source: josm/trunk/src/org/openstreetmap/josm/tools/Geometry.java@ 9542

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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 {
46 FIRST_INSIDE_SECOND,
47 SECOND_INSIDE_FIRST,
48 OUTSIDE,
49 CROSSING
50 }
51
52 /**
53 * Will find all intersection and add nodes there for list of given ways.
54 * Handles self-intersections too.
55 * And makes commands to add the intersection points to ways.
56 *
57 * Prerequisite: no two nodes have the same coordinates.
58 *
59 * @param ways a list of ways to test
60 * @param test if false, do not build list of Commands, just return nodes
61 * @param cmds list of commands, typically empty when handed to this method.
62 * Will be filled with commands that add intersection nodes to
63 * the ways.
64 * @return list of new nodes
65 */
66 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
67
68 int n = ways.size();
69 @SuppressWarnings("unchecked")
70 List<Node>[] newNodes = new ArrayList[n];
71 BBox[] wayBounds = new BBox[n];
72 boolean[] changedWays = new boolean[n];
73
74 Set<Node> intersectionNodes = new LinkedHashSet<>();
75
76 //copy node arrays for local usage.
77 for (int pos = 0; pos < n; pos++) {
78 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
79 wayBounds[pos] = getNodesBounds(newNodes[pos]);
80 changedWays[pos] = false;
81 }
82
83 //iterate over all way pairs and introduce the intersections
84 Comparator<Node> coordsComparator = new NodePositionComparator();
85 for (int seg1Way = 0; seg1Way < n; seg1Way++) {
86 for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
87
88 //do not waste time on bounds that do not intersect
89 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
90 continue;
91 }
92
93 List<Node> way1Nodes = newNodes[seg1Way];
94 List<Node> way2Nodes = newNodes[seg2Way];
95
96 //iterate over primary segmemt
97 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
98
99 //iterate over secondary segment
100 int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
101
102 for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
103
104 //need to get them again every time, because other segments may be changed
105 Node seg1Node1 = way1Nodes.get(seg1Pos);
106 Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
107 Node seg2Node1 = way2Nodes.get(seg2Pos);
108 Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
109
110 int commonCount = 0;
111 //test if we have common nodes to add.
112 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
113 commonCount++;
114
115 if (seg1Way == seg2Way &&
116 seg1Pos == 0 &&
117 seg2Pos == way2Nodes.size() -2) {
118 //do not add - this is first and last segment of the same way.
119 } else {
120 intersectionNodes.add(seg1Node1);
121 }
122 }
123
124 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
125 commonCount++;
126
127 intersectionNodes.add(seg1Node2);
128 }
129
130 //no common nodes - find intersection
131 if (commonCount == 0) {
132 EastNorth intersection = getSegmentSegmentIntersection(
133 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
134 seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
135
136 if (intersection != null) {
137 if (test) {
138 intersectionNodes.add(seg2Node1);
139 return intersectionNodes;
140 }
141
142 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
143 Node intNode = newNode;
144 boolean insertInSeg1 = false;
145 boolean insertInSeg2 = false;
146 //find if the intersection point is at end point of one of the segments, if so use that point
147
148 //segment 1
149 if (coordsComparator.compare(newNode, seg1Node1) == 0) {
150 intNode = seg1Node1;
151 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
152 intNode = seg1Node2;
153 } else {
154 insertInSeg1 = true;
155 }
156
157 //segment 2
158 if (coordsComparator.compare(newNode, seg2Node1) == 0) {
159 intNode = seg2Node1;
160 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
161 intNode = seg2Node2;
162 } else {
163 insertInSeg2 = true;
164 }
165
166 if (insertInSeg1) {
167 way1Nodes.add(seg1Pos +1, intNode);
168 changedWays[seg1Way] = true;
169
170 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
171 if (seg2Way == seg1Way) {
172 seg2Pos++;
173 }
174 }
175
176 if (insertInSeg2) {
177 way2Nodes.add(seg2Pos +1, intNode);
178 changedWays[seg2Way] = true;
179
180 //Do not need to compare again to already split segment
181 seg2Pos++;
182 }
183
184 intersectionNodes.add(intNode);
185
186 if (intNode == newNode) {
187 cmds.add(new AddCommand(intNode));
188 }
189 }
190 } else if (test && !intersectionNodes.isEmpty())
191 return intersectionNodes;
192 }
193 }
194 }
195 }
196
197
198 for (int pos = 0; pos < ways.size(); pos++) {
199 if (!changedWays[pos]) {
200 continue;
201 }
202
203 Way way = ways.get(pos);
204 Way newWay = new Way(way);
205 newWay.setNodes(newNodes[pos]);
206
207 cmds.add(new ChangeCommand(way, newWay));
208 }
209
210 return intersectionNodes;
211 }
212
213 private static BBox getNodesBounds(List<Node> nodes) {
214
215 BBox bounds = new BBox(nodes.get(0));
216 for (Node n: nodes) {
217 bounds.add(n.getCoor());
218 }
219 return bounds;
220 }
221
222 /**
223 * Tests if given point is to the right side of path consisting of 3 points.
