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.OsmPrimitiveType;
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30 | import org.openstreetmap.josm.data.osm.Relation;
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31 | import org.openstreetmap.josm.data.osm.RelationMember;
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32 | import org.openstreetmap.josm.data.osm.Way;
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33 |
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34 | /**
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35 | * Some tools for geometry related tasks.
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36 | *
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37 | * @author viesturs
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38 | */
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39 | public final class Geometry {
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40 |
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41 | private Geometry() {
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42 | // Hide default constructor for utils classes
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43 | }
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44 |
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45 | public enum PolygonIntersection {
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46 | FIRST_INSIDE_SECOND,
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47 | SECOND_INSIDE_FIRST,
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48 | OUTSIDE,
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49 | CROSSING
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50 | }
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51 |
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52 | /**
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53 | * Will find all intersection and add nodes there for list of given ways.
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54 | * Handles self-intersections too.
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55 | * And makes commands to add the intersection points to ways.
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56 | *
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57 | * Prerequisite: no two nodes have the same coordinates.
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58 | *
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59 | * @param ways a list of ways to test
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60 | * @param test if false, do not build list of Commands, just return nodes
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61 | * @param cmds list of commands, typically empty when handed to this method.
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62 | * Will be filled with commands that add intersection nodes to
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63 | * the ways.
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64 | * @return list of new nodes
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65 | */
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66 | public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
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67 |
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68 | int n = ways.size();
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69 | @SuppressWarnings("unchecked")
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70 | List<Node>[] newNodes = new ArrayList[n];
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71 | BBox[] wayBounds = new BBox[n];
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72 | boolean[] changedWays = new boolean[n];
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73 |
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74 | Set<Node> intersectionNodes = new LinkedHashSet<>();
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75 |
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76 | //copy node arrays for local usage.
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77 | for (int pos = 0; pos < n; pos++) {
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78 | newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
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79 | wayBounds[pos] = getNodesBounds(newNodes[pos]);
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80 | changedWays[pos] = false;
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81 | }
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82 |
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83 | //iterate over all way pairs and introduce the intersections
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84 | Comparator<Node> coordsComparator = new NodePositionComparator();
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85 | for (int seg1Way = 0; seg1Way < n; seg1Way++) {
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86 | for (int seg2Way = seg1Way; seg2Way < n; seg2Way++) {
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87 |
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88 | //do not waste time on bounds that do not intersect
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89 | if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
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90 | continue;
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91 | }
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92 |
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93 | List<Node> way1Nodes = newNodes[seg1Way];
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94 | List<Node> way2Nodes = newNodes[seg2Way];
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95 |
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96 | //iterate over primary segmemt
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97 | for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos++) {
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98 |
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99 | //iterate over secondary segment
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100 | int seg2Start = seg1Way != seg2Way ? 0 : seg1Pos + 2; //skip the adjacent segment
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101 |
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102 | for (int seg2Pos = seg2Start; seg2Pos + 1 < way2Nodes.size(); seg2Pos++) {
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103 |
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104 | //need to get them again every time, because other segments may be changed
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105 | Node seg1Node1 = way1Nodes.get(seg1Pos);
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106 | Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
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107 | Node seg2Node1 = way2Nodes.get(seg2Pos);
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108 | Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
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109 |
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110 | int commonCount = 0;
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111 | //test if we have common nodes to add.
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112 | if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
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113 | commonCount++;
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114 |
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115 | if (seg1Way == seg2Way &&
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116 | seg1Pos == 0 &&
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117 | seg2Pos == way2Nodes.size() -2) {
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118 | //do not add - this is first and last segment of the same way.
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119 | } else {
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120 | intersectionNodes.add(seg1Node1);
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121 | }
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122 | }
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123 |
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124 | if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
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125 | commonCount++;
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126 |
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127 | intersectionNodes.add(seg1Node2);
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128 | }
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129 |
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130 | //no common nodes - find intersection
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131 | if (commonCount == 0) {
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132 | EastNorth intersection = getSegmentSegmentIntersection(
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133 | seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
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134 | seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
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135 |
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136 | if (intersection != null) {
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137 | if (test) {
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138 | intersectionNodes.add(seg2Node1);
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139 | return intersectionNodes;
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140 | }
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141 |
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142 | Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
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143 | Node intNode = newNode;
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144 | boolean insertInSeg1 = false;
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145 | boolean insertInSeg2 = false;
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146 | //find if the intersection point is at end point of one of the segments, if so use that point
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147 |
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148 | //segment 1
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149 | if (coordsComparator.compare(newNode, seg1Node1) == 0) {
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150 | intNode = seg1Node1;
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151 | } else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
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152 | intNode = seg1Node2;
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153 | } else {
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154 | insertInSeg1 = true;
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155 | }
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156 |
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157 | //segment 2
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158 | if (coordsComparator.compare(newNode, seg2Node1) == 0) {
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159 | intNode = seg2Node1;
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160 | } else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
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161 | intNode = seg2Node2;
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162 | } else {
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163 | insertInSeg2 = true;
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164 | }
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165 |
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166 | if (insertInSeg1) {
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167 | way1Nodes.add(seg1Pos +1, intNode);
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168 | changedWays[seg1Way] = true;
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169 |
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170 | //fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
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171 | if (seg2Way == seg1Way) {
