001// License: GPL. For details, see LICENSE file. 002package org.openstreetmap.josm.tools; 003 004import java.awt.Rectangle; 005import java.awt.geom.Area; 006import java.awt.geom.Line2D; 007import java.awt.geom.Path2D; 008import java.math.BigDecimal; 009import java.math.MathContext; 010import java.util.ArrayList; 011import java.util.Collections; 012import java.util.Comparator; 013import java.util.EnumSet; 014import java.util.LinkedHashSet; 015import java.util.List; 016import java.util.Set; 017import java.util.function.Predicate; 018import java.util.stream.Collectors; 019 020import org.openstreetmap.josm.Main; 021import org.openstreetmap.josm.command.AddCommand; 022import org.openstreetmap.josm.command.ChangeCommand; 023import org.openstreetmap.josm.command.Command; 024import org.openstreetmap.josm.data.coor.EastNorth; 025import org.openstreetmap.josm.data.coor.ILatLon; 026import org.openstreetmap.josm.data.osm.BBox; 027import org.openstreetmap.josm.data.osm.DataSet; 028import org.openstreetmap.josm.data.osm.INode; 029import org.openstreetmap.josm.data.osm.IPrimitive; 030import org.openstreetmap.josm.data.osm.MultipolygonBuilder; 031import org.openstreetmap.josm.data.osm.MultipolygonBuilder.JoinedPolygon; 032import org.openstreetmap.josm.data.osm.Node; 033import org.openstreetmap.josm.data.osm.NodePositionComparator; 034import org.openstreetmap.josm.data.osm.Relation; 035import org.openstreetmap.josm.data.osm.Way; 036import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon; 037import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache; 038import org.openstreetmap.josm.data.projection.Projection; 039import org.openstreetmap.josm.data.projection.Projections; 040 041/** 042 * Some tools for geometry related tasks. 043 * 044 * @author viesturs 045 */ 046public final class Geometry { 047 048 private Geometry() { 049 // Hide default constructor for utils classes 050 } 051 052 /** 053 * The result types for a {@link Geometry#polygonIntersection(Area, Area)} test 054 */ 055 public enum PolygonIntersection { 056 /** 057 * The first polygon is inside the second one 058 */ 059 FIRST_INSIDE_SECOND, 060 /** 061 * The second one is inside the first 062 */ 063 SECOND_INSIDE_FIRST, 064 /** 065 * The polygons do not overlap 066 */ 067 OUTSIDE, 068 /** 069 * The polygon borders cross each other 070 */ 071 CROSSING 072 } 073 074 /** 075 * Will find all intersection and add nodes there for list of given ways. 076 * Handles self-intersections too. 077 * And makes commands to add the intersection points to ways. 078 * 079 * Prerequisite: no two nodes have the same coordinates. 080 * 081 * @param ways a list of ways to test 082 * @param test if false, do not build list of Commands, just return nodes 083 * @param cmds list of commands, typically empty when handed to this method. 084 * Will be filled with commands that add intersection nodes to 085 * the ways. 086 * @return list of new nodes 087 */ 088 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) { 089 090 int n = ways.size(); 091 @SuppressWarnings("unchecked") 092 List<Node>[] newNodes = new ArrayList[n]; 093 BBox[] wayBounds = new BBox[n]; 094 boolean[] changedWays = new boolean[n]; 095 096 Set<Node> intersectionNodes = new LinkedHashSet<>(); 097 098 //copy node arrays for local usage. 099 for (int pos = 0; pos < n; pos++) { 100 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes()); 101 wayBounds[pos] = getNodesBounds(newNodes[pos]); 102 changedWays[pos] = false; 103 } 104 105 DataSet dataset = ways.get(0).getDataSet(); 106 107 //iterate over all way pairs and introduce the intersections 108 Comparator<Node> coordsComparator = new NodePositionComparator(); 109 for (int seg1Way = 0; seg1Way < n; seg1Way++) { 110 for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) { 111 112 //do not waste time on bounds that do not intersect 113 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) { 114 continue; 115 } 116 117 List<Node> way1Nodes = newNodes[seg1Way]; 118 List<Node> way2Nodes = newNodes[seg2Way]; 119 120 //iterate over primary segmemt 121 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) { 122 123 //iterate over secondary segment 124 int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment 125 126 for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) { 127 128 //need to get them again every time, because other