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.OsmPrimitive;
030import org.openstreetmap.josm.data.osm.OsmPrimitiveType;
031import org.openstreetmap.josm.data.osm.Relation;
032import org.openstreetmap.josm.data.osm.RelationMember;
033import org.openstreetmap.josm.data.osm.Way;
034import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon;
035import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache;
036import org.openstreetmap.josm.data.projection.Projection;
037import org.openstreetmap.josm.data.projection.Projections;
038
039/**
040 * Some tools for geometry related tasks.
041 *
042 * @author viesturs
043 */
044public final class Geometry {
045
046    private Geometry() {
047        // Hide default constructor for utils classes
048    }
049
050    public enum PolygonIntersection {
051        FIRST_INSIDE_SECOND,
052        SECOND_INSIDE_FIRST,
053        OUTSIDE,
054        CROSSING
055    }
056
057    /**
058     * Will find all intersection and add nodes there for list of given ways.
059     * Handles self-intersections too.
060     * And makes commands to add the intersection points to ways.
061     *
062     * Prerequisite: no two nodes have the same coordinates.
063     *
064     * @param ways  a list of ways to test
065     * @param test  if false, do not build list of Commands, just return nodes
066     * @param cmds  list of commands, typically empty when handed to this method.
067     *              Will be filled with commands that add intersection nodes to
068     *              the ways.
069     * @return list of new nodes
070     */
071    public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
072
073        int n = ways.size();
074        @SuppressWarnings("unchecked")
075        List<Node>[] newNodes = new ArrayList[n];
076        BBox[] wayBounds = new BBox[n];
077        boolean[] changedWays = new boolean[n];
078
079        Set<Node> intersectionNodes = new LinkedHashSet<>();
080
081        //copy node arrays for local usage.
082        for (int pos = 0; pos < n; pos++) {
083            newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
084            wayBounds[pos] = getNodesBounds(newNodes[pos]);
085            changedWays[pos] = false;
086        }
087
088        //iterate over all way pairs and introduce the intersections
089        Comparator<Node> coordsComparator = new NodePositionComparator();
090        for (int seg1Way = 0; seg1Way < n; seg1Way++) {
091            for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
092
093                //do not waste time on bounds that do not intersect
094                if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
095                    continue;
096                }
097
098                List<Node> way1Nodes = newNodes[seg1Way];
099                List<Node> way2Nodes = newNodes[seg2Way];
100
101                //iterate over primary segmemt
102                for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
103
104                    //iterate over secondary segment
105                    int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
106
107                    for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
108
109                        //need to get them again every time, because other segments may be changed
110                        Node seg1Node1 = way1Nodes.get(seg1Pos);
111                        Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
112                        Node seg2Node1 = way2Nodes.get(seg2Pos);
113                        Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
114
115                        int commonCount = 0;
116                        //test if we have common nodes to add.
117                        if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
118                            commonCount++;
119
120                            if (seg1Way == seg2Way &&
121                                    seg1Pos == 0 &&
122                                    seg2Pos == way2Nodes.size() -2) {
123                                //do not add - this is first and last segment of the same way.
