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 "SkIntersections.h" 9 #include "SkPathOpsCubic.h" 10 #include "SkPathOpsLine.h" 11 #include "SkPathOpsPoint.h" 12 #include "SkPathOpsQuad.h" 13 #include "SkPathOpsRect.h" 14 #include "SkReduceOrder.h" 15 #include "SkTSort.h" 16 17 #if ONE_OFF_DEBUG 18 static const double tLimits1[2][2] = {{0.3, 0.4}, {0.8, 0.9}}; 19 static const double tLimits2[2][2] = {{-0.8, -0.9}, {-0.8, -0.9}}; 20 #endif 21 22 #define DEBUG_QUAD_PART ONE_OFF_DEBUG && 1 23 #define DEBUG_QUAD_PART_SHOW_SIMPLE DEBUG_QUAD_PART && 0 24 #define SWAP_TOP_DEBUG 0 25 26 static const int kCubicToQuadSubdivisionDepth = 8; // slots reserved for cubic to quads subdivision 27 28 static int quadPart(const SkDCubic& cubic, double tStart, double tEnd, SkReduceOrder* reducer) { 29 SkDCubic part = cubic.subDivide(tStart, tEnd); 30 SkDQuad quad = part.toQuad(); 31 // FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an 32 // extremely shallow quadratic? 33 int order = reducer->reduce(quad); 34 #if DEBUG_QUAD_PART 35 SkDebugf("%s cubic=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)" 36 " t=(%1.9g,%1.9g)\n", __FUNCTION__, cubic[0].fX, cubic[0].fY, 37 cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY, 38 cubic[3].fX, cubic[3].fY, tStart, tEnd); 39 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n" 40 " {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", 41 part[0].fX, part[0].fY, part[1].fX, part[1].fY, part[2].fX, part[2].fY, 42 part[3].fX, part[3].fY, quad[0].fX, quad[0].fY, 43 quad[1].fX, quad[1].fY, quad[2].fX, quad[2].fY); 44 #if DEBUG_QUAD_PART_SHOW_SIMPLE 45 SkDebugf("%s simple=(%1.9g,%1.9g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY); 46 if (order > 1) { 47 SkDebugf(" %1.9g,%1.9g", reducer->fQuad[1].fX, reducer->fQuad[1].fY); 48 } 49 if (order > 2) { 50 SkDebugf(" %1.9g,%1.9g", reducer->fQuad[2].fX, reducer->fQuad[2].fY); 51 } 52 SkDebugf(")\n"); 53 SkASSERT(order < 4 && order > 0); 54 #endif 55 #endif 56 return order; 57 } 58 59 static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2, 60 int order2, SkIntersections& i) { 61 if (order1 == 3 && order2 == 3) { 62 i.intersect(simple1, simple2); 63 } else if (order1 <= 2 && order2 <= 2) { 64 i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2); 65 } else if (order1 == 3 && order2 <= 2) { 66 i.intersect(simple1, (const SkDLine&) simple2); 67 } else { 68 SkASSERT(order1 <= 2 && order2 == 3); 69 i.intersect(simple2, (const SkDLine&) simple1); 70 i.swapPts(); 71 } 72 } 73 74 // this flavor centers potential intersections recursively. In contrast, '2' may inadvertently 75 // chase intersections near quadratic ends, requiring odd hacks to find them. 76 static void intersect(const SkDCubic& cubic1, double t1s, double t1e, const SkDCubic& cubic2, 77 double t2s, double t2e, double precisionScale, SkIntersections& i) { 78 i.upDepth(); 79 SkDCubic c1 = cubic1.subDivide(t1s, t1e); 80 SkDCubic c2 = cubic2.subDivide(t2s, t2e); 81 SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts1; 82 // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection) 83 c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1); 84 SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts2; 85 c2.toQuadraticTs(c2.calcPrecision() * precisionScale, &ts2); 86 double t1Start = t1s; 87 int ts1Count = ts1.count(); 88 for (int i1 = 0; i1 <= ts1Count; ++i1) { 89 const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1; 90 const double t1 = t1s + (t1e - t1s) * tEnd1; 91 SkReduceOrder s1; 92 int o1 = quadPart(cubic1, t1Start, t1, &s1); 93 double t2Start = t2s; 94 int ts2Count = ts2.count(); 95 for (int i2 = 0; i2 <= ts2Count; ++i2) { 96 const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1; 97 const double t2 = t2s + (t2e - t2s) * tEnd2; 98 if (&cubic1 == &cubic2 && t1Start >= t2Start) { 99 t2Start = t2; 100 continue; 101 } 102 SkReduceOrder s2; 103 int o2 = quadPart(cubic2, t2Start, t2, &s2); 104 #if ONE_OFF_DEBUG 105 char tab[] = " "; 106 if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1 107 && tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) { 