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.LatLon; 025import org.openstreetmap.josm.data.osm.BBox; 026import org.openstreetmap.josm.data.osm.DataSet; 027import org.openstreetmap.josm.data.osm.MultipolygonBuilder; 028import org.openstreetmap.josm.data.osm.MultipolygonBuilder.JoinedPolygon; 029import org.openstreetmap.josm.data.osm.Node; 030import org.openstreetmap.josm.data.osm.NodePositionComparator; 031import org.openstreetmap.josm.data.osm.OsmPrimitive; 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; 038import org.openstreetmap.josm.gui.layer.OsmDataLayer; 039 040/** 041 * Some tools for geometry related tasks. 042 * 043 * @author viesturs 044 */ 045public final class Geometry { 046 047 private Geometry() { 048 // Hide default constructor for utils classes 049 } 050 051 public enum PolygonIntersection { 052 FIRST_INSIDE_SECOND, 053 SECOND_INSIDE_FIRST, 054 OUTSIDE, 055 CROSSING 056 } 057 058 /** 059 * Will find all intersection and add nodes there for list of given ways. 060 * Handles self-intersections too. 061 * And makes commands to add the intersection points to ways. 062 * 063 * Prerequisite: no two nodes have the same coordinates. 064 * 065 * @param ways a list of ways to test 066 * @param test if false, do not build list of Commands, just return nodes 067 * @param cmds list of commands, typically empty when handed to this method. 068 * Will be filled with commands that add intersection nodes to 069 * the ways. 070 * @return list of new nodes 071 */ 072 public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) { 073 074 int n = ways.size(); 075 @SuppressWarnings("unchecked") 076 List<Node>[] newNodes = new ArrayList[n]; 077 BBox[] wayBounds = new BBox[n]; 078 boolean[] changedWays = new boolean[n]; 079 080 Set<Node> intersectionNodes = new LinkedHashSet<>(); 081 082 //copy node arrays for local usage. 083 for (int pos = 0; pos < n; pos++) { 084 newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes()); 085 wayBounds[pos] = getNodesBounds(newNodes[pos]); 086 changedWays[pos] = false; 087 } 088 089 OsmDataLayer layer = Main.getLayerManager().getEditLayer(); 090 DataSet dataset = ways.iterator().next().getDataSet(); 091 092 //iterate over all way pairs and introduce the intersections 093 Comparator<Node> coordsComparator = new NodePositionComparator(); 094 for (int seg1Way = 0; seg1Way < n; seg1Way++) { 095 for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) { 096 097 //do not waste time on bounds that do not intersect 098 if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) { 099 continue; 100 } 101 102 List<Node> way1Nodes = newNodes[seg1Way]; 103 List<Node> way2Nodes = newNodes[seg2Way]; 104 105 //iterate over primary segmemt 106 for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) { 107 108 //iterate over secondary segment 109 int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment 110 111 for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) { 112 113 //need to get them again every time, because other segments may be changed 114 Node seg1Node1 = way1Nodes.get(seg1Pos); 115 Node seg1Node2 = way1Nodes.get(seg1Pos + 1); 116 Node seg2Node1 = way2Nodes.get(seg2Pos); 117 Node seg2Node2 = way2Nodes.get(seg2Pos + 1); 118 119 int commonCount = 0; 120 //test if we have common nodes to add. 121 if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) { 122 commonCount++; 123 124 if (seg1Way == seg2Way && 125 seg1Pos == 0 && 126 seg2Pos == way2Nodes.size() -2) { 127 //do not add - this is first and last segment of the same way. 128 } else { 129 intersectionNodes.add(seg1Node1); 130 } 131 } 132 133 if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) { 134 commonCount++; 135 136 intersectionNodes.add(seg1Node2); 137 } 138 139 //no common nodes - find intersection 140 if (commonCount == 0) { 141 EastNorth intersection = getSegmentSegmentIntersection( 142 seg1Node1.getEastNorth(), seg1Node2.getEastNorth(), 143 seg2Node1.getEastNorth(), seg2Node2.getEastNorth()); 144 145 if (intersection != null) { 146 if (test) { 147 