001// License: GPL. For details, see LICENSE file.
002package org.openstreetmap.josm.tools;
003
004import java.awt.Rectangle;
005import java.awt.geom.Area;
006import java.awt.geom.Line2D;
007import java.awt.geom.Path2D;
008import java.math.BigDecimal;
009import java.math.MathContext;
010import java.util.ArrayList;
011import java.util.Collections;
012import java.util.Comparator;
013import java.util.EnumSet;
014import java.util.HashSet;
015import java.util.LinkedHashSet;
016import java.util.List;
017import java.util.Set;
018
019import org.openstreetmap.josm.Main;
020import org.openstreetmap.josm.command.AddCommand;
021import org.openstreetmap.josm.command.ChangeCommand;
022import org.openstreetmap.josm.command.Command;
023import org.openstreetmap.josm.data.coor.EastNorth;
024import org.openstreetmap.josm.data.coor.LatLon;
025import org.openstreetmap.josm.data.osm.BBox;
026import org.openstreetmap.josm.data.osm.MultipolygonBuilder;
027import org.openstreetmap.josm.data.osm.Node;
028import org.openstreetmap.josm.data.osm.NodePositionComparator;
029import org.openstreetmap.josm.data.osm.OsmPrimitiveType;
030import org.openstreetmap.josm.data.osm.Relation;
031import org.openstreetmap.josm.data.osm.RelationMember;
032import org.openstreetmap.josm.data.osm.Way;
033
034/**
035 * Some tools for geometry related tasks.
036 *
037 * @author viesturs
038 */
039public final class Geometry {
040
041    private Geometry() {
042        // Hide default constructor for utils classes
043    }
044
045    public enum PolygonIntersection {
046        FIRST_INSIDE_SECOND,
047        SECOND_INSIDE_FIRST,
048        OUTSIDE,
049        CROSSING
050    }
051
052    /**
053     * Will find all intersection and add nodes there for list of given ways.
054     * Handles self-intersections too.
055     * And makes commands to add the intersection points to ways.
056     *
057     * Prerequisite: no two nodes have the same coordinates.
058     *
059     * @param ways  a list of ways to test
060     * @param test  if false, do not build list of Commands, just return nodes
061     * @param cmds  list of commands, typically empty when handed to this method.
062     *              Will be filled with commands that add intersection nodes to
063     *              the ways.
064     * @return list of new nodes
065     */
066    public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
067
068        int n = ways.size();
069        @SuppressWarnings("unchecked")
070        List<Node>[] newNodes = new ArrayList[n];
071        BBox[] wayBounds = new BBox[n];
072        boolean[] changedWays = new boolean[n];
073
074        Set<Node> intersectionNodes = new LinkedHashSet<>();
075
076        //copy node arrays for local usage.
077        for (int pos = 0; pos < n; pos++) {
078            newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
079            wayBounds[pos] = getNodesBounds(newNodes[pos]);
080            changedWays[pos] = false;
081        }
082
083        //iterate over all way pairs and introduce the intersections
084        Comparator<Node> coordsComparator = new NodePositionComparator();
085        for (int seg1Way = 0; seg1Way < n; seg1Way++) {
086            for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
087
088                //do not waste time on bounds that do not intersect
089                if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
090                    continue;
091                }
092
093                List<Node> way1Nodes = newNodes[seg1Way];
094                List<Node> way2Nodes = newNodes[seg2Way];
095
096                //iterate over primary segmemt
097                for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
098
099                    //iterate over secondary segment
100                    int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
101
102                    for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
103
104                        //need to get them again every time, because other segments may be changed
105                        Node seg1Node1 = way1Nodes.get(seg1Pos);
106                        Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
107                        Node seg2Node1 = way2Nodes.get(seg2Pos);
108                        Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
109
110                        int commonCount = 0;
111                        //test if we have common nodes to add.
112                        if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
113                            commonCount++;
114
115                            if (seg1Way == seg2Way &&
116                                    seg1Pos == 0 &&
117                                    seg2Pos == way2Nodes.size() -2) {
118                                //do not add - this is first and last segment of the same way.
