001    // License: GPL. For details, see LICENSE file.
002    package org.openstreetmap.josm.tools;
003    
004    import java.awt.geom.Line2D;
005    import java.math.BigDecimal;
006    import java.math.MathContext;
007    import java.util.ArrayList;
008    import java.util.Comparator;
009    import java.util.HashSet;
010    import java.util.LinkedHashSet;
011    import java.util.List;
012    import java.util.Set;
013    
014    import org.openstreetmap.josm.Main;
015    import org.openstreetmap.josm.command.AddCommand;
016    import org.openstreetmap.josm.command.ChangeCommand;
017    import org.openstreetmap.josm.command.Command;
018    import org.openstreetmap.josm.data.coor.EastNorth;
019    import org.openstreetmap.josm.data.coor.LatLon;
020    import org.openstreetmap.josm.data.osm.BBox;
021    import org.openstreetmap.josm.data.osm.Node;
022    import org.openstreetmap.josm.data.osm.NodePositionComparator;
023    import org.openstreetmap.josm.data.osm.Way;
024    
025    /**
026     * Some tools for geometry related tasks.
027     *
028     * @author viesturs
029     */
030    public class Geometry {
031        public enum PolygonIntersection {FIRST_INSIDE_SECOND, SECOND_INSIDE_FIRST, OUTSIDE, CROSSING}
032    
033        /**
034         * Will find all intersection and add nodes there for list of given ways.
035         * Handles self-intersections too.
036         * And makes commands to add the intersection points to ways.
037         *
038         * Prerequisite: no two nodes have the same coordinates.
039         * 
040         * @param ways  a list of ways to test
041         * @param test  if false, do not build list of Commands, just return nodes
042         * @param cmds  list of commands, typically empty when handed to this method.
043         *              Will be filled with commands that add intersection nodes to
044         *              the ways.
045         * @return list of new nodes
046         */
047        public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
048    
049            //stupid java, cannot instantiate array of generic classes..
050            @SuppressWarnings("unchecked")
051            ArrayList<Node>[] newNodes = new ArrayList[ways.size()];
052            BBox[] wayBounds = new BBox[ways.size()];
053            boolean[] changedWays = new boolean[ways.size()];
054    
055            Set<Node> intersectionNodes = new LinkedHashSet<Node>();
056    
057            //copy node arrays for local usage.
058            for (int pos = 0; pos < ways.size(); pos ++) {
059                newNodes[pos] = new ArrayList<Node>(ways.get(pos).getNodes());
060                wayBounds[pos] = getNodesBounds(newNodes[pos]);
061                changedWays[pos] = false;
062            }
063    
064            //iterate over all way pairs and introduce the intersections
065            Comparator<Node> coordsComparator = new NodePositionComparator();
066    
067            WayLoop: for (int seg1Way = 0; seg1Way < ways.size(); seg1Way ++) {
068                for (int seg2Way = seg1Way; seg2Way < ways.size(); seg2Way ++) {
069    
070                    //do not waste time on bounds that do not intersect
071                    if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
072                        continue;
073                    }
074    
075                    ArrayList<Node> way1Nodes = newNodes[seg1Way];
076                    ArrayList<Node> way2Nodes = newNodes[seg2Way];
077    
078                    //iterate over primary segmemt
079                    for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos ++) {
080    
081                        //iterate over secondary segment
082                        int seg2Start = seg1Way != seg2Way ? 0: seg1Pos + 2;//skip the adjacent segment
083    
084                        for (int seg2Pos = seg2Start; seg2Pos + 1< way2Nodes.size(); seg2Pos ++) {
085    
086                            //need to get them again every time, because other segments may be changed
087                            Node seg1Node1 = way1Nodes.get(seg1Pos);
088                            Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
089                            Node seg2Node1 = way2Nodes.get(seg2Pos);
090                            Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
091    
092                            int commonCount = 0;
093                            //test if we have common nodes to add.
094                            if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
095                                commonCount ++;
096    
097                                if (seg1Way == seg2Way &&
098                                        seg1Pos == 0 &&
099                                        seg2Pos == way2Nodes.size() -2) {
100                                    //do not add - this is first and last segment of the same way.
