| /* |
| * Copyright 2012 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| #include "src/core/SkTSort.h" |
| #include "src/pathops/SkOpAngle.h" |
| #include "src/pathops/SkOpSegment.h" |
| #include "src/pathops/SkPathOpsCurve.h" |
| |
| /* Angles are sorted counterclockwise. The smallest angle has a positive x and the smallest |
| positive y. The largest angle has a positive x and a zero y. */ |
| |
| #if DEBUG_ANGLE |
| static bool CompareResult(const char* func, SkString* bugOut, SkString* bugPart, int append, |
| bool compare) { |
| SkDebugf("%s %c %d\n", bugOut->c_str(), compare ? 'T' : 'F', append); |
| SkDebugf("%sPart %s\n", func, bugPart[0].c_str()); |
| SkDebugf("%sPart %s\n", func, bugPart[1].c_str()); |
| SkDebugf("%sPart %s\n", func, bugPart[2].c_str()); |
| return compare; |
| } |
| |
| #define COMPARE_RESULT(append, compare) CompareResult(__FUNCTION__, &bugOut, bugPart, append, \ |
| compare) |
| #else |
| #define COMPARE_RESULT(append, compare) compare |
| #endif |
| |
| /* quarter angle values for sector |
| |
| 31 x > 0, y == 0 horizontal line (to the right) |
| 0 x > 0, y == epsilon quad/cubic horizontal tangent eventually going +y |
| 1 x > 0, y > 0, x > y nearer horizontal angle |
| 2 x + e == y quad/cubic 45 going horiz |
| 3 x > 0, y > 0, x == y 45 angle |
| 4 x == y + e quad/cubic 45 going vert |
| 5 x > 0, y > 0, x < y nearer vertical angle |
| 6 x == epsilon, y > 0 quad/cubic vertical tangent eventually going +x |
| 7 x == 0, y > 0 vertical line (to the top) |
| |
| 8 7 6 |
| 9 | 5 |
| 10 | 4 |
| 11 | 3 |
| 12 \ | / 2 |
| 13 | 1 |
| 14 | 0 |
| 15 --------------+------------- 31 |
| 16 | 30 |
| 17 | 29 |
| 18 / | \ 28 |
| 19 | 27 |
| 20 | 26 |
| 21 | 25 |
| 22 23 24 |
| */ |
| |
| // return true if lh < this < rh |
| bool SkOpAngle::after(SkOpAngle* test) { |
| SkOpAngle* lh = test; |
| SkOpAngle* rh = lh->fNext; |
| SkASSERT(lh != rh); |
| fPart.fCurve = fOriginalCurvePart; |
| lh->fPart.fCurve = lh->fOriginalCurvePart; |
| lh->fPart.fCurve.offset(lh->segment()->verb(), fPart.fCurve[0] - lh->fPart.fCurve[0]); |
| rh->fPart.fCurve = rh->fOriginalCurvePart; |
| rh->fPart.fCurve.offset(rh->segment()->verb(), fPart.fCurve[0] - rh->fPart.fCurve[0]); |
| |
| #if DEBUG_ANGLE |
| SkString bugOut; |
| bugOut.printf("%s [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" |
| " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" |
| " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g ", __FUNCTION__, |
| lh->segment()->debugID(), lh->debugID(), lh->fSectorStart, lh->fSectorEnd, |
| lh->fStart->t(), lh->fEnd->t(), |
| segment()->debugID(), debugID(), fSectorStart, fSectorEnd, fStart->t(), fEnd->t(), |
| rh->segment()->debugID(), rh->debugID(), rh->fSectorStart, rh->fSectorEnd, |
| rh->fStart->t(), rh->fEnd->t()); |
| SkString bugPart[3] = { lh->debugPart(), this->debugPart(), rh->debugPart() }; |
| #endif |
| if (lh->fComputeSector && !lh->computeSector()) { |
| return COMPARE_RESULT(1, true); |
| } |
| if (fComputeSector && !this->computeSector()) { |
| return COMPARE_RESULT(2, true); |
| } |
| if (rh->fComputeSector && !rh->computeSector()) { |
| return COMPARE_RESULT(3, true); |
| } |
| #if DEBUG_ANGLE // reset bugOut with computed sectors |
| bugOut.printf("%s [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" |
| " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g" |
| " < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g ", __FUNCTION__, |
| lh->segment()->debugID(), lh->debugID(), lh->fSectorStart, lh->fSectorEnd, |
| lh->fStart->t(), lh->fEnd->t(), |
| segment()->debugID(), debugID(), fSectorStart, fSectorEnd, fStart->t(), fEnd->t(), |
| rh->segment()->debugID(), rh->debugID(), rh->fSectorStart, rh->fSectorEnd, |
| rh->fStart->t(), rh->fEnd->t()); |
| #endif |
| bool ltrOverlap = (lh->fSectorMask | rh->fSectorMask) & fSectorMask; |
| bool lrOverlap = lh->fSectorMask & rh->fSectorMask; |
| int lrOrder; // set to -1 if either order works |
| if (!lrOverlap) { // no lh/rh sector overlap |
| if (!ltrOverlap) { // no lh/this/rh sector overlap |
| return COMPARE_RESULT(4, (lh->fSectorEnd > rh->fSectorStart) |
| ^ (fSectorStart > lh->fSectorEnd) ^ (fSectorStart > rh->fSectorStart)); |
| } |
| int lrGap = (rh->fSectorStart - lh->fSectorStart + 32) & 0x1f; |
| /* A tiny change can move the start +/- 4. The order can only be determined if |
| lr gap is not 12 to 20 or -12 to -20. |
| -31 ..-21 1 |
| -20 ..-12 -1 |
| -11 .. -1 0 |
| 0 shouldn't get here |
| 11 .. 1 1 |
| 12 .. 20 -1 |
| 21 .. 31 0 |
| */ |
| lrOrder = lrGap > 20 ? 0 : lrGap > 11 ? -1 : 1; |
| } else { |
| lrOrder = lh->orderable(rh); |
| if (!ltrOverlap && lrOrder >= 0) { |
| return COMPARE_RESULT(5, !lrOrder); |
| } |
| } |
| int ltOrder; |
| SkASSERT((lh->fSectorMask & fSectorMask) || (rh->fSectorMask & fSectorMask) || -1 == lrOrder); |
| if (lh->fSectorMask & fSectorMask) { |
| ltOrder = lh->orderable(this); |
| } else { |
| int ltGap = (fSectorStart - lh->fSectorStart + 32) & 0x1f; |
