1 | // License: GPL. For details, see LICENSE file.
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2 | package org.openstreetmap.josm.tools;
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3 |
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4 | import java.awt.Rectangle;
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5 | import java.awt.geom.Area;
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6 | import java.awt.geom.Line2D;
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7 | import java.awt.geom.Path2D;
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8 | import java.math.BigDecimal;
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9 | import java.math.MathContext;
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10 | import java.util.ArrayList;
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11 | import java.util.Collections;
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12 | import java.util.Comparator;
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13 | import java.util.EnumSet;
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14 | import java.util.HashSet;
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15 | import java.util.LinkedHashSet;
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16 | import java.util.List;
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17 | import java.util.Set;
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18 |
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19 | import org.openstreetmap.josm.Main;
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20 | import org.openstreetmap.josm.command.AddCommand;
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21 | import org.openstreetmap.josm.command.ChangeCommand;
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22 | import org.openstreetmap.josm.command.Command;
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23 | import org.openstreetmap.josm.data.coor.EastNorth;
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24 | import org.openstreetmap.josm.data.coor.LatLon;
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25 | import org.openstreetmap.josm.data.osm.BBox;
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26 | import org.openstreetmap.josm.data.osm.MultipolygonBuilder;
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27 | import org.openstreetmap.josm.data.osm.Node;
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28 | import org.openstreetmap.josm.data.osm.NodePositionComparator;
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29 | import org.openstreetmap.josm.data.osm.OsmPrimitive;
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30 | import org.openstreetmap.josm.data.osm.OsmPrimitiveType;
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31 | import org.openstreetmap.josm.data.osm.Relation;
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32 | import org.openstreetmap.josm.data.osm.RelationMember;
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33 | import org.openstreetmap.josm.data.osm.Way;
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34 | import org.openstreetmap.josm.data.osm.visitor.paint.relations.Multipolygon;
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35 | import org.openstreetmap.josm.data.osm.visitor.paint.relations.MultipolygonCache;
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36 | import org.openstreetmap.josm.data.projection.Projection;
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37 | import org.openstreetmap.josm.data.projection.Projections;
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38 |
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39 | /**
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40 | * Some tools for geometry related tasks.
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41 | *
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42 | * @author viesturs
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43 | */
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44 | public final class Geometry {
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45 |
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46 | private Geometry() {
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47 | // Hide default constructor for utils classes
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48 | }
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49 |
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50 | public enum PolygonIntersection {
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51 | FIRST_INSIDE_SECOND,
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52 | SECOND_INSIDE_FIRST,
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53 | OUTSIDE,
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54 | CROSSING
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55 | }
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56 |
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57 | /**
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58 | * Will find all intersection and add nodes there for list of given ways.
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59 | * Handles self-intersections too.
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60 | * And makes commands to add the intersection points to ways.
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61 | *
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62 | * Prerequisite: no two nodes have the same coordinates.
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63 | *
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64 | * @param ways a list of ways to test
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65 | * @param test if false, do not build list of Commands, just return nodes
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66 | * @param cmds list of commands, typically empty when handed to this method.
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67 | * Will be filled with commands that add intersection nodes to
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68 | * the ways.
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69 | * @return list of new nodes
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70 | */
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71 | public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
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72 |
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73 | int n = ways.size();
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74 | @SuppressWarnings("unchecked")
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75 | List<Node>[] newNodes = new ArrayList[n];
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76 | BBox[] wayBounds = new BBox[n];
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77 | boolean[] changedWays = new boolean[n];
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78 |
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79 | Set<Node> intersectionNodes = new LinkedHashSet<>();
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80 |
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81 | //copy node arrays for local usage.
