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; 018 019import org.openstreetmap.josm.Main; 020import org.openstreetmap.josm.command.AddCommand; 021import org.openstreetmap.josm.command.ChangeCommand; 022import org.openstreetmap.josm.command.Command; 023import org.openstreetmap.josm.data.coor.EastNorth; 024import org.openstreetmap.josm.data.coor.ILatLon; 025import org.openstreetmap.josm.data.osm.BBox; 026import org.openstreetmap.josm.data.osm.DataSet; 027import org.openstreetmap.josm.data.osm.IPrimitive; 028import org.openstreetmap.josm.data.osm.MultipolygonBuilder; 029import org.openstreetmap.josm.data.osm.MultipolygonBuilder.JoinedPolygon; 030import org.openstreetmap.josm.data.osm.Node; 031import org.openstreetmap.josm.data.osm.NodePositionComparator; 032import org.openstreetmap.josm.data.osm.Relation; 033import org.openstreetmap.josm.data.osm.Way; 034import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon; 035import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache; 036import org.openstreetmap.josm.data.projection.Projection; 037import org.openstreetmap.josm.data.projection.Projections; 038 039/** 040 * Some tools for geometry related tasks. 041 * 042 * @author viesturs 043 */ 044public final class Geometry { 045 046 private Geometry() { 047 // Hide default constructor for utils classes 048 } 049 050 /** 051 * The result types for a {@link Geometry#polygonIntersection(Area, Area)} test 052 */ 053 public enum PolygonIntersection { 054 /** 055 * The first polygon is inside the second one 056 */ 057 FIRST_INSIDE_SECOND, 058 /** 059 * The second one is inside the first 060 */ 061 SECOND_INSIDE_FIRST, 062 /** 063 * The polygons do not overlap 064 */ 065 OUTSIDE, 066 /** 067 * The polygon borders cross each other 068 */ 069 CROSSING 070 } 071 072 /** 073 * Will find all intersection and add nodes there for list of given ways. 074 * Handles self-intersections too. 075 * And makes commands to add the intersection points to ways. 076 * 077 * Prerequisite: no two nodes have the same coordinates. 078 * 079 * @param ways a list of ways to test 080 * @param test if false, do not build list of Commands, just return nodes 081 * @param cmds list of commands, typically empty when handed to this method. 082 * Will be filled with commands that add intersection nodes to 083 * the ways. 084 * @return list of new nodes 085 */ 086 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) { 087 088 int n = ways.size(); 089 @SuppressWarnings("unchecked") 090 List<Node>[] newNodes = new ArrayList[n]; 091 BBox[] wayBounds = new BBox[n]; 092 boolean[] changedWays = new boolean[n]; 093 094 Set<Node> intersectionNodes = new LinkedHashSet<>(); 095 096 //copy node arrays for local usage. 097 for (int pos = 0; pos < n; pos++) { 098 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes()); 099 wayBounds[pos] = getNodesBounds(newNodes[pos]); 100 changedWays[pos] = false; 101 } 102 103 DataSet dataset = ways.get(0).getDataSet(); 104 105 //iterate over all way pairs and introduce the intersections 106 Comparator<Node> coordsComparator = new NodePositionComparator(); 107 for (int seg1Way = 0; seg1Way < n; seg1Way++) { 108 for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) { 109 110 //do not waste time on bounds that do not intersect 111 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) { 112 continue; 113 } 114 115 List<Node> way1Nodes = newNodes[seg1Way]; 116 List<Node> way2Nodes = newNodes[seg2Way]; 117 118 //iterate over primary segmemt 119 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) { 120 121 //iterate over secondary segment 122 int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment 123 124 for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) { 125 126 //need to get them again every time, because other segments may be changed 127 Node seg1Node1 = way1Nodes.get(seg1Pos); 128 Node seg1Node2 = way1Nodes.get(seg1Pos + 1); 129 Node seg2Node1 = way2Nodes.get(seg2Pos); 130 Node seg2Node2 = way2Nodes.get(seg2Pos + 1); 131 132 int commonCount = 0; 133 //test if we have common nodes to add. 134 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) { 135 commonCount++; 136 137 if (seg1Way == seg2Way && 138 seg1Pos == 0 && 139 seg2Pos == way2Nodes.size() -2) { 140 //do not add - this is first and last segment of the same way. 141 } else { 142 intersectionNodes.add(seg1Node1); 143 } 144 } 145 146 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) { 147 commonCount++; 148 149 intersectionNodes.add(seg1Node2); 150 } 151 152 //no common nodes - find intersection 153 if (commonCount == 0) { 154 EastNorth intersection = getSegmentSegmentIntersection( 155 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(), 156 seg2Node1.getEastNorth(), seg2Node2.getEastNorth()); 157 158 if (intersection != null) { 159 if (test) { 160 intersectionNodes.add(seg2Node1); 161 return intersectionNodes; 162 } 163 164 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection)); 165 Node intNode = newNode; 166 boolean insertInSeg1 = false; 167 boolean insertInSeg2 = false; 168 //find if the intersection point is at end point of one of the segments, if so use that point 169 170 //segment 1 171 if (coordsComparator.compare(newNode, seg1Node1) == 0) { 172 intNode = seg1Node1; 173 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) { 174 intNode = seg1Node2; 175 } else { 176 insertInSeg1 = true; 177 } 178 179 //segment 2 180 if (coordsComparator.compare(newNode, seg2Node1) == 0) { 181 intNode = seg2Node1; 182 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) { 183 intNode = seg2Node2; 184 } else { 185 insertInSeg2 = true; 186 } 187 188 if (insertInSeg1) { 189 way1Nodes.add(seg1Pos +1, intNode); 190 changedWays[seg1Way] = true; 191 192 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment. 193 if (seg2Way == seg1Way) { 194 seg2Pos++; 195 } 196 } 197 198 if (insertInSeg2) { 199 way2Nodes.add(seg2Pos +1, intNode); 200 changedWays[seg2Way] = true; 201 202 //Do not need to compare again to already split segment 203 seg2Pos++; 204 } 205 206 intersectionNodes.add(intNode); 207 208 if (intNode == newNode) { 209 cmds.add(new AddCommand(dataset, intNode)); 210 } 211 } 212 } else if (test && !intersectionNodes.isEmpty()) 213 return intersectionNodes; 214 } 215 } 216 } 217 } 218 219 220 for (int pos = 0; pos < ways.size(); pos++) { 221 if (!changedWays[pos]) { 222 continue; 223 } 224 225 Way way = ways.get(pos); 226 Way newWay = new Way(way); 227 newWay.setNodes(newNodes[pos]); 228 229 cmds.add(new ChangeCommand(dataset, way, newWay)); 230 } 231 232 return intersectionNodes; 233 } 234 235 private static BBox getNodesBounds(List<Node> nodes) { 236 237 BBox bounds = new BBox(nodes.get(0)); 238 for (Node n: nodes) { 239 bounds.add(n); 240 } 241 return bounds; 242 } 243 244 /** 245 * Tests if given point is to the right side of path consisting of 3 points. 246 * 247 * (Imagine the path is continued beyond the endpoints, so you get two rays 248 * starting from lineP2 and going through lineP1 and lineP3 respectively 249 * which divide the plane into two parts. The test returns true, if testPoint 250 * lies in the part that is to the right when traveling in the direction 251 * lineP1, lineP2, lineP3.) 252 * 253 * @param lineP1 first point in path 254 * @param lineP2 second point in path 255 * @param lineP3 third point in path 256 * @param testPoint point to test 257 * @return true if to the right side, false otherwise 258 */ 259 public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) { 260 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3); 261 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint); 262 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint); 263 264 if (pathBendToRight) 265 return rightOfSeg1 && rightOfSeg2; 266 else 267 return !(!rightOfSeg1 && !rightOfSeg2); 268 } 269 270 /** 271 * This method tests if secondNode is clockwise to first node. 272 * @param commonNode starting point for both vectors 273 * @param firstNode first vector end node 274 * @param secondNode second vector end node 275 * @return true if first vector is clockwise before second vector. 276 */ 277 public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) { 278 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth()); 279 } 280 281 /** 282 * Finds the intersection of two line segments. 