src/pathops/SkPathOpsTSect.cpp

/*
 * Copyright 2014 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */

#include "src/pathops/SkPathOpsTSect.h"

#define COINCIDENT_SPAN_COUNT 9

void SkTCoincident::setPerp(const SkTCurve& c1, double t,
        const SkDPoint& cPt, const SkTCurve& c2) {
    SkDVector dxdy = c1.dxdyAtT(t);
    SkDLine perp = {{ cPt, {cPt.fX + dxdy.fY, cPt.fY - dxdy.fX} }};
    SkIntersections i  SkDEBUGCODE((c1.globalState()));
    int used = i.intersectRay(c2, perp);
    // only keep closest
    if (used == 0 || used == 3) {
        this->init();
        return;
    }
    fPerpT = i[0][0];
    fPerpPt = i.pt(0);
    SkASSERT(used <= 2);
    if (used == 2) {
        double distSq = (fPerpPt - cPt).lengthSquared();
        double dist2Sq = (i.pt(1) - cPt).lengthSquared();
        if (dist2Sq < distSq) {
            fPerpT = i[0][1];
            fPerpPt = i.pt(1);
        }
    }
#if DEBUG_T_SECT
    SkDebugf("setPerp t=%1.9g cPt=(%1.9g,%1.9g) %s oppT=%1.9g fPerpPt=(%1.9g,%1.9g)\n",
            t, cPt.fX, cPt.fY,
            cPt.approximatelyEqual(fPerpPt) ? "==" : "!=", fPerpT, fPerpPt.fX, fPerpPt.fY);
#endif
    fMatch = cPt.approximatelyEqual(fPerpPt);
#if DEBUG_T_SECT
    if (fMatch) {
        SkDebugf("");  // allow setting breakpoint
    }
#endif
}

void SkTSpan::addBounded(SkTSpan* span, SkArenaAlloc* heap) {
    SkTSpanBounded* bounded = heap->make<SkTSpanBounded>();
    bounded->fBounded = span;
    bounded->fNext = fBounded;
    fBounded = bounded;
}

SkTSpan* SkTSect::addFollowing(
        SkTSpan* prior) {
    SkTSpan* result = this->addOne();
    SkDEBUGCODE(result->debugSetGlobalState(this->globalState()));
    result->fStartT = prior ? prior->fEndT : 0;
    SkTSpan* next = prior ? prior->fNext : fHead;
    result->fEndT = next ? next->fStartT : 1;
    result->fPrev = prior;
    result->fNext = next;
    if (prior) {
        prior->fNext = result;
    } else {
        fHead = result;
    }
    if (next) {
        next->fPrev = result;
    }
    result->resetBounds(fCurve);
    // world may not be consistent to call validate here
    result->validate();
    return result;
}

void SkTSect::addForPerp(SkTSpan* span, double t) {
    if (!span->hasOppT(t)) {
        SkTSpan* priorSpan;
        SkTSpan* opp = this->spanAtT(t, &priorSpan);
        if (!opp) {
            opp = this->addFollowing(priorSpan);
#if DEBUG_PERP
            SkDebugf("%s priorSpan=%d t=%1.9g opp=%d\n", __FUNCTION__, priorSpan ?
                    priorSpan->debugID() : -1, t, opp->debugID());
#endif
        }
#if DEBUG_PERP
        opp->dump(); SkDebugf("\n");
        SkDebugf("%s addBounded span=%d opp=%d\n", __FUNCTION__, priorSpan ?
                priorSpan->debugID() : -1, opp->debugID());
#endif
        opp->addBounded(span, &fHeap);
        span->addBounded(opp, &fHeap);
    }
    this->validate();
#if DEBUG_T_SECT
    span->validatePerpT(t);
#endif
}

double SkTSpan::closestBoundedT(const SkDPoint& pt) const {
    double result = -1;
    double closest = DBL_MAX;
    const SkTSpanBounded* testBounded = fBounded;
    while (testBounded) {
        const SkTSpan* test = testBounded->fBounded;
        double startDist = test->pointFirst().distanceSquared(pt);
        if (closest > startDist) {
            closest = startDist;
            result = test->fStartT;
        }
        double endDist = test->pointLast().distanceSquared(pt);
        if (closest > endDist) {
            closest = endDist;
            result = test->fEndT;
        }
        testBounded = testBounded->fNext;
    }
    SkASSERT(between(0, result, 1));
    return result;
}

#ifdef SK_DEBUG

bool SkTSpan::debugIsBefore(const SkTSpan* span) const {
    const SkTSpan* work = this;
    do {
        if (span == work) {
            return true;
        }
    } while ((work = work->fNext));
    return false;
}
#endif

bool SkTSpan::contains(double t) const {
    const SkTSpan* work = this;
    do {
        if (between(work->fStartT, t, work->fEndT)) {
            return true;
        }
    } while ((work = work->fNext));
    return false;
}

const SkTSect* SkTSpan::debugOpp() const {
    return SkDEBUGRELEASE(fDebugSect->debugOpp(), nullptr);
}

SkTSpan* SkTSpan::findOppSpan(
        const SkTSpan* opp) const {
    SkTSpanBounded* bounded = fBounded;
    while (bounded) {
        SkTSpan* test = bounded->fBounded;
        if (opp == test) {
            return test;
        }
        bounded = bounded->fNext;
    }
    return nullptr;
}