intersectionNodes.add(seg2Node1); 148 return intersectionNodes; 149 } 150 151 Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection)); 152 Node intNode = newNode; 153 boolean insertInSeg1 = false; 154 boolean insertInSeg2 = false; 155 //find if the intersection point is at end point of one of the segments, if so use that point 156 157 //segment 1 158 if (coordsComparator.compare(newNode, seg1Node1) == 0) { 159 intNode = seg1Node1; 160 } else if (coordsComparator.compare(newNode, seg1Node2) == 0) { 161 intNode = seg1Node2; 162 } else { 163 insertInSeg1 = true; 164 } 165 166 //segment 2 167 if (coordsComparator.compare(newNode, seg2Node1) == 0) { 168 intNode = seg2Node1; 169 } else if (coordsComparator.compare(newNode, seg2Node2) == 0) { 170 intNode = seg2Node2; 171 } else { 172 insertInSeg2 = true; 173 } 174 175 if (insertInSeg1) { 176 way1Nodes.add(seg1Pos +1, intNode); 177 changedWays[seg1Way] = true; 178 179 //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment. 180 if (seg2Way == seg1Way) { 181 seg2Pos++; 182 } 183 } 184 185 if (insertInSeg2) { 186 way2Nodes.add(seg2Pos +1, intNode); 187 changedWays[seg2Way] = true; 188 189 //Do not need to compare again to already split segment 190 seg2Pos++; 191 } 192 193 intersectionNodes.add(intNode); 194 195 if (intNode == newNode) { 196 cmds.add(layer != null ? new AddCommand(layer, intNode) : new AddCommand(dataset, intNode)); 197 } 198 } 199 } else if (test && !intersectionNodes.isEmpty()) 200 return intersectionNodes; 201 } 202 } 203 } 204 } 205 206 207 for (int pos = 0; pos < ways.size(); pos++) { 208 if (!changedWays[pos]) { 209 continue; 210 } 211 212 Way way = ways.get(pos); 213 Way newWay = new Way(way); 214 newWay.setNodes(newNodes[pos]); 215 216 cmds.add(new ChangeCommand(way, newWay)); 217 } 218 219 return intersectionNodes; 220 } 221 222 private static BBox getNodesBounds(List<Node> nodes) { 223 224 BBox bounds = new BBox(nodes.get(0)); 225 for (Node n: nodes) { 226 bounds.add(n.getCoor()); 227 } 228 return bounds; 229 } 230 231 /** 232 * Tests if given point is to the right side of path consisting of 3 points. 233 * 234 * (Imagine the path is continued beyond the endpoints, so you get two rays 235 * starting from lineP2 and going through lineP1 and lineP3 respectively 236 * which divide the plane into two parts. The test returns true, if testPoint 237 * lies in the part that is to the right when traveling in the direction 238 * lineP1, lineP2, lineP3.) 239 * 240 * @param lineP1 first point in path 241 * @param lineP2 second point in path 242 * @param lineP3 third point in path 243 * @param testPoint point to test 244 * @return true if to the right side, false otherwise 245 */ 246 public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) { 247 boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3); 248 boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint); 249 boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint); 250 251 if (pathBendToRight) 252 return rightOfSeg1 && rightOfSeg2; 253 else 254 return !(!rightOfSeg1 && !rightOfSeg2); 255 } 256 257 /** 258 * This method tests if secondNode is clockwise to first node. 259 * @param commonNode starting point for both vectors 260 * @param firstNode first vector end node 261 * @param secondNode second vector end node 262 * @return true if first vector is clockwise before second vector. 263 */ 264 public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) { 265 return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth()); 266 } 267 268 /** 269 * Finds the intersection of two line segments. 