108 SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab, 109 __FUNCTION__, t1Start, t1, t2Start, t2); 110 SkIntersections xlocals; 111 xlocals.allowNear(false); 112 intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals); 113 SkDebugf(" xlocals.fUsed=%d\n", xlocals.used()); 114 } 115 #endif 116 SkIntersections locals; 117 locals.allowNear(false); 118 intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals); 119 int tCount = locals.used(); 120 for (int tIdx = 0; tIdx < tCount; ++tIdx) { 121 double to1 = t1Start + (t1 - t1Start) * locals[0][tIdx]; 122 double to2 = t2Start + (t2 - t2Start) * locals[1][tIdx]; 123 // if the computed t is not sufficiently precise, iterate 124 SkDPoint p1 = cubic1.ptAtT(to1); 125 SkDPoint p2 = cubic2.ptAtT(to2); 126 if (p1.approximatelyEqual(p2)) { 127 // FIXME: local edge may be coincident -- experiment with not propagating coincidence to caller 128 // SkASSERT(!locals.isCoincident(tIdx)); 129 if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) { 130 if (i.swapped()) { // FIXME: insert should respect swap 131 i.insert(to2, to1, p1); 132 } else { 133 i.insert(to1, to2, p1); 134 } 135 } 136 } else { 137 /*for random cubics, 16 below catches 99.997% of the intersections. To test for the remaining 0.003% 138 look for nearly coincident curves. and check each 1/16th section. 139 */ 140 double offset = precisionScale / 16; // FIXME: const is arbitrary: test, refine 141 double c1Bottom = tIdx == 0 ? 0 : 142 (t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2; 143 double c1Min = SkTMax(c1Bottom, to1 - offset); 144 double c1Top = tIdx == tCount - 1 ? 1 : 145 (t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2; 146 double c1Max = SkTMin(c1Top, to1 + offset); 147 double c2Min = SkTMax(0., to2 - offset); 148 double c2Max = SkTMin(1., to2 + offset); 149 #if ONE_OFF_DEBUG 150 SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, 151 __FUNCTION__, 152 c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max 153 && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, 154 to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset 155 && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, 156 c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max 157 && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, 158 to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset 159 && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); 160 SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" 161 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", 162 i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1., 163 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); 164 SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" 165 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, 166 c1Max, c2Min, c2Max); 167 #endif 168 intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); 169 #if ONE_OFF_DEBUG 170 SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, 171 i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); 172 #endif 173 if (tCount > 1) { 174 c1Min = SkTMax(0., to1 - offset); 175 c1Max = SkTMin(1., to1 + offset); 176 double c2Bottom = tIdx == 0 ? to2 : 177 (t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2; 178 double c2Top = tIdx == tCount - 1 ? to2 : 179 (t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2; 180 if (c2Bottom > c2Top) { 181 SkTSwap(c2Bottom, c2Top); 182 } 183 if (c2Bottom == to2) { 184 c2Bottom = 0; 185 } 186 if (c2Top == to2) { 187 c2Top = 1; 188 } 189 c2Min = SkTMax(c2Bottom, to2 - offset); 190 c2Max = SkTMin(c2Top, to2 + offset); 191 #if ONE_OFF_DEBUG 192 SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, 193 __FUNCTION__, 194 c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max 195 && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, 196 to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset 197 && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, 198 c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max 199 && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, 200 