283 * @param p1 the coordinates of the start point of the first specified line segment 284 * @param p2 the coordinates of the end point of the first specified line segment 285 * @param p3 the coordinates of the start point of the second specified line segment 286 * @param p4 the coordinates of the end point of the second specified line segment 287 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise 288 */ 289 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 290 291 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 292 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 293 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 294 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid); 295 296 double x1 = p1.getX(); 297 double y1 = p1.getY(); 298 double x2 = p2.getX(); 299 double y2 = p2.getY(); 300 double x3 = p3.getX(); 301 double y3 = p3.getY(); 302 double x4 = p4.getX(); 303 double y4 = p4.getY(); 304 305 //TODO: do this locally. 306 //TODO: remove this check after careful testing 307 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null; 308 309 // solve line-line intersection in parametric form: 310 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v 311 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1) 312 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u ) 313 314 double a1 = x2 - x1; 315 double b1 = x3 - x4; 316 double c1 = x3 - x1; 317 318 double a2 = y2 - y1; 319 double b2 = y3 - y4; 320 double c2 = y3 - y1; 321 322 // Solve the equations 323 double det = a1*b2 - a2*b1; 324 325 double uu = b2*c1 - b1*c2; 326 double vv = a1*c2 - a2*c1; 327 double mag = Math.abs(uu)+Math.abs(vv); 328 329 if (Math.abs(det) > 1e-12 * mag) { 330 double u = uu/det, v = vv/det; 331 if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) { 332 if (u < 0) u = 0; 333 if (u > 1) u = 1.0; 334 return new EastNorth(x1+a1*u, y1+a2*u); 335 } else { 336 return null; 337 } 338 } else { 339 // parallel lines 340 return null; 341 } 342 } 343 344 /** 345 * Finds the intersection of two lines of infinite length. 346 * 347 * @param p1 first point on first line 348 * @param p2 second point on first line 349 * @param p3 first point on second line 350 * @param p4 second point on second line 351 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise 352 * @throws IllegalArgumentException if a parameter is null or without valid coordinates 353 */ 354 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 355 356 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 357 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 358 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 359 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid); 360 361 // Basically, the formula from wikipedia is used: 362 // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection 363 // However, large numbers lead to rounding errors (see #10286). 364 // To avoid this, p1 is first substracted from each of the points: 365 // p1' = 0 366 // p2' = p2 - p1 367 // p3' = p3 - p1 368 // p4' = p4 - p1 369 // In the end, p1 is added to the intersection point of segment p1'/p2' 370 // and segment p3'/p4'. 371 372 // Convert line from (point, point) form to ax+by=c 373 double a1 = p2.getY() - p1.getY(); 374 double b1 = p1.getX() - p2.getX(); 375 376 double a2 = p4.getY() - p3.getY(); 377 double b2 = p3.getX() - p4.getX(); 378 379 // Solve the equations 380 double det = a1 * b2 - a2 * b1; 381 if (det == 0) 382 return null; // Lines are parallel 383 384 double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY()); 385 386 return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY()); 387 } 388 389 /** 390 * Check if the segment p1 - p2 is parallel to p3 - p4 391 * @param p1 First point for first segment 392 * @param p2 Second point for first segment 393 * @param p3 First point for second segment 394 * @param p4 Second point for second segment 395 * @return <code>true</code> if they are parallel or close to parallel 396 */ 397 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 398 399 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 400 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 401 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 402 CheckParameterUtil.ensure(p4, "p4", EastNorth::isValid); 403 404 // Convert line from (point, point) form to ax+by=c 405 double a1 = p2.getY() - p1.getY(); 406 double b1 = p1.getX() - p2.getX(); 407 408 double a2 = p4.getY() - p3.getY(); 409 double b2 = p3.getX() - p4.getX(); 410 411 // Solve the equations 412 double det = a1 * b2 - a2 * b1; 413 // remove influence of of scaling factor 414 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2); 415 return Math.abs(det) < 1e-3; 416 } 417 418 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) { 419 CheckParameterUtil.ensureParameterNotNull(p1, "p1"); 420 CheckParameterUtil.ensureParameterNotNull(p2, "p2"); 421 CheckParameterUtil.ensureParameterNotNull(point, "point"); 422 423 double ldx = p2.getX() - p1.getX(); 424 double ldy = p2.getY() - p1.getY(); 425 426 //segment zero length 427 if (ldx == 0 && ldy == 0) 428 return p1; 429 430 double pdx = point.getX() - p1.getX(); 431 double pdy = point.getY() - p1.getY(); 432 433 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy); 434 435 if (segmentOnly && offset <= 0) 436 return p1; 437 else if (segmentOnly && offset >= 1) 438 return p2; 439 else 440 return p1.interpolate(p2, offset); 441 } 442 443 /** 444 * Calculates closest point to a line segment. 445 * @param segmentP1 First point determining line segment 446 * @param segmentP2 Second point determining line segment 447 * @param point Point for which a closest point is searched on line segment [P1,P2] 448 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point, 449 * a new point if closest point is between segmentP1 and segmentP2. 450 * @see #closestPointToLine 451 * @since 3650 452 */ 453 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) { 454 return closestPointTo(segmentP1, segmentP2, point, true); 455 } 456 457 /** 458 * Calculates closest point to a line. 459 * @param lineP1 First point determining line 460 * @param lineP2 Second point determining line 461 * @param point Point for which a closest point is searched on line (P1,P2) 462 * @return The closest point found on line. It may be outside the segment [P1,P2]. 463 * @see #closestPointToSegment 464 * @since 4134 465 */ 466 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) { 467 return closestPointTo(lineP1, lineP2, point, false); 468 } 469 470 /** 471 * This method tests if secondNode is clockwise to first node. 472 * 473 * The line through the two points commonNode and firstNode divides the 474 * plane into two parts. The test returns true, if secondNode lies in 475 * the part that is to the right when traveling in the direction from 476 * commonNode to firstNode. 477 * 478 * @param commonNode starting point for both vectors 479 * @param firstNode first vector end node 480 * @param secondNode second vector end node 481 * @return true if first vector is clockwise before second vector. 482 */ 483 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) { 484 485 CheckParameterUtil.ensure(commonNode, "commonNode", EastNorth::isValid); 486 CheckParameterUtil.ensure(firstNode, "firstNode", EastNorth::isValid); 487 CheckParameterUtil.ensure(secondNode, "secondNode", EastNorth::isValid); 488 489 double dy1 = firstNode.getY() - commonNode.getY(); 490 double dy2 = secondNode.getY() - commonNode.getY(); 491 double dx1 = firstNode.getX() - commonNode.getX(); 492 double dx2 = secondNode.getX() - commonNode.getX(); 493 494 return dy1 * dx2 - dx1 * dy2 > 0; 495 } 496 497 /** 498 * Returns the Area of a polygon, from its list of nodes. 499 * @param polygon List of nodes forming polygon 500 * @return Area for the given list of nodes (EastNorth coordinates) 501 * @since 6841 502 */ 503 public static Area getArea(List<Node> polygon) { 504 Path2D path = new Path2D.Double(); 505 506 boolean begin = true; 507 for (Node n : polygon) { 508 EastNorth en = n.getEastNorth(); 509 if (en != null) { 510 if (begin) { 511 path.moveTo(en.getX(), en.getY()); 512 begin = false; 513 } else { 514 path.lineTo(en.getX(), en.getY()); 515 } 516 } 517 } 518 if (!begin) { 519 path.closePath(); 520 } 521 522 return new Area(path); 523 } 524 525 /** 526 * Builds a path from a list of nodes 527 * @param polygon Nodes, forming a closed polygon 528 * @param path2d path to add to; can be null, then a new path is created 529 * @return the path (LatLon coordinates) 530 * @since 13638 (signature) 531 */ 532 public static Path2D buildPath2DLatLon(List<? extends ILatLon> polygon, Path2D path2d) { 533 Path2D path = path2d != null ? path2d : new Path2D.Double(); 534 boolean begin = true; 535 for (ILatLon n : polygon) { 536 if (begin) { 537 path.moveTo(n.lon(), n.lat()); 538 begin = false; 539 } else { 540 path.lineTo(n.lon(), n.lat()); 541 } 542 } 543 if (!begin) { 544 path.closePath(); 545 } 546 return path; 547 } 548 549 /** 550 * Returns the Area of a polygon, from the multipolygon relation. 