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1 /* |
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2 * Copyright 1998-2006 Sun Microsystems, Inc. All Rights Reserved. |
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3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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4 * |
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5 * This code is free software; you can redistribute it and/or modify it |
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6 * under the terms of the GNU General Public License version 2 only, as |
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7 * published by the Free Software Foundation. Sun designates this |
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8 * particular file as subject to the "Classpath" exception as provided |
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9 * by Sun in the LICENSE file that accompanied this code. |
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10 * |
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11 * This code is distributed in the hope that it will be useful, but WITHOUT |
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12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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14 * version 2 for more details (a copy is included in the LICENSE file that |
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15 * accompanied this code). |
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16 * |
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17 * You should have received a copy of the GNU General Public License version |
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18 * 2 along with this work; if not, write to the Free Software Foundation, |
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19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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20 * |
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21 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara, |
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22 * CA 95054 USA or visit www.sun.com if you need additional information or |
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23 * have any questions. |
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24 */ |
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25 |
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26 package sun.awt.geom; |
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27 |
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28 import java.awt.geom.Rectangle2D; |
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29 import java.awt.geom.QuadCurve2D; |
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30 import java.awt.geom.CubicCurve2D; |
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31 import java.awt.geom.PathIterator; |
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32 import java.awt.geom.IllegalPathStateException; |
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33 import java.util.Vector; |
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34 |
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35 public abstract class Curve { |
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36 public static final int INCREASING = 1; |
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37 public static final int DECREASING = -1; |
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38 |
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39 protected int direction; |
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40 |
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41 public static void insertMove(Vector curves, double x, double y) { |
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42 curves.add(new Order0(x, y)); |
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43 } |
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44 |
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45 public static void insertLine(Vector curves, |
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46 double x0, double y0, |
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47 double x1, double y1) |
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48 { |
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49 if (y0 < y1) { |
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50 curves.add(new Order1(x0, y0, |
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51 x1, y1, |
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52 INCREASING)); |
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53 } else if (y0 > y1) { |
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54 curves.add(new Order1(x1, y1, |
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55 x0, y0, |
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56 DECREASING)); |
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57 } else { |
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58 // Do not add horizontal lines |
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59 } |
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60 } |
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61 |
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62 public static void insertQuad(Vector curves, |
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63 double x0, double y0, |
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64 double coords[]) |
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65 { |
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66 double y1 = coords[3]; |
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67 if (y0 > y1) { |
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68 Order2.insert(curves, coords, |
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69 coords[2], y1, |
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70 coords[0], coords[1], |
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71 x0, y0, |
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72 DECREASING); |
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73 } else if (y0 == y1 && y0 == coords[1]) { |
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74 // Do not add horizontal lines |
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75 return; |
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76 } else { |
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77 Order2.insert(curves, coords, |
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78 x0, y0, |
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79 coords[0], coords[1], |
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80 coords[2], y1, |
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81 INCREASING); |
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82 } |
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83 } |
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84 |
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85 public static void insertCubic(Vector curves, |
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86 double x0, double y0, |
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87 double coords[]) |
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88 { |
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89 double y1 = coords[5]; |
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90 if (y0 > y1) { |
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91 Order3.insert(curves, coords, |
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92 coords[4], y1, |
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93 coords[2], coords[3], |
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94 coords[0], coords[1], |
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95 x0, y0, |
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96 DECREASING); |
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97 } else if (y0 == y1 && y0 == coords[1] && y0 == coords[3]) { |
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98 // Do not add horizontal lines |
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99 return; |
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100 } else { |
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101 Order3.insert(curves, coords, |
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102 x0, y0, |