224 *
225 * (Imagine the path is continued beyond the endpoints, so you get two rays
226 * starting from lineP2 and going through lineP1 and lineP3 respectively
227 * which divide the plane into two parts. The test returns true, if testPoint
228 * lies in the part that is to the right when traveling in the direction
229 * lineP1, lineP2, lineP3.)
230 *
231 * @param lineP1 first point in path
232 * @param lineP2 second point in path
233 * @param lineP3 third point in path
234 * @param testPoint point to test
235 * @return true if to the right side, false otherwise
236 */
237 public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
238 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
239 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
240 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
241
242 if (pathBendToRight)
243 return rightOfSeg1 && rightOfSeg2;
244 else
245 return !(!rightOfSeg1 && !rightOfSeg2);
246 }
247
248 /**
249 * This method tests if secondNode is clockwise to first node.
250 * @param commonNode starting point for both vectors
251 * @param firstNode first vector end node
252 * @param secondNode second vector end node
253 * @return true if first vector is clockwise before second vector.
254 */
255 public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
256 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
257 }
258
259 /**
260 * Finds the intersection of two line segments.
261 * @param p1 the coordinates of the start point of the first specified line segment
262 * @param p2 the coordinates of the end point of the first specified line segment
263 * @param p3 the coordinates of the start point of the second specified line segment
264 * @param p4 the coordinates of the end point of the second specified line segment
265 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
266 */
267 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
268
269 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
270 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
271 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
272 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
273
274 double x1 = p1.getX();
275 double y1 = p1.getY();
276 double x2 = p2.getX();
277 double y2 = p2.getY();
278 double x3 = p3.getX();
279 double y3 = p3.getY();
280 double x4 = p4.getX();
281 double y4 = p4.getY();
282
283 //TODO: do this locally.
284 //TODO: remove this check after careful testing
285 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
286
287 // solve line-line intersection in parametric form:
288 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v
289 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
290 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
291
292 double a1 = x2 - x1;
293 double b1 = x3 - x4;
294 double c1 = x3 - x1;
295
296 double a2 = y2 - y1;
297 double b2 = y3 - y4;
298 double c2 = y3 - y1;
299
300 // Solve the equations
301 double det = a1*b2 - a2*b1;
302
303 double uu = b2*c1 - b1*c2;
304 double vv = a1*c2 - a2*c1;
305 double mag = Math.abs(uu)+Math.abs(vv);
306
307 if (Math.abs(det) > 1e-12 * mag) {
308 double u = uu/det, v = vv/det;
309 if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
310 if (u < 0) u = 0;
311 if (u > 1) u = 1.0;
312 return new EastNorth(x1+a1*u, y1+a2*u);
313 } else {
314 return null;
315 }
316 } else {
317 // parallel lines
318 return null;
319 }
320 }
321
322 /**
323 * Finds the intersection of two lines of infinite length.