segments may be changed 129 Node seg1Node1 = way1Nodes.get(seg1Pos); 130 Node seg1Node2 = way1Nodes.get(seg1Pos + 1); 131 Node seg2Node1 = way2Nodes.get(seg2Pos); 132 Node seg2Node2 = way2Nodes.get(seg2Pos + 1); 133 134 int commonCount = 0; 135 //test if we have common nodes to add. 136 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) { 137 commonCount++; 138 139 if (seg1Way == seg2Way && 140 seg1Pos == 0 && 141 seg2Pos == way2Nodes.size() -2) { 142 //do not add - this is first and last segment of the same way. 143 } else { 144 intersectionNodes.add(seg1Node1); 145 } 146 } 147 148 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) { 149 commonCount++; 150 151 intersectionNodes.add(seg1Node2); 152 } 153 154 //no common nodes - find intersection 155 if (commonCount == 0) { 156 EastNorth intersection = getSegmentSegmentIntersection( 157 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(), 158 seg2Node1.getEastNorth(), seg2Node2.getEastNorth()); 159 160 if (intersection != null) { 161 if (test) { 162 intersectionNodes.add(seg2Node1); 163 return intersectionNodes; 164 } 165 166 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection)); 167 Node intNode = newNode; 168 boolean insertInSeg1 = false; 169 boolean insertInSeg2 = false; 170 //find if the intersection point is at end point of one of the segments, if so use that point 171 172 //segment 1 173 if (coordsComparator.compare(newNode, seg1Node1) == 0) { 174 intNode = seg1Node1; 175 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) { 176 intNode = seg1Node2; 177 } else { 178 insertInSeg1 = true; 179 } 180 181 //segment 2 182 if (coordsComparator.compare(newNode, seg2Node1) == 0) { 183 intNode = seg2Node1; 184 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) { 185 intNode = seg2Node2; 186 } else { 187 insertInSeg2 = true; 188 } 189 190 if (insertInSeg1) { 191 way1Nodes.add(seg1Pos +1, intNode); 192 changedWays[seg1Way] = true; 193 194 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment. 195 if (seg2Way == seg1Way) { 196 seg2Pos++; 197 } 198 } 199 200 if (insertInSeg2) { 201 way2Nodes.add(seg2Pos +1, intNode); 202 changedWays[seg2Way] = true; 203 204 //Do not need to compare again to already split segment 205 seg2Pos++; 206 } 207 208 intersectionNodes.add(intNode); 209 210 if (intNode == newNode) { 211 cmds.add(new AddCommand(dataset, intNode)); 212 } 213 } 214 } else if (test && !intersectionNodes.isEmpty()) 215 return intersectionNodes; 216 } 217 } 218 } 219 } 220 221 222 for (int pos = 0; pos < ways.size(); pos++) { 223 if (!changedWays[pos]) { 224 continue; 225 } 226 227 Way way = ways.get(pos); 228 Way newWay = new Way(way); 229 newWay.setNodes(newNodes[pos]); 230 231 cmds.add(new ChangeCommand(dataset, way, newWay)); 232 } 233 234 return intersectionNodes; 235 } 236 237 private static BBox getNodesBounds(List<Node> nodes) { 238 239 BBox bounds = new BBox(nodes.get(0)); 240 for (Node n: nodes) { 241 bounds.add(n); 242 } 243 return bounds; 244 } 245 246 /** 247 * Tests if given point is to the right side of path consisting of 3 points. 248 * 249 * (Imagine the path is continued beyond the endpoints, so you get two rays 250 * starting from lineP2 and going through lineP1 and lineP3 respectively 251 * which divide the plane into two parts. The test returns true, if testPoint 252 * lies in the part that is to the right when traveling in the direction 253 * lineP1, lineP2, lineP3.) 254 * 255 * @param <N> type of node 256 * @param lineP1 first point in path 257 * @param lineP2 second point in path 258 * @param lineP3 third point in path 259 * @param testPoint point to test 260 * @return true if to the right side, false otherwise 261 */ 262 public static <N extends INode> boolean isToTheRightSideOfLine(N lineP1, N lineP2, N lineP3, N testPoint) { 263 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3); 264 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint); 265 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint); 266 267 if (pathBendToRight) 268 return rightOfSeg1 && rightOfSeg2; 269 else 270 return !(!rightOfSeg1 && !rightOfSeg2); 271 } 272 273 /** 274 * This method tests if secondNode is clockwise to first node. 275 * @param <N> type of node 276 * @param commonNode starting point for both vectors 277 * @param firstNode first vector end node 278 * @param secondNode second vector end node 279 * @return true if first vector is clockwise before second vector. 