1 /* 2 * Copyright 2012 Google Inc. 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 8 #include "src/pathops/SkPathOpsTypes.h" 9 #include "tests/PathOpsCubicIntersectionTestData.h" 10 11 #include <array> 12 #include <cfloat> 13 14 namespace PathOpsCubicIntersectionTestData { 15 16 static const double D = FLT_EPSILON / 2; 17 static const double G = FLT_EPSILON / 3; 18 static const double N = -FLT_EPSILON / 2; 19 static const double M = -FLT_EPSILON / 3; 20 21 const CubicPts pointDegenerates[] = { 22 {{{0, 0}, {0, 0}, {0, 0}, {0, 0}}}, 23 {{{1, 1}, {1, 1}, {1, 1}, {1, 1}}}, 24 {{{1 + FLT_EPSILON_HALF, 1}, {1, 1 + FLT_EPSILON_HALF}, {1, 1}, {1, 1}}}, 25 {{{1 + D, 1}, {1 - D, 1}, {1, 1}, {1, 1}}}, 26 {{{0, 0}, {0, 0}, {1, 0}, {0, 0}}}, 27 {{{0, 0}, {1, 0}, {0, 0}, {0, 0}}}, 28 {{{0, 0}, {0, 0}, {0, 1}, {0, 0}}}, 29 {{{0, 0}, {0, 1}, {0, 0}, {0, 0}}}, 30 {{{0, 0}, {0, 0}, {1, 1}, {0, 0}}}, 31 {{{0, 0}, {1, 1}, {0, 0}, {0, 0}}}, 32 {{{0, 0}, {1, 1}, {2, 2}, {0, 0}}}, 33 {{{1, 1}, {2, 2}, {2, 2}, {1, 1}}}, 34 {{{0, 0}, {0, D}, {1, 0}, {0, 0}}}, 35 {{{0, 0}, {1, 0}, {0, D}, {0, 0}}}, 36 {{{0, 0}, {D, 0}, {0, 1}, {0, 0}}}, 37 {{{0, 0}, {0, 1}, {D, 0}, {0, 0}}}, 38 {{{1, 1}, {2, 2}, {2, 2+D}, {1, 1}}}, 39 {{{0, 0}, {0, N}, {1, 0}, {0, 0}}}, 40 {{{0, 0}, {1, 0}, {0, N}, {0, 0}}}, 41 {{{0, 0}, {N, 0}, {0, 1}, {0, 0}}}, 42 {{{0, 0}, {0, 1}, {N, 0}, {0, 0}}}, 43 {{{0, 0}, {1, 1}, {N, 0}, {0, 0}}}, 44 {{{0, 0}, {D, 0}, {1, 1}, {0, 0}}}, 45 {{{0, 0}, {1, 1}, {D, 0}, {0, 0}}}, 46 {{{0, 0}, {N, 0}, {1, 1}, {0, 0}}}, 47 {{{1, 1}, {2, 2}, {2, 2+N}, {1, 1}}}, 48 }; 49 50 const size_t pointDegenerates_count = std::size(pointDegenerates); 51 52 const CubicPts notPointDegenerates[] = { 53 {{{1 + FLT_EPSILON * 8, 1}, {1, FLT_EPSILON * 8}, {1, 1}, {1, 1}}}, 54 {{{1 + FLT_EPSILON * 8, 1}, {1 - FLT_EPSILON * 8, 1}, {1, 1}, {1, 1}}} 55 }; 56 57 const size_t notPointDegenerates_count = 58 std::size(notPointDegenerates); 59 60 // from http://www.truetex.com/bezint.htm 61 const CubicPts tests[][2] = { 62 { // intersects in one place (data gives bezier clip fits 63 {{{0, 45}, 64 {6.0094158284751593, 51.610357411322688}, 65 {12.741093228940867, 55.981703949474607}, 66 {20.021417396476362, 58.652245509710262}}}, 67 {{{2.2070737699246674, 52.703494107327209}, 68 {31.591482272629477, 23.811002295222025}, 69 {76.824588616426425, 44.049473790502674}, 70 {119.25488947221436, 55.599248272955073}}} 71 }, { // intersects in three places 72 {{{0, 45}, {50, 100}, {150, 0}, {200, 55}}}, 73 {{{0, 55}, {50, 0}, {150, 100}, {200, 45}}} 74 }, { // intersects in one place, cross over is nearly parallel 75 {{{0, 0}, {0, 100}, {200, 0}, {200, 100}}}, 76 {{{0, 100}, {0, 0}, {200, 100}, {200, 0}}} 77 }, { // intersects in two places 78 {{{0, 0}, {0, 100}, {200, 100}, {200, 0}}}, 79 {{{0, 100}, {0, 0}, {200, 0}, {200, 100}}} 80 }, { 81 {{{150, 100}, {150 + 0.1, 150}, {150, 200}, {150, 250}}}, 82 {{{250, 150}, {200, 150 + 0.1}, {150, 150}, {100, 150}}} 83 }, { // single intersection around 168,185 84 {{{200, 100}, {150, 100}, {150, 150}, {200, 150}}}, 85 {{{250, 150}, {250, 100}, {100, 100}, {100, 150}}} 86 }, { 87 {{{1.0, 1.5}, {15.5, 0.5}, {-8.0, 3.5}, {5.0, 1.5}}}, 88 {{{4.0, 0.5}, {5.0, 15.0}, {2.0, -8.5}, {4.0, 4.5}}} 89 }, { 90 {{{664.00168, 0}, {726.11545, 124.22757}, {736.89069, 267.89743}, 91 {694.0017, 400.0002}}}, 92 {{{850.66843, 115.55563}, {728.515, 115.55563}, {725.21347, 275.15309}, 93 {694.0017, 400.0002}}} 94 }, { 95 {{{1, 1}, {12.5, 6.5}, {-4, 6.5}, {7.5, 1}}}, 96 {{{1, 6.5}, {12.5, 1}, {-4, 1}, {.5, 6}}} 97 }, { 98 {{{315.748, 312.84}, {312.644, 318.134}, {305.836, 319.909}, {300.542, 316.804}}}, 99 {{{317.122, 309.05}, {316.112, 315.102}, {310.385, 319.19}, {304.332, 318.179}}} 100 }, { 101 {{{1046.604051, 172.937967}, {1046.604051, 178.9763059}, {1041.76745, 183.9279165}, {1035.703842, 184.0432409}}}, 102 {{{1046.452235, 174.7640504}, {1045.544872, 180.1973817}, {1040.837966, 184.0469882}, {1035.505925, 184.0469882}}} 103 }, { 104 {{{125.79356, 199.57382}, {51.16556, 128.93575}, {87.494, 16.67848}, {167.29361, 16.67848}}}, 105 {{{167.29361, 55.81876}, {100.36128, 55.81876}, {68.64099, 145.4755}, {125.7942, 199.57309}}} 106 }, { 107 {{{104.11546583642826, 370.21352558595504}, {122.96968232592344, 404.54489231839295}, 108 {169.90881005384728, 425.00067000000007}, {221.33045999999999, 425.00067000000001}}}, 109 {{{116.32365976159625, 381.71048540582598}, {103.86096590870899, 381.71048540581626}, 110 {91.394188003200725, 377.17917781762833}, {82.622283093355179, 368.11683661930334}}} 111 } 112 }; 113 114 const size_t tests_count = std::size(tests); 115 116 const CubicPts lines[] = { 117 {{{0, 0}, {0, 0}, {0, 0}, {1, 0}}}, // 0: horizontal 118 {{{1, 0}, {0, 0}, {0, 0}, {0, 0}}}, 119 {{{1, 0}, {2, 0}, {3, 0}, {4, 0}}}, 120 {{{0, 0}, {0, 0}, {0, 0}, {0, 1}}}, // 5: vertical 121 {{{0, 1}, {0, 0}, {0, 0}, {0, 0}}}, 122 {{{0, 1}, {0, 2}, {0, 3}, {0, 4}}}, 123 {{{0, 0}, {0, 0}, {0, 0}, {1, 1}}}, // 10: 3 coincident 124 {{{1, 1}, {0, 0}, {0, 0}, {0, 0}}}, 125 {{{0, 0}, {0, 0}, {1, 1}, {2, 2}}}, // 14: 2 coincident 126 {{{0, 0}, {1, 1}, {0, 0}, {2, 2}}}, 127 {{{1, 1}, {0, 0}, {0, 0}, {2, 2}}}, // 17: 128 {{{1, 1}, {0, 0}, {2, 2}, {0, 0}}}, 129 {{{1, 1}, {2, 2}, {0, 0}, {0, 0}}}, 130 {{{1, 1}, {2, 2}, {3, 3}, {2, 2}}}, // middle-last coincident 131 {{{1, 1}, {2, 2}, {3, 3}, {3, 3}}}, // middle-last coincident 132 {{{1, 1}, {1, 1}, {2, 2}, {2, 2}}}, // 2 pairs coincident 133 {{{1, 1}, {2, 2}, {1, 1}, {2, 2}}}, 134 {{{1, 1}, {1, 1}, {3, 3}, {3, 3}}}, // first-middle middle-last coincident 135 {{{1, 1}, {2, 2}, {3, 3}, {4, 4}}}, // no coincident 136 {{{1, 1}, {3, 3}, {2, 2}, {4, 4}}}, 137 {{{1, 1}, {2, 2}, {4, 4}, {3, 3}}}, 138 {{{1, 1}, {3, 3}, {4, 4}, {2, 2}}}, 139 {{{1, 1}, {4, 4}, {2, 2}, {3, 3}}}, 140 {{{1, 1}, {4, 4}, {3, 3}, {2, 2}}}, 141 {{{2, 2}, {1, 1}, {3, 3}, {4, 4}}}, 142 {{{2, 2}, {1, 1}, {4, 4}, {3, 3}}}, 143 {{{2, 2}, {3, 3}, {1, 1}, {4, 4}}}, 144 {{{2, 2}, {3, 3}, {4, 4}, {1, 1}}}, 145 {{{2, 2}, {4, 4}, {1, 1}, {3, 3}}}, 146 {{{2, 2}, {4, 4}, {3, 3}, {1, 1}}}, 147 }; 148 149 const size_t lines_count = std::size(lines); 150 151 // 'not a line' tries to fool the line detection code 152 const CubicPts notLines[] = { 153 {{{0, 0}, {0, 0}, {0, 1}, {1, 0}}}, 154 {{{0, 0}, {0, 1}, {0, 0}, {1, 0}}}, 155 {{{0, 0}, {0, 1}, {1, 0}, {0, 0}}}, 156 {{{0, 1}, {0, 0}, {0, 0}, {1, 0}}}, 157 {{{0, 1}, {0, 0}, {1, 0}, {0, 0}}}, 158 {{{0, 1}, {1, 0}, {0, 0}, {0, 0}}}, 159 }; 160 161 const size_t notLines_count = std::size(notLines); 162 163 static const double E = FLT_EPSILON * 8; 164 static const double F = FLT_EPSILON * 8; 165 166 const CubicPts modEpsilonLines[] = { 167 {{{0, E}, {0, 0}, {0, 0}, {1, 0}}}, // horizontal 168 {{{0, 0}, {0, E}, {1, 0}, {0, 0}}}, 169 {{{0, 0}, {1, 0}, {0, E}, {0, 0}}}, 170 {{{1, 0}, {0, 0}, {0, 0}, {0, E}}}, 171 {{{1, E}, {2, 0}, {3, 0}, {4, 0}}}, 172 {{{E, 0}, {0, 0}, {0, 0}, {0, 1}}}, // vertical 173 {{{0, 0}, {E, 0}, {0, 1}, {0, 0}}}, 174 {{{0, 0}, {0, 1}, {E, 0}, {0, 0}}}, 175 {{{0, 1}, {0, 0}, {0, 0}, {E, 0}}}, 176 {{{E, 1}, {0, 2}, {0, 3}, {0, 4}}}, 177 {{{E, 0}, {0, 0}, {0, 0}, {1, 1}}}, // 3 coincident 178 {{{0, 0}, {E, 0}, {1, 1}, {0, 0}}}, 179 {{{0, 0}, {1, 1}, {E, 0}, {0, 0}}}, 180 {{{1, 1}, {0, 