324 *
325 * @param p1 first point on first line
326 * @param p2 second point on first line
327 * @param p3 first point on second line
328 * @param p4 second point on second line
329 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
330 * @throws IllegalArgumentException if a parameter is null or without valid coordinates
331 */
332 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
333
334 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
335 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
336 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
337 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
338
339 if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
340
341 // Basically, the formula from wikipedia is used:
342 // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
343 // However, large numbers lead to rounding errors (see #10286).
344 // To avoid this, p1 is first substracted from each of the points:
345 // p1' = 0
346 // p2' = p2 - p1
347 // p3' = p3 - p1
348 // p4' = p4 - p1
349 // In the end, p1 is added to the intersection point of segment p1'/p2'
350 // and segment p3'/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 if (det == 0)
362 return null; // Lines are parallel
363
364 double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
365
366 return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
367 }
368
369 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
370
371 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
372 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
373 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
374 CheckParameterUtil.ensureValidCoordinates(p4, "p4");
375
376 // Convert line from (point, point) form to ax+by=c
377 double a1 = p2.getY() - p1.getY();
378 double b1 = p1.getX() - p2.getX();
379
380 double a2 = p4.getY() - p3.getY();
381 double b2 = p3.getX() - p4.getX();
382
383 // Solve the equations
384 double det = a1 * b2 - a2 * b1;
385 // remove influence of of scaling factor
386 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
387 return Math.abs(det) < 1e-3;
388 }
389
390 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
391 CheckParameterUtil.ensureParameterNotNull(p1, "p1");
392 CheckParameterUtil.ensureParameterNotNull(p2, "p2");
393 CheckParameterUtil.ensureParameterNotNull(point, "point");
394
395 double ldx = p2.getX() - p1.getX();
396 double ldy = p2.getY() - p1.getY();
397
398 //segment zero length
399 if (ldx == 0 && ldy == 0)
400 return p1;
401
402 double pdx = point.getX() - p1.getX();
403 double pdy = point.getY() - p1.getY();
404
405 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
406
407 if (segmentOnly && offset <= 0)
408 return p1;
409 else if (segmentOnly && offset >= 1)
410 return p2;
411 else
412 return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
413 }
414
415 /**
416 * Calculates closest point to a line segment.
417 * @param segmentP1 First point determining line segment
418 * @param segmentP2 Second point determining line segment
419 * @param point Point for which a closest point is searched on line segment [P1,P2]
420 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
421 * a new point if closest point is between segmentP1 and segmentP2.
422 * @see #closestPointToLine
423 * @since 3650
424 */
425 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
426 return closestPointTo(segmentP1, segmentP2, point, true);
427 }
428
429 /**
430 * Calculates closest point to a line.
431 * @param lineP1 First point determining line
432 * @param lineP2 Second point determining line
433 * @param point Point for which a closest point is searched on line (P1,P2)
434 * @return The closest point found on line. It may be outside the segment [P1,P2].
435 * @see #closestPointToSegment
436 * @since 4134
437 */
438 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
439 return closestPointTo(lineP1, lineP2, point, false);
440 }
441
442 /**
443 * This method tests if secondNode is clockwise to first node.
444 *
445 * The line through the two points commonNode and firstNode divides the
446 * plane into two parts. The test returns true, if secondNode lies in
447 * the part that is to the right when traveling in the direction from
448 * commonNode to firstNode.
449 *
450 * @param commonNode starting point for both vectors
451 * @param firstNode first vector end node
452 * @param secondNode second vector end node
453 * @return true if first vector is clockwise before second vector.
454 */
455 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
456
457 CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
458 CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
459 CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
460
461 double dy1 = firstNode.getY() - commonNode.getY();
462 double dy2 = secondNode.getY() - commonNode.getY();
463 double dx1 = firstNode.getX() - commonNode.getX();
464 double dx2 = secondNode.getX() - commonNode.getX();
465
466 return dy1 * dx2 - dx1 * dy2 > 0;
467 }
468
469 /**
470 * Returns the Area of a polygon, from its list of nodes.