124                            } else {
125                                intersectionNodes.add(seg1Node1);
126                            }
127                        }
128
129                        if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
130                            commonCount++;
131
132                            intersectionNodes.add(seg1Node2);
133                        }
134
135                        //no common nodes - find intersection
136                        if (commonCount == 0) {
137                            EastNorth intersection = getSegmentSegmentIntersection(
138                                    seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
139                                    seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
140
141                            if (intersection != null) {
142                                if (test) {
143                                    intersectionNodes.add(seg2Node1);
144                                    return intersectionNodes;
145                                }
146
147                                Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
148                                Node intNode = newNode;
149                                boolean insertInSeg1 = false;
150                                boolean insertInSeg2 = false;
151                                //find if the intersection point is at end point of one of the segments, if so use that point
152
153                                //segment 1
154                                if (coordsComparator.compare(newNode, seg1Node1) == 0) {
155                                    intNode = seg1Node1;
156                                } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
157                                    intNode = seg1Node2;
158                                } else {
159                                    insertInSeg1 = true;
160                                }
161
162                                //segment 2
163                                if (coordsComparator.compare(newNode, seg2Node1) == 0) {
164                                    intNode = seg2Node1;
165                                } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
166                                    intNode = seg2Node2;
167                                } else {
168                                    insertInSeg2 = true;
169                                }
170
171                                if (insertInSeg1) {
172                                    way1Nodes.add(seg1Pos +1, intNode);
173                                    changedWays[seg1Way] = true;
174
175                                    //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
176                                    if (seg2Way == seg1Way) {
177                                        seg2Pos++;
178                                    }
179                                }
180
181                                if (insertInSeg2) {
182                                    way2Nodes.add(seg2Pos +1, intNode);
183                                    changedWays[seg2Way] = true;
184
185                                    //Do not need to compare again to already split segment
186                                    seg2Pos++;
187                                }
188
189                                intersectionNodes.add(intNode);
190
191                                if (intNode == newNode) {
192                                    cmds.add(new AddCommand(intNode));
193                                }
194                            }
195                        } else if (test && !intersectionNodes.isEmpty())
196                            return intersectionNodes;
197                    }
198                }
199            }
200        }
201
202
203        for (int pos = 0; pos < ways.size(); pos++) {
204            if (!changedWays[pos]) {
205                continue;
206            }
207
208            Way way = ways.get(pos);
209            Way newWay = new Way(way);
210            newWay.setNodes(newNodes[pos]);
211
212            cmds.add(new ChangeCommand(way, newWay));
213        }
214
215        return intersectionNodes;
216    }
217
218    private static BBox getNodesBounds(List<Node> nodes) {
219
220        BBox bounds = new BBox(nodes.get(0));
221        for (Node n: nodes) {
222            bounds.add(n.getCoor());
223        }
224        return bounds;
225    }
226
227    /**
228     * Tests if given point is to the right side of path consisting of 3 points.
229     *
230     * (Imagine the path is continued beyond the endpoints, so you get two rays
231     * starting from lineP2 and going through lineP1 and lineP3 respectively
232     * which divide the plane into two parts. The test returns true, if testPoint
233     * lies in the part that is to the right when traveling in the direction
234     * lineP1, lineP2, lineP3.)
235     *
236     * @param lineP1 first point in path
237     * @param lineP2 second point in path
238     * @param lineP3 third point in path
239     * @param testPoint point to test
240     * @return true if to the right side, false otherwise
241     */
242    public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
243        boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
244        boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
245        boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
246
247        if (pathBendToRight)
248            return rightOfSeg1 && rightOfSeg2;
249        else
250            return !(!rightOfSeg1 && !rightOfSeg2);
251    }
252
253    /**
254     * This method tests if secondNode is clockwise to first node.
255     * @param commonNode starting point for both vectors
256     * @param firstNode first vector end node
257     * @param secondNode second vector end node
258     * @return true if first vector is clockwise before second vector.
259     */
260    public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
261        return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
262    }
263
264    /**
265     * Finds the intersection of two line segments.
266     * @param p1 the coordinates of the start point of the first specified line segment
267     * @param p2 the coordinates of the end point of the first specified line segment
268     * @param p3 the coordinates of the start point of the second specified line segment
269     * @param p4 the coordinates of the end point of the second specified line segment
270     * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
271     */
272    public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
273
274        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
275        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
276        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
277        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
278
279        double x1 = p1.getX();
280        double y1 = p1.getY();
281        double x2 = p2.getX();
282        double y2 = p2.getY();
283        double x3 = p3.getX();
284        double y3 = p3.getY();
285        double x4 = p4.getX();
286        double y4 = p4.getY();
287
288        //TODO: do this locally.
289        //TODO: remove this check after careful testing
290        if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
291
292        // solve line-line intersection in parametric form:
293        // (x1,y1) + (x2-x1,y2-y1)* u  = (x3,y3) + (x4-x3,y4-y3)* v
294        // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
295        // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
296
297        double a1 = x2 - x1;
298        double b1 = x3 - x4;
299        double c1 = x3 - x1;
300
301        double a2 = y2 - y1;
302        double b2 = y3 - y4;
303        double c2 = y3 - y1;
304
305        // Solve the equations
306        double det = a1*b2 - a2*b1;
307
308        double uu = b2*c1 - b1*c2;
309        double vv = a1*c2 - a2*c1;
310        double mag = Math.abs(uu)+Math.abs(vv);
311
312        if (Math.abs(det) > 1e-12 * mag) {
313            double u = uu/det, v = vv/det;
314            if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
315                if (u < 0) u = 0;
316                if (u > 1) u = 1.0;
317                return new EastNorth(x1+a1*u, y1+a2*u);
318            } else {
319                return null;
320            }
321        } else {
322            // parallel lines
323            return null;
324        }
325    }
326
327    /**
328     * Finds the intersection of two lines of infinite length.