119                            } else {
120                                intersectionNodes.add(seg1Node1);
121                            }
122                        }
123
124                        if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
125                            commonCount++;
126
127                            intersectionNodes.add(seg1Node2);
128                        }
129
130                        //no common nodes - find intersection
131                        if (commonCount == 0) {
132                            EastNorth intersection = getSegmentSegmentIntersection(
133                                    seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
134                                    seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
135
136                            if (intersection != null) {
137                                if (test) {
138                                    intersectionNodes.add(seg2Node1);
139                                    return intersectionNodes;
140                                }
141
142                                Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
143                                Node intNode = newNode;
144                                boolean insertInSeg1 = false;
145                                boolean insertInSeg2 = false;
146                                //find if the intersection point is at end point of one of the segments, if so use that point
147
148                                //segment 1
149                                if (coordsComparator.compare(newNode, seg1Node1) == 0) {
150                                    intNode = seg1Node1;
151                                } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
152                                    intNode = seg1Node2;
153                                } else {
154                                    insertInSeg1 = true;
155                                }
156
157                                //segment 2
158                                if (coordsComparator.compare(newNode, seg2Node1) == 0) {
159                                    intNode = seg2Node1;
160                                } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
161                                    intNode = seg2Node2;
162                                } else {
163                                    insertInSeg2 = true;
164                                }
165
166                                if (insertInSeg1) {
167                                    way1Nodes.add(seg1Pos +1, intNode);
168                                    changedWays[seg1Way] = true;
169
170                                    //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
171                                    if (seg2Way == seg1Way) {
172                                        seg2Pos++;
173                                    }
174                                }
175
176                                if (insertInSeg2) {
177                                    way2Nodes.add(seg2Pos +1, intNode);
178                                    changedWays[seg2Way] = true;
179
180                                    //Do not need to compare again to already split segment
181                                    seg2Pos++;
182                                }
183
184                                intersectionNodes.add(intNode);
185
186                                if (intNode == newNode) {
187                                    cmds.add(new AddCommand(intNode));
188                                }
189                            }
190                        } else if (test && !intersectionNodes.isEmpty())
191                            return intersectionNodes;
192                    }
193                }
194            }
195        }
196
197
198        for (int pos = 0; pos < ways.size(); pos++) {
199            if (!changedWays[pos]) {
200                continue;
201            }
202
203            Way way = ways.get(pos);
204            Way newWay = new Way(way);
205            newWay.setNodes(newNodes[pos]);
206
207            cmds.add(new ChangeCommand(way, newWay));
208        }
209
210        return intersectionNodes;
211    }
212
213    private static BBox getNodesBounds(List<Node> nodes) {
214
215        BBox bounds = new BBox(nodes.get(0));
216        for (Node n: nodes) {
217            bounds.add(n.getCoor());
218        }
219        return bounds;
220    }
221
222    /**
223     * Tests if given point is to the right side of path consisting of 3 points.
224     *
225     * (Imagine the path is continued beyond the endpoints, so you get two rays
226     * starting from lineP2 and going through lineP1 and lineP3 respectively
227     * which divide the plane into two parts. The test returns true, if testPoint
228     * lies in the part that is to the right when traveling in the direction
229     * lineP1, lineP2, lineP3.)
230     *
231     * @param lineP1 first point in path
232     * @param lineP2 second point in path
233     * @param lineP3 third point in path
234     * @param testPoint point to test
235     * @return true if to the right side, false otherwise
236     */
237    public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
238        boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
239        boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
240        boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
241
242        if (pathBendToRight)
243            return rightOfSeg1 && rightOfSeg2;
244        else
245            return !(!rightOfSeg1 && !rightOfSeg2);
246    }
247
248    /**
249     * This method tests if secondNode is clockwise to first node.
250     * @param commonNode starting point for both vectors
251     * @param firstNode first vector end node
252     * @param secondNode second vector end node
253     * @return true if first vector is clockwise before second vector.
254     */
255    public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
256        return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
257    }
258
259    /**
260     * Finds the intersection of two line segments.
261     * @param p1 the coordinates of the start point of the first specified line segment
262     * @param p2 the coordinates of the end point of the first specified line segment
263     * @param p3 the coordinates of the start point of the second specified line segment
264     * @param p4 the coordinates of the end point of the second specified line segment
265     * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
266     */
267    public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
268
269        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
270        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
271        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
272        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
273
274        double x1 = p1.getX();
275        double y1 = p1.getY();
276        double x2 = p2.getX();
277        double y2 = p2.getY();
278        double x3 = p3.getX();
279        double y3 = p3.getY();
280        double x4 = p4.getX();
281        double y4 = p4.getY();
282
283        //TODO: do this locally.