471 * @param polygon List of nodes forming polygon (EastNorth coordinates)
472 * @return Area for the given list of nodes
473 * @since 6841
474 */
475 public static Area getArea(List<Node> polygon) {
476 Path2D path = new Path2D.Double();
477
478 boolean begin = true;
479 for (Node n : polygon) {
480 EastNorth en = n.getEastNorth();
481 if (en != null) {
482 if (begin) {
483 path.moveTo(en.getX(), en.getY());
484 begin = false;
485 } else {
486 path.lineTo(en.getX(), en.getY());
487 }
488 }
489 }
490 if (!begin) {
491 path.closePath();
492 }
493
494 return new Area(path);
495 }
496
497 /**
498 * Returns the Area of a polygon, from its list of nodes.
499 * @param polygon List of nodes forming polygon (LatLon coordinates)
500 * @return Area for the given list of nodes
501 * @since 6841
502 */
503 public static Area getAreaLatLon(List<Node> polygon) {
504 Path2D path = new Path2D.Double();
505
506 boolean begin = true;
507 for (Node n : polygon) {
508 if (begin) {
509 path.moveTo(n.getCoor().lon(), n.getCoor().lat());
510 begin = false;
511 } else {
512 path.lineTo(n.getCoor().lon(), n.getCoor().lat());
513 }
514 }
515 if (!begin) {
516 path.closePath();
517 }
518
519 return new Area(path);
520 }
521
522 /**
523 * Tests if two polygons intersect.
524 * @param first List of nodes forming first polygon
525 * @param second List of nodes forming second polygon
526 * @return intersection kind
527 */
528 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
529 Area a1 = getArea(first);
530 Area a2 = getArea(second);
531 return polygonIntersection(a1, a2);
532 }
533
534 /**
535 * Tests if two polygons intersect.
536 * @param a1 Area of first polygon
537 * @param a2 Area of second polygon
538 * @return intersection kind
539 * @since 6841
540 */
541 public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
542 return polygonIntersection(a1, a2, 1.0);
543 }
544
545 /**
546 * Tests if two polygons intersect.
547 * @param a1 Area of first polygon
548 * @param a2 Area of second polygon
549 * @param eps an area threshold, everything below is considered an empty intersection
550 * @return intersection kind
551 */
552 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
553
554 Area inter = new Area(a1);
555 inter.intersect(a2);
556
557 Rectangle bounds = inter.getBounds();
558
559 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
560 return PolygonIntersection.OUTSIDE;
561 } else if (inter.equals(a1)) {
562 return PolygonIntersection.FIRST_INSIDE_SECOND;
563 } else if (inter.equals(a2)) {
564 return PolygonIntersection.SECOND_INSIDE_FIRST;
565 } else {
566 return PolygonIntersection.CROSSING;
567 }
568 }
569
570 /**
571 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
572 * @param polygonNodes list of nodes from polygon path.
573 * @param point the point to test
574 * @return true if the point is inside polygon.
575 */
576 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
577 if (polygonNodes.size() < 2)
578 return false;
579
580 //iterate each side of the polygon, start with the last segment
581 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
582
583 if (!oldPoint.isLatLonKnown()) {
584 return false;
585 }
586
587 boolean inside = false;
588 Node p1, p2;
589
590 for (Node newPoint : polygonNodes) {
591 //skip duplicate points
592 if (newPoint.equals(oldPoint)) {
593 continue;
594 }
595
596 if (!newPoint.isLatLonKnown()) {
597 return false;
598 }
599
600 //order points so p1.lat <= p2.lat
601 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
602 p1 = oldPoint;
603 p2 = newPoint;
604 } else {
605 p1 = newPoint;
606 p2 = oldPoint;
607 }
608
609 EastNorth pEN = point.getEastNorth();
610 EastNorth opEN = oldPoint.getEastNorth();
611 EastNorth npEN = newPoint.getEastNorth();
612 EastNorth p1EN = p1.getEastNorth();
613 EastNorth p2EN = p2.getEastNorth();
614
615 if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
616 //test if the line is crossed and if so invert the inside flag.
