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 #include "SkOpAngle.h" 8 #include "SkOpSegment.h" 9 #include "SkPathOpsCurve.h" 10 #include "SkTSort.h" 11 12 /* Angles are sorted counterclockwise. The smallest angle has a positive x and the smallest 13 positive y. The largest angle has a positive x and a zero y. */ 14 15 #if DEBUG_ANGLE 16 static bool CompareResult(const char* func, SkString* bugOut, SkString* bugPart, int append, 17 bool compare) { 18 SkDebugf("%s %c %d\n", bugOut->c_str(), compare ? 'T' : 'F', append); 19 SkDebugf("%sPart %s\n", func, bugPart[0].c_str()); 20 SkDebugf("%sPart %s\n", func, bugPart[1].c_str()); 21 SkDebugf("%sPart %s\n", func, bugPart[2].c_str()); 22 return compare; 23 } 24 25 #define COMPARE_RESULT(append, compare) CompareResult(__FUNCTION__, &bugOut, bugPart, append, \ 26 compare) 27 #else 28 #define COMPARE_RESULT(append, compare) compare 29 #endif 30 31 /* quarter angle values for sector 32 33 31 x > 0, y == 0 horizontal line (to the right) 34 0 x > 0, y == epsilon quad/cubic horizontal tangent eventually going +y 35 1 x > 0, y > 0, x > y nearer horizontal angle 36 2 x + e == y quad/cubic 45 going horiz 37 3 x > 0, y > 0, x == y 45 angle 38 4 x == y + e quad/cubic 45 going vert 39 5 x > 0, y > 0, x < y nearer vertical angle 40 6 x == epsilon, y > 0 quad/cubic vertical tangent eventually going +x 41 7 x == 0, y > 0 vertical line (to the top) 42 43 8 7 6 44 9 | 5 45 10 | 4 46 11 | 3 47 12 \ | / 2 48 13 | 1 49 14 | 0 50 15 --------------+------------- 31 51 16 | 30 52 17 | 29 53 18 / | \ 28 54 19 | 27 55 20 | 26 56 21 | 25 57 22 23 24 58 */ 59 60 // return true if lh < this < rh 61 bool SkOpAngle::after(SkOpAngle* test) { 62 SkOpAngle* lh = test; 63 SkOpAngle* rh = lh->fNext; 64 SkASSERT(lh != rh); 65 #if DEBUG_ANGLE 66 SkString bugOut; 67 bugOut.printf("%s [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" 68 " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" 69 " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g ", __FUNCTION__, 70 lh->segment()->debugID(), lh->debugID(), lh->fSectorStart, lh->fSectorEnd, 71 lh->fStart->t(), lh->fEnd->t(), 72 segment()->debugID(), debugID(), fSectorStart, fSectorEnd, fStart->t(), fEnd->t(), 73 rh->segment()->debugID(), rh->debugID(), rh->fSectorStart, rh->fSectorEnd, 74 rh->fStart->t(), rh->fEnd->t()); 75 SkString bugPart[3] = { lh->debugPart(), this->debugPart(), rh->debugPart() }; 76 #endif 77 if (lh->fComputeSector && !lh->computeSector()) { 78 return COMPARE_RESULT(1, true); 79 } 80 if (fComputeSector && !this->computeSector()) { 81 return COMPARE_RESULT(2, true); 82 } 83 if (rh->fComputeSector && !rh->computeSector()) { 84 return COMPARE_RESULT(3, true); 85 } 86 #if DEBUG_ANGLE // reset bugOut with computed sectors 87 bugOut.printf("%s [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" 88 " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" 89 " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g ", __FUNCTION__, 90 lh->segment()->debugID(), lh->debugID(), lh->fSectorStart, lh->fSectorEnd, 91 lh->fStart->t(), lh->fEnd->t(), 92 segment()->debugID(), debugID(), fSectorStart, fSectorEnd, fStart->t(), fEnd->t(), 93 rh->segment()->debugID(), rh->debugID(), rh->fSectorStart, rh->fSectorEnd, 94 rh->fStart->t(), rh->fEnd->t()); 95 #endif 96 bool ltrOverlap = (lh->fSectorMask | rh->fSectorMask) & fSectorMask; 97 bool lrOverlap = lh->fSectorMask & rh->fSectorMask; 98 int lrOrder; // set to -1 if either order works 99 if (!lrOverlap) { // no lh/rh sector overlap 100 if (!ltrOverlap) { // no lh/this/rh sector overlap 101 return COMPARE_RESULT(4, (lh->fSectorEnd > rh->fSectorStart) 102 ^ (fSectorStart > lh->fSectorEnd) ^ (fSectorStart > rh->fSectorStart)); 103 } 104 int lrGap = (rh->fSectorStart - lh->fSectorStart + 32) & 0x1f; 105 /* A tiny change can move the start +/- 4. The order can only be determined if 106 lr gap is not 12 to 20 or -12 to -20. 107 -31 ..-21 1 108 -20 ..-12 -1 109 -11 .. -1 0 110 0 shouldn't get here 111 11 .. 1 1 112 12 .. 20 -1 113 21 .. 31 0 114 */ 115 lrOrder = lrGap > 20 ? 0 : lrGap > 11 ? -1 : 1; 116 } else { 117 lrOrder = (int) lh->orderable(rh); 118 if (!ltrOverlap) { 119 return COMPARE_RESULT(5, !lrOrder); 120 } 121 } 122 int ltOrder; 123 SkASSERT((lh->fSectorMask & fSectorMask) || (rh->fSectorMask & fSectorMask)); 124 if (lh->fSectorMask & fSectorMask) { 125 ltOrder = (int) lh->orderable(this); 126 } else { 127 int ltGap = (fSectorStart - lh->fSectorStart + 32) & 0x1f; 128 ltOrder = ltGap > 20 ? 