| ltOrder = ltGap > 20 ? 0 : ltGap > 11 ? -1 : 1; |
| } |
| int trOrder; |
| if (rh->fSectorMask & fSectorMask) { |
| trOrder = this->orderable(rh); |
| } else { |
| int trGap = (rh->fSectorStart - fSectorStart + 32) & 0x1f; |
| trOrder = trGap > 20 ? 0 : trGap > 11 ? -1 : 1; |
| } |
| this->alignmentSameSide(lh, <Order); |
| this->alignmentSameSide(rh, &trOrder); |
| if (lrOrder >= 0 && ltOrder >= 0 && trOrder >= 0) { |
| return COMPARE_RESULT(7, lrOrder ? (ltOrder & trOrder) : (ltOrder | trOrder)); |
| } |
| // SkASSERT(lrOrder >= 0 || ltOrder >= 0 || trOrder >= 0); |
| // There's not enough information to sort. Get the pairs of angles in opposite planes. |
| // If an order is < 0, the pair is already in an opposite plane. Check the remaining pairs. |
| // FIXME : once all variants are understood, rewrite this more simply |
| if (ltOrder == 0 && lrOrder == 0) { |
| SkASSERT(trOrder < 0); |
| // FIXME : once this is verified to work, remove one opposite angle call |
| SkDEBUGCODE(bool lrOpposite = lh->oppositePlanes(rh)); |
| bool ltOpposite = lh->oppositePlanes(this); |
| SkOPASSERT(lrOpposite != ltOpposite); |
| return COMPARE_RESULT(8, ltOpposite); |
| } else if (ltOrder == 1 && trOrder == 0) { |
| SkASSERT(lrOrder < 0); |
| bool trOpposite = oppositePlanes(rh); |
| return COMPARE_RESULT(9, trOpposite); |
| } else if (lrOrder == 1 && trOrder == 1) { |
| SkASSERT(ltOrder < 0); |
| // SkDEBUGCODE(bool trOpposite = oppositePlanes(rh)); |
| bool lrOpposite = lh->oppositePlanes(rh); |
| // SkASSERT(lrOpposite != trOpposite); |
| return COMPARE_RESULT(10, lrOpposite); |
| } |
| // If a pair couldn't be ordered, there's not enough information to determine the sort. |
| // Refer to: https://docs.google.com/drawings/d/1KV-8SJTedku9fj4K6fd1SB-8divuV_uivHVsSgwXICQ |
| if (fUnorderable || lh->fUnorderable || rh->fUnorderable) { |
| // limit to lines; should work with curves, but wait for a failing test to verify |
| if (!fPart.isCurve() && !lh->fPart.isCurve() && !rh->fPart.isCurve()) { |
| // see if original raw data is orderable |
| // if two share a point, check if third has both points in same half plane |
| int ltShare = lh->fOriginalCurvePart[0] == fOriginalCurvePart[0]; |
| int lrShare = lh->fOriginalCurvePart[0] == rh->fOriginalCurvePart[0]; |
| int trShare = fOriginalCurvePart[0] == rh->fOriginalCurvePart[0]; |
| // if only one pair are the same, the third point touches neither of the pair |
| if (ltShare + lrShare + trShare == 1) { |
| if (lrShare) { |
| int ltOOrder = lh->linesOnOriginalSide(this); |
| int rtOOrder = rh->linesOnOriginalSide(this); |
| if ((rtOOrder ^ ltOOrder) == 1) { |
| return ltOOrder; |
| } |
| } else if (trShare) { |
| int tlOOrder = this->linesOnOriginalSide(lh); |
| int rlOOrder = rh->linesOnOriginalSide(lh); |
| if ((tlOOrder ^ rlOOrder) == 1) { |
| return rlOOrder; |
| } |
| } else { |
| SkASSERT(ltShare); |
| int trOOrder = rh->linesOnOriginalSide(this); |
| int lrOOrder = lh->linesOnOriginalSide(rh); |
| // result must be 0 and 1 or 1 and 0 to be valid |
| if ((lrOOrder ^ trOOrder) == 1) { |
| return trOOrder; |
| } |
| } |
| } |
| } |
| } |
| if (lrOrder < 0) { |
| if (ltOrder < 0) { |
| return COMPARE_RESULT(11, trOrder); |
| } |
| return COMPARE_RESULT(12, ltOrder); |
| } |
| return COMPARE_RESULT(13, !lrOrder); |
| } |
| |
| int SkOpAngle::lineOnOneSide(const SkDPoint& origin, const SkDVector& line, const SkOpAngle* test, |
| bool useOriginal) const { |
| double crosses[3]; |
| SkPath::Verb testVerb = test->segment()->verb(); |
| int iMax = SkPathOpsVerbToPoints(testVerb); |
| // SkASSERT(origin == test.fCurveHalf[0]); |
| const SkDCurve& testCurve = useOriginal ? test->fOriginalCurvePart : test->fPart.fCurve; |
| for (int index = 1; index <= iMax; ++index) { |
| double xy1 = line.fX * (testCurve[index].fY - origin.fY); |
| double xy2 = line.fY * (testCurve[index].fX - origin.fX); |
| crosses[index - 1] = AlmostBequalUlps(xy1, xy2) ? 0 : xy1 - xy2; |
| } |
| if (crosses[0] * crosses[1] < 0) { |
| return -1; |
| } |
| if (SkPath::kCubic_Verb == testVerb) { |
| if (crosses[0] * crosses[2] < 0 || crosses[1] * crosses[2] < 0) { |
| return -1; |
| } |
| } |
| if (crosses[0]) { |
| return crosses[0] < 0; |
| } |
| if (crosses[1]) { |
| return crosses[1] < 0; |
| } |
| if (SkPath::kCubic_Verb == testVerb && crosses[2]) { |
| return crosses[2] < 0; |
| } |
| return -2; |
| } |
| |
| // given a line, see if the opposite curve's convex hull is all on one side |
| // returns -1=not on one side 0=this CW of test 1=this CCW of test |
| int SkOpAngle::lineOnOneSide(const SkOpAngle* test, bool useOriginal) { |
| SkASSERT(!fPart.isCurve()); |
| SkASSERT(test->fPart.isCurve()); |
| SkDPoint origin = fPart.fCurve[0]; |
| SkDVector line = fPart.fCurve[1] - origin; |
| int result = this->lineOnOneSide(origin, line, test, useOriginal); |
| if (-2 == result) { |
| fUnorderable = true; |
| result = -1; |
| } |
| return result; |
| } |
| |
| // experiment works only with lines for now |