329     *
330     * @param p1 first point on first line
331     * @param p2 second point on first line
332     * @param p3 first point on second line
333     * @param p4 second point on second line
334     * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
335     * @throws IllegalArgumentException if a parameter is null or without valid coordinates
336     */
337    public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
338
339        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
340        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
341        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
342        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
343
344        if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
345
346        // Basically, the formula from wikipedia is used:
347        //  https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
348        // However, large numbers lead to rounding errors (see #10286).
349        // To avoid this, p1 is first substracted from each of the points:
350        //  p1' = 0
351        //  p2' = p2 - p1
352        //  p3' = p3 - p1
353        //  p4' = p4 - p1
354        // In the end, p1 is added to the intersection point of segment p1'/p2'
355        // and segment p3'/p4'.
356
357        // Convert line from (point, point) form to ax+by=c
358        double a1 = p2.getY() - p1.getY();
359        double b1 = p1.getX() - p2.getX();
360
361        double a2 = p4.getY() - p3.getY();
362        double b2 = p3.getX() - p4.getX();
363
364        // Solve the equations
365        double det = a1 * b2 - a2 * b1;
366        if (det == 0)
367            return null; // Lines are parallel
368
369        double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
370
371        return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
372    }
373
374    public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
375
376        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
377        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
378        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
379        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
380
381        // Convert line from (point, point) form to ax+by=c
382        double a1 = p2.getY() - p1.getY();
383        double b1 = p1.getX() - p2.getX();
384
385        double a2 = p4.getY() - p3.getY();
386        double b2 = p3.getX() - p4.getX();
387
388        // Solve the equations
389        double det = a1 * b2 - a2 * b1;
390        // remove influence of of scaling factor
391        det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
392        return Math.abs(det) < 1e-3;
393    }
394
395    private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
396        CheckParameterUtil.ensureParameterNotNull(p1, "p1");
397        CheckParameterUtil.ensureParameterNotNull(p2, "p2");
398        CheckParameterUtil.ensureParameterNotNull(point, "point");
399
400        double ldx = p2.getX() - p1.getX();
401        double ldy = p2.getY() - p1.getY();
402
403        //segment zero length
404        if (ldx == 0 && ldy == 0)
405            return p1;
406
407        double pdx = point.getX() - p1.getX();
408        double pdy = point.getY() - p1.getY();
409
410        double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
411
412        if (segmentOnly && offset <= 0)
413            return p1;
414        else if (segmentOnly && offset >= 1)
415            return p2;
416        else
417            return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
418    }
419
420    /**
421     * Calculates closest point to a line segment.
422     * @param segmentP1 First point determining line segment
423     * @param segmentP2 Second point determining line segment
424     * @param point Point for which a closest point is searched on line segment [P1,P2]
425     * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
426     * a new point if closest point is between segmentP1 and segmentP2.
427     * @see #closestPointToLine
428     * @since 3650
429     */
430    public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
431        return closestPointTo(segmentP1, segmentP2, point, true);
432    }
433
434    /**
435     * Calculates closest point to a line.
436     * @param lineP1 First point determining line
437     * @param lineP2 Second point determining line
438     * @param point Point for which a closest point is searched on line (P1,P2)
439     * @return The closest point found on line. It may be outside the segment [P1,P2].
440     * @see #closestPointToSegment
441     * @since 4134
442     */
443    public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
444        return closestPointTo(lineP1, lineP2, point, false);
445    }
446
447    /**
448     * This method tests if secondNode is clockwise to first node.
449     *
450     * The line through the two points commonNode and firstNode divides the
451     * plane into two parts. The test returns true, if secondNode lies in
452     * the part that is to the right when traveling in the direction from
453     * commonNode to firstNode.