0 : ltGap > 11 ? -1 : 1; 129 } 130 int trOrder; 131 if (rh->fSectorMask & fSectorMask) { 132 trOrder = (int) orderable(rh); 133 } else { 134 int trGap = (rh->fSectorStart - fSectorStart + 32) & 0x1f; 135 trOrder = trGap > 20 ? 0 : trGap > 11 ? -1 : 1; 136 } 137 if (lrOrder >= 0 && ltOrder >= 0 && trOrder >= 0) { 138 return COMPARE_RESULT(7, lrOrder ? (ltOrder & trOrder) : (ltOrder | trOrder)); 139 } 140 SkASSERT(lrOrder >= 0 || ltOrder >= 0 || trOrder >= 0); 141 // There's not enough information to sort. Get the pairs of angles in opposite planes. 142 // If an order is < 0, the pair is already in an opposite plane. Check the remaining pairs. 143 // FIXME : once all variants are understood, rewrite this more simply 144 if (ltOrder == 0 && lrOrder == 0) { 145 SkASSERT(trOrder < 0); 146 // FIXME : once this is verified to work, remove one opposite angle call 147 SkDEBUGCODE(bool lrOpposite = lh->oppositePlanes(rh)); 148 bool ltOpposite = lh->oppositePlanes(this); 149 SkASSERT(lrOpposite != ltOpposite); 150 return COMPARE_RESULT(8, ltOpposite); 151 } else if (ltOrder == 1 && trOrder == 0) { 152 SkASSERT(lrOrder < 0); 153 SkDEBUGCODE(bool ltOpposite = lh->oppositePlanes(this)); 154 bool trOpposite = oppositePlanes(rh); 155 SkASSERT(ltOpposite != trOpposite); 156 return COMPARE_RESULT(9, trOpposite); 157 } else if (lrOrder == 1 && trOrder == 1) { 158 SkASSERT(ltOrder < 0); 159 SkDEBUGCODE(bool trOpposite = oppositePlanes(rh)); 160 bool lrOpposite = lh->oppositePlanes(rh); 161 SkASSERT(lrOpposite != trOpposite); 162 return COMPARE_RESULT(10, lrOpposite); 163 } 164 if (lrOrder < 0) { 165 if (ltOrder < 0) { 166 return COMPARE_RESULT(11, trOrder); 167 } 168 return COMPARE_RESULT(12, ltOrder); 169 } 170 return COMPARE_RESULT(13, !lrOrder); 171 } 172 173 // given a line, see if the opposite curve's convex hull is all on one side 174 // returns -1=not on one side 0=this CW of test 1=this CCW of test 175 int SkOpAngle::allOnOneSide(const SkOpAngle* test) { 176 SkASSERT(!fIsCurve); 177 SkASSERT(test->fIsCurve); 178 const SkDPoint& origin = test->fCurvePart[0]; 179 SkVector line; 180 if (segment()->verb() == SkPath::kLine_Verb) { 181 const SkPoint* linePts = segment()->pts(); 182 int lineStart = fStart->t() < fEnd->t() ? 0 : 1; 183 line = linePts[lineStart ^ 1] - linePts[lineStart]; 184 } else { 185 line = (fCurvePart[1] - fCurvePart[0]).asSkVector(); 186 } 187 float crosses[3]; 188 SkPath::Verb testVerb = test->segment()->verb(); 189 int iMax = SkPathOpsVerbToPoints(testVerb); 190 // SkASSERT(origin == test.fCurveHalf[0]); 191 const SkDCurve& testCurve = test->fCurvePart; 192 for (int index = 1; index <= iMax; ++index) { 193 float xy1 = (float) (line.fX * (testCurve[index].fY - origin.fY)); 194 float xy2 = (float) (line.fY * (testCurve[index].fX - origin.fX)); 195 crosses[index - 1] = AlmostEqualUlps(xy1, xy2) ? 0 : xy1 - xy2; 196 } 197 if (crosses[0] * crosses[1] < 0) { 198 return -1; 199 } 200 if (SkPath::kCubic_Verb == testVerb) { 201 if (crosses[0] * crosses[2] < 0 || crosses[1] * crosses[2] < 0) { 202 return -1; 203 } 204 } 205 if (crosses[0]) { 206 return crosses[0] < 0; 207 } 208 if (crosses[1]) { 209 return crosses[1] < 0; 210 } 211 if (SkPath::kCubic_Verb == testVerb && crosses[2]) { 212 return crosses[2] < 0; 213 } 214 fUnorderable = true; 215 return -1; 216 } 217 218 bool SkOpAngle::checkCrossesZero() const { 219 int start = SkTMin(fSectorStart, fSectorEnd); 220 int end = SkTMax(fSectorStart, fSectorEnd); 221 bool crossesZero = end - start > 16; 222 return crossesZero; 223 } 224 225 bool SkOpAngle::checkParallel(SkOpAngle* rh) { 226 SkDVector scratch[2]; 227 const SkDVector* sweep, * tweep; 228 if (!this->fUnorderedSweep) { 229 sweep = this->fSweep; 230 } else { 231 scratch[0] = this->fCurvePart[1] - this->fCurvePart[0]; 232 sweep = &scratch[0]; 233 } 234 if (!rh->fUnorderedSweep) { 235 tweep = rh->fSweep; 236 } else { 237 scratch[1] = rh->fCurvePart[1] - rh->fCurvePart[0]; 238 tweep = &scratch[1]; 239 } 240 double s0xt0 = sweep->crossCheck(*tweep); 241 if (tangentsDiverge(rh, s0xt0)) { 242 return s0xt0 < 0; 243 } 244 // compute the perpendicular to the endpoints and see where it intersects the opposite curve 245 // if the intersections within the t range, do a cross check on those 246 bool inside; 247 