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172 | seg2Pos++;
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173 | }
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174 | }
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175 |
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176 | if (insertInSeg2) {
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177 | way2Nodes.add(seg2Pos +1, intNode);
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178 | changedWays[seg2Way] = true;
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179 |
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180 | //Do not need to compare again to already split segment
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181 | seg2Pos++;
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182 | }
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183 |
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184 | intersectionNodes.add(intNode);
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185 |
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186 | if (intNode == newNode) {
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187 | cmds.add(new AddCommand(intNode));
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188 | }
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189 | }
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190 | } else if (test && !intersectionNodes.isEmpty())
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191 | return intersectionNodes;
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192 | }
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193 | }
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194 | }
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195 | }
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196 |
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197 |
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198 | for (int pos = 0; pos < ways.size(); pos++) {
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199 | if (!changedWays[pos]) {
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200 | continue;
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201 | }
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202 |
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203 | Way way = ways.get(pos);
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204 | Way newWay = new Way(way);
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205 | newWay.setNodes(newNodes[pos]);
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206 |
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207 | cmds.add(new ChangeCommand(way, newWay));
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208 | }
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209 |
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210 | return intersectionNodes;
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211 | }
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212 |
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213 | private static BBox getNodesBounds(List<Node> nodes) {
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214 |
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215 | BBox bounds = new BBox(nodes.get(0));
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216 | for (Node n: nodes) {
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217 | bounds.add(n.getCoor());
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218 | }
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219 | return bounds;
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220 | }
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221 |
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222 | /**
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223 | * Tests if given point is to the right side of path consisting of 3 points.
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224 | *
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225 | * (Imagine the path is continued beyond the endpoints, so you get two rays
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226 | * starting from lineP2 and going through lineP1 and lineP3 respectively
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227 | * which divide the plane into two parts. The test returns true, if testPoint
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228 | * lies in the part that is to the right when traveling in the direction
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229 | * lineP1, lineP2, lineP3.)
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230 | *
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231 | * @param lineP1 first point in path
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232 | * @param lineP2 second point in path
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233 | * @param lineP3 third point in path
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234 | * @param testPoint point to test
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235 | * @return true if to the right side, false otherwise
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236 | */
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237 | public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
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238 | boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
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239 | boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
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240 | boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
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241 |
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242 | if (pathBendToRight)
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243 | return rightOfSeg1 && rightOfSeg2;
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244 | else
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245 | return !(!rightOfSeg1 && !rightOfSeg2);
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246 | }
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247 |
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248 | /**
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249 | * This method tests if secondNode is clockwise to first node.
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250 | * @param commonNode starting point for both vectors
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251 | * @param firstNode first vector end node
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252 | * @param secondNode second vector end node
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253 | * @return true if first vector is clockwise before second vector.
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254 | */
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255 | public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
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256 | return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
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257 | }
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258 |
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259 | /**
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260 | * Finds the intersection of two line segments
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261 | * @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
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262 | */
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263 | public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
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264 |
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265 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
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266 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
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267 | CheckParameterUtil.ensureValidCoordinates(p3, "p3");
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268 | CheckParameterUtil.ensureValidCoordinates(p4, "p4");
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269 |
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270 | double x1 = p1.getX();
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271 | double y1 = p1.getY();
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272 | double x2 = p2.getX();
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273 | double y2 = p2.getY();
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274 | double x3 = p3.getX();
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275 | double y3 = p3.getY();
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276 | double x4 = p4.getX();
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277 | double y4 = p4.getY();
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278 |
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279 | //TODO: do this locally.
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280 | //TODO: remove this check after careful testing
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281 | if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
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282 |
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283 | // solve line-line intersection in parametric form:
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284 | // (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v
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285 | // (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
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286 | // if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
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287 |
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288 | double a1 = x2 - x1;
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289 | double b1 = x3 - x4;
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290 | double c1 = x3 - x1;
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291 |
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292 | double a2 = y2 - y1;
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293 | double b2 = y3 - y4;
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294 | double c2 = y3 - y1;
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295 |
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296 | // Solve the equations
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297 | double det = a1*b2 - a2*b1;
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298 |
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299 | double uu = b2*c1 - b1*c2;
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300 | double vv = a1*c2 - a2*c1;
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301 | double mag = Math.abs(uu)+Math.abs(vv);
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302 |
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303 | if (Math.abs(det) > 1e-12 * mag) {
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304 | double u = uu/det, v = vv/det;
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305 | if (u > -1e-8 && u < 1+1e-8 && v > -1e-8 && v < 1+1e-8) {
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306 | if (u < 0) u = 0;
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307 | if (u > 1) u = 1.0;
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308 | return new EastNorth(x1+a1*u, y1+a2*u);
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309 | } else {
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310 | return null;
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311 | }
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312 | } else {
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313 | // parallel lines
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314 | return null;
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315 | }
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316 | }
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317 |
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318 | /**
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319 | * Finds the intersection of two lines of infinite length.