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82 | for (int pos = 0; pos < n; pos++) {
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83 | newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
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84 | wayBounds[pos] = getNodesBounds(newNodes[pos]);
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85 | changedWays[pos] = false;
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86 | }
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87 |
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88 | //iterate over all way pairs and introduce the intersections
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89 | Comparator<Node> coordsComparator = new NodePositionComparator();
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90 | for (int seg1Way = 0; seg1Way < n; seg1Way++) {
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91 | for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
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92 |
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93 | //do not waste time on bounds that do not intersect
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94 | if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
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95 | continue;
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96 | }
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97 |
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98 | List<Node> way1Nodes = newNodes[seg1Way];
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99 | List<Node> way2Nodes = newNodes[seg2Way];
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100 |
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101 | //iterate over primary segmemt
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102 | for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
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103 |
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104 | //iterate over secondary segment
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105 | int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
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106 |
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107 | for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
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108 |
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109 | //need to get them again every time, because other segments may be changed
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110 | Node seg1Node1 = way1Nodes.get(seg1Pos);
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111 | Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
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112 | Node seg2Node1 = way2Nodes.get(seg2Pos);
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113 | Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
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114 |
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115 | int commonCount = 0;
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116 | //test if we have common nodes to add.
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117 | if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
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118 | commonCount++;
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119 |
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120 | if (seg1Way == seg2Way &&
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121 | seg1Pos == 0 &&
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122 | seg2Pos == way2Nodes.size() -2) {
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123 | //do not add - this is first and last segment of the same way.
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124 | } else {
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125 | intersectionNodes.add(seg1Node1);
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126 | }
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127 | }
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128 |
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129 | if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
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130 | commonCount++;
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131 |
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132 | intersectionNodes.add(seg1Node2);
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133 | }
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134 |
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135 | //no common nodes - find intersection
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136 | if (commonCount == 0) {
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137 | EastNorth intersection = getSegmentSegmentIntersection(
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138 | seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
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139 | seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
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140 |
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141 | if (intersection != null) {
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142 | if (test) {
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143 | intersectionNodes.add(seg2Node1);
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144 | return intersectionNodes;
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145 | }
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146 |
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147 | Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
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148 | Node intNode = newNode;
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149 | boolean insertInSeg1 = false;
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150 | boolean insertInSeg2 = false;
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151 | //find if the intersection point is at end point of one of the segments, if so use that point
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152 |
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153 | //segment 1
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154 | if (coordsComparator.compare(newNode, seg1Node1) == 0) {
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155 | intNode = seg1Node1;
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156 | } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
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157 | intNode = seg1Node2;
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158 | } else {
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159 | insertInSeg1 = true;
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160 | }
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161 |
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162 | //segment 2
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163 | if (coordsComparator.compare(newNode, seg2Node1) == 0) {
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164 | intNode = seg2Node1;
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165 | } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
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166 | intNode = seg2Node2;
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167 | } else {
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168 | insertInSeg2 = true;
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169 | }
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170 |
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171 | if (insertInSeg1) {
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172 | way1Nodes.add(seg1Pos +1, intNode);
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173 | changedWays[seg1Way] = true;
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174 |
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175 | //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
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176 | if (seg2Way == seg1Way) {
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177 | seg2Pos++;
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178 | }
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179 | }
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180 |
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181 | if (insertInSeg2) {
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182 | way2Nodes.add(seg2Pos +1, intNode);
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183 | changedWays[seg2Way] = true;
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184 |
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185 | //Do not need to compare again to already split segment
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186 | seg2Pos++;
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187 | }
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188 |
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189 | intersectionNodes.add(intNode);
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190 |
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191 | if (intNode == newNode) {
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192 | cmds.add(new AddCommand(intNode));
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193 | }
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194 | }
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195 | } else if (test && !intersectionNodes.isEmpty())
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196 | return intersectionNodes;
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197 | }
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198 | }
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199 | }
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200 | }
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201 |
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202 |
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203 | for (int pos = 0; pos < ways.size(); pos++) {
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204 | if (!changedWays[pos]) {
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205 | continue;
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206 | }
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207 |
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208 | Way way = ways.get(pos);
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209 | Way newWay = new Way(way);
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210 | newWay.setNodes(newNodes[pos]);
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211 |
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212 | cmds.add(new ChangeCommand(way, newWay));
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213 | }
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214 |
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215 | return intersectionNodes;
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216 | }
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217 |
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218 | private static BBox getNodesBounds(List<Node> nodes) {
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219 |
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220 | BBox bounds = new BBox(nodes.get(0));
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221 | for (Node n: nodes) {
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222 | bounds.add(n.getCoor());
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223 | }
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224 | return bounds;
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225 | }
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226 |
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227 | /**
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228 | * Tests if given point is to the right side of path consisting of 3 points.
