diff options
Diffstat (limited to 'src/pathops/SkOpAngle.cpp')
| -rw-r--r-- | src/pathops/SkOpAngle.cpp | 1214 |
1 files changed, 913 insertions, 301 deletions
diff --git a/src/pathops/SkOpAngle.cpp b/src/pathops/SkOpAngle.cpp index 742a161f6c..364ab1bf1f 100644 --- a/src/pathops/SkOpAngle.cpp +++ b/src/pathops/SkOpAngle.cpp @@ -12,19 +12,14 @@ #if DEBUG_ANGLE #include "SkString.h" - -static const char funcName[] = "SkOpSegment::operator<"; -static const int bugChar = strlen(funcName) + 1; #endif /* 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(SkString* bugOut, const char* append, bool compare) { - bugOut->appendf("%s", append); - bugOut->writable_str()[bugChar] = "><"[compare]; - SkDebugf("%s\n", bugOut->c_str()); + static bool CompareResult(SkString* bugOut, int append, bool compare) { + SkDebugf("%s %c %d\n", bugOut->c_str(), compare ? 'T' : 'F', append); return compare; } @@ -33,7 +28,197 @@ static const int bugChar = strlen(funcName) + 1; #define COMPARE_RESULT(append, compare) compare #endif -bool SkOpAngle::calcSlop(double x, double y, double rx, double ry, bool* result) const{ +/* 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(const SkOpAngle* test) const { + const SkOpAngle& lh = *test; + const SkOpAngle& rh = *lh.fNext; + SkASSERT(&lh != &rh); +#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.fSegment->debugID(), lh.debugID(), lh.fSectorStart, lh.fSectorEnd, + lh.fSegment->t(lh.fStart), lh.fSegment->t(lh.fEnd), + fSegment->debugID(), debugID(), fSectorStart, fSectorEnd, fSegment->t(fStart), + fSegment->t(fEnd), + rh.fSegment->debugID(), rh.debugID(), rh.fSectorStart, rh.fSectorEnd, + rh.fSegment->t(rh.fStart), rh.fSegment->t(rh.fEnd)); +#endif + if (lh.fComputeSector && !const_cast<SkOpAngle&>(lh).computeSector()) { + return COMPARE_RESULT(1, true); + } + if (fComputeSector && !const_cast<SkOpAngle*>(this)->computeSector()) { + return COMPARE_RESULT(2, true); + } + if (rh.fComputeSector && !const_cast<SkOpAngle&>(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.fSegment->debugID(), lh.debugID(), lh.fSectorStart, lh.fSectorEnd, + lh.fSegment->t(lh.fStart), lh.fSegment->t(lh.fEnd), + fSegment->debugID(), debugID(), fSectorStart, fSectorEnd, fSegment->t(fStart), + fSegment->t(fEnd), + rh.fSegment->debugID(), rh.debugID(), rh.fSectorStart, rh.fSectorEnd, + rh.fSegment->t(rh.fStart), rh.fSegment->t(rh.fEnd)); +#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 = (int) lh.orderable(rh); + if (!ltrOverlap) { + return COMPARE_RESULT(5, !lrOrder); + } + } + int ltOrder; + SkASSERT((lh.fSectorMask & fSectorMask) || (rh.fSectorMask & fSectorMask)); + if (lh.fSectorMask & fSectorMask) { + ltOrder = (int) 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 = (int) orderable(rh); + } else { + int trGap = (rh.fSectorStart - fSectorStart + 32) & 0x1f; + trOrder = trGap > 20 ? 0 : trGap > 11 ? -1 : 1; + } + 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); + SkASSERT(lrOpposite != ltOpposite); + return COMPARE_RESULT(8, ltOpposite); + } else if (ltOrder == 1 && trOrder == 0) { + SkASSERT(lrOrder < 0); + SkDEBUGCODE(bool ltOpposite = lh.oppositePlanes(*this)); + bool trOpposite = oppositePlanes(rh); + SkASSERT(ltOpposite != trOpposite); + 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 (lrOrder < 0) { + if (ltOrder < 0) { + return COMPARE_RESULT(11, trOrder); + } + return COMPARE_RESULT(12, ltOrder); + } + return COMPARE_RESULT(13, !lrOrder); +} + +// 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::allOnOneSide(const SkOpAngle& test) const { + SkASSERT(!fIsCurve); + SkASSERT(test.fIsCurve); + const SkDPoint& origin = test.fCurvePart[0]; + SkVector line; + if (fSegment->verb() == SkPath::kLine_Verb) { + const SkPoint* linePts = fSegment->pts(); + int lineStart = fStart < fEnd ? 