michael@0: /*
michael@0:  * Copyright 2012 Google Inc.
michael@0:  *
michael@0:  * Use of this source code is governed by a BSD-style license that can be
michael@0:  * found in the LICENSE file.
michael@0:  */
michael@0: #include "SkIntersections.h"
michael@0: #include "SkOpAngle.h"
michael@0: #include "SkOpSegment.h"
michael@0: #include "SkPathOpsCurve.h"
michael@0: #include "SkTSort.h"
michael@0: 
michael@0: #if DEBUG_ANGLE
michael@0: #include "SkString.h"
michael@0: 
michael@0: static const char funcName[] = "SkOpSegment::operator<";
michael@0: static const int bugChar = strlen(funcName) + 1;
michael@0: #endif
michael@0: 
michael@0: /* Angles are sorted counterclockwise. The smallest angle has a positive x and the smallest
michael@0:    positive y. The largest angle has a positive x and a zero y. */
michael@0: 
michael@0: #if DEBUG_ANGLE
michael@0:     static bool CompareResult(SkString* bugOut, const char* append, bool compare) {
michael@0:         bugOut->appendf("%s", append);
michael@0:         bugOut->writable_str()[bugChar] = "><"[compare];
michael@0:         SkDebugf("%s\n", bugOut->c_str());
michael@0:         return compare;
michael@0:     }
michael@0: 
michael@0:     #define COMPARE_RESULT(append, compare) CompareResult(&bugOut, append, compare)
michael@0: #else
michael@0:     #define COMPARE_RESULT(append, compare) compare
michael@0: #endif
michael@0: 
michael@0: bool SkOpAngle::calcSlop(double x, double y, double rx, double ry, bool* result) const{
michael@0:     double absX = fabs(x);
michael@0:     double absY = fabs(y);
michael@0:     double length = absX < absY ? absX / 2 + absY : absX + absY / 2;
michael@0:     int exponent;
michael@0:     (void) frexp(length, &exponent);
michael@0:     double epsilon = ldexp(FLT_EPSILON, exponent);
michael@0:     SkPath::Verb verb = fSegment->verb();
michael@0:     SkASSERT(verb == SkPath::kQuad_Verb || verb == SkPath::kCubic_Verb);
michael@0:     // FIXME: the quad and cubic factors are made up ; determine actual values
michael@0:     double slop = verb == SkPath::kQuad_Verb ? 4 * epsilon : 512 * epsilon;
michael@0:     double xSlop = slop;
michael@0:     double ySlop = x * y < 0 ? -xSlop : xSlop; // OPTIMIZATION: use copysign / _copysign ?
michael@0:     double x1 = x - xSlop;
michael@0:     double y1 = y + ySlop;
michael@0:     double x_ry1 = x1 * ry;
michael@0:     double rx_y1 = rx * y1;
michael@0:     *result = x_ry1 < rx_y1;
michael@0:     double x2 = x + xSlop;
michael@0:     double y2 = y - ySlop;
michael@0:     double x_ry2 = x2 * ry;
michael@0:     double rx_y2 = rx * y2;
michael@0:     bool less2 = x_ry2 < rx_y2;
michael@0:     return *result == less2;
michael@0: }
michael@0: 
michael@0: /*
michael@0: for quads and cubics, set up a parameterized line (e.g. LineParameters )
michael@0: for points [0] to [1]. See if point [2] is on that line, or on one side
michael@0: or the other. If it both quads' end points are on the same side, choose
michael@0: the shorter tangent. If the tangents are equal, choose the better second
michael@0: tangent angle
michael@0: 
michael@0: FIXME: maybe I could set up LineParameters lazily
michael@0: */
michael@0: bool SkOpAngle::operator<(const SkOpAngle& rh) const {  // this/lh: left-hand; rh: right-hand
michael@0:     double y = dy();
michael@0:     double ry = rh.dy();
michael@0: #if DEBUG_ANGLE
michael@0:     SkString bugOut;
michael@0:     bugOut.printf("%s _ id=%d segId=%d tStart=%1.9g tEnd=%1.9g"
michael@0:         " | id=%d segId=%d tStart=%1.9g tEnd=%1.9g ", funcName,
michael@0:         fID, fSegment->debugID(), fSegment->t(fStart), fSegment->t(fEnd),
