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.MultipolygonCreate; 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 {FIRST_INSIDE_SECOND, SECOND_INSIDE_FIRST, OUTSIDE, CROSSING} 046 047 /** 048 * Will find all intersection and add nodes there for list of given ways. 049 * Handles self-intersections too. 050 * And makes commands to add the intersection points to ways. 051 * 052 * Prerequisite: no two nodes have the same coordinates. 053 * 054 * @param ways a list of ways to test 055 * @param test if false, do not build list of Commands, just return nodes 056 * @param cmds list of commands, typically empty when handed to this method. 057 * Will be filled with commands that add intersection nodes to 058 * the ways. 059 * @return list of new nodes 060 */ 061 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) { 062 063 int n = ways.size(); 064 @SuppressWarnings("unchecked") 065 List<Node>[] newNodes = new ArrayList[n]; 066 BBox[] wayBounds = new BBox[n]; 067 boolean[] changedWays = new boolean[n]; 068 069 Set<Node> intersectionNodes = new LinkedHashSet<>(); 070 071 //copy node arrays for local usage. 072 for (int pos = 0; pos < n; pos ++) { 073 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes()); 074 wayBounds[pos] = getNodesBounds(newNodes[pos]); 075 changedWays[pos] = false; 076 } 077 078 //iterate over all way pairs and introduce the intersections 079 Comparator<Node> coordsComparator = new NodePositionComparator(); 080 for (int seg1Way = 0; seg1Way < n; seg1Way ++) { 081 for (int seg2Way = seg1Way; seg2Way < n; seg2Way ++) { 082 083 //do not waste time on bounds that do not intersect 084 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) { 085 continue; 086 } 087 088 List<Node> way1Nodes = newNodes[seg1Way]; 089 List<Node> way2Nodes = newNodes[seg2Way]; 090 091 //iterate over primary segmemt 092 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos ++) { 093 094 //iterate over secondary segment 095 int seg2Start = seg1Way != seg2Way ? 0: seg1Pos + 2;//skip the adjacent segment 096 097 for (int seg2Pos = seg2Start; seg2Pos + 1< way2Nodes.size(); seg2Pos ++) { 098 099 //need to get them again every time, because other segments may be changed 100 Node seg1Node1 = way1Nodes.get(seg1Pos); 101 Node seg1Node2 = way1Nodes.get(seg1Pos + 1); 102 Node seg2Node1 = way2Nodes.get(seg2Pos); 103 Node seg2Node2 = way2Nodes.get(seg2Pos + 1); 104 105 int commonCount = 0; 106 //test if we have common nodes to add. 107 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) { 108 commonCount ++; 109 110 if (seg1Way == seg2Way && 111 seg1Pos == 0 && 112 seg2Pos == way2Nodes.size() -2) { 113 //do not add - this is first and last segment of the same way. 114 } else { 115 intersectionNodes.add(seg1Node1); 116 } 117 } 118 119 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) { 120 commonCount ++; 121 122 intersectionNodes.add(seg1Node2); 123 } 124 125 //no common nodes - find intersection 126 if (commonCount == 0) { 127 EastNorth intersection = getSegmentSegmentIntersection( 128 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(), 129 seg2Node1.getEastNorth(), seg2Node2.getEastNorth()); 130 131 if (intersection != null) { 132 if (test) { 133 intersectionNodes.add(seg2Node1); 134 return intersectionNodes; 135 } 136 137 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection)); 138 Node intNode = newNode; 139 boolean insertInSeg1 = false; 140 boolean insertInSeg2 = false; 141 //find if the intersection point is at end point of one of the segments, if so use that point 142 143 //segment 1 144 if (coordsComparator.compare(newNode, seg1Node1) == 0) { 145 intNode = seg1Node1; 146 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) { 147 intNode = seg1Node2; 148 } else { 149 insertInSeg1 = true; 150 } 151 152 //segment 2 153 if (coordsComparator.compare(newNode, seg2Node1) == 0) { 154 intNode = seg2Node1; 155 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) { 156 intNode = seg2Node2; 157 } else { 158 insertInSeg2 = true; 159 } 160 161 if (insertInSeg1) { 162 way1Nodes.add(seg1Pos +1, intNode); 163 