0 : 1; + line = linePts[lineStart ^ 1] - linePts[lineStart]; + } else { + SkPoint shortPts[2] = { fCurvePart[0].asSkPoint(), fCurvePart[1].asSkPoint() }; + line = shortPts[1] - shortPts[0]; + } + float crosses[3]; + SkPath::Verb testVerb = test.fSegment->verb(); + int iMax = SkPathOpsVerbToPoints(testVerb); +// SkASSERT(origin == test.fCurveHalf[0]); + const SkDCubic& testCurve = test.fCurvePart; +// do { + for (int index = 1; index <= iMax; ++index) { + float xy1 = (float) (line.fX * (testCurve[index].fY - origin.fY)); + float xy2 = (float) (line.fY * (testCurve[index].fX - origin.fX)); + crosses[index - 1] = AlmostEqualUlps(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; + } + fUnorderable = true; + return -1; +} + +bool SkOpAngle::calcSlop(double x, double y, double rx, double ry, bool* result) const { double absX = fabs(x); double absY = fabs(y); double length = absX < absY ? absX / 2 + absY : absX + absY / 2; @@ -59,280 +244,733 @@ bool SkOpAngle::calcSlop(double x, double y, double rx, double ry, bool* result) return *result == less2; } -/* -for quads and cubics, set up a parameterized line (e.g. LineParameters ) -for points [0] to [1]. See if point [2] is on that line, or on one side -or the other. If it both quads' end points are on the same side, choose -the shorter tangent. If the tangents are equal, choose the better second -tangent angle +bool SkOpAngle::checkCrossesZero() const { + int start = SkTMin(fSectorStart, fSectorEnd); + int end = SkTMax(fSectorStart, fSectorEnd); + bool crossesZero = end - start > 16; + return crossesZero; +} -FIXME: maybe I could set up LineParameters lazily -*/ -bool SkOpAngle::operator<(const SkOpAngle& rh) const { // this/lh: left-hand; rh: right-hand - double y = dy(); - double ry = rh.dy(); -#if DEBUG_ANGLE - SkString bugOut; - bugOut.printf("%s _ id=%d segId=%d tStart=%1.9g tEnd=%1.9g" - " | id=%d segId=%d tStart=%1.9g tEnd=%1.9g ", funcName, - fID, fSegment->debugID(), fSegment->t(fStart), fSegment->t(fEnd), - rh.fID, rh.fSegment->debugID(), rh.fSegment->t(rh.fStart), rh.fSegment->t(rh.fEnd)); -#endif - double y_ry = y * ry; - if (y_ry < 0) { // if y's are opposite signs, we can do a quick return - return COMPARE_RESULT("1 y * ry < 0", y < 0); - } - // at this point, both y's must be the same sign, or one (or both) is zero - double x = dx(); - double rx = rh.dx(); - if (x * rx < 0) { // if x's are opposite signs, use y to determine first or second half - if (y < 0 && ry < 0) { // if y's are negative, lh x is smaller if positive - return COMPARE_RESULT("2 x_rx < 0 && y < 0 ...", x > 0); - } - if (y >= 0 && ry >= 0) { // if y's are zero or positive, lh x is smaller if negative - return COMPARE_RESULT("3 x_rx < 0 && y >= 0 ...", x < 0); - } - SkASSERT((y == 0) ^ (ry == 0)); // if one y is zero and one is negative, neg y is smaller - return COMPARE_RESULT("4 x_rx < 0 && y == 0 ...", y < 0); - } - // at this point, both x's must be the same sign, or one (or both) is zero - if (y_ry == 0) { // if either y is zero - if (y + ry < 0) { // if the other y is less than zero, it must be smaller - return COMPARE_RESULT("5 y_ry == 0 && y + ry < 0", y < 0); - } - if (y + ry > 0) { // if a y is greater than zero and an x is positive, non zero is smaller - return COMPARE_RESULT("6 y_ry == 0 && y + ry > 0", (x + rx > 0) ^ (y == 0)); - } - // at this point, both y's are zero, so lines are coincident or one is degenerate - SkASSERT(x * rx != 0); // and a degenerate line should haven't gotten this far - } - // see if either curve can be lengthened before trying the tangent - if (fSegment->other(fEnd) != rh.fSegment // tangents not absolutely identical - && rh.fSegment->other(rh.fEnd) != fSegment - && y != -DBL_EPSILON - && ry != -DBL_EPSILON) { // and not intersecting - SkOpAngle longer = *this; - SkOpAngle rhLonger = rh; - if ((longer.lengthen(rh) | rhLonger.lengthen(*this)) // lengthen both - && (fUnorderable || !longer.fUnorderable) - && (rh.fUnorderable || !rhLonger.fUnorderable)) { -#if DEBUG_ANGLE - bugOut.prepend(" "); -#endif - return COMPARE_RESULT("10 longer.lengthen(rh) ...", longer < rhLonger); +bool SkOpAngle::checkParallel(const SkOpAngle& rh) const { + SkDVector scratch[2]; + const SkDVector* sweep, * tweep; + if (!fUnorderedSweep) { + sweep = fSweep; + } else { + scratch[0] = fCurvePart[1] - fCurvePart[0]; + sweep = &scratch[0]; + } + if (!rh.fUnorderedSweep) { + tweep = rh.fSweep; + } else { + scratch[1] = rh.fCurvePart[1] - rh.fCurvePart[0]; + tweep = &scratch[1]; + } + double s0xt0 = sweep->crossCheck(*tweep); + if (tangentsDiverge(rh, s0xt0)) { + return s0xt0 < 0; + } + SkDVector m0 = fSegment->dPtAtT(midT()) - fCurvePart[0]; + SkDVector m1 = rh.fSegment->dPtAtT(rh.midT()) - rh.fCurvePart[0]; + double m0xm1 = m0.crossCheck(m1); + if (m0xm1 == 0) { + 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) { + // FIXME: logically, this should return !fUnorderable, but doing so breaks testQuadratic51 + // -- but in general, this code may not work so this may be the least of problems + // adding the bang fixes testQuads46x in release, however + return fUnorderable; + } + SkASSERT(fSegment->verb() != SkPath::kLine_Verb && small()); + fComputedSector = true; + int step = fStart < fEnd ? 