284        //TODO: remove this check after careful testing
285        if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
286
287        // solve line-line intersection in parametric form:
288        // (x1,y1) + (x2-x1,y2-y1)* u  = (x3,y3) + (x4-x3,y4-y3)* v
289        // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
290        // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
291
292        double a1 = x2 - x1;
293        double b1 = x3 - x4;
294        double c1 = x3 - x1;
295
296        double a2 = y2 - y1;
297        double b2 = y3 - y4;
298        double c2 = y3 - y1;
299
300        // Solve the equations
301        double det = a1*b2 - a2*b1;
302
303        double uu = b2*c1 - b1*c2;
304        double vv = a1*c2 - a2*c1;
305        double mag = Math.abs(uu)+Math.abs(vv);
306
307        if (Math.abs(det) > 1e-12 * mag) {
308            double u = uu/det, v = vv/det;
309            if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
310                if (u < 0) u = 0;
311                if (u > 1) u = 1.0;
312                return new EastNorth(x1+a1*u, y1+a2*u);
313            } else {
314                return null;
315            }
316        } else {
317            // parallel lines
318            return null;
319        }
320    }
321
322    /**
323     * Finds the intersection of two lines of infinite length.
324     *
325     * @param p1 first point on first line
326     * @param p2 second point on first line
327     * @param p3 first point on second line
328     * @param p4 second point on second line
329     * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
330     * @throws IllegalArgumentException if a parameter is null or without valid coordinates
331     */
332    public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
333
334        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
335        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
336        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
337        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
338
339        if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
340
341        // Basically, the formula from wikipedia is used:
342        //  https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
343        // However, large numbers lead to rounding errors (see #10286).
344        // To avoid this, p1 is first substracted from each of the points:
345        //  p1' = 0
346        //  p2' = p2 - p1
347        //  p3' = p3 - p1
348        //  p4' = p4 - p1
349        // In the end, p1 is added to the intersection point of segment p1'/p2'
350        // and segment p3'/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        if (det == 0)
362            return null; // Lines are parallel
363
364        double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
365
366        return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
367    }
368
369    public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
370
371        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
372        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
373        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
374        CheckParameterUtil.ensureValidCoordinates(p4, "p4");
375
376        // Convert line from (point, point) form to ax+by=c
377        double a1 = p2.getY() - p1.getY();
378        double b1 = p1.getX() - p2.getX();
379
380        double a2 = p4.getY() - p3.getY();
381        double b2 = p3.getX() - p4.getX();
382
383        // Solve the equations
384        double det = a1 * b2 - a2 * b1;
385        // remove influence of of scaling factor
386        det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
387        return Math.abs(det) < 1e-3;
388    }
389
390    private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
391        CheckParameterUtil.ensureParameterNotNull(p1, "p1");
392        CheckParameterUtil.ensureParameterNotNull(p2, "p2");
393        CheckParameterUtil.ensureParameterNotNull(point, "point");
394
395        double ldx = p2.getX() - p1.getX();
396        double ldy = p2.getY() - p1.getY();
397
398        //segment zero length
399        if (ldx == 0 && ldy == 0)
400            return p1;
401
402        double pdx = point.getX() - p1.getX();
403        double pdy = point.getY() - p1.getY();
404
405        double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
406
407        if (segmentOnly && offset <= 0)
408            return p1;
409        else if (segmentOnly && offset >= 1)
410            return p2;
411        else
412            return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
413    }
414
415    /**
416     * Calculates closest point to a line segment.
417     * @param segmentP1 First point determining line segment
418     * @param segmentP2 Second point determining line segment
419     * @param point Point for which a closest point is searched on line segment [P1,P2]
420     * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
421     * a new point if closest point is between segmentP1 and segmentP2.
422     * @see #closestPointToLine
423     * @since 3650
424     */
425    public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
426        return closestPointTo(segmentP1, segmentP2, point, true);
427    }
428
429    /**
430     * Calculates closest point to a line.