454     *
455     * @param commonNode starting point for both vectors
456     * @param firstNode first vector end node
457     * @param secondNode second vector end node
458     * @return true if first vector is clockwise before second vector.
459     */
460    public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
461
462        CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
463        CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
464        CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
465
466        double dy1 = firstNode.getY() - commonNode.getY();
467        double dy2 = secondNode.getY() - commonNode.getY();
468        double dx1 = firstNode.getX() - commonNode.getX();
469        double dx2 = secondNode.getX() - commonNode.getX();
470
471        return dy1 * dx2 - dx1 * dy2 > 0;
472    }
473
474    /**
475     * Returns the Area of a polygon, from its list of nodes.
476     * @param polygon List of nodes forming polygon (EastNorth coordinates)
477     * @return Area for the given list of nodes
478     * @since 6841
479     */
480    public static Area getArea(List<Node> polygon) {
481        Path2D path = new Path2D.Double();
482
483        boolean begin = true;
484        for (Node n : polygon) {
485            EastNorth en = n.getEastNorth();
486            if (en != null) {
487                if (begin) {
488                    path.moveTo(en.getX(), en.getY());
489                    begin = false;
490                } else {
491                    path.lineTo(en.getX(), en.getY());
492                }
493            }
494        }
495        if (!begin) {
496            path.closePath();
497        }
498
499        return new Area(path);
500    }
501
502    /**
503     * Returns the Area of a polygon, from its list of nodes.
504     * @param polygon List of nodes forming polygon (LatLon coordinates)
505     * @return Area for the given list of nodes
506     * @since 6841
507     */
508    public static Area getAreaLatLon(List<Node> polygon) {
509        Path2D path = new Path2D.Double();
510
511        boolean begin = true;
512        for (Node n : polygon) {
513            if (begin) {
514                path.moveTo(n.getCoor().lon(), n.getCoor().lat());
515                begin = false;
516            } else {
517                path.lineTo(n.getCoor().lon(), n.getCoor().lat());
518            }
519        }
520        if (!begin) {
521            path.closePath();
522        }
523
524        return new Area(path);
525    }
526
527    /**
528     * Tests if two polygons intersect.
529     * @param first List of nodes forming first polygon
530     * @param second List of nodes forming second polygon
531     * @return intersection kind
532     */
533    public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
534        Area a1 = getArea(first);
535        Area a2 = getArea(second);
536        return polygonIntersection(a1, a2);
537    }
538
539    /**
540     * Tests if two polygons intersect.
541     * @param a1 Area of first polygon
542     * @param a2 Area of second polygon
543     * @return intersection kind
544     * @since 6841
545     */
546    public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
547        return polygonIntersection(a1, a2, 1.0);
548    }
549
550    /**
551     * Tests if two polygons intersect.
552     * @param a1 Area of first polygon
553     * @param a2 Area of second polygon
554     * @param eps an area threshold, everything below is considered an empty intersection
555     * @return intersection kind
556     */
557    public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
558
559        Area inter = new Area(a1);
560        inter.intersect(a2);
561
562        Rectangle bounds = inter.getBounds();
563
564        if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
565            return PolygonIntersection.OUTSIDE;
566        } else if (inter.equals(a1)) {
567            return PolygonIntersection.FIRST_INSIDE_SECOND;
568        } else if (inter.equals(a2)) {
569            return PolygonIntersection.SECOND_INSIDE_FIRST;
570        } else {
571            return PolygonIntersection.CROSSING;
572        }
573    }
574
575    /**
576     * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
577     * @param polygonNodes list of nodes from polygon path.
578     * @param point the point to test
579     * @return true if the point is inside polygon.
580     */
581    public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
582        if (polygonNodes.size() < 2)
583            return false;
584
585        //iterate each side of the polygon, start with the last segment
586        Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
587
588        if (!oldPoint.isLatLonKnown()) {
589            return false;
590        }
591
592        boolean inside = false;
593        Node p1, p2;
594
595        for (Node newPoint : polygonNodes) {
596            //skip duplicate points
597            if (newPoint.equals(oldPoint)) {
598                continue;
599            }
600
601            if (!newPoint.isLatLonKnown()) {
602                return false;
603            }
604
605            //order points so p1.lat <= p2.lat
606            if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
607                p1 = oldPoint;
608                p2 = newPoint;
609            } else {
610                p1 = newPoint;
611                p2 = oldPoint;
612            }
613
614            EastNorth pEN = point.getEastNorth();
615            EastNorth opEN = oldPoint.getEastNorth();
616            EastNorth npEN = newPoint.getEastNorth();
617            EastNorth p1EN = p1.getEastNorth();
618            EastNorth p2EN = p2.getEastNorth();
619
620            if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
621                //test if the line is crossed and if so invert the inside flag.