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103 coords[0], coords[1], |
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104 coords[2], coords[3], |
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105 coords[4], y1, |
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106 INCREASING); |
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107 } |
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108 } |
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109 |
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110 /** |
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111 * Calculates the number of times the given path |
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112 * crosses the ray extending to the right from (px,py). |
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113 * If the point lies on a part of the path, |
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114 * then no crossings are counted for that intersection. |
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115 * +1 is added for each crossing where the Y coordinate is increasing |
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116 * -1 is added for each crossing where the Y coordinate is decreasing |
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117 * The return value is the sum of all crossings for every segment in |
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118 * the path. |
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119 * The path must start with a SEG_MOVETO, otherwise an exception is |
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120 * thrown. |
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121 * The caller must check p[xy] for NaN values. |
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122 * The caller may also reject infinite p[xy] values as well. |
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123 */ |
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124 public static int pointCrossingsForPath(PathIterator pi, |
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125 double px, double py) |
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126 { |
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127 if (pi.isDone()) { |
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128 return 0; |
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129 } |
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130 double coords[] = new double[6]; |
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131 if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) { |
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132 throw new IllegalPathStateException("missing initial moveto "+ |
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133 "in path definition"); |
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134 } |
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135 pi.next(); |
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136 double movx = coords[0]; |
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137 double movy = coords[1]; |
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138 double curx = movx; |
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139 double cury = movy; |
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140 double endx, endy; |
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141 int crossings = 0; |
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142 while (!pi.isDone()) { |
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143 switch (pi.currentSegment(coords)) { |
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144 case PathIterator.SEG_MOVETO: |
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145 if (cury != movy) { |
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146 crossings += pointCrossingsForLine(px, py, |
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147 curx, cury, |
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148 movx, movy); |
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149 } |
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150 movx = curx = coords[0]; |
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151 movy = cury = coords[1]; |
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152 break; |
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153 case PathIterator.SEG_LINETO: |
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154 endx = coords[0]; |
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155 endy = coords[1]; |
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156 crossings += pointCrossingsForLine(px, py, |
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157 curx, cury, |
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158 endx, endy); |
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159 curx = endx; |
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160 cury = endy; |
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161 break; |
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162 case PathIterator.SEG_QUADTO: |
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163 endx = coords[2]; |
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164 endy = coords[3]; |
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165 crossings += pointCrossingsForQuad(px, py, |
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166 curx, cury, |
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167 coords[0], coords[1], |
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168 endx, endy, 0); |
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169 curx = endx; |
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170 cury = endy; |
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171 break; |
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172 case PathIterator.SEG_CUBICTO: |
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173 endx = coords[4]; |
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174 endy = coords[5]; |
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175 crossings += pointCrossingsForCubic(px, py, |
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176 curx, cury, |
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177 coords[0], coords[1], |
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178 coords[2], coords[3], |
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179 endx, endy, 0); |
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180 curx = endx; |
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181 cury = endy; |
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182 break; |
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183 case PathIterator.SEG_CLOSE: |
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184 if (cury != movy) { |
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185 crossings += pointCrossingsForLine(px, py, |
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186 curx, cury, |
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187 movx, movy); |
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188 } |
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189 curx = movx; |
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190 cury = movy; |
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191 break; |
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192 } |
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193 pi.next(); |
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194 } |
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195 if (cury != movy) { |
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196 crossings += pointCrossingsForLine(px, py, |
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197 curx, cury, |
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198 movx, movy); |
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199 } |
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200 return crossings; |
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201 } |
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202 |
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203 /** |
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204 * Calculates the number of times the line from (x0,y0) to (x1,y1) |
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205 * crosses the ray extending to the right from (px,py). |