270 * @param p1 the coordinates of the start point of the first specified line segment 271 * @param p2 the coordinates of the end point of the first specified line segment 272 * @param p3 the coordinates of the start point of the second specified line segment 273 * @param p4 the coordinates of the end point of the second specified line segment 274 * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise 275 */ 276 public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 277 278 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 279 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 280 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 281 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 282 283 double x1 = p1.getX(); 284 double y1 = p1.getY(); 285 double x2 = p2.getX(); 286 double y2 = p2.getY(); 287 double x3 = p3.getX(); 288 double y3 = p3.getY(); 289 double x4 = p4.getX(); 290 double y4 = p4.getY(); 291 292 //TODO: do this locally. 293 //TODO: remove this check after careful testing 294 if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null; 295 296 // solve line-line intersection in parametric form: 297 // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v 298 // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1) 299 // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u ) 300 301 double a1 = x2 - x1; 302 double b1 = x3 - x4; 303 double c1 = x3 - x1; 304 305 double a2 = y2 - y1; 306 double b2 = y3 - y4; 307 double c2 = y3 - y1; 308 309 // Solve the equations 310 double det = a1*b2 - a2*b1; 311 312 double uu = b2*c1 - b1*c2; 313 double vv = a1*c2 - a2*c1; 314 double mag = Math.abs(uu)+Math.abs(vv); 315 316 if (Math.abs(det) > 1e-12 * mag) { 317 double u = uu/det, v = vv/det; 318 if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) { 319 if (u < 0) u = 0; 320 if (u > 1) u = 1.0; 321 return new EastNorth(x1+a1*u, y1+a2*u); 322 } else { 323 return null; 324 } 325 } else { 326 // parallel lines 327 return null; 328 } 329 } 330 331 /** 332 * Finds the intersection of two lines of infinite length. 333 * 334 * @param p1 first point on first line 335 * @param p2 second point on first line 336 * @param p3 first point on second line 337 * @param p4 second point on second line 338 * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise 339 * @throws IllegalArgumentException if a parameter is null or without valid coordinates 340 */ 341 public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 342 343 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 344 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 345 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 346 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 347 348 if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid"); 349 350 // Basically, the formula from wikipedia is used: 351 // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection 352 // However, large numbers lead to rounding errors (see #10286). 353 // To avoid this, p1 is first substracted from each of the points: 354 // p1' = 0 355 // p2' = p2 - p1 356 // p3' = p3 - p1 357 // p4' = p4 - p1 358 // In the end, p1 is added to the intersection point of segment p1'/p2' 359 // and segment p3'/p4'. 360 361 // Convert line from (point, point) form to ax+by=c 362 double a1 = p2.getY() - p1.getY(); 363 double b1 = p1.getX() - p2.getX(); 364 365 double a2 = p4.getY() - p3.getY(); 366 double b2 = p3.getX() - p4.getX(); 367 368 // Solve the equations 369 double det = a1 * b2 - a2 * b1; 370 if (det == 0) 371 return null; // Lines are parallel 372 373 double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY()); 374 375 return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY()); 376 } 377 378 public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) { 379 380 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 381 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 382 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 383 CheckParameterUtil.ensureValidCoordinates(p4, "p4"); 384 385 // Convert line from (point, point) form to ax+by=c 386 double a1 = p2.getY() - p1.getY(); 387 double b1 = p1.getX() - p2.getX(); 388 389 double a2 = p4.getY() - p3.getY(); 390 double b2 = p3.getX() - p4.getX(); 391 392 // Solve the equations 393 double det = a1 * b2 - a2 * b1; 394 // remove influence of of scaling factor 395 det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2); 396 return Math.abs(det) < 1e-3; 397 } 398 399 private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) { 