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.HashSet; 015import java.util.LinkedHashSet; 016import java.util.List; 017import java.util.Set; 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.LatLon; 025import org.openstreetmap.josm.data.osm.BBox; 026import org.openstreetmap.josm.data.osm.MultipolygonBuilder; 027import org.openstreetmap.josm.data.osm.Node; 028import org.openstreetmap.josm.data.osm.NodePositionComparator; 029import org.openstreetmap.josm.data.osm.OsmPrimitiveType; 030import org.openstreetmap.josm.data.osm.Relation; 031import org.openstreetmap.josm.data.osm.RelationMember; 032import org.openstreetmap.josm.data.osm.Way; 033 034/** 035 * Some tools for geometry related tasks. 036 * 037 * @author viesturs 038 */ 039public final class Geometry { 040 041 private Geometry() { 042 // Hide default constructor for utils classes 043 } 044 045 public enum PolygonIntersection { 046 FIRST_INSIDE_SECOND, 047 SECOND_INSIDE_FIRST, 048 OUTSIDE, 049 CROSSING 050 } 051 052 /** 053 * Will find all intersection and add nodes there for list of given ways. 054 * Handles self-intersections too. 055 * And makes commands to add the intersection points to ways. 056 * 057 * Prerequisite: no two nodes have the same coordinates. 058 * 059 * @param ways a list of ways to test 060 * @param test if false, do not build list of Commands, just return nodes 061 * @param cmds list of commands, typically empty when handed to this method. 062 * Will be filled with commands that add intersection nodes to 063 * the ways. 064 * @return list of new nodes 065 */ 066 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) { 067 068 int n = ways.size(); 069 @SuppressWarnings("unchecked") 070 List<Node>[] newNodes = new ArrayList[n]; 071 BBox[] wayBounds = new BBox[n]; 072 boolean[] changedWays = new boolean[n]; 073 074 Set<Node> intersectionNodes = new LinkedHashSet<>(); 075 076 //copy node arrays for local usage. 077 for (int pos = 0; pos < n; pos++) { 078 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes()); 079 wayBounds[pos] = getNodesBounds(newNodes[pos]); 080 changedWays[pos] = false; 081 } 082 083 //iterate over all way pairs and introduce the intersections 084 Comparator<Node> coordsComparator = new NodePositionComparator(); 085 for (int seg1Way = 0; seg1Way < n; seg1Way++) { 086 for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) { 087 088 //do not waste time on bounds that do not intersect 089 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) { 090 continue; 091 } 092 093 List<Node> way1Nodes = newNodes[seg1Way]; 094 List<Node> way2Nodes = newNodes[seg2Way]; 095 096 //iterate over primary segmemt 097 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) { 098 099 //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 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise 262 */ 263 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 264 265 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 266 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 267 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 268 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 269 270 double x1 = p1.getX(); 271 double y1 = p1.getY(); 272 double x2 = p2.getX(); 273 double y2 = p2.getY(); 274 double x3 = p3.getX(); 275 double y3 = p3.getY(); 276 double x4 = p4.getX(); 277 double y4 = p4.getY(); 278 279 //TODO: do this locally. 280 //TODO: remove this check after careful testing 281 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null; 282 283 // solve line-line intersection in parametric form: 284 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v 285 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1) 286 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u ) 287 288 double a1 = x2 - x1; 289 double b1 = x3 - x4; 290 double c1 = x3 - x1; 291 292 double a2 = y2 - y1; 293 double b2 = y3 - y4; 294 double c2 = y3 - y1; 295 296 // Solve the equations 297 double det = a1*b2 - a2*b1; 298 299 double uu = b2*c1 - b1*c2; 300 double vv = a1*c2 - a2*c1; 301 double mag = Math.abs(uu)+Math.abs(vv); 302 303 if (Math.abs(det) > 1e-12 * mag) { 304 double u = uu/det, v = vv/det; 305 if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) { 306 if (u < 0) u = 0; 307 if (u > 1) u = 1.0; 308 return new EastNorth(x1+a1*u, y1+a2*u); 309 } else { 310 return null; 311 } 312 } else { 313 // parallel lines 314 return null; 315 } 316 } 317 318 /** 319 * Finds the intersection of two lines of infinite length. 