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Unified Diff: src/pathops/SkOpAngle.cpp

Issue 131103009: update pathops to circle sort (Closed) Base URL: https://skia.googlesource.com/skia.git@master
Patch Set: disable old test that still fails on linux 32 release Created 6 years, 8 months ago
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Index: src/pathops/SkOpAngle.cpp
diff --git a/src/pathops/SkOpAngle.cpp b/src/pathops/SkOpAngle.cpp
index 742a161f6c49221e373c78f1144ffb8af480fda3..364ab1bf1f53555e7ae98c76286628dd32a21b87 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
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