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320 | *
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321 | * @param p1 first point on first line
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322 | * @param p2 second point on first line
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323 | * @param p3 first point on second line
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324 | * @param p4 second point on second line
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325 | * @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
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326 | * @throws IllegalArgumentException if a parameter is null or without valid coordinates
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327 | */
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328 | public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
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329 |
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330 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
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331 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
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332 | CheckParameterUtil.ensureValidCoordinates(p3, "p3");
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333 | CheckParameterUtil.ensureValidCoordinates(p4, "p4");
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334 |
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335 | if (!p1.isValid()) throw new IllegalArgumentException(p1+" is invalid");
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336 |
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337 | // Basically, the formula from wikipedia is used:
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338 | // https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
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339 | // However, large numbers lead to rounding errors (see #10286).
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340 | // To avoid this, p1 is first substracted from each of the points:
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341 | // p1' = 0
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342 | // p2' = p2 - p1
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343 | // p3' = p3 - p1
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344 | // p4' = p4 - p1
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345 | // In the end, p1 is added to the intersection point of segment p1'/p2'
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346 | // and segment p3'/p4'.
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347 |
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348 | // Convert line from (point, point) form to ax+by=c
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349 | double a1 = p2.getY() - p1.getY();
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350 | double b1 = p1.getX() - p2.getX();
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351 |
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352 | double a2 = p4.getY() - p3.getY();
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353 | double b2 = p3.getX() - p4.getX();
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354 |
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355 | // Solve the equations
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356 | double det = a1 * b2 - a2 * b1;
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357 | if (det == 0)
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358 | return null; // Lines are parallel
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359 |
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360 | double c2 = (p4.getX() - p1.getX()) * (p3.getY() - p1.getY()) - (p3.getX() - p1.getX()) * (p4.getY() - p1.getY());
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361 |
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362 | return new EastNorth(b1 * c2 / det + p1.getX(), -a1 * c2 / det + p1.getY());
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363 | }
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364 |
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365 | public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
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366 |
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367 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
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368 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
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369 | CheckParameterUtil.ensureValidCoordinates(p3, "p3");
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370 | CheckParameterUtil.ensureValidCoordinates(p4, "p4");
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371 |
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372 | // Convert line from (point, point) form to ax+by=c
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373 | double a1 = p2.getY() - p1.getY();
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374 | double b1 = p1.getX() - p2.getX();
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375 |
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376 | double a2 = p4.getY() - p3.getY();
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377 | double b2 = p3.getX() - p4.getX();
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378 |
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379 | // Solve the equations
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380 | double det = a1 * b2 - a2 * b1;
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381 | // remove influence of of scaling factor
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382 | det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
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383 | return Math.abs(det) < 1e-3;
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384 | }
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385 |
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386 | private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
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387 | CheckParameterUtil.ensureParameterNotNull(p1, "p1");
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388 | CheckParameterUtil.ensureParameterNotNull(p2, "p2");
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389 | CheckParameterUtil.ensureParameterNotNull(point, "point");
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390 |
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391 | double ldx = p2.getX() - p1.getX();
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392 | double ldy = p2.getY() - p1.getY();
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393 |
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394 | //segment zero length
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395 | if (ldx == 0 && ldy == 0)
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396 | return p1;
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397 |
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398 | double pdx = point.getX() - p1.getX();
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399 | double pdy = point.getY() - p1.getY();
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400 |
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401 | double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
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402 |
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403 | if (segmentOnly && offset <= 0)
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404 | return p1;
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405 | else if (segmentOnly && offset >= 1)
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406 | return p2;
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407 | else
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408 | return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
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409 | }
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410 |
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411 | /**
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412 | * Calculates closest point to a line segment.
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413 | * @param segmentP1 First point determining line segment
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414 | * @param segmentP2 Second point determining line segment
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415 | * @param point Point for which a closest point is searched on line segment [P1,P2]
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416 | * @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
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417 | * a new point if closest point is between segmentP1 and segmentP2.
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418 | * @see #closestPointToLine
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419 | * @since 3650
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420 | */
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421 | public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
|
---|
422 | return closestPointTo(segmentP1, segmentP2, point, true);
|
---|
423 | }
|
---|
424 |
|
---|
425 | /**
|
---|
426 | * Calculates closest point to a line.
|
---|
427 | * @param lineP1 First point determining line
|
---|
428 | * @param lineP2 Second point determining line
|
---|
429 | * @param point Point for which a closest point is searched on line (P1,P2)
|
---|
430 | * @return The closest point found on line. It may be outside the segment [P1,P2].
|
---|
431 | * @see #closestPointToSegment
|
---|
432 | * @since 4134
|
---|
433 | */
|
---|
434 | public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
|
---|
435 | return closestPointTo(lineP1, lineP2, point, false);
|
---|
436 | }
|
---|
437 |
|
---|
438 | /**
|
---|
439 | * This method tests if secondNode is clockwise to first node.
|
---|
440 | *
|
---|
441 | * The line through the two points commonNode and firstNode divides the
|
---|
442 | * plane into two parts. The test returns true, if secondNode lies in
|
---|
443 | * the part that is to the right when traveling in the direction from
|
---|
444 | * commonNode to firstNode.
|
---|
445 | *
|
---|
446 | * @param commonNode starting point for both vectors
|
---|
447 | * @param firstNode first vector end node
|
---|
448 | * @param secondNode second vector end node
|
---|
449 | * @return true if first vector is clockwise before second vector.