320 * 321 * @param p1 first point on first line 322 * @param p2 second point on first line 323 * @param p3 first point on second line 324 * @param p4 second point on second line 325 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise 326 * @throws IllegalArgumentException if a parameter is null or without valid coordinates 327 */ 328 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 329 330 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 331 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 332 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 333 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 334 335 if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid"); 336 337 // Basically, the formula from wikipedia is used: 338 // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection 339 // However, large numbers lead to rounding errors (see #10286). 340 // To avoid this, p1 is first substracted from each of the points: 341 // p1' = 0 342 // p2' = p2 - p1 343 // p3' = p3 - p1 344 // p4' = p4 - p1 345 // In the end, p1 is added to the intersection point of segment p1'/p2' 346 // and segment p3'/p4'. 347 348 // Convert line from (point, point) form to ax+by=c 349 double a1 = p2.getY() - p1.getY(); 350 double b1 = p1.getX() - p2.getX(); 351 352 double a2 = p4.getY() - p3.getY(); 353 double b2 = p3.getX() - p4.getX(); 354 double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY()); 355 356 // Solve the equations 357 double det = a1 * b2 - a2 * b1; 358 if (det == 0) 359 return null; // Lines are parallel 360 361 return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY()); 362 } 363 364 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 365 366 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 367 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 368 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 369 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 370 371 // Convert line from (point, point) form to ax+by=c 372 double a1 = p2.getY() - p1.getY(); 373 double b1 = p1.getX() - p2.getX(); 374 375 double a2 = p4.getY() - p3.getY(); 376 double b2 = p3.getX() - p4.getX(); 377 378 // Solve the equations 379 double det = a1 * b2 - a2 * b1; 380 // remove influence of of scaling factor 381 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2); 382 return Math.abs(det) < 1e-3; 383 } 384 385 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) { 386 CheckParameterUtil.ensureParameterNotNull(p1, "p1"); 387 CheckParameterUtil.ensureParameterNotNull(p2, "p2"); 388 CheckParameterUtil.ensureParameterNotNull(point, "point"); 389 390 double ldx = p2.getX() - p1.getX(); 391 double ldy = p2.getY() - p1.getY(); 392 393 //segment zero length 394 if (ldx == 0 && ldy == 0) 395 return p1; 396 397 double pdx = point.getX() - p1.getX(); 398 double pdy = point.getY() - p1.getY(); 399 400 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy); 401 402 if (segmentOnly && offset <= 0) 403 return p1; 404 else if (segmentOnly && offset >= 1) 405 return p2; 406 else 407 return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset); 408 } 409 410 /** 411 * Calculates closest point to a line segment. 412 * @param segmentP1 First point determining line segment 413 * @param segmentP2 Second point determining line segment 414 * @param point Point for which a closest point is searched on line segment [P1,P2] 415 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point, 416 * a new point if closest point is between segmentP1 and segmentP2. 417 * @see #closestPointToLine 418 * @since 3650 419 */ 420 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) { 421 return closestPointTo(segmentP1, segmentP2, point, true); 422 } 423 424 /** 425 * Calculates closest point to a line. 426 * @param lineP1 First point determining line 427 * @param lineP2 Second point determining line 428 * @param point Point for which a closest point is searched on line (P1,P2) 429 * @return The closest point found on line. It may be outside the segment [P1,P2]. 