| int SkOpAngle::linesOnOriginalSide(const SkOpAngle* test) { |
| SkASSERT(!fPart.isCurve()); |
| SkASSERT(!test->fPart.isCurve()); |
| SkDPoint origin = fOriginalCurvePart[0]; |
| SkDVector line = fOriginalCurvePart[1] - origin; |
| double dots[2]; |
| double crosses[2]; |
| const SkDCurve& testCurve = test->fOriginalCurvePart; |
| for (int index = 0; index < 2; ++index) { |
| SkDVector testLine = testCurve[index] - origin; |
| double xy1 = line.fX * testLine.fY; |
| double xy2 = line.fY * testLine.fX; |
| dots[index] = line.fX * testLine.fX + line.fY * testLine.fY; |
| crosses[index] = AlmostBequalUlps(xy1, xy2) ? 0 : xy1 - xy2; |
| } |
| if (crosses[0] * crosses[1] < 0) { |
| return -1; |
| } |
| if (crosses[0]) { |
| return crosses[0] < 0; |
| } |
| if (crosses[1]) { |
| return crosses[1] < 0; |
| } |
| if ((!dots[0] && dots[1] < 0) || (dots[0] < 0 && !dots[1])) { |
| return 2; // 180 degrees apart |
| } |
| fUnorderable = true; |
| return -1; |
| } |
| |
| // To sort the angles, all curves are translated to have the same starting point. |
| // If the curve's control point in its original position is on one side of a compared line, |
| // and translated is on the opposite side, reverse the previously computed order. |
| void SkOpAngle::alignmentSameSide(const SkOpAngle* test, int* order) const { |
| if (*order < 0) { |
| return; |
| } |
| if (fPart.isCurve()) { |
| // This should support all curve types, but only bug that requires this has lines |
| // Turning on for curves causes existing tests to fail |
| return; |
| } |
| if (test->fPart.isCurve()) { |
| return; |
| } |
| const SkDPoint& xOrigin = test->fPart.fCurve.fLine[0]; |
| const SkDPoint& oOrigin = test->fOriginalCurvePart.fLine[0]; |
| if (xOrigin == oOrigin) { |
| return; |
| } |
| int iMax = SkPathOpsVerbToPoints(this->segment()->verb()); |
| SkDVector xLine = test->fPart.fCurve.fLine[1] - xOrigin; |
| SkDVector oLine = test->fOriginalCurvePart.fLine[1] - oOrigin; |
| for (int index = 1; index <= iMax; ++index) { |
| const SkDPoint& testPt = fPart.fCurve[index]; |
| double xCross = oLine.crossCheck(testPt - xOrigin); |
| double oCross = xLine.crossCheck(testPt - oOrigin); |
| if (oCross * xCross < 0) { |
| *order ^= 1; |
| break; |
| } |
| } |
| } |
| |
| bool SkOpAngle::checkCrossesZero() const { |
| int start = std::min(fSectorStart, fSectorEnd); |
| int end = std::max(fSectorStart, fSectorEnd); |
| bool crossesZero = end - start > 16; |
| return crossesZero; |
| } |
| |
| bool SkOpAngle::checkParallel(SkOpAngle* rh) { |
| SkDVector scratch[2]; |
| const SkDVector* sweep, * tweep; |
| if (this->fPart.isOrdered()) { |
| sweep = this->fPart.fSweep; |
| } else { |
| scratch[0] = this->fPart.fCurve[1] - this->fPart.fCurve[0]; |
| sweep = &scratch[0]; |
| } |
| if (rh->fPart.isOrdered()) { |
| tweep = rh->fPart.fSweep; |
| } else { |
| scratch[1] = rh->fPart.fCurve[1] - rh->fPart.fCurve[0]; |
| tweep = &scratch[1]; |
| } |
| double s0xt0 = sweep->crossCheck(*tweep); |
| if (tangentsDiverge(rh, s0xt0)) { |
| return s0xt0 < 0; |
| } |
| // compute the perpendicular to the endpoints and see where it intersects the opposite curve |
| // if the intersections within the t range, do a cross check on those |
| bool inside; |
| if (!fEnd->contains(rh->fEnd)) { |
| if (this->endToSide(rh, &inside)) { |
| return inside; |
| } |
| if (rh->endToSide(this, &inside)) { |
| return !inside; |
| } |
| } |
| if (this->midToSide(rh, &inside)) { |
| return inside; |
| } |
| if (rh->midToSide(this, &inside)) { |
| return !inside; |
| } |
| // compute the cross check from the mid T values (last resort) |
| SkDVector m0 = segment()->dPtAtT(this->midT()) - this->fPart.fCurve[0]; |
| SkDVector m1 = rh->segment()->dPtAtT(rh->midT()) - rh->fPart.fCurve[0]; |
| double m0xm1 = m0.crossCheck(m1); |
| if (m0xm1 == 0) { |
| this->fUnorderable = true; |
| rh->fUnorderable = true; |
| return true; |
| } |
| return m0xm1 < 0; |
| } |
| |
| // the original angle is too short to get meaningful sector information |
| // lengthen it until it is long enough to be meaningful or leave it unset if lengthening it |
| // would cause it to intersect one of the adjacent angles |
| bool SkOpAngle::computeSector() { |
| if (fComputedSector) { |
| return !fUnorderable; |
| } |
| fComputedSector = true; |
| bool stepUp = fStart->t() < fEnd->t(); |
| SkOpSpanBase* checkEnd = fEnd; |
| if (checkEnd->final() && stepUp) { |
| fUnorderable = true; |
| return false; |
| } |
| do { |
| // advance end |
| const SkOpSegment* other = checkEnd->segment(); |
| const SkOpSpanBase* oSpan = other->head(); |
| do { |
| if (oSpan->segment() != segment()) { |
| continue; |
| } |
| if (oSpan == checkEnd) { |
| continue; |
| } |
| if (!approximately_equal(oSpan->t(), checkEnd->t())) { |
| continue; |
| } |
| goto recomputeSector; |
| } while (!oSpan->final() && (oSpan = oSpan->upCast()->next())); |
| checkEnd = stepUp ? !checkEnd->final() |
| ? checkEnd->upCast()->next() : nullptr |