622                if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
623                        && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
624                        < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
625                    inside = !inside;
626                }
627            }
628
629            oldPoint = newPoint;
630        }
631
632        return inside;
633    }
634
635    /**
636     * Returns area of a closed way in square meters.
637     *
638     * @param way Way to measure, should be closed (first node is the same as last node)
639     * @return area of the closed way.
640     */
641    public static double closedWayArea(Way way) {
642        return getAreaAndPerimeter(way.getNodes(), Projections.getProjectionByCode("EPSG:54008")).getArea();
643    }
644
645    /**
646     * Returns area of a multipolygon in square meters.
647     *
648     * @param multipolygon the multipolygon to measure
649     * @return area of the multipolygon.
650     */
651    public static double multipolygonArea(Relation multipolygon) {
652        double area = 0.0;
653        final Multipolygon mp = Main.map == null || Main.map.mapView == null
654                ? new Multipolygon(multipolygon)
655                : MultipolygonCache.getInstance().get(Main.map.mapView, multipolygon);
656        for (Multipolygon.PolyData pd : mp.getCombinedPolygons()) {
657            area += pd.getAreaAndPerimeter(Projections.getProjectionByCode("EPSG:54008")).getArea();
658        }
659        return area;
660    }
661
662    /**
663     * Computes the area of a closed way and multipolygon in square meters, or {@code null} for other primitives
664     *
665     * @param osm the primitive to measure
666     * @return area of the primitive, or {@code null}
667     */
668    public static Double computeArea(OsmPrimitive osm) {
669        if (osm instanceof Way && ((Way) osm).isClosed()) {
670            return closedWayArea((Way) osm);
671        } else if (osm instanceof Relation && ((Relation) osm).isMultipolygon() && !((Relation) osm).hasIncompleteMembers()) {
672            return multipolygonArea((Relation) osm);
673        } else {
674            return null;
675        }
676    }
677
678    /**
679     * Determines whether a way is oriented clockwise.
680     *
681     * Internals: Assuming a closed non-looping way, compute twice the area
682     * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
683     * If the area is negative the way is ordered in a clockwise direction.
684     *
685     * See http://paulbourke.net/geometry/polyarea/
686     *
687     * @param w the way to be checked.
688     * @return true if and only if way is oriented clockwise.
689     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
690     */
691    public static boolean isClockwise(Way w) {
692        return isClockwise(w.getNodes());
693    }
694
695    /**
696     * Determines whether path from nodes list is oriented clockwise.
697     * @param nodes Nodes list to be checked.
698     * @return true if and only if way is oriented clockwise.
699     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
700     * @see #isClockwise(Way)
701     */
702    public static boolean isClockwise(List<Node> nodes) {
703        int nodesCount = nodes.size();
704        if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
705            throw new IllegalArgumentException("Way must be closed to check orientation.");
706        }
707        double area2 = 0.;
708
709        for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
710            LatLon coorPrev = nodes.get(node - 1).getCoor();
711            LatLon coorCurr = nodes.get(node % nodesCount).getCoor();
712            area2 += coorPrev.lon() * coorCurr.lat();
713            area2 -= coorCurr.lon() * coorPrev.lat();
714        }
715        return area2 < 0;
716    }
717
718    /**
719     * Returns angle of a segment defined with 2 point coordinates.
720     *
721     * @param p1 first point
722     * @param p2 second point
723     * @return Angle in radians (-pi, pi]
724     */
725    public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
726
727        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
728        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
729
730        return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
731    }
732
733    /**
734     * Returns angle of a corner defined with 3 point coordinates.