551 * @param multipolygon the multipolygon relation 552 * @return Area for the multipolygon (LatLon coordinates) 553 */ 554 public static Area getAreaLatLon(Relation multipolygon) { 555 final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon); 556 Path2D path = new Path2D.Double(); 557 path.setWindingRule(Path2D.WIND_EVEN_ODD); 558 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) { 559 buildPath2DLatLon(pd.getNodes(), path); 560 for (Multipolygon.PolyData pdInner : pd.getInners()) { 561 buildPath2DLatLon(pdInner.getNodes(), path); 562 } 563 } 564 return new Area(path); 565 } 566 567 /** 568 * Tests if two polygons intersect. 569 * @param first List of nodes forming first polygon 570 * @param second List of nodes forming second polygon 571 * @return intersection kind 572 */ 573 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) { 574 Area a1 = getArea(first); 575 Area a2 = getArea(second); 576 return polygonIntersection(a1, a2); 577 } 578 579 /** 580 * Tests if two polygons intersect. 581 * @param a1 Area of first polygon 582 * @param a2 Area of second polygon 583 * @return intersection kind 584 * @since 6841 585 */ 586 public static PolygonIntersection polygonIntersection(Area a1, Area a2) { 587 return polygonIntersection(a1, a2, 1.0); 588 } 589 590 /** 591 * Tests if two polygons intersect. 592 * @param a1 Area of first polygon 593 * @param a2 Area of second polygon 594 * @param eps an area threshold, everything below is considered an empty intersection 595 * @return intersection kind 596 */ 597 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) { 598 599 Area inter = new Area(a1); 600 inter.intersect(a2); 601 602 Rectangle bounds = inter.getBounds(); 603 604 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) { 605 return PolygonIntersection.OUTSIDE; 606 } else if (a2.getBounds2D().contains(a1.getBounds2D()) && inter.equals(a1)) { 607 return PolygonIntersection.FIRST_INSIDE_SECOND; 608 } else if (a1.getBounds2D().contains(a2.getBounds2D()) && inter.equals(a2)) { 609 return PolygonIntersection.SECOND_INSIDE_FIRST; 610 } else { 611 return PolygonIntersection.CROSSING; 612 } 613 } 614 615 /** 616 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner. 617 * @param polygonNodes list of nodes from polygon path. 618 * @param point the point to test 619 * @return true if the point is inside polygon. 620 */ 621 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) { 622 if (polygonNodes.size() < 2) 623 return false; 624 625 //iterate each side of the polygon, start with the last segment 626 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1); 627 628 if (!oldPoint.isLatLonKnown()) { 629 return false; 630 } 631 632 boolean inside = false; 633 Node p1, p2; 634 635 for (Node newPoint : polygonNodes) { 636 //skip duplicate points 637 if (newPoint.equals(oldPoint)) { 638 continue; 639 } 640 641 if (!newPoint.isLatLonKnown()) { 642 return false; 643 } 644 645 //order points so p1.lat <= p2.lat 646 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) { 647 p1 = oldPoint; 648 p2 = newPoint; 649 } else { 650 p1 = newPoint; 651 p2 = oldPoint; 652 } 653 654 EastNorth pEN = point.getEastNorth(); 655 EastNorth opEN = oldPoint.getEastNorth(); 656 EastNorth npEN = newPoint.getEastNorth(); 657 EastNorth p1EN = p1.getEastNorth(); 658 EastNorth p2EN = p2.getEastNorth(); 659 660 if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) { 661 //test if the line is crossed and if so invert the inside flag. 662 if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY()) 663 && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY()) 664 < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) { 665 inside = !inside; 666 } 667 } 668 669 oldPoint = newPoint; 670 } 671 672 return inside; 673 } 674 675 /** 676 * Returns area of a closed way in square meters. 