| : checkEnd->prev(); |
| } while (checkEnd); |
| recomputeSector: |
| SkOpSpanBase* computedEnd = stepUp ? checkEnd ? checkEnd->prev() : fEnd->segment()->head() |
| : checkEnd ? checkEnd->upCast()->next() : fEnd->segment()->tail(); |
| if (checkEnd == fEnd || computedEnd == fEnd || computedEnd == fStart) { |
| fUnorderable = true; |
| return false; |
| } |
| if (stepUp != (fStart->t() < computedEnd->t())) { |
| fUnorderable = true; |
| return false; |
| } |
| SkOpSpanBase* saveEnd = fEnd; |
| fComputedEnd = fEnd = computedEnd; |
| setSpans(); |
| setSector(); |
| fEnd = saveEnd; |
| return !fUnorderable; |
| } |
| |
| int SkOpAngle::convexHullOverlaps(const SkOpAngle* rh) { |
| const SkDVector* sweep = this->fPart.fSweep; |
| const SkDVector* tweep = rh->fPart.fSweep; |
| double s0xs1 = sweep[0].crossCheck(sweep[1]); |
| double s0xt0 = sweep[0].crossCheck(tweep[0]); |
| double s1xt0 = sweep[1].crossCheck(tweep[0]); |
| bool tBetweenS = s0xs1 > 0 ? s0xt0 > 0 && s1xt0 < 0 : s0xt0 < 0 && s1xt0 > 0; |
| double s0xt1 = sweep[0].crossCheck(tweep[1]); |
| double s1xt1 = sweep[1].crossCheck(tweep[1]); |
| tBetweenS |= s0xs1 > 0 ? s0xt1 > 0 && s1xt1 < 0 : s0xt1 < 0 && s1xt1 > 0; |
| double t0xt1 = tweep[0].crossCheck(tweep[1]); |
| if (tBetweenS) { |
| return -1; |
| } |
| if ((s0xt0 == 0 && s1xt1 == 0) || (s1xt0 == 0 && s0xt1 == 0)) { // s0 to s1 equals t0 to t1 |
| return -1; |
| } |
| bool sBetweenT = t0xt1 > 0 ? s0xt0 < 0 && s0xt1 > 0 : s0xt0 > 0 && s0xt1 < 0; |
| sBetweenT |= t0xt1 > 0 ? s1xt0 < 0 && s1xt1 > 0 : s1xt0 > 0 && s1xt1 < 0; |
| if (sBetweenT) { |
| return -1; |
| } |
| // if all of the sweeps are in the same half plane, then the order of any pair is enough |
| if (s0xt0 >= 0 && s0xt1 >= 0 && s1xt0 >= 0 && s1xt1 >= 0) { |
| return 0; |
| } |
| if (s0xt0 <= 0 && s0xt1 <= 0 && s1xt0 <= 0 && s1xt1 <= 0) { |
| return 1; |
| } |
| // if the outside sweeps are greater than 180 degress: |
| // first assume the inital tangents are the ordering |
| // if the midpoint direction matches the inital order, that is enough |
| SkDVector m0 = this->segment()->dPtAtT(this->midT()) - this->fPart.fCurve[0]; |
| SkDVector m1 = rh->segment()->dPtAtT(rh->midT()) - rh->fPart.fCurve[0]; |
| double m0xm1 = m0.crossCheck(m1); |
| if (s0xt0 > 0 && m0xm1 > 0) { |
| return 0; |
| } |
| if (s0xt0 < 0 && m0xm1 < 0) { |
| return 1; |
| } |
| if (tangentsDiverge(rh, s0xt0)) { |
| return s0xt0 < 0; |
| } |
| return m0xm1 < 0; |
| } |
| |
| // OPTIMIZATION: longest can all be either lazily computed here or precomputed in setup |
| double SkOpAngle::distEndRatio(double dist) const { |
| double longest = 0; |
| const SkOpSegment& segment = *this->segment(); |
| int ptCount = SkPathOpsVerbToPoints(segment.verb()); |
| const SkPoint* pts = segment.pts(); |
| for (int idx1 = 0; idx1 <= ptCount - 1; ++idx1) { |
| for (int idx2 = idx1 + 1; idx2 <= ptCount; ++idx2) { |
| if (idx1 == idx2) { |
| continue; |
| } |
| SkDVector v; |
| v.set(pts[idx2] - pts[idx1]); |
| double lenSq = v.lengthSquared(); |
| longest = std::max(longest, lenSq); |
| } |
| } |
| return sqrt(longest) / dist; |
| } |
| |
| bool SkOpAngle::endsIntersect(SkOpAngle* rh) { |
| SkPath::Verb lVerb = this->segment()->verb(); |
| SkPath::Verb rVerb = rh->segment()->verb(); |
| int lPts = SkPathOpsVerbToPoints(lVerb); |
| int rPts = SkPathOpsVerbToPoints(rVerb); |
| SkDLine rays[] = {{{this->fPart.fCurve[0], rh->fPart.fCurve[rPts]}}, |
| {{this->fPart.fCurve[0], this->fPart.fCurve[lPts]}}}; |
| if (this->fEnd->contains(rh->fEnd)) { |
| return checkParallel(rh); |
| } |
| double smallTs[2] = {-1, -1}; |
| bool limited[2] = {false, false}; |
| for (int index = 0; index < 2; ++index) { |
| SkPath::Verb cVerb = index ? rVerb : lVerb; |
| // if the curve is a line, then the line and the ray intersect only at their crossing |
| if (cVerb == SkPath::kLine_Verb) { |
| continue; |
| } |
| const SkOpSegment& segment = index ? *rh->segment() : *this->segment(); |
| SkIntersections i; |
| (*CurveIntersectRay[cVerb])(segment.pts(), segment.weight(), rays[index], &i); |
| double tStart = index ? rh->fStart->t() : this->fStart->t(); |
| double tEnd = index ? rh->fComputedEnd->t() : this->fComputedEnd->t(); |
| bool testAscends = tStart < (index ? rh->fComputedEnd->t() : this->fComputedEnd->t()); |
| double t = testAscends ? 0 : 1; |
| for (int idx2 = 0; idx2 < i.used(); ++idx2) { |
| double testT = i[0][idx2]; |
| if (!approximately_between_orderable(tStart, testT, tEnd)) { |
| continue; |
| } |
| if (approximately_equal_orderable(tStart, testT)) { |
| continue; |
| } |
| smallTs[index] = t = testAscends ? std::max(t, testT) : std::min(t, testT); |
| limited[index] = approximately_equal_orderable(t, tEnd); |
| } |
| } |
| bool sRayLonger = false; |
| SkDVector sCept = {0, 0}; |
| double sCeptT = -1; |
| int sIndex = -1; |
| bool useIntersect = false; |
| for (int index = 0; index < 2; ++index) { |
| if (smallTs[index] < 0) { |
| continue; |
| } |