735     *
736     * @param p1 first point
737     * @param p2 Common endpoint
738     * @param p3 third point
739     * @return Angle in radians (-pi, pi]
740     */
741    public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
742
743        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
744        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
745        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
746
747        Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
748        if (result <= -Math.PI) {
749            result += 2 * Math.PI;
750        }
751
752        if (result > Math.PI) {
753            result -= 2 * Math.PI;
754        }
755
756        return result;
757    }
758
759    /**
760     * Compute the centroid/barycenter of nodes
761     * @param nodes Nodes for which the centroid is wanted
762     * @return the centroid of nodes
763     * @see Geometry#getCenter
764     */
765    public static EastNorth getCentroid(List<Node> nodes) {
766
767        BigDecimal area = BigDecimal.ZERO;
768        BigDecimal north = BigDecimal.ZERO;
769        BigDecimal east = BigDecimal.ZERO;
770
771        // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
772        for (int i = 0; i < nodes.size(); i++) {
773            EastNorth n0 = nodes.get(i).getEastNorth();
774            EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
775
776            if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
777                BigDecimal x0 = BigDecimal.valueOf(n0.east());
778                BigDecimal y0 = BigDecimal.valueOf(n0.north());
779                BigDecimal x1 = BigDecimal.valueOf(n1.east());
780                BigDecimal y1 = BigDecimal.valueOf(n1.north());
781
782                BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
783
784                area = area.add(k, MathContext.DECIMAL128);
785                east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
786                north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
787            }
788        }
789
790        BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
791        area = area.multiply(d, MathContext.DECIMAL128);
792        if (area.compareTo(BigDecimal.ZERO) != 0) {
793            north = north.divide(area, MathContext.DECIMAL128);
794            east = east.divide(area, MathContext.DECIMAL128);
795        }
796
797        return new EastNorth(east.doubleValue(), north.doubleValue());
798    }
799
800    /**
801     * Compute center of the circle closest to different nodes.
802     *
803     * Ensure exact center computation in case nodes are already aligned in circle.
804     * This is done by least square method.
805     * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
806     * Center must be intersection of all bisectors.
807     * <pre>
808     *          [ a1  b1  ]         [ -c1 ]
809     * With A = [ ... ... ] and Y = [ ... ]
810     *          [ an  bn  ]         [ -cn ]
811     * </pre>
812     * An approximation of center of circle is (At.A)^-1.At.Y
813     * @param nodes Nodes parts of the circle (at least 3)
814     * @return An approximation of the center, of null if there is no solution.
815     * @see Geometry#getCentroid
816     * @since 6934
817     */
818    public static EastNorth getCenter(List<Node> nodes) {
819        int nc = nodes.size();
820        if (nc < 3) return null;
821        /**
822         * Equation of each bisector ax + by + c = 0
823         */
824        double[] a = new double[nc];
825        double[] b = new double[nc];
826        double[] c = new double[nc];
827        // Compute equation of bisector
828        for (int i = 0; i < nc; i++) {
829            EastNorth pt1 = nodes.get(i).getEastNorth();
830            EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
831            a[i] = pt1.east() - pt2.east();
832            b[i] = pt1.north() - pt2.north();
833            double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
834            if (d == 0) return null;
835            a[i] /= d;
836            b[i] /= d;
837            double xC = (pt1.east() + pt2.east()) / 2;
838            double yC = (pt1.north() + pt2.north()) / 2;
839            c[i] = -(a[i]*xC + b[i]*yC);
840        }
841        // At.A = [aij]
842        double a11 = 0, a12 = 0, a22 = 0;
843        // At.Y = [bi]
844        double b1 = 0, b2 = 0;
845        for (int i = 0; i < nc; i++) {
846            a11 += a[i]*a[i];
847            a12 += a[i]*b[i];
848            a22 += b[i]*b[i];
849            b1 -= a[i]*c[i];
850            b2 -= b[i]*c[i];
851        }
852        // (At.A)^-1 = [invij]
853        double det = a11*a22 - a12*a12;
854        if (Math.abs(det) < 1e-5) return null;
855        double inv11 = a22/det;
856        double inv12 = -a12/det;
857        double inv22 = a11/det;
858        // center (xC, yC) = (At.A)^-1.At.y
859        double xC = inv11*b1 + inv12*b2;
860        double yC = inv12*b1 + inv22*b2;
861        return new EastNorth(xC, yC);
862    }
863
864    public static class MultiPolygonMembers {
865        public final Set<Way> outers = new HashSet<>();
866        public final Set<Way> inners = new HashSet<>();
867
868        public MultiPolygonMembers(Relation multiPolygon) {
869            for (RelationMember m : multiPolygon.getMembers()) {
870                if (m.getType().equals(OsmPrimitiveType.WAY)) {
871                    if ("outer".equals(m.getRole())) {
872                        outers.add(m.getWay());
873                    } else if ("inner".equals(m.getRole())) {
874                        inners.add(m.getWay());
875                    }
