J. Duke | 319a3b9 | 2007-12-01 00:00:00 +0000 | [diff] [blame^] | 1 | /* |
| 2 | * Copyright 1998-2006 Sun Microsystems, Inc. All Rights Reserved. |
| 3 | * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| 4 | * |
| 5 | * This code is free software; you can redistribute it and/or modify it |
| 6 | * under the terms of the GNU General Public License version 2 only, as |
| 7 | * published by the Free Software Foundation. Sun designates this |
| 8 | * particular file as subject to the "Classpath" exception as provided |
| 9 | * by Sun in the LICENSE file that accompanied this code. |
| 10 | * |
| 11 | * This code is distributed in the hope that it will be useful, but WITHOUT |
| 12 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| 13 | * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| 14 | * version 2 for more details (a copy is included in the LICENSE file that |
| 15 | * accompanied this code). |
| 16 | * |
| 17 | * You should have received a copy of the GNU General Public License version |
| 18 | * 2 along with this work; if not, write to the Free Software Foundation, |
| 19 | * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| 20 | * |
| 21 | * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara, |
| 22 | * CA 95054 USA or visit www.sun.com if you need additional information or |
| 23 | * have any questions. |
| 24 | */ |
| 25 | |
| 26 | package sun.awt.geom; |
| 27 | |
| 28 | import java.awt.geom.Rectangle2D; |
| 29 | import java.awt.geom.QuadCurve2D; |
| 30 | import java.awt.geom.CubicCurve2D; |
| 31 | import java.awt.geom.PathIterator; |
| 32 | import java.awt.geom.IllegalPathStateException; |
| 33 | import java.util.Vector; |
| 34 | |
| 35 | public abstract class Curve { |
| 36 | public static final int INCREASING = 1; |
| 37 | public static final int DECREASING = -1; |
| 38 | |
| 39 | protected int direction; |
| 40 | |
| 41 | public static void insertMove(Vector curves, double x, double y) { |
| 42 | curves.add(new Order0(x, y)); |
| 43 | } |
| 44 | |
| 45 | public static void insertLine(Vector curves, |
| 46 | double x0, double y0, |
| 47 | double x1, double y1) |
| 48 | { |
| 49 | if (y0 < y1) { |
| 50 | curves.add(new Order1(x0, y0, |
| 51 | x1, y1, |
| 52 | INCREASING)); |
| 53 | } else if (y0 > y1) { |
| 54 | curves.add(new Order1(x1, y1, |
| 55 | x0, y0, |
| 56 | DECREASING)); |
| 57 | } else { |
| 58 | // Do not add horizontal lines |
| 59 | } |
| 60 | } |
| 61 | |
| 62 | public static void insertQuad(Vector curves, |
| 63 | double x0, double y0, |
| 64 | double coords[]) |
| 65 | { |
| 66 | double y1 = coords[3]; |
| 67 | if (y0 > y1) { |
| 68 | Order2.insert(curves, coords, |
| 69 | coords[2], y1, |
| 70 | coords[0], coords[1], |
| 71 | x0, y0, |
| 72 | DECREASING); |
| 73 | } else if (y0 == y1 && y0 == coords[1]) { |
| 74 | // Do not add horizontal lines |
| 75 | return; |
| 76 | } else { |
| 77 | Order2.insert(curves, coords, |
| 78 | x0, y0, |
| 79 | coords[0], coords[1], |
| 80 | coords[2], y1, |
| 81 | INCREASING); |
| 82 | } |
| 83 | } |
| 84 | |
| 85 | public static void insertCubic(Vector curves, |
| 86 | double x0, double y0, |
| 87 | double coords[]) |
| 88 | { |
| 89 | double y1 = coords[5]; |
| 90 | if (y0 > y1) { |
| 91 | Order3.insert(curves, coords, |
| 92 | coords[4], y1, |
| 93 | coords[2], coords[3], |
| 94 | coords[0], coords[1], |
| 95 | x0, y0, |
| 96 | DECREASING); |
| 97 | } else if (y0 == y1 && y0 == coords[1] && y0 == coords[3]) { |
| 98 | // Do not add horizontal lines |
| 99 | return; |
| 100 | } else { |
| 101 | Order3.insert(curves, coords, |
| 102 | x0, y0, |
| 103 | coords[0], coords[1], |
| 104 | coords[2], coords[3], |
| 105 | coords[4], y1, |
| 106 | INCREASING); |
| 107 | } |
| 108 | } |
| 109 | |
| 110 | /** |
| 111 | * Calculates the number of times the given path |
| 112 | * crosses the ray extending to the right from (px,py). |