431     * @param lineP1 First point determining line
432     * @param lineP2 Second point determining line
433     * @param point Point for which a closest point is searched on line (P1,P2)
434     * @return The closest point found on line. It may be outside the segment [P1,P2].
435     * @see #closestPointToSegment
436     * @since 4134
437     */
438    public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
439        return closestPointTo(lineP1, lineP2, point, false);
440    }
441
442    /**
443     * This method tests if secondNode is clockwise to first node.
444     *
445     * The line through the two points commonNode and firstNode divides the
446     * plane into two parts. The test returns true, if secondNode lies in
447     * the part that is to the right when traveling in the direction from
448     * commonNode to firstNode.
449     *
450     * @param commonNode starting point for both vectors
451     * @param firstNode first vector end node
452     * @param secondNode second vector end node
453     * @return true if first vector is clockwise before second vector.
454     */
455    public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
456
457        CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
458        CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
459        CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
460
461        double dy1 = firstNode.getY() - commonNode.getY();
462        double dy2 = secondNode.getY() - commonNode.getY();
463        double dx1 = firstNode.getX() - commonNode.getX();
464        double dx2 = secondNode.getX() - commonNode.getX();
465
466        return dy1 * dx2 - dx1 * dy2 > 0;
467    }
468
469    /**
470     * Returns the Area of a polygon, from its list of nodes.
471     * @param polygon List of nodes forming polygon (EastNorth coordinates)
472     * @return Area for the given list of nodes
473     * @since 6841
474     */
475    public static Area getArea(List<Node> polygon) {
476        Path2D path = new Path2D.Double();
477
478        boolean begin = true;
479        for (Node n : polygon) {
480            EastNorth en = n.getEastNorth();
481            if (en != null) {
482                if (begin) {
483                    path.moveTo(en.getX(), en.getY());
484                    begin = false;
485                } else {
486                    path.lineTo(en.getX(), en.getY());
487                }
488            }
489        }
490        if (!begin) {
491            path.closePath();
492        }
493
494        return new Area(path);
495    }
496
497    /**
498     * Returns the Area of a polygon, from its list of nodes.
499     * @param polygon List of nodes forming polygon (LatLon coordinates)
500     * @return Area for the given list of nodes
501     * @since 6841
502     */
503    public static Area getAreaLatLon(List<Node> polygon) {
504        Path2D path = new Path2D.Double();
505
506        boolean begin = true;
507        for (Node n : polygon) {
508            if (begin) {
509                path.moveTo(n.getCoor().lon(), n.getCoor().lat());
510                begin = false;
511            } else {
512                path.lineTo(n.getCoor().lon(), n.getCoor().lat());
513            }
514        }
515        if (!begin) {
516            path.closePath();
517        }
518
519        return new Area(path);
520    }
521
522    /**
523     * Tests if two polygons intersect.
524     * @param first List of nodes forming first polygon
525     * @param second List of nodes forming second polygon
526     * @return intersection kind
527     */
528    public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
529        Area a1 = getArea(first);
530        Area a2 = getArea(second);
531        return polygonIntersection(a1, a2);
532    }
533
534    /**
535     * Tests if two polygons intersect.
536     * @param a1 Area of first polygon
537     * @param a2 Area of second polygon
538     * @return intersection kind
539     * @since 6841
540     */
541    public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
542        return polygonIntersection(a1, a2, 1.0);
543    }
544
545    /**
546     * Tests if two polygons intersect.
547     * @param a1 Area of first polygon
548     * @param a2 Area of second polygon
549     * @param eps an area threshold, everything below is considered an empty intersection
550     * @return intersection kind
551     */
552    public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
553
554        Area inter = new Area(a1);
555        inter.intersect(a2);
556
557        Rectangle bounds = inter.getBounds();
558
559        if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
560            return PolygonIntersection.OUTSIDE;
561        } else if (inter.equals(a1)) {
562            return PolygonIntersection.FIRST_INSIDE_SECOND;
563        } else if (inter.equals(a2)) {
564            return PolygonIntersection.SECOND_INSIDE_FIRST;
565        } else {
566            return PolygonIntersection.CROSSING;
567        }
568    }
569
570    /**
571     * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
572     * @param polygonNodes list of nodes from polygon path.
573     * @param point the point to test
574     * @return true if the point is inside polygon.