430 * @see #closestPointToSegment 431 * @since 4134 432 */ 433 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) { 434 return closestPointTo(lineP1, lineP2, point, false); 435 } 436 437 /** 438 * This method tests if secondNode is clockwise to first node. 439 * 440 * The line through the two points commonNode and firstNode divides the 441 * plane into two parts. The test returns true, if secondNode lies in 442 * the part that is to the right when traveling in the direction from 443 * commonNode to firstNode. 444 * 445 * @param commonNode starting point for both vectors 446 * @param firstNode first vector end node 447 * @param secondNode second vector end node 448 * @return true if first vector is clockwise before second vector. 449 */ 450 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) { 451 452 CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode"); 453 CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode"); 454 CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode"); 455 456 double dy1 = firstNode.getY() - commonNode.getY(); 457 double dy2 = secondNode.getY() - commonNode.getY(); 458 double dx1 = firstNode.getX() - commonNode.getX(); 459 double dx2 = secondNode.getX() - commonNode.getX(); 460 461 return dy1 * dx2 - dx1 * dy2 > 0; 462 } 463 464 /** 465 * Returns the Area of a polygon, from its list of nodes. 466 * @param polygon List of nodes forming polygon (EastNorth coordinates) 467 * @return Area for the given list of nodes 468 * @since 6841 469 */ 470 public static Area getArea(List<Node> polygon) { 471 Path2D path = new Path2D.Double(); 472 473 boolean begin = true; 474 for (Node n : polygon) { 475 EastNorth en = n.getEastNorth(); 476 if (en != null) { 477 if (begin) { 478 path.moveTo(en.getX(), en.getY()); 479 begin = false; 480 } else { 481 path.lineTo(en.getX(), en.getY()); 482 } 483 } 484 } 485 if (!begin) { 486 path.closePath(); 487 } 488 489 return new Area(path); 490 } 491 492 /** 493 * Returns the Area of a polygon, from its list of nodes. 494 * @param polygon List of nodes forming polygon (LatLon coordinates) 495 * @return Area for the given list of nodes 496 * @since 6841 497 */ 498 public static Area getAreaLatLon(List<Node> polygon) { 499 Path2D path = new Path2D.Double(); 500 501 boolean begin = true; 502 for (Node n : polygon) { 503 if (begin) { 504 path.moveTo(n.getCoor().lon(), n.getCoor().lat()); 505 begin = false; 506 } else { 507 path.lineTo(n.getCoor().lon(), n.getCoor().lat()); 508 } 509 } 510 if (!begin) { 511 path.closePath(); 512 } 513 514 return new Area(path); 515 } 516 517 /** 518 * Tests if two polygons intersect. 519 * @param first List of nodes forming first polygon 520 * @param second List of nodes forming second polygon 521 * @return intersection kind 522 */ 523 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) { 524 Area a1 = getArea(first); 525 Area a2 = getArea(second); 526 return polygonIntersection(a1, a2); 527 } 528 529 /** 530 * Tests if two polygons intersect. 531 * @param a1 Area of first polygon 532 * @param a2 Area of second polygon 533 * @return intersection kind 534 * @since 6841 535 */ 536 public static PolygonIntersection polygonIntersection(Area a1, Area a2) { 537 return polygonIntersection(a1, a2, 1.0); 538 } 539 540 /** 541 * Tests if two polygons intersect. 542 * @param a1 Area of first polygon 543 * @param a2 Area of second polygon 544 * @param eps an area threshold, everything below is considered an empty intersection 545 * @return intersection kind 546 */ 547 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) { 548 549 Area inter = new Area(a1); 550 inter.intersect(a2); 551 552 Rectangle bounds = inter.getBounds(); 553 554 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) { 555 return PolygonIntersection.OUTSIDE; 556 } else if (inter.equals(a1)) { 557 return PolygonIntersection.FIRST_INSIDE_SECOND; 558 } else if (inter.equals(a2)) { 559 return PolygonIntersection.SECOND_INSIDE_FIRST; 560 } else { 561 return PolygonIntersection.CROSSING; 562 } 563 } 564 565 /** 566 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner. 567 * @param polygonNodes list of nodes from polygon path. 568 * @param point the point to test 569 * @return true if the point is inside polygon. 