101                                } else {
102                                    intersectionNodes.add(seg1Node1);
103                                }
104                            }
105    
106                            if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
107                                commonCount ++;
108    
109                                intersectionNodes.add(seg1Node2);
110                            }
111    
112                            //no common nodes - find intersection
113                            if (commonCount == 0) {
114                                EastNorth intersection = getSegmentSegmentIntersection(
115                                        seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
116                                        seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
117    
118                                if (intersection != null) {
119                                    if (test) {
120                                        intersectionNodes.add(seg2Node1);
121                                        return intersectionNodes;
122                                    }
123    
124                                    Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
125                                    Node intNode = newNode;
126                                    boolean insertInSeg1 = false;
127                                    boolean insertInSeg2 = false;
128    
129                                    //find if the intersection point is at end point of one of the segments, if so use that point
130    
131                                    //segment 1
132                                    if (coordsComparator.compare(newNode, seg1Node1) == 0) {
133                                        intNode = seg1Node1;
134                                    } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
135                                        intNode = seg1Node2;
136                                    } else {
137                                        insertInSeg1 = true;
138                                    }
139    
140                                    //segment 2
141                                    if (coordsComparator.compare(newNode, seg2Node1) == 0) {
142                                        intNode = seg2Node1;
143                                    } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
144                                        intNode = seg2Node2;
145                                    } else {
146                                        insertInSeg2 = true;
147                                    }
148    
149                                    if (insertInSeg1) {
150                                        way1Nodes.add(seg1Pos +1, intNode);
151                                        changedWays[seg1Way] = true;
152    
153                                        //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
154                                        if (seg2Way == seg1Way) {
155                                            seg2Pos ++;
156                                        }
157                                    }
158    
159                                    if (insertInSeg2) {
160                                        way2Nodes.add(seg2Pos +1, intNode);
161                                        changedWays[seg2Way] = true;
162    
163                                        //Do not need to compare again to already split segment
164                                        seg2Pos ++;
165                                    }
166    
167                                    intersectionNodes.add(intNode);
168    
169                                    if (intNode == newNode) {
170                                        cmds.add(new AddCommand(intNode));
171                                    }
172                                }
173                            }
174                            else if (test && intersectionNodes.size() > 0)
175                                return intersectionNodes;
176                        }
177                    }
178                }
179            }
180    
181    
182            for (int pos = 0; pos < ways.size(); pos ++) {
183                if (changedWays[pos] == false) {
184                    continue;
185                }
186    
187                Way way = ways.get(pos);
188                Way newWay = new Way(way);
189                newWay.setNodes(newNodes[pos]);
190    
191                cmds.add(new ChangeCommand(way, newWay));
192            }
193    
194            return intersectionNodes;
195        }
196    
197        private static BBox getNodesBounds(ArrayList<Node> nodes) {
198    
199            BBox bounds = new BBox(nodes.get(0));
200            for(Node n: nodes) {
201                bounds.add(n.getCoor());
202            }
203            return bounds;
204        }
205    
206        /**
207         * Tests if given point is to the right side of path consisting of 3 points.
208         * @param lineP1 first point in path
209         * @param lineP2 second point in path
210         * @param lineP3 third point in path
211         * @param testPoint
212         * @return true if to the right side, false otherwise
213         */
214        public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
215            boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
216            boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
217            boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
218    
219            if (pathBendToRight)
220                return rightOfSeg1 && rightOfSeg2;
221            else
222                return !(!rightOfSeg1 && !rightOfSeg2);
223        }
224    
225        /**
226         * This method tests if secondNode is clockwise to first node.
227         * @param commonNode starting point for both vectors
228         * @param firstNode first vector end node
229         * @param secondNode second vector end node
230         * @return true if first vector is clockwise before second vector.
231         */
232        public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
233            return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
234        }
235    
236        /**
237         * Finds the intersection of two line segments
238         * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
239         */
240        public static EastNorth getSegmentSegmentIntersection(
241                EastNorth p1, EastNorth p2,
242                EastNorth p3, EastNorth p4) {
243            double x1 = p1.getX();
244            double y1 = p1.getY();
245            double x2 = p2.getX();
246            double y2 = p2.getY();
247            double x3 = p3.getX();
248            double y3 = p3.getY();
249            double x4 = p4.getX();
250            double y4 = p4.getY();
251    
252            //TODO: do this locally.