|
---|
450 | */
|
---|
451 | public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
|
---|
452 |
|
---|
453 | CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
|
---|
454 | CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
|
---|
455 | CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
|
---|
456 |
|
---|
457 | double dy1 = firstNode.getY() - commonNode.getY();
|
---|
458 | double dy2 = secondNode.getY() - commonNode.getY();
|
---|
459 | double dx1 = firstNode.getX() - commonNode.getX();
|
---|
460 | double dx2 = secondNode.getX() - commonNode.getX();
|
---|
461 |
|
---|
462 | return dy1 * dx2 - dx1 * dy2 > 0;
|
---|
463 | }
|
---|
464 |
|
---|
465 | /**
|
---|
466 | * Returns the Area of a polygon, from its list of nodes.
|
---|
467 | * @param polygon List of nodes forming polygon (EastNorth coordinates)
|
---|
468 | * @return Area for the given list of nodes
|
---|
469 | * @since 6841
|
---|
470 | */
|
---|
471 | public static Area getArea(List<Node> polygon) {
|
---|
472 | Path2D path = new Path2D.Double();
|
---|
473 |
|
---|
474 | boolean begin = true;
|
---|
475 | for (Node n : polygon) {
|
---|
476 | EastNorth en = n.getEastNorth();
|
---|
477 | if (en != null) {
|
---|
478 | if (begin) {
|
---|
479 | path.moveTo(en.getX(), en.getY());
|
---|
480 | begin = false;
|
---|
481 | } else {
|
---|
482 | path.lineTo(en.getX(), en.getY());
|
---|
483 | }
|
---|
484 | }
|
---|
485 | }
|
---|
486 | if (!begin) {
|
---|
487 | path.closePath();
|
---|
488 | }
|
---|
489 |
|
---|
490 | return new Area(path);
|
---|
491 | }
|
---|
492 |
|
---|
493 | /**
|
---|
494 | * Returns the Area of a polygon, from its list of nodes.
|
---|
495 | * @param polygon List of nodes forming polygon (LatLon coordinates)
|
---|
496 | * @return Area for the given list of nodes
|
---|
497 | * @since 6841
|
---|
498 | */
|
---|
499 | public static Area getAreaLatLon(List<Node> polygon) {
|
---|
500 | Path2D path = new Path2D.Double();
|
---|
501 |
|
---|
502 | boolean begin = true;
|
---|
503 | for (Node n : polygon) {
|
---|
504 | if (begin) {
|
---|
505 | path.moveTo(n.getCoor().lon(), n.getCoor().lat());
|
---|
506 | begin = false;
|
---|
507 | } else {
|
---|
508 | path.lineTo(n.getCoor().lon(), n.getCoor().lat());
|
---|
509 | }
|
---|
510 | }
|
---|
511 | if (!begin) {
|
---|
512 | path.closePath();
|
---|
513 | }
|
---|
514 |
|
---|
515 | return new Area(path);
|
---|
516 | }
|
---|
517 |
|
---|
518 | /**
|
---|
519 | * Tests if two polygons intersect.
|
---|
520 | * @param first List of nodes forming first polygon
|
---|
521 | * @param second List of nodes forming second polygon
|
---|
522 | * @return intersection kind
|
---|
523 | */
|
---|
524 | public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
|
---|
525 | Area a1 = getArea(first);
|
---|
526 | Area a2 = getArea(second);
|
---|
527 | return polygonIntersection(a1, a2);
|
---|
528 | }
|
---|
529 |
|
---|
530 | /**
|
---|
531 | * Tests if two polygons intersect.
|
---|
532 | * @param a1 Area of first polygon
|
---|
533 | * @param a2 Area of second polygon
|
---|
534 | * @return intersection kind
|
---|
535 | * @since 6841
|
---|
536 | */
|
---|
537 | public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
|
---|
538 | return polygonIntersection(a1, a2, 1.0);
|
---|
539 | }
|
---|
540 |
|
---|
541 | /**
|
---|
542 | * Tests if two polygons intersect.
|
---|
543 | * @param a1 Area of first polygon
|
---|
544 | * @param a2 Area of second polygon
|
---|
545 | * @param eps an area threshold, everything below is considered an empty intersection
|
---|
546 | * @return intersection kind
|
---|
547 | */
|
---|
548 | public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
|
---|
549 |
|
---|
550 | Area inter = new Area(a1);
|
---|
551 | inter.intersect(a2);
|
---|
552 |
|
---|
553 | Rectangle bounds = inter.getBounds();
|
---|
554 |
|
---|
555 | if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
|
---|
556 | return PolygonIntersection.OUTSIDE;
|
---|
557 | } else if (inter.equals(a1)) {
|
---|
558 | return PolygonIntersection.FIRST_INSIDE_SECOND;
|
---|
559 | } else if (inter.equals(a2)) {
|
---|
560 | return PolygonIntersection.SECOND_INSIDE_FIRST;
|
---|
561 | } else {
|
---|
562 | return PolygonIntersection.CROSSING;
|
---|
563 | }
|
---|
564 | }
|
---|
565 |
|
---|
566 | /**
|
---|
567 | * Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
|
---|
568 | * @param polygonNodes list of nodes from polygon path.