| 113 | * If the point lies on a part of the path, |
| 114 | * then no crossings are counted for that intersection. |
| 115 | * +1 is added for each crossing where the Y coordinate is increasing |
| 116 | * -1 is added for each crossing where the Y coordinate is decreasing |
| 117 | * The return value is the sum of all crossings for every segment in |
| 118 | * the path. |
| 119 | * The path must start with a SEG_MOVETO, otherwise an exception is |
| 120 | * thrown. |
| 121 | * The caller must check p[xy] for NaN values. |
| 122 | * The caller may also reject infinite p[xy] values as well. |
| 123 | */ |
| 124 | public static int pointCrossingsForPath(PathIterator pi, |
| 125 | double px, double py) |
| 126 | { |
| 127 | if (pi.isDone()) { |
| 128 | return 0; |
| 129 | } |
| 130 | double coords[] = new double[6]; |
| 131 | if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) { |
| 132 | throw new IllegalPathStateException("missing initial moveto "+ |
| 133 | "in path definition"); |
| 134 | } |
| 135 | pi.next(); |
| 136 | double movx = coords[0]; |
| 137 | double movy = coords[1]; |
| 138 | double curx = movx; |
| 139 | double cury = movy; |
| 140 | double endx, endy; |
| 141 | int crossings = 0; |
| 142 | while (!pi.isDone()) { |
| 143 | switch (pi.currentSegment(coords)) { |
| 144 | case PathIterator.SEG_MOVETO: |
| 145 | if (cury != movy) { |
| 146 | crossings += pointCrossingsForLine(px, py, |
| 147 | curx, cury, |
| 148 | movx, movy); |
| 149 | } |
| 150 | movx = curx = coords[0]; |
| 151 | movy = cury = coords[1]; |
| 152 | break; |
| 153 | case PathIterator.SEG_LINETO: |
| 154 | endx = coords[0]; |
| 155 | endy = coords[1]; |
| 156 | crossings += pointCrossingsForLine(px, py, |
| 157 | curx, cury, |
| 158 | endx, endy); |
| 159 | curx = endx; |
| 160 | cury = endy; |
| 161 | break; |
| 162 | case PathIterator.SEG_QUADTO: |
| 163 | endx = coords[2]; |
| 164 | endy = coords[3]; |
| 165 | crossings += pointCrossingsForQuad(px, py, |
| 166 | curx, cury, |
| 167 | coords[0], coords[1], |
| 168 | endx, endy, 0); |
| 169 | curx = endx; |
| 170 | cury = endy; |
| 171 | break; |
| 172 | case PathIterator.SEG_CUBICTO: |
| 173 | endx = coords[4]; |
| 174 | endy = coords[5]; |
| 175 | crossings += pointCrossingsForCubic(px, py, |
| 176 | curx, cury, |
| 177 | coords[0], coords[1], |
| 178 | coords[2], coords[3], |
| 179 | endx, endy, 0); |
| 180 | curx = endx; |
| 181 | cury = endy; |
| 182 | break; |
| 183 | case PathIterator.SEG_CLOSE: |
| 184 | if (cury != movy) { |
| 185 | crossings += pointCrossingsForLine(px, py, |
| 186 | curx, cury, |
| 187 | movx, movy); |
| 188 | } |
| 189 | curx = movx; |
| 190 | cury = movy; |
| 191 | break; |
| 192 | } |
| 193 | pi.next(); |
| 194 | } |
| 195 | if (cury != movy) { |
| 196 | crossings += pointCrossingsForLine(px, py, |
| 197 | curx, cury, |
| 198 | movx, movy); |
| 199 | } |
| 200 | return crossings; |
| 201 | } |
| 202 | |
| 203 | /** |
| 204 | * Calculates the number of times the line from (x0,y0) to (x1,y1) |
| 205 | * crosses the ray extending to the right from (px,py). |
| 206 | * If the point lies on the line, then no crossings are recorded. |
| 207 | * +1 is returned for a crossing where the Y coordinate is increasing |
| 208 | * -1 is returned for a crossing where the Y coordinate is decreasing |
| 209 | */ |
| 210 | public static int pointCrossingsForLine(double px, double py, |
| 211 | double x0, double y0, |
| 212 | double x1, double y1) |
| 213 | { |
| 214 | if (py < y0 && py < y1) return 0; |
| 215 | if (py >= y0 && py >= y1) return 0; |
| 216 | // assert(y0 != y1); |
| 217 | if (px >= x0 && px >= x1) return 0; |
| 218 | if (px < x0 && px < x1) return (y0 < y1) ? 1 : -1; |
| 219 | double xintercept = x0 + (py - y0) * (x1 - x0) / (y1 - y0); |
| 220 | if (px >= xintercept) return 0; |
| 221 | return (y0 < y1) ? 1 : -1; |