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206 * If the point lies on the line, then no crossings are recorded. |
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207 * +1 is returned for a crossing where the Y coordinate is increasing |
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208 * -1 is returned for a crossing where the Y coordinate is decreasing |
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209 */ |
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210 public static int pointCrossingsForLine(double px, double py, |
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211 double x0, double y0, |
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212 double x1, double y1) |
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213 { |
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214 if (py < y0 && py < y1) return 0; |
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215 if (py >= y0 && py >= y1) return 0; |
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216 // assert(y0 != y1); |
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217 if (px >= x0 && px >= x1) return 0; |
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218 if (px < x0 && px < x1) return (y0 < y1) ? 1 : -1; |
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219 double xintercept = x0 + (py - y0) * (x1 - x0) / (y1 - y0); |
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220 if (px >= xintercept) return 0; |
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221 return (y0 < y1) ? 1 : -1; |
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222 } |
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223 |
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224 /** |
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225 * Calculates the number of times the quad from (x0,y0) to (x1,y1) |
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226 * crosses the ray extending to the right from (px,py). |
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227 * If the point lies on a part of the curve, |
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228 * then no crossings are counted for that intersection. |
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229 * the level parameter should be 0 at the top-level call and will count |
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230 * up for each recursion level to prevent infinite recursion |
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231 * +1 is added for each crossing where the Y coordinate is increasing |
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232 * -1 is added for each crossing where the Y coordinate is decreasing |
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233 */ |
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234 public static int pointCrossingsForQuad(double px, double py, |
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235 double x0, double y0, |
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236 double xc, double yc, |
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237 double x1, double y1, int level) |
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238 { |
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239 if (py < y0 && py < yc && py < y1) return 0; |
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240 if (py >= y0 && py >= yc && py >= y1) return 0; |
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241 // Note y0 could equal y1... |
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242 if (px >= x0 && px >= xc && px >= x1) return 0; |
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243 if (px < x0 && px < xc && px < x1) { |
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244 if (py >= y0) { |
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245 if (py < y1) return 1; |
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246 } else { |
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247 // py < y0 |
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248 if (py >= y1) return -1; |
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249 } |
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250 // py outside of y01 range, and/or y0==y1 |
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251 return 0; |
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252 } |
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253 // double precision only has 52 bits of mantissa |
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254 if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1); |
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255 double x0c = (x0 + xc) / 2; |
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256 double y0c = (y0 + yc) / 2; |
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257 double xc1 = (xc + x1) / 2; |
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258 double yc1 = (yc + y1) / 2; |
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259 xc = (x0c + xc1) / 2; |
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260 yc = (y0c + yc1) / 2; |
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261 if (Double.isNaN(xc) || Double.isNaN(yc)) { |
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262 // [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN |
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263 // [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN |
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264 // These values are also NaN if opposing infinities are added |
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265 return 0; |
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266 } |
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267 return (pointCrossingsForQuad(px, py, |
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268 x0, y0, x0c, y0c, xc, yc, |
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269 level+1) + |
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270 pointCrossingsForQuad(px, py, |
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271 xc, yc, xc1, yc1, x1, y1, |
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272 level+1)); |
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273 } |
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274 |
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275 /** |
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276 * Calculates the number of times the cubic from (x0,y0) to (x1,y1) |
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277 * crosses the ray extending to the right from (px,py). |
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278 * If the point lies on a part of the curve, |
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279 * then no crossings are counted for that intersection. |
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280 * the level parameter should be 0 at the top-level call and will count |
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281 * up for each recursion level to prevent infinite recursion |
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282 * +1 is added for each crossing where the Y coordinate is increasing |
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283 * -1 is added for each crossing where the Y coordinate is decreasing |
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284 */ |
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285 public static int pointCrossingsForCubic(double px, double py, |
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286 double x0, double y0, |
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287 double xc0, double yc0, |
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288 double xc1, double yc1, |
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289 double x1, double y1, int level) |
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290 { |
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291 if (py < y0 && py < yc0 && py < yc1 && py < y1) return 0; |
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292 if (py >= y0 && py >= yc0 && py >= yc1 && py >= y1) return 0; |
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293 // Note y0 could equal yc0... |
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294 if (px >= x0 && px >= xc0 && px >= xc1 && px >= x1) return 0; |
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295 if (px < x0 && px < xc0 && px < xc1 && px < x1) { |