// returns 0 if no hull intersection
//         1 if hulls intersect
//         2 if hulls only share a common endpoint
//        -1 if linear and further checking is required

int SkTSpan::hullCheck(const SkTSpan* opp,
        bool* start, bool* oppStart) {
    if (fIsLinear) {
        return -1;
    }
    bool ptsInCommon;
    if (onlyEndPointsInCommon(opp, start, oppStart, &ptsInCommon)) {
        SkASSERT(ptsInCommon);
        return 2;
    }
    bool linear;
    if (fPart->hullIntersects(*opp->fPart, &linear)) {
        if (!linear) {  // check set true if linear
            return 1;
        }
        fIsLinear = true;
        fIsLine = fPart->controlsInside();
        return ptsInCommon ? 1 : -1;
    } else {  // hull is not linear; check set true if intersected at the end points
        return ((int) ptsInCommon) << 1;  // 0 or 2
    }
    return 0;
}

// OPTIMIZE ? If at_most_end_pts_in_common detects that one quad is near linear,
// use line intersection to guess a better split than 0.5
// OPTIMIZE Once at_most_end_pts_in_common detects linear, mark span so all future splits are linear

int SkTSpan::hullsIntersect(SkTSpan* opp,
        bool* start, bool* oppStart) {
    if (!fBounds.intersects(opp->fBounds)) {
        return 0;
    }
    int hullSect = this->hullCheck(opp, start, oppStart);
    if (hullSect >= 0) {
        return hullSect;
    }
    hullSect = opp->hullCheck(this, oppStart, start);
    if (hullSect >= 0) {
        return hullSect;
    }
    return -1;
}

void SkTSpan::init(const SkTCurve& c) {
    fPrev = fNext = nullptr;
    fStartT = 0;
    fEndT = 1;
    fBounded = nullptr;
    resetBounds(c);
}

bool SkTSpan::initBounds(const SkTCurve& c) {
    if (SkDoubleIsNaN(fStartT) || SkDoubleIsNaN(fEndT)) {
        return false;
    }
    c.subDivide(fStartT, fEndT, fPart);
    fBounds.setBounds(*fPart);
    fCoinStart.init();
    fCoinEnd.init();
    fBoundsMax = SkTMax(fBounds.width(), fBounds.height());
    fCollapsed = fPart->collapsed();
    fHasPerp = false;
    fDeleted = false;
#if DEBUG_T_SECT
    if (fCollapsed) {
        SkDebugf("");  // for convenient breakpoints
    }
#endif
    return fBounds.valid();
}

bool SkTSpan::linearsIntersect(SkTSpan* span) {
    int result = this->linearIntersects(*span->fPart);
    if (result <= 1) {
        return SkToBool(result);
    }
    SkASSERT(span->fIsLinear);
    result = span->linearIntersects(*fPart);
//    SkASSERT(result <= 1);
    return SkToBool(result);
}

double SkTSpan::linearT(const SkDPoint& pt) const {
    SkDVector len = this->pointLast() - this->pointFirst();
    return fabs(len.fX) > fabs(len.fY)
            ? (pt.fX - this->pointFirst().fX) / len.fX
            : (pt.fY - this->pointFirst().fY) / len.fY;
}

int SkTSpan::linearIntersects(const SkTCurve& q2) const {
    // looks like q1 is near-linear
    int start = 0, end = fPart->pointLast();  // the outside points are usually the extremes
    if (!fPart->controlsInside()) {
        double dist = 0;  // if there's any question, compute distance to find best outsiders
        for (int outer = 0; outer < this->pointCount() - 1; ++outer) {
            for (int inner = outer + 1; inner < this->pointCount(); ++inner) {
                double test = ((*fPart)[outer] - (*fPart)[inner]).lengthSquared();
                if (dist > test) {
                    continue;
                }
                dist = test;
                start = outer;
                end = inner;
            }
        }
    }
    // see if q2 is on one side of the line formed by the extreme points
    double origX = (*fPart)[start].fX;
    double origY = (*fPart)[start].fY;
    double adj = (*fPart)[end].fX - origX;
    double opp = (*fPart)[end].fY - origY;
    double maxPart = SkTMax(fabs(adj), fabs(opp));
    double sign = 0;  // initialization to shut up warning in release build
    for (int n = 0; n < q2.pointCount(); ++n) {
        double dx = q2[n].fY - origY;
        double dy = q2[n].fX - origX;
        double maxVal = SkTMax(maxPart, SkTMax(fabs(dx), fabs(dy)));
        double test = (q2[n].fY - origY) * adj - (q2[n].fX - origX) * opp;
        if (precisely_zero_when_compared_to(test, maxVal)) {
            return 1;
        }
        if (approximately_zero_when_compared_to(test, maxVal)) {
            return 3;
        }
        if (n == 0) {
            sign = test;
            continue;
        }
        if (test * sign < 0) {
            return 1;
        }
    }
    return 0;
}