| 222 | } |
| 223 | |
| 224 | /** |
| 225 | * Calculates the number of times the quad from (x0,y0) to (x1,y1) |
| 226 | * crosses the ray extending to the right from (px,py). |
| 227 | * If the point lies on a part of the curve, |
| 228 | * then no crossings are counted for that intersection. |
| 229 | * the level parameter should be 0 at the top-level call and will count |
| 230 | * up for each recursion level to prevent infinite recursion |
| 231 | * +1 is added for each crossing where the Y coordinate is increasing |
| 232 | * -1 is added for each crossing where the Y coordinate is decreasing |
| 233 | */ |
| 234 | public static int pointCrossingsForQuad(double px, double py, |
| 235 | double x0, double y0, |
| 236 | double xc, double yc, |
| 237 | double x1, double y1, int level) |
| 238 | { |
| 239 | if (py < y0 && py < yc && py < y1) return 0; |
| 240 | if (py >= y0 && py >= yc && py >= y1) return 0; |
| 241 | // Note y0 could equal y1... |
| 242 | if (px >= x0 && px >= xc && px >= x1) return 0; |
| 243 | if (px < x0 && px < xc && px < x1) { |
| 244 | if (py >= y0) { |
| 245 | if (py < y1) return 1; |
| 246 | } else { |
| 247 | // py < y0 |
| 248 | if (py >= y1) return -1; |
| 249 | } |
| 250 | // py outside of y01 range, and/or y0==y1 |
| 251 | return 0; |
| 252 | } |
| 253 | // double precision only has 52 bits of mantissa |
| 254 | if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1); |
| 255 | double x0c = (x0 + xc) / 2; |
| 256 | double y0c = (y0 + yc) / 2; |
| 257 | double xc1 = (xc + x1) / 2; |
| 258 | double yc1 = (yc + y1) / 2; |
| 259 | xc = (x0c + xc1) / 2; |
| 260 | yc = (y0c + yc1) / 2; |
| 261 | if (Double.isNaN(xc) || Double.isNaN(yc)) { |
| 262 | // [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN |
| 263 | // [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN |
| 264 | // These values are also NaN if opposing infinities are added |
| 265 | return 0; |
| 266 | } |
| 267 | return (pointCrossingsForQuad(px, py, |
| 268 | x0, y0, x0c, y0c, xc, yc, |
| 269 | level+1) + |
| 270 | pointCrossingsForQuad(px, py, |
| 271 | xc, yc, xc1, yc1, x1, y1, |
| 272 | level+1)); |
| 273 | } |
| 274 | |
| 275 | /** |
| 276 | * Calculates the number of times the cubic from (x0,y0) to (x1,y1) |
| 277 | * crosses the ray extending to the right from (px,py). |
| 278 | * If the point lies on a part of the curve, |
| 279 | * then no crossings are counted for that intersection. |
| 280 | * the level parameter should be 0 at the top-level call and will count |
| 281 | * up for each recursion level to prevent infinite recursion |
| 282 | * +1 is added for each crossing where the Y coordinate is increasing |
| 283 | * -1 is added for each crossing where the Y coordinate is decreasing |
| 284 | */ |
| 285 | public static int pointCrossingsForCubic(double px, double py, |
| 286 | double x0, double y0, |
| 287 | double xc0, double yc0, |
| 288 | double xc1, double yc1, |
| 289 | double x1, double y1, int level) |
| 290 | { |
| 291 | if (py < y0 && py < yc0 && py < yc1 && py < y1) return 0; |
| 292 | if (py >= y0 && py >= yc0 && py >= yc1 && py >= y1) return 0; |
| 293 | // Note y0 could equal yc0... |
| 294 | if (px >= x0 && px >= xc0 && px >= xc1 && px >= x1) return 0; |
| 295 | if (px < x0 && px < xc0 && px < xc1 && px < x1) { |
| 296 | if (py >= y0) { |
| 297 | if (py < y1) return 1; |
| 298 | } else { |
| 299 | // py < y0 |
| 300 | if (py >= y1) return -1; |
| 301 | } |
| 302 | // py outside of y01 range, and/or y0==yc0 |
| 303 | return 0; |
| 304 | } |
| 305 | // double precision only has 52 bits of mantissa |
| 306 | if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1); |
| 307 | double xmid = (xc0 + xc1) / 2; |
| 308 | double ymid = (yc0 + yc1) / 2; |
| 309 | xc0 = (x0 + xc0) / 2; |
| 310 | yc0 = (y0 + yc0) / 2; |
| 311 | xc1 = (xc1 + x1) / 2; |
| 312 | yc1 = (yc1 + y1) / 2; |