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296 if (py >= y0) { |
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297 if (py < y1) return 1; |
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298 } else { |
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299 // py < y0 |
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300 if (py >= y1) return -1; |
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301 } |
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302 // py outside of y01 range, and/or y0==yc0 |
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303 return 0; |
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304 } |
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305 // double precision only has 52 bits of mantissa |
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306 if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1); |
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307 double xmid = (xc0 + xc1) / 2; |
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308 double ymid = (yc0 + yc1) / 2; |
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309 xc0 = (x0 + xc0) / 2; |
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310 yc0 = (y0 + yc0) / 2; |
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311 xc1 = (xc1 + x1) / 2; |
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312 yc1 = (yc1 + y1) / 2; |
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313 double xc0m = (xc0 + xmid) / 2; |
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314 double yc0m = (yc0 + ymid) / 2; |
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315 double xmc1 = (xmid + xc1) / 2; |
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316 double ymc1 = (ymid + yc1) / 2; |
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317 xmid = (xc0m + xmc1) / 2; |
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318 ymid = (yc0m + ymc1) / 2; |
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319 if (Double.isNaN(xmid) || Double.isNaN(ymid)) { |
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320 // [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN |
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321 // [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN |
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322 // These values are also NaN if opposing infinities are added |
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323 return 0; |
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324 } |
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325 return (pointCrossingsForCubic(px, py, |
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326 x0, y0, xc0, yc0, |
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327 xc0m, yc0m, xmid, ymid, level+1) + |
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328 pointCrossingsForCubic(px, py, |
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329 xmid, ymid, xmc1, ymc1, |
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330 xc1, yc1, x1, y1, level+1)); |
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331 } |
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332 |
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333 /** |
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334 * The rectangle intersection test counts the number of times |
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335 * that the path crosses through the shadow that the rectangle |
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336 * projects to the right towards (x => +INFINITY). |
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337 * |
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338 * During processing of the path it actually counts every time |
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339 * the path crosses either or both of the top and bottom edges |
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340 * of that shadow. If the path enters from the top, the count |
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341 * is incremented. If it then exits back through the top, the |
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342 * same way it came in, the count is decremented and there is |
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343 * no impact on the winding count. If, instead, the path exits |
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344 * out the bottom, then the count is incremented again and a |
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345 * full pass through the shadow is indicated by the winding count |
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346 * having been incremented by 2. |
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347 * |
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348 * Thus, the winding count that it accumulates is actually double |
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349 * the real winding count. Since the path is continuous, the |
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350 * final answer should be a multiple of 2, otherwise there is a |
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351 * logic error somewhere. |
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352 * |
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353 * If the path ever has a direct hit on the rectangle, then a |
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354 * special value is returned. This special value terminates |
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355 * all ongoing accumulation on up through the call chain and |
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356 * ends up getting returned to the calling function which can |
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357 * then produce an answer directly. For intersection tests, |
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358 * the answer is always "true" if the path intersects the |
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359 * rectangle. For containment tests, the answer is always |
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360 * "false" if the path intersects the rectangle. Thus, no |
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361 * further processing is ever needed if an intersection occurs. |
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362 */ |
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363 public static final int RECT_INTERSECTS = 0x80000000; |
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364 |
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365 /** |
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366 * Accumulate the number of times the path crosses the shadow |
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367 * extending to the right of the rectangle. See the comment |
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368 * for the RECT_INTERSECTS constant for more complete details. |
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369 * The return value is the sum of all crossings for both the |
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370 * top and bottom of the shadow for every segment in the path, |
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371 * or the special value RECT_INTERSECTS if the path ever enters |
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372 * the interior of the rectangle. |
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373 * The path must start with a SEG_MOVETO, otherwise an exception is |
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374 * thrown. |
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375 * The caller must check r[xy]{min,max} for NaN values. |
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376 */ |
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377 public static int rectCrossingsForPath(PathIterator pi, |
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378 double rxmin, double rymin, |
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379 double rxmax, double rymax) |
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380 { |
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381 if (rxmax <= rxmin || rymax <= rymin) { |
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382 return 0; |
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383 } |
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384 if (pi.isDone()) { |