changedWays[seg1Way] = true; 164 165 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment. 166 if (seg2Way == seg1Way) { 167 seg2Pos ++; 168 } 169 } 170 171 if (insertInSeg2) { 172 way2Nodes.add(seg2Pos +1, intNode); 173 changedWays[seg2Way] = true; 174 175 //Do not need to compare again to already split segment 176 seg2Pos ++; 177 } 178 179 intersectionNodes.add(intNode); 180 181 if (intNode == newNode) { 182 cmds.add(new AddCommand(intNode)); 183 } 184 } 185 } 186 else if (test && !intersectionNodes.isEmpty()) 187 return intersectionNodes; 188 } 189 } 190 } 191 } 192 193 194 for (int pos = 0; pos < ways.size(); pos ++) { 195 if (!changedWays[pos]) { 196 continue; 197 } 198 199 Way way = ways.get(pos); 200 Way newWay = new Way(way); 201 newWay.setNodes(newNodes[pos]); 202 203 cmds.add(new ChangeCommand(way, newWay)); 204 } 205 206 return intersectionNodes; 207 } 208 209 private static BBox getNodesBounds(List<Node> nodes) { 210 211 BBox bounds = new BBox(nodes.get(0)); 212 for (Node n: nodes) { 213 bounds.add(n.getCoor()); 214 } 215 return bounds; 216 } 217 218 /** 219 * Tests if given point is to the right side of path consisting of 3 points. 220 * 221 * (Imagine the path is continued beyond the endpoints, so you get two rays 222 * starting from lineP2 and going through lineP1 and lineP3 respectively 223 * which divide the plane into two parts. The test returns true, if testPoint 224 * lies in the part that is to the right when traveling in the direction 225 * lineP1, lineP2, lineP3.) 226 * 227 * @param lineP1 first point in path 228 * @param lineP2 second point in path 229 * @param lineP3 third point in path 230 * @param testPoint 231 * @return true if to the right side, false otherwise 232 */ 233 public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) { 234 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3); 235 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint); 236 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint); 237 238 if (pathBendToRight) 239 return rightOfSeg1 && rightOfSeg2; 240 else 241 return !(!rightOfSeg1 && !rightOfSeg2); 242 } 243 244 /** 245 * This method tests if secondNode is clockwise to first node. 246 * @param commonNode starting point for both vectors 247 * @param firstNode first vector end node 248 * @param secondNode second vector end node 249 * @return true if first vector is clockwise before second vector. 250 */ 251 public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) { 252 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth()); 253 } 254 255 /** 256 * Finds the intersection of two line segments 257 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise 258 */ 259 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 260 261 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 262 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 263 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 264 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 265 266 double x1 = p1.getX(); 267 double y1 = p1.getY(); 268 double x2 = p2.getX(); 269 double y2 = p2.getY(); 270 double x3 = p3.getX(); 271 double y3 = p3.getY(); 272 double x4 = p4.getX(); 273 double y4 = p4.getY(); 274 275 //TODO: do this locally. 276 //TODO: remove this check after careful testing 277 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null; 278 279 // solve line-line intersection in parametric form: 280 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v 281 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1) 282 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u ) 283 284 double a1 = x2 - x1; 285 double b1 = x3 - x4; 286 double c1 = x3 - x1; 287 288 double a2 = y2 - y1; 289 double b2 = y3 - y4; 290 double c2 = y3 - y1; 291 292 // Solve the equations 293 double det = a1*b2 - a2*b1; 294 295 double uu = b2*c1 - b1*c2 ; 296 double vv = a1*c2 - a2*c1; 297 double mag = Math.abs(uu)+Math.abs(vv); 298 299 if (Math.abs(det) > 1e-12 * mag) { 300 double u = uu/det, v = vv/det; 301 if (u>-1e-8 && u < 1+1e-8 && v>-1e-8 && v < 1+1e-8 ) { 302 if (u<0) u=0; 303 if (u>1) u=1.0; 304 return new EastNorth(x1+a1*u, y1+a2*u); 305 } else { 306 return null; 307 } 308 } else { 309 // parallel lines 310 return null; 311 } 312 } 313 314 /** 315 * Finds the intersection of two lines of infinite length. 