to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset 201 && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); 202 SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" 203 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", 204 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, 205 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); 206 SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" 207 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, 208 c1Max, c2Min, c2Max); 209 #endif 210 intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); 211 #if ONE_OFF_DEBUG 212 SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, 213 i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); 214 #endif 215 c1Min = SkTMax(c1Bottom, to1 - offset); 216 c1Max = SkTMin(c1Top, to1 + offset); 217 #if ONE_OFF_DEBUG 218 SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, 219 __FUNCTION__, 220 c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max 221 && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, 222 to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset 223 && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, 224 c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max 225 && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, 226 to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset 227 && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); 228 SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" 229 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", 230 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, 231 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); 232 SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" 233 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, 234 c1Max, c2Min, c2Max); 235 #endif 236 intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); 237 #if ONE_OFF_DEBUG 238 SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, 239 i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); 240 #endif 241 } 242 // intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); 243 // FIXME: if no intersection is found, either quadratics intersected where 244 // cubics did not, or the intersection was missed. In the former case, expect 245 // the quadratics to be nearly parallel at the point of intersection, and check 246 // for that. 247 } 248 } 249 t2Start = t2; 250 } 251 t1Start = t1; 252 } 253 i.downDepth(); 254 } 255 256 // if two ends intersect, check middle for coincidence 257 bool SkIntersections::cubicCheckCoincidence(const SkDCubic& c1, const SkDCubic& c2) { 258 if (fUsed < 2) { 259 return false; 260 } 261 int last = fUsed - 1; 262 double tRange1 = fT[0][last] - fT[0][0]; 263 double tRange2 = fT[1][last] - fT[1][0]; 264 for (int index = 1; index < 5; ++index) { 265 double testT1 = fT[0][0] + tRange1 * index / 5; 266 double testT2 = fT[1][0] + tRange2 * index / 5; 267 SkDPoint testPt1 = c1.ptAtT(testT1); 268 SkDPoint testPt2 = c2.ptAtT(testT2); 269 if (!testPt1.approximatelyEqual(testPt2)) { 270 return false; 271 } 272 } 273 if (fUsed > 2) { 274 fPt[1] = fPt[last]; 275 fT[0][1] = fT[0][last]; 276 fT[1][1] = fT[1][last]; 277 fUsed = 2; 278 } 279 fIsCoincident[0] = fIsCoincident[1] = 0x03; 280 return true; 281 } 282 283 #define LINE_FRACTION 0.1 284 285 // intersect the end of the cubic with the other. Try lines from the end to control and opposite 286 // end to determine range of t on opposite cubic. 287 bool SkIntersections::cubicExactEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2) { 288 int t1Index = start ? 