bool SkTSpan::onlyEndPointsInCommon(const SkTSpan* opp,
        bool* start, bool* oppStart, bool* ptsInCommon) {
    if (opp->pointFirst() == this->pointFirst()) {
        *start = *oppStart = true;
    } else if (opp->pointFirst() == this->pointLast()) {
        *start = false;
        *oppStart = true;
    } else if (opp->pointLast() == this->pointFirst()) {
        *start = true;
        *oppStart = false;
    } else if (opp->pointLast() == this->pointLast()) {
        *start = *oppStart = false;
    } else {
        *ptsInCommon = false;
        return false;
    }
    *ptsInCommon = true;
    const SkDPoint* otherPts[4], * oppOtherPts[4];
//  const SkDPoint* otherPts[this->pointCount() - 1], * oppOtherPts[opp->pointCount() - 1];
    int baseIndex = *start ? 0 : fPart->pointLast();
    fPart->otherPts(baseIndex, otherPts);
    opp->fPart->otherPts(*oppStart ? 0 : opp->fPart->pointLast(), oppOtherPts);
    const SkDPoint& base = (*fPart)[baseIndex];
    for (int o1 = 0; o1 < this->pointCount() - 1; ++o1) {
        SkDVector v1 = *otherPts[o1] - base;
        for (int o2 = 0; o2 < opp->pointCount() - 1; ++o2) {
            SkDVector v2 = *oppOtherPts[o2] - base;
            if (v2.dot(v1) >= 0) {
                return false;
            }
        }
    }
    return true;
}

SkTSpan* SkTSpan::oppT(double t) const {
    SkTSpanBounded* bounded = fBounded;
    while (bounded) {
        SkTSpan* test = bounded->fBounded;
        if (between(test->fStartT, t, test->fEndT)) {
            return test;
        }
        bounded = bounded->fNext;
    }
    return nullptr;
}

bool SkTSpan::removeAllBounded() {
    bool deleteSpan = false;
    SkTSpanBounded* bounded = fBounded;
    while (bounded) {
        SkTSpan* opp = bounded->fBounded;
        deleteSpan |= opp->removeBounded(this);
        bounded = bounded->fNext;
    }
    return deleteSpan;
}

bool SkTSpan::removeBounded(const SkTSpan* opp) {
    if (fHasPerp) {
        bool foundStart = false;
        bool foundEnd = false;
        SkTSpanBounded* bounded = fBounded;
        while (bounded) {
            SkTSpan* test = bounded->fBounded;
            if (opp != test) {
                foundStart |= between(test->fStartT, fCoinStart.perpT(), test->fEndT);
                foundEnd |= between(test->fStartT, fCoinEnd.perpT(), test->fEndT);
            }
            bounded = bounded->fNext;
        }
        if (!foundStart || !foundEnd) {
            fHasPerp = false;
            fCoinStart.init();
            fCoinEnd.init();
        }
    }
    SkTSpanBounded* bounded = fBounded;
    SkTSpanBounded* prev = nullptr;
    while (bounded) {
        SkTSpanBounded* boundedNext = bounded->fNext;
        if (opp == bounded->fBounded) {
            if (prev) {
                prev->fNext = boundedNext;
                return false;
            } else {
                fBounded = boundedNext;
                return fBounded == nullptr;
            }
        }
        prev = bounded;
        bounded = boundedNext;
    }
    SkOPASSERT(0);
    return false;
}

bool SkTSpan::splitAt(SkTSpan* work, double t, SkArenaAlloc* heap) {
    fStartT = t;
    fEndT = work->fEndT;
    if (fStartT == fEndT) {
        fCollapsed = true;
        return false;
    }
    work->fEndT = t;
    if (work->fStartT == work->fEndT) {
        work->fCollapsed = true;
        return false;
    }
    fPrev = work;
    fNext = work->fNext;
    fIsLinear = work->fIsLinear;
    fIsLine = work->fIsLine;

    work->fNext = this;
    if (fNext) {
        fNext->fPrev = this;
    }
    this->validate();
    SkTSpanBounded* bounded = work->fBounded;
    fBounded = nullptr;
    while (bounded) {
        this->addBounded(bounded->fBounded, heap);
        bounded = bounded->fNext;
    }
    bounded = fBounded;
    while (bounded) {
        bounded->fBounded->addBounded(this, heap);
        bounded = bounded->fNext;
    }
    return true;
}

void SkTSpan::validate() const {
#if DEBUG_VALIDATE
    SkASSERT(this != fPrev);
    SkASSERT(this != fNext);
    SkASSERT(fNext == nullptr || fNext != fPrev);
    SkASSERT(fNext == nullptr || this == fNext->fPrev);
    SkASSERT(fPrev == nullptr || this == fPrev->fNext);
    this->validateBounded();
#endif
#if DEBUG_T_SECT
    SkASSERT(fBounds.width() || fBounds.height() || fCollapsed);
    SkASSERT(fBoundsMax == SkTMax(fBounds.width(), fBounds.height()) || fCollapsed == 0xFF);
    SkASSERT(0 <= fStartT);
    SkASSERT(fEndT <= 1);
    SkASSERT(fStartT <= fEndT);
    SkASSERT(fBounded || fCollapsed == 0xFF);
    if (fHasPerp) {
        if (fCoinStart.isMatch()) {
            validatePerpT(fCoinStart.perpT());
            validatePerpPt(fCoinStart.perpT(), fCoinStart.perpPt());
        }
        if (fCoinEnd.isMatch()) {
            validatePerpT(fCoinEnd.perpT());
            validatePerpPt(fCoinEnd.perpT(), fCoinEnd.perpPt());
        }
    }
#endif
}