316 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise 317 * @throws IllegalArgumentException if a parameter is null or without valid coordinates 318 */ 319 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 320 321 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 322 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 323 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 324 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 325 326 if (!p1.isValid()) throw new IllegalArgumentException(); 327 328 // Convert line from (point, point) form to ax+by=c 329 double a1 = p2.getY() - p1.getY(); 330 double b1 = p1.getX() - p2.getX(); 331 double c1 = p2.getX() * p1.getY() - p1.getX() * p2.getY(); 332 333 double a2 = p4.getY() - p3.getY(); 334 double b2 = p3.getX() - p4.getX(); 335 double c2 = p4.getX() * p3.getY() - p3.getX() * p4.getY(); 336 337 // Solve the equations 338 double det = a1 * b2 - a2 * b1; 339 if (det == 0) 340 return null; // Lines are parallel 341 342 return new EastNorth((b1 * c2 - b2 * c1) / det, (a2 * c1 - a1 * c2) / det); 343 } 344 345 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 346 347 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 348 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 349 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 350 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 351 352 // Convert line from (point, point) form to ax+by=c 353 double a1 = p2.getY() - p1.getY(); 354 double b1 = p1.getX() - p2.getX(); 355 356 double a2 = p4.getY() - p3.getY(); 357 double b2 = p3.getX() - p4.getX(); 358 359 // Solve the equations 360 double det = a1 * b2 - a2 * b1; 361 // remove influence of of scaling factor 362 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2); 363 return Math.abs(det) < 1e-3; 364 } 365 366 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) { 367 CheckParameterUtil.ensureParameterNotNull(p1, "p1"); 368 CheckParameterUtil.ensureParameterNotNull(p2, "p2"); 369 CheckParameterUtil.ensureParameterNotNull(point, "point"); 370 371 double ldx = p2.getX() - p1.getX(); 372 double ldy = p2.getY() - p1.getY(); 373 374 if (ldx == 0 && ldy == 0) //segment zero length 375 return p1; 376 377 double pdx = point.getX() - p1.getX(); 378 double pdy = point.getY() - p1.getY(); 379 380 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy); 381 382 if (segmentOnly && offset <= 0) 383 return p1; 384 else if (segmentOnly && offset >= 1) 385 return p2; 386 else 387 return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset); 388 } 389 390 /** 391 * Calculates closest point to a line segment. 392 * @param segmentP1 First point determining line segment 393 * @param segmentP2 Second point determining line segment 394 * @param point Point for which a closest point is searched on line segment [P1,P2] 395 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point, 396 * a new point if closest point is between segmentP1 and segmentP2. 397 * @since 3650 398 * @see #closestPointToLine 399 */ 400 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) { 401 return closestPointTo(segmentP1, segmentP2, point, true); 402 } 403 404 /** 405 * Calculates closest point to a line. 406 * @param lineP1 First point determining line 407 * @param lineP2 Second point determining line 408 * @param point Point for which a closest point is searched on line (P1,P2) 409 * @return The closest point found on line. It may be outside the segment [P1,P2]. 410 * @since 4134 411 * @see #closestPointToSegment 412 */ 413 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) { 414 return closestPointTo(lineP1, lineP2, point, false); 415 } 416 417 /** 418 * This method tests if secondNode is clockwise to first node. 419 * 420 * The line through the two points commonNode and firstNode divides the 421 * plane into two parts. The test returns true, if secondNode lies in 422 * the part that is to the right when traveling in the direction from 423 * commonNode to firstNode. 