|
---|
569 | * @param point the point to test
|
---|
570 | * @return true if the point is inside polygon.
|
---|
571 | */
|
---|
572 | public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
|
---|
573 | if (polygonNodes.size() < 2)
|
---|
574 | return false;
|
---|
575 |
|
---|
576 | //iterate each side of the polygon, start with the last segment
|
---|
577 | Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
|
---|
578 |
|
---|
579 | if (!oldPoint.isLatLonKnown()) {
|
---|
580 | return false;
|
---|
581 | }
|
---|
582 |
|
---|
583 | boolean inside = false;
|
---|
584 | Node p1, p2;
|
---|
585 |
|
---|
586 | for (Node newPoint : polygonNodes) {
|
---|
587 | //skip duplicate points
|
---|
588 | if (newPoint.equals(oldPoint)) {
|
---|
589 | continue;
|
---|
590 | }
|
---|
591 |
|
---|
592 | if (!newPoint.isLatLonKnown()) {
|
---|
593 | return false;
|
---|
594 | }
|
---|
595 |
|
---|
596 | //order points so p1.lat <= p2.lat
|
---|
597 | if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
|
---|
598 | p1 = oldPoint;
|
---|
599 | p2 = newPoint;
|
---|
600 | } else {
|
---|
601 | p1 = newPoint;
|
---|
602 | p2 = oldPoint;
|
---|
603 | }
|
---|
604 |
|
---|
605 | EastNorth pEN = point.getEastNorth();
|
---|
606 | EastNorth opEN = oldPoint.getEastNorth();
|
---|
607 | EastNorth npEN = newPoint.getEastNorth();
|
---|
608 | EastNorth p1EN = p1.getEastNorth();
|
---|
609 | EastNorth p2EN = p2.getEastNorth();
|
---|
610 |
|
---|
611 | if (pEN != null && opEN != null && npEN != null && p1EN != null && p2EN != null) {
|
---|
612 | //test if the line is crossed and if so invert the inside flag.
|
---|
613 | if ((npEN.getY() < pEN.getY()) == (pEN.getY() <= opEN.getY())
|
---|
614 | && (pEN.getX() - p1EN.getX()) * (p2EN.getY() - p1EN.getY())
|
---|
615 | < (p2EN.getX() - p1EN.getX()) * (pEN.getY() - p1EN.getY())) {
|
---|
616 | inside = !inside;
|
---|
617 | }
|
---|
618 | }
|
---|
619 |
|
---|
620 | oldPoint = newPoint;
|
---|
621 | }
|
---|
622 |
|
---|
623 | return inside;
|
---|
624 | }
|
---|
625 |
|
---|
626 | /**
|
---|
627 | * Returns area of a closed way in square meters.
|
---|
628 | * (approximate(?), but should be OK for small areas)
|
---|
629 | *
|
---|
630 | * Relies on the current projection: Works correctly, when
|
---|
631 | * one unit in projected coordinates corresponds to one meter.
|
---|
632 | * This is true for most projections, but not for WGS84 and
|
---|
633 | * Mercator (EPSG:3857).
|
---|
634 | *
|
---|
635 | * @param way Way to measure, should be closed (first node is the same as last node)
|
---|
636 | * @return area of the closed way.
|
---|
637 | */
|
---|
638 | public static double closedWayArea(Way way) {
|
---|
639 |
|
---|
640 | //http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
|
---|
641 | double area = 0;
|
---|
642 | Node lastN = null;
|
---|
643 | for (Node n : way.getNodes()) {
|
---|
644 | if (lastN != null) {
|
---|
645 | area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
|
---|
646 | }
|
---|
647 | lastN = n;
|
---|
648 | }
|
---|
649 | return Math.abs(area/2);
|
---|
650 | }
|
---|
651 |
|
---|
652 | protected static double calcX(Node p1) {
|
---|
653 | double lat1, lon1, lat2, lon2;
|
---|
654 | double dlon, dlat;
|
---|
655 |
|
---|
656 | lat1 = p1.getCoor().lat() * Math.PI / 180.0;
|
---|
657 | lon1 = p1.getCoor().lon() * Math.PI / 180.0;
|
---|
658 | lat2 = lat1;
|
---|
659 | lon2 = 0;
|
---|
660 |
|
---|
661 | dlon = lon2 - lon1;
|
---|
662 | dlat = lat2 - lat1;
|
---|
663 |
|
---|
664 | double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2);
|
---|
665 | double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
|
---|
666 | return 6367000 * c;
|
---|
667 | }
|
---|
668 |
|
---|
669 | protected static double calcY(Node p1) {
|
---|
670 | double lat1, lon1, lat2, lon2;
|
---|
671 | double dlon, dlat;
|
---|
672 |
|
---|
673 | lat1 = p1.getCoor().lat() * Math.PI / 180.0;
|
---|
674 | lon1 = p1.getCoor().lon() * Math.PI / 180.0;
|
---|
675 | lat2 = 0;
|
---|
676 | lon2 = lon1;
|
---|
677 |
|
---|
678 | dlon = lon2 - lon1;
|
---|
679 | dlat = lat2 - lat1;
|
---|
680 |
|
---|
681 | double a = Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2);
|
---|
682 | double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
|
---|
683 | return 6367000 * c;
|
---|
684 | }
|
---|
685 |
|
---|
686 | /**
|
---|
687 | * Determines whether a way is oriented clockwise.