| const SkOpSegment& segment = index ? *rh->segment() : *this->segment(); |
| const SkDPoint& dPt = segment.dPtAtT(smallTs[index]); |
| SkDVector cept = dPt - rays[index][0]; |
| // If this point is on the curve, it should have been detected earlier by ordinary |
| // curve intersection. This may be hard to determine in general, but for lines, |
| // the point could be close to or equal to its end, but shouldn't be near the start. |
| if ((index ? lPts : rPts) == 1) { |
| SkDVector total = rays[index][1] - rays[index][0]; |
| if (cept.lengthSquared() * 2 < total.lengthSquared()) { |
| continue; |
| } |
| } |
| SkDVector end = rays[index][1] - rays[index][0]; |
| if (cept.fX * end.fX < 0 || cept.fY * end.fY < 0) { |
| continue; |
| } |
| double rayDist = cept.length(); |
| double endDist = end.length(); |
| bool rayLonger = rayDist > endDist; |
| if (limited[0] && limited[1] && rayLonger) { |
| useIntersect = true; |
| sRayLonger = rayLonger; |
| sCept = cept; |
| sCeptT = smallTs[index]; |
| sIndex = index; |
| break; |
| } |
| double delta = fabs(rayDist - endDist); |
| double minX, minY, maxX, maxY; |
| minX = minY = SK_ScalarInfinity; |
| maxX = maxY = -SK_ScalarInfinity; |
| const SkDCurve& curve = index ? rh->fPart.fCurve : this->fPart.fCurve; |
| int ptCount = index ? rPts : lPts; |
| for (int idx2 = 0; idx2 <= ptCount; ++idx2) { |
| minX = std::min(minX, curve[idx2].fX); |
| minY = std::min(minY, curve[idx2].fY); |
| maxX = std::max(maxX, curve[idx2].fX); |
| maxY = std::max(maxY, curve[idx2].fY); |
| } |
| double maxWidth = std::max(maxX - minX, maxY - minY); |
| delta = sk_ieee_double_divide(delta, maxWidth); |
| // FIXME: move these magic numbers |
| // This fixes skbug.com/8380 |
| // Larger changes (like changing the constant in the next block) cause other |
| // tests to fail as documented in the bug. |
| // This could probably become a more general test: e.g., if translating the |
| // curve causes the cross product of any control point or end point to change |
| // sign with regard to the opposite curve's hull, treat the curves as parallel. |
| |
| // Moreso, this points to the general fragility of this approach of assigning |
| // winding by sorting the angles of curves sharing a common point, as mentioned |
| // in the bug. |
| if (delta < 4e-3 && delta > 1e-3 && !useIntersect && fPart.isCurve() |
| && rh->fPart.isCurve() && fOriginalCurvePart[0] != fPart.fCurve.fLine[0]) { |
| // see if original curve is on one side of hull; translated is on the other |
| const SkDPoint& origin = rh->fOriginalCurvePart[0]; |
| int count = SkPathOpsVerbToPoints(rh->segment()->verb()); |
| const SkDVector line = rh->fOriginalCurvePart[count] - origin; |
| int originalSide = rh->lineOnOneSide(origin, line, this, true); |
| if (originalSide >= 0) { |
| int translatedSide = rh->lineOnOneSide(origin, line, this, false); |
| if (originalSide != translatedSide) { |
| continue; |
| } |
| } |
| } |
| if (delta > 1e-3 && (useIntersect ^= true)) { |
| sRayLonger = rayLonger; |
| sCept = cept; |
| sCeptT = smallTs[index]; |
| sIndex = index; |
| } |
| } |
| if (useIntersect) { |
| const SkDCurve& curve = sIndex ? rh->fPart.fCurve : this->fPart.fCurve; |
| const SkOpSegment& segment = sIndex ? *rh->segment() : *this->segment(); |
| double tStart = sIndex ? rh->fStart->t() : fStart->t(); |
| SkDVector mid = segment.dPtAtT(tStart + (sCeptT - tStart) / 2) - curve[0]; |
| double septDir = mid.crossCheck(sCept); |
| if (!septDir) { |
| return checkParallel(rh); |
| } |
| return sRayLonger ^ (sIndex == 0) ^ (septDir < 0); |
| } else { |
| return checkParallel(rh); |
| } |
| } |
| |
| bool SkOpAngle::endToSide(const SkOpAngle* rh, bool* inside) const { |
| const SkOpSegment* segment = this->segment(); |
| SkPath::Verb verb = segment->verb(); |
| SkDLine rayEnd; |
| rayEnd[0].set(this->fEnd->pt()); |
| rayEnd[1] = rayEnd[0]; |
| SkDVector slopeAtEnd = (*CurveDSlopeAtT[verb])(segment->pts(), segment->weight(), |
| this->fEnd->t()); |
| rayEnd[1].fX += slopeAtEnd.fY; |
| rayEnd[1].fY -= slopeAtEnd.fX; |
| SkIntersections iEnd; |
| const SkOpSegment* oppSegment = rh->segment(); |
| SkPath::Verb oppVerb = oppSegment->verb(); |
| (*CurveIntersectRay[oppVerb])(oppSegment->pts(), oppSegment->weight(), rayEnd, &iEnd); |
| double endDist; |
| int closestEnd = iEnd.closestTo(rh->fStart->t(), rh->fEnd->t(), rayEnd[0], &endDist); |
| if (closestEnd < 0) { |
| return false; |
| } |
| if (!endDist) { |
| return false; |
| } |
| SkDPoint start; |
| start.set(this->fStart->pt()); |
| // OPTIMIZATION: multiple times in the code we find the max scalar |
| double minX, minY, maxX, maxY; |
| minX = minY = SK_ScalarInfinity; |
| maxX = maxY = -SK_ScalarInfinity; |
| const SkDCurve& curve = rh->fPart.fCurve; |
| int oppPts = SkPathOpsVerbToPoints(oppVerb); |
| for (int idx2 = 0; idx2 <= oppPts; ++idx2) { |
| minX = std::min(minX, curve[idx2].fX); |
| minY = std::min(minY, curve[idx2].fY); |
| maxX = std::max(maxX, curve[idx2].fX); |
| maxY = std::max(maxY, curve[idx2].fY); |