| 313 | double xc0m = (xc0 + xmid) / 2; |
| 314 | double yc0m = (yc0 + ymid) / 2; |
| 315 | double xmc1 = (xmid + xc1) / 2; |
| 316 | double ymc1 = (ymid + yc1) / 2; |
| 317 | xmid = (xc0m + xmc1) / 2; |
| 318 | ymid = (yc0m + ymc1) / 2; |
| 319 | if (Double.isNaN(xmid) || Double.isNaN(ymid)) { |
| 320 | // [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN |
| 321 | // [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN |
| 322 | // These values are also NaN if opposing infinities are added |
| 323 | return 0; |
| 324 | } |
| 325 | return (pointCrossingsForCubic(px, py, |
| 326 | x0, y0, xc0, yc0, |
| 327 | xc0m, yc0m, xmid, ymid, level+1) + |
| 328 | pointCrossingsForCubic(px, py, |
| 329 | xmid, ymid, xmc1, ymc1, |
| 330 | xc1, yc1, x1, y1, level+1)); |
| 331 | } |
| 332 | |
| 333 | /** |
| 334 | * The rectangle intersection test counts the number of times |
| 335 | * that the path crosses through the shadow that the rectangle |
| 336 | * projects to the right towards (x => +INFINITY). |
| 337 | * |
| 338 | * During processing of the path it actually counts every time |
| 339 | * the path crosses either or both of the top and bottom edges |
| 340 | * of that shadow. If the path enters from the top, the count |
| 341 | * is incremented. If it then exits back through the top, the |
| 342 | * same way it came in, the count is decremented and there is |
| 343 | * no impact on the winding count. If, instead, the path exits |
| 344 | * out the bottom, then the count is incremented again and a |
| 345 | * full pass through the shadow is indicated by the winding count |
| 346 | * having been incremented by 2. |
| 347 | * |
| 348 | * Thus, the winding count that it accumulates is actually double |
| 349 | * the real winding count. Since the path is continuous, the |
| 350 | * final answer should be a multiple of 2, otherwise there is a |
| 351 | * logic error somewhere. |
| 352 | * |
| 353 | * If the path ever has a direct hit on the rectangle, then a |
| 354 | * special value is returned. This special value terminates |
| 355 | * all ongoing accumulation on up through the call chain and |
| 356 | * ends up getting returned to the calling function which can |
| 357 | * then produce an answer directly. For intersection tests, |
| 358 | * the answer is always "true" if the path intersects the |
| 359 | * rectangle. For containment tests, the answer is always |
| 360 | * "false" if the path intersects the rectangle. Thus, no |
| 361 | * further processing is ever needed if an intersection occurs. |
| 362 | */ |
| 363 | public static final int RECT_INTERSECTS = 0x80000000; |
| 364 | |
| 365 | /** |
| 366 | * Accumulate the number of times the path crosses the shadow |
| 367 | * extending to the right of the rectangle. See the comment |
| 368 | * for the RECT_INTERSECTS constant for more complete details. |
| 369 | * The return value is the sum of all crossings for both the |
| 370 | * top and bottom of the shadow for every segment in the path, |
| 371 | * or the special value RECT_INTERSECTS if the path ever enters |
| 372 | * the interior of the rectangle. |
| 373 | * The path must start with a SEG_MOVETO, otherwise an exception is |
| 374 | * thrown. |
| 375 | * The caller must check r[xy]{min,max} for NaN values. |
| 376 | */ |
| 377 | public static int rectCrossingsForPath(PathIterator pi, |
| 378 | double rxmin, double rymin, |
| 379 | double rxmax, double rymax) |
| 380 | { |
| 381 | if (rxmax <= rxmin || rymax <= rymin) { |
| 382 | return 0; |
| 383 | } |
| 384 | if (pi.isDone()) { |
| 385 | return 0; |
| 386 | } |
| 387 | double coords[] = new double[6]; |
| 388 | if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) { |
| 389 | throw new IllegalPathStateException("missing initial moveto "+ |
| 390 | "in path definition"); |
| 391 | } |
| 392 | pi.next(); |
| 393 | double curx, cury, movx, movy, endx, endy; |