if (!fCurvePart[SkPathOpsVerbToPoints(this->segment()->verb())].approximatelyEqual( 248 rh->fCurvePart[SkPathOpsVerbToPoints(rh->segment()->verb())])) { 249 if (this->endToSide(rh, &inside)) { 250 return inside; 251 } 252 if (rh->endToSide(this, &inside)) { 253 return !inside; 254 } 255 } 256 if (this->midToSide(rh, &inside)) { 257 return inside; 258 } 259 if (rh->midToSide(this, &inside)) { 260 return !inside; 261 } 262 // compute the cross check from the mid T values (last resort) 263 SkDVector m0 = segment()->dPtAtT(this->midT()) - this->fCurvePart[0]; 264 SkDVector m1 = rh->segment()->dPtAtT(rh->midT()) - rh->fCurvePart[0]; 265 double m0xm1 = m0.crossCheck(m1); 266 if (m0xm1 == 0) { 267 this->fUnorderable = true; 268 rh->fUnorderable = true; 269 return true; 270 } 271 return m0xm1 < 0; 272 } 273 274 // the original angle is too short to get meaningful sector information 275 // lengthen it until it is long enough to be meaningful or leave it unset if lengthening it 276 // would cause it to intersect one of the adjacent angles 277 bool SkOpAngle::computeSector() { 278 if (fComputedSector) { 279 return !fUnorderable; 280 } 281 fComputedSector = true; 282 bool stepUp = fStart->t() < fEnd->t(); 283 const SkOpSpanBase* checkEnd = fEnd; 284 if (checkEnd->final() && stepUp) { 285 fUnorderable = true; 286 return false; 287 } 288 do { 289 // advance end 290 const SkOpSegment* other = checkEnd->segment(); 291 const SkOpSpanBase* oSpan = other->head(); 292 do { 293 if (oSpan->segment() != segment()) { 294 continue; 295 } 296 if (oSpan == checkEnd) { 297 continue; 298 } 299 if (!approximately_equal(oSpan->t(), checkEnd->t())) { 300 continue; 301 } 302 goto recomputeSector; 303 } while (!oSpan->final() && (oSpan = oSpan->upCast()->next())); 304 checkEnd = stepUp ? !checkEnd->final() 305 ? checkEnd->upCast()->next() : nullptr 306 : checkEnd->prev(); 307 } while (checkEnd); 308 recomputeSector: 309 SkOpSpanBase* computedEnd = stepUp ? checkEnd ? checkEnd->prev() : fEnd->segment()->head() 310 : checkEnd ? checkEnd->upCast()->next() : fEnd->segment()->tail(); 311 if (checkEnd == fEnd || computedEnd == fEnd || computedEnd == fStart) { 312 fUnorderable = true; 313 return false; 314 } 315 if (stepUp != (fStart->t() < computedEnd->t())) { 316 fUnorderable = true; 317 return false; 318 } 319 SkOpSpanBase* saveEnd = fEnd; 320 fComputedEnd = fEnd = computedEnd; 321 setSpans(); 322 setSector(); 323 fEnd = saveEnd; 324 return !fUnorderable; 325 } 326 327 int SkOpAngle::convexHullOverlaps(const SkOpAngle* rh) const { 328 const SkDVector* sweep = this->fSweep; 329 const SkDVector* tweep = rh->fSweep; 330 double s0xs1 = sweep[0].crossCheck(sweep[1]); 331 double s0xt0 = sweep[0].crossCheck(tweep[0]); 332 double s1xt0 = sweep[1].crossCheck(tweep[0]); 333 bool tBetweenS = s0xs1 > 0 ? s0xt0 > 0 && s1xt0 < 0 : s0xt0 < 0 && s1xt0 > 0; 334 double s0xt1 = sweep[0].crossCheck(tweep[1]); 335 double s1xt1 = sweep[1].crossCheck(tweep[1]); 336 tBetweenS |= s0xs1 > 0 ? s0xt1 > 0 && s1xt1 < 0 : s0xt1 < 0 && s1xt1 > 0; 337 double t0xt1 = tweep[0].crossCheck(tweep[1]); 338 if (tBetweenS) { 339 return -1; 340 } 341 if ((s0xt0 == 0 && s1xt1 == 0) || (s1xt0 == 0 && s0xt1 == 0)) { // s0 to s1 equals t0 to t1 342 return -1; 343 } 344 bool sBetweenT = t0xt1 > 0 ? s0xt0 < 0 && s0xt1 > 0 : s0xt0 > 0 && s0xt1 < 0; 345 sBetweenT |= t0xt1 > 0 ? s1xt0 < 0 && s1xt1 > 0 : s1xt0 > 0 && s1xt1 < 0; 346 if (sBetweenT) { 347 return -1; 348 } 349 // if all of the sweeps are in the same half plane, then the order of any pair is enough 350 if (s0xt0 >= 0 && s0xt1 >= 0 && s1xt0 >= 0 && s1xt1 >= 0) { 351 return 0; 352 } 353 if (s0xt0 <= 0 && s0xt1 <= 0 && s1xt0 <= 0 && s1xt1 <= 0) { 354 return 1; 355 } 356 // if the outside sweeps are greater than 180 degress: 357 // first assume the inital tangents are the ordering 358 // if the midpoint direction matches the inital order, that is enough 359 SkDVector m0 = this->segment()->dPtAtT(this->midT()) - this->fCurvePart[0]; 360 SkDVector m1 = rh->segment()->dPtAtT(rh->midT()) - rh->fCurvePart[0]; 361 double m0xm1 = m0.crossCheck(m1); 362 if (s0xt0 > 0 && m0xm1 > 0) { 363 return 0; 364 } 365 if (s0xt0 < 0 && m0xm1 < 0) { 366 return 1; 367 } 368 if (tangentsDiverge(rh, s0xt0)) { 369 return s0xt0 < 0; 370 } 371 return m0xm1 < 0; 372 } 373 374 // OPTIMIZATION: longest can all be either lazily computed here or precomputed in setup 375 