617 if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
618 && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
619 < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
620 inside = !inside;
621 }
622 }
623
624 oldPoint = newPoint;
625 }
626
627 return inside;
628 }
629
630 /**
631 * Returns area of a closed way in square meters.
632 * (approximate(?), but should be OK for small areas)
633 *
634 * Relies on the current projection: Works correctly, when
635 * one unit in projected coordinates corresponds to one meter.
636 * This is true for most projections, but not for WGS84 and
637 * Mercator (EPSG:3857).
638 *
639 * @param way Way to measure, should be closed (first node is the same as last node)
640 * @return area of the closed way.
641 */
642 public static double closedWayArea(Way way) {
643
644 //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
645 double area = 0;
646 Node lastN = null;
647 for (Node n : way.getNodes()) {
648 if (lastN != null) {
649 area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
650 }
651 lastN = n;
652 }
653 return Math.abs(area/2);
654 }
655
656 protected static double calcX(Node p1) {
657 double lat1, lon1, lat2, lon2;
658 double dlon, dlat;
659
660 lat1 = p1.getCoor().lat() * Math.PI / 180.0;
661 lon1 = p1.getCoor().lon() * Math.PI / 180.0;
662 lat2 = lat1;
663 lon2 = 0;
664
665 dlon = lon2 - lon1;
666 dlat = lat2 - lat1;
667
668 double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2);
669 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
670 return 6367000 * c;
671 }
672
673 protected static double calcY(Node p1) {
674 double lat1, lon1, lat2, lon2;
675 double dlon, dlat;
676
677 lat1 = p1.getCoor().lat() * Math.PI / 180.0;
678 lon1 = p1.getCoor().lon() * Math.PI / 180.0;
679 lat2 = 0;
680 lon2 = lon1;
681
682 dlon = lon2 - lon1;
683 dlat = lat2 - lat1;
684
685 double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2);
686 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
687 return 6367000 * c;
688 }
689
690 /**
691 * Determines whether a way is oriented clockwise.
692 *
693 * Internals: Assuming a closed non-looping way, compute twice the area
694 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
695 * If the area is negative the way is ordered in a clockwise direction.
696 *
697 * See http://paulbourke.net/geometry/polyarea/
698 *
699 * @param w the way to be checked.
700 * @return true if and only if way is oriented clockwise.
701 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
702 */
703 public static boolean isClockwise(Way w) {
704 return isClockwise(w.getNodes());
705 }
706
707 /**
708 * Determines whether path from nodes list is oriented clockwise.
709 * @param nodes Nodes list to be checked.
710 * @return true if and only if way is oriented clockwise.
711 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
712 * @see #isClockwise(Way)
713 */
714 public static boolean isClockwise(List<Node> nodes) {
715 int nodesCount = nodes.size();
716 if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
717 throw new IllegalArgumentException("Way must be closed to check orientation.");
718 }
719 double area2 = 0.;
720
721 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
722 LatLon coorPrev = nodes.get(node - 1).getCoor();
723 LatLon coorCurr = nodes.get(node % nodesCount).getCoor();
724 area2 += coorPrev.lon() * coorCurr.lat();
725 area2 -= coorCurr.lon() * coorPrev.lat();
726 }
727 return area2 < 0;
728 }
729
730 /**
731 * Returns angle of a segment defined with 2 point coordinates.
732 *
733 * @param p1 first point
734 * @param p2 second point
735 * @return Angle in radians (-pi, pi]
736 */
737 public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
738
739 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
740 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
741
742 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
743 }
744
745 /**
746 * Returns angle of a corner defined with 3 point coordinates.