570 */ 571 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) { 572 if (polygonNodes.size() < 2) 573 return false; 574 575 boolean inside = false; 576 Node p1, p2; 577 578 //iterate each side of the polygon, start with the last segment 579 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1); 580 581 if (!oldPoint.isLatLonKnown()) { 582 return false; 583 } 584 585 for (Node newPoint : polygonNodes) { 586 //skip duplicate points 587 if (newPoint.equals(oldPoint)) { 588 continue; 589 } 590 591 if (!newPoint.isLatLonKnown()) { 592 return false; 593 } 594 595 //order points so p1.lat <= p2.lat 596 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) { 597 p1 = oldPoint; 598 p2 = newPoint; 599 } else { 600 p1 = newPoint; 601 p2 = oldPoint; 602 } 603 604 EastNorth pEN = point.getEastNorth(); 605 EastNorth opEN = oldPoint.getEastNorth(); 606 EastNorth npEN = newPoint.getEastNorth(); 607 EastNorth p1EN = p1.getEastNorth(); 608 EastNorth p2EN = p2.getEastNorth(); 609 610 if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) { 611 //test if the line is crossed and if so invert the inside flag. 612 if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY()) 613 && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY()) 614 < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) { 615 inside = !inside; 616 } 617 } 618 619 oldPoint = newPoint; 620 } 621 622 return inside; 623 } 624 625 /** 626 * Returns area of a closed way in square meters. 627 * (approximate(?), but should be OK for small areas) 628 * 629 * Relies on the current projection: Works correctly, when 630 * one unit in projected coordinates corresponds to one meter. 631 * This is true for most projections, but not for WGS84 and 632 * Mercator (EPSG:3857). 633 * 634 * @param way Way to measure, should be closed (first node is the same as last node) 635 * @return area of the closed way. 636 */ 637 public static double closedWayArea(Way way) { 638 639 //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/ 640 double area = 0; 641 Node lastN = null; 642 for (Node n : way.getNodes()) { 643 if (lastN != null) { 644 area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN)); 645 } 646 lastN = n; 647 } 648 return Math.abs(area/2); 649 } 650 651 protected static double calcX(Node p1) { 652 double lat1, lon1, lat2, lon2; 653 double dlon, dlat; 654 655 lat1 = p1.getCoor().lat() * Math.PI / 180.0; 656 lon1 = p1.getCoor().lon() * Math.PI / 180.0; 657 lat2 = lat1; 658 lon2 = 0; 659 660 dlon = lon2 - lon1; 661 dlat = lat2 - lat1; 662 663 double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2); 664 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 665 return 6367000 * c; 666 } 667 668 protected static double calcY(Node p1) { 669 double lat1, lon1, lat2, lon2; 670 double dlon, dlat; 671 672 lat1 = p1.getCoor().lat() * Math.PI / 180.0; 673 lon1 = p1.getCoor().lon() * Math.PI / 180.0; 674 lat2 = 0; 675 lon2 = lon1; 676 677 dlon = lon2 - lon1; 678 dlat = lat2 - lat1; 679 680 double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2); 681 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 682 return 6367000 * c; 683 } 684 685 /** 686 * Determines whether a way is oriented clockwise. 687 * 688 * Internals: Assuming a closed non-looping way, compute twice the area 689 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}. 690 * If the area is negative the way is ordered in a clockwise direction. 691 * 692 * See http://paulbourke.net/geometry/polyarea/ 693 * 694 * @param w the way to be checked. 695 * @return true if and only if way is oriented clockwise. 696 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 697 */ 698 public static boolean isClockwise(Way w) { 699 return isClockwise(w.getNodes()); 700 } 701 702 /** 703 * Determines whether path from nodes list is oriented clockwise. 704 * @param nodes Nodes list to be checked. 705 * @return true if and only if way is oriented clockwise. 