253            if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
254    
255            // Convert line from (point, point) form to ax+by=c
256            double a1 = y2 - y1;
257            double b1 = x1 - x2;
258            double c1 = x2*y1 - x1*y2;
259    
260            double a2 = y4 - y3;
261            double b2 = x3 - x4;
262            double c2 = x4*y3 - x3*y4;
263    
264            // Solve the equations
265            double det = a1*b2 - a2*b1;
266            if (det == 0) return null; // Lines are parallel
267    
268            double x = (b1*c2 - b2*c1)/det;
269            double y = (a2*c1 -a1*c2)/det;
270    
271            return new EastNorth(x, y);
272        }
273    
274        /**
275         * Finds the intersection of two lines of infinite length.
276         * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
277         */
278        public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
279    
280            // Convert line from (point, point) form to ax+by=c
281            double a1 = p2.getY() - p1.getY();
282            double b1 = p1.getX() - p2.getX();
283            double c1 = p2.getX() * p1.getY() - p1.getX() * p2.getY();
284    
285            double a2 = p4.getY() - p3.getY();
286            double b2 = p3.getX() - p4.getX();
287            double c2 = p4.getX() * p3.getY() - p3.getX() * p4.getY();
288    
289            // Solve the equations
290            double det = a1 * b2 - a2 * b1;
291            if (det == 0)
292                return null; // Lines are parallel
293    
294            return new EastNorth((b1 * c2 - b2 * c1) / det, (a2 * c1 - a1 * c2) / det);
295        }
296    
297        public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
298            // Convert line from (point, point) form to ax+by=c
299            double a1 = p2.getY() - p1.getY();
300            double b1 = p1.getX() - p2.getX();
301    
302            double a2 = p4.getY() - p3.getY();
303            double b2 = p3.getX() - p4.getX();
304    
305            // Solve the equations
306            double det = a1 * b2 - a2 * b1;
307            // remove influence of of scaling factor
308            det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
309            return Math.abs(det) < 1e-3;
310        }
311    
312        /**
313         * Calculates closest point to a line segment.
314         * @param segmentP1
315         * @param segmentP2
316         * @param point
317         * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
318         * a new point if closest point is between segmentP1 and segmentP2.
319         */
320        public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
321    
322            double ldx = segmentP2.getX() - segmentP1.getX();
323            double ldy = segmentP2.getY() - segmentP1.getY();
324    
325            if (ldx == 0 && ldy == 0) //segment zero length
326                return segmentP1;
327    
328            double pdx = point.getX() - segmentP1.getX();
329            double pdy = point.getY() - segmentP1.getY();
330    
331            double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
332    
333            if (offset <= 0)
334                return segmentP1;
335            else if (offset >= 1)
336                return segmentP2;
337            else
338                return new EastNorth(segmentP1.getX() + ldx * offset, segmentP1.getY() + ldy * offset);
339        }
340    
341        public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
342            double ldx = lineP2.getX() - lineP1.getX();
343            double ldy = lineP2.getY() - lineP1.getY();
344    
345            if (ldx == 0 && ldy == 0) //segment zero length
346                return lineP1;
347    
348            double pdx = point.getX() - lineP1.getX();
349            double pdy = point.getY() - lineP1.getY();
350    
351            double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
352            return new EastNorth(lineP1.getX() + ldx * offset, lineP1.getY() + ldy * offset);
353        }
354    
355        /**
356         * This method tests if secondNode is clockwise to first node.
357         * @param commonNode starting point for both vectors
358         * @param firstNode first vector end node
359         * @param secondNode second vector end node
360         * @return true if first vector is clockwise before second vector.
361         */
362        public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
363            double dy1 = (firstNode.getY() - commonNode.getY());
364            double dy2 = (secondNode.getY() - commonNode.getY());
365            double dx1 = (firstNode.getX() - commonNode.getX());
366            double dx2 = (secondNode.getX() - commonNode.getX());
367    
368            return dy1 * dx2 - dx1 * dy2 > 0;
369        }
370    
371        /**
372         * Tests if two polygons intersect.
373         * @param first
374         * @param second
375         * @return intersection kind
376         * TODO: test segments, not only points
377         * TODO: is O(N*M), should use sweep for better performance.
378         */
379        public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
380            Set<Node> firstSet = new HashSet<Node>(first);
381            Set<Node> secondSet = new HashSet<Node>(second);
382    
383            int nodesInsideSecond = 0;
384            int nodesOutsideSecond = 0;
385            int nodesInsideFirst = 0;
386            int nodesOutsideFirst = 0;
387    
388            for (Node insideNode : first) {
389                if (secondSet.contains(insideNode)) {
390                    continue;
391                    //ignore touching nodes.