677 * 678 * @param way Way to measure, should be closed (first node is the same as last node) 679 * @return area of the closed way. 680 */ 681 public static double closedWayArea(Way way) { 682 return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea(); 683 } 684 685 /** 686 * Returns area of a multipolygon in square meters. 687 * 688 * @param multipolygon the multipolygon to measure 689 * @return area of the multipolygon. 690 */ 691 public static double multipolygonArea(Relation multipolygon) { 692 double area = 0.0; 693 final Multipolygon mp = MultipolygonCache.getInstance().get(multipolygon); 694 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) { 695 area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea(); 696 } 697 return area; 698 } 699 700 /** 701 * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives 702 * 703 * @param osm the primitive to measure 704 * @return area of the primitive, or {@code null} 705 * @since 13638 (signature) 706 */ 707 public static Double computeArea(IPrimitive osm) { 708 if (osm instanceof Way && ((Way) osm).isClosed()) { 709 return closedWayArea((Way) osm); 710 } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) { 711 return multipolygonArea((Relation) osm); 712 } else { 713 return null; 714 } 715 } 716 717 /** 718 * Determines whether a way is oriented clockwise. 719 * 720 * Internals: Assuming a closed non-looping way, compute twice the area 721 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}. 722 * If the area is negative the way is ordered in a clockwise direction. 723 * 724 * See http://paulbourke.net/geometry/polyarea/ 725 * 726 * @param w the way to be checked. 727 * @return true if and only if way is oriented clockwise. 728 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 729 */ 730 public static boolean isClockwise(Way w) { 731 return isClockwise(w.getNodes()); 732 } 733 734 /** 735 * Determines whether path from nodes list is oriented clockwise. 736 * @param nodes Nodes list to be checked. 737 * @return true if and only if way is oriented clockwise. 738 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 739 * @see #isClockwise(Way) 740 */ 741 public static boolean isClockwise(List<Node> nodes) { 742 int nodesCount = nodes.size(); 743 if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) { 744 throw new IllegalArgumentException("Way must be closed to check orientation."); 745 } 746 double area2 = 0.; 747 748 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) { 749 Node coorPrev = nodes.get(node - 1); 750 Node coorCurr = nodes.get(node % nodesCount); 751 area2 += coorPrev.lon() * coorCurr.lat(); 752 area2 -= coorCurr.lon() * coorPrev.lat(); 753 } 754 return area2 < 0; 755 } 756 757 /** 758 * Returns angle of a segment defined with 2 point coordinates. 759 * 760 * @param p1 first point 761 * @param p2 second point 762 * @return Angle in radians (-pi, pi] 763 */ 764 public static double getSegmentAngle(EastNorth p1, EastNorth p2) { 765 766 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 767 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 768 769 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east()); 770 } 771 772 /** 773 * Returns angle of a corner defined with 3 point coordinates. 774 * 775 * @param p1 first point 776 * @param p2 Common endpoint 777 * @param p3 third point 778 * @return Angle in radians (-pi, pi] 779 */ 780 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) { 781 782 CheckParameterUtil.ensure(p1, "p1", EastNorth::isValid); 783 CheckParameterUtil.ensure(p2, "p2", EastNorth::isValid); 784 CheckParameterUtil.ensure(p3, "p3", EastNorth::isValid); 785 786 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3); 787 if (result <= -Math.PI) { 788 result += 2 * Math.PI; 789 } 790 791 if (result > Math.PI) { 792 result -= 2 * Math.PI; 793 } 794 795 return result; 796 } 797 798 /** 799 * Get angles in radians and return it's value in range [0, 180]. 