0}, {0, 0}, {E, 0}}}, 181 {{{0, E}, {0, 0}, {1, 1}, {2, 2}}}, // 2 coincident 182 {{{0, 0}, {1, 1}, {0, E}, {2, 2}}}, 183 {{{0, 0}, {1, 1}, {2, 2}, {0, E}}}, 184 {{{1, 1}, {0, E}, {0, 0}, {2, 2}}}, 185 {{{1, 1}, {0, E}, {2, 2}, {0, 0}}}, 186 {{{1, 1}, {2, 2}, {E, 0}, {0, 0}}}, 187 {{{1, 1}, {2, 2+E}, {3, 3}, {2, 2}}}, // middle-last coincident 188 {{{1, 1}, {2+E, 2}, {3, 3}, {3, 3}}}, // middle-last coincident 189 {{{1, 1}, {1, 1}, {2, 2}, {2+E, 2}}}, // 2 pairs coincident 190 {{{1, 1}, {2, 2}, {1, 1}, {2+E, 2}}}, 191 {{{1, 1}, {2, 2}, {2, 2+E}, {1, 1}}}, 192 {{{1, 1}, {1, 1+E}, {3, 3}, {3, 3}}}, // first-middle middle-last coincident 193 {{{1, 1}, {2+E, 2}, {3, 3}, {4, 4}}}, // no coincident 194 {{{1, 1}, {3, 3}, {2, 2}, {4, 4+F+F}}}, // INVESTIGATE: why the epsilon is bigger 195 {{{1, 1+F+F}, {2, 2}, {4, 4}, {3, 3}}}, // INVESTIGATE: why the epsilon is bigger 196 {{{1, 1}, {3, 3}, {4, 4+E}, {2, 2}}}, 197 {{{1, 1}, {4, 4}, {2, 2}, {3, 3+E}}}, 198 {{{1, 1}, {4, 4}, {3, 3}, {2+E, 2}}}, 199 {{{2, 2}, {1, 1}, {3+E, 3}, {4, 4}}}, 200 {{{2, 2}, {1+E, 1}, {4, 4}, {3, 3}}}, 201 {{{2, 2+E}, {3, 3}, {1, 1}, {4, 4}}}, 202 {{{2+E, 2}, {3, 3}, {4, 4}, {1, 1}}}, 203 {{{2, 2}, {4+E, 4}, {1, 1}, {3, 3}}}, 204 {{{2, 2}, {4, 4}, {3, 3}, {1, 1+E}}}, 205 }; 206 207 const size_t modEpsilonLines_count = std::size(modEpsilonLines); 208 209 const CubicPts lessEpsilonLines[] = { 210 {{{0, D}, {0, 0}, {0, 0}, {1, 0}}}, // horizontal 211 {{{1, 0}, {0, 0}, {0, 0}, {0, D}}}, 212 {{{1, D}, {2, 0}, {3, 0}, {4, 0}}}, 213 {{{D, 0}, {0, 0}, {0, 0}, {0, 1}}}, // vertical 214 {{{0, 1}, {0, 0}, {0, 0}, {D, 0}}}, 215 {{{D, 1}, {0, 2}, {0, 3}, {0, 4}}}, 216 {{{D, 0}, {0, 0}, {0, 0}, {1, 1}}}, // 3 coincident 217 {{{1, 1}, {0, 0}, {0, 0}, {D, 0}}}, 218 {{{0, D}, {0, 0}, {1, 1}, {2, 2}}}, // 2 coincident 219 {{{0, 0}, {1, 1}, {0, D}, {2, 2}}}, 220 {{{0, 0}, {1, 1}, {2, 2}, {1, 1+D}}}, 221 {{{1, 1}, {0, D}, {0, 0}, {2, 2}}}, 222 {{{1, 1}, {0, D}, {2, 2}, {0, 0}}}, 223 {{{1, 1}, {2, 2}, {D, 0}, {0, 0}}}, 224 {{{1, 1}, {2, 2+D}, {3, 3}, {2, 2}}}, // middle-last coincident 225 {{{1, 1}, {2+D, 2}, {3, 3}, {3, 3}}}, // middle-last coincident 226 {{{1, 1}, {1, 1}, {2, 2}, {2+D, 2}}}, // 2 pairs coincident 227 {{{1, 1}, {2, 2}, {1, 1}, {2+D, 2}}}, 228 {{{1, 1}, {1, 1+D}, {3, 3}, {3, 3}}}, // first-middle middle-last coincident 229 {{{1, 1}, {2+D/2, 2}, {3, 3}, {4, 4}}}, // no coincident (FIXME: N as opposed to N/2 