|
---|
688 | *
|
---|
689 | * Internals: Assuming a closed non-looping way, compute twice the area
|
---|
690 | * of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
|
---|
691 | * If the area is negative the way is ordered in a clockwise direction.
|
---|
692 | *
|
---|
693 | * See http://paulbourke.net/geometry/polyarea/
|
---|
694 | *
|
---|
695 | * @param w the way to be checked.
|
---|
696 | * @return true if and only if way is oriented clockwise.
|
---|
697 | * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
|
---|
698 | */
|
---|
699 | public static boolean isClockwise(Way w) {
|
---|
700 | return isClockwise(w.getNodes());
|
---|
701 | }
|
---|
702 |
|
---|
703 | /**
|
---|
704 | * Determines whether path from nodes list is oriented clockwise.
|
---|
705 | * @param nodes Nodes list to be checked.
|
---|
706 | * @return true if and only if way is oriented clockwise.
|
---|
707 | * @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
|
---|
708 | * @see #isClockwise(Way)
|
---|
709 | */
|
---|
710 | public static boolean isClockwise(List<Node> nodes) {
|
---|
711 | int nodesCount = nodes.size();
|
---|
712 | if (nodesCount < 3 || nodes.get(0) != nodes.get(nodesCount - 1)) {
|
---|
713 | throw new IllegalArgumentException("Way must be closed to check orientation.");
|
---|
714 | }
|
---|
715 | double area2 = 0.;
|
---|
716 |
|
---|
717 | for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
|
---|
718 | LatLon coorPrev = nodes.get(node - 1).getCoor();
|
---|
719 | LatLon coorCurr = nodes.get(node % nodesCount).getCoor();
|
---|
720 | area2 += coorPrev.lon() * coorCurr.lat();
|
---|
721 | area2 -= coorCurr.lon() * coorPrev.lat();
|
---|
722 | }
|
---|
723 | return area2 < 0;
|
---|
724 | }
|
---|
725 |
|
---|
726 | /**
|
---|
727 | * Returns angle of a segment defined with 2 point coordinates.
|
---|
728 | *
|
---|
729 | * @param p1 first point
|
---|
730 | * @param p2 second point
|
---|
731 | * @return Angle in radians (-pi, pi]
|
---|
732 | */
|
---|
733 | public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
|
---|
734 |
|
---|
735 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
|
---|
736 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
|
---|
737 |
|
---|
738 | return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
|
---|
739 | }
|
---|
740 |
|
---|
741 | /**
|
---|
742 | * Returns angle of a corner defined with 3 point coordinates.
|
---|
743 | *
|
---|
744 | * @param p1 first point
|
---|
745 | * @param p2 Common endpoint
|
---|
746 | * @param p3 third point
|
---|
747 | * @return Angle in radians (-pi, pi]
|
---|
748 | */
|
---|
749 | public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
|
---|
750 |
|
---|
751 | CheckParameterUtil.ensureValidCoordinates(p1, "p1");
|
---|
752 | CheckParameterUtil.ensureValidCoordinates(p2, "p2");
|
---|
753 | CheckParameterUtil.ensureValidCoordinates(p3, "p3");
|
---|
754 |
|
---|
755 | Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
|
---|
756 | if (result <= -Math.PI) {
|
---|
757 | result += 2 * Math.PI;
|
---|
758 | }
|
---|
759 |
|
---|
760 | if (result > Math.PI) {
|
---|
761 | result -= 2 * Math.PI;
|
---|
762 | }
|
---|
763 |
|
---|
764 | return result;
|
---|
765 | }
|
---|
766 |
|
---|
767 | /**
|
---|
768 | * Compute the centroid/barycenter of nodes
|
---|
769 | * @param nodes Nodes for which the centroid is wanted
|
---|
770 | * @return the centroid of nodes
|
---|
771 | * @see Geometry#getCenter
|
---|
772 | */
|
---|
773 | public static EastNorth getCentroid(List<Node> nodes) {
|
---|
774 |
|
---|
775 | BigDecimal area = BigDecimal.ZERO;
|
---|
776 | BigDecimal north = BigDecimal.ZERO;
|
---|
777 | BigDecimal east = BigDecimal.ZERO;
|
---|
778 |
|
---|
779 | // See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
|
---|
780 | for (int i = 0; i < nodes.size(); i++) {
|
---|
781 | EastNorth n0 = nodes.get(i).getEastNorth();
|
---|
782 | EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
|
---|
783 |
|
---|
784 | if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
|
---|
785 | BigDecimal x0 = BigDecimal.valueOf(n0.east());
|
---|
786 | BigDecimal y0 = BigDecimal.valueOf(n0.north());
|
---|
787 | BigDecimal x1 = BigDecimal.valueOf(n1.east());
|
---|
788 | BigDecimal y1 = BigDecimal.valueOf(n1.north());
|
---|
789 |
|
---|
790 | BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
|
---|
791 |
|
---|
792 | area = area.add(k, MathContext.DECIMAL128);
|
---|
793 | east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
|
---|
794 | north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
|
---|
795 | }
|
---|
796 | }
|
---|
797 |
|
---|
798 | BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
|
---|
799 | area = area.multiply(d, MathContext.DECIMAL128);
|
---|
800 | if (area.compareTo(BigDecimal.ZERO) != 0) {
|
---|
801 | north = north.divide(area, MathContext.DECIMAL128);
|
---|
802 | east = east.divide(area, MathContext.DECIMAL128);
|
---|
803 | }
|
---|
804 |
|
---|
805 | return new EastNorth(east.doubleValue(), north.doubleValue());
|
---|
806 | }
|
---|
807 |
|
---|
808 | /**
|
---|
809 | * Compute center of the circle closest to different nodes.