392                }
393    
394                if (nodeInsidePolygon(insideNode, second)) {
395                    nodesInsideSecond ++;
396                }
397                else {
398                    nodesOutsideSecond ++;
399                }
400            }
401    
402            for (Node insideNode : second) {
403                if (firstSet.contains(insideNode)) {
404                    continue;
405                    //ignore touching nodes.
406                }
407    
408                if (nodeInsidePolygon(insideNode, first)) {
409                    nodesInsideFirst ++;
410                }
411                else {
412                    nodesOutsideFirst ++;
413                }
414            }
415    
416            if (nodesInsideFirst == 0) {
417                if (nodesInsideSecond == 0){
418                    if (nodesOutsideFirst + nodesInsideSecond > 0)
419                        return PolygonIntersection.OUTSIDE;
420                    else
421                        //all nodes common
422                        return PolygonIntersection.CROSSING;
423                } else
424                    return PolygonIntersection.FIRST_INSIDE_SECOND;
425            }
426            else
427            {
428                if (nodesInsideSecond == 0)
429                    return PolygonIntersection.SECOND_INSIDE_FIRST;
430                else
431                    return PolygonIntersection.CROSSING;
432            }
433        }
434    
435        /**
436         * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
437         * @param polygonNodes list of nodes from polygon path.
438         * @param point the point to test
439         * @return true if the point is inside polygon.
440         */
441        public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
442            if (polygonNodes.size() < 2)
443                return false;
444    
445            boolean inside = false;
446            Node p1, p2;
447    
448            //iterate each side of the polygon, start with the last segment
449            Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
450    
451            for (Node newPoint : polygonNodes) {
452                //skip duplicate points
453                if (newPoint.equals(oldPoint)) {
454                    continue;
455                }
456    
457                //order points so p1.lat <= p2.lat;
458                if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
459                    p1 = oldPoint;
460                    p2 = newPoint;
461                } else {
462                    p1 = newPoint;
463                    p2 = oldPoint;
464                }
465    
466                //test if the line is crossed and if so invert the inside flag.
467                if ((newPoint.getEastNorth().getY() < point.getEastNorth().getY()) == (point.getEastNorth().getY() <= oldPoint.getEastNorth().getY())
468                        && (point.getEastNorth().getX() - p1.getEastNorth().getX()) * (p2.getEastNorth().getY() - p1.getEastNorth().getY())
469                        < (p2.getEastNorth().getX() - p1.getEastNorth().getX()) * (point.getEastNorth().getY() - p1.getEastNorth().getY()))
470                {
471                    inside = !inside;
472                }
473    
474                oldPoint = newPoint;
475            }
476    
477            return inside;
478        }
479    
480        /**
481         * Returns area of a closed way in square meters.
482         * (approximate(?), but should be OK for small areas)
483         *
484         * Relies on the current projection: Works correctly, when
485         * one unit in projected coordinates corresponds to one meter.
486         * This is true for most projections, but not for WGS84 and
487         * Mercator (EPSG:3857).
488         *
489         * @param way Way to measure, should be closed (first node is the same as last node)
490         * @return area of the closed way.
491         */
492        public static double closedWayArea(Way way) {
493    
494            //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
495            double area = 0;
496            Node lastN = null;
497            for (Node n : way.getNodes()) {
498                if (lastN != null) {
499                    n.getEastNorth().getX();
500    
501                    area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
502                }
503                lastN = n;
504            }
505            return Math.abs(area/2);
506        }
507    
508        protected static double calcX(Node p1){
509            double lat1, lon1, lat2, lon2;
510            double dlon, dlat;
511    
512            lat1 = p1.getCoor().lat() * Math.PI / 180.0;
513            lon1 = p1.getCoor().lon() * Math.PI / 180.0;
514            lat2 = lat1;
515            lon2 = 0;
516    
517            dlon = lon2 - lon1;
518            dlat = lat2 - lat1;
519    
520            double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
521            double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
522            return 6367000 * c;
523        }
524    
525        protected static double calcY(Node p1){
526            double lat1, lon1, lat2, lon2;
527            double dlon, dlat;
528    
529            lat1 = p1.getCoor().lat() * Math.PI / 180.0;
530            lon1 = p1.getCoor().lon() * Math.PI / 180.0;
531            lat2 = 0;
532            lon2 = lon1;
533    
534            dlon = lon2 - lon1;
535            dlat = lat2 - lat1;
536    
537            double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
538            double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
539            return 6367000 * c;
540        }
541    
542        /**
543         * Determines whether a way is oriented clockwise.