424 * 425 * @param commonNode starting point for both vectors 426 * @param firstNode first vector end node 427 * @param secondNode second vector end node 428 * @return true if first vector is clockwise before second vector. 429 */ 430 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) { 431 432 CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode"); 433 CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode"); 434 CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode"); 435 436 double dy1 = (firstNode.getY() - commonNode.getY()); 437 double dy2 = (secondNode.getY() - commonNode.getY()); 438 double dx1 = (firstNode.getX() - commonNode.getX()); 439 double dx2 = (secondNode.getX() - commonNode.getX()); 440 441 return dy1 * dx2 - dx1 * dy2 > 0; 442 } 443 444 /** 445 * Returns the Area of a polygon, from its list of nodes. 446 * @param polygon List of nodes forming polygon (EastNorth coordinates) 447 * @return Area for the given list of nodes 448 * @since 6841 449 */ 450 public static Area getArea(List<Node> polygon) { 451 Path2D path = new Path2D.Double(); 452 453 boolean begin = true; 454 for (Node n : polygon) { 455 EastNorth en = n.getEastNorth(); 456 if (en != null) { 457 if (begin) { 458 path.moveTo(en.getX(), en.getY()); 459 begin = false; 460 } else { 461 path.lineTo(en.getX(), en.getY()); 462 } 463 } 464 } 465 if (!begin) { 466 path.closePath(); 467 } 468 469 return new Area(path); 470 } 471 472 /** 473 * Returns the Area of a polygon, from its list of nodes. 474 * @param polygon List of nodes forming polygon (LatLon coordinates) 475 * @return Area for the given list of nodes 476 * @since 6841 477 */ 478 public static Area getAreaLatLon(List<Node> polygon) { 479 Path2D path = new Path2D.Double(); 480 481 boolean begin = true; 482 for (Node n : polygon) { 483 if (begin) { 484 path.moveTo(n.getCoor().lon(), n.getCoor().lat()); 485 begin = false; 486 } else { 487 path.lineTo(n.getCoor().lon(), n.getCoor().lat()); 488 } 489 } 490 if (!begin) { 491 path.closePath(); 492 } 493 494 return new Area(path); 495 } 496 497 /** 498 * Tests if two polygons intersect. 499 * @param first List of nodes forming first polygon 500 * @param second List of nodes forming second polygon 501 * @return intersection kind 502 */ 503 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) { 504 Area a1 = getArea(first); 505 Area a2 = getArea(second); 506 return polygonIntersection(a1, a2); 507 } 508 509 /** 510 * Tests if two polygons intersect. 511 * @param a1 Area of first polygon 512 * @param a2 Area of second polygon 513 * @return intersection kind 514 * @since 6841 515 */ 516 public static PolygonIntersection polygonIntersection(Area a1, Area a2) { 517 return polygonIntersection(a1, a2, 1.0); 518 } 519 520 /** 521 * Tests if two polygons intersect. 522 * @param a1 Area of first polygon 523 * @param a2 Area of second polygon 524 * @param eps an area threshold, everything below is considered an empty intersection 525 * @return intersection kind 526 */ 527 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) { 528 529 Area inter = new Area(a1); 530 inter.intersect(a2); 531 532 Rectangle bounds = inter.getBounds(); 533 534 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) { 535 return PolygonIntersection.OUTSIDE; 536 } else if (inter.equals(a1)) { 537 return PolygonIntersection.FIRST_INSIDE_SECOND; 538 } else if (inter.equals(a2)) { 539 return PolygonIntersection.SECOND_INSIDE_FIRST; 540 } else { 541 return PolygonIntersection.CROSSING; 542 } 543 } 544 545 /** 546 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner. 547 * @param polygonNodes list of nodes from polygon path. 548 * @param point the point to test 549 * @return true if the point is inside polygon. 