280 */ 281 public static <N extends INode> boolean angleIsClockwise(N commonNode, N firstNode, N secondNode) { 282 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth()); 283 } 284 285 /** 286 * Finds the intersection of two line segments. 287 * @param p1 the coordinates of the start point of the first specified line segment 288 * @param p2 the coordinates of the end point of the first specified line segment 289 * @param p3 the coordinates of the start point of the second specified line segment 290 * @param p4 the coordinates of the end point of the second specified line segment 291 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise 292 */ 293 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 294 295 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 296 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 297 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 298 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid); 299 300 double x1 = p1.getX(); 301 double y1 = p1.getY(); 302 double x2 = p2.getX(); 303 double y2 = p2.getY(); 304 double x3 = p3.getX(); 305 double y3 = p3.getY(); 306 double x4 = p4.getX(); 307 double y4 = p4.getY(); 308 309 //TODO: do this locally. 310 //TODO: remove this check after careful testing 311 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null; 312 313 // solve line-line intersection in parametric form: 314 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v 315 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1) 316 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u ) 317 318 double a1 = x2 - x1; 319 double b1 = x3 - x4; 320 double c1 = x3 - x1; 321 322 double a2 = y2 - y1; 323 double b2 = y3 - y4; 324 double c2 = y3 - y1; 325 326 // Solve the equations 327 double det = a1*b2 - a2*b1; 328 329 double uu = b2*c1 - b1*c2; 330 double vv = a1*c2 - a2*c1; 331 double mag = Math.abs(uu)+Math.abs(vv); 332 333 if (Math.abs(det) > 1e-12 * mag) { 334 double u = uu/det, v = vv/det; 335 if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) { 336 if (u < 0) u = 0; 337 if (u > 1) u = 1.0; 338 return new EastNorth(x1+a1*u, y1+a2*u); 339 } else { 340 return null; 341 } 342 } else { 343 // parallel lines 344 return null; 345 } 346 } 347 348 /** 349 * Finds the intersection of two lines of infinite length. 350 * 351 * @param p1 first point on first line 352 * @param p2 second point on first line 353 * @param p3 first point on second line 354 * @param p4 second point on second line 355 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise 356 * @throws IllegalArgumentException if a parameter is null or without valid coordinates 357 */ 358 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 359 360 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 361 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 362 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 363 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid); 364 365 // Basically, the formula from wikipedia is used: 366 // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection 367 // However, large numbers lead to rounding errors (see #10286). 368 // To avoid this, p1 is first substracted from each of the points: 369 // p1' = 0 370 // p2' = p2 - p1 371 // p3' = p3 - p1 372 // p4' = p4 - p1 373 // In the end, p1 is added to the intersection point of segment p1'/p2' 374 // and segment p3'/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 if (det == 0) 386 return null; // Lines are parallel 387 388 double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY()); 389 390 return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY()); 391 } 392 393 /** 394 * Check if the segment p1 - p2 is parallel to p3 - p4 395 * @param p1 First point for first segment 396 * @param p2 Second point for first segment 397 * @param p3 First point for second segment 398 * @param p4 Second point for second segment 399 * @return <code>true</code> if they are parallel or close to parallel 400 */ 401 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 402 403 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 404 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 405 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 406 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid); 407 408 // Convert line