void SkTSpan::validateBounded() const {
#if DEBUG_VALIDATE
    const SkTSpanBounded* testBounded = fBounded;
    while (testBounded) {
        SkDEBUGCODE(const SkTSpan* overlap = testBounded->fBounded);
        SkASSERT(!overlap->fDeleted);
#if DEBUG_T_SECT
        SkASSERT(((this->debugID() ^ overlap->debugID()) & 1) == 1);
        SkASSERT(overlap->findOppSpan(this));
#endif
        testBounded = testBounded->fNext;
    }
#endif
}

void SkTSpan::validatePerpT(double oppT) const {
    const SkTSpanBounded* testBounded = fBounded;
    while (testBounded) {
        const SkTSpan* overlap = testBounded->fBounded;
        if (precisely_between(overlap->fStartT, oppT, overlap->fEndT)) {
            return;
        }
        testBounded = testBounded->fNext;
    }
    SkASSERT(0);
}

void SkTSpan::validatePerpPt(double t, const SkDPoint& pt) const {
    SkASSERT(fDebugSect->fOppSect->fCurve.ptAtT(t) == pt);
}

SkTSect::SkTSect(const SkTCurve& c
        SkDEBUGPARAMS(SkOpGlobalState* debugGlobalState)
        PATH_OPS_DEBUG_T_SECT_PARAMS(int id))
    : fCurve(c)
    , fHeap(sizeof(SkTSpan) * 4)
    , fCoincident(nullptr)
    , fDeleted(nullptr)
    , fActiveCount(0)
    , fHung(false)
    SkDEBUGPARAMS(fDebugGlobalState(debugGlobalState))
    PATH_OPS_DEBUG_T_SECT_PARAMS(fID(id))
    PATH_OPS_DEBUG_T_SECT_PARAMS(fDebugCount(0))
    PATH_OPS_DEBUG_T_SECT_PARAMS(fDebugAllocatedCount(0))
{
    this->resetRemovedEnds();
    fHead = this->addOne();
    SkDEBUGCODE(fHead->debugSetGlobalState(debugGlobalState));
    fHead->init(c);
}

SkTSpan* SkTSect::addOne() {
    SkTSpan* result;
    if (fDeleted) {
        result = fDeleted;
        fDeleted = result->fNext;
    } else {
        result = fHeap.make<SkTSpan>(fCurve, fHeap);
#if DEBUG_T_SECT
        ++fDebugAllocatedCount;
#endif
    }
    result->reset();
    result->fHasPerp = false;
    result->fDeleted = false;
    ++fActiveCount;
    PATH_OPS_DEBUG_T_SECT_CODE(result->fID = fDebugCount++ * 2 + fID);
    SkDEBUGCODE(result->fDebugSect = this);
#ifdef SK_DEBUG
    result->debugInit(fCurve, fHeap);
    result->fCoinStart.debugInit();
    result->fCoinEnd.debugInit();
    result->fPrev = result->fNext = nullptr;
    result->fBounds.debugInit();
    result->fStartT = result->fEndT = result->fBoundsMax = SK_ScalarNaN;
    result->fCollapsed = result->fIsLinear = result->fIsLine = 0xFF;
#endif
    return result;
}

bool SkTSect::binarySearchCoin(SkTSect* sect2, double tStart,
        double tStep, double* resultT, double* oppT, SkTSpan** oppFirst) {
    SkTSpan work(fCurve, fHeap);
    double result = work.fStartT = work.fEndT = tStart;
    SkDEBUGCODE(work.fDebugSect = this);
    SkDPoint last = fCurve.ptAtT(tStart);
    SkDPoint oppPt;
    bool flip = false;
    bool contained = false;
    bool down = tStep < 0;
    const SkTCurve& opp = sect2->fCurve;
    do {
        tStep *= 0.5;
        work.fStartT += tStep;
        if (flip) {
            tStep = -tStep;
            flip = false;
        }
        work.initBounds(fCurve);
        if (work.fCollapsed) {
            return false;
        }
        if (last.approximatelyEqual(work.pointFirst())) {
            break;
        }
        last = work.pointFirst();
        work.fCoinStart.setPerp(fCurve, work.fStartT, last, opp);
        if (work.fCoinStart.isMatch()) {
#if DEBUG_T_SECT
            work.validatePerpPt(work.fCoinStart.perpT(), work.fCoinStart.perpPt());
#endif
            double oppTTest = work.fCoinStart.perpT();
            if (sect2->fHead->contains(oppTTest)) {
                *oppT = oppTTest;
                oppPt = work.fCoinStart.perpPt();
                contained = true;
                if (down ? result <= work.fStartT : result >= work.fStartT) {
                    *oppFirst = nullptr;    // signal caller to fail
                    return false;
                }
                result = work.fStartT;
                continue;
            }
        }
        tStep = -tStep;
        flip = true;
    } while (true);
    if (!contained) {
        return false;
    }
    if (last.approximatelyEqual(fCurve[0])) {
        result = 0;
    } else if (last.approximatelyEqual(this->pointLast())) {
        result = 1;
    }
    if (oppPt.approximatelyEqual(opp[0])) {
        *oppT = 0;
    } else if (oppPt.approximatelyEqual(sect2->pointLast())) {
        *oppT = 1;
    }
    *resultT = result;
    return true;
}