double SkOpAngle::distEndRatio(double dist) const { 376 double longest = 0; 377 const SkOpSegment& segment = *this->segment(); 378 int ptCount = SkPathOpsVerbToPoints(segment.verb()); 379 const SkPoint* pts = segment.pts(); 380 for (int idx1 = 0; idx1 <= ptCount - 1; ++idx1) { 381 for (int idx2 = idx1 + 1; idx2 <= ptCount; ++idx2) { 382 if (idx1 == idx2) { 383 continue; 384 } 385 SkDVector v; 386 v.set(pts[idx2] - pts[idx1]); 387 double lenSq = v.lengthSquared(); 388 longest = SkTMax(longest, lenSq); 389 } 390 } 391 return sqrt(longest) / dist; 392 } 393 394 bool SkOpAngle::endsIntersect(SkOpAngle* rh) { 395 SkPath::Verb lVerb = this->segment()->verb(); 396 SkPath::Verb rVerb = rh->segment()->verb(); 397 int lPts = SkPathOpsVerbToPoints(lVerb); 398 int rPts = SkPathOpsVerbToPoints(rVerb); 399 SkDLine rays[] = {{{this->fCurvePart[0], rh->fCurvePart[rPts]}}, 400 {{this->fCurvePart[0], this->fCurvePart[lPts]}}}; 401 if (rays[0][1] == rays[1][1]) { 402 return checkParallel(rh); 403 } 404 double smallTs[2] = {-1, -1}; 405 bool limited[2] = {false, false}; 406 for (int index = 0; index < 2; ++index) { 407 SkPath::Verb cVerb = index ? rVerb : lVerb; 408 // if the curve is a line, then the line and the ray intersect only at their crossing 409 if (cVerb == SkPath::kLine_Verb) { 410 continue; 411 } 412 const SkOpSegment& segment = index ? *rh->segment() : *this->segment(); 413 SkIntersections i; 414 (*CurveIntersectRay[cVerb])(segment.pts(), segment.weight(), rays[index], &i); 415 double tStart = index ? rh->fStart->t() : this->fStart->t(); 416 double tEnd = index ? rh->fComputedEnd->t() : this->fComputedEnd->t(); 417 bool testAscends = tStart < (index ? rh->fComputedEnd->t() : this->fComputedEnd->t()); 418 double t = testAscends ? 0 : 1; 419 for (int idx2 = 0; idx2 < i.used(); ++idx2) { 420 double testT = i[0][idx2]; 421 if (!approximately_between_orderable(tStart, testT, tEnd)) { 422 continue; 423 } 424 if (approximately_equal_orderable(tStart, testT)) { 425 continue; 426 } 427 smallTs[index] = t = testAscends ? SkTMax(t, testT) : SkTMin(t, testT); 428 limited[index] = approximately_equal_orderable(t, tEnd); 429 } 430 } 431 bool sRayLonger = false; 432 SkDVector sCept = {0, 0}; 433 double sCeptT = -1; 434 int sIndex = -1; 435 bool useIntersect = false; 436 for (int index = 0; index < 2; ++index) { 437 if (smallTs[index] < 0) { 438 continue; 439 } 440 const SkOpSegment& segment = index ? *rh->segment() : *this->segment(); 441 const SkDPoint& dPt = segment.dPtAtT(smallTs[index]); 442 SkDVector cept = dPt - rays[index][0]; 443 // If this point is on the curve, it should have been detected earlier by ordinary 444 // curve intersection. This may be hard to determine in general, but for lines, 445 // the point could be close to or equal to its end, but shouldn't be near the start. 446 if ((index ? lPts : rPts) == 1) { 447 SkDVector total = rays[index][1] - rays[index][0]; 448 if (cept.lengthSquared() * 2 < total.lengthSquared()) { 449 continue; 450 } 451 } 452 SkDVector end = rays[index][1] - rays[index][0]; 453 if (cept.fX * end.fX < 0 || cept.fY * end.fY < 0) { 454 continue; 455 } 456 double rayDist = cept.length(); 457 double endDist = end.length(); 458 bool rayLonger = rayDist > endDist; 459 if (limited[0] && limited[1] && rayLonger) { 460 useIntersect = true; 461 sRayLonger = rayLonger; 462 sCept = cept; 463 sCeptT = smallTs[index]; 464 sIndex = index; 465 break; 466 } 467 double delta = fabs(rayDist - endDist); 468 double minX, minY, maxX, maxY; 469 minX = minY = SK_ScalarInfinity; 470 maxX = maxY = -SK_ScalarInfinity; 471 const SkDCurve& curve = index ? rh->fCurvePart : this->fCurvePart; 472 int ptCount = index ? rPts : lPts; 473 for (int idx2 = 0; idx2 <= ptCount; ++idx2) { 474 minX = SkTMin(minX, curve[idx2].fX); 475 minY = SkTMin(minY, curve[idx2].fY); 476 maxX = SkTMax(maxX, curve[idx2].fX); 477 maxY = SkTMax(maxY, curve[idx2].fY); 478 } 479 double maxWidth = SkTMax(maxX - minX, maxY - minY); 480 delta /= maxWidth; 481 if (delta > 1e-3 && (useIntersect ^= true)) { // FIXME: move this magic number 482 sRayLonger = rayLonger; 483 sCept = cept; 484 sCeptT = smallTs[index]; 485 sIndex = index; 486 } 487 } 488 if (useIntersect) { 489 const SkDCurve& curve = sIndex ? rh->fCurvePart : this->fCurvePart; 490 const SkOpSegment& segment = sIndex ? *rh->segment() : *this->segment(); 491 double tStart = sIndex ? rh->fStart->t() : fStart->t(); 492 SkDVector mid = segment.dPtAtT(tStart + (sCeptT - tStart) / 2) - curve[0]; 493 double septDir = mid.crossCheck(sCept); 494 if (!septDir) { 495 return checkParallel(rh); 496 } 497 return sRayLonger ^ (sIndex == 0) ^ (septDir < 0); 498 } else { 499 return checkParallel(rh); 500 } 501 } 502 503 bool SkOpAngle::endToSide(const SkOpAngle* rh, bool* inside) const { 504 const SkOpSegment* segment = this->segment(); 505 SkPath::Verb verb = segment->verb(); 506 SkDLine rayEnd; 507 rayEnd[0].set(this->fEnd->pt()); 508 rayEnd[1] = rayEnd[0]; 509 SkDVector slopeAtEnd = (*CurveDSlopeAtT[verb])(segment->pts(), segment->weight(), 510 this->fEnd->t()); 511 rayEnd[1].fX += slopeAtEnd.fY; 512 rayEnd[1].fY -= slopeAtEnd.fX; 513 SkIntersections iEnd; 514 const SkOpSegment* oppSegment = rh->segment(); 515 SkPath::Verb oppVerb = oppSegment->verb(); 516 (*CurveIntersectRay[oppVerb])(oppSegment->pts(), oppSegment->weight(), rayEnd, &iEnd); 517 double endDist; 518 int closestEnd = iEnd.closestTo(rh->fStart->t(), rh->fEnd->t(), rayEnd[0], &endDist); 519 if (closestEnd < 0) { 520 return false; 521 } 522 if (!endDist) { 523 return false; 524 } 525 SkDPoint start; 526 start.set(this->fStart->pt()); 527 // OPTIMIZATION: multiple times in the code we find the max scalar 528 double minX, minY, maxX, maxY; 529 minX = minY = SK_ScalarInfinity; 530 maxX = maxY = -SK_ScalarInfinity; 531 const SkDCurve& curve = rh->fCurvePart; 532 int oppPts = SkPathOpsVerbToPoints(oppVerb); 533 for (int idx2 = 0; idx2 <= oppPts; ++idx2) { 534 minX = SkTMin(minX, curve[idx2].fX); 535 minY = SkTMin(minY, curve[idx2].fY); 536 maxX = SkTMax(maxX, curve[idx2].fX); 537 maxY = SkTMax(maxY, curve[idx2].fY); 538 } 539 double maxWidth = SkTMax(maxX - minX, maxY - minY); 540 endDist /= maxWidth; 541 if (endDist < 5e-11) { // empirically found 542 return false; 543 } 544 const SkDPoint* endPt = &rayEnd[0]; 545 SkDPoint oppPt = iEnd.pt(closestEnd); 546 SkDVector vLeft = *endPt - start; 547 SkDVector vRight = oppPt - start; 548 double dir = vLeft.crossCheck(vRight); 549 if (!dir) { 550 return false; 551 } 552 *inside = dir < 0; 553 return true; 554 } 555 556 /* y<0 y==0 y>0 x<0 x==0 x>0 xy<0 xy==0 xy>0 557 0 x x x 558 1 x x x 559 2 x x x 560 3 x x x 561 4 x x x 562 5 x x x 563 6 x x x 564 7 x x x 565 8 x x x 566 9 x x x 567 10 x x x 568 11 x x x 569 12 x x x 570 13 x x x 571 14 x x x 572 15 x x x 573 */ 574 int SkOpAngle::findSector(SkPath::Verb verb, double x, double y) const { 575 double absX = fabs(x); 576 double absY = fabs(y); 577 double xy = SkPath::kLine_Verb == verb || !AlmostEqualUlps(absX, absY) ? absX - absY : 0; 578 // If there are four quadrants and eight octants, and since the Latin for sixteen is sedecim, 579 // one could coin the term sedecimant for a space divided into 16 sections. 580 // http://english.stackexchange.com/questions/133688/word-for-something-partitioned-into-16-parts 581 static const int sedecimant[3][3][3] = { 582 // y<0 y==0 y>0 583 // x<0 x==0 x>0 x<0 x==0 x>0 x<0 x==0 x>0 584 {{ 4, 3, 2}, { 7, -1, 15}, {10, 11, 12}}, // abs(x) < abs(y) 585 {{ 5, -1, 1}, {-1, -1, -1}, { 9, -1, 13}}, // abs(x) == abs(y) 586 {{ 6, 3, 0}, { 7, -1, 15}, { 8, 11, 14}}, // abs(x) > abs(y) 587 }; 588 int sector = sedecimant[(xy >= 0) + (xy > 0)][(y >= 0) + (y > 0)][(x >= 0) + (x > 0)] * 2 + 1; 589 // SkASSERT(SkPath::kLine_Verb == verb || sector >= 0); 590 return sector; 591 } 592 593 SkOpGlobalState* SkOpAngle::globalState() const { 594 return this->segment()->globalState(); 595 } 596 597 598 // OPTIMIZE: if this loops to only one other angle, after first compare fails, insert on other side 599 // OPTIMIZE: return where insertion succeeded. Then, start next insertion on opposite side 600 void SkOpAngle::insert(SkOpAngle* angle) { 601 if (angle->fNext) { 602 if (loopCount() >= angle->loopCount()) { 603 if (!merge(angle)) { 604 return; 605 } 606 } else if (fNext) { 607 if (!angle->merge(this)) { 608 return; 609 } 610 } else { 611 angle->insert(this); 612 } 613 return; 614 } 615 bool singleton = nullptr == fNext; 616 if (singleton) { 617 fNext = this; 618 } 619 SkOpAngle* next = fNext; 620 if (next->fNext == this) { 621 if (singleton || angle->after(this)) { 622 this->fNext = angle; 623 angle->fNext = next; 624 } else { 625 next->fNext = angle; 626 angle->fNext = this; 627 } 628 debugValidateNext(); 629 return; 630 } 631 SkOpAngle* last = this; 