|
---|
810 | *
|
---|
811 | * Ensure exact center computation in case nodes are already aligned in circle.
|
---|
812 | * This is done by least square method.
|
---|
813 | * Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
|
---|
814 | * Center must be intersection of all bisectors.
|
---|
815 | * <pre>
|
---|
816 | * [ a1 b1 ] [ -c1 ]
|
---|
817 | * With A = [ ... ... ] and Y = [ ... ]
|
---|
818 | * [ an bn ] [ -cn ]
|
---|
819 | * </pre>
|
---|
820 | * An approximation of center of circle is (At.A)^-1.At.Y
|
---|
821 | * @param nodes Nodes parts of the circle (at least 3)
|
---|
822 | * @return An approximation of the center, of null if there is no solution.
|
---|
823 | * @see Geometry#getCentroid
|
---|
824 | * @since 6934
|
---|
825 | */
|
---|
826 | public static EastNorth getCenter(List<Node> nodes) {
|
---|
827 | int nc = nodes.size();
|
---|
828 | if (nc < 3) return null;
|
---|
829 | /**
|
---|
830 | * Equation of each bisector ax + by + c = 0
|
---|
831 | */
|
---|
832 | double[] a = new double[nc];
|
---|
833 | double[] b = new double[nc];
|
---|
834 | double[] c = new double[nc];
|
---|
835 | // Compute equation of bisector
|
---|
836 | for (int i = 0; i < nc; i++) {
|
---|
837 | EastNorth pt1 = nodes.get(i).getEastNorth();
|
---|
838 | EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
|
---|
839 | a[i] = pt1.east() - pt2.east();
|
---|
840 | b[i] = pt1.north() - pt2.north();
|
---|
841 | double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
|
---|
842 | if (d == 0) return null;
|
---|
843 | a[i] /= d;
|
---|
844 | b[i] /= d;
|
---|
845 | double xC = (pt1.east() + pt2.east()) / 2;
|
---|
846 | double yC = (pt1.north() + pt2.north()) / 2;
|
---|
847 | c[i] = -(a[i]*xC + b[i]*yC);
|
---|
848 | }
|
---|
849 | // At.A = [aij]
|
---|
850 | double a11 = 0, a12 = 0, a22 = 0;
|
---|
851 | // At.Y = [bi]
|
---|
852 | double b1 = 0, b2 = 0;
|
---|
853 | for (int i = 0; i < nc; i++) {
|
---|
854 | a11 += a[i]*a[i];
|
---|
855 | a12 += a[i]*b[i];
|
---|
856 | a22 += b[i]*b[i];
|
---|
857 | b1 -= a[i]*c[i];
|
---|
858 | b2 -= b[i]*c[i];
|
---|
859 | }
|
---|
860 | // (At.A)^-1 = [invij]
|
---|
861 | double det = a11*a22 - a12*a12;
|
---|
862 | if (Math.abs(det) < 1e-5) return null;
|
---|
863 | double inv11 = a22/det;
|
---|
864 | double inv12 = -a12/det;
|
---|
865 | double inv22 = a11/det;
|
---|
866 | // center (xC, yC) = (At.A)^-1.At.y
|
---|
867 | double xC = inv11*b1 + inv12*b2;
|
---|
868 | double yC = inv12*b1 + inv22*b2;
|
---|
869 | return new EastNorth(xC, yC);
|
---|
870 | }
|
---|
871 |
|
---|
872 | public static class MultiPolygonMembers {
|
---|
873 | public final Set<Way> outers = new HashSet<>();
|
---|
874 | public final Set<Way> inners = new HashSet<>();
|
---|
875 |
|
---|
876 | public MultiPolygonMembers(Relation multiPolygon) {
|
---|
877 | for (RelationMember m : multiPolygon.getMembers()) {
|
---|
878 | if (m.getType().equals(OsmPrimitiveType.WAY)) {
|
---|
879 | if ("outer".equals(m.getRole())) {
|
---|
880 | outers.add(m.getWay());
|
---|
881 | } else if ("inner".equals(m.getRole())) {
|
---|
882 | inners.add(m.getWay());
|
---|
883 | }
|
---|
884 | }
|
---|
885 | }
|
---|
886 | }
|
---|
887 | }
|
---|
888 |
|
---|
889 | /**
|
---|
890 | * Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
|
---|
891 | * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
|
---|
892 | * @param node node
|
---|
893 | * @param multiPolygon multipolygon
|
---|
894 | * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
|
---|
895 | * @return {@code true} if the node is inside the multipolygon
|
---|
896 | */
|
---|
897 | public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
|
---|
898 | return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
|
---|
899 | }
|
---|
900 |
|
---|
901 | /**
|
---|
902 | * Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
|
---|
903 | * {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
|
---|
904 | * <p>
|
---|
905 | * If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
|
---|
906 | * @param nodes nodes forming the polygon
|
---|