400 CheckParameterUtil.ensureParameterNotNull(p1, "p1"); 401 CheckParameterUtil.ensureParameterNotNull(p2, "p2"); 402 CheckParameterUtil.ensureParameterNotNull(point, "point"); 403 404 double ldx = p2.getX() - p1.getX(); 405 double ldy = p2.getY() - p1.getY(); 406 407 //segment zero length 408 if (ldx == 0 && ldy == 0) 409 return p1; 410 411 double pdx = point.getX() - p1.getX(); 412 double pdy = point.getY() - p1.getY(); 413 414 double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy); 415 416 if (segmentOnly && offset <= 0) 417 return p1; 418 else if (segmentOnly && offset >= 1) 419 return p2; 420 else 421 return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset); 422 } 423 424 /** 425 * Calculates closest point to a line segment. 426 * @param segmentP1 First point determining line segment 427 * @param segmentP2 Second point determining line segment 428 * @param point Point for which a closest point is searched on line segment [P1,P2] 429 * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point, 430 * a new point if closest point is between segmentP1 and segmentP2. 431 * @see #closestPointToLine 432 * @since 3650 433 */ 434 public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) { 435 return closestPointTo(segmentP1, segmentP2, point, true); 436 } 437 438 /** 439 * Calculates closest point to a line. 440 * @param lineP1 First point determining line 441 * @param lineP2 Second point determining line 442 * @param point Point for which a closest point is searched on line (P1,P2) 443 * @return The closest point found on line. It may be outside the segment [P1,P2]. 444 * @see #closestPointToSegment 445 * @since 4134 446 */ 447 public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) { 448 return closestPointTo(lineP1, lineP2, point, false); 449 } 450 451 /** 452 * This method tests if secondNode is clockwise to first node. 453 * 454 * The line through the two points commonNode and firstNode divides the 455 * plane into two parts. The test returns true, if secondNode lies in 456 * the part that is to the right when traveling in the direction from 457 * commonNode to firstNode. 458 * 459 * @param commonNode starting point for both vectors 460 * @param firstNode first vector end node 461 * @param secondNode second vector end node 462 * @return true if first vector is clockwise before second vector. 463 */ 464 public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) { 465 466 CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode"); 467 CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode"); 468 CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode"); 469 470 double dy1 = firstNode.getY() - commonNode.getY(); 471 double dy2 = secondNode.getY() - commonNode.getY(); 472 double dx1 = firstNode.getX() - commonNode.getX(); 473 double dx2 = secondNode.getX() - commonNode.getX(); 474 475 return dy1 * dx2 - dx1 * dy2 > 0; 476 } 477 478 /** 479 * Returns the Area of a polygon, from its list of nodes. 480 * @param polygon List of nodes forming polygon 481 * @return Area for the given list of nodes (EastNorth coordinates) 482 * @since 6841 483 */ 484 public static Area getArea(List<Node> polygon) { 485 Path2D path = new Path2D.Double(); 486 487 boolean begin = true; 488 for (Node n : polygon) { 489 EastNorth en = n.getEastNorth(); 490 if (en != null) { 491 if (begin) { 492 path.moveTo(en.getX(), en.getY()); 493 begin = false; 494 } else { 495 path.lineTo(en.getX(), en.getY()); 496 } 497 } 498 } 499 if (!begin) { 500 path.closePath(); 501 } 502 503 return new Area(path); 504 } 505 506 /** 507 * Builds a path from a list of nodes 508 * @param polygon Nodes, forming a closed polygon 509 * @param path2d path to add to; can be null, then a new path is created 510 * @return the path (LatLon coordinates) 511 */ 512 public static Path2D buildPath2DLatLon(List<Node> polygon, Path2D path2d) { 513 Path2D path = path2d != null ? path2d : new Path2D.Double(); 514 boolean begin = true; 515 for (Node n : polygon) { 516 if (begin) { 517 path.moveTo(n.getCoor().lon(), n.getCoor().lat()); 518 begin = false; 519 } else { 520 path.lineTo(n.getCoor().lon(), n.getCoor().lat()); 521 } 522 } 523 if (!begin) { 524 path.closePath(); 525 } 526 return path; 527 } 528 529 /** 530 * Returns the Area of a polygon, from the multipolygon relation. 