706 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 707 * @see #isClockwise(Way) 708 */ 709 public static boolean isClockwise(List<Node> nodes) { 710 double area2 = 0.; 711 int nodesCount = nodes.size(); 712 if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) { 713 throw new IllegalArgumentException("Way must be closed to check orientation."); 714 } 715 716 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) { 717 LatLon coorPrev = nodes.get(node - 1).getCoor(); 718 LatLon coorCurr = nodes.get(node % nodesCount).getCoor(); 719 area2 += coorPrev.lon() * coorCurr.lat(); 720 area2 -= coorCurr.lon() * coorPrev.lat(); 721 } 722 return area2 < 0; 723 } 724 725 /** 726 * Returns angle of a segment defined with 2 point coordinates. 727 * 728 * @param p1 first point 729 * @param p2 second point 730 * @return Angle in radians (-pi, pi] 731 */ 732 public static double getSegmentAngle(EastNorth p1, EastNorth p2) { 733 734 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 735 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 736 737 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east()); 738 } 739 740 /** 741 * Returns angle of a corner defined with 3 point coordinates. 742 * 743 * @param p1 first point 744 * @param p2 Common endpoint 745 * @param p3 third point 746 * @return Angle in radians (-pi, pi] 747 */ 748 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) { 749 750 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 751 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 752 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 753 754 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3); 755 if (result <= -Math.PI) { 756 result += 2 * Math.PI; 757 } 758 759 if (result > Math.PI) { 760 result -= 2 * Math.PI; 761 } 762 763 return result; 764 } 765 766 /** 767 * Compute the centroid/barycenter of nodes 768 * @param nodes Nodes for which the centroid is wanted 769 * @return the centroid of nodes 770 * @see Geometry#getCenter 771 */ 772 public static EastNorth getCentroid(List<Node> nodes) { 773 774 BigDecimal area = BigDecimal.ZERO; 775 BigDecimal north = BigDecimal.ZERO; 776 BigDecimal east = BigDecimal.ZERO; 777 778 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here 779 for (int i = 0; i < nodes.size(); i++) { 780 EastNorth n0 = nodes.get(i).getEastNorth(); 781 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth(); 782 783 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) { 784 BigDecimal x0 = BigDecimal.valueOf(n0.east()); 785 BigDecimal y0 = BigDecimal.valueOf(n0.north()); 786 BigDecimal x1 = BigDecimal.valueOf(n1.east()); 787 BigDecimal y1 = BigDecimal.valueOf(n1.north()); 788 789 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128)); 790 791 area = area.add(k, MathContext.DECIMAL128); 792 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 793 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 794 } 795 } 796 797 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3 798 area = area.multiply(d, MathContext.DECIMAL128); 799 if (area.compareTo(BigDecimal.ZERO) != 0) { 800 north = north.divide(area, MathContext.DECIMAL128); 801 east = east.divide(area, MathContext.DECIMAL128); 802 } 803 804 return new EastNorth(east.doubleValue(), north.doubleValue()); 805 } 806 807 /** 808 * Compute center of the circle closest to different nodes. 809 * 810 * Ensure exact center computation in case nodes are already aligned in circle. 811 * This is done by least square method. 812 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges. 813 * Center must be intersection of all bisectors. 814 * <pre> 815 * [ a1 b1 ] [ -c1 ] 816 * With A = [ ... ... ] and Y = [ ... ] 817 * [ an bn ] [ -cn ] 818 * </pre> 819 * An approximation of center of circle is (At.A)^-1.At.Y 820 * @param nodes Nodes parts of the circle (at least 3) 821 * @return An approximation of the center, of null if there is no solution. 