from (point, point) form to ax+by=c 409 double a1 = p2.getY() - p1.getY(); 410 double b1 = p1.getX() - p2.getX(); 411 412 double a2 = p4.getY() - p3.getY(); 413 double b2 = p3.getX() - p4.getX(); 414 415 // Solve the equations 416 double det = a1 * b2 - a2 * b1; 417 // remove influence of of scaling factor 418 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2); 419 return Math.abs(det) < 1e-3; 420 } 421 422 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) { 423 CheckParameterUtil.ensureParameterNotNull(p1, "p1"); 424 CheckParameterUtil.ensureParameterNotNull(p2, "p2"); 425 CheckParameterUtil.ensureParameterNotNull(point, "point"); 426 427 double ldx = p2.getX() - p1.getX(); 428 double ldy = p2.getY() - p1.getY(); 429 430 //segment zero length 431 if (ldx == 0 && ldy == 0) 432 return p1; 433 434 double pdx = point.getX() - p1.getX(); 435 double pdy = point.getY() - p1.getY(); 436 437 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy); 438 439 if (segmentOnly && offset <= 0) 440 return p1; 441 else if (segmentOnly && offset >= 1) 442 return p2; 443 else 444 return p1.interpolate(p2, offset); 445 } 446 447 /** 448 * Calculates closest point to a line segment. 449 * @param segmentP1 First point determining line segment 450 * @param segmentP2 Second point determining line segment 451 * @param point Point for which a closest point is searched on line segment [P1,P2] 452 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point, 453 * a new point if closest point is between segmentP1 and segmentP2. 454 * @see #closestPointToLine 455 * @since 3650 456 */ 457 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) { 458 return closestPointTo(segmentP1, segmentP2, point, true); 459 } 460 461 /** 462 * Calculates closest point to a line. 463 * @param lineP1 First point determining line 464 * @param lineP2 Second point determining line 465 * @param point Point for which a closest point is searched on line (P1,P2) 466 * @return The closest point found on line. It may be outside the segment [P1,P2]. 467 * @see #closestPointToSegment 468 * @since 4134 469 */ 470 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) { 471 return closestPointTo(lineP1, lineP2, point, false); 472 } 473 474 /** 475 * This method tests if secondNode is clockwise to first node. 476 * 477 * The line through the two points commonNode and firstNode divides the 478 * plane into two parts. The test returns true, if secondNode lies in 479 * the part that is to the right when traveling in the direction from 480 * commonNode to firstNode. 481 * 482 * @param commonNode starting point for both vectors 483 * @param firstNode first vector end node 484 * @param secondNode second vector end node 485 * @return true if first vector is clockwise before second vector. 486 */ 487 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) { 488 489 CheckParameterUtil.ensure(commonNode, "commonNode", EastNorth::isValid); 490 CheckParameterUtil.ensure(firstNode, "firstNode", EastNorth::isValid); 491 CheckParameterUtil.ensure(secondNode, "secondNode", EastNorth::isValid); 492 493 double dy1 = firstNode.getY() - commonNode.getY(); 494 double dy2 = secondNode.getY() - commonNode.getY(); 495 double dx1 = firstNode.getX() - commonNode.getX(); 496 double dx2 = secondNode.getX() - commonNode.getX(); 497 498 return dy1 * dx2 - dx1 * dy2 > 0; 499 } 500 501 /** 502 * Returns the Area of a polygon, from its list of nodes. 503 * @param polygon List of nodes forming polygon 504 * @return Area for the given list of nodes (EastNorth coordinates) 505 * @since 6841 506 */ 507 public static Area getArea(List<? extends INode> polygon) { 508 Path2D path = new Path2D.Double(); 509 510 boolean begin = true; 511 for (INode n : polygon) { 512 EastNorth en = n.getEastNorth(); 513 if (en != null) { 514 if (begin) { 515 path.moveTo(en.getX(), en.getY()); 516 begin = false; 517 } else { 518 path.lineTo(en.getX(), en.getY()); 519 } 520 } 521 } 522 if (!begin) { 523 path.closePath(); 524 } 525 526 return new Area(path); 527 } 528 529 /** 530 * Builds a path from a list of nodes 531 * @param polygon Nodes, forming a closed polygon 532 * @param path2d path to add to; can be null, then a new path is created 533 * @return the path (LatLon coordinates) 534 * @since 13638 (signature) 535 */ 536 public static Path2D buildPath2DLatLon(List<? extends ILatLon> polygon, Path2D path2d) { 537 Path2D path = path2d != null ? path2d : new Path2D.Double(); 538 boolean begin = true; 539 for (ILatLon n : polygon) { 540 if (begin) { 541 path.moveTo(n.lon(), n.lat()); 542 begin = false; 543 } else { 544 path.lineTo(n.lon(), n.lat()); 545 } 546 } 547 if (!begin) { 548 path.closePath(); 549 } 550 return path; 551 } 552 553 /** 554 * Returns the Area of a polygon, from the multipolygon relation. 