531 * @param multipolygon the multipolygon relation 532 * @return Area for the multipolygon (LatLon coordinates) 533 */ 534 public static Area getAreaLatLon(Relation multipolygon) { 535 final Multipolygon mp = Main.map == null || Main.map.mapView == null 536 ? new Multipolygon(multipolygon) 537 : MultipolygonCache.getInstance().get(Main.map.mapView, multipolygon); 538 Path2D path = new Path2D.Double(); 539 path.setWindingRule(Path2D.WIND_EVEN_ODD); 540 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) { 541 buildPath2DLatLon(pd.getNodes(), path); 542 for (Multipolygon.PolyData pdInner : pd.getInners()) { 543 buildPath2DLatLon(pdInner.getNodes(), path); 544 } 545 } 546 return new Area(path); 547 } 548 549 /** 550 * Tests if two polygons intersect. 551 * @param first List of nodes forming first polygon 552 * @param second List of nodes forming second polygon 553 * @return intersection kind 554 */ 555 public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) { 556 Area a1 = getArea(first); 557 Area a2 = getArea(second); 558 return polygonIntersection(a1, a2); 559 } 560 561 /** 562 * Tests if two polygons intersect. 563 * @param a1 Area of first polygon 564 * @param a2 Area of second polygon 565 * @return intersection kind 566 * @since 6841 567 */ 568 public static PolygonIntersection polygonIntersection(Area a1, Area a2) { 569 return polygonIntersection(a1, a2, 1.0); 570 } 571 572 /** 573 * Tests if two polygons intersect. 574 * @param a1 Area of first polygon 575 * @param a2 Area of second polygon 576 * @param eps an area threshold, everything below is considered an empty intersection 577 * @return intersection kind 578 */ 579 public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) { 580 581 Area inter = new Area(a1); 582 inter.intersect(a2); 583 584 Rectangle bounds = inter.getBounds(); 585 586 if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) { 587 return PolygonIntersection.OUTSIDE; 588 } else if (a2.getBounds2D().contains(a1.getBounds2D()) && inter.equals(a1)) { 589 return PolygonIntersection.FIRST_INSIDE_SECOND; 590 } else if (a1.getBounds2D().contains(a2.getBounds2D()) && inter.equals(a2)) { 591 return PolygonIntersection.SECOND_INSIDE_FIRST; 592 } else { 593 return PolygonIntersection.CROSSING; 594 } 595 } 596 597 /** 598 * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner. 599 * @param polygonNodes list of nodes from polygon path. 600 * @param point the point to test 601 * @return true if the point is inside polygon. 602 */ 603 public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) { 604 if (polygonNodes.size() < 2) 605 return false; 606 607 //iterate each side of the polygon, start with the last segment 608 Node oldPoint = polygonNodes.get(polygonNodes.size() - 1); 609 610 if (!oldPoint.isLatLonKnown()) { 611 return false; 612 } 613 614 boolean inside = false; 615 Node p1, p2; 616 617 for (Node newPoint : polygonNodes) { 618 //skip duplicate points 619 if (newPoint.equals(oldPoint)) { 620 continue; 621 } 622 623 if (!newPoint.isLatLonKnown()) { 624 return false; 625 } 626 627 //order points so p1.lat <= p2.lat 628 if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) { 629 p1 = oldPoint; 630 p2 = newPoint; 631 } else { 632 p1 = newPoint; 633 p2 = oldPoint; 634 } 635 636 EastNorth pEN = point.getEastNorth(); 637 EastNorth opEN = oldPoint.getEastNorth(); 638 EastNorth npEN = newPoint.getEastNorth(); 639 EastNorth p1EN = p1.getEastNorth(); 640 EastNorth p2EN = p2.getEastNorth(); 641 642 if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) { 643 //test if the line is crossed and if so invert the inside flag. 644 if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY()) 645 && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY()) 646 < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) { 647 inside = !inside; 648 } 649 } 650 651 oldPoint = newPoint; 652 } 653 654 return inside; 655 } 656 657 /** 658 * Returns area of a closed way in square meters. 