// OPTIMIZE ? keep a sorted list of sizes in the form of a doubly-linked list in quad span
//            so that each quad sect has a pointer to the largest, and can update it as spans
//            are split

SkTSpan* SkTSect::boundsMax() {
    SkTSpan* test = fHead;
    SkTSpan* largest = fHead;
    bool lCollapsed = largest->fCollapsed;
    int safetyNet = 10000;
    while ((test = test->fNext)) {
        if (!--safetyNet) {
            fHung = true;
            return nullptr;
        }
        bool tCollapsed = test->fCollapsed;
        if ((lCollapsed && !tCollapsed) || (lCollapsed == tCollapsed &&
                largest->fBoundsMax < test->fBoundsMax)) {
            largest = test;
            lCollapsed = test->fCollapsed;
        }
    }
    return largest;
}

bool SkTSect::coincidentCheck(SkTSect* sect2) {
    SkTSpan* first = fHead;
    if (!first) {
        return false;
    }
    SkTSpan* last, * next;
    do {
        int consecutive = this->countConsecutiveSpans(first, &last);
        next = last->fNext;
        if (consecutive < COINCIDENT_SPAN_COUNT) {
            continue;
        }
        this->validate();
        sect2->validate();
        this->computePerpendiculars(sect2, first, last);
        this->validate();
        sect2->validate();
        // check to see if a range of points are on the curve
        SkTSpan* coinStart = first;
        do {
            bool success = this->extractCoincident(sect2, coinStart, last, &coinStart);
            if (!success) {
                return false;
            }
        } while (coinStart && !last->fDeleted);
        if (!fHead || !sect2->fHead) {
            break;
        }
        if (!next || next->fDeleted) {
            break;
        }
    } while ((first = next));
    return true;
}

void SkTSect::coincidentForce(SkTSect* sect2,
        double start1s, double start1e) {
    SkTSpan* first = fHead;
    SkTSpan* last = this->tail();
    SkTSpan* oppFirst = sect2->fHead;
    SkTSpan* oppLast = sect2->tail();
    if (!last || !oppLast) {
        return;
    }
    bool deleteEmptySpans = this->updateBounded(first, last, oppFirst);
    deleteEmptySpans |= sect2->updateBounded(oppFirst, oppLast, first);
    this->removeSpanRange(first, last);
    sect2->removeSpanRange(oppFirst, oppLast);
    first->fStartT = start1s;
    first->fEndT = start1e;
    first->resetBounds(fCurve);
    first->fCoinStart.setPerp(fCurve, start1s, fCurve[0], sect2->fCurve);
    first->fCoinEnd.setPerp(fCurve, start1e, this->pointLast(), sect2->fCurve);
    bool oppMatched = first->fCoinStart.perpT() < first->fCoinEnd.perpT();
    double oppStartT = first->fCoinStart.perpT() == -1 ? 0 : SkTMax(0., first->fCoinStart.perpT());
    double oppEndT = first->fCoinEnd.perpT() == -1 ? 1 : SkTMin(1., first->fCoinEnd.perpT());
    if (!oppMatched) {
        using std::swap;
        swap(oppStartT, oppEndT);
    }
    oppFirst->fStartT = oppStartT;
    oppFirst->fEndT = oppEndT;
    oppFirst->resetBounds(sect2->fCurve);
    this->removeCoincident(first, false);
    sect2->removeCoincident(oppFirst, true);
    if (deleteEmptySpans) {
        this->deleteEmptySpans();
        sect2->deleteEmptySpans();
    }
}

bool SkTSect::coincidentHasT(double t) {
    SkTSpan* test = fCoincident;
    while (test) {
        if (between(test->fStartT, t, test->fEndT)) {
            return true;
        }
        test = test->fNext;
    }
    return false;
}

int SkTSect::collapsed() const {
    int result = 0;
    const SkTSpan* test = fHead;
    while (test) {
        if (test->fCollapsed) {
            ++result;
        }
        test = test->next();
    }
    return result;
}

void SkTSect::computePerpendiculars(SkTSect* sect2,
        SkTSpan* first, SkTSpan* last) {
    if (!last) {
        return;
    }
    const SkTCurve& opp = sect2->fCurve;
    SkTSpan* work = first;
    SkTSpan* prior = nullptr;
    do {
        if (!work->fHasPerp && !work->fCollapsed) {
            if (prior) {
                work->fCoinStart = prior->fCoinEnd;
            } else {
                work->fCoinStart.setPerp(fCurve, work->fStartT, work->pointFirst(), opp);
            }
            if (work->fCoinStart.isMatch()) {
                double perpT = work->fCoinStart.perpT();
                if (sect2->coincidentHasT(perpT)) {
                    work->fCoinStart.init();
                } else {
                    sect2->addForPerp(work, perpT);
                }
            }
            work->fCoinEnd.setPerp(fCurve, work->fEndT, work->pointLast(), opp);
            if (work->fCoinEnd.isMatch()) {
                double perpT = work->fCoinEnd.perpT();
                if (sect2->coincidentHasT(perpT)) {
                    work->fCoinEnd.init();
                } else {
                    sect2->addForPerp(work, perpT);
                }
            }
            work->fHasPerp = true;
        }
        if (work == last) {
            break;
        }
        prior = work;
        work = work->fNext;
        SkASSERT(work);
    } while (true);
}