michael@0:         rh.fID, rh.fSegment->debugID(), rh.fSegment->t(rh.fStart), rh.fSegment->t(rh.fEnd));
michael@0: #endif
michael@0:     double y_ry = y * ry;
michael@0:     if (y_ry < 0) {  // if y's are opposite signs, we can do a quick return
michael@0:         return COMPARE_RESULT("1 y * ry < 0", y < 0);
michael@0:     }
michael@0:     // at this point, both y's must be the same sign, or one (or both) is zero
michael@0:     double x = dx();
michael@0:     double rx = rh.dx();
michael@0:     if (x * rx < 0) {  // if x's are opposite signs, use y to determine first or second half
michael@0:         if (y < 0 && ry < 0) {  // if y's are negative, lh x is smaller if positive
michael@0:             return COMPARE_RESULT("2 x_rx < 0 && y < 0 ...", x > 0);
michael@0:         }
michael@0:         if (y >= 0 && ry >= 0) {  // if y's are zero or positive, lh x is smaller if negative
michael@0:             return COMPARE_RESULT("3 x_rx < 0 && y >= 0 ...", x < 0);
michael@0:         }
michael@0:         SkASSERT((y == 0) ^ (ry == 0));  // if one y is zero and one is negative, neg y is smaller
michael@0:         return COMPARE_RESULT("4 x_rx < 0 && y == 0 ...", y < 0);
michael@0:     }
michael@0:     // at this point, both x's must be the same sign, or one (or both) is zero
michael@0:     if (y_ry == 0) { // if either y is zero
michael@0:         if (y + ry < 0) { // if the other y is less than zero, it must be smaller
michael@0:             return COMPARE_RESULT("5 y_ry == 0 && y + ry < 0", y < 0);
michael@0:         }
michael@0:         if (y + ry > 0) { // if a y is greater than zero and an x is positive,  non zero is smaller
michael@0:             return COMPARE_RESULT("6 y_ry == 0 && y + ry > 0", (x + rx > 0) ^ (y == 0));
michael@0:         }
michael@0:         // at this point, both y's are zero, so lines are coincident or one is degenerate
michael@0:         SkASSERT(x * rx != 0);  // and a degenerate line should haven't gotten this far
michael@0:     }
michael@0:     // see if either curve can be lengthened before trying the tangent
michael@0:     if (fSegment->other(fEnd) != rh.fSegment  // tangents not absolutely identical
michael@0:             && rh.fSegment->other(rh.fEnd) != fSegment
michael@0:             && y != -DBL_EPSILON
michael@0:             && ry != -DBL_EPSILON) {  // and not intersecting
michael@0:         SkOpAngle longer = *this;
michael@0:         SkOpAngle rhLonger = rh;
michael@0:         if ((longer.lengthen(rh) | rhLonger.lengthen(*this))  // lengthen both
michael@0:                 && (fUnorderable || !longer.fUnorderable)
michael@0:                 && (rh.fUnorderable || !rhLonger.fUnorderable)) {
michael@0: #if DEBUG_ANGLE
michael@0:             bugOut.prepend("  ");
michael@0: #endif
michael@0:             return COMPARE_RESULT("10 longer.lengthen(rh) ...", longer < rhLonger);
michael@0:         }
michael@0:     }
michael@0:     SkPath::Verb verb = fSegment->verb();
michael@0:     SkPath::Verb rVerb = rh.fSegment->verb();
michael@0:     if (y_ry != 0) { // if they aren't coincident, look for a stable cross product
michael@0:         // at this point, y's are the same sign, neither is zero
michael@0:         //   and x's are the same sign, or one (or both) is zero
michael@0:         double x_ry = x * ry;
michael@0:         double rx_y = rx * y;
michael@0:         if (!fComputed && !rh.fComputed) {
michael@0:             if (!SkDLine::NearRay(x, y, rx, ry) && x_ry != rx_y) {
michael@0:                 return COMPARE_RESULT("7 !fComputed && !rh.fComputed", x_ry < rx_y);
michael@0:             }