659 * 660 * @param way Way to measure, should be closed (first node is the same as last node) 661 * @return area of the closed way. 662 */ 663 public static double closedWayArea(Way way) { 664 return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea(); 665 } 666 667 /** 668 * Returns area of a multipolygon in square meters. 669 * 670 * @param multipolygon the multipolygon to measure 671 * @return area of the multipolygon. 672 */ 673 public static double multipolygonArea(Relation multipolygon) { 674 double area = 0.0; 675 final Multipolygon mp = Main.map == null || Main.map.mapView == null 676 ? new Multipolygon(multipolygon) 677 : MultipolygonCache.getInstance().get(Main.map.mapView, multipolygon); 678 for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) { 679 area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea(); 680 } 681 return area; 682 } 683 684 /** 685 * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives 686 * 687 * @param osm the primitive to measure 688 * @return area of the primitive, or {@code null} 689 */ 690 public static Double computeArea(OsmPrimitive osm) { 691 if (osm instanceof Way && ((Way) osm).isClosed()) { 692 return closedWayArea((Way) osm); 693 } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) { 694 return multipolygonArea((Relation) osm); 695 } else { 696 return null; 697 } 698 } 699 700 /** 701 * Determines whether a way is oriented clockwise. 702 * 703 * Internals: Assuming a closed non-looping way, compute twice the area 704 * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}. 705 * If the area is negative the way is ordered in a clockwise direction. 706 * 707 * See http://paulbourke.net/geometry/polyarea/ 708 * 709 * @param w the way to be checked. 710 * @return true if and only if way is oriented clockwise. 711 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 712 */ 713 public static boolean isClockwise(Way w) { 714 return isClockwise(w.getNodes()); 715 } 716 717 /** 718 * Determines whether path from nodes list is oriented clockwise. 719 * @param nodes Nodes list to be checked. 720 * @return true if and only if way is oriented clockwise. 721 * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}). 722 * @see #isClockwise(Way) 723 */ 724 public static boolean isClockwise(List<Node> nodes) { 725 int nodesCount = nodes.size(); 726 if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) { 727 throw new IllegalArgumentException("Way must be closed to check orientation."); 728 } 729 double area2 = 0.; 730 731 for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) { 732 LatLon coorPrev = nodes.get(node - 1).getCoor(); 733 LatLon coorCurr = nodes.get(node % nodesCount).getCoor(); 734 area2 += coorPrev.lon() * coorCurr.lat(); 735 area2 -= coorCurr.lon() * coorPrev.lat(); 736 } 737 return area2 < 0; 738 } 739 740 /** 741 * Returns angle of a segment defined with 2 point coordinates. 742 * 743 * @param p1 first point 744 * @param p2 second point 745 * @return Angle in radians (-pi, pi] 746 */ 747 public static double getSegmentAngle(EastNorth p1, EastNorth p2) { 748 749 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 750 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 751 752 return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east()); 753 } 754 755 /** 756 * Returns angle of a corner defined with 3 point coordinates. 