| } |
| double maxWidth = std::max(maxX - minX, maxY - minY); |
| endDist = sk_ieee_double_divide(endDist, maxWidth); |
| if (!(endDist >= 5e-12)) { // empirically found |
| return false; // ! above catches NaN |
| } |
| const SkDPoint* endPt = &rayEnd[0]; |
| SkDPoint oppPt = iEnd.pt(closestEnd); |
| SkDVector vLeft = *endPt - start; |
| SkDVector vRight = oppPt - start; |
| double dir = vLeft.crossNoNormalCheck(vRight); |
| if (!dir) { |
| return false; |
| } |
| *inside = dir < 0; |
| return true; |
| } |
| |
| /* y<0 y==0 y>0 x<0 x==0 x>0 xy<0 xy==0 xy>0 |
| 0 x x x |
| 1 x x x |
| 2 x x x |
| 3 x x x |
| 4 x x x |
| 5 x x x |
| 6 x x x |
| 7 x x x |
| 8 x x x |
| 9 x x x |
| 10 x x x |
| 11 x x x |
| 12 x x x |
| 13 x x x |
| 14 x x x |
| 15 x x x |
| */ |
| int SkOpAngle::findSector(SkPath::Verb verb, double x, double y) const { |
| double absX = fabs(x); |
| double absY = fabs(y); |
| double xy = SkPath::kLine_Verb == verb || !AlmostEqualUlps(absX, absY) ? absX - absY : 0; |
| // If there are four quadrants and eight octants, and since the Latin for sixteen is sedecim, |
| // one could coin the term sedecimant for a space divided into 16 sections. |
| // http://english.stackexchange.com/questions/133688/word-for-something-partitioned-into-16-parts |
| static const int sedecimant[3][3][3] = { |
| // y<0 y==0 y>0 |
| // x<0 x==0 x>0 x<0 x==0 x>0 x<0 x==0 x>0 |
| {{ 4, 3, 2}, { 7, -1, 15}, {10, 11, 12}}, // abs(x) < abs(y) |
| {{ 5, -1, 1}, {-1, -1, -1}, { 9, -1, 13}}, // abs(x) == abs(y) |
| {{ 6, 3, 0}, { 7, -1, 15}, { 8, 11, 14}}, // abs(x) > abs(y) |
| }; |
| int sector = sedecimant[(xy >= 0) + (xy > 0)][(y >= 0) + (y > 0)][(x >= 0) + (x > 0)] * 2 + 1; |
| // SkASSERT(SkPath::kLine_Verb == verb || sector >= 0); |
| return sector; |
| } |
| |
| SkOpGlobalState* SkOpAngle::globalState() const { |
| return this->segment()->globalState(); |
| } |
| |
| |
| // OPTIMIZE: if this loops to only one other angle, after first compare fails, insert on other side |
| // OPTIMIZE: return where insertion succeeded. Then, start next insertion on opposite side |
| bool SkOpAngle::insert(SkOpAngle* angle) { |
| if (angle->fNext) { |
| if (loopCount() >= angle->loopCount()) { |
| if (!merge(angle)) { |
| return true; |
| } |
| } else if (fNext) { |
| if (!angle->merge(this)) { |
| return true; |
| } |
| } else { |
| angle->insert(this); |
| } |
| return true; |
| } |
| bool singleton = nullptr == fNext; |
| if (singleton) { |
| fNext = this; |
| } |
| SkOpAngle* next = fNext; |
| if (next->fNext == this) { |
| if (singleton || angle->after(this)) { |
| this->fNext = angle; |
| angle->fNext = next; |
| } else { |
| next->fNext = angle; |
| angle->fNext = this; |
| } |
| debugValidateNext(); |
| return true; |
| } |
| SkOpAngle* last = this; |
| bool flipAmbiguity = false; |
| do { |
| SkASSERT(last->fNext == next); |
| if (angle->after(last) ^ (angle->tangentsAmbiguous() & flipAmbiguity)) { |
| last->fNext = angle; |
| angle->fNext = next; |
| debugValidateNext(); |
| return true; |
| } |
| last = next; |
| if (last == this) { |
| FAIL_IF(flipAmbiguity); |
| // We're in a loop. If a sort was ambiguous, flip it to end the loop. |
| flipAmbiguity = true; |
| } |
| next = next->fNext; |
| } while (true); |
| return true; |
| } |
| |
| SkOpSpanBase* SkOpAngle::lastMarked() const { |
| if (fLastMarked) { |
| if (fLastMarked->chased()) { |
| return nullptr; |
| } |
| fLastMarked->setChased(true); |
| } |
| return fLastMarked; |
| } |
| |
| bool SkOpAngle::loopContains(const SkOpAngle* angle) const { |
| if (!fNext) { |
| return false; |
| } |
| const SkOpAngle* first = this; |
| const SkOpAngle* loop = this; |
| const SkOpSegment* tSegment = angle->fStart->segment(); |
| double tStart = angle->fStart->t(); |
| double tEnd = angle->fEnd->t(); |
| do { |
| const SkOpSegment* lSegment = loop->fStart->segment(); |
| if (lSegment != tSegment) { |
| continue; |
| } |
| double lStart = loop->fStart->t(); |
| if (lStart != tEnd) { |
| continue; |
| } |
| double lEnd = loop->fEnd->t(); |
| if (lEnd == tStart) { |
| return true; |
| } |
| } while ((loop = loop->fNext) != first); |
| return false; |
| } |
| |
| int SkOpAngle::loopCount() const { |
| int count = 0; |
| const SkOpAngle* first = this; |
| const SkOpAngle* next = this; |
| do { |
| next = next->fNext; |
| ++count; |
| } while (next && next != first); |
| return count; |
| } |
| |
| bool SkOpAngle::merge(SkOpAngle* angle) { |
| SkASSERT(fNext); |
| SkASSERT(angle->fNext); |
| SkOpAngle* working = angle; |
| do { |
| if (this == working) { |
| return false; |
| } |
| working = working->fNext; |
| } while (working != angle); |
| do { |
| SkOpAngle* next = working->fNext; |
| working->fNext = nullptr; |
| insert(working); |
| working = next; |
| } while (working != angle); |
| // it's likely that a pair of the angles are unorderable |
| debugValidateNext(); |
| return true; |
| } |
| |
| double SkOpAngle::midT() const { |