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229 | *
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230 | * (Imagine the path is continued beyond the endpoints, so you get two rays
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231 | * starting from lineP2 and going through lineP1 and lineP3 respectively
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232 | * which divide the plane into two parts. The test returns true, if testPoint
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233 | * lies in the part that is to the right when traveling in the direction
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234 | * lineP1, lineP2, lineP3.)
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235 | *
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236 | * @param lineP1 first point in path
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237 | * @param lineP2 second point in path
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238 | * @param lineP3 third point in path
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239 | * @param testPoint point to test
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240 | * @return true if to the right side, false otherwise
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241 | */
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242 | public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
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243 | boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
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244 | boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
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245 | boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
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246 |
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247 | if (pathBendToRight)
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248 | return rightOfSeg1 && rightOfSeg2;
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249 | else
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250 | return !(!rightOfSeg1 && !rightOfSeg2);
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251 | }
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252 |
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253 | /**
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254 | * This method tests if secondNode is clockwise to first node.
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255 | * @param commonNode starting point for both vectors
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256 | * @param firstNode first vector end node
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257 | * @param secondNode second vector end node
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258 | * @return true if first vector is clockwise before second vector.
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259 | */
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260 | public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
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261 | return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
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262 | }
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263 |
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264 | /**
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265 | * Finds the intersection of two line segments.
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266 | * @param p1 the coordinates of the start point of the first specified line segment
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267 | * @param p2 the coordinates of the end point of the first specified line segment
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268 | * @param p3 the coordinates of the start point of the second specified line segment
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269 | * @param p4 the coordinates of the end point of the second specified line segment
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270 | * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
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271 | */
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272 | public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
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273 |
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274 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
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275 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
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276 | CheckParameterUtil.ensureValidCoordinates(p3, "p3");
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277 | CheckParameterUtil.ensureValidCoordinates(p4, "p4");
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278 |
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279 | double x1 = p1.getX();
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280 | double y1 = p1.getY();
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281 | double x2 = p2.getX();
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282 | double y2 = p2.getY();
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283 | double x3 = p3.getX();
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284 | double y3 = p3.getY();
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285 | double x4 = p4.getX();
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286 | double y4 = p4.getY();
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287 |
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288 | //TODO: do this locally.
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289 | //TODO: remove this check after careful testing
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290 | if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
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291 |
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292 | // solve line-line intersection in parametric form:
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293 | // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v
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294 | // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
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295 | // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
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296 |
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297 | double a1 = x2 - x1;
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298 | double b1 = x3 - x4;
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299 | double c1 = x3 - x1;
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300 |
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301 | double a2 = y2 - y1;
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302 | double b2 = y3 - y4;
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303 | double c2 = y3 - y1;
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304 |
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305 | // Solve the equations
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306 | double det = a1*b2 - a2*b1;
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307 |
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308 | double uu = b2*c1 - b1*c2;
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309 | double vv = a1*c2 - a2*c1;
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310 | double mag = Math.abs(uu)+Math.abs(vv);
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311 |
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312 | if (Math.abs(det) > 1e-12 * mag) {
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313 | double u = uu/det, v = vv/det;
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314 | if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
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315 | if (u < 0) u = 0;
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316 | if (u > 1) u = 1.0;
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317 | return new EastNorth(x1+a1*u, y1+a2*u);
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318 | } else {
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319 | return null;
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320 | }
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321 | } else {
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322 | // parallel lines
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323 | return null;
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324 | }
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325 | }
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326 |
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327 | /**
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328 | * Finds the intersection of two lines of infinite length.