800 * 801 * @param angle the angle in radians 802 * @return normalized angle in degrees 803 * @since 13670 804 */ 805 public static double getNormalizedAngleInDegrees(double angle) { 806 return Math.abs(180 * angle / Math.PI); 807 } 808 809 /** 810 * Compute the centroid/barycenter of nodes 811 * @param nodes Nodes for which the centroid is wanted 812 * @return the centroid of nodes 813 * @see Geometry#getCenter 814 */ 815 public static EastNorth getCentroid(List<Node> nodes) { 816 817 BigDecimal area = BigDecimal.ZERO; 818 BigDecimal north = BigDecimal.ZERO; 819 BigDecimal east = BigDecimal.ZERO; 820 821 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here 822 for (int i = 0; i < nodes.size(); i++) { 823 EastNorth n0 = nodes.get(i).getEastNorth(); 824 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth(); 825 826 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) { 827 BigDecimal x0 = BigDecimal.valueOf(n0.east()); 828 BigDecimal y0 = BigDecimal.valueOf(n0.north()); 829 BigDecimal x1 = BigDecimal.valueOf(n1.east()); 830 BigDecimal y1 = BigDecimal.valueOf(n1.north()); 831 832 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128)); 833 834 area = area.add(k, MathContext.DECIMAL128); 835 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 836 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 837 } 838 } 839 840 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3 841 area = area.multiply(d, MathContext.DECIMAL128); 842 if (area.compareTo(BigDecimal.ZERO) != 0) { 843 north = north.divide(area, MathContext.DECIMAL128); 844 east = east.divide(area, MathContext.DECIMAL128); 845 } 846 847 return new EastNorth(east.doubleValue(), north.doubleValue()); 848 } 849 850 /** 851 * Compute center of the circle closest to different nodes. 852 * 853 * Ensure exact center computation in case nodes are already aligned in circle. 854 * This is done by least square method. 855 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges. 856 * Center must be intersection of all bisectors. 857 * <pre> 858 * [ a1 b1 ] [ -c1 ] 859 * With A = [ ... ... ] and Y = [ ... ] 860 * [ an bn ] [ -cn ] 861 * </pre> 862 * An approximation of center of circle is (At.A)^-1.At.Y 863 * @param nodes Nodes parts of the circle (at least 3) 864 * @return An approximation of the center, of null if there is no solution. 865 * @see Geometry#getCentroid 866 * @since 6934 867 */ 868 public static EastNorth getCenter(List<Node> nodes) { 869 int nc = nodes.size(); 870 if (nc < 3) return null; 871 /** 872 * Equation of each bisector ax + by + c = 0 873 */ 874 double[] a = new double[nc]; 875 double[] b = new double[nc]; 876 double[] c = new double[nc]; 877 // Compute equation of bisector 878 for (int i = 0; i < nc; i++) { 879 EastNorth pt1 = nodes.get(i).getEastNorth(); 880 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth(); 881 a[i] = pt1.east() - pt2.east(); 882 b[i] = pt1.north() - pt2.north(); 883 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]); 884 if (d == 0) return null; 885 a[i] /= d; 886 b[i] /= d; 887 double xC = (pt1.east() + pt2.east()) / 2; 888 double yC = (pt1.north() + pt2.north()) / 2; 889 c[i] = -(a[i]*xC + b[i]*yC); 890 } 891 // At.A = [aij] 892 double a11 = 0, a12 = 0, a22 = 0; 893 // At.Y = [bi] 894 double b1 = 0, b2 = 0; 895 for (int i = 0; i < nc; i++) { 896 a11 += a[i]*a[i]; 897 a12 += a[i]*b[i]; 898 a22 += b[i]*b[i]; 899 b1 -= a[i]*c[i]; 900 b2 -= b[i]*c[i]; 901 } 902 // (At.A)^-1 = [invij] 903 double det = a11*a22 - a12*a12; 904 if (Math.abs(det) < 1e-5) return null; 905 double inv11 = a22/det; 906 double inv12 = -a12/det; 907 double inv22 = a11/det; 908 // center (xC, yC) = (At.A)^-1.At.y 909 double xC = inv11*b1 + inv12*b2; 910 double yC = inv12*b1 + inv22*b2; 911 return new EastNorth(xC, yC); 912 } 913 914 /** 915 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument 916 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 917 * @param node node 918 * @param multiPolygon multipolygon 919 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 920 * @return {@code true} if the node is inside the multipolygon 921 */ 922 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 923 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch); 924 } 925 926 /** 927 