0 : 3; 289 double testT = (double) !start; 290 bool swap = swapped(); 291 // quad/quad at this point checks to see if exact matches have already been found 292 // cubic/cubic can't reject so easily since cubics can intersect same point more than once 293 SkDLine tmpLine; 294 tmpLine[0] = tmpLine[1] = cubic2[t1Index]; 295 tmpLine[1].fX += cubic2[2 - start].fY - cubic2[t1Index].fY; 296 tmpLine[1].fY -= cubic2[2 - start].fX - cubic2[t1Index].fX; 297 SkIntersections impTs; 298 impTs.allowNear(false); 299 impTs.intersectRay(cubic1, tmpLine); 300 for (int index = 0; index < impTs.used(); ++index) { 301 SkDPoint realPt = impTs.pt(index); 302 if (!tmpLine[0].approximatelyEqual(realPt)) { 303 continue; 304 } 305 if (swap) { 306 cubicInsert(testT, impTs[0][index], tmpLine[0], cubic2, cubic1); 307 } else { 308 cubicInsert(impTs[0][index], testT, tmpLine[0], cubic1, cubic2); 309 } 310 return true; 311 } 312 return false; 313 } 314 315 316 void SkIntersections::cubicInsert(double one, double two, const SkDPoint& pt, 317 const SkDCubic& cubic1, const SkDCubic& cubic2) { 318 for (int index = 0; index < fUsed; ++index) { 319 if (fT[0][index] == one) { 320 double oldTwo = fT[1][index]; 321 if (oldTwo == two) { 322 return; 323 } 324 SkDPoint mid = cubic2.ptAtT((oldTwo + two) / 2); 325 if (mid.approximatelyEqual(fPt[index])) { 326 return; 327 } 328 } 329 if (fT[1][index] == two) { 330 SkDPoint mid = cubic1.ptAtT((fT[0][index] + two) / 2); 331 if (mid.approximatelyEqual(fPt[index])) { 332 return; 333 } 334 } 335 } 336 insert(one, two, pt); 337 } 338 339 void SkIntersections::cubicNearEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2, 340 const SkDRect& bounds2) { 341 SkDLine line; 342 int t1Index = start ? 0 : 3; 343 double testT = (double) !start; 344 // don't bother if the two cubics are connnected 345 static const int kPointsInCubic = 4; // FIXME: move to DCubic, replace '4' with this 346 static const int kMaxLineCubicIntersections = 3; 347 SkSTArray<(kMaxLineCubicIntersections - 1) * kMaxLineCubicIntersections, double, true> tVals; 348 line[0] = cubic1[t1Index]; 349 // this variant looks for intersections with the end point and lines parallel to other points 350 for (int index = 0; index < kPointsInCubic; ++index) { 351 if (index == t1Index) { 352 continue; 353 } 354 SkDVector dxy1 = cubic1[index] - line[0]; 355 dxy1 /= SkDCubic::gPrecisionUnit; 356 line[1] = line[0] + dxy1; 357 SkDRect lineBounds; 358 lineBounds.setBounds(line); 359 if (!bounds2.intersects(&lineBounds)) { 360 continue; 361 } 362 SkIntersections local; 363 if (!local.intersect(cubic2, line)) { 364 continue; 365 } 366 for (int idx2 = 0; idx2 < local.used(); ++idx2) { 367 double foundT = local[0][idx2]; 368 if (approximately_less_than_zero(foundT) 369 || approximately_greater_than_one(foundT)) { 370 continue; 371 } 372 if (local.pt(idx2).approximatelyEqual(line[0])) { 373 if (swapped()) { // FIXME: insert should respect swap 374 insert(foundT, testT, line[0]); 375 } else { 376 insert(testT, foundT, line[0]); 377 } 378 } else { 379 tVals.push_back(foundT); 380 } 381 } 382 } 383 if (tVals.count() == 0) { 384 return; 385 } 386 SkTQSort<double>(tVals.begin(), tVals.end() - 1); 387 double tMin1 = start ? 0 : 1 - LINE_FRACTION; 388 double tMax1 = start ? LINE_FRACTION : 1; 389 int tIdx = 0; 390 do { 391 int tLast = tIdx; 392 while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) { 393 ++tLast; 394 } 395 double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0); 396 double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0); 397 int lastUsed = used(); 398 if (start ? tMax1 < tMin2 : tMax2 < tMin1) { 399 ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this); 400 } 401 if (lastUsed == used()) { 402 tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0); 403 tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0); 404 if (start ? tMax1 < tMin2 : tMax2 < tMin1) { 405 ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this); 406 } 407 } 408 tIdx = tLast + 1; 409 } while (tIdx < tVals.count()); 410 return; 411 } 412 413 const double CLOSE_ENOUGH = 0.001; 414 415 static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { 416 if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) { 417 return false; 418 } 419 pt = cubic.ptAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2); 420 return true; 421 } 422 423 static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { 424 int last = i.used() - 1; 425 if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) { 426 return false; 427 } 428 pt = cubic.ptAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2); 429 return