757 * 758 * @param p1 first point 759 * @param p2 Common endpoint 760 * @param p3 third point 761 * @return Angle in radians (-pi, pi] 762 */ 763 public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) { 764 765 CheckParameterUtil.ensureValidCoordinates(p1, "p1"); 766 CheckParameterUtil.ensureValidCoordinates(p2, "p2"); 767 CheckParameterUtil.ensureValidCoordinates(p3, "p3"); 768 769 Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3); 770 if (result <= -Math.PI) { 771 result += 2 * Math.PI; 772 } 773 774 if (result > Math.PI) { 775 result -= 2 * Math.PI; 776 } 777 778 return result; 779 } 780 781 /** 782 * Compute the centroid/barycenter of nodes 783 * @param nodes Nodes for which the centroid is wanted 784 * @return the centroid of nodes 785 * @see Geometry#getCenter 786 */ 787 public static EastNorth getCentroid(List<Node> nodes) { 788 789 BigDecimal area = BigDecimal.ZERO; 790 BigDecimal north = BigDecimal.ZERO; 791 BigDecimal east = BigDecimal.ZERO; 792 793 // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here 794 for (int i = 0; i < nodes.size(); i++) { 795 EastNorth n0 = nodes.get(i).getEastNorth(); 796 EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth(); 797 798 if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) { 799 BigDecimal x0 = BigDecimal.valueOf(n0.east()); 800 BigDecimal y0 = BigDecimal.valueOf(n0.north()); 801 BigDecimal x1 = BigDecimal.valueOf(n1.east()); 802 BigDecimal y1 = BigDecimal.valueOf(n1.north()); 803 804 BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128)); 805 806 area = area.add(k, MathContext.DECIMAL128); 807 east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 808 north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128)); 809 } 810 } 811 812 BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3 813 area = area.multiply(d, MathContext.DECIMAL128); 814 if (area.compareTo(BigDecimal.ZERO) != 0) { 815 north = north.divide(area, MathContext.DECIMAL128); 816 east = east.divide(area, MathContext.DECIMAL128); 817 } 818 819 return new EastNorth(east.doubleValue(), north.doubleValue()); 820 } 821 822 /** 823 * Compute center of the circle closest to different nodes. 824 * 825 * Ensure exact center computation in case nodes are already aligned in circle. 826 * This is done by least square method. 827 * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges. 828 * Center must be intersection of all bisectors. 829 * <pre> 830 * [ a1 b1 ] [ -c1 ] 831 * With A = [ ... ... ] and Y = [ ... ] 832 * [ an bn ] [ -cn ] 833 * </pre> 834 * An approximation of center of circle is (At.A)^-1.At.Y 835 * @param nodes Nodes parts of the circle (at least 3) 836 * @return An approximation of the center, of null if there is no solution. 837 * @see Geometry#getCentroid 838 * @since 6934 839 */ 840 public static EastNorth getCenter(List<Node> nodes) { 841 int nc = nodes.size(); 842 if (nc < 3) return null; 843 /** 844 * Equation of each bisector ax + by + c = 0 845 */ 846 double[] a = new double[nc]; 847 double[] b = new double[nc]; 848 double[] c = new double[nc]; 849 // Compute equation of bisector 850 for (int i = 0; i < nc; i++) { 851 EastNorth pt1 = nodes.get(i).getEastNorth(); 852 EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth(); 853 a[i] = pt1.east() - pt2.east(); 854 b[i] = pt1.north() - pt2.north(); 855 double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]); 856 if (d == 0) return null; 857 a[i] /= d; 858 b[i] /= d; 859 double xC = (pt1.east() + pt2.east()) / 2; 860 double yC = (pt1.north() + pt2.north()) / 2; 861 c[i] = -(a[i]*xC + b[i]*yC); 862 } 863 // At.A = [aij] 864 double a11 = 0, a12 = 0, a22 = 0; 865 // At.Y = [bi] 866 double b1 = 0, b2 = 0; 867 for (int i = 0; i < nc; i++) { 868 a11 += a[i]*a[i]; 869 a12 += a[i]*b[i]; 870 a22 += b[i]*b[i]; 871 b1 -= a[i]*c[i]; 872 b2 -= b[i]*c[i]; 873 } 874 // (At.A)^-1 = [invij] 875 double det = a11*a22 - a12*a12; 876 if (Math.abs(det) < 1e-5) return null; 877 double inv11 = a22/det; 878 double inv12 = -a12/det; 879 double inv22 = a11/det; 880 // center (xC, yC) = (At.A)^-1.At.y 881 double xC = inv11*b1 + inv12*b2; 882 double yC = inv12*b1 + inv22*b2; 883 return new EastNorth(xC, yC); 884 } 885 886 /** 887 * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument 888 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 889 * @param node node 890 * @param multiPolygon multipolygon 891 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 892 * @return {@code true} if the node is inside the multipolygon 893 */ 894 public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 895 return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch); 896 } 897 898 /** 899 * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument 900 * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match. 