575     */
576    public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
577        if (polygonNodes.size() < 2)
578            return false;
579
580        //iterate each side of the polygon, start with the last segment
581        Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
582
583        if (!oldPoint.isLatLonKnown()) {
584            return false;
585        }
586
587        boolean inside = false;
588        Node p1, p2;
589
590        for (Node newPoint : polygonNodes) {
591            //skip duplicate points
592            if (newPoint.equals(oldPoint)) {
593                continue;
594            }
595
596            if (!newPoint.isLatLonKnown()) {
597                return false;
598            }
599
600            //order points so p1.lat <= p2.lat
601            if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
602                p1 = oldPoint;
603                p2 = newPoint;
604            } else {
605                p1 = newPoint;
606                p2 = oldPoint;
607            }
608
609            EastNorth pEN = point.getEastNorth();
610            EastNorth opEN = oldPoint.getEastNorth();
611            EastNorth npEN = newPoint.getEastNorth();
612            EastNorth p1EN = p1.getEastNorth();
613            EastNorth p2EN = p2.getEastNorth();
614
615            if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
616                //test if the line is crossed and if so invert the inside flag.
617                if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
618                        && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
619                        < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
620                    inside = !inside;
621                }
622            }
623
624            oldPoint = newPoint;
625        }
626
627        return inside;
628    }
629
630    /**
631     * Returns area of a closed way in square meters.
632     * (approximate(?), but should be OK for small areas)
633     *
634     * Relies on the current projection: Works correctly, when
635     * one unit in projected coordinates corresponds to one meter.
636     * This is true for most projections, but not for WGS84 and
637     * Mercator (EPSG:3857).
638     *
639     * @param way Way to measure, should be closed (first node is the same as last node)
640     * @return area of the closed way.
641     */
642    public static double closedWayArea(Way way) {
643
644        //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
645        double area = 0;
646        Node lastN = null;
647        for (Node n : way.getNodes()) {
648            if (lastN != null) {
649                area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
650            }
651            lastN = n;
652        }
653        return Math.abs(area/2);
654    }
655
656    protected static double calcX(Node p1) {
657        double lat1, lon1, lat2, lon2;
658        double dlon, dlat;
659
660        lat1 = p1.getCoor().lat() * Math.PI / 180.0;
661        lon1 = p1.getCoor().lon() * Math.PI / 180.0;
662        lat2 = lat1;
663        lon2 = 0;
664
665        dlon = lon2 - lon1;
666        dlat = lat2 - lat1;
667
668        double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2);
669        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
670        return 6367000 * c;
671    }
672
673    protected static double calcY(Node p1) {
674        double lat1, lon1, lat2, lon2;
675        double dlon, dlat;
676
677        lat1 = p1.getCoor().lat() * Math.PI / 180.0;
678        lon1 = p1.getCoor().lon() * Math.PI / 180.0;
679        lat2 = 0;
680        lon2 = lon1;
681
682        dlon = lon2 - lon1;
683        dlat = lat2 - lat1;
684
685        double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2);
686        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
687        return 6367000 * c;
688    }
689
690    /**
691     * Determines whether a way is oriented clockwise.
692     *
693     * Internals: Assuming a closed non-looping way, compute twice the area
694     * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
695     * If the area is negative the way is ordered in a clockwise direction.
696     *
697     * See http://paulbourke.net/geometry/polyarea/
698     *
699     * @param w the way to be checked.
700     * @return true if and only if way is oriented clockwise.
701     * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
702     */
703    public static boolean isClockwise(Way w) {
704        return isClockwise(w.getNodes());
705    }
706
707    /**
708     * Determines whether path from nodes list is oriented clockwise.
709     * @param nodes Nodes list 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     * @see #isClockwise(Way)
713     */
714    public static boolean isClockwise(List<Node> nodes) {
715        int nodesCount = nodes.size();
716        if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
717            throw new IllegalArgumentException("Way must be closed to check orientation.");
718        }
719        double area2 = 0.;
720
721        for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
722            LatLon coorPrev = nodes.get(node - 1).getCoor();
723            LatLon coorCurr = nodes.get(node % nodesCount).getCoor();
724            area2 += coorPrev.lon() * coorCurr.lat();
725            area2 -= coorCurr.lon() * coorPrev.lat();
726        }
727        return area2 < 0;
728    }
729
730    /**
731     * Returns angle of a segment defined with 2 point coordinates.