michael@0:             if (fSide2 == 0 && rh.fSide2 == 0) {
michael@0:                 return COMPARE_RESULT("7a !fComputed && !rh.fComputed", x_ry < rx_y);
michael@0:             }
michael@0:         } else {
michael@0:             // if the vector was a result of subdividing a curve, see if it is stable
michael@0:             bool sloppy1 = x_ry < rx_y;
michael@0:             bool sloppy2 = !sloppy1;
michael@0:             if ((!fComputed || calcSlop(x, y, rx, ry, &sloppy1))
michael@0:                     && (!rh.fComputed || rh.calcSlop(rx, ry, x, y, &sloppy2))
michael@0:                     && sloppy1 != sloppy2) {
michael@0:                 return COMPARE_RESULT("8 CalcSlop(x, y ...", sloppy1);
michael@0:             }
michael@0:         }
michael@0:     }
michael@0:     if (fSide2 * rh.fSide2 == 0) {  // one is zero
michael@0: #if DEBUG_ANGLE
michael@0:         if (fSide2 == rh.fSide2 && y_ry) {  // both is zero; coincidence was undetected
michael@0:             SkDebugf("%s coincidence!\n", __FUNCTION__);
michael@0:         }
michael@0: #endif
michael@0:         return COMPARE_RESULT("9a fSide2 * rh.fSide2 == 0 ...", fSide2 < rh.fSide2);
michael@0:     }
michael@0:     // at this point, the initial tangent line is nearly coincident
michael@0:     // see if edges curl away from each other
michael@0:     if (fSide * rh.fSide < 0 && (!approximately_zero(fSide) || !approximately_zero(rh.fSide))) {
michael@0:         return COMPARE_RESULT("9b fSide * rh.fSide < 0 ...", fSide < rh.fSide);
michael@0:     }
michael@0:     if (fUnsortable || rh.fUnsortable) {
michael@0:         // even with no solution, return a stable sort
michael@0:         return COMPARE_RESULT("11 fUnsortable || rh.fUnsortable", this < &rh);
michael@0:     }
michael@0:     if ((verb == SkPath::kLine_Verb && approximately_zero(y) && approximately_zero(x))
michael@0:             || (rVerb == SkPath::kLine_Verb
michael@0:             && approximately_zero(ry) && approximately_zero(rx))) {
michael@0:         // See general unsortable comment below. This case can happen when
michael@0:         // one line has a non-zero change in t but no change in x and y.
michael@0:         fUnsortable = true;
michael@0:         return COMPARE_RESULT("12 verb == SkPath::kLine_Verb ...", this < &rh);
michael@0:     }
michael@0:     if (fSegment->isTiny(this) || rh.fSegment->isTiny(&rh)) {
michael@0:         fUnsortable = true;
michael@0:         return COMPARE_RESULT("13 verb == fSegment->isTiny(this) ...", this < &rh);
michael@0:     }
michael@0:     SkASSERT(verb >= SkPath::kQuad_Verb);
michael@0:     SkASSERT(rVerb >= SkPath::kQuad_Verb);
michael@0:     // FIXME: until I can think of something better, project a ray from the
michael@0:     // end of the shorter tangent to midway between the end points
michael@0:     // through both curves and use the resulting angle to sort
michael@0:     // FIXME: some of this setup can be moved to set() if it works, or cached if it's expensive
michael@0:     double len = fTangentPart.normalSquared();
michael@0:     double rlen = rh.fTangentPart.normalSquared();
michael@0:     SkDLine ray;
michael@0:     SkIntersections i, ri;
michael@0:     int roots, rroots;
michael@0:     bool flip = false;
michael@0:     bool useThis;
michael@0:     bool leftLessThanRight = fSide > 0;
michael@0:     do {
michael@0:         useThis = (len < rlen) ^ flip;
michael@0:         const SkDCubic& part = useThis ? fCurvePart : rh.fCurvePart;
michael@0:         SkPath::Verb partVerb = useThis ? verb : rVerb;
michael@0:         ray[0] = partVerb == SkPath::kCubic_Verb && part[0].approximatelyEqual(part[1]) ?