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument 928 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 929 * <p> 930 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon. 931 * @param nodes nodes forming the polygon 932 * @param multiPolygon multipolygon 933 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 934 * @return {@code true} if the polygon formed by nodes is inside the multipolygon 935 */ 936 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 937 // Extract outer/inner members from multipolygon 938 final Pair<List<JoinedPolygon>, List<JoinedPolygon>> outerInner; 939 try { 940 outerInner = MultipolygonBuilder.joinWays(multiPolygon); 941 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) { 942 Logging.trace(ex); 943 Logging.debug("Invalid multipolygon " + multiPolygon); 944 return false; 945 } 946 // Test if object is inside an outer member 947 for (JoinedPolygon out : outerInner.a) { 948 if (nodes.size() == 1 949 ? nodeInsidePolygon(nodes.get(0), out.getNodes()) 950 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains( 951 polygonIntersection(nodes, out.getNodes()))) { 952 boolean insideInner = false; 953 // If inside an outer, check it is not inside an inner 954 for (JoinedPolygon in : outerInner.b) { 955 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND 956 && (nodes.size() == 1 957 ? nodeInsidePolygon(nodes.get(0), in.getNodes()) 958 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) { 959 insideInner = true; 960 break; 961 } 962 } 963 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon 964 if (!insideInner) { 965 // Final check using predicate 966 if (isOuterWayAMatch == null || isOuterWayAMatch.test(out.ways.get(0) 967 /* TODO give a better representation of the outer ring to the predicate */)) { 968 return true; 969 } 970 } 971 } 972 } 973 return false; 974 } 975 976 /** 977 * Data class to hold two double values (area and perimeter of a polygon). 978 */ 979 public static class AreaAndPerimeter { 980 private final double area; 981 private final double perimeter; 982 983 /** 984 * Create a new {@link AreaAndPerimeter} 985 * @param area The area 986 * @param perimeter The perimeter 987 */ 988 public AreaAndPerimeter(double area, double perimeter) { 989 this.area = area; 990 this.perimeter = perimeter; 991 } 992 993 /** 994 * Gets the area 995 * @return The area size 996 */ 997 public double getArea() { 998 return area; 999 } 1000 1001 /** 1002 * Gets the perimeter 1003 * @return The perimeter length 1004 */ 1005 public double getPerimeter() { 1006 return perimeter; 1007 } 1008 } 1009 1010 /** 1011 * Calculate area and perimeter length of a polygon. 1012 * 1013 * Uses current projection; units are that of the projected coordinates. 1014 * 1015 * @param nodes the list of nodes representing the polygon 1016 * @return area and perimeter 1017 */ 1018 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) { 1019 return getAreaAndPerimeter(nodes, null); 1020 } 1021 1022 /** 1023 * Calculate area and perimeter length of a polygon in the given projection. 1024 * 1025 * @param nodes the list of nodes representing the polygon 1026 * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()} 1027 * @return area and perimeter 1028 * @since 13638 (signature) 1029 */ 1030 public static AreaAndPerimeter getAreaAndPerimeter(List<? extends ILatLon> nodes, Projection projection) { 1031 CheckParameterUtil.ensureParameterNotNull(nodes, "nodes"); 1032 double area = 0; 1033 double perimeter = 0; 1034 Projection useProjection = projection == null ? Main.getProjection() : projection; 1035 1036 if (!nodes.isEmpty()) { 1037 boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1); 1038 int numSegments = closed ? nodes.size() - 1 : nodes.size(); 1039 EastNorth p1 = nodes.get(0).getEastNorth(useProjection); 1040 for (int i = 1; i <= numSegments; i++) { 1041 final ILatLon node = nodes.get(i == numSegments ? 0 : i); 1042 final EastNorth p2 = node.getEastNorth(useProjection); 1043 if (p1 != null && p2 != null) { 1044 area += p1.east() * p2.north() - p2.east() * p1.north(); 1045 perimeter += p1.distance(p2); 1046 } 1047 p1 = p2; 1048 } 1049 } 1050 return new AreaAndPerimeter(Math.abs(area) / 2, perimeter); 1051 } 1052}