555 * @param multipolygon the multipolygon relation 556 * @return Area for the multipolygon (LatLon coordinates) 557 */ 558 public static Area getAreaLatLon(Relation multipolygon) { 559 final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon); 560 Path2D path = new Path2D.Double(); 561 path.setWindingRule(Path2D.WIND_EVEN_ODD); 562 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) { 563 buildPath2DLatLon(pd.getNodes(), path); 564 for (Multipolygon.PolyData pdInner : pd.getInners()) { 565 buildPath2DLatLon(pdInner.getNodes(), path); 566 } 567 } 568 return new Area(path); 569 } 570 571 /** 572 * Tests if two polygons intersect. 573 * @param first List of nodes forming first polygon 574 * @param second List of nodes forming second polygon 575 * @return intersection kind 576 */ 577 public static PolygonIntersection polygonIntersection(List<? extends INode> first, List<? extends INode> second) { 578 Area a1 = getArea(first); 579 Area a2 = getArea(second); 580 return polygonIntersection(a1, a2); 581 } 582 583 /** 584 * Tests if two polygons intersect. 585 * @param a1 Area of first polygon 586 * @param a2 Area of second polygon 587 * @return intersection kind 588 * @since 6841 589 */ 590 public static PolygonIntersection polygonIntersection(Area a1, Area a2) { 591 return polygonIntersection(a1, a2, 1.0); 592 } 593 594 /** 595 * Tests if two polygons intersect. 596 * @param a1 Area of first polygon 597 * @param a2 Area of second polygon 598 * @param eps an area threshold, everything below is considered an empty intersection 599 * @return intersection kind 600 */ 601 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) { 602 603 Area inter = new Area(a1); 604 inter.intersect(a2); 605 606 Rectangle bounds = inter.getBounds(); 607 608 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) { 609 return PolygonIntersection.OUTSIDE; 610 } else if (a2.getBounds2D().contains(a1.getBounds2D()) && inter.equals(a1)) { 611 return PolygonIntersection.FIRST_INSIDE_SECOND; 612 } else if (a1.getBounds2D().contains(a2.getBounds2D()) && inter.equals(a2)) { 613 return PolygonIntersection.SECOND_INSIDE_FIRST; 614 } else { 615 return PolygonIntersection.CROSSING; 616 } 617 } 618 619 /** 620 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner. 621 * @param polygonNodes list of nodes from polygon path. 622 * @param point the point to test 623 * @return true if the point is inside polygon. 624 */ 625 public static boolean nodeInsidePolygon(INode point, List<? extends INode> polygonNodes) { 626 if (polygonNodes.size() < 2) 627 return false; 628 629 //iterate each side of the polygon, start with the last segment 630 INode oldPoint = polygonNodes.get(polygonNodes.size() - 1); 631 632 if (!oldPoint.isLatLonKnown()) { 633 return false; 634 } 635 636 boolean inside = false; 637 INode p1, p2; 638 639 for (INode newPoint : polygonNodes) { 640 //skip duplicate points 641 if (newPoint.equals(oldPoint)) { 642 continue; 643 } 644 645 if (!newPoint.isLatLonKnown()) { 646 return false; 647 } 648 649 //order points so p1.lat <= p2.lat 650 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) { 651 p1 = oldPoint; 652 p2 = newPoint; 653 } else { 654 p1 = newPoint; 655 p2 = oldPoint; 656 } 657 658 EastNorth pEN = point.getEastNorth(); 659 EastNorth opEN = oldPoint.getEastNorth(); 660 EastNorth npEN = newPoint.getEastNorth(); 661 EastNorth p1EN = p1.getEastNorth(); 662 EastNorth p2EN = p2.getEastNorth(); 663 664 if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) { 665 //test if the line is crossed and if so invert the inside flag. 666 if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY()) 667 && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY()) 668 < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) { 669 inside = !inside; 670 } 671 } 672 673 oldPoint = newPoint; 674 } 675 676 return inside; 677 } 678 679 /** 680 * Returns area of a closed way in square meters. 