true; 430 } 431 432 static bool only_end_pts_in_common(const SkDCubic& c1, const SkDCubic& c2) { 433 // the idea here is to see at minimum do a quick reject by rotating all points 434 // to either side of the line formed by connecting the endpoints 435 // if the opposite curves points are on the line or on the other side, the 436 // curves at most intersect at the endpoints 437 for (int oddMan = 0; oddMan < 4; ++oddMan) { 438 const SkDPoint* endPt[3]; 439 for (int opp = 1; opp < 4; ++opp) { 440 int end = oddMan ^ opp; // choose a value not equal to oddMan 441 endPt[opp - 1] = &c1[end]; 442 } 443 for (int triTest = 0; triTest < 3; ++triTest) { 444 double origX = endPt[triTest]->fX; 445 double origY = endPt[triTest]->fY; 446 int oppTest = triTest + 1; 447 if (3 == oppTest) { 448 oppTest = 0; 449 } 450 double adj = endPt[oppTest]->fX - origX; 451 double opp = endPt[oppTest]->fY - origY; 452 if (adj == 0 && opp == 0) { // if the other point equals the test point, ignore it 453 continue; 454 } 455 double sign = (c1[oddMan].fY - origY) * adj - (c1[oddMan].fX - origX) * opp; 456 if (approximately_zero(sign)) { 457 goto tryNextHalfPlane; 458 } 459 for (int n = 0; n < 4; ++n) { 460 double test = (c2[n].fY - origY) * adj - (c2[n].fX - origX) * opp; 461 if (test * sign > 0 && !precisely_zero(test)) { 462 goto tryNextHalfPlane; 463 } 464 } 465 } 466 return true; 467 tryNextHalfPlane: 468 ; 469 } 470 return false; 471 } 472 473 int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) { 474 if (fMax == 0) { 475 fMax = 9; 476 } 477 bool selfIntersect = &c1 == &c2; 478 if (selfIntersect) { 479 if (c1[0].approximatelyEqual(c1[3])) { 480 insert(0, 1, c1[0]); 481 return fUsed; 482 } 483 } else { 484 // OPTIMIZATION: set exact end bits here to avoid cubic exact end later 485 for (int i1 = 0; i1 < 4; i1 += 3) { 486 for (int i2 = 0; i2 < 4; i2 += 3) { 487 if (c1[i1].approximatelyEqual(c2[i2])) { 488 insert(i1 >> 1, i2 >> 1, c1[i1]); 489 } 490 } 491 } 492 } 493 SkASSERT(fUsed < 4); 494 if (!selfIntersect) { 495 if (only_end_pts_in_common(c1, c2)) { 496 return fUsed; 497 } 498 if (only_end_pts_in_common(c2, c1)) { 499 return fUsed; 500 } 501 } 502 // quad/quad does linear test here -- cubic does not 503 // cubics which are really lines should have been detected in reduce step earlier 504 int exactEndBits = 0; 505 if (selfIntersect) { 506 if (fUsed) { 507 return fUsed; 508 } 509 } else { 510 exactEndBits |= cubicExactEnd(c1, false, c2) << 0; 511 exactEndBits |= cubicExactEnd(c1, true, c2) << 1; 512 swap(); 513 exactEndBits |= cubicExactEnd(c2, false, c1) << 2; 514 exactEndBits |= cubicExactEnd(c2, true, c1) << 3; 515 swap(); 516 } 517 if (cubicCheckCoincidence(c1, c2)) { 518 SkASSERT(!selfIntersect); 519 return fUsed; 520 } 521 // FIXME: pass in cached bounds from caller 522 SkDRect c2Bounds; 523 c2Bounds.setBounds(c2); 524 if (!(exactEndBits & 4)) { 525 cubicNearEnd(c1, false, c2, c2Bounds); 526 } 527 if (!(exactEndBits & 8)) { 528 if (selfIntersect && fUsed) { 529 return fUsed; 530 } 531 cubicNearEnd(c1, true, c2, c2Bounds); 532 if (selfIntersect && fUsed && ((approximately_less_than_zero(fT[0][0]) 533 && approximately_less_than_zero(fT[1][0])) 534 || (approximately_greater_than_one(fT[0][0]) 535 && approximately_greater_than_one(fT[1][0])))) { 536 SkASSERT(fUsed == 1); 537 fUsed = 0; 538 return fUsed; 539 } 540 } 541 if (!selfIntersect) { 542 SkDRect c1Bounds; 543 c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ? 544 swap(); 545 if (!(exactEndBits & 1)) { 546 cubicNearEnd(c2, false, c1, c1Bounds); 547 } 548 if (!