failed) 230 {{{1, 1}, {3, 3}, {2, 2}, {4, 4+D}}}, 231 {{{1, 1+D}, {2, 2}, {4, 4}, {3, 3}}}, 232 {{{1, 1}, {3, 3}, {4, 4+D}, {2, 2}}}, 233 {{{1, 1}, {4, 4}, {2, 2}, {3, 3+D}}}, 234 {{{1, 1}, {4, 4}, {3, 3}, {2+G, 2}}}, // INVESTIGATE: why the epsilon is smaller 235 {{{2, 2}, {1, 1}, {3+D, 3}, {4, 4}}}, 236 {{{2, 2}, {1+D, 1}, {4, 4}, {3, 3}}}, 237 {{{2, 2+D}, {3, 3}, {1, 1}, {4, 4}}}, 238 {{{2+G, 2}, {3, 3}, {4, 4}, {1, 1}}}, // INVESTIGATE: why the epsilon is smaller 239 {{{2, 2}, {4+D, 4}, {1, 1}, {3, 3}}}, 240 {{{2, 2}, {4, 4}, {3, 3}, {1, 1+D}}}, 241 }; 242 243 const size_t lessEpsilonLines_count = std::size(lessEpsilonLines); 244 245 const CubicPts negEpsilonLines[] = { 246 {{{0, N}, {0, 0}, {0, 0}, {1, 0}}}, // horizontal 247 {{{1, 0}, {0, 0}, {0, 0}, {0, N}}}, 248 {{{1, N}, {2, 0}, {3, 0}, {4, 0}}}, 249 {{{N, 0}, {0, 0}, {0, 0}, {0, 1}}}, // vertical 250 {{{0, 1}, {0, 0}, {0, 0}, {N, 0}}}, 251 {{{N, 1}, {0, 2}, {0, 3}, {0, 4}}}, 252 {{{N, 0}, {0, 0}, {0, 0}, {1, 1}}}, // 3 coincident 253 {{{1, 1}, {0, 0}, {0, 0}, {N, 0}}}, 254 {{{0, N}, {0, 0}, {1, 1}, {2, 2}}}, // 2 coincident 255 {{{0, 0}, {1, 1}, {0, N}, {2, 2}}}, 256 {{{0, 0}, {1, 1}, {2, 2}, {1, 1+N}}}, 257 {{{1, 1}, {0, N}, {0, 0}, {2, 2}}}, 258 {{{1, 1}, {0, N}, {2, 2}, {0, 0}}}, 259 {{{1, 1}, {2, 2}, {N, 0}, {0, 0}}}, 260 {{{1, 1}, {2, 2+N}, {3, 3}, {2, 2}}}, // middle-last coincident 261 {{{1, 1}, {2+N, 2}, {3, 3}, {3, 3}}}, // middle-last coincident 262 {{{1, 1}, {1, 1}, {2, 2}, {2+N, 2}}}, // 2 pairs coincident 263 {{{1, 1}, {2, 2}, {1, 1}, {2+N, 2}}}, 264 {{{1, 1}, {1, 1+N}, {3, 3}, {3, 3}}}, // first-middle middle-last coincident 265 {{{1, 1}, {2+N/2, 2}, {3, 3}, {4, 4}}}, // no coincident (FIXME: N as opposed to N/2 failed) 266 {{{1, 1}, {3, 3}, {2, 2}, {4, 4+N}}}, 267 {{{1, 1+N}, {2, 2}, {4, 4}, {3, 3}}}, 268 {{{1, 1}, {3, 3}, {4, 4+N}, {2, 2}}}, 269 {{{1, 1}, {4, 4}, {2, 2}, {3, 3+N}}}, 270 {{{1, 1}, {4, 4}, {3, 3}, {2+M, 2}}}, // INVESTIGATE: why the epsilon is smaller 271 {{{2, 2}, {1, 1}, {3+N, 3}, {4, 4}}}, 272 {{{2, 2}, {1+N, 1}, {4, 4}, {3, 3}}}, 273 {{{2, 2+N}, {3, 3}, {1, 1}, {4, 4}}}, 274 {{{2+M, 2}, {3, 3}, {4, 4}, {1, 1}}}, // INVESTIGATE: why the epsilon is smaller 275 {{{2, 2}, {4+N, 4}, {1, 1}, {3, 3}}}, 276 {{{2, 2}, {4, 4}, {3, 3}, {1, 1+N}}}, 277 }; 278 279 const size_t negEpsilonLines_count = std::size(negEpsilonLines); 280 281 } // namespace PathOpsCubicIntersectionTestData 282