550 */ 551 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) { 552 if (polygonNodes.size() < 2) 553 return false; 554 555 boolean inside = false; 556 Node p1, p2; 557 558 //iterate each side of the polygon, start with the last segment 559 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1); 560 561 for (Node newPoint : polygonNodes) { 562 //skip duplicate points 563 if (newPoint.equals(oldPoint)) { 564 continue; 565 } 566 567 //order points so p1.lat <= p2.lat 568 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) { 569 p1 = oldPoint; 570 p2 = newPoint; 571 } else { 572 p1 = newPoint; 573 p2 = oldPoint; 574 } 575 576 //test if the line is crossed and if so invert the inside flag. 577 if ((newPoint.getEastNorth().getY() < point.getEastNorth().getY()) == (point.getEastNorth().getY() <= oldPoint.getEastNorth().getY()) 578 && (point.getEastNorth().getX() - p1.getEastNorth().getX()) * (p2.getEastNorth().getY() - p1.getEastNorth().getY()) 579 < (p2.getEastNorth().getX() - p1.getEastNorth().getX()) * (point.getEastNorth().getY() - p1.getEastNorth().getY())) 580 { 581 inside = !inside; 582 } 583 584 oldPoint = newPoint; 585 } 586 587 return inside; 588 } 589 590 /** 591 * Returns area of a closed way in square meters. 592 * (approximate(?), but should be OK for small areas) 593 * 594 * Relies on the current projection: Works correctly, when 595 * one unit in projected coordinates corresponds to one meter. 596 * This is true for most projections, but not for WGS84 and 597 * Mercator (EPSG:3857). 598 * 599 * @param way Way to measure, should be closed (first node is the same as last node) 600 * @return area of the closed way. 601 */ 602 public static double closedWayArea(Way way) { 603 604 //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/ 605 double area = 0; 606 Node lastN = null; 607 for (Node n : way.getNodes()) { 608 if (lastN != null) { 609 n.getEastNorth().getX(); 610 611 area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN)); 612 } 613 lastN = n; 614 } 615 return Math.abs(area/2); 616 } 617 618 protected static double calcX(Node p1){ 619 double lat1, lon1, lat2, lon2; 620 double dlon, dlat; 621 622 lat1 = p1.getCoor().lat() * Math.PI / 180.0; 623 lon1 = p1.getCoor().lon() * Math.PI / 180.0; 624 lat2 = lat1; 625 lon2 = 0; 626 627 dlon = lon2 - lon1; 628 dlat = lat2 - lat1; 629 630 double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2)); 631 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 632 return 6367000 * c; 633 } 634 635 protected static double calcY(Node p1){ 636 double lat1, lon1, lat2, lon2; 637 double dlon, dlat; 638 639 lat1 = p1.getCoor().lat() * Math.PI / 180.0; 640 lon1 = p1.getCoor().lon() * Math.PI / 180.0; 641 lat2 = 0; 642 lon2 = lon1; 643 644 dlon = lon2 - lon1; 645 dlat = lat2 - lat1; 646 647 double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2)); 648 double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 649 return 6367000 * c; 650 } 651 652 /** 653 * Determines whether a way is oriented clockwise. 654 * 655 * Internals: Assuming a closed non-looping way, compute twice the area 656 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}. 657 * If the area is negative the way is ordered in a clockwise direction. 658 * 659 * See http://paulbourke.net/geometry/polyarea/ 660 * 661 * @param w the way to be checked. 662 * @return true if and only if way is oriented clockwise. 663 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 664 */ 665 public static boolean isClockwise(Way w) { 666 if (!w.isClosed()) { 667 throw new IllegalArgumentException("Way must be closed to check orientation."); 668 } 669 670 double area2 = 0.; 671 int nodesCount = w.getNodesCount(); 672 673 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) { 674 LatLon coorPrev = w.getNode(node - 1).getCoor(); 675 LatLon coorCurr = w.getNode(node % nodesCount).getCoor(); 676 area2 += coorPrev.lon() * coorCurr.lat(); 677 area2 -= coorCurr.lon() * coorPrev.lat(); 678 } 679 return area2 < 0; 680 } 681 682 /** 683 * Returns angle of a segment defined with 2 point coordinates. 684 * 685 * @param p1 686 * @param p2 687 * @return Angle in radians (-pi, pi] 688 */ 689 public static double getSegmentAngle(EastNorth p1, EastNorth p2) { 690 691 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 692 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 693 694 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east()); 695 } 696 697 /** 698 * Returns angle of a corner defined with 3 point coordinates. 