822 * @see Geometry#getCentroid 823 * @since 6934 824 */ 825 public static EastNorth getCenter(List<Node> nodes) { 826 int nc = nodes.size(); 827 if (nc < 3) return null; 828 /** 829 * Equation of each bisector ax + by + c = 0 830 */ 831 double[] a = new double[nc]; 832 double[] b = new double[nc]; 833 double[] c = new double[nc]; 834 // Compute equation of bisector 835 for (int i = 0; i < nc; i++) { 836 EastNorth pt1 = nodes.get(i).getEastNorth(); 837 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth(); 838 a[i] = pt1.east() - pt2.east(); 839 b[i] = pt1.north() - pt2.north(); 840 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]); 841 if (d == 0) return null; 842 a[i] /= d; 843 b[i] /= d; 844 double xC = (pt1.east() + pt2.east()) / 2; 845 double yC = (pt1.north() + pt2.north()) / 2; 846 c[i] = -(a[i]*xC + b[i]*yC); 847 } 848 // At.A = [aij] 849 double a11 = 0, a12 = 0, a22 = 0; 850 // At.Y = [bi] 851 double b1 = 0, b2 = 0; 852 for (int i = 0; i < nc; i++) { 853 a11 += a[i]*a[i]; 854 a12 += a[i]*b[i]; 855 a22 += b[i]*b[i]; 856 b1 -= a[i]*c[i]; 857 b2 -= b[i]*c[i]; 858 } 859 // (At.A)^-1 = [invij] 860 double det = a11*a22 - a12*a12; 861 if (Math.abs(det) < 1e-5) return null; 862 double inv11 = a22/det; 863 double inv12 = -a12/det; 864 double inv22 = a11/det; 865 // center (xC, yC) = (At.A)^-1.At.y 866 double xC = inv11*b1 + inv12*b2; 867 double yC = inv12*b1 + inv22*b2; 868 return new EastNorth(xC, yC); 869 } 870 871 public static class MultiPolygonMembers { 872 public final Set<Way> outers = new HashSet<>(); 873 public final Set<Way> inners = new HashSet<>(); 874 875 public MultiPolygonMembers(Relation multiPolygon) { 876 for (RelationMember m : multiPolygon.getMembers()) { 877 if (m.getType().equals(OsmPrimitiveType.WAY)) { 878 if ("outer".equals(m.getRole())) { 879 outers.add(m.getWay()); 880 } else if ("inner".equals(m.getRole())) { 881 inners.add(m.getWay()); 882 } 883 } 884 } 885 } 886 } 887 888 /** 889 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument 890 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 891 * @param node node 892 * @param multiPolygon multipolygon 893 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 894 * @return {@code true} if the node is inside the multipolygon 895 */ 896 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 897 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch); 898 } 899 900 /** 901 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument 902 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 903 * <p> 904 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon. 905 * @param nodes nodes forming the polygon 906 * @param multiPolygon multipolygon 907 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 908 * @return {@code true} if the polygon formed by nodes is inside the multipolygon 909 */ 910 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 911 // Extract outer/inner members from multipolygon 912 final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon); 913 // Construct complete rings for the inner/outer members 914 final List<MultipolygonBuilder.JoinedPolygon> outerRings; 915 final List<MultipolygonBuilder.JoinedPolygon> innerRings; 916 try { 917 outerRings = MultipolygonBuilder.joinWays(mpm.outers); 918 innerRings = MultipolygonBuilder.joinWays(mpm.inners); 919 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) { 920 Main.debug("Invalid multipolygon " + multiPolygon); 921 return false; 922 } 923 // Test if object is inside an outer member 924 for (MultipolygonBuilder.JoinedPolygon out : outerRings) { 925 if (nodes.size() == 1 926 ? nodeInsidePolygon(nodes.get(0), out.getNodes()) 927 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains( 928 polygonIntersection(nodes, out.getNodes()))) { 929 boolean insideInner = false; 930 // If inside an outer, check it is not inside an inner 931 for (MultipolygonBuilder.JoinedPolygon in : innerRings) { 932 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND 933 && (nodes.size() == 1 934 ? nodeInsidePolygon(nodes.get(0), in.getNodes()) 935 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) { 936 insideInner = true; 937 break; 938 } 939 } 940 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon 941 if (!insideInner) { 942 // Final check using predicate 943 if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0) 944 /* TODO give a better representation of the outer ring to the predicate */)) { 945 return true; 946 } 947 } 948 } 949 } 950 return false; 951 } 952}