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385 return 0; |
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386 } |
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387 double coords[] = new double[6]; |
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388 if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) { |
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389 throw new IllegalPathStateException("missing initial moveto "+ |
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390 "in path definition"); |
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391 } |
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392 pi.next(); |
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393 double curx, cury, movx, movy, endx, endy; |
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394 curx = movx = coords[0]; |
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395 cury = movy = coords[1]; |
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396 int crossings = 0; |
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397 while (crossings != RECT_INTERSECTS && !pi.isDone()) { |
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398 switch (pi.currentSegment(coords)) { |
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399 case PathIterator.SEG_MOVETO: |
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400 if (curx != movx || cury != movy) { |
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401 crossings = rectCrossingsForLine(crossings, |
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402 rxmin, rymin, |
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403 rxmax, rymax, |
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404 curx, cury, |
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405 movx, movy); |
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406 } |
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407 // Count should always be a multiple of 2 here. |
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408 // assert((crossings & 1) != 0); |
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409 movx = curx = coords[0]; |
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410 movy = cury = coords[1]; |
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411 break; |
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412 case PathIterator.SEG_LINETO: |
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413 endx = coords[0]; |
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414 endy = coords[1]; |
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415 crossings = rectCrossingsForLine(crossings, |
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416 rxmin, rymin, |
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417 rxmax, rymax, |
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418 curx, cury, |
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419 endx, endy); |
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420 curx = endx; |
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421 cury = endy; |
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422 break; |
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423 case PathIterator.SEG_QUADTO: |
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424 endx = coords[2]; |
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425 endy = coords[3]; |
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426 crossings = rectCrossingsForQuad(crossings, |
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427 rxmin, rymin, |
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428 rxmax, rymax, |
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429 curx, cury, |
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430 coords[0], coords[1], |
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431 endx, endy, 0); |
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432 curx = endx; |
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433 cury = endy; |
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434 break; |
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435 case PathIterator.SEG_CUBICTO: |
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436 endx = coords[4]; |
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437 endy = coords[5]; |
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438 crossings = rectCrossingsForCubic(crossings, |
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439 rxmin, rymin, |
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440 rxmax, rymax, |
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441 curx, cury, |
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442 coords[0], coords[1], |
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443 coords[2], coords[3], |
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444 endx, endy, 0); |
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445 curx = endx; |
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446 cury = endy; |
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447 break; |
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448 case PathIterator.SEG_CLOSE: |
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449 if (curx != movx || cury != movy) { |
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450 crossings = rectCrossingsForLine(crossings, |
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451 rxmin, rymin, |
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452 rxmax, rymax, |
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453 curx, cury, |
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454 movx, movy); |
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455 } |
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456 curx = movx; |
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457 cury = movy; |
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458 // Count should always be a multiple of 2 here. |
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459 // assert((crossings & 1) != 0); |
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460 break; |
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461 } |
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462 pi.next(); |
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463 } |
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464 if (crossings != RECT_INTERSECTS && (curx != movx || cury != movy)) { |
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465 crossings = rectCrossingsForLine(crossings, |
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466 rxmin, rymin, |
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467 rxmax, rymax, |
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468 curx, cury, |
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469 movx, movy); |
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470 } |
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471 // Count should always be a multiple of 2 here. |
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472 // assert((crossings & 1) != 0); |
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473 return crossings; |
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474 } |
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475 |
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476 /** |
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477 * Accumulate the number of times the line crosses the shadow |
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478 * extending to the right of the rectangle. See the comment |
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479 * for the RECT_INTERSECTS constant for more complete details. |
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480 */ |
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481 public static int rectCrossingsForLine(int crossings, |
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482 double rxmin, double rymin, |
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483 double rxmax, double rymax, |
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484 double x0, double y0, |
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485 double x1, double y1) |
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486 { |
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487 if (y0 >= rymax && y1 >= rymax) return crossings; |