| 394 | curx = movx = coords[0]; |
| 395 | cury = movy = coords[1]; |
| 396 | int crossings = 0; |
| 397 | while (crossings != RECT_INTERSECTS && !pi.isDone()) { |
| 398 | switch (pi.currentSegment(coords)) { |
| 399 | case PathIterator.SEG_MOVETO: |
| 400 | if (curx != movx || cury != movy) { |
| 401 | crossings = rectCrossingsForLine(crossings, |
| 402 | rxmin, rymin, |
| 403 | rxmax, rymax, |
| 404 | curx, cury, |
| 405 | movx, movy); |
| 406 | } |
| 407 | // Count should always be a multiple of 2 here. |
| 408 | // assert((crossings & 1) != 0); |
| 409 | movx = curx = coords[0]; |
| 410 | movy = cury = coords[1]; |
| 411 | break; |
| 412 | case PathIterator.SEG_LINETO: |
| 413 | endx = coords[0]; |
| 414 | endy = coords[1]; |
| 415 | crossings = rectCrossingsForLine(crossings, |
| 416 | rxmin, rymin, |
| 417 | rxmax, rymax, |
| 418 | curx, cury, |
| 419 | endx, endy); |
| 420 | curx = endx; |
| 421 | cury = endy; |
| 422 | break; |
| 423 | case PathIterator.SEG_QUADTO: |
| 424 | endx = coords[2]; |
| 425 | endy = coords[3]; |
| 426 | crossings = rectCrossingsForQuad(crossings, |
| 427 | rxmin, rymin, |
| 428 | rxmax, rymax, |
| 429 | curx, cury, |
| 430 | coords[0], coords[1], |
| 431 | endx, endy, 0); |
| 432 | curx = endx; |
| 433 | cury = endy; |
| 434 | break; |
| 435 | case PathIterator.SEG_CUBICTO: |
| 436 | endx = coords[4]; |
| 437 | endy = coords[5]; |
| 438 | crossings = rectCrossingsForCubic(crossings, |
| 439 | rxmin, rymin, |
| 440 | rxmax, rymax, |
| 441 | curx, cury, |
| 442 | coords[0], coords[1], |
| 443 | coords[2], coords[3], |
| 444 | endx, endy, 0); |
| 445 | curx = endx; |
| 446 | cury = endy; |
| 447 | break; |
| 448 | case PathIterator.SEG_CLOSE: |
| 449 | if (curx != movx || cury != movy) { |
| 450 | crossings = rectCrossingsForLine(crossings, |
| 451 | rxmin, rymin, |
| 452 | rxmax, rymax, |
| 453 | curx, cury, |
| 454 | movx, movy); |
| 455 | } |
| 456 | curx = movx; |
| 457 | cury = movy; |
| 458 | // Count should always be a multiple of 2 here. |
| 459 | // assert((crossings & 1) != 0); |
| 460 | break; |
| 461 | } |
| 462 | pi.next(); |
| 463 | } |
| 464 | if (crossings != RECT_INTERSECTS && (curx != movx || cury != movy)) { |
| 465 | crossings = rectCrossingsForLine(crossings, |
| 466 | rxmin, rymin, |
| 467 | rxmax, rymax, |
| 468 | curx, cury, |
| 469 | movx, movy); |
| 470 | } |
| 471 | // Count should always be a multiple of 2 here. |
| 472 | // assert((crossings & 1) != 0); |
| 473 | return crossings; |
| 474 | } |
| 475 | |
| 476 | /** |
| 477 | * Accumulate the number of times the line crosses the shadow |
| 478 | * extending to the right of the rectangle. See the comment |
| 479 | * for the RECT_INTERSECTS constant for more complete details. |
| 480 | */ |
| 481 | public static int rectCrossingsForLine(int crossings, |
| 482 | double rxmin, double rymin, |
| 483 | double rxmax, double rymax, |
| 484 | double x0, double y0, |
| 485 | double x1, double y1) |
| 486 | { |
| 487 | if (y0 >= rymax && y1 >= rymax) return crossings; |
| 488 | if (y0 <= rymin && y1 <= rymin) return crossings; |
| 489 | if (x0 <= rxmin && x1 <= rxmin) return crossings; |
| 490 | if (x0 >= rxmax && x1 >= rxmax) { |
| 491 | // Line is entirely to the right of the rect |
| 492 | // and the vertical ranges of the two overlap by a non-empty amount |
| 493 | // Thus, this line segment is partially in the "right-shadow" |
| 494 | // Path may have done a complete crossing |
| 495 | // Or path may have entered or exited the right-shadow |
| 496 | if (y0 < y1) { |
| 497 | // y-increasing line segment... |
| 498 | // We know that y0 < rymax and y1 > rymin |
| 499 | if (y0 <= rymin) crossings++; |
| 500 | if (y1 >= rymax) crossings++; |
| 501 | } else if (y1 < y0) { |
| 502 | // y-decreasing line segment... |
| 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 | } |