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329 | *
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330 | * @param p1 first point on first line
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331 | * @param p2 second point on first line
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332 | * @param p3 first point on second line
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333 | * @param p4 second point on second line
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334 | * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
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335 | * @throws IllegalArgumentException if a parameter is null or without valid coordinates
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336 | */
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337 | public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
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338 |
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339 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
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340 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
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341 | CheckParameterUtil.ensureValidCoordinates(p3, "p3");
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342 | CheckParameterUtil.ensureValidCoordinates(p4, "p4");
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343 |
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344 | if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
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345 |
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346 | // Basically, the formula from wikipedia is used:
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347 | // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
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348 | // However, large numbers lead to rounding errors (see #10286).
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349 | // To avoid this, p1 is first substracted from each of the points:
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350 | // p1' = 0
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351 | // p2' = p2 - p1
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352 | // p3' = p3 - p1
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353 | // p4' = p4 - p1
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354 | // In the end, p1 is added to the intersection point of segment p1'/p2'
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355 | // and segment p3'/p4'.
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356 |
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357 | // Convert line from (point, point) form to ax+by=c
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358 | double a1 = p2.getY() - p1.getY();
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359 | double b1 = p1.getX() - p2.getX();
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360 |
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361 | double a2 = p4.getY() - p3.getY();
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362 | double b2 = p3.getX() - p4.getX();
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363 |
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364 | // Solve the equations
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365 | double det = a1 * b2 - a2 * b1;
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366 | if (det == 0)
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367 | return null; // Lines are parallel
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368 |
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369 | double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
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370 |
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371 | return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
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372 | }
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373 |
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374 | public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
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375 |
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376 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
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377 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
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378 | CheckParameterUtil.ensureValidCoordinates(p3, "p3");
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379 | CheckParameterUtil.ensureValidCoordinates(p4, "p4");
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380 |
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381 | // Convert line from (point, point) form to ax+by=c
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382 | double a1 = p2.getY() - p1.getY();
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383 | double b1 = p1.getX() - p2.getX();
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384 |
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385 | double a2 = p4.getY() - p3.getY();
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386 | double b2 = p3.getX() - p4.getX();
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387 |
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388 | // Solve the equations
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389 | double det = a1 * b2 - a2 * b1;
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390 | // remove influence of of scaling factor
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391 | det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
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392 | return Math.abs(det) < 1e-3;
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393 | }
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394 |
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395 | private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
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396 | CheckParameterUtil.ensureParameterNotNull(p1, "p1");
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397 | CheckParameterUtil.ensureParameterNotNull(p2, "p2");
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398 | CheckParameterUtil.ensureParameterNotNull(point, "point");
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399 |
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400 | double ldx = p2.getX() - p1.getX();
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401 | double ldy = p2.getY() - p1.getY();
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402 |
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403 | //segment zero length
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404 | if (ldx == 0 && ldy == 0)
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405 | return p1;
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406 |
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407 | double pdx = point.getX() - p1.getX();
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408 | double pdy = point.getY() - p1.getY();
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409 |
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410 | double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
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411 |
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412 | if (segmentOnly && offset <= 0)
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413 | return p1;
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414 | else if (segmentOnly && offset >= 1)
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415 | return p2;
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416 | else
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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.trace(ex);
|
---|
914 | Main.debug("Invalid multipolygon " + multiPolygon);
|
---|
915 | return false;
|
---|
916 | }
|
---|
917 | // Test if object is inside an outer member
|
---|
918 | for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
|
---|
919 | if (nodes.size() == 1
|
---|
920 | ? nodeInsidePolygon(nodes.get(0), out.getNodes())
|
---|
921 | : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
|
---|
922 | polygonIntersection(nodes, out.getNodes()))) {
|
---|
923 | boolean insideInner = false;
|
---|
924 | // If inside an outer, check it is not inside an inner
|
---|
925 | for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
|
---|
926 | if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
|
---|
927 | && (nodes.size() == 1
|
---|
928 | ? nodeInsidePolygon(nodes.get(0), in.getNodes())
|
---|
929 | : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
|
---|
930 | insideInner = true;
|
---|
931 | break;
|
---|
932 | }
|
---|
933 | }
|
---|
934 | // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
|
---|
935 | if (!insideInner) {
|
---|
936 | // Final check using predicate
|
---|
937 | if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0)
|
---|
938 | /* TODO give a better representation of the outer ring to the predicate */)) {
|
---|
939 | return true;
|
---|
940 | }
|
---|
941 | }
|
---|
942 | }
|
---|
943 | }
|
---|
944 | return false;
|
---|
945 | }
|
---|
946 |
|
---|
947 | /**
|
---|
948 | * Data class to hold two double values (area and perimeter of a polygon).