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488 if (y0 <= rymin && y1 <= rymin) return crossings; |
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489 if (x0 <= rxmin && x1 <= rxmin) return crossings; |
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490 if (x0 >= rxmax && x1 >= rxmax) { |
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491 // Line is entirely to the right of the rect |
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492 // and the vertical ranges of the two overlap by a non-empty amount |
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493 // Thus, this line segment is partially in the "right-shadow" |
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494 // Path may have done a complete crossing |
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495 // Or path may have entered or exited the right-shadow |
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496 if (y0 < y1) { |
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497 // y-increasing line segment... |
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498 // We know that y0 < rymax and y1 > rymin |
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499 if (y0 <= rymin) crossings++; |
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500 if (y1 >= rymax) crossings++; |
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501 } else if (y1 < y0) { |
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502 // y-decreasing line segment... |
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503 // We know that y1 < rymax and y0 > rymin |
|
504 if (y1 <= rymin) crossings--; |
|
505 if (y0 >= rymax) crossings--; |
|
506 } |
|
507 return crossings; |
|
508 } |
|
509 // Remaining case: |
|
510 // Both x and y ranges overlap by a non-empty amount |
|
511 // First do trivial INTERSECTS rejection of the cases |
|
512 // where one of the endpoints is inside the rectangle. |
|
513 if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) || |
|
514 (x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax)) |
|
515 { |
|
516 return RECT_INTERSECTS; |
|
517 } |
|
518 // Otherwise calculate the y intercepts and see where |
|
519 // they fall with respect to the rectangle |
|
520 double xi0 = x0; |
|
521 if (y0 < rymin) { |
|
522 xi0 += ((rymin - y0) * (x1 - x0) / (y1 - y0)); |
|
523 } else if (y0 > rymax) { |
|
524 xi0 += ((rymax - y0) * (x1 - x0) / (y1 - y0)); |
|
525 } |
|
526 double xi1 = x1; |
|
527 if (y1 < rymin) { |
|
528 xi1 += ((rymin - y1) * (x0 - x1) / (y0 - y1)); |
|
529 } else if (y1 > rymax) { |
|
530 xi1 += ((rymax - y1) * (x0 - x1) / (y0 - y1)); |
|
531 } |
|
532 if (xi0 <= rxmin && xi1 <= rxmin) return crossings; |
|
533 if (xi0 >= rxmax && xi1 >= rxmax) { |
|
534 if (y0 < y1) { |
|
535 // y-increasing line segment... |
|
536 // We know that y0 < rymax and y1 > rymin |
|
537 if (y0 <= rymin) crossings++; |
|
538 if (y1 >= rymax) crossings++; |
|
539 } else if (y1 < y0) { |
|
540 // y-decreasing line segment... |
|
541 // We know that y1 < rymax and y0 > rymin |
|
542 if (y1 <= rymin) crossings--; |
|
543 if (y0 >= rymax) crossings--; |
|
544 } |
|
545 return crossings; |
|
546 } |
|
547 return RECT_INTERSECTS; |
|
548 } |
|
549 |
|
550 /** |
|
551 * Accumulate the number of times the quad crosses the shadow |
|
552 * extending to the right of the rectangle. See the comment |
|
553 * for the RECT_INTERSECTS constant for more complete details. |
|
554 */ |
|
555 public static int rectCrossingsForQuad(int crossings, |
|
556 double rxmin, double rymin, |
|
557 double rxmax, double rymax, |
|
558 double x0, double y0, |
|
559 double xc, double yc, |
|
560 double x1, double y1, |
|
561 int level) |
|
562 { |
|
563 if (y0 >= rymax && yc >= rymax && y1 >= rymax) return crossings; |
|
564 if (y0 <= rymin && yc <= rymin && y1 <= rymin) return crossings; |
|
565 if (x0 <= rxmin && xc <= rxmin && x1 <= rxmin) return crossings; |
|
566 if (x0 >= rxmax && xc >= rxmax && x1 >= rxmax) { |
|
567 // Quad is entirely to the right of the rect |
|
568 // and the vertical range of the 3 Y coordinates of the quad |
|
569 // overlaps the vertical range of the rect by a non-empty amount |
|
570 // We now judge the crossings solely based on the line segment |
|
571 // connecting the endpoints of the quad. |
|
572 // Note that we may have 0, 1, or 2 crossings as the control |
|
573 // point may be causing the Y range intersection while the |
|
574 // two endpoints are entirely above or below. |
|
575 if (y0 < y1) { |
|
576 // y-increasing line segment... |
|
577 if (y0 <= rymin && y1 > rymin) crossings++; |
|
578 if (y0 < rymax && y1 >= rymax) crossings++; |
|
579 } else if (y1 < y0) { |
|
580 // y-decreasing line segment... |
|
581 if (y1 <= rymin && y0 > rymin) crossings--; |
|
582 if (y1 < rymax && y0 >= rymax) crossings--; |
|
583 } |
|
584 return crossings; |
|
585 } |
|
586 // The intersection of ranges is more complicated |
|
587 // First do trivial INTERSECTS rejection of the cases |
|
588 // where one of the endpoints is inside the rectangle. |
|
589 if ((x0 < rxmax && x0 > rxmin && y0 < rymax && y0 > rymin) || |
|
590 (x1 < rxmax && x1 > rxmin && y1 < rymax && y1 > rymin)) |
|
591 { |
|
592 return RECT_INTERSECTS; |
|
593 } |
|
594 // Otherwise, subdivide and look for one of the cases above. |
|
595 // double precision only has 52 bits of mantissa |
|
596 if (level > 52) { |
|
597 return rectCrossingsForLine(crossings, |
|
598 rxmin, rymin, rxmax, rymax, |
|
599 x0, y0, x1, y1); |
|
600 } |
|
601 double x0c = (x0 + xc) / 2; |
|
602 double y0c = (y0 + yc) / 2; |
|
603 double xc1 = (xc + x1) / 2; |
|
604 double yc1 = (yc + y1) / 2; |
|
605 xc = (x0c + xc1) / 2; |
|
606 yc = (y0c + yc1) / 2; |
|
607 if (Double.isNaN(xc) || Double.isNaN(yc)) { |
|
608 // [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN |
|
609 // [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN |
|
610 // These values are also NaN if opposing infinities are added |
|
611 return 0; |
|
612 } |
|
613 crossings = rectCrossingsForQuad(crossings, |
|
614 rxmin, rymin, rxmax, rymax, |
|
615 x0, y0, x0c, y0c, xc, yc, |
|
616 level+1); |
|
617 if (crossings != RECT_INTERSECTS) { |
|
618 crossings = rectCrossingsForQuad(crossings, |
|
619 rxmin, rymin, rxmax, rymax, |
|
620 xc, yc, xc1, yc1, x1, y1, |
|
621 level+1); |
|
622 } |
|
623 return crossings; |
|
624 } |
|
625 |
|
626 /** |
|
627 * Accumulate the number of times the cubic crosses the shadow |
|
628 * extending to the right of the rectangle. See the comment |
|
629 * for the RECT_INTERSECTS constant for more complete details. |
|
630 */ |
|
631 public static int rectCrossingsForCubic(int crossings, |
|
632 double rxmin, double rymin, |
|
633 double rxmax, double rymax, |
|
634 double x0, double y0, |
|
635 double xc0, double yc0, |
|
636 double xc1, double yc1, |
|
637 double x1, double y1, |
|
638 int level) |
|
639 { |
|
640 if (y0 >= rymax && yc0 >= rymax && yc1 >= rymax && y1 >= rymax) { |
|
641 return crossings; |
|
642 } |
|
643 if (y0 <= rymin && yc0 <= rymin && yc1 <= rymin && y1 <= rymin) { |
|
644 return crossings; |
|
645 } |
|
646 if (x0 <= rxmin && xc0 <= rxmin && xc1 <= rxmin && x1 <= rxmin) { |
|
647 return crossings; |
|
648 } |
|
649 if (x0 >= rxmax && xc0 >= rxmax && xc1 >= rxmax && x1 >= rxmax) { |
|
650 // Cubic is entirely to the right of the rect |
|
651 // and the vertical range of the 4 Y coordinates of the cubic |
|
652 // overlaps the vertical range of the rect by a non-empty amount |
|
653 // We now judge the crossings solely based on the line segment |
|
654 // connecting the endpoints of the cubic. |
|
655 // Note that we may have 0, 1, or 2 crossings as the control |
|
656 // points may be causing the Y range intersection while the |
|
657 // two endpoints are entirely above or below. |
|
658 if (y0 < y1) { |
|
659 // y-increasing line segment... |
|
660 if (y0 <= rymin && y1 > rymin) crossings++; |
|
661 if (y0 < rymax && y1 >= rymax) crossings++; |
|
662 } else if (y1 < y0) { |
|
663 // y-decreasing line segment... |
|
664 if (y1 <= rymin && y0 > rymin) crossings--; |
|
665 if (y1 < rymax && y0 >= rymax) crossings--; |
|
666 } |
|
667 return crossings; |
|
668 } |
|
669 // The intersection of ranges is more complicated |
|
670 // First do trivial INTERSECTS rejection of the cases |
|
671 // where one of the endpoints is inside the rectangle. |
|
672 if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) || |