747 *
748 * @param p1 first point
749 * @param p2 Common endpoint
750 * @param p3 third point
751 * @return Angle in radians (-pi, pi]
752 */
753 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
754
755 CheckParameterUtil.ensureValidCoordinates(p1, "p1");
756 CheckParameterUtil.ensureValidCoordinates(p2, "p2");
757 CheckParameterUtil.ensureValidCoordinates(p3, "p3");
758
759 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
760 if (result <= -Math.PI) {
761 result += 2 * Math.PI;
762 }
763
764 if (result > Math.PI) {
765 result -= 2 * Math.PI;
766 }
767
768 return result;
769 }
770
771 /**
772 * Compute the centroid/barycenter of nodes
773 * @param nodes Nodes for which the centroid is wanted
774 * @return the centroid of nodes
775 * @see Geometry#getCenter
776 */
777 public static EastNorth getCentroid(List<Node> nodes) {
778
779 BigDecimal area = BigDecimal.ZERO;
780 BigDecimal north = BigDecimal.ZERO;
781 BigDecimal east = BigDecimal.ZERO;
782
783 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
784 for (int i = 0; i < nodes.size(); i++) {
785 EastNorth n0 = nodes.get(i).getEastNorth();
786 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
787
788 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
789 BigDecimal x0 = BigDecimal.valueOf(n0.east());
790 BigDecimal y0 = BigDecimal.valueOf(n0.north());
791 BigDecimal x1 = BigDecimal.valueOf(n1.east());
792 BigDecimal y1 = BigDecimal.valueOf(n1.north());
793
794 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
795
796 area = area.add(k, MathContext.DECIMAL128);
797 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
798 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
799 }
800 }
801
802 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
803 area = area.multiply(d, MathContext.DECIMAL128);
804 if (area.compareTo(BigDecimal.ZERO) != 0) {
805 north = north.divide(area, MathContext.DECIMAL128);
806 east = east.divide(area, MathContext.DECIMAL128);
807 }
808
809 return new EastNorth(east.doubleValue(), north.doubleValue());
810 }
811
812 /**
813 * Compute center of the circle closest to different nodes.
814 *
815 * Ensure exact center computation in case nodes are already aligned in circle.
816 * This is done by least square method.
817 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
818 * Center must be intersection of all bisectors.
819 * <pre>
820 * [ a1 b1 ] [ -c1 ]
821 * With A = [ ... ... ] and Y = [ ... ]
822 * [ an bn ] [ -cn ]
823 * </pre>
824 * An approximation of center of circle is (At.A)^-1.At.Y
825 * @param nodes Nodes parts of the circle (at least 3)
826 * @return An approximation of the center, of null if there is no solution.
827 * @see Geometry#getCentroid
828 * @since 6934
829 */
830 public static EastNorth getCenter(List<Node> nodes) {
831 int nc = nodes.size();
832 if (nc < 3) return null;
833 /**
834 * Equation of each bisector ax + by + c = 0
835 */
836 double[] a = new double[nc];
837 double[] b = new double[nc];
838 double[] c = new double[nc];
839 // Compute equation of bisector
840 for (int i = 0; i < nc; i++) {
841 EastNorth pt1 = nodes.get(i).getEastNorth();
842 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
843 a[i] = pt1.east() - pt2.east();
844 b[i] = pt1.north() - pt2.north();
845 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
846 if (d == 0) return null;
847 a[i] /= d;
848 b[i] /= d;
849 double xC = (pt1.east() + pt2.east()) / 2;
850 double yC = (pt1.north() + pt2.north()) / 2;
851 c[i] = -(a[i]*xC + b[i]*yC);
852 }
853 // At.A = [aij]
854 double a11 = 0, a12 = 0, a22 = 0;
855 // At.Y = [bi]
856 double b1 = 0, b2 = 0;
857 for (int i = 0; i < nc; i++) {
858 a11 += a[i]*a[i];
859 a12 += a[i]*b[i];
860 a22 += b[i]*b[i];
861 b1 -= a[i]*c[i];
862 b2 -= b[i]*c[i];
863 }
864 // (At.A)^-1 = [invij]
865 double det = a11*a22 - a12*a12;
866 if (Math.abs(det) < 1e-5) return null;
867 double inv11 = a22/det;
868 double inv12 = -a12/det;
869 double inv22 = a11/det;
870 // center (xC, yC) = (At.A)^-1.At.y
871 double xC = inv11*b1 + inv12*b2;
872 double yC = inv12*b1 + inv22*b2;
873 return new EastNorth(xC, yC);
874 }
875
876 public static class MultiPolygonMembers {