681 * 682 * @param way Way to measure, should be closed (first node is the same as last node) 683 * @return area of the closed way. 684 */ 685 public static double closedWayArea(Way way) { 686 return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea(); 687 } 688 689 /** 690 * Returns area of a multipolygon in square meters. 691 * 692 * @param multipolygon the multipolygon to measure 693 * @return area of the multipolygon. 694 */ 695 public static double multipolygonArea(Relation multipolygon) { 696 double area = 0.0; 697 final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon); 698 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) { 699 area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea(); 700 } 701 return area; 702 } 703 704 /** 705 * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives 706 * 707 * @param osm the primitive to measure 708 * @return area of the primitive, or {@code null} 709 * @since 13638 (signature) 710 */ 711 public static Double computeArea(IPrimitive osm) { 712 if (osm instanceof Way && ((Way) osm).isClosed()) { 713 return closedWayArea((Way) osm); 714 } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) { 715 return multipolygonArea((Relation) osm); 716 } else { 717 return null; 718 } 719 } 720 721 /** 722 * Determines whether a way is oriented clockwise. 723 * 724 * Internals: Assuming a closed non-looping way, compute twice the area 725 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}. 726 * If the area is negative the way is ordered in a clockwise direction. 727 * 728 * See http://paulbourke.net/geometry/polyarea/ 729 * 730 * @param w the way to be checked. 731 * @return true if and only if way is oriented clockwise. 732 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 733 */ 734 public static boolean isClockwise(Way w) { 735 return isClockwise(w.getNodes()); 736 } 737 738 /** 739 * Determines whether path from nodes list is oriented clockwise. 740 * @param nodes Nodes list to be checked. 741 * @return true if and only if way is oriented clockwise. 742 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 743 * @see #isClockwise(Way) 744 */ 745 public static boolean isClockwise(List<? extends INode> nodes) { 746 int nodesCount = nodes.size(); 747 if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) { 748 throw new IllegalArgumentException("Way must be closed to check orientation."); 749 } 750 double area2 = 0.; 751 752 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) { 753 INode coorPrev = nodes.get(node - 1); 754 INode coorCurr = nodes.get(node % nodesCount); 755 area2 += coorPrev.lon() * coorCurr.lat(); 756 area2 -= coorCurr.lon() * coorPrev.lat(); 757 } 758 return area2 < 0; 759 } 760 761 /** 762 * Returns angle of a segment defined with 2 point coordinates. 763 * 764 * @param p1 first point 765 * @param p2 second point 766 * @return Angle in radians (-pi, pi] 767 */ 768 public static double getSegmentAngle(EastNorth p1, EastNorth p2) { 769 770 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 771 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 772 773 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east()); 774 } 775 776 /** 777 * Returns angle of a corner defined with 3 point coordinates. 778 * 779 * @param p1 first point 780 * @param p2 Common endpoint 781 * @param p3 third point 782 * @return Angle in radians (-pi, pi] 783 */ 784 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) { 785 786 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 787 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 788 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 789 790 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3); 791 if (result <= -Math.PI) { 792 result += 2 * Math.PI; 793 } 794 795 if (result > Math.PI) { 796 result -= 2 * Math.PI; 797 } 798 799 return result; 800 } 801 802 /** 803 * Get angles in radians and return it's value in range [0, 180]. 