int SkTSect::countConsecutiveSpans(SkTSpan* first,
        SkTSpan** lastPtr) const {
    int consecutive = 1;
    SkTSpan* last = first;
    do {
        SkTSpan* next = last->fNext;
        if (!next) {
            break;
        }
        if (next->fStartT > last->fEndT) {
            break;
        }
        ++consecutive;
        last = next;
    } while (true);
    *lastPtr = last;
    return consecutive;
}

bool SkTSect::hasBounded(const SkTSpan* span) const {
    const SkTSpan* test = fHead;
    if (!test) {
        return false;
    }
    do {
        if (test->findOppSpan(span)) {
            return true;
        }
    } while ((test = test->next()));
    return false;
}

bool SkTSect::deleteEmptySpans() {
    SkTSpan* test;
    SkTSpan* next = fHead;
    int safetyHatch = 1000;
    while ((test = next)) {
        next = test->fNext;
        if (!test->fBounded) {
            if (!this->removeSpan(test)) {
                return false;
            }
        }
        if (--safetyHatch < 0) {
            return false;
        }
    }
    return true;
}

bool SkTSect::extractCoincident(
        SkTSect* sect2,
        SkTSpan* first, SkTSpan* last,
        SkTSpan** result) {
    first = findCoincidentRun(first, &last);
    if (!first || !last) {
        *result = nullptr;
        return true;
    }
    // march outwards to find limit of coincidence from here to previous and next spans
    double startT = first->fStartT;
    double oppStartT SK_INIT_TO_AVOID_WARNING;
    double oppEndT SK_INIT_TO_AVOID_WARNING;
    SkTSpan* prev = first->fPrev;
    SkASSERT(first->fCoinStart.isMatch());
    SkTSpan* oppFirst = first->findOppT(first->fCoinStart.perpT());
    SkOPASSERT(last->fCoinEnd.isMatch());
    bool oppMatched = first->fCoinStart.perpT() < first->fCoinEnd.perpT();
    double coinStart;
    SkDEBUGCODE(double coinEnd);
    SkTSpan* cutFirst;
    if (prev && prev->fEndT == startT
            && this->binarySearchCoin(sect2, startT, prev->fStartT - startT, &coinStart,
                                      &oppStartT, &oppFirst)
            && prev->fStartT < coinStart && coinStart < startT
            && (cutFirst = prev->oppT(oppStartT))) {
        oppFirst = cutFirst;
        first = this->addSplitAt(prev, coinStart);
        first->markCoincident();
        prev->fCoinEnd.markCoincident();
        if (oppFirst->fStartT < oppStartT && oppStartT < oppFirst->fEndT) {
            SkTSpan* oppHalf = sect2->addSplitAt(oppFirst, oppStartT);
            if (oppMatched) {
                oppFirst->fCoinEnd.markCoincident();
                oppHalf->markCoincident();
                oppFirst = oppHalf;
            } else {
                oppFirst->markCoincident();
                oppHalf->fCoinStart.markCoincident();
            }
        }
    } else {
        if (!oppFirst) {
            return false;
        }
        SkDEBUGCODE(coinStart = first->fStartT);
        SkDEBUGCODE(oppStartT = oppMatched ? oppFirst->fStartT : oppFirst->fEndT);
    }
    // FIXME: incomplete : if we're not at the end, find end of coin
    SkTSpan* oppLast;
    SkOPASSERT(last->fCoinEnd.isMatch());
    oppLast = last->findOppT(last->fCoinEnd.perpT());
    SkDEBUGCODE(coinEnd = last->fEndT);
#ifdef SK_DEBUG
    if (!this->globalState() || !this->globalState()->debugSkipAssert()) {
        oppEndT = oppMatched ? oppLast->fEndT : oppLast->fStartT;
    }
#endif
    if (!oppMatched) {
        using std::swap;
        swap(oppFirst, oppLast);
        swap(oppStartT, oppEndT);
    }
    SkOPASSERT(oppStartT < oppEndT);
    SkASSERT(coinStart == first->fStartT);
    SkASSERT(coinEnd == last->fEndT);
    if (!oppFirst) {
        *result = nullptr;
        return true;
    }
    SkOPASSERT(oppStartT == oppFirst->fStartT);
    if (!oppLast) {
        *result = nullptr;
        return true;
    }
    SkOPASSERT(oppEndT == oppLast->fEndT);
    // reduce coincident runs to single entries
    this->validate();
    sect2->validate();
    bool deleteEmptySpans = this->updateBounded(first, last, oppFirst);
    deleteEmptySpans |= sect2->updateBounded(oppFirst, oppLast, first);
    this->removeSpanRange(first, last);
    sect2->removeSpanRange(oppFirst, oppLast);
    first->fEndT = last->fEndT;
    first->resetBounds(this->fCurve);
    first->fCoinStart.setPerp(fCurve, first->fStartT, first->pointFirst(), sect2->fCurve);
    first->fCoinEnd.setPerp(fCurve, first->fEndT, first->pointLast(), sect2->fCurve);
    oppStartT = first->fCoinStart.perpT();
    oppEndT = first->fCoinEnd.perpT();
    if (between(0, oppStartT, 1) && between(0, oppEndT, 1)) {
        if (!oppMatched) {
            using std::swap;
            swap(oppStartT, oppEndT);
        }
        oppFirst->fStartT = oppStartT;
        oppFirst->fEndT = oppEndT;
        oppFirst->resetBounds(sect2->fCurve);
    }
    this->validateBounded();
    sect2->validateBounded();
    last = first->fNext;
    if (!this->removeCoincident(first, false)) {
        return false;
    }
    if (!sect2->removeCoincident(oppFirst, true)) {
        return false;
    }
    if (deleteEmptySpans) {
        if (!this->deleteEmptySpans() || !sect2->deleteEmptySpans()) {
            *result = nullptr;
            return false;
        }
    }
    this->validate();
    sect2->validate();
    *result = last && !last->fDeleted && fHead && sect2->fHead ? last : nullptr;
    return true;
}