michael@0:             part[2] : part[1];
michael@0:         ray[1] = SkDPoint::Mid(part[0], part[SkPathOpsVerbToPoints(partVerb)]);
michael@0:         SkASSERT(ray[0] != ray[1]);
michael@0:         roots = (i.*CurveRay[SkPathOpsVerbToPoints(verb)])(fSegment->pts(), ray);
michael@0:         rroots = (ri.*CurveRay[SkPathOpsVerbToPoints(rVerb)])(rh.fSegment->pts(), ray);
michael@0:     } while ((roots == 0 || rroots == 0) && (flip ^= true));
michael@0:     if (roots == 0 || rroots == 0) {
michael@0:         // FIXME: we don't have a solution in this case. The interim solution
michael@0:         // is to mark the edges as unsortable, exclude them from this and
michael@0:         // future computations, and allow the returned path to be fragmented
michael@0:         fUnsortable = true;
michael@0:         return COMPARE_RESULT("roots == 0 || rroots == 0", this < &rh);
michael@0:     }
michael@0:     SkASSERT(fSide != 0 && rh.fSide != 0);
michael@0:     if (fSide * rh.fSide < 0) {
michael@0:         fUnsortable = true;
michael@0:         return COMPARE_RESULT("14 fSide * rh.fSide < 0", this < &rh);
michael@0:     }
michael@0:     SkDPoint lLoc;
michael@0:     double best = SK_ScalarInfinity;
michael@0: #if DEBUG_SORT
michael@0:     SkDebugf("lh=%d rh=%d use-lh=%d ray={{%1.9g,%1.9g}, {%1.9g,%1.9g}} %c\n",
michael@0:             fSegment->debugID(), rh.fSegment->debugID(), useThis, ray[0].fX, ray[0].fY,
michael@0:             ray[1].fX, ray[1].fY, "-+"[fSide > 0]);
michael@0: #endif
michael@0:     for (int index = 0; index < roots; ++index) {
michael@0:         SkDPoint loc = i.pt(index);
michael@0:         SkDVector dxy = loc - ray[0];
michael@0:         double dist = dxy.lengthSquared();
michael@0: #if DEBUG_SORT
michael@0:         SkDebugf("best=%1.9g dist=%1.9g loc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n",
michael@0:                 best, dist, loc.fX, loc.fY, dxy.fX, dxy.fY);
michael@0: #endif
michael@0:         if (best > dist) {
michael@0:             lLoc = loc;
michael@0:             best = dist;
michael@0:         }
michael@0:     }
michael@0:     flip = false;
michael@0:     SkDPoint rLoc;
michael@0:     for (int index = 0; index < rroots; ++index) {
michael@0:         rLoc = ri.pt(index);
michael@0:         SkDVector dxy = rLoc - ray[0];
michael@0:         double dist = dxy.lengthSquared();
michael@0: #if DEBUG_SORT
michael@0:         SkDebugf("best=%1.9g dist=%1.9g %c=(fSide < 0) rLoc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n",
michael@0:                 best, dist, "><"[fSide < 0], rLoc.fX, rLoc.fY, dxy.fX, dxy.fY);
michael@0: #endif
michael@0:         if (best > dist) {
michael@0:             flip = true;
michael@0:             break;
michael@0:         }
michael@0:     }
michael@0:     if (flip) {
michael@0:         leftLessThanRight = !leftLessThanRight;
michael@0:     }
michael@0:     return COMPARE_RESULT("15 leftLessThanRight", leftLessThanRight);
michael@0: }
michael@0: 
michael@0: bool SkOpAngle::isHorizontal() const {
michael@0:     return dy() == 0 && fSegment->verb() == SkPath::kLine_Verb;
michael@0: }
michael@0: 
michael@0: // lengthen cannot cross opposite angle
michael@0: bool SkOpAngle::lengthen(const SkOpAngle& opp) {
michael@0:     if (fSegment->other(fEnd) == opp.fSegment) {
michael@0:         return false;
michael@0:     }
michael@0:     // FIXME: make this a while loop instead and make it as large as possible?