1 : -1; + int limit = step > 0 ? fSegment->count() : -1; + int checkEnd = fEnd; + do { +// advance end + const SkOpSpan& span = fSegment->span(checkEnd); + const SkOpSegment* other = span.fOther; + int oCount = other->count(); + for (int oIndex = 0; oIndex < oCount; ++oIndex) { + const SkOpSpan& oSpan = other->span(oIndex); + if (oSpan.fOther != fSegment) { + continue; + } + if (oSpan.fOtherIndex == checkEnd) { + continue; + } + if (!approximately_equal(oSpan.fOtherT, span.fT)) { + continue; + } + goto recomputeSector; } + checkEnd += step; + } while (checkEnd != limit); +recomputeSector: + if (checkEnd == fEnd || checkEnd - step == fEnd) { + fUnorderable = true; + return false; } - SkPath::Verb verb = fSegment->verb(); - SkPath::Verb rVerb = rh.fSegment->verb(); - if (y_ry != 0) { // if they aren't coincident, look for a stable cross product - // at this point, y's are the same sign, neither is zero - // and x's are the same sign, or one (or both) is zero - double x_ry = x * ry; - double rx_y = rx * y; - if (!fComputed && !rh.fComputed) { - if (!SkDLine::NearRay(x, y, rx, ry) && x_ry != rx_y) { - return COMPARE_RESULT("7 !fComputed && !rh.fComputed", x_ry < rx_y); + fEnd = checkEnd - step; + setSpans(); + setSector(); + return !fUnorderable; +} + +// returns -1 if overlaps 0 if no overlap cw 1 if no overlap ccw +int SkOpAngle::convexHullOverlaps(const SkOpAngle& rh) const { + const SkDVector* sweep = fSweep; + const SkDVector* tweep = rh.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 = fSegment->dPtAtT(midT()) - fCurvePart[0]; + SkDVector m1 = rh.fSegment->dPtAtT(rh.midT()) - rh.fCurvePart[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; } - if (fSide2 == 0 && rh.fSide2 == 0) { - return COMPARE_RESULT("7a !fComputed && !rh.fComputed", x_ry < rx_y); + SkDVector v; + v.set(pts[idx2] - pts[idx1]); + double lenSq = v.lengthSquared(); + longest = SkTMax(longest, lenSq); + } + } + return sqrt(longest) / dist; +} + +bool SkOpAngle::endsIntersect(const SkOpAngle& rh) const { + SkPath::Verb lVerb = fSegment->verb(); + SkPath::Verb rVerb = rh.fSegment->verb(); + int lPts = SkPathOpsVerbToPoints(lVerb); + int rPts = SkPathOpsVerbToPoints(rVerb); + SkDLine rays[] = {{{fCurvePart[0], rh.fCurvePart[rPts]}}, + {{fCurvePart[0], fCurvePart[lPts]}}}; + if (rays[0][1] == rays[1][1]) { + return checkParallel(rh); + } + double smallTs[2] = {-1, -1}; + bool limited[2] = {false, false}; + for (int index = 0; index < 2; ++index) { + const SkOpSegment& segment = index ? *rh.fSegment : *fSegment; + SkIntersections i; + (*CurveIntersectRay[index ? rPts : lPts])(segment.pts(), rays[index], &i); +// SkASSERT(i.used() >= 1); + if (i.used() <= 1) { + continue; + } + double tStart = segment.t(index ? rh.fStart : fStart); + double tEnd = segment.t(index ? rh.fEnd : fEnd); + bool testAscends = index ? rh.fStart < rh.fEnd : fStart < fEnd; + 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; } - } else { - // if the vector was a result of subdividing a curve, see if it is stable - bool sloppy1 = x_ry < rx_y; - bool sloppy2 = !sloppy1; - if ((!fComputed || calcSlop(x, y, rx, ry, &sloppy1)) - && (!rh.fComputed || rh.calcSlop(rx, ry, x, y, &sloppy2)) - && sloppy1 != sloppy2) { - return COMPARE_RESULT("8 CalcSlop(x, y ...", sloppy1); + if (approximately_equal_orderable(tStart, testT)) { + continue; } + smallTs[index] = t = testAscends ? SkTMax(t, testT) : SkTMin(t, testT); + limited[index] = approximately_equal_orderable(t, tEnd); } } - if (fSide2 * rh.fSide2 == 0) { // one is zero -#if DEBUG_ANGLE - if (fSide2 == rh.fSide2 && y_ry) { // both is zero; coincidence was undetected - SkDebugf("%s coincidence!