732     *
733     * @param p1 first point
734     * @param p2 second point
735     * @return Angle in radians (-pi, pi]
736     */
737    public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
738
739        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
740        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
741
742        return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
743    }
744
745    /**
746     * Returns angle of a corner defined with 3 point coordinates.
747     *
748     * @param p1 first point
749     * @param p2 Common endpoint
750     * @param p3 third point
751     * @return Angle in radians (-pi, pi]
752     */
753    public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
754
755        CheckParameterUtil.ensureValidCoordinates(p1, "p1");
756        CheckParameterUtil.ensureValidCoordinates(p2, "p2");
757        CheckParameterUtil.ensureValidCoordinates(p3, "p3");
758
759        Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
760        if (result <= -Math.PI) {
761            result += 2 * Math.PI;
762        }
763
764        if (result > Math.PI) {
765            result -= 2 * Math.PI;
766        }
767
768        return result;
769    }
770
771    /**
772     * Compute the centroid/barycenter of nodes
773     * @param nodes Nodes for which the centroid is wanted
774     * @return the centroid of nodes
775     * @see Geometry#getCenter
776     */
777    public static EastNorth getCentroid(List<Node> nodes) {
778
779        BigDecimal area = BigDecimal.ZERO;
780        BigDecimal north = BigDecimal.ZERO;
781        BigDecimal east = BigDecimal.ZERO;
782
783        // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
784        for (int i = 0; i < nodes.size(); i++) {
785            EastNorth n0 = nodes.get(i).getEastNorth();
786            EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
787
788            if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
789                BigDecimal x0 = BigDecimal.valueOf(n0.east());
790                BigDecimal y0 = BigDecimal.valueOf(n0.north());
791                BigDecimal x1 = BigDecimal.valueOf(n1.east());
792                BigDecimal y1 = BigDecimal.valueOf(n1.north());
793
794                BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
795
796                area = area.add(k, MathContext.DECIMAL128);
797                east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
798                north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
799            }
800        }
801
802        BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
803        area  = area.multiply(d, MathContext.DECIMAL128);
804        if (area.compareTo(BigDecimal.ZERO) != 0) {
805            north = north.divide(area, MathContext.DECIMAL128);
806            east = east.divide(area, MathContext.DECIMAL128);
807        }
808
809        return new EastNorth(east.doubleValue(), north.doubleValue());
810    }
811
812    /**
813     * Compute center of the circle closest to different nodes.
814     *
815     * Ensure exact center computation in case nodes are already aligned in circle.
816     * This is done by least square method.
817     * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
818     * Center must be intersection of all bisectors.
819     * <pre>
820     *          [ a1  b1  ]         [ -c1 ]
821     * With A = [ ... ... ] and Y = [ ... ]
822     *          [ an  bn  ]         [ -cn ]
823     * </pre>
824     * An approximation of center of circle is (At.A)^-1.At.Y
825     * @param nodes Nodes parts of the circle (at least 3)
826     * @return An approximation of the center, of null if there is no solution.