michael@0:     int newEnd = fEnd;
michael@0:     if (fStart < fEnd ? ++newEnd < fSegment->count() : --newEnd >= 0) {
michael@0:         fEnd = newEnd;
michael@0:         setSpans();
michael@0:         return true;
michael@0:     }
michael@0:     return false;
michael@0: }
michael@0: 
michael@0: void SkOpAngle::set(const SkOpSegment* segment, int start, int end) {
michael@0:     fSegment = segment;
michael@0:     fStart = start;
michael@0:     fEnd = end;
michael@0:     setSpans();
michael@0: }
michael@0: 
michael@0: void SkOpAngle::setSpans() {
michael@0:     fUnorderable = fSegment->isTiny(this);
michael@0:     fLastMarked = NULL;
michael@0:     fUnsortable = false;
michael@0:     const SkPoint* pts = fSegment->pts();
michael@0:     if (fSegment->verb() != SkPath::kLine_Verb) {
michael@0:         fComputed = fSegment->subDivide(fStart, fEnd, &fCurvePart);
michael@0:         fSegment->subDivide(fStart, fStart < fEnd ? fSegment->count() - 1 : 0, &fCurveHalf);
michael@0:     }
michael@0:     // FIXME: slight errors in subdivision cause sort trouble later on. As an experiment, try
michael@0:     // rounding the curve part to float precision here
michael@0:     // fCurvePart.round(fSegment->verb());
michael@0:     switch (fSegment->verb()) {
michael@0:     case SkPath::kLine_Verb: {
michael@0:         SkASSERT(fStart != fEnd);
michael@0:         fCurvePart[0].set(pts[fStart > fEnd]);
michael@0:         fCurvePart[1].set(pts[fStart < fEnd]);
michael@0:         fComputed = false;
michael@0:         // OPTIMIZATION: for pure line compares, we never need fTangentPart.c
michael@0:         fTangentPart.lineEndPoints(*SkTCast<SkDLine*>(&fCurvePart));
michael@0:         fSide = 0;
michael@0:         fSide2 = 0;
michael@0:         } break;
michael@0:     case SkPath::kQuad_Verb: {
michael@0:         fSide2 = -fTangentHalf.quadPart(*SkTCast<SkDQuad*>(&fCurveHalf));
michael@0:         SkDQuad& quad = *SkTCast<SkDQuad*>(&fCurvePart);
michael@0:         fTangentPart.quadEndPoints(quad);
michael@0:         fSide = -fTangentPart.pointDistance(fCurvePart[2]);  // not normalized -- compare sign only
michael@0:         if (fComputed && dx() > 0 && approximately_zero(dy())) {
michael@0:             SkDCubic origCurve; // can't use segment's curve in place since it may be flipped
michael@0:             int last = fSegment->count() - 1;
michael@0:             fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve);
michael@0:             SkLineParameters origTan;
michael@0:             origTan.quadEndPoints(*SkTCast<SkDQuad*>(&origCurve));
michael@0:             if (origTan.dx() <= 0
michael@0:                     || (dy() != origTan.dy() && dy() * origTan.dy() <= 0)) { // signs match?
michael@0:                 fUnorderable = true;
michael@0:                 return;
michael@0:             }
michael@0:         }
michael@0:         } break;
michael@0:     case SkPath::kCubic_Verb: {
michael@0:         double startT = fSegment->t(fStart);
michael@0:         fSide2 = -fTangentHalf.cubicPart(fCurveHalf);
michael@0:         fTangentPart.cubicEndPoints(fCurvePart);
michael@0:         double testTs[4];
michael@0:         // OPTIMIZATION: keep inflections precomputed with cubic segment?
michael@0:         int testCount = SkDCubic::FindInflections(pts, testTs);
michael@0:         double endT = fSegment->t(fEnd);
michael@0:         double limitT = endT;
michael@0:         int index;
michael@0:         for (index = 0; index < testCount; ++index) {
michael@0:             if (!between(startT, testTs[index], limitT)) {
michael@0:                 testTs[index] = -1;
michael@0:             }
michael@0:         }
michael@0:         testTs[testCount++] = startT;
michael@0:         testTs[testCount++] = endT;
michael@0:         SkTQSort<double>(testTs, &testTs[testCount - 1]);
michael@0:         double bestSide = 0;
michael@0:         int testCases = (testCount << 1) - 1;
michael@0:         index = 0;
michael@0:         while (testTs[index] < 0) {
michael@0:             ++index;
michael@0:         }
michael@0:         index <<= 1;
michael@0:         for (; index < testCases; ++index) {
michael@0:             int testIndex = index >> 1;
michael@0:             double testT = testTs[testIndex];