876                }
877            }
878        }
879    }
880
881    /**
882     * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
883     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
884     * @param node node
885     * @param multiPolygon multipolygon
886     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
887     * @return {@code true} if the node is inside the multipolygon
888     */
889    public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
890        return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
891    }
892
893    /**
894     * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
895     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
896     * <p>
897     * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
898     * @param nodes nodes forming the polygon
899     * @param multiPolygon multipolygon
900     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
901     * @return {@code true} if the polygon formed by nodes is inside the multipolygon
902     */
903    public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
904        // Extract outer/inner members from multipolygon
905        final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
906        // Construct complete rings for the inner/outer members
907        final List<MultipolygonBuilder.JoinedPolygon> outerRings;
908        final List<MultipolygonBuilder.JoinedPolygon> innerRings;
909        try {
910            outerRings = MultipolygonBuilder.joinWays(mpm.outers);
911            innerRings = MultipolygonBuilder.joinWays(mpm.inners);
912        } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
913            Main.debug("Invalid multipolygon " + multiPolygon);
914            return false;
915        }
916        // Test if object is inside an outer member
917        for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
918            if (nodes.size() == 1
919                    ? nodeInsidePolygon(nodes.get(0), out.getNodes())
920                    : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
921                            polygonIntersection(nodes, out.getNodes()))) {
922                boolean insideInner = false;
923                // If inside an outer, check it is not inside an inner
924                for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
925                    if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
926                            && (nodes.size() == 1
927                            ? nodeInsidePolygon(nodes.get(0), in.getNodes())
928                            : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
929                        insideInner = true;
930                        break;
931                    }
932                }
933                // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
934                if (!insideInner) {
935                    // Final check using predicate
936                    if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0)
937                            /* TODO give a better representation of the outer ring to the predicate */)) {
938                        return true;
939                    }
940                }
941            }
942        }
943        return false;
944    }
945
946    /**
947     * Data class to hold two double values (area and perimeter of a polygon).
948     */
949    public static class AreaAndPerimeter {
950        private final double area;
951        private final double perimeter;
952
953        public AreaAndPerimeter(double area, double perimeter) {
954            this.area = area;
955            this.perimeter = perimeter;
956        }
957
958        public double getArea() {
959            return area;
960        }
961
962        public double getPerimeter() {
963            return perimeter;
964        }
965    }
966
967    /**
968     * Calculate area and perimeter length of a polygon.
969     *
970     * Uses current projection; units are that of the projected coordinates.
971     *
972     * @param nodes the list of nodes representing the polygon
973     * @return area and perimeter
974     */
975    public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) {
976        return getAreaAndPerimeter(nodes, null);
977    }
978
979    /**
980     * Calculate area and perimeter length of a polygon in the given projection.
981     *
982     * @param nodes the list of nodes representing the polygon
983     * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()}
984     * @return area and perimeter
985     */
986    public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes, Projection projection) {
987        CheckParameterUtil.ensureParameterNotNull(nodes, "nodes");
988        double area = 0;
989        double perimeter = 0;
990        if (!nodes.isEmpty()) {
991            boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1);
992            int numSegments = closed ? nodes.size() - 1 : nodes.size();
993            EastNorth p1 = projection == null ? nodes.get(0).getEastNorth() : projection.latlon2eastNorth(nodes.get(0).getCoor());
994            for (int i = 1; i <= numSegments; i++) {
995                final Node node = nodes.get(i == numSegments ? 0 : i);
996                final EastNorth p2 = projection == null ? node.getEastNorth() : projection.latlon2eastNorth(node.getCoor());
997                area += p1.east() * p2.north() - p2.east() * p1.north();
998                perimeter += p1.distance(p2);
999                p1 = p2;
1000            }
1001        }
1002        return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
1003    }
1004}