877 public final Set<Way> outers = new HashSet<>();
878 public final Set<Way> inners = new HashSet<>();
879
880 public MultiPolygonMembers(Relation multiPolygon) {
881 for (RelationMember m : multiPolygon.getMembers()) {
882 if (m.getType().equals(OsmPrimitiveType.WAY)) {
883 if ("outer".equals(m.getRole())) {
884 outers.add(m.getWay());
885 } else if ("inner".equals(m.getRole())) {
886 inners.add(m.getWay());
887 }
888 }
889 }
890 }
891 }
892
893 /**
894 * Tests if the {@code node} 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 * @param node node
897 * @param multiPolygon multipolygon
898 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
899 * @return {@code true} if the node is inside the multipolygon
900 */
901 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
902 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
903 }
904
905 /**
906 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
907 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
908 * <p>
909 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
910 * @param nodes nodes forming the polygon
911 * @param multiPolygon multipolygon
912 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
913 * @return {@code true} if the polygon formed by nodes is inside the multipolygon
914 */
915 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
916 // Extract outer/inner members from multipolygon
917 final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
918 // Construct complete rings for the inner/outer members
919 final List<MultipolygonBuilder.JoinedPolygon> outerRings;
920 final List<MultipolygonBuilder.JoinedPolygon> innerRings;
921 try {
922 outerRings = MultipolygonBuilder.joinWays(mpm.outers);
923 innerRings = MultipolygonBuilder.joinWays(mpm.inners);
924 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
925 Main.debug("Invalid multipolygon " + multiPolygon);
926 return false;
927 }
928 // Test if object is inside an outer member
929 for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
930 if (nodes.size() == 1
931 ? nodeInsidePolygon(nodes.get(0), out.getNodes())
932 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
933 polygonIntersection(nodes, out.getNodes()))) {
934 boolean insideInner = false;
935 // If inside an outer, check it is not inside an inner
936 for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
937 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
938 && (nodes.size() == 1
939 ? nodeInsidePolygon(nodes.get(0), in.getNodes())
940 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
941 insideInner = true;
942 break;
943 }
944 }
945 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
946 if (!insideInner) {
947 // Final check using predicate
948 if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0)
949 /* TODO give a better representation of the outer ring to the predicate */)) {
950 return true;
951 }
952 }
953 }
954 }
955 return false;
956 }
957
958 /**
959 * Data class to hold two double values (area and perimeter of a polygon).
960 */
961 public static class AreaAndPerimeter {
962 private final double area;
963 private final double perimeter;
964
965 public AreaAndPerimeter(double area, double perimeter) {
966 this.area = area;
967 this.perimeter = perimeter;
968 }
969
970 public double getArea() {
971 return area;
972 }
973
974 public double getPerimeter() {
975 return perimeter;
976 }
977 }
978
979 /**
980 * Calculate area and perimeter length of a polygon.
981 *
982 * Uses current projection; units are that of the projected coordinates.
983 *
984 * @param nodes the list of nodes representing the polygon
985 * @return area and perimeter
986 */
987 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> 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 = nodes.get(0).getEastNorth();
994 for (int i = 1; i <= numSegments; i++) {
995 EastNorth p2 = nodes.get(i == numSegments ? 0 : i).getEastNorth();
996 area += p1.east() * p2.north() - p2.east() * p1.north();
997 perimeter += p1.distance(p2);
998 p1 = p2;
999 }
1000 }
1001 return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
1002 }
1003}
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