michael@0:             if (index & 1) {
michael@0:                 testT = (testT + testTs[testIndex + 1]) / 2;
michael@0:             }
michael@0:             // OPTIMIZE: could avoid call for t == startT, endT
michael@0:             SkDPoint pt = dcubic_xy_at_t(pts, testT);
michael@0:             double testSide = fTangentPart.pointDistance(pt);
michael@0:             if (fabs(bestSide) < fabs(testSide)) {
michael@0:                 bestSide = testSide;
michael@0:             }
michael@0:         }
michael@0:         fSide = -bestSide;  // compare sign only
michael@0:         SkASSERT(fSide == 0 || fSide2 != 0);
michael@0:         if (fComputed && dx() > 0 && approximately_zero(dy())) {
michael@0:             SkDCubic origCurve; // can't use segment's curve in place since it may be flipped
michael@0:             int last = fSegment->count() - 1;
michael@0:             fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve);
michael@0:             SkDCubicPair split = origCurve.chopAt(startT);
michael@0:             SkLineParameters splitTan;
michael@0:             splitTan.cubicEndPoints(fStart < fEnd ? split.second() : split.first());
michael@0:             if (splitTan.dx() <= 0) {
michael@0:                 fUnorderable = true;
michael@0:                 fUnsortable = fSegment->isTiny(this);
michael@0:                 return;
michael@0:             }
michael@0:             // if one is < 0 and the other is >= 0
michael@0:             if (dy() * splitTan.dy() < 0) {
michael@0:                 fUnorderable = true;
michael@0:                 fUnsortable = fSegment->isTiny(this);
michael@0:                 return;
michael@0:             }
michael@0:         }
michael@0:         } break;
michael@0:     default:
michael@0:         SkASSERT(0);
michael@0:     }
michael@0:     if ((fUnsortable = approximately_zero(dx()) && approximately_zero(dy()))) {
michael@0:         return;
michael@0:     }
michael@0:     if (fSegment->verb() == SkPath::kLine_Verb) {
michael@0:         return;
michael@0:     }
michael@0:     SkASSERT(fStart != fEnd);
michael@0:     int smaller = SkMin32(fStart, fEnd);
michael@0:     int larger = SkMax32(fStart, fEnd);
michael@0:     while (smaller < larger && fSegment->span(smaller).fTiny) {
michael@0:         ++smaller;
michael@0:     }
michael@0:     if (precisely_equal(fSegment->span(smaller).fT, fSegment->span(larger).fT)) {
michael@0:     #if DEBUG_UNSORTABLE
michael@0:         SkPoint iPt = fSegment->xyAtT(fStart);
michael@0:         SkPoint ePt = fSegment->xyAtT(fEnd);
michael@0:         SkDebugf("%s all tiny unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__,
michael@0:             fStart, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY);
michael@0:     #endif
michael@0:         fUnsortable = true;
michael@0:         return;
michael@0:     }
michael@0:     fUnsortable = fStart < fEnd ? fSegment->span(smaller).fUnsortableStart
michael@0:             : fSegment->span(larger).fUnsortableEnd;
michael@0: #if DEBUG_UNSORTABLE
michael@0:     if (fUnsortable) {
michael@0:         SkPoint iPt = fSegment->xyAtT(smaller);
michael@0:         SkPoint ePt = fSegment->xyAtT(larger);
michael@0:         SkDebugf("%s unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__,
michael@0:                 smaller, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY);
michael@0:     }
michael@0: #endif
michael@0:     return;
michael@0: }
michael@0: 
michael@0: #ifdef SK_DEBUG
michael@0: void SkOpAngle::dump() const {
michael@0:     const SkOpSpan& spanStart = fSegment->span(fStart);
michael@0:     const SkOpSpan& spanEnd = fSegment->span(fEnd);
michael@0:     const SkOpSpan& spanMin = fStart < fEnd ? spanStart : spanEnd;
michael@0:     SkDebugf("id=%d (%1.9g,%1.9g) start=%d (%1.9g) end=%d (%1.9g) sumWind=",
michael@0:             fSegment->debugID(), fSegment->xAtT(fStart), fSegment->yAtT(fStart),
michael@0:             fStart, spanStart.fT, fEnd, spanEnd.fT);
michael@0:     SkPathOpsDebug::WindingPrintf(spanMin.fWindSum);
michael@0:     SkDebugf(" oppWind=");
michael@0:     SkPathOpsDebug::WindingPrintf(spanMin.fOppSum),
michael@0:     SkDebugf(" done=%d\n", spanMin.fDone);
michael@0: }
michael@0: #endif