SkTSpan* SkTSect::findCoincidentRun(
        SkTSpan* first, SkTSpan** lastPtr) {
    SkTSpan* work = first;
    SkTSpan* lastCandidate = nullptr;
    first = nullptr;
    // find the first fully coincident span
    do {
        if (work->fCoinStart.isMatch()) {
#if DEBUG_T_SECT
            work->validatePerpT(work->fCoinStart.perpT());
            work->validatePerpPt(work->fCoinStart.perpT(), work->fCoinStart.perpPt());
#endif
            SkOPASSERT(work->hasOppT(work->fCoinStart.perpT()));
            if (!work->fCoinEnd.isMatch()) {
                break;
            }
            lastCandidate = work;
            if (!first) {
                first = work;
            }
        } else if (first && work->fCollapsed) {
            *lastPtr = lastCandidate;
            return first;
        } else {
            lastCandidate = nullptr;
            SkOPASSERT(!first);
        }
        if (work == *lastPtr) {
            return first;
        }
        work = work->fNext;
        if (!work) {
            return nullptr;
        }
    } while (true);
    if (lastCandidate) {
        *lastPtr = lastCandidate;
    }
    return first;
}

int SkTSect::intersects(SkTSpan* span,
        SkTSect* opp,
        SkTSpan* oppSpan, int* oppResult) {
    bool spanStart, oppStart;
    int hullResult = span->hullsIntersect(oppSpan, &spanStart, &oppStart);
    if (hullResult >= 0) {
        if (hullResult == 2) {  // hulls have one point in common
            if (!span->fBounded || !span->fBounded->fNext) {
                SkASSERT(!span->fBounded || span->fBounded->fBounded == oppSpan);
                if (spanStart) {
                    span->fEndT = span->fStartT;
                } else {
                    span->fStartT = span->fEndT;
                }
            } else {
                hullResult = 1;
            }
            if (!oppSpan->fBounded || !oppSpan->fBounded->fNext) {
                if (oppSpan->fBounded && oppSpan->fBounded->fBounded != span) {
                    return 0;
                }
                if (oppStart) {
                    oppSpan->fEndT = oppSpan->fStartT;
                } else {
                    oppSpan->fStartT = oppSpan->fEndT;
                }
                *oppResult = 2;
            } else {
                *oppResult = 1;
            }
        } else {
            *oppResult = 1;
        }
        return hullResult;
    }
    if (span->fIsLine && oppSpan->fIsLine) {
        SkIntersections i;
        int sects = this->linesIntersect(span, opp, oppSpan, &i);
        if (sects == 2) {
            return *oppResult = 1;
        }
        if (!sects) {
            return -1;
        }
        this->removedEndCheck(span);
        span->fStartT = span->fEndT = i[0][0];
        opp->removedEndCheck(oppSpan);
        oppSpan->fStartT = oppSpan->fEndT = i[1][0];
        return *oppResult = 2;
    }
    if (span->fIsLinear || oppSpan->fIsLinear) {
        return *oppResult = (int) span->linearsIntersect(oppSpan);
    }
    return *oppResult = 1;
}

template<typename SkTCurve>
static bool is_parallel(const SkDLine& thisLine, const SkTCurve& opp) {
    if (!opp.IsConic()) {
        return false; // FIXME : breaks a lot of stuff now
    }
    int finds = 0;
    SkDLine thisPerp;
    thisPerp.fPts[0].fX = thisLine.fPts[1].fX + (thisLine.fPts[1].fY - thisLine.fPts[0].fY);
    thisPerp.fPts[0].fY = thisLine.fPts[1].fY + (thisLine.fPts[0].fX - thisLine.fPts[1].fX);
    thisPerp.fPts[1] = thisLine.fPts[1];
    SkIntersections perpRayI;
    perpRayI.intersectRay(opp, thisPerp);
    for (int pIndex = 0; pIndex < perpRayI.used(); ++pIndex) {
        finds += perpRayI.pt(pIndex).approximatelyEqual(thisPerp.fPts[1]);
    }
    thisPerp.fPts[1].fX = thisLine.fPts[0].fX + (thisLine.fPts[1].fY - thisLine.fPts[0].fY);
    thisPerp.fPts[1].fY = thisLine.fPts[0].fY + (thisLine.fPts[0].fX - thisLine.fPts[1].fX);
    thisPerp.fPts[0] = thisLine.fPts[0];
    perpRayI.intersectRay(opp, thisPerp);
    for (int pIndex = 0; pIndex < perpRayI.used(); ++pIndex) {
        finds += perpRayI.pt(pIndex).approximatelyEqual(thisPerp.fPts[0]);
    }
    return finds >= 2;
}