632 do { 633 SkASSERT(last->fNext == next); 634 if (angle->after(last)) { 635 last->fNext = angle; 636 angle->fNext = next; 637 debugValidateNext(); 638 return; 639 } 640 last = next; 641 next = next->fNext; 642 if (last == this) { 643 if (next->fUnorderable) { 644 fUnorderable = true; 645 } else { 646 globalState()->setAngleCoincidence(); 647 this->fNext = angle; 648 angle->fNext = next; 649 angle->fCheckCoincidence = true; 650 } 651 return; 652 } 653 } while (true); 654 } 655 656 SkOpSpanBase* SkOpAngle::lastMarked() const { 657 if (fLastMarked) { 658 if (fLastMarked->chased()) { 659 return nullptr; 660 } 661 fLastMarked->setChased(true); 662 } 663 return fLastMarked; 664 } 665 666 bool SkOpAngle::loopContains(const SkOpAngle* angle) const { 667 if (!fNext) { 668 return false; 669 } 670 const SkOpAngle* first = this; 671 const SkOpAngle* loop = this; 672 const SkOpSegment* tSegment = angle->fStart->segment(); 673 double tStart = angle->fStart->t(); 674 double tEnd = angle->fEnd->t(); 675 do { 676 const SkOpSegment* lSegment = loop->fStart->segment(); 677 if (lSegment != tSegment) { 678 continue; 679 } 680 double lStart = loop->fStart->t(); 681 if (lStart != tEnd) { 682 continue; 683 } 684 double lEnd = loop->fEnd->t(); 685 if (lEnd == tStart) { 686 return true; 687 } 688 } while ((loop = loop->fNext) != first); 689 return false; 690 } 691 692 int SkOpAngle::loopCount() const { 693 int count = 0; 694 const SkOpAngle* first = this; 695 const SkOpAngle* next = this; 696 do { 697 next = next->fNext; 698 ++count; 699 } while (next && next != first); 700 return count; 701 } 702 703 bool SkOpAngle::merge(SkOpAngle* angle) { 704 SkASSERT(fNext); 705 SkASSERT(angle->fNext); 706 SkOpAngle* working = angle; 707 do { 708 if (this == working) { 709 return false; 710 } 711 working = working->fNext; 712 } while (working != angle); 713 do { 714 SkOpAngle* next = working->fNext; 715 working->fNext = nullptr; 716 insert(working); 717 working = next; 718 } while (working != angle); 719 // it's likely that a pair of the angles are unorderable 720 debugValidateNext(); 721 return true; 722 } 723 724 double SkOpAngle::midT() const { 725 return (fStart->t() + fEnd->t()) / 2; 726 } 727 728 bool SkOpAngle::midToSide(const SkOpAngle* rh, bool* inside) const { 729 const SkOpSegment* segment = this->segment(); 730 SkPath::Verb verb = segment->verb(); 731 const SkPoint& startPt = this->fStart->pt(); 732 const SkPoint& endPt = this->fEnd->pt(); 733 SkDPoint dStartPt; 734 dStartPt.set(startPt); 735 SkDLine rayMid; 736 rayMid[0].fX = (startPt.fX + endPt.fX) / 2; 737 rayMid[0].fY = (startPt.fY + endPt.fY) / 2; 738 rayMid[1].fX = rayMid[0].fX + (endPt.fY - startPt.fY); 739 rayMid[1].fY = rayMid[0].fY - (endPt.fX - startPt.fX); 740 SkIntersections iMid; 741 (*CurveIntersectRay[verb])(segment->pts(), segment->weight(), rayMid, &iMid); 742 int iOutside = iMid.mostOutside(this->fStart->t(), this->fEnd->t(), dStartPt); 743 if (iOutside < 0) { 744 return false; 745 } 746 const SkOpSegment* oppSegment = rh->segment(); 747 SkPath::Verb oppVerb = oppSegment->verb(); 748 SkIntersections oppMid; 749 (*CurveIntersectRay[oppVerb])(oppSegment->pts(), oppSegment->weight(), rayMid, &oppMid); 750 int oppOutside = oppMid.mostOutside(rh->fStart->t(), rh->fEnd->t(), dStartPt); 751 if (oppOutside < 0) { 752 return false; 753 } 754 SkDVector iSide = iMid.pt(iOutside) - dStartPt; 755 SkDVector oppSide = oppMid.pt(oppOutside) - dStartPt; 756 double dir = iSide.crossCheck(oppSide); 757 if (!dir) { 758 return false; 759 } 760 *inside = dir < 0; 761 return true; 762 } 763 764 bool SkOpAngle::oppositePlanes(const SkOpAngle* rh) const { 765 int startSpan = SkTAbs(rh->fSectorStart - fSectorStart); 766 return startSpan >= 8; 767 } 768 769 bool SkOpAngle::orderable(SkOpAngle* rh) { 770 int result; 771 if (!fIsCurve) { 772 if (!rh->fIsCurve) { 773 double leftX = fTangentHalf.dx(); 774 double leftY = fTangentHalf.dy(); 775 double rightX = rh->fTangentHalf.dx(); 776 double rightY = rh->fTangentHalf.dy(); 777 double x_ry = leftX * rightY; 778 double rx_y = rightX * leftY; 779 if (x_ry == rx_y) { 780 if (leftX * rightX < 0 || leftY * rightY < 0) { 781 return true; // exactly 180 degrees apart 782 } 783 goto unorderable; 784 } 785 SkASSERT(x_ry != rx_y); // indicates an undetected coincidence -- worth finding earlier 786 return x_ry < rx_y; 787 } 788 if ((result = allOnOneSide(rh)) >= 