804 * 805 * @param angle the angle in radians 806 * @return normalized angle in degrees 807 * @since 13670 808 */ 809 public static double getNormalizedAngleInDegrees(double angle) { 810 return Math.abs(180 * angle / Math.PI); 811 } 812 813 /** 814 * Compute the centroid/barycenter of nodes 815 * @param nodes Nodes for which the centroid is wanted 816 * @return the centroid of nodes 817 * @see Geometry#getCenter 818 */ 819 public static EastNorth getCentroid(List<? extends INode> nodes) { 820 return getCentroidEN(nodes.stream().map(INode::getEastNorth).collect(Collectors.toList())); 821 } 822 823 /** 824 * Compute the centroid/barycenter of nodes 825 * @param nodes Coordinates for which the centroid is wanted 826 * @return the centroid of nodes 827 * @since 13712 828 */ 829 public static EastNorth getCentroidEN(List<EastNorth> nodes) { 830 831 final int size = nodes.size(); 832 if (size == 1) { 833 return nodes.get(0); 834 } else if (size == 2) { 835 return nodes.get(0).getCenter(nodes.get(1)); 836 } 837 838 BigDecimal area = BigDecimal.ZERO; 839 BigDecimal north = BigDecimal.ZERO; 840 BigDecimal east = BigDecimal.ZERO; 841 842 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_a_polygon for the equation used here 843 for (int i = 0; i < size; i++) { 844 EastNorth n0 = nodes.get(i); 845 EastNorth n1 = nodes.get((i+1) % size); 846 847 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) { 848 BigDecimal x0 = BigDecimal.valueOf(n0.east()); 849 BigDecimal y0 = BigDecimal.valueOf(n0.north()); 850 BigDecimal x1 = BigDecimal.valueOf(n1.east()); 851 BigDecimal y1 = BigDecimal.valueOf(n1.north()); 852 853 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128)); 854 855 area = area.add(k, MathContext.DECIMAL128); 856 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 857 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 858 } 859 } 860 861 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3 862 area = area.multiply(d, MathContext.DECIMAL128); 863 if (area.compareTo(BigDecimal.ZERO) != 0) { 864 north = north.divide(area, MathContext.DECIMAL128); 865 east = east.divide(area, MathContext.DECIMAL128); 866 } 867 868 return new EastNorth(east.doubleValue(), north.doubleValue()); 869 } 870 871 /** 872 * Compute center of the circle closest to different nodes. 873 * 874 * Ensure exact center computation in case nodes are already aligned in circle. 875 * This is done by least square method. 876 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges. 877 * Center must be intersection of all bisectors. 878 * <pre> 879 * [ a1 b1 ] [ -c1 ] 880 * With A = [ ... ... ] and Y = [ ... ] 881 * [ an bn ] [ -cn ] 882 * </pre> 883 * An approximation of center of circle is (At.A)^-1.At.Y 884 * @param nodes Nodes parts of the circle (at least 3) 885 * @return An approximation of the center, of null if there is no solution. 886 * @see Geometry#getCentroid 887 * @since 6934 888 */ 889 public static EastNorth getCenter(List<? extends INode> nodes) { 890 int nc = nodes.size(); 891 if (nc < 3) return null; 892 /** 893 * Equation of each bisector ax + by + c = 0 894 */ 895 double[] a = new double[nc]; 896 double[] b = new double[nc]; 897 double[] c = new double[nc]; 898 // Compute equation of bisector 899 for (int i = 0; i < nc; i++) { 900 EastNorth pt1 = nodes.get(i).getEastNorth(); 901 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth(); 902 a[i] = pt1.east() - pt2.east(); 903 b[i] = pt1.north() - pt2.north(); 904 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]); 905 if (d == 0) return null; 906 a[i] /= d; 907 b[i] /= d; 908 double xC = (pt1.east() + pt2.east()) / 2; 909 double yC = (pt1.north() + pt2.north()) / 2; 910 c[i] = -(a[i]*xC + b[i]*yC); 911 } 912 // At.A = [aij] 913 double a11 = 0, a12 = 0, a22 = 0; 914 // At.Y = [bi] 915 double b1 = 0, b2 = 0; 916 for (int i = 0; i < nc; i++) { 917 a11 += a[i]*a[i]; 918 a12 += a[i]*b[i]; 919 a22 += b[i]*b[i]; 920 b1 -= a[i]*c[i]; 921 b2 -= b[i]*c[i]; 922 } 923 // (At.A)^-1 = [invij] 924 double det = a11*a22 - a12*a12; 925 if (Math.abs(det) < 1e-5) return null; 926 double inv11 = a22/det; 927 double inv12 = -a12/det; 928 double inv22 = a11/det; 929 // center (xC, yC) = (At.A)^-1.At.y 930 double xC = inv11*b1 + inv12*b2; 931 double yC = inv12*b1 + inv22*b2; 932 return new EastNorth(xC, yC); 933 } 934 935 /** 936 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument 937 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 938 * @param node node 939 * @param multiPolygon multipolygon 940 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 941 * @return {@code true} if the node is inside the multipolygon 942 */ 943 public static boolean isNodeInsideMultiPolygon(INode node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 944 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch); 