(exactEndBits & 2)) { 549 cubicNearEnd(c2, true, c1, c1Bounds); 550 } 551 swap(); 552 } 553 if (cubicCheckCoincidence(c1, c2)) { 554 SkASSERT(!selfIntersect); 555 return fUsed; 556 } 557 SkIntersections i; 558 i.fAllowNear = false; 559 i.fMax = 9; 560 ::intersect(c1, 0, 1, c2, 0, 1, 1, i); 561 int compCount = i.used(); 562 if (compCount) { 563 int exactCount = used(); 564 if (exactCount == 0) { 565 *this = i; 566 } else { 567 // at least one is exact or near, and at least one was computed. Eliminate duplicates 568 for (int exIdx = 0; exIdx < exactCount; ++exIdx) { 569 for (int cpIdx = 0; cpIdx < compCount; ) { 570 if (fT[0][0] == i[0][0] && fT[1][0] == i[1][0]) { 571 i.removeOne(cpIdx); 572 --compCount; 573 continue; 574 } 575 double tAvg = (fT[0][exIdx] + i[0][cpIdx]) / 2; 576 SkDPoint pt = c1.ptAtT(tAvg); 577 if (!pt.approximatelyEqual(fPt[exIdx])) { 578 ++cpIdx; 579 continue; 580 } 581 tAvg = (fT[1][exIdx] + i[1][cpIdx]) / 2; 582 pt = c2.ptAtT(tAvg); 583 if (!pt.approximatelyEqual(fPt[exIdx])) { 584 ++cpIdx; 585 continue; 586 } 587 i.removeOne(cpIdx); 588 --compCount; 589 } 590 } 591 // if mid t evaluates to nearly the same point, skip the t 592 for (int cpIdx = 0; cpIdx < compCount - 1; ) { 593 double tAvg = (fT[0][cpIdx] + i[0][cpIdx + 1]) / 2; 594 SkDPoint pt = c1.ptAtT(tAvg); 595 if (!pt.approximatelyEqual(fPt[cpIdx])) { 596 ++cpIdx; 597 continue; 598 } 599 tAvg = (fT[1][cpIdx] + i[1][cpIdx + 1]) / 2; 600 pt = c2.ptAtT(tAvg); 601 if (!pt.approximatelyEqual(fPt[cpIdx])) { 602 ++cpIdx; 603 continue; 604 } 605 i.removeOne(cpIdx); 606 --compCount; 607 } 608 // in addition to adding below missing function, think about how to say 609 append(i); 610 } 611 } 612 // If an end point and a second point very close to the end is returned, the second 613 // point may have been detected because the approximate quads 614 // intersected at the end and close to it. Verify that the second point is valid. 615 if (fUsed <= 1) { 616 return fUsed; 617 } 618 SkDPoint pt[2]; 619 if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1]) 620 && pt[0].approximatelyEqual(pt[1])) { 621 removeOne(1); 622 } 623 if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1]) 624 && pt[0].approximatelyEqual(pt[1])) { 625 removeOne(used() - 2); 626 } 627 // vet the pairs of t values to see if the mid value is also on the curve. If so, mark 628 // the span as coincident 629 if (fUsed >= 2 && !coincidentUsed()) { 630 int last = fUsed - 1; 631 int match = 0; 632 for (int index = 0; index < last; ++index) { 633 double mid1 = (fT[0][index] + fT[0][index + 1]) / 2; 634 double mid2 = (fT[1][index] + fT[1][index + 1]) / 2; 635 pt[0] = c1.ptAtT(mid1); 636 pt[1] = c2.ptAtT(mid2); 637 if (pt[0].approximatelyEqual(pt[1])) { 638 match |= 1 << index; 639 } 640 } 641 if (match) { 642 #if DEBUG_CONCIDENT 643 if (((match + 1) & match) != 0) { 644 SkDebugf("%s coincident hole\n", __FUNCTION__); 645 } 646 #endif 647 // for now, assume that everything from start to finish is coincident 648 if (fUsed > 2) { 649 fPt[1] = fPt[last]; 650 fT[0][1] = fT[0][last]; 651 fT[1][1] = fT[1][last]; 652 fIsCoincident[0] = 0x03; 653 fIsCoincident[1] = 0x03; 654 fUsed = 2; 655 } 656 } 657 } 658 return fUsed; 659 } 660 661 // Up promote the quad to a cubic. 662 // OPTIMIZATION If this is a common use case, optimize by duplicating 663 // the intersect 3 loop to avoid the promotion / demotion code 664 int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) { 665 fMax = 6; 666 SkDCubic up = quad.toCubic(); 667 (void) intersect(cubic, up); 668 return used(); 669 } 670 671 /* http://www.ag.jku.at/compass/compasssample.pdf 672 ( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen 673 Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth (at) math.uio.no 674 SINTEF Applied Mathematics http://www.sintef.no ) 675 describes a method to find the self intersection of a cubic by taking the gradient of the implicit 676 form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/ 677 678 int SkIntersections::intersect(const SkDCubic& c) { 679 fMax = 1; 680 // check to see if x or y end points are the extrema. Are other quick rejects possible? 681 if (c.endsAreExtremaInXOrY()) { 682 return false; 683 } 684 // OPTIMIZATION: could quick reject if neither end point tangent ray intersected the line 685 // segment formed by the opposite end point to the control point 686 (void) intersect(c, c); 687 if (used() > 0) { 688 if (approximately_equal_double(fT[0][0], fT[1][0])) { 689 fUsed = 0; 690 } else { 691 SkASSERT(used() == 1); 692 if (fT[0][0] > fT[1][0]) { 693 swapPts(); 694 } 695 } 696 } 697 return used(); 698 } 699