699 * 700 * @param p1 701 * @param p2 Common endpoint 702 * @param p3 703 * @return Angle in radians (-pi, pi] 704 */ 705 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) { 706 707 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 708 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 709 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 710 711 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3); 712 if (result <= -Math.PI) { 713 result += 2 * Math.PI; 714 } 715 716 if (result > Math.PI) { 717 result -= 2 * Math.PI; 718 } 719 720 return result; 721 } 722 723 /** 724 * Compute the centroid/barycenter of nodes 725 * @param nodes Nodes for which the centroid is wanted 726 * @return the centroid of nodes 727 * @see Geometry#getCenter 728 */ 729 public static EastNorth getCentroid(List<Node> nodes) { 730 731 BigDecimal area = BigDecimal.ZERO; 732 BigDecimal north = BigDecimal.ZERO; 733 BigDecimal east = BigDecimal.ZERO; 734 735 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here 736 for (int i = 0; i < nodes.size(); i++) { 737 EastNorth n0 = nodes.get(i).getEastNorth(); 738 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth(); 739 740 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) { 741 BigDecimal x0 = new BigDecimal(n0.east()); 742 BigDecimal y0 = new BigDecimal(n0.north()); 743 BigDecimal x1 = new BigDecimal(n1.east()); 744 BigDecimal y1 = new BigDecimal(n1.north()); 745 746 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128)); 747 748 area = area.add(k, MathContext.DECIMAL128); 749 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 750 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 751 } 752 } 753 754 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3 755 area = area.multiply(d, MathContext.DECIMAL128); 756 if (area.compareTo(BigDecimal.ZERO) != 0) { 757 north = north.divide(area, MathContext.DECIMAL128); 758 east = east.divide(area, MathContext.DECIMAL128); 759 } 760 761 return new EastNorth(east.doubleValue(), north.doubleValue()); 762 } 763 764 /** 765 * Compute center of the circle closest to different nodes. 766 * 767 * Ensure exact center computation in case nodes are already aligned in circle. 768 * This is done by least square method. 769 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges. 770 * Center must be intersection of all bisectors. 771 * <pre> 772 * [ a1 b1 ] [ -c1 ] 773 * With A = [ ... ... ] and Y = [ ... ] 774 * [ an bn ] [ -cn ] 775 * </pre> 776 * An approximation of center of circle is (At.A)^-1.At.Y 777 * @param nodes Nodes parts of the circle (at least 3) 778 * @return An approximation of the center, of null if there is no solution. 779 * @see Geometry#getCentroid 780 * @since 6934 781 */ 782 public static EastNorth getCenter(List<Node> nodes) { 783 int nc = nodes.size(); 784 if(nc < 3) return null; 785 /** 786 * Equation of each bisector ax + by + c = 0 787 */ 788 double[] a = new double[nc]; 789 double[] b = new double[nc]; 790 double[] c = new double[nc]; 791 // Compute equation of bisector 792 for(int i = 0; i < nc; i++) { 793 EastNorth pt1 = nodes.get(i).getEastNorth(); 794 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth(); 795 a[i] = pt1.east() - pt2.east(); 796 b[i] = pt1.north() - pt2.north(); 797 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]); 798 if(d == 0) return null; 799 a[i] /= d; 800 b[i] /= d; 801 double xC = (pt1.east() + pt2.east()) / 2; 802 double yC = (pt1.north() + pt2.north()) / 2; 803 c[i] = -(a[i]*xC + b[i]*yC); 804 } 805 // At.A = [aij] 806 double a11 = 0, a12 = 0, a22 = 0; 807 // At.Y = [bi] 808 double b1 = 0, b2 = 0; 809 for(int i = 0; i < nc; i++) { 810 a11 += a[i]*a[i]; 811 a12 += a[i]*b[i]; 812 a22 += b[i]*b[i]; 813 b1 -= a[i]*c[i]; 814 b2 -= b[i]*c[i]; 815 } 816 // (At.A)^-1 = [invij] 817 double det = a11*a22 - a12*a12; 818 if(Math.abs(det) < 1e-5) return null; 819 double inv11 = a22/det; 820 double inv12 = -a12/det; 821 double inv22 = a11/det; 822 // center (xC, yC) = (At.A)^-1.At.y 823 double xC = inv11*b1 + inv12*b2; 824 double yC = inv12*b1 + inv22*b2; 825 return new EastNorth(xC, yC); 826 } 827 828 /** 829 * Returns the coordinate of intersection of segment sp1-sp2 and an altitude 830 * to it starting at point ap. If the line defined with sp1-sp2 intersects 831 * its altitude out of sp1-sp2, null is returned. 