| return (fStart->t() + fEnd->t()) / 2; |
| } |
| |
| bool SkOpAngle::midToSide(const SkOpAngle* rh, bool* inside) const { |
| const SkOpSegment* segment = this->segment(); |
| SkPath::Verb verb = segment->verb(); |
| const SkPoint& startPt = this->fStart->pt(); |
| const SkPoint& endPt = this->fEnd->pt(); |
| SkDPoint dStartPt; |
| dStartPt.set(startPt); |
| SkDLine rayMid; |
| rayMid[0].fX = (startPt.fX + endPt.fX) / 2; |
| rayMid[0].fY = (startPt.fY + endPt.fY) / 2; |
| rayMid[1].fX = rayMid[0].fX + (endPt.fY - startPt.fY); |
| rayMid[1].fY = rayMid[0].fY - (endPt.fX - startPt.fX); |
| SkIntersections iMid; |
| (*CurveIntersectRay[verb])(segment->pts(), segment->weight(), rayMid, &iMid); |
| int iOutside = iMid.mostOutside(this->fStart->t(), this->fEnd->t(), dStartPt); |
| if (iOutside < 0) { |
| return false; |
| } |
| const SkOpSegment* oppSegment = rh->segment(); |
| SkPath::Verb oppVerb = oppSegment->verb(); |
| SkIntersections oppMid; |
| (*CurveIntersectRay[oppVerb])(oppSegment->pts(), oppSegment->weight(), rayMid, &oppMid); |
| int oppOutside = oppMid.mostOutside(rh->fStart->t(), rh->fEnd->t(), dStartPt); |
| if (oppOutside < 0) { |
| return false; |
| } |
| SkDVector iSide = iMid.pt(iOutside) - dStartPt; |
| SkDVector oppSide = oppMid.pt(oppOutside) - dStartPt; |
| double dir = iSide.crossCheck(oppSide); |
| if (!dir) { |
| return false; |
| } |
| *inside = dir < 0; |
| return true; |
| } |
| |
| bool SkOpAngle::oppositePlanes(const SkOpAngle* rh) const { |
| int startSpan = SkTAbs(rh->fSectorStart - fSectorStart); |
| return startSpan >= 8; |
| } |
| |
| int SkOpAngle::orderable(SkOpAngle* rh) { |
| int result; |
| if (!fPart.isCurve()) { |
| if (!rh->fPart.isCurve()) { |
| double leftX = fTangentHalf.dx(); |
| double leftY = fTangentHalf.dy(); |
| double rightX = rh->fTangentHalf.dx(); |
| double rightY = rh->fTangentHalf.dy(); |
| double x_ry = leftX * rightY; |
| double rx_y = rightX * leftY; |
| if (x_ry == rx_y) { |
| if (leftX * rightX < 0 || leftY * rightY < 0) { |
| return 1; // exactly 180 degrees apart |
| } |
| goto unorderable; |
| } |
| SkASSERT(x_ry != rx_y); // indicates an undetected coincidence -- worth finding earlier |
| return x_ry < rx_y ? 1 : 0; |
| } |
| if ((result = this->lineOnOneSide(rh, false)) >= 0) { |
| return result; |
| } |
| if (fUnorderable || approximately_zero(rh->fSide)) { |
| goto unorderable; |
| } |
| } else if (!rh->fPart.isCurve()) { |
| if ((result = rh->lineOnOneSide(this, false)) >= 0) { |
| return result ? 0 : 1; |
| } |
| if (rh->fUnorderable || approximately_zero(fSide)) { |
| goto unorderable; |
| } |
| } else if ((result = this->convexHullOverlaps(rh)) >= 0) { |
| return result; |
| } |
| return this->endsIntersect(rh) ? 1 : 0; |
| unorderable: |
| fUnorderable = true; |
| rh->fUnorderable = true; |
| return -1; |
| } |
| |
| // OPTIMIZE: if this shows up in a profile, add a previous pointer |
| // as is, this should be rarely called |
| SkOpAngle* SkOpAngle::previous() const { |
| SkOpAngle* last = fNext; |
| do { |
| SkOpAngle* next = last->fNext; |
| if (next == this) { |
| return last; |
| } |
| last = next; |
| } while (true); |
| } |
| |
| SkOpSegment* SkOpAngle::segment() const { |
| return fStart->segment(); |
| } |
| |
| void SkOpAngle::set(SkOpSpanBase* start, SkOpSpanBase* end) { |
| fStart = start; |
| fComputedEnd = fEnd = end; |
| SkASSERT(start != end); |
| fNext = nullptr; |
| fComputeSector = fComputedSector = fCheckCoincidence = fTangentsAmbiguous = false; |
| setSpans(); |
| setSector(); |
| SkDEBUGCODE(fID = start ? start->globalState()->nextAngleID() : -1); |
| } |
| |
| void SkOpAngle::setSpans() { |
| fUnorderable = false; |
| fLastMarked = nullptr; |
| if (!fStart) { |
| fUnorderable = true; |
| return; |
| } |
| const SkOpSegment* segment = fStart->segment(); |
| const SkPoint* pts = segment->pts(); |
| SkDEBUGCODE(fPart.fCurve.fVerb = SkPath::kCubic_Verb); // required for SkDCurve debug check |
| SkDEBUGCODE(fPart.fCurve[2].fX = fPart.fCurve[2].fY = fPart.fCurve[3].fX = fPart.fCurve[3].fY |
| = SK_ScalarNaN); // make the non-line part uninitialized |
| SkDEBUGCODE(fPart.fCurve.fVerb = segment->verb()); // set the curve type for real |
| segment->subDivide(fStart, fEnd, &fPart.fCurve); // set at least the line part if not more |
| fOriginalCurvePart = fPart.fCurve; |
| const SkPath::Verb verb = segment->verb(); |
| fPart.setCurveHullSweep(verb); |
| if (SkPath::kLine_Verb != verb && !fPart.isCurve()) { |
| SkDLine lineHalf; |
| fPart.fCurve[1] = fPart.fCurve[SkPathOpsVerbToPoints(verb)]; |
| fOriginalCurvePart[1] = fPart.fCurve[1]; |
| lineHalf[0].set(fPart.fCurve[0].asSkPoint()); |
| lineHalf[1].set(fPart.fCurve[1].asSkPoint()); |
| fTangentHalf.lineEndPoints(lineHalf); |
| fSide = 0; |
| } |
| switch (verb) { |
| case SkPath::kLine_Verb: { |
| SkASSERT(fStart != fEnd); |
| const SkPoint& cP1 = pts[fStart->t() < fEnd->t()]; |
| SkDLine lineHalf; |
| lineHalf[0].set(fStart->pt()); |
| lineHalf[1].set(cP1); |