// while the intersection points are sufficiently far apart:
// construct the tangent lines from the intersections
// find the point where the tangent line intersects the opposite curve

int SkTSect::linesIntersect(SkTSpan* span,
        SkTSect* opp,
        SkTSpan* oppSpan, SkIntersections* i) {
    SkIntersections thisRayI  SkDEBUGCODE((span->fDebugGlobalState));
    SkIntersections oppRayI  SkDEBUGCODE((span->fDebugGlobalState));
    SkDLine thisLine = {{ span->pointFirst(), span->pointLast() }};
    SkDLine oppLine = {{ oppSpan->pointFirst(), oppSpan->pointLast() }};
    int loopCount = 0;
    double bestDistSq = DBL_MAX;
    if (!thisRayI.intersectRay(opp->fCurve, thisLine)) {
        return 0;
    }
    if (!oppRayI.intersectRay(this->fCurve, oppLine)) {
        return 0;
    }
    // if the ends of each line intersect the opposite curve, the lines are coincident
    if (thisRayI.used() > 1) {
        int ptMatches = 0;
        for (int tIndex = 0; tIndex < thisRayI.used(); ++tIndex) {
            for (int lIndex = 0; lIndex < (int) SK_ARRAY_COUNT(thisLine.fPts); ++lIndex) {
                ptMatches += thisRayI.pt(tIndex).approximatelyEqual(thisLine.fPts[lIndex]);
            }
        }
        if (ptMatches == 2 || is_parallel(thisLine, opp->fCurve)) {
            return 2;
        }
    }
    if (oppRayI.used() > 1) {
        int ptMatches = 0;
        for (int oIndex = 0; oIndex < oppRayI.used(); ++oIndex) {
            for (int lIndex = 0; lIndex < (int) SK_ARRAY_COUNT(oppLine.fPts); ++lIndex) {
                ptMatches += oppRayI.pt(oIndex).approximatelyEqual(oppLine.fPts[lIndex]);
            }
        }
        if (ptMatches == 2|| is_parallel(oppLine, this->fCurve)) {
            return 2;
        }
    }
    do {
        // pick the closest pair of points
        double closest = DBL_MAX;
        int closeIndex SK_INIT_TO_AVOID_WARNING;
        int oppCloseIndex SK_INIT_TO_AVOID_WARNING;
        for (int index = 0; index < oppRayI.used(); ++index) {
            if (!roughly_between(span->fStartT, oppRayI[0][index], span->fEndT)) {
                continue;
            }
            for (int oIndex = 0; oIndex < thisRayI.used(); ++oIndex) {
                if (!roughly_between(oppSpan->fStartT, thisRayI[0][oIndex], oppSpan->fEndT)) {
                    continue;
                }
                double distSq = thisRayI.pt(index).distanceSquared(oppRayI.pt(oIndex));
                if (closest > distSq) {
                    closest = distSq;
                    closeIndex = index;
                    oppCloseIndex = oIndex;
                }
            }
        }
        if (closest == DBL_MAX) {
            break;
        }
        const SkDPoint& oppIPt = thisRayI.pt(oppCloseIndex);
        const SkDPoint& iPt = oppRayI.pt(closeIndex);
        if (between(span->fStartT, oppRayI[0][closeIndex], span->fEndT)
                && between(oppSpan->fStartT, thisRayI[0][oppCloseIndex], oppSpan->fEndT)
                && oppIPt.approximatelyEqual(iPt)) {
            i->merge(oppRayI, closeIndex, thisRayI, oppCloseIndex);
            return i->used();
        }
        double distSq = oppIPt.distanceSquared(iPt);
        if (bestDistSq < distSq || ++loopCount > 5) {
            return 0;
        }
        bestDistSq = distSq;
        double oppStart = oppRayI[0][closeIndex];
        thisLine[0] = fCurve.ptAtT(oppStart);
        thisLine[1] = thisLine[0] + fCurve.dxdyAtT(oppStart);
        if (!thisRayI.intersectRay(opp->fCurve, thisLine)) {
            break;
        }
        double start = thisRayI[0][oppCloseIndex];
        oppLine[0] = opp->fCurve.ptAtT(start);
        oppLine[1] = oppLine[0] + opp->fCurve.dxdyAtT(start);
        if (!oppRayI.intersectRay(this->fCurve, oppLine)) {
            break;
        }
    } while (true);
    // convergence may fail if the curves are nearly coincident
    SkTCoincident oCoinS, oCoinE;
    oCoinS.setPerp(opp->fCurve, oppSpan->fStartT, oppSpan->pointFirst(), fCurve);
    oCoinE.setPerp(opp->fCurve, oppSpan->fEndT, oppSpan->pointLast(), fCurve);
    double tStart = oCoinS.perpT();
    double tEnd = oCoinE.perpT();
    bool swap = tStart > tEnd;
    if (swap) {
        using std::swap;
        swap(tStart, tEnd);
    }
    tStart = SkTMax(tStart, span->fStartT);
    tEnd = SkTMin(tEnd, span->fEndT);
    