\n", __FUNCTION__); +#if 0 + if (smallTs[0] < 0 && smallTs[1] < 0) { // if neither ray intersects, do endpoint sort + double m0xm1 = 0; + if (lVerb == SkPath::kLine_Verb) { + SkASSERT(rVerb != SkPath::kLine_Verb); + SkDVector m0 = rays[1][1] - fCurvePart[0]; + SkDPoint endPt; + endPt.set(rh.fSegment->pts()[rh.fStart < rh.fEnd ? rPts : 0]); + SkDVector m1 = endPt - fCurvePart[0]; + m0xm1 = m0.crossCheck(m1); } + if (rVerb == SkPath::kLine_Verb) { + SkDPoint endPt; + endPt.set(fSegment->pts()[fStart < fEnd ? lPts : 0]); + SkDVector m0 = endPt - fCurvePart[0]; + SkDVector m1 = rays[0][1] - fCurvePart[0]; + m0xm1 = m0.crossCheck(m1); + } + if (m0xm1 != 0) { + return m0xm1 < 0; + } + } #endif - return COMPARE_RESULT("9a fSide2 * rh.fSide2 == 0 ...", fSide2 < rh.fSide2); - } - // at this point, the initial tangent line is nearly coincident - // see if edges curl away from each other - if (fSide * rh.fSide < 0 && (!approximately_zero(fSide) || !approximately_zero(rh.fSide))) { - return COMPARE_RESULT("9b fSide * rh.fSide < 0 ...", fSide < rh.fSide); - } - if (fUnsortable || rh.fUnsortable) { - // even with no solution, return a stable sort - return COMPARE_RESULT("11 fUnsortable || rh.fUnsortable", this < &rh); - } - if ((verb == SkPath::kLine_Verb && approximately_zero(y) && approximately_zero(x)) - || (rVerb == SkPath::kLine_Verb - && approximately_zero(ry) && approximately_zero(rx))) { - // See general unsortable comment below. This case can happen when - // one line has a non-zero change in t but no change in x and y. - fUnsortable = true; - return COMPARE_RESULT("12 verb == SkPath::kLine_Verb ...", this < &rh); - } - if (fSegment->isTiny(this) || rh.fSegment->isTiny(&rh)) { - fUnsortable = true; - return COMPARE_RESULT("13 verb == fSegment->isTiny(this) ...", this < &rh); - } - SkASSERT(verb >= SkPath::kQuad_Verb); - SkASSERT(rVerb >= SkPath::kQuad_Verb); - // FIXME: until I can think of something better, project a ray from the - // end of the shorter tangent to midway between the end points - // through both curves and use the resulting angle to sort - // FIXME: some of this setup can be moved to set() if it works, or cached if it's expensive - double len = fTangentPart.normalSquared(); - double rlen = rh.fTangentPart.normalSquared(); - SkDLine ray; - SkIntersections i, ri; - int roots, rroots; - bool flip = false; - bool useThis; - bool leftLessThanRight = fSide > 0; - do { - useThis = (len < rlen) ^ flip; - const SkDCubic& part = useThis ? fCurvePart : rh.fCurvePart; - SkPath::Verb partVerb = useThis ? verb : rVerb; - ray[0] = partVerb == SkPath::kCubic_Verb && part[0].approximatelyEqual(part[1]) ? - part[2] : part[1]; - ray[1] = SkDPoint::Mid(part[0], part[SkPathOpsVerbToPoints(partVerb)]); - SkASSERT(ray[0] != ray[1]); - roots = (i.*CurveRay[SkPathOpsVerbToPoints(verb)])(fSegment->pts(), ray); - rroots = (ri.*CurveRay[SkPathOpsVerbToPoints(rVerb)])(rh.fSegment->pts(), ray); - } while ((roots == 0 || rroots == 0) && (flip ^= true)); - if (roots == 0 || rroots == 0) { - // FIXME: we don't have a solution in this case. The interim solution - // is to mark the edges as unsortable, exclude them from this and - // future computations, and allow the returned path to be fragmented - fUnsortable = true; - return COMPARE_RESULT("roots == 0 || rroots == 0", this < &rh); - } - SkASSERT(fSide != 0 && rh.fSide != 0); - if (fSide * rh.fSide < 0) { - fUnsortable = true; - return COMPARE_RESULT("14 fSide * rh.fSide < 0", this < &rh); - } - SkDPoint lLoc; - double best = SK_ScalarInfinity; -#if DEBUG_SORT - SkDebugf("lh=%d rh=%d use-lh=%d ray={{%1.9g,%1.9g}, {%1.9g,%1.9g}} %c\n", - fSegment->debugID(), rh.fSegment->debugID(), useThis, ray[0].fX, ray[0].fY, - ray[1].fX, ray[1].fY, "-+"[fSide > 0]); -#endif - for (int index = 0; index < roots; ++index) { - SkDPoint loc = i.pt(index); - SkDVector dxy = loc - ray[0]; - double dist = dxy.lengthSquared(); -#if DEBUG_SORT - SkDebugf("best=%1.9g dist=%1.9g loc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n", - best, dist, loc.fX, loc.fY, dxy.fX, dxy.fY); -#endif - if (best > dist) { - lLoc = loc; - best = dist; - } - } - flip = false; - SkDPoint rLoc; - for (int index = 0; index < rroots; ++index) { - rLoc = ri.pt(index); - SkDVector dxy = rLoc - ray[0]; - double dist = dxy.lengthSquared(); -#if DEBUG_SORT - SkDebugf("best=%1.9g dist=%1.9g %c=(fSide < 0) rLoc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n", - best, dist, "><"[fSide < 0], rLoc.fX, rLoc.fY, dxy.fX, dxy.fY); -#endif - if (best > dist) { - flip = true; + 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.fSegment : *fSegment; + 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 SkDCubic& curve = index ? rh.fCurvePart : fCurvePart; + int ptCount = index ? rPts : lPts; + for (int idx2 = 0; idx2 <= ptCount; ++idx2) { + minX = SkTMin(minX, curve[idx2].fX); + minY = SkTMin(minY, curve[idx2].fY); + maxX = SkTMax(maxX, curve[idx2].fX); + maxY = SkTMax(maxY, curve[idx2].fY); + } + double maxWidth = SkTMax(maxX - minX, maxY - minY); + delta /= maxWidth; + if (delta > 1e-4 && (useIntersect ^= true)) { // FIXME: move this magic number + sRayLonger = rayLonger; + sCept = cept; + sCeptT = smallTs[index]; + sIndex = index; + } + } + if (useIntersect) { + const SkDCubic& curve = sIndex ? rh.fCurvePart : fCurvePart; + const SkOpSegment& segment = sIndex ? *rh.fSegment : *fSegment; + double tStart = segment.t(sIndex ? rh.fStart : fStart); + 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); + } +} + +// Most of the time, the first one can be found trivially by detecting the smallest sector value. +// If all angles have the same sector value, actual sorting is required. +const SkOpAngle* SkOpAngle::findFirst() const { + const SkOpAngle* best = this; + int bestStart = SkTMin(fSectorStart, fSectorEnd); + const SkOpAngle* angle = this; + while ((angle = angle->fNext) != this) { + int angleEnd = SkTMax(angle->fSectorStart, angle->fSectorEnd); + if (angleEnd < bestStart) { + return angle; // we wrapped around + } + int angleStart = SkTMin(angle->fSectorStart, angle->fSectorEnd); + if (bestStart > angleStart) { + best = angle; + bestStart = angleStart; + } + } + // back up to the first possible angle + const SkOpAngle* firstBest = best; + angle = best; + int bestEnd = SkTMax(best->fSectorStart, best->fSectorEnd); + while ((angle = angle->previous()) != firstBest) { + if (angle->fStop) { break; } + int angleStart = SkTMin(angle->fSectorStart, angle->fSectorEnd); + // angles that are smaller by one aren't necessary better, since the larger may be a line + // and the smaller may be a curve that curls to the other side of the line. + if (bestEnd + 1 < angleStart) { + return best; + } + best = angle; + bestEnd = SkTMax(angle->fSectorStart, angle->fSectorEnd); + } + // in the case where all angles are nearly in the same sector, check the order to find the best + firstBest = best; + angle = best; + do { + angle = angle->fNext; + if (angle->fStop) { + return firstBest; + } + bool orderable = best->orderable(*angle); // note: may return an unorderable angle + if (orderable == 0) { + return angle; + } + best = angle; + } while (angle != firstBest); + // if the angles are equally ordered, fall back on the initial tangent + bool foundBelow = false; + while ((angle = angle->fNext)) { + SkDVector scratch[2]; + const SkDVector* sweep; + if (!angle->fUnorderedSweep) { + sweep = angle->fSweep; + } else { + scratch[0] = angle->fCurvePart[1] - angle->fCurvePart[0]; + sweep = &scratch[0]; + } + bool isAbove = sweep->fY <= 0; + if (isAbove && foundBelow) { + return angle; + } + foundBelow |= !isAbove; + if (angle == firstBest) { + return NULL; // should not loop around + } + } + SkASSERT(0); // should never get here + return NULL; +} + +/* 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; +} + +// 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 +void SkOpAngle::insert(SkOpAngle* angle) { + if (angle->fNext) { + if (loopCount() >= angle->loopCount()) { + if (!merge(angle)) { + return; + } + } else if (fNext) { + if (!angle->merge(this)) { + return; + } + } else { + angle->insert(this); + } + return; } - if (flip) { - leftLessThanRight = !leftLessThanRight; + bool singleton = NULL == fNext; + if (singleton) { + fNext = this; } - return COMPARE_RESULT("15 leftLessThanRight", leftLessThanRight); + 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; + } + SkOpAngle* last = this; + do { + SkASSERT(last->fNext == next); + if (angle->after(last)) { + last->fNext = angle; + angle->fNext = next; + debugValidateNext(); + return; + } + last = next; + next = next->fNext; + if (last == this && next->fUnorderable) { + fUnorderable = true; + return; + } + SkASSERT(last != this); + } while (true); } bool SkOpAngle::isHorizontal() const { - return dy() == 0 && fSegment->verb() == SkPath::kLine_Verb; + return !fIsCurve && fSweep[0].fY == 0; } -// lengthen cannot cross opposite angle -bool SkOpAngle::lengthen(const SkOpAngle& opp) { - if (fSegment->other(fEnd) == opp.fSegment) { - return false; +SkOpSpan* SkOpAngle::lastMarked() const { + if (fLastMarked) { + if (fLastMarked->fChased) { + return NULL; + } + fLastMarked->fChased = true; } - // FIXME: make this a while loop instead and make it as large as possible? - int newEnd = fEnd; - if (fStart < fEnd ? ++newEnd < fSegment->count() : --newEnd >= 0) { - fEnd = newEnd; - setSpans(); - return true; + return fLastMarked; +} + +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; +} + +// OPTIMIZATION: can this be done better in after when angles are sorted? +void SkOpAngle::markStops() { + SkOpAngle* angle = this; + int lastEnd = SkTMax(fSectorStart, fSectorEnd); + do { + angle = angle->fNext; + int angleStart = SkTMin(angle->fSectorStart, angle->fSectorEnd); + // angles that are smaller by one aren't necessary better, since the larger may be a line + // and the smaller may be a curve that curls to the other side of the line. + if (lastEnd + 1 < angleStart) { + angle->fStop = true; + } + lastEnd = SkTMax(angle->fSectorStart, angle->fSectorEnd); + } while (angle != this); +} + +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 = NULL; + insert(working); + working = next; + } while (working != angle); + // it's likely that a pair of the angles are unorderable +#if DEBUG_ANGLE + SkOpAngle* last = angle; + working = angle->fNext; + do { + SkASSERT(last->fNext == working); + last->fNext = working->fNext; + SkASSERT(working->after(last)); + last->fNext = working; + last = working; + working = working->fNext; + } while (last != angle); +#endif + debugValidateNext(); + return true; +} + +double SkOpAngle::midT() const { + return (fSegment->t(fStart) + fSegment->t(fEnd)) / 2; +} + +bool SkOpAngle::oppositePlanes(const SkOpAngle& rh) const { + int startSpan = abs(rh.fSectorStart - fSectorStart); + return startSpan >= 8; +} + +bool SkOpAngle::orderable(const SkOpAngle& rh) const { + int result; + if (!fIsCurve) { + if (!rh.fIsCurve) { + 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 true; // exactly 180 degrees apart + } + goto unorderable; + } + SkASSERT(x_ry != rx_y); // indicates an undetected coincidence -- worth finding earlier + return x_ry < rx_y; + } + if ((result = allOnOneSide(rh)) >= 0) { + return result; + } + if (fUnorderable || approximately_zero(rh.fSide)) { + goto unorderable; + } + } else if (!rh.fIsCurve) { + if ((result = rh.allOnOneSide(*this)) >= 0) { + return !result; + } + if (rh.fUnorderable || approximately_zero(fSide)) { + goto unorderable; + } } - return false; + if ((result = convexHullOverlaps(rh)) >= 0) { + return result; + } + return endsIntersect(rh); +unorderable: + fUnorderable = true; + rh.fUnorderable = true; + return true; +} + +// 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); } void SkOpAngle::set(const SkOpSegment* segment, int start, int end) { +#if DEBUG_ANGLE + fID = 0; +#endif fSegment = segment; fStart = start; fEnd = end; + fNext = NULL; + fComputeSector = fComputedSector = false; + fStop = false; setSpans(); + setSector(); +} + +void SkOpAngle::setCurveHullSweep() { + fUnorderedSweep = false; + fSweep[0] = fCurvePart[1] - fCurvePart[0]; + if (SkPath::kLine_Verb == fSegment->verb()) { + fSweep[1] = fSweep[0]; + return; + } + fSweep[1] = fCurvePart[2] - fCurvePart[0]; + if (SkPath::kCubic_Verb != fSegment->verb()) { + if (!fSweep[0].fX && !fSweep[0].fY) { + fSweep[0] = fSweep[1]; + } + return; + } + SkDVector thirdSweep = fCurvePart[3] - fCurvePart[0]; + if (fSweep[0].fX == 0 && fSweep[0].fY == 0) { + fSweep[0] = fSweep[1]; + fSweep[1] = thirdSweep; + if (fSweep[0].fX == 0 && fSweep[0].fY == 0) { + fSweep[0] = fSweep[1]; + fCurvePart[1] = fCurvePart[3]; + fIsCurve = false; + } + return; + } + double s1x3 = fSweep[0].crossCheck(thirdSweep); + double s3x2 = thirdSweep.crossCheck(fSweep[1]); + if (s1x3 * s3x2 >= 0) { // if third vector is on or between first two vectors + return; + } + double s2x1 = fSweep[1].crossCheck(fSweep[0]); + // FIXME: If the sweep of the cubic is greater than 180 degrees, we're in trouble + // probably such wide sweeps should be artificially subdivided earlier so that never happens + SkASSERT(s1x3 * s2x1 < 0 || s1x3 * s3x2 < 0); + if (s3x2 * s2x1 < 0) { + SkASSERT(s2x1 * s1x3 > 0); + fSweep[0] = fSweep[1]; + fUnorderedSweep = true; + } + fSweep[1] = thirdSweep; +} + +void SkOpAngle::setSector() { + SkPath::Verb verb = fSegment->verb(); + if (SkPath::kLine_Verb != verb && small()) { + fSectorStart = fSectorEnd = -1; + fSectorMask = 0; + fComputeSector = true; // can't determine sector until segment length can be found + return; + } + fSectorStart = findSector(verb, fSweep[0].fX, fSweep[0].fY); + if (!fIsCurve) { // 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 = findSector(verb, fSweep[1].fX, fSweep[1].fY); + if (fSectorEnd == fSectorStart) { + SkASSERT((fSectorStart & 3) != 3); // if the sector has no span, it can't be an exact angle + fSectorMask = 1 << fSectorStart; + return; + } + bool crossesZero = checkCrossesZero(); + int start = SkTMin(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 = checkCrossesZero(); + start = SkTMin(fSectorStart, fSectorEnd); + int end = SkTMax(fSectorStart, fSectorEnd); + if (!crossesZero) { + fSectorMask = (unsigned) -1 >> (31 - end + start) << start; + } else { + fSectorMask = (unsigned) -1 >> (31 - start) | (-1 << end); + } } void SkOpAngle::setSpans() { fUnorderable = fSegment->isTiny(this); fLastMarked = NULL; - fUnsortable = false; const SkPoint* pts = fSegment->pts(); - if (fSegment->verb() != SkPath::kLine_Verb) { - fComputed = fSegment->subDivide(fStart, fEnd, &fCurvePart); - fSegment->subDivide(fStart, fStart < fEnd ? fSegment->count() - 1 : 0, &fCurveHalf); - } - // FIXME: slight errors in subdivision cause sort trouble later on. As an experiment, try - // rounding the curve part to float precision here - // fCurvePart.round(fSegment->verb()); - switch (fSegment->verb()) { + SkDEBUGCODE(fCurvePart[2].fX = fCurvePart[2].fY = fCurvePart[3].fX = fCurvePart[3].fY + = SK_ScalarNaN); + fSegment->subDivide(fStart, fEnd, &fCurvePart); + setCurveHullSweep(); + const SkPath::Verb verb = fSegment->verb(); + if (verb != SkPath::kLine_Verb + && !(fIsCurve = fSweep[0].crossCheck(fSweep[1]) != 0)) { + SkDLine lineHalf; + lineHalf[0].set(fCurvePart[0].asSkPoint()); + lineHalf[1].set(fCurvePart[SkPathOpsVerbToPoints(verb)].asSkPoint()); + fTangentHalf.lineEndPoints(lineHalf); + fSide = 0; + } + switch (verb) { case SkPath::kLine_Verb: { SkASSERT(fStart != fEnd); - fCurvePart[0].set(pts[fStart > fEnd]); - fCurvePart[1].set(pts[fStart < fEnd]); - fComputed = false; - // OPTIMIZATION: for pure line compares, we never need fTangentPart.c - fTangentPart.lineEndPoints(*SkTCast<SkDLine*>(&fCurvePart)); + const SkPoint& cP1 = pts[fStart < fEnd]; + SkDLine lineHalf; + lineHalf[0].set(fSegment->span(fStart).fPt); + lineHalf[1].set(cP1); + fTangentHalf.lineEndPoints(lineHalf); fSide = 0; - fSide2 = 0; - } break; + fIsCurve = false; + } return; case SkPath::kQuad_Verb: { - fSide2 = -fTangentHalf.quadPart(*SkTCast<SkDQuad*>(&fCurveHalf)); - SkDQuad& quad = *SkTCast<SkDQuad*>(&fCurvePart); - fTangentPart.quadEndPoints(quad); - fSide = -fTangentPart.pointDistance(fCurvePart[2]); // not normalized -- compare sign only - if (fComputed && dx() > 0 && approximately_zero(dy())) { - SkDCubic origCurve; // can't use segment's curve in place since it may be flipped - int last = fSegment->count() - 1; - fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve); - SkLineParameters origTan; - origTan.quadEndPoints(*SkTCast<SkDQuad*>(&origCurve)); - if (origTan.dx() <= 0 - || (dy() != origTan.dy() && dy() * origTan.dy() <= 0)) { // signs match? - fUnorderable = true; - return; - } - } + SkLineParameters tangentPart; + SkDQuad& quad2 = *SkTCast<SkDQuad*>(&fCurvePart); + (void) tangentPart.quadEndPoints(quad2); + fSide = -tangentPart.pointDistance(fCurvePart[2]); // not normalized -- compare sign only } break; case SkPath::kCubic_Verb: { - double startT = fSegment->t(fStart); - fSide2 = -fTangentHalf.cubicPart(fCurveHalf); - fTangentPart.cubicEndPoints(fCurvePart); + SkLineParameters tangentPart; + (void) tangentPart.cubicPart(fCurvePart); + fSide = -tangentPart.pointDistance(fCurvePart[3]); double testTs[4]; // OPTIMIZATION: keep inflections precomputed with cubic segment? int testCount = SkDCubic::FindInflections(pts, testTs); + double startT = fSegment->t(fStart); double endT = fSegment->t(fEnd); double limitT = endT; int index; for (index = 0; index < testCount; ++index) { - if (!between(startT, testTs[index], limitT)) { + if (!::between(startT, testTs[index], limitT)) { testTs[index] = -1; } } @@ -354,82 +992,56 @@ void SkOpAngle::setSpans() { } // OPTIMIZE: could avoid call for t == startT, endT SkDPoint pt = dcubic_xy_at_t(pts, testT); - double testSide = fTangentPart.pointDistance(pt); + SkLineParameters tangentPart; + tangentPart.cubicEndPoints(fCurvePart); + double testSide = tangentPart.pointDistance(pt); if (fabs(bestSide) < fabs(testSide)) { bestSide = testSide; } } fSide = -bestSide; // compare sign only - SkASSERT(fSide == 0 || fSide2 != 0); - if (fComputed && dx() > 0 && approximately_zero(dy())) { - SkDCubic origCurve; // can't use segment's curve in place since it may be flipped - int last = fSegment->count() - 1; - fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve); - SkDCubicPair split = origCurve.chopAt(startT); - SkLineParameters splitTan; - splitTan.cubicEndPoints(fStart < fEnd ? split.second() : split.first()); - if (splitTan.dx() <= 0) { - fUnorderable = true; - fUnsortable = fSegment->isTiny(this); - return; - } - // if one is < 0 and the other is >= 0 - if (dy() * splitTan.dy() < 0) { - fUnorderable = true; - fUnsortable = fSegment->isTiny(this); - return; - } - } } break; default: SkASSERT(0); } - if ((fUnsortable = approximately_zero(dx()) && approximately_zero(dy()))) { - return; - } - if (fSegment->verb() == SkPath::kLine_Verb) { - return; - } - SkASSERT(fStart != fEnd); - int smaller = SkMin32(fStart, fEnd); - int larger = SkMax32(fStart, fEnd); - while (smaller < larger && fSegment->span(smaller).fTiny) { - ++smaller; - } - if (precisely_equal(fSegment->span(smaller).fT, fSegment->span(larger).fT)) { - #if DEBUG_UNSORTABLE - SkPoint iPt = fSegment->xyAtT(fStart); - SkPoint ePt = fSegment->xyAtT(fEnd); - SkDebugf("%s all tiny unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__, - fStart, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY); - #endif - fUnsortable = true; - return; - } - fUnsortable = fStart < fEnd ? fSegment->span(smaller).fUnsortableStart - : fSegment->span(larger).fUnsortableEnd; -#if DEBUG_UNSORTABLE - if (fUnsortable) { - SkPoint iPt = fSegment->xyAtT(smaller); - SkPoint ePt = fSegment->xyAtT(larger); - SkDebugf("%s unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__, - smaller, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY); +} + +bool SkOpAngle::small() const { + int min = SkMin32(fStart, fEnd); + int max = SkMax32(fStart, fEnd); + for (int index = min; index < max; ++index) { + const SkOpSpan& mSpan = fSegment->span(index); + if (!mSpan.fSmall) { + return false; + } } -#endif - return; + return true; } -#ifdef SK_DEBUG -void SkOpAngle::dump() const { - const SkOpSpan& spanStart = fSegment->span(fStart); - const SkOpSpan& spanEnd = fSegment->span(fEnd); - const SkOpSpan& spanMin = fStart < fEnd ? spanStart : spanEnd; - SkDebugf("id=%d (%1.9g,%1.9g) start=%d (%1.9g) end=%d (%1.9g) sumWind=", - fSegment->debugID(), fSegment->xAtT(fStart), fSegment->yAtT(fStart), - fStart, spanStart.fT, fEnd, spanEnd.fT); - SkPathOpsDebug::WindingPrintf(spanMin.fWindSum); - SkDebugf(" oppWind="); - SkPathOpsDebug::WindingPrintf(spanMin.fOppSum), - SkDebugf(" done=%d\n", spanMin.fDone); +bool SkOpAngle::tangentsDiverge(const SkOpAngle& rh, double s0xt0) const { + 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 = fSweep; + const SkDVector* tweep = rh.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 ? distEndRatio(sDist) : rh.distEndRatio(tDist)); + return mFactor < 5000; // empirically found limit } -#endif |