0) { 789 return result; 790 } 791 if (fUnorderable || approximately_zero(rh->fSide)) { 792 goto unorderable; 793 } 794 } else if (!rh->fIsCurve) { 795 if ((result = rh->allOnOneSide(this)) >= 0) { 796 return !result; 797 } 798 if (rh->fUnorderable || approximately_zero(fSide)) { 799 goto unorderable; 800 } 801 } 802 if ((result = convexHullOverlaps(rh)) >= 0) { 803 return result; 804 } 805 return endsIntersect(rh); 806 unorderable: 807 fUnorderable = true; 808 rh->fUnorderable = true; 809 return true; 810 } 811 812 // OPTIMIZE: if this shows up in a profile, add a previous pointer 813 // as is, this should be rarely called 814 SkOpAngle* SkOpAngle::previous() const { 815 SkOpAngle* last = fNext; 816 do { 817 SkOpAngle* next = last->fNext; 818 if (next == this) { 819 return last; 820 } 821 last = next; 822 } while (true); 823 } 824 825 SkOpSegment* SkOpAngle::segment() const { 826 return fStart->segment(); 827 } 828 829 void SkOpAngle::set(SkOpSpanBase* start, SkOpSpanBase* end) { 830 fStart = start; 831 fComputedEnd = fEnd = end; 832 SkASSERT(start != end); 833 fNext = nullptr; 834 fComputeSector = fComputedSector = fCheckCoincidence = false; 835 setSpans(); 836 setSector(); 837 SkDEBUGCODE(fID = start ? start->globalState()->nextAngleID() : -1); 838 } 839 840 void SkOpAngle::setCurveHullSweep() { 841 fUnorderedSweep = false; 842 fSweep[0] = fCurvePart[1] - fCurvePart[0]; 843 const SkOpSegment* segment = fStart->segment(); 844 if (SkPath::kLine_Verb == segment->verb()) { 845 fSweep[1] = fSweep[0]; 846 return; 847 } 848 fSweep[1] = fCurvePart[2] - fCurvePart[0]; 849 if (SkPath::kCubic_Verb != segment->verb()) { 850 if (!fSweep[0].fX && !fSweep[0].fY) { 851 fSweep[0] = fSweep[1]; 852 } 853 return; 854 } 855 SkDVector thirdSweep = fCurvePart[3] - fCurvePart[0]; 856 if (fSweep[0].fX == 0 && fSweep[0].fY == 0) { 857 fSweep[0] = fSweep[1]; 858 fSweep[1] = thirdSweep; 859 if (fSweep[0].fX == 0 && fSweep[0].fY == 0) { 860 fSweep[0] = fSweep[1]; 861 fCurvePart[1] = fCurvePart[3]; 862 fIsCurve = false; 863 } 864 return; 865 } 866 double s1x3 = fSweep[0].crossCheck(thirdSweep); 867 double s3x2 = thirdSweep.crossCheck(fSweep[1]); 868 if (s1x3 * s3x2 >= 0) { // if third vector is on or between first two vectors 869 return; 870 } 871 double s2x1 = fSweep[1].crossCheck(fSweep[0]); 872 // FIXME: If the sweep of the cubic is greater than 180 degrees, we're in trouble 873 // probably such wide sweeps should be artificially subdivided earlier so that never happens 874 SkASSERT(s1x3 * s2x1 < 0 || s1x3 * s3x2 < 0); 875 if (s3x2 * s2x1 < 0) { 876 SkASSERT(s2x1 * s1x3 > 0); 877 fSweep[0] = fSweep[1]; 878 fUnorderedSweep = true; 879 } 880 fSweep[1] = thirdSweep; 881 } 882 883 void SkOpAngle::setSpans() { 884 fUnorderable = false; 885 fLastMarked = nullptr; 886 if (!fStart) { 887 fUnorderable = true; 888 return; 889 } 890 const SkOpSegment* segment = fStart->segment(); 891 const SkPoint* pts = segment->pts(); 892 SkDEBUGCODE(fCurvePart.fVerb = SkPath::kCubic_Verb); 893 SkDEBUGCODE(fCurvePart[2].fX = fCurvePart[2].fY = fCurvePart[3].fX = fCurvePart[3].fY 894 = SK_ScalarNaN); 895 SkDEBUGCODE(fCurvePart.fVerb = segment->verb()); 896 segment->subDivide(fStart, fEnd, &fCurvePart); 897 setCurveHullSweep(); 898 const SkPath::Verb verb = segment->verb(); 899 if (verb != SkPath::kLine_Verb 900 && !(fIsCurve = fSweep[0].crossCheck(fSweep[1]) != 0)) { 901 SkDLine lineHalf; 902 lineHalf[0].set(fCurvePart[0].asSkPoint()); 903 lineHalf[1].set(fCurvePart[SkPathOpsVerbToPoints(verb)].asSkPoint()); 904 fTangentHalf.lineEndPoints(lineHalf); 905 fSide = 0; 906 } 907 switch (verb) { 908 case SkPath::kLine_Verb: { 909 SkASSERT(fStart != fEnd); 910 const SkPoint& cP1 = pts[fStart->t() < fEnd->t()]; 911 SkDLine lineHalf; 912 lineHalf[0].set(fStart->pt()); 913 lineHalf[1].set(cP1); 914 fTangentHalf.lineEndPoints(lineHalf); 915 fSide = 0; 916 fIsCurve = false; 917 } return; 918 case SkPath::kQuad_Verb: 919 case SkPath::kConic_Verb: { 920 SkLineParameters tangentPart; 921 (void) tangentPart.quadEndPoints(fCurvePart.fQuad); 922 fSide = -tangentPart.pointDistance(fCurvePart[2]); // not normalized -- compare sign only 923 } break; 924 case SkPath::kCubic_Verb: { 925 SkLineParameters tangentPart; 926 (void) tangentPart.cubicPart(fCurvePart.fCubic); 927 fSide = -tangentPart.pointDistance(fCurvePart[3]); 928 double testTs[4]; 929 // OPTIMIZATION: keep inflections precomputed with cubic segment? 