.DECIMAL128);
758 east = east.divide(area, MathContext.DECIMAL128);
759 }
760
761 return new EastNorth(east.doubleValue(), north.doubleValue());
762 }
763
764 /**
765 * Compute center of the circle closest to different nodes.
766 *
767 * Ensure exact center computation in case nodes are already aligned in circle.
768 * This is done by least square method.
769 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
770 * Center must be intersection of all bisectors.
771 * <pre>
772 * [ a1 b1 ] [ -c1 ]
773 * With A = [ ... ... ] and Y = [ ... ]
774 * [ an bn ] [ -cn ]
775 * </pre>
776 * An approximation of center of circle is (At.A)^-1.At.Y
777 * @param nodes Nodes parts of the circle (at least 3)
778 * @return An approximation of the center, of null if there is no solution.
779 * @see Geometry#getCentroid
780 * @since 6934
781 */
782 public static EastNorth getCenter(List<Node> nodes) {
783 int nc = nodes.size();
784 if(nc < 3) return null;
785 /**
786 * Equation of each bisector ax + by + c = 0
787 */
788 double[] a = new double[nc];
789 double[] b = new double[nc];
790 double[] c = new double[nc];
791 // Compute equation of bisector
792 for(int i = 0; i < nc; i++) {
793 EastNorth pt1 = nodes.get(i).getEastNorth();
794 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
795 a[i] = pt1.east() - pt2.east();
796 b[i] = pt1.north() - pt2.north();
797 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
798 if(d == 0) return null;
799 a[i] /= d;
800 b[i] /= d;
801 double xC = (pt1.east() + pt2.east()) / 2;
802 double yC = (pt1.north() + pt2.north()) / 2;
803 c[i] = -(a[i]*xC + b[i]*yC);
804 }
805 // At.A = [aij]
806 double a11 = 0, a12 = 0, a22 = 0;
807 // At.Y = [bi]
808 double b1 = 0, b2 = 0;
809 for(int i = 0; i < nc; i++) {
810 a11 += a[i]*a[i];
811 a12 += a[i]*b[i];
812 a22 += b[i]*b[i];
813 b1 -= a[i]*c[i];
814 b2 -= b[i]*c[i];
815 }
816 // (At.A)^-1 = [invij]
817 double det = a11*a22 - a12*a12;
818 if(Math.abs(det) < 1e-5) return null;
819 double inv11 = a22/det;
820 double inv12 = -a12/det;
821 double inv22 = a11/det;
822 // center (xC, yC) = (At.A)^-1.At.y
823 double xC = inv11*b1 + inv12*b2;
824 double yC = inv12*b1 + inv22*b2;
825 return new EastNorth(xC, yC);
826 }
827
828 /**
829 * Returns the coordinate of intersection of segment sp1-sp2 and an altitude
830 * to it starting at point ap. If the line defined with sp1-sp2 intersects
831 * its altitude out of sp1-sp2, null is returned.
832 *
833 * @param sp1
834 * @param sp2
835 * @param ap
836 * @return Intersection coordinate or null
837 */
838 public static EastNorth getSegmentAltituteIntersection(EastNorth sp1, EastNorth sp2, EastNorth ap) {
839
840 CheckParameterUtil.ensureValidCoordinates(sp1, "sp1");
841 CheckParameterUtil.ensureValidCoordinates(sp2, "sp2");
842 CheckParameterUtil.ensureValidCoordinates(ap, "ap");
843
844 Double segmentLenght = sp1.distance(sp2);
845 Double altitudeAngle = getSegmentAngle(sp1, sp2) + Math.PI / 2;
846
847 // Taking a random point on the altitude line (angle is known).
848 EastNorth ap2 = new EastNorth(ap.east() + 1000
849 * Math.cos(altitudeAngle), ap.north() + 1000
850 * Math.sin(altitudeAngle));
851
852 // Finding the intersection of two lines
853 EastNorth resultCandidate = Geometry.getLineLineIntersection(sp1, sp2,
854 ap, ap2);
855
856 // Filtering result
857 if (resultCandidate != null
858 && resultCandidate.distance(sp1) * .999 < segmentLenght
859 && resultCandidate.distance(sp2) * .999 < segmentLenght) {
860 return resultCandidate;
861 } else {
862 return null;
863 }
864 }
865
866 public static class MultiPolygonMembers {
867 public final Set<Way> outers = new HashSet<>();
868 public final Set<Way> inners = new HashSet<>();
869
870 public MultiPolygonMembers(Relation multiPolygon) {
871 for (RelationMember m : multiPolygon.getMembers()) {
872 if (m.getType().equals(OsmPrimitiveType.WAY)) {
873 if ("outer".equals(m.getRole())) {
874 outers.add(m.getWay());
875 } else if ("inner".equals(m.getRole())) {
876 inners.add(m.getWay());
877 }
878 }
879 }
880 }
881 }
882
883 /**
884 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
885 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
886 */
887 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
888 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
889 }
890
891 /**
892 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
893 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
894 * <p>
895 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
896 */
897 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
898 // Extract outer/inner members from multipolygon
899 final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
900 // Construct complete rings for the inner/outer members
901 final List<MultipolygonBuilder.JoinedPolygon> outerRings;
902 final List<MultipolygonBuilder.JoinedPolygon> innerRings;
903 try {
904 outerRings = MultipolygonBuilder.joinWays(mpm.outers);
905 innerRings = MultipolygonBuilder.joinWays(mpm.inners);
906 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
907 Main.debug("Invalid multipolygon " + multiPolygon);
908 return false;
909 }
910 // Test if object is inside an outer member
911 for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
912 if (nodes.size() == 1
913 ? nodeInsidePolygon(nodes.get(0), out.getNodes())
914 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(polygonIntersection(nodes, out.getNodes()))) {
915 boolean insideInner = false;
916 // If inside an outer, check it is not inside an inner
917 for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
918 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
919 && (nodes.size() == 1
920 ? nodeInsidePolygon(nodes.get(0), in.getNodes())
921 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
922 insideInner = true;
923 break;
924 }
925 }
926 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
927 if (!insideInner) {
928 // Final check using predicate
929 if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0) /* TODO give a better representation of the outer ring to the predicate */)) {
930 return true;
931 }
932 }
933 }
934 }
935 return false;
936 }
937}
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