|
673 (x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax)) |
|
674 { |
|
675 return RECT_INTERSECTS; |
|
676 } |
|
677 // Otherwise, subdivide and look for one of the cases above. |
|
678 // double precision only has 52 bits of mantissa |
|
679 if (level > 52) { |
|
680 return rectCrossingsForLine(crossings, |
|
681 rxmin, rymin, rxmax, rymax, |
|
682 x0, y0, x1, y1); |
|
683 } |
|
684 double xmid = (xc0 + xc1) / 2; |
|
685 double ymid = (yc0 + yc1) / 2; |
|
686 xc0 = (x0 + xc0) / 2; |
|
687 yc0 = (y0 + yc0) / 2; |
|
688 xc1 = (xc1 + x1) / 2; |
|
689 yc1 = (yc1 + y1) / 2; |
|
690 double xc0m = (xc0 + xmid) / 2; |
|
691 double yc0m = (yc0 + ymid) / 2; |
|
692 double xmc1 = (xmid + xc1) / 2; |
|
693 double ymc1 = (ymid + yc1) / 2; |
|
694 xmid = (xc0m + xmc1) / 2; |
|
695 ymid = (yc0m + ymc1) / 2; |
|
696 if (Double.isNaN(xmid) || Double.isNaN(ymid)) { |
|
697 // [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN |
|
698 // [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN |
|
699 // These values are also NaN if opposing infinities are added |
|
700 return 0; |
|
701 } |
|
702 crossings = rectCrossingsForCubic(crossings, |
|
703 rxmin, rymin, rxmax, rymax, |
|
704 x0, y0, xc0, yc0, |
|
705 xc0m, yc0m, xmid, ymid, level+1); |
|
706 if (crossings != RECT_INTERSECTS) { |
|
707 crossings = rectCrossingsForCubic(crossings, |
|
708 rxmin, rymin, rxmax, rymax, |
|
709 xmid, ymid, xmc1, ymc1, |
|
710 xc1, yc1, x1, y1, level+1); |
|
711 } |
|
712 return crossings; |
|
713 } |
|
714 |
|
715 public Curve(int direction) { |
|
716 this.direction = direction; |
|
717 } |
|
718 |
|
719 public final int getDirection() { |
|
720 return direction; |
|
721 } |
|
722 |
|
723 public final Curve getWithDirection(int direction) { |
|
724 return (this.direction == direction ? this : getReversedCurve()); |
|
725 } |
|
726 |
|
727 public static double round(double v) { |
|
728 //return Math.rint(v*10)/10; |
|
729 return v; |
|
730 } |
|
731 |
|
732 public static int orderof(double x1, double x2) { |
|
733 if (x1 < x2) { |
|
734 return -1; |
|
735 } |
|
736 if (x1 > x2) { |
|
737 return 1; |
|
738 } |
|
739 return 0; |
|
740 } |
|
741 |
|
742 public static long signeddiffbits(double y1, double y2) { |
|
743 return (Double.doubleToLongBits(y1) - Double.doubleToLongBits(y2)); |
|
744 } |
|
745 public static long diffbits(double y1, double y2) { |
|
746 return Math.abs(Double.doubleToLongBits(y1) - |
|
747 Double.doubleToLongBits(y2)); |
|
748 } |
|
749 public static double prev(double v) { |
|
750 return Double.longBitsToDouble(Double.doubleToLongBits(v)-1); |
|
751 } |
|
752 public static double next(double v) { |
|
753 return Double.longBitsToDouble(Double.doubleToLongBits(v)+1); |
|
754 } |
|
755 |
|
756 public String toString() { |
|
757 return ("Curve["+ |
|
758 getOrder()+", "+ |
|
759 ("("+round(getX0())+", "+round(getY0())+"), ")+ |
|
760 controlPointString()+ |
|
761 ("("+round(getX1())+", "+round(getY1())+"), ")+ |
|
762 (direction == INCREASING ? "D" : "U")+ |
|
763 "]"); |
|
764 } |
|
765 |
|
766 public String controlPointString() { |
|
767 return ""; |
|
768 } |
|
769 |
|
770 public abstract int getOrder(); |
|
771 |
|
772 public abstract double getXTop(); |
|
773 public abstract double getYTop(); |
|
774 public abstract double getXBot(); |
|
775 public abstract double getYBot(); |
|
776 |
|
777 public abstract double getXMin(); |
|
778 public abstract double getXMax(); |
|
779 |
|
780 public abstract double getX0(); |
|
781 public abstract double getY0(); |
|
782 public abstract double getX1(); |
|
783 public abstract double getY1(); |
|
784 |
|
785 public abstract double XforY(double y); |
|
786 public abstract double TforY(double y); |
|
787 public abstract double XforT(double t); |
|
788 public abstract double YforT(double t); |
|
789 public abstract double dXforT(double t, int deriv); |
|
790 public abstract double dYforT(double t, int deriv); |
|
791 |
|
792 public abstract double nextVertical(double t0, double t1); |
|
793 |
|
794 public int crossingsFor(double x, double y) { |
|
795 if (y >= getYTop() && y < getYBot()) { |
|
796 if (x < getXMax() && (x < getXMin() || x < XforY(y))) { |
|
797 return 1; |
|
798 } |
|
799 } |
|
800 return 0; |
|
801 } |
|
802 |
|
803 public boolean accumulateCrossings(Crossings c) { |
|
804 double xhi = c.getXHi(); |
|
805 if (getXMin() >= xhi) { |
|
806 return false; |
|
807 } |
|
808 double xlo = c.getXLo(); |
|
809 double ylo = c.getYLo(); |
|
810 double yhi = c.getYHi(); |
|
811 double y0 = getYTop(); |
|
812 double y1 = getYBot(); |
|
813 double tstart, ystart, tend, yend; |
|
814 if (y0 < ylo) { |
|
815 if (y1 <= ylo) { |
|
816 return false; |
|
817 } |
|
818 ystart = ylo; |
|
819 tstart = TforY(ylo); |
|
820 } else { |
|
821 if (y0 >= yhi) { |
|
822 return false; |
|
823 } |
|
824 ystart = y0; |
|
825 tstart = 0; |
|
826 } |
|
827 if (y1 > yhi) { |
|
828 yend = yhi; |
|
829 tend = TforY(yhi); |
|
830 } else { |
|
831 yend = y1; |
|
832 tend = 1; |
|
833 } |
|
834 boolean hitLo = false; |
|
835 boolean hitHi = false; |
|
836 while (true) { |
|
837 double x = XforT(tstart); |
|
838 if (x < xhi) { |
|
839 if (hitHi || x > xlo) { |
|
840 return true; |
|
841 } |
|
842 hitLo = true; |
|
843 } else { |
|
844 if (hitLo) { |
|
845 return true; |
|
846 } |
|
847 hitHi = true; |
|
848 } |
|
849 if (tstart >= tend) { |
|
850 break; |
|
851 } |
|
852 tstart = nextVertical(tstart, tend); |
|
853 } |
|
854 if (hitLo) { |
|
855 c.record(ystart, yend, direction); |
|
856 } |
|
857 return false; |
|
858 } |
|
859 |
|
860 public abstract void enlarge(Rectangle2D r); |
|
861 |
|
862 public Curve getSubCurve(double ystart, double yend) { |
|
863 return getSubCurve(ystart, yend, direction); |
|
864 } |
|
865 |
|
866 public abstract Curve getReversedCurve(); |
|
867 public abstract Curve getSubCurve(double ystart, double yend, int dir); |
|
868 |
|
869 public int compareTo(Curve that, double yrange[]) { |
|
870 /* |
|
871 System.out.println(this+".compareTo("+that+")"); |
|
872 System.out.println("target range = "+yrange[0]+"=>"+yrange[1]); |
|
873 */ |
|
874 double y0 = yrange[0]; |
|
875 double y1 = yrange[1]; |
|
876 y1 = Math.min(Math.min(y1, this.getYBot()), that.getYBot()); |
|
877 if (y1 <= yrange[0]) { |
|
878 System.err.println("this == "+this); |
|
879 System.err.println("that == "+that); |
|
880 System.out.println("target range = "+yrange[0]+"=>"+yrange[1]); |
|
881 throw new InternalError("backstepping from "+yrange[0]+" to "+y1); |
|
882 } |
|
883 yrange[1] = y1; |
|
884 if (this.getXMax() <= that.getXMin()) { |
|
885 if (this.getXMin() == that.getXMax()) { |
|
886 return 0; |
|
887 } |
|
888 return -1; |
|
889 } |
|
890 if (this.getXMin() >= that.getXMax()) { |
|
891 return 1; |
|
892 } |
|
893 // Parameter s for thi(s) curve and t for tha(t) curve |
|
894 // [st]0 = parameters for top of current section of interest |
|
895 // [st]1 = parameters for bottom of valid range |
|
896 // [st]h = parameters for hypothesis point |
|
897 // [d][xy]s = valuations of thi(s) curve at sh |
|
898 // [d][xy]t = valuations of tha(t) curve at th |
|
899 double s0 = this.TforY(y0); |
|
900 double ys0 = this.YforT(s0); |
|
901 if (ys0 < y0) { |
|
902 s0 = refineTforY(s0, ys0, y0); |
|
903 ys0 = this.YforT(s0); |
|
904 } |
|
905 double s1 = this.TforY(y1); |
|
906 if (this.YforT(s1) < y0) { |
|
907 s1 = refineTforY(s1, this.YforT(s1), y0); |
|
908 //System.out.println("s1 problem!"); |
|
909 } |
|
910 double t0 = that.TforY(y0); |
|
911 double yt0 = that.YforT(t0); |
|
912 if (yt0 < y0) { |
|
913 t0 = that.refineTforY(t0, yt0, y0); |
|
914 yt0 = that.YforT(t0); |
|
915 } |
|
916 double t1 = that.TforY(y1); |
|
917 if (that.YforT(t1) < y0) { |
|
918 t1 = that.refineTforY(t1, that.YforT(t1), y0); |
|
919 //System.out.println("t1 problem!"); |
|
920 } |
|
921 double xs0 = this.XforT(s0); |
|
922 double xt0 = that.XforT(t0); |
|
923 double scale = Math.max(Math.abs(y0), Math.abs(y1)); |
|
924 double ymin = Math.max(scale * 1E-14, 1E-300); |
|
925 if (fairlyClose(xs0, xt0)) { |
|
926 double bump = ymin; |
|
927 double maxbump = Math.min(ymin * 1E13, (y1 - y0) * .1); |
|
928 double y = y0 + bump; |
|
929 while (y <= y1) { |
|
930 if (fairlyClose(this.XforY(y), that.XforY(y))) { |
|
931 if ((bump *= 2) > maxbump) { |
|
932 bump = maxbump; |
|
933 } |
|
934 } else { |
|
935 y -= bump; |
|
936 while (true) { |
|
937 bump /= 2; |
|
938 double newy = y + bump; |