|
---|
949 | */
|
---|
950 | public static class AreaAndPerimeter {
|
---|
951 | private final double area;
|
---|
952 | private final double perimeter;
|
---|
953 |
|
---|
954 | public AreaAndPerimeter(double area, double perimeter) {
|
---|
955 | this.area = area;
|
---|
956 | this.perimeter = perimeter;
|
---|
957 | }
|
---|
958 |
|
---|
959 | public double getArea() {
|
---|
960 | return area;
|
---|
961 | }
|
---|
962 |
|
---|
963 | public double getPerimeter() {
|
---|
964 | return perimeter;
|
---|
965 | }
|
---|
966 | }
|
---|
967 |
|
---|
968 | /**
|
---|
969 | * Calculate area and perimeter length of a polygon.
|
---|
970 | *
|
---|
971 | * Uses current projection; units are that of the projected coordinates.
|
---|
972 | *
|
---|
973 | * @param nodes the list of nodes representing the polygon
|
---|
974 | * @return area and perimeter
|
---|
975 | */
|
---|
976 | public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) {
|
---|
977 | return getAreaAndPerimeter(nodes, null);
|
---|
978 | }
|
---|
979 |
|
---|
980 | /**
|
---|
981 | * Calculate area and perimeter length of a polygon in the given projection.
|
---|
982 | *
|
---|
983 | * @param nodes the list of nodes representing the polygon
|
---|
984 | * @param projection the projection to use for the calculation, {@code null} defaults to {@link Main#getProjection()}
|
---|
985 | * @return area and perimeter
|
---|
986 | */
|
---|
987 | public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes, Projection projection) {
|
---|
988 | CheckParameterUtil.ensureParameterNotNull(nodes, "nodes");
|
---|
989 | double area = 0;
|
---|
990 | double perimeter = 0;
|
---|
991 | if (!nodes.isEmpty()) {
|
---|
992 | boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1);
|
---|
993 | int numSegments = closed ? nodes.size() - 1 : nodes.size();
|
---|
994 | EastNorth p1 = projection == null ? nodes.get(0).getEastNorth() : projection.latlon2eastNorth(nodes.get(0).getCoor());
|
---|
995 | for (int i = 1; i <= numSegments; i++) {
|
---|
996 | final Node node = nodes.get(i == numSegments ? 0 : i);
|
---|
997 | final EastNorth p2 = projection == null ? node.getEastNorth() : projection.latlon2eastNorth(node.getCoor());
|
---|
998 | area += p1.east() * p2.north() - p2.east() * p1.north();
|
---|
999 | perimeter += p1.distance(p2);
|
---|
1000 | p1 = p2;
|
---|
1001 | }
|
---|
1002 | }
|
---|
1003 | return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
|
---|
1004 | }
|
---|
1005 | }
|
---|