827     * @see Geometry#getCentroid
828     * @since 6934
829     */
830    public static EastNorth getCenter(List<Node> nodes) {
831        int nc = nodes.size();
832        if (nc < 3) return null;
833        /**
834         * Equation of each bisector ax + by + c = 0
835         */
836        double[] a = new double[nc];
837        double[] b = new double[nc];
838        double[] c = new double[nc];
839        // Compute equation of bisector
840        for (int i = 0; i < nc; i++) {
841            EastNorth pt1 = nodes.get(i).getEastNorth();
842            EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
843            a[i] = pt1.east() - pt2.east();
844            b[i] = pt1.north() - pt2.north();
845            double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
846            if (d == 0) return null;
847            a[i] /= d;
848            b[i] /= d;
849            double xC = (pt1.east() + pt2.east()) / 2;
850            double yC = (pt1.north() + pt2.north()) / 2;
851            c[i] = -(a[i]*xC + b[i]*yC);
852        }
853        // At.A = [aij]
854        double a11 = 0, a12 = 0, a22 = 0;
855        // At.Y = [bi]
856        double b1 = 0, b2 = 0;
857        for (int i = 0; i < nc; i++) {
858            a11 += a[i]*a[i];
859            a12 += a[i]*b[i];
860            a22 += b[i]*b[i];
861            b1 -= a[i]*c[i];
862            b2 -= b[i]*c[i];
863        }
864        // (At.A)^-1 = [invij]
865        double det = a11*a22 - a12*a12;
866        if (Math.abs(det) < 1e-5) return null;
867        double inv11 = a22/det;
868        double inv12 = -a12/det;
869        double inv22 = a11/det;
870        // center (xC, yC) = (At.A)^-1.At.y
871        double xC = inv11*b1 + inv12*b2;
872        double yC = inv12*b1 + inv22*b2;
873        return new EastNorth(xC, yC);
874    }
875
876    public static class MultiPolygonMembers {
877        public final Set<Way> outers = new HashSet<>();
878        public final Set<Way> inners = new HashSet<>();
879
880        public MultiPolygonMembers(Relation multiPolygon) {
881            for (RelationMember m : multiPolygon.getMembers()) {
882                if (m.getType().equals(OsmPrimitiveType.WAY)) {
883                    if ("outer".equals(m.getRole())) {
884                        outers.add(m.getWay());
885                    } else if ("inner".equals(m.getRole())) {
886                        inners.add(m.getWay());
887                    }
888                }
889            }
890        }
891    }
892
893    /**
894     * Tests if the {@code node} 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     * @param node node
897     * @param multiPolygon multipolygon
898     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
899     * @return {@code true} if the node is inside the multipolygon
900     */
901    public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
902        return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
903    }
904
905    /**
906     * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
907     * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
908     * <p>
909     * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
910     * @param nodes nodes forming the polygon
911     * @param multiPolygon multipolygon
912     * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
913     * @return {@code true} if the polygon formed by nodes is inside the multipolygon
914     */
915    public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
916        // Extract outer/inner members from multipolygon
917        final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
918        // Construct complete rings for the inner/outer members
919        final List<MultipolygonBuilder.JoinedPolygon> outerRings;
920        final List<MultipolygonBuilder.JoinedPolygon> innerRings;
921        try {
922            outerRings = MultipolygonBuilder.joinWays(mpm.outers);
923            innerRings = MultipolygonBuilder.joinWays(mpm.inners);
924        } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
925            Main.debug("Invalid multipolygon " + multiPolygon);
926            return false;
927        }
928        // Test if object is inside an outer member
929        for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
930            if (nodes.size() == 1
931                    ? nodeInsidePolygon(nodes.get(0), out.getNodes())
932                    : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
933                            polygonIntersection(nodes, out.getNodes()))) {
934                boolean insideInner = false;
935                // If inside an outer, check it is not inside an inner
936                for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
937                    if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
938                            && (nodes.size() == 1
939                            ? nodeInsidePolygon(nodes.get(0), in.getNodes())
940                            : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
941                        insideInner = true;
942                        break;
943                    }
944                }
945                // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
946                if (!insideInner) {
947                    // Final check using predicate
948                    if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0)
949                            /* TODO give a better representation of the outer ring to the predicate */)) {
950                        return true;
951                    }
952                }
953            }
954        }
955        return false;
956    }
957
958    /**
959     * Data class to hold two double values (area and perimeter of a polygon).
960     */
961    public static class AreaAndPerimeter {
962        private final double area;
963        private final double perimeter;
964
965        public AreaAndPerimeter(double area, double perimeter) {
966            this.area = area;
967            this.perimeter = perimeter;
968        }
969
970        public double getArea() {
971            return area;
972        }
973
974        public double getPerimeter() {
975            return perimeter;
976        }
977    }
978
979    /**
980     * Calculate area and perimeter length of a polygon.
981     *
982     * Uses current projection; units are that of the projected coordinates.
983     *
984     * @param nodes the list of nodes representing the polygon
985     * @return area and perimeter
986     */
987    public static AreaAndPerimeter getAreaAndPerimeter(List<Node> 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 = nodes.get(0).getEastNorth();
994            for (int i = 1; i <= numSegments; i++) {
995                EastNorth p2 = nodes.get(i == numSegments ? 0 : i).getEastNorth();
996                area += p1.east() * p2.north() - p2.east() * p1.north();
997                perimeter += p1.distance(p2);
998                p1 = p2;
999            }
1000        }
1001        return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
1002    }
1003}