| fTangentHalf.lineEndPoints(lineHalf); |
| fSide = 0; |
| } return; |
| case SkPath::kQuad_Verb: |
| case SkPath::kConic_Verb: { |
| SkLineParameters tangentPart; |
| (void) tangentPart.quadEndPoints(fPart.fCurve.fQuad); |
| fSide = -tangentPart.pointDistance(fPart.fCurve[2]); // not normalized -- compare sign only |
| } break; |
| case SkPath::kCubic_Verb: { |
| SkLineParameters tangentPart; |
| (void) tangentPart.cubicPart(fPart.fCurve.fCubic); |
| fSide = -tangentPart.pointDistance(fPart.fCurve[3]); |
| double testTs[4]; |
| // OPTIMIZATION: keep inflections precomputed with cubic segment? |
| int testCount = SkDCubic::FindInflections(pts, testTs); |
| double startT = fStart->t(); |
| double endT = fEnd->t(); |
| double limitT = endT; |
| int index; |
| for (index = 0; index < testCount; ++index) { |
| if (!::between(startT, testTs[index], limitT)) { |
| testTs[index] = -1; |
| } |
| } |
| testTs[testCount++] = startT; |
| testTs[testCount++] = endT; |
| SkTQSort<double>(testTs, testTs + testCount); |
| double bestSide = 0; |
| int testCases = (testCount << 1) - 1; |
| index = 0; |
| while (testTs[index] < 0) { |
| ++index; |
| } |
| index <<= 1; |
| for (; index < testCases; ++index) { |
| int testIndex = index >> 1; |
| double testT = testTs[testIndex]; |
| if (index & 1) { |
| testT = (testT + testTs[testIndex + 1]) / 2; |
| } |
| // OPTIMIZE: could avoid call for t == startT, endT |
| SkDPoint pt = dcubic_xy_at_t(pts, segment->weight(), testT); |
| SkLineParameters tangentPart; |
| tangentPart.cubicEndPoints(fPart.fCurve.fCubic); |
| double testSide = tangentPart.pointDistance(pt); |
| if (fabs(bestSide) < fabs(testSide)) { |
| bestSide = testSide; |
| } |
| } |
| fSide = -bestSide; // compare sign only |
| } break; |
| default: |
| SkASSERT(0); |
| } |
| } |
| |
| void SkOpAngle::setSector() { |
| if (!fStart) { |
| fUnorderable = true; |
| return; |
| } |
| const SkOpSegment* segment = fStart->segment(); |
| SkPath::Verb verb = segment->verb(); |
| fSectorStart = this->findSector(verb, fPart.fSweep[0].fX, fPart.fSweep[0].fY); |
| if (fSectorStart < 0) { |
| goto deferTilLater; |
| } |
| if (!fPart.isCurve()) { // if it's a line or line-like, note that both sectors are the same |
| SkASSERT(fSectorStart >= 0); |
| fSectorEnd = fSectorStart; |
| fSectorMask = 1 << fSectorStart; |
| return; |
| } |
| SkASSERT(SkPath::kLine_Verb != verb); |
| fSectorEnd = this->findSector(verb, fPart.fSweep[1].fX, fPart.fSweep[1].fY); |
| if (fSectorEnd < 0) { |
| deferTilLater: |
| fSectorStart = fSectorEnd = -1; |
| fSectorMask = 0; |
| fComputeSector = true; // can't determine sector until segment length can be found |
| return; |
| } |
| if (fSectorEnd == fSectorStart |
| && (fSectorStart & 3) != 3) { // if the sector has no span, it can't be an exact angle |
| fSectorMask = 1 << fSectorStart; |
| return; |
| } |
| bool crossesZero = this->checkCrossesZero(); |
| int start = std::min(fSectorStart, fSectorEnd); |
| bool curveBendsCCW = (fSectorStart == start) ^ crossesZero; |
| // bump the start and end of the sector span if they are on exact compass points |
| if ((fSectorStart & 3) == 3) { |
| fSectorStart = (fSectorStart + (curveBendsCCW ? 1 : 31)) & 0x1f; |
| } |
| if ((fSectorEnd & 3) == 3) { |
| fSectorEnd = (fSectorEnd + (curveBendsCCW ? 31 : 1)) & 0x1f; |
| } |
| crossesZero = this->checkCrossesZero(); |
| start = std::min(fSectorStart, fSectorEnd); |
| int end = std::max(fSectorStart, fSectorEnd); |
| if (!crossesZero) { |
| fSectorMask = (unsigned) -1 >> (31 - end + start) << start; |
| } else { |
| fSectorMask = (unsigned) -1 >> (31 - start) | ((unsigned) -1 << end); |
| } |
| } |
| |
| SkOpSpan* SkOpAngle::starter() { |
| return fStart->starter(fEnd); |
| } |
| |
| bool SkOpAngle::tangentsDiverge(const SkOpAngle* rh, double s0xt0) { |
| if (s0xt0 == 0) { |
| return false; |
| } |
| // if the ctrl tangents are not nearly parallel, use them |
| // solve for opposite direction displacement scale factor == m |
| // initial dir = v1.cross(v2) == v2.x * v1.y - v2.y * v1.x |
| // displacement of q1[1] : dq1 = { -m * v1.y, m * v1.x } + q1[1] |
| // straight angle when : v2.x * (dq1.y - q1[0].y) == v2.y * (dq1.x - q1[0].x) |
| // v2.x * (m * v1.x + v1.y) == v2.y * (-m * v1.y + v1.x) |
| // - m * (v2.x * v1.x + v2.y * v1.y) == v2.x * v1.y - v2.y * v1.x |
| // m = (v2.y * v1.x - v2.x * v1.y) / (v2.x * v1.x + v2.y * v1.y) |
| // m = v1.cross(v2) / v1.dot(v2) |
| const SkDVector* sweep = fPart.fSweep; |
| const SkDVector* tweep = rh->fPart.fSweep; |
| double s0dt0 = sweep[0].dot(tweep[0]); |
| if (!s0dt0) { |
| return true; |
| } |
| SkASSERT(s0dt0 != 0); |
| double m = s0xt0 / s0dt0; |
| double sDist = sweep[0].length() * m; |
| double tDist = tweep[0].length() * m; |
| bool useS = fabs(sDist) < fabs(tDist); |
| double mFactor = fabs(useS ? this->distEndRatio(sDist) : rh->distEndRatio(tDist)); |
| fTangentsAmbiguous = mFactor >= 50 && mFactor < 200; |
| return mFactor < 50; // empirically found limit |
| } |