907 | * @param multiPolygon multipolygon
|
---|
908 | * @param isOuterWayAMatch allows to decide if the immediate {@code outer} way of the multipolygon is a match
|
---|
909 | * @return {@code true} if the polygon formed by nodes is inside the multipolygon
|
---|
910 | */
|
---|
911 | public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
|
---|
912 | // Extract outer/inner members from multipolygon
|
---|
913 | final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
|
---|
914 | // Construct complete rings for the inner/outer members
|
---|
915 | final List<MultipolygonBuilder.JoinedPolygon> outerRings;
|
---|
916 | final List<MultipolygonBuilder.JoinedPolygon> innerRings;
|
---|
917 | try {
|
---|
918 | outerRings = MultipolygonBuilder.joinWays(mpm.outers);
|
---|
919 | innerRings = MultipolygonBuilder.joinWays(mpm.inners);
|
---|
920 | } catch (MultipolygonBuilder.JoinedPolygonCreationException ex) {
|
---|
921 | Main.debug("Invalid multipolygon " + multiPolygon);
|
---|
922 | return false;
|
---|
923 | }
|
---|
924 | // Test if object is inside an outer member
|
---|
925 | for (MultipolygonBuilder.JoinedPolygon out : outerRings) {
|
---|
926 | if (nodes.size() == 1
|
---|
927 | ? nodeInsidePolygon(nodes.get(0), out.getNodes())
|
---|
928 | : EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(
|
---|
929 | polygonIntersection(nodes, out.getNodes()))) {
|
---|
930 | boolean insideInner = false;
|
---|
931 | // If inside an outer, check it is not inside an inner
|
---|
932 | for (MultipolygonBuilder.JoinedPolygon in : innerRings) {
|
---|
933 | if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
|
---|
934 | && (nodes.size() == 1
|
---|
935 | ? nodeInsidePolygon(nodes.get(0), in.getNodes())
|
---|
936 | : polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
|
---|
937 | insideInner = true;
|
---|
938 | break;
|
---|
939 | }
|
---|
940 | }
|
---|
941 | // Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
|
---|
942 | if (!insideInner) {
|
---|
943 | // Final check using predicate
|
---|
944 | if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0)
|
---|
945 | /* TODO give a better representation of the outer ring to the predicate */)) {
|
---|
946 | return true;
|
---|
947 | }
|
---|
948 | }
|
---|
949 | }
|
---|
950 | }
|
---|
951 | return false;
|
---|
952 | }
|
---|
953 |
|
---|
954 | /**
|
---|
955 | * Data class to hold two double values (area and perimeter of a polygon).
|
---|
956 | */
|
---|
957 | public static class AreaAndPerimeter {
|
---|
958 | private final double area;
|
---|
959 | private final double perimeter;
|
---|
960 |
|
---|
961 | public AreaAndPerimeter(double area, double perimeter) {
|
---|
962 | this.area = area;
|
---|
963 | this.perimeter = perimeter;
|
---|
964 | }
|
---|
965 |
|
---|
966 | public double getArea() {
|
---|
967 | return area;
|
---|
968 | }
|
---|
969 |
|
---|
970 | public double getPerimeter() {
|
---|
971 | return perimeter;
|
---|
972 | }
|
---|
973 | }
|
---|
974 |
|
---|
975 | /**
|
---|
976 | * Calculate area and perimeter length of a polygon.
|
---|
977 | *
|
---|
978 | * Uses current projection; units are that of the projected coordinates.
|
---|
979 | *
|
---|
980 | * @param nodes the list of nodes representing the polygon
|
---|
981 | * @return area and perimeter
|
---|
982 | */
|
---|
983 | public static AreaAndPerimeter getAreaAndPerimeter(List<Node> nodes) {
|
---|
984 | double area = 0;
|
---|
985 | double perimeter = 0;
|
---|
986 | if (!nodes.isEmpty()) {
|
---|
987 | boolean closed = nodes.get(0) == nodes.get(nodes.size() - 1);
|
---|
988 | int numSegments = closed ? nodes.size() - 1 : nodes.size();
|
---|
989 | EastNorth p1 = nodes.get(0).getEastNorth();
|
---|
990 | for (int i = 1; i <= numSegments; i++) {
|
---|
991 | EastNorth p2 = nodes.get(i == numSegments ? 0 : i).getEastNorth();
|
---|
992 | area += p1.east() * p2.north() - p2.east() * p1.north();
|
---|
993 | perimeter += p1.distance(p2);
|
---|
994 | p1 = p2;
|
---|
995 | }
|
---|
996 | }
|
---|
997 | return new AreaAndPerimeter(Math.abs(area) / 2, perimeter);
|
---|
998 | }
|
---|
999 | }
|
---|