930 int testCount = SkDCubic::FindInflections(pts, testTs); 931 double startT = fStart->t(); 932 double endT = fEnd->t(); 933 double limitT = endT; 934 int index; 935 for (index = 0; index < testCount; ++index) { 936 if (!::between(startT, testTs[index], limitT)) { 937 testTs[index] = -1; 938 } 939 } 940 testTs[testCount++] = startT; 941 testTs[testCount++] = endT; 942 SkTQSort<double>(testTs, &testTs[testCount - 1]); 943 double bestSide = 0; 944 int testCases = (testCount << 1) - 1; 945 index = 0; 946 while (testTs[index] < 0) { 947 ++index; 948 } 949 index <<= 1; 950 for (; index < testCases; ++index) { 951 int testIndex = index >> 1; 952 double testT = testTs[testIndex]; 953 if (index & 1) { 954 testT = (testT + testTs[testIndex + 1]) / 2; 955 } 956 // OPTIMIZE: could avoid call for t == startT, endT 957 SkDPoint pt = dcubic_xy_at_t(pts, segment->weight(), testT); 958 SkLineParameters tangentPart; 959 tangentPart.cubicEndPoints(fCurvePart.fCubic); 960 double testSide = tangentPart.pointDistance(pt); 961 if (fabs(bestSide) < fabs(testSide)) { 962 bestSide = testSide; 963 } 964 } 965 fSide = -bestSide; // compare sign only 966 } break; 967 default: 968 SkASSERT(0); 969 } 970 } 971 972 void SkOpAngle::setSector() { 973 if (!fStart) { 974 fUnorderable = true; 975 return; 976 } 977 const SkOpSegment* segment = fStart->segment(); 978 SkPath::Verb verb = segment->verb(); 979 fSectorStart = this->findSector(verb, fSweep[0].fX, fSweep[0].fY); 980 if (fSectorStart < 0) { 981 goto deferTilLater; 982 } 983 if (!fIsCurve) { // if it's a line or line-like, note that both sectors are the same 984 SkASSERT(fSectorStart >= 0); 985 fSectorEnd = fSectorStart; 986 fSectorMask = 1 << fSectorStart; 987 return; 988 } 989 SkASSERT(SkPath::kLine_Verb != verb); 990 fSectorEnd = this->findSector(verb, fSweep[1].fX, fSweep[1].fY); 991 if (fSectorEnd < 0) { 992 deferTilLater: 993 fSectorStart = fSectorEnd = -1; 994 fSectorMask = 0; 995 fComputeSector = true; // can't determine sector until segment length can be found 996 return; 997 } 998 if (fSectorEnd == fSectorStart 999 && (fSectorStart & 3) != 3) { // if the sector has no span, it can't be an exact angle 1000 fSectorMask = 1 << fSectorStart; 1001 return; 1002 } 1003 bool crossesZero = this->checkCrossesZero(); 1004 int start = SkTMin(fSectorStart, fSectorEnd); 1005 bool curveBendsCCW = (fSectorStart == start) ^ crossesZero; 1006 // bump the start and end of the sector span if they are on exact compass points 1007 if ((fSectorStart & 3) == 3) { 1008 fSectorStart = (fSectorStart + (curveBendsCCW ? 1 : 31)) & 0x1f; 1009 } 1010 if ((fSectorEnd & 3) == 3) { 1011 fSectorEnd = (fSectorEnd + (curveBendsCCW ? 31 : 1)) & 0x1f; 1012 } 1013 crossesZero = this->checkCrossesZero(); 1014 start = SkTMin(fSectorStart, fSectorEnd); 1015 int end = SkTMax(fSectorStart, fSectorEnd); 1016 if (!crossesZero) { 1017 fSectorMask = (unsigned) -1 >> (31 - end + start) << start; 1018 } else { 1019 fSectorMask = (unsigned) -1 >> (31 - start) | ((unsigned) -1 << end); 1020 } 1021 } 1022 1023 SkOpSpan* SkOpAngle::starter() { 1024 return fStart->starter(fEnd); 1025 } 1026 1027 bool SkOpAngle::tangentsDiverge(const SkOpAngle* rh, double s0xt0) const { 1028 if (s0xt0 == 0) { 1029 return false; 1030 } 1031 // if the ctrl tangents are not nearly parallel, use them 1032 // solve for opposite direction displacement scale factor == m 1033 // initial dir = v1.cross(v2) == v2.x * v1.y - v2.y * v1.x 1034 // displacement of q1[1] : dq1 = { -m * v1.y, m * v1.x } + q1[1] 1035 // straight angle when : v2.x * (dq1.y - q1[0].y) == v2.y * (dq1.x - q1[0].x) 1036 // v2.x * (m * v1.x + v1.y) == v2.y * (-m * v1.y + v1.x) 1037 // - m * (v2.x * v1.x + v2.y * v1.y) == v2.x * v1.y - v2.y * v1.x 1038 // m = (v2.y * v1.x - v2.x * v1.y) / (v2.x * v1.x + v2.y * v1.y) 1039 // m = v1.cross(v2) / v1.dot(v2) 1040 const SkDVector* sweep = fSweep; 1041 const SkDVector* tweep = rh->fSweep; 1042 double s0dt0 = sweep[0].dot(tweep[0]); 1043 if (!s0dt0) { 1044 return true; 1045 } 1046 SkASSERT(s0dt0 != 0); 1047 double m = s0xt0 / s0dt0; 1048 double sDist = sweep[0].length() * m; 1049 double tDist = tweep[0].length() * m; 1050 bool useS = fabs(sDist) < fabs(tDist); 1051 double mFactor = fabs(useS ? this->distEndRatio(sDist) : rh->distEndRatio(tDist)); 1052 return mFactor < 2400; // empirically found limit 1053 } 1054