901 * <p> 902 * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon. 903 * @param nodes nodes forming the polygon 904 * @param multiPolygon multipolygon 905 * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match 906 * @return {@code true} if the polygon formed by nodes is inside the multipolygon 907 */ 908 public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) { 909 // Extract outer/inner members from multipolygon 910 final Pair<List<JoinedPolygon>, List<JoinedPolygon>> outerInner; 911 try { 912 outerInner = MultipolygonBuilder.joinWays(multiPolygon); 913 } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) { 914 Main.trace(ex); 915 Main.debug("Invalid multipolygon " + multiPolygon); 916 return false; 917 } 918 // Test if object is inside an outer member 919 for (JoinedPolygon out : outerInner.a) { 920 if (nodes.size() == 1 921 ? nodeInsidePolygon(nodes.get(0), out.getNodes()) 922 : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains( 923 polygonIntersection(nodes, out.getNodes()))) { 924 boolean insideInner = false; 925 // If inside an outer, check it is not inside an inner 926 for (JoinedPolygon in : outerInner.b) { 927 if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND 928 && (nodes.size() == 1 929 ? nodeInsidePolygon(nodes.get(0), in.getNodes()) 930 : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) { 931 insideInner = true; 932 break; 933 } 934 } 935 // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon 936 if (!insideInner) { 937 // Final check using predicate 938 if (isOuterWayAMatch == null || isOuterWayAMatch.test(out.ways.get(0) 939 /* TODO give a better representation of the outer ring to the predicate */)) { 940 return true; 941 } 942 } 943 } 944 } 945 return false; 946 } 947 948 /** 949 * Data class to hold two double values (area and perimeter of a polygon). 950 */ 951 public static class AreaAndPerimeter { 952 private final double area; 953 private final double perimeter; 954 955 public AreaAndPerimeter(double area, double perimeter) { 956 this.area = area; 957 this.perimeter = perimeter; 958 } 959 960 public double getArea() { 961 return area; 962 } 963 964 public double getPerimeter() { 965 return perimeter; 966 } 967 } 968 969 /** 970 * Calculate area and perimeter length of a polygon. 971 * 972 * Uses current projection; units are that of the projected coordinates. 973 * 974 * @param nodes the list of nodes representing the polygon 975 * @return area and perimeter 976 */ 977 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) { 978 return getAreaAndPerimeter(nodes, null); 979 } 980 981 /** 982 * Calculate area and perimeter length of a polygon in the given projection. 983 * 984 * @param nodes the list of nodes representing the polygon 985 * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()} 986 * @return area and perimeter 987 */ 988 public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes, Projection projection) { 989 CheckParameterUtil.ensureParameterNotNull(nodes, "nodes"); 990 double area = 0; 991 double perimeter = 0; 992 if (!nodes.isEmpty()) { 993 boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1); 994 int numSegments = closed ? nodes.size() - 1 : nodes.size(); 995 EastNorth p1 = projection == null ? nodes.get(0).getEastNorth() : projection.latlon2eastNorth(nodes.get(0).getCoor()); 996 for (int i = 1; i <= numSegments; i++) { 997 final Node node = nodes.get(i == numSegments ? 0 : i); 998 final EastNorth p2 = projection == null ? node.getEastNorth() : projection.latlon2eastNorth(node.getCoor()); 999 if (p1 != null && p2 != null) { 1000 area += p1.east() * p2.north() - p2.east() * p1.north(); 1001 perimeter += p1.distance(p2); 1002 } 1003 p1 = p2; 1004 } 1005 } 1006 return new AreaAndPerimeter(Math.abs(area) / 2, perimeter); 1007 } 1008}