832 * 833 * @param sp1 834 * @param sp2 835 * @param ap 836 * @return Intersection coordinate or null 837 */ 838 public static EastNorth getSegmentAltituteIntersection(EastNorth sp1, EastNorth sp2, EastNorth ap) { 839 840 CheckParameterUtil.ensureValidCoordinates(sp1, "sp1"); 841 CheckParameterUtil.ensureValidCoordinates(sp2, "sp2"); 842 CheckParameterUtil.ensureValidCoordinates(ap, "ap"); 843 844 Double segmentLenght = sp1.distance(sp2); 845 Double altitudeAngle = getSegmentAngle(sp1, sp2) + Math.PI / 2; 846 847 // Taking a random point on the altitude line (angle is known). 848 EastNorth ap2 = new EastNorth(ap.east() + 1000 849 * Math.cos(altitudeAngle), ap.north() + 1000 850 * Math.sin(altitudeAngle)); 851 852 // Finding the intersection of two lines 853 EastNorth resultCandidate = Geometry.getLineLineIntersection(sp1, sp2, 854 ap, ap2); 855 856 // Filtering result 857 if (resultCandidate != null 858 && resultCandidate.distance(sp1) * .999 < segmentLenght 859 && resultCandidate.distance(sp2) * .999 < segmentLenght) { 860 return resultCandidate; 861 } else { 862 return null; 863 } 864 } 865 866 public static class MultiPolygonMembers { 867 public final Set<Way> outers = new HashSet<>(); 868 public final Set<Way> inners = new HashSet<>(); 869 870 public MultiPolygonMembers(Relation multiPolygon) { 871 for (RelationMember m : multiPolygon.getMembers()) { 872 if (m.getType().equals(OsmPrimitiveType.WAY)) { 873 if ("outer".equals(m.getRole())) { 874 outers.add(m.getWay()); 875 } else if ("inner".equals(m.getRole())) { 876 inners.add(m.getWay()); 877 } 878 } 879 } 880 } 881 } 882 883 /** 884 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument 885 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 886 */ 887 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 888 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch); 889 } 890 891 /** 892 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument 893 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 894 * <p> 895 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon. 896 */ 897 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 898 // Extract outer/inner members from multipolygon 899 final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon); 900 // Construct complete rings for the inner/outer members 901 final List<MultipolygonCreate.JoinedPolygon> outerRings; 902 final List<MultipolygonCreate.JoinedPolygon> innerRings; 903 try { 904 outerRings = MultipolygonCreate.joinWays(mpm.outers); 905 innerRings = MultipolygonCreate.joinWays(mpm.inners); 906 } catch (MultipolygonCreate.JoinedPolygonCreationException ex) { 907 Main.debug("Invalid multipolygon " + multiPolygon); 908 return false; 909 } 910 // Test if object is inside an outer member 911 for (MultipolygonCreate.JoinedPolygon out : outerRings) { 912 if (nodes.size() == 1 913 ? nodeInsidePolygon(nodes.get(0), out.getNodes()) 914 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(polygonIntersection(nodes, out.getNodes()))) { 915 boolean insideInner = false; 916 // If inside an outer, check it is not inside an inner 917 for (MultipolygonCreate.JoinedPolygon in : innerRings) { 918 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND 919 && (nodes.size() == 1 920 ? nodeInsidePolygon(nodes.get(0), in.getNodes()) 921 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) { 922 insideInner = true; 923 break; 924 } 925 } 926 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon 927 if (!insideInner) { 928 // Final check using predicate 929 if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0) /* TODO give a better representation of the outer ring to the predicate */)) { 930 return true; 931 } 932 } 933 } 934 } 935 return false; 936 } 937}