544         *
545         * Internals: Assuming a closed non-looping way, compute twice the area
546         * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
547         * If the area is negative the way is ordered in a clockwise direction.
548         *
549         * See http://paulbourke.net/geometry/polyarea/
550         *
551         * @param w the way to be checked.
552         * @return true if and only if way is oriented clockwise.
553         * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
554         */
555        public static boolean isClockwise(Way w) {
556            if (!w.isClosed()) {
557                throw new IllegalArgumentException("Way must be closed to check orientation.");
558            }
559    
560            double area2 = 0.;
561            int nodesCount = w.getNodesCount();
562    
563            for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
564                LatLon coorPrev = w.getNode(node - 1).getCoor();
565                LatLon coorCurr = w.getNode(node % nodesCount).getCoor();
566                area2 += coorPrev.lon() * coorCurr.lat();
567                area2 -= coorCurr.lon() * coorPrev.lat();
568            }
569            return area2 < 0;
570        }
571    
572        /**
573         * Returns angle of a segment defined with 2 point coordinates.
574         *
575         * @param p1
576         * @param p2
577         * @return Angle in radians (-pi, pi]
578         */
579        public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
580            return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
581        }
582    
583        /**
584         * Returns angle of a corner defined with 3 point coordinates.
585         *
586         * @param p1
587         * @param p2 Common endpoint
588         * @param p3
589         * @return Angle in radians (-pi, pi]
590         */
591        public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
592            Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
593            if (result <= -Math.PI) {
594                result += 2 * Math.PI;
595            }
596    
597            if (result > Math.PI) {
598                result -= 2 * Math.PI;
599            }
600    
601            return result;
602        }
603        
604        public static EastNorth getCentroid(List<Node> nodes) {
605            // Compute the centroid of nodes
606    
607            BigDecimal area = new BigDecimal(0);
608            BigDecimal north = new BigDecimal(0);
609            BigDecimal east = new BigDecimal(0);
610    
611            // See http://en.wikipedia.org/w/index.php?title=Centroid&oldid=294224857#Centroid_of_polygon for the equation used here
612            for (int i = 0; i < nodes.size(); i++) {
613                EastNorth n0 = nodes.get(i).getEastNorth();
614                EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
615    
616                BigDecimal x0 = new BigDecimal(n0.east());
617                BigDecimal y0 = new BigDecimal(n0.north());
618                BigDecimal x1 = new BigDecimal(n1.east());
619                BigDecimal y1 = new BigDecimal(n1.north());
620    
621                BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
622    
623                area = area.add(k, MathContext.DECIMAL128);
624                east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
625                north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
626            }
627    
628            BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
629            area  = area.multiply(d, MathContext.DECIMAL128);
630            if (area.compareTo(BigDecimal.ZERO) != 0) {
631                north = north.divide(area, MathContext.DECIMAL128);
632                east = east.divide(area, MathContext.DECIMAL128);
633            }
634    
635            return new EastNorth(east.doubleValue(), north.doubleValue());
636        }
637    
638        /**
639         * Returns the coordinate of intersection of segment sp1-sp2 and an altitude
640         * to it starting at point ap. If the line defined with sp1-sp2 intersects
641         * its altitude out of sp1-sp2, null is returned.
642         *
643         * @param sp1
644         * @param sp2
645         * @param ap
646         * @return Intersection coordinate or null
647         */
648        public static EastNorth getSegmentAltituteIntersection(EastNorth sp1,
649                EastNorth sp2, EastNorth ap) {
650            Double segmentLenght = sp1.distance(sp2);
651            Double altitudeAngle = getSegmentAngle(sp1, sp2) + Math.PI / 2;
652    
653            // Taking a random point on the altitude line (angle is known).
654            EastNorth ap2 = new EastNorth(ap.east() + 1000
655                    * Math.cos(altitudeAngle), ap.north() + 1000
656                    * Math.sin(altitudeAngle));
657    
658            // Finding the intersection of two lines
659            EastNorth resultCandidate = Geometry.getLineLineIntersection(sp1, sp2,
660                    ap, ap2);
661    
662            // Filtering result
663            if (resultCandidate != null
664                    && resultCandidate.distance(sp1) * .999 < segmentLenght
665                    && resultCandidate.distance(sp2) * .999 < segmentLenght) {
666                return resultCandidate;
667            } else {
668                return null;
669            }
670        }
671    }