945 } 946 947 /** 948 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument 949 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 950 * <p> 951 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon. 952 * @param nodes nodes forming the polygon 953 * @param multiPolygon multipolygon 954 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 955 * @return {@code true} if the polygon formed by nodes is inside the multipolygon 956 */ 957 public static boolean isPolygonInsideMultiPolygon(List<? extends INode> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 958 // Extract outer/inner members from multipolygon 959 final Pair<List<JoinedPolygon>, List<JoinedPolygon>> outerInner; 960 try { 961 outerInner = MultipolygonBuilder.joinWays(multiPolygon); 962 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) { 963 Logging.trace(ex); 964 Logging.debug("Invalid multipolygon " + multiPolygon); 965 return false; 966 } 967 // Test if object is inside an outer member 968 for (JoinedPolygon out : outerInner.a) { 969 if (nodes.size() == 1 970 ? nodeInsidePolygon(nodes.get(0), out.getNodes()) 971 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains( 972 polygonIntersection(nodes, out.getNodes()))) { 973 boolean insideInner = false; 974 // If inside an outer, check it is not inside an inner 975 for (JoinedPolygon in : outerInner.b) { 976 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND 977 && (nodes.size() == 1 978 ? nodeInsidePolygon(nodes.get(0), in.getNodes()) 979 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) { 980 insideInner = true; 981 break; 982 } 983 } 984 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon 985 if (!insideInner) { 986 // Final check using predicate 987 if (isOuterWayAMatch == null || isOuterWayAMatch.test(out.ways.get(0) 988 /* TODO give a better representation of the outer ring to the predicate */)) { 989 return true; 990 } 991 } 992 } 993 } 994 return false; 995 } 996 997 /** 998 * Data class to hold two double values (area and perimeter of a polygon). 999 */ 1000 public static class AreaAndPerimeter { 1001 private final double area; 1002 private final double perimeter; 1003 1004 /** 1005 * Create a new {@link AreaAndPerimeter} 1006 * @param area The area 1007 * @param perimeter The perimeter 1008 */ 1009 public AreaAndPerimeter(double area, double perimeter) { 1010 this.area = area; 1011 this.perimeter = perimeter; 1012 } 1013 1014 /** 1015 * Gets the area 1016 * @return The area size 1017 */ 1018 public double getArea() { 1019 return area; 1020 } 1021 1022 /** 1023 * Gets the perimeter 1024 * @return The perimeter length 1025 */ 1026 public double getPerimeter() { 1027 return perimeter; 1028 } 1029 } 1030 1031 /** 1032 * Calculate area and perimeter length of a polygon. 1033 * 1034 * Uses current projection; units are that of the projected coordinates. 1035 * 1036 * @param nodes the list of nodes representing the polygon 1037 * @return area and perimeter 1038 */ 1039 public static AreaAndPerimeter getAreaAndPerimeter(List<? extends ILatLon> nodes) { 1040 return getAreaAndPerimeter(nodes, null); 1041 } 1042 1043 /** 1044 * Calculate area and perimeter length of a polygon in the given projection. 1045 * 1046 * @param nodes the list of nodes representing the polygon 1047 * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()} 1048 * @return area and perimeter 1049 * @since 13638 (signature) 1050 */ 1051 public static AreaAndPerimeter getAreaAndPerimeter(List<? extends ILatLon> nodes, Projection projection) { 1052 CheckParameterUtil.ensureParameterNotNull(nodes, "nodes"); 1053 double area = 0; 1054 double perimeter = 0; 1055 Projection useProjection = projection == null ? Main.getProjection() : projection; 1056 1057 if (!nodes.isEmpty()) { 1058 boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1); 1059 int numSegments = closed ? nodes.size() - 1 : nodes.size(); 1060 EastNorth p1 = nodes.get(0).getEastNorth(useProjection); 1061 for (int i = 1; i <= numSegments; i++) { 1062 final ILatLon node = nodes.get(i == numSegments ? 0 : i); 1063 final EastNorth p2 = node.getEastNorth(useProjection); 1064 if (p1 != null && p2 != null) { 1065 area += p1.east() * p2.north() - p2.east() * p1.north(); 1066 perimeter += p1.distance(p2); 1067 } 1068 p1 = p2; 1069 } 1070 } 1071 return new AreaAndPerimeter(Math.abs(area) / 2, perimeter); 1072 } 1073}