|
939 if (newy <= y) { |
|
940 break; |
|
941 } |
|
942 if (fairlyClose(this.XforY(newy), that.XforY(newy))) { |
|
943 y = newy; |
|
944 } |
|
945 } |
|
946 break; |
|
947 } |
|
948 y += bump; |
|
949 } |
|
950 if (y > y0) { |
|
951 if (y < y1) { |
|
952 yrange[1] = y; |
|
953 } |
|
954 return 0; |
|
955 } |
|
956 } |
|
957 //double ymin = y1 * 1E-14; |
|
958 if (ymin <= 0) { |
|
959 System.out.println("ymin = "+ymin); |
|
960 } |
|
961 /* |
|
962 System.out.println("s range = "+s0+" to "+s1); |
|
963 System.out.println("t range = "+t0+" to "+t1); |
|
964 */ |
|
965 while (s0 < s1 && t0 < t1) { |
|
966 double sh = this.nextVertical(s0, s1); |
|
967 double xsh = this.XforT(sh); |
|
968 double ysh = this.YforT(sh); |
|
969 double th = that.nextVertical(t0, t1); |
|
970 double xth = that.XforT(th); |
|
971 double yth = that.YforT(th); |
|
972 /* |
|
973 System.out.println("sh = "+sh); |
|
974 System.out.println("th = "+th); |
|
975 */ |
|
976 try { |
|
977 if (findIntersect(that, yrange, ymin, 0, 0, |
|
978 s0, xs0, ys0, sh, xsh, ysh, |
|
979 t0, xt0, yt0, th, xth, yth)) { |
|
980 break; |
|
981 } |
|
982 } catch (Throwable t) { |
|
983 System.err.println("Error: "+t); |
|
984 System.err.println("y range was "+yrange[0]+"=>"+yrange[1]); |
|
985 System.err.println("s y range is "+ys0+"=>"+ysh); |
|
986 System.err.println("t y range is "+yt0+"=>"+yth); |
|
987 System.err.println("ymin is "+ymin); |
|
988 return 0; |
|
989 } |
|
990 if (ysh < yth) { |
|
991 if (ysh > yrange[0]) { |
|
992 if (ysh < yrange[1]) { |
|
993 yrange[1] = ysh; |
|
994 } |
|
995 break; |
|
996 } |
|
997 s0 = sh; |
|
998 xs0 = xsh; |
|
999 ys0 = ysh; |
|
1000 } else { |
|
1001 if (yth > yrange[0]) { |
|
1002 if (yth < yrange[1]) { |
|
1003 yrange[1] = yth; |
|
1004 } |
|
1005 break; |
|
1006 } |
|
1007 t0 = th; |
|
1008 xt0 = xth; |
|
1009 yt0 = yth; |
|
1010 } |
|
1011 } |
|
1012 double ymid = (yrange[0] + yrange[1]) / 2; |
|
1013 /* |
|
1014 System.out.println("final this["+s0+", "+sh+", "+s1+"]"); |
|
1015 System.out.println("final y["+ys0+", "+ysh+"]"); |
|
1016 System.out.println("final that["+t0+", "+th+", "+t1+"]"); |
|
1017 System.out.println("final y["+yt0+", "+yth+"]"); |
|
1018 System.out.println("final order = "+orderof(this.XforY(ymid), |
|
1019 that.XforY(ymid))); |
|
1020 System.out.println("final range = "+yrange[0]+"=>"+yrange[1]); |
|
1021 */ |
|
1022 /* |
|
1023 System.out.println("final sx = "+this.XforY(ymid)); |
|
1024 System.out.println("final tx = "+that.XforY(ymid)); |
|
1025 System.out.println("final order = "+orderof(this.XforY(ymid), |
|
1026 that.XforY(ymid))); |
|
1027 */ |
|
1028 return orderof(this.XforY(ymid), that.XforY(ymid)); |
|
1029 } |
|
1030 |
|
1031 public static final double TMIN = 1E-3; |
|
1032 |
|
1033 public boolean findIntersect(Curve that, double yrange[], double ymin, |
|
1034 int slevel, int tlevel, |
|
1035 double s0, double xs0, double ys0, |
|
1036 double s1, double xs1, double ys1, |
|
1037 double t0, double xt0, double yt0, |
|
1038 double t1, double xt1, double yt1) |
|
1039 { |
|
1040 /* |
|
1041 String pad = " "; |
|
1042 pad = pad+pad+pad+pad+pad; |
|
1043 pad = pad+pad; |
|
1044 System.out.println("----------------------------------------------"); |
|
1045 System.out.println(pad.substring(0, slevel)+ys0); |
|
1046 System.out.println(pad.substring(0, slevel)+ys1); |
|
1047 System.out.println(pad.substring(0, slevel)+(s1-s0)); |
|
1048 System.out.println("-------"); |
|
1049 System.out.println(pad.substring(0, tlevel)+yt0); |
|
1050 System.out.println(pad.substring(0, tlevel)+yt1); |
|
1051 System.out.println(pad.substring(0, tlevel)+(t1-t0)); |
|
1052 */ |
|
1053 if (ys0 > yt1 || yt0 > ys1) { |
|
1054 return false; |
|
1055 } |
|
1056 if (Math.min(xs0, xs1) > Math.max(xt0, xt1) || |
|
1057 Math.max(xs0, xs1) < Math.min(xt0, xt1)) |
|
1058 { |
|
1059 return false; |
|
1060 } |
|
1061 // Bounding boxes intersect - back off the larger of |
|
1062 // the two subcurves by half until they stop intersecting |
|
1063 // (or until they get small enough to switch to a more |
|
1064 // intensive algorithm). |
|
1065 if (s1 - s0 > TMIN) { |
|
1066 double s = (s0 + s1) / 2; |
|
1067 double xs = this.XforT(s); |
|
1068 double ys = this.YforT(s); |
|
1069 if (s == s0 || s == s1) { |
|
1070 System.out.println("s0 = "+s0); |
|
1071 System.out.println("s1 = "+s1); |
|
1072 throw new InternalError("no s progress!"); |
|
1073 } |
|
1074 if (t1 - t0 > TMIN) { |
|
1075 double t = (t0 + t1) / 2; |
|
1076 double xt = that.XforT(t); |
|
1077 double yt = that.YforT(t); |
|
1078 if (t == t0 || t == t1) { |
|
1079 System.out.println("t0 = "+t0); |
|
1080 System.out.println("t1 = "+t1); |
|
1081 throw new InternalError("no t progress!"); |
|
1082 } |
|
1083 if (ys >= yt0 && yt >= ys0) { |
|
1084 if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1, |
|
1085 s0, xs0, ys0, s, xs, ys, |
|
1086 t0, xt0, yt0, t, xt, yt)) { |
|
1087 return true; |
|
1088 } |
|
1089 } |
|
1090 if (ys >= yt) { |
|
1091 if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1, |
|
1092 s0, xs0, ys0, s, xs, ys, |
|
1093 t, xt, yt, t1, xt1, yt1)) { |
|
1094 return true; |
|
1095 } |
|
1096 } |
|
1097 if (yt >= ys) { |
|
1098 if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1, |
|
1099 s, xs, ys, s1, xs1, ys1, |
|
1100 t0, xt0, yt0, t, xt, yt)) { |
|
1101 return true; |
|
1102 } |
|
1103 } |
|
1104 if (ys1 >= yt && yt1 >= ys) { |
|
1105 if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1, |
|
1106 s, xs, ys, s1, xs1, ys1, |
|
1107 t, xt, yt, t1, xt1, yt1)) { |
|
1108 return true; |
|
1109 } |
|
1110 } |
|
1111 } else { |
|
1112 if (ys >= yt0) { |
|
1113 if (findIntersect(that, yrange, ymin, slevel+1, tlevel, |
|
1114 s0, xs0, ys0, s, xs, ys, |
|
1115 t0, xt0, yt0, t1, xt1, yt1)) { |
|
1116 return true; |
|
1117 } |
|
1118 } |
|
1119 if (yt1 >= ys) { |
|
1120 if (findIntersect(that, yrange, ymin, slevel+1, tlevel, |
|
1121 s, xs, ys, s1, xs1, ys1, |
|
1122 t0, xt0, yt0, t1, xt1, yt1)) { |
|
1123 return true; |
|
1124 } |
|
1125 } |
|
1126 } |
|
1127 } else if (t1 - t0 > TMIN) { |
|
1128 double t = (t0 + t1) / 2; |
|
1129 double xt = that.XforT(t); |
|
1130 double yt = that.YforT(t); |
|
1131 if (t == t0 || t == t1) { |
|
1132 System.out.println("t0 = "+t0); |
|
1133 System.out.println("t1 = "+t1); |
|
1134 throw new InternalError("no t progress!"); |
|
1135 } |
|
1136 if (yt >= ys0) { |
|
1137 if (findIntersect(that, yrange, ymin, slevel, tlevel+1, |
|
1138 s0, xs0, ys0, s1, xs1, ys1, |
|
1139 t0, xt0, yt0, t, xt, yt)) { |
|
1140 return true; |
|
1141 } |
|
1142 } |
|
1143 if (ys1 >= yt) { |
|
1144 if (findIntersect(that, yrange, ymin, slevel, tlevel+1, |
|
1145 s0, xs0, ys0, s1, xs1, ys1, |
|
1146 t, xt, yt, t1, xt1, yt1)) { |
|
1147 return true; |
|
1148 } |
|
1149 } |
|
1150 } else { |
|
1151 // No more subdivisions |
|
1152 double xlk = xs1 - xs0; |
|
1153 double ylk = ys1 - ys0; |
|
1154 double xnm = xt1 - xt0; |
|
1155 double ynm = yt1 - yt0; |
|
1156 double xmk = xt0 - xs0; |
|
1157 double ymk = yt0 - ys0; |
|
1158 double det = xnm * ylk - ynm * xlk; |
|
1159 if (det != 0) { |
|
1160 double detinv = 1 / det; |
|
1161 double s = (xnm * ymk - ynm * xmk) * detinv; |
|
1162 double t = (xlk * ymk - ylk * xmk) * detinv; |
|
1163 if (s >= 0 && s <= 1 && t >= 0 && t <= 1) { |
|
1164 s = s0 + s * (s1 - s0); |
|
1165 t = t0 + t * (t1 - t0); |
|
1166 if (s < 0 || s > 1 || t < 0 || t > 1) { |
|
1167 System.out.println("Uh oh!"); |
|
1168 } |
|
1169 double y = (this.YforT(s) + that.YforT(t)) / 2; |
|
1170 if (y <= yrange[1] && y > yrange[0]) { |
|
1171 yrange[1] = y; |
|
1172 return true; |
|
1173 } |
|
1174 } |
|
1175 } |
|
1176 //System.out.println("Testing lines!"); |
|
1177 } |
|
1178 return false; |
|
1179 } |
|
1180 |
|
1181 public double refineTforY(double t0, double yt0, double y0) { |
|
1182 double t1 = 1; |
|
1183 while (true) { |
|
1184 double th = (t0 + t1) / 2; |
|
1185 if (th == t0 || th == t1) { |
|
1186 return t1; |
|
1187 } |
|
1188 double y = YforT(th); |
|
1189 if (y < y0) { |
|
1190 t0 = th; |
|
1191 yt0 = y; |
|
1192 } else if (y > y0) { |
|
1193 t1 = th; |
|
1194 } else { |
|
1195 return t1; |
|
1196 } |
|
1197 } |
|
1198 } |
|
1199 |
|
1200 public boolean fairlyClose(double v1, double v2) { |
|
1201 return (Math.abs(v1 - v2) < |
|
1202 Math.max(Math.abs(v1), Math.abs(v2)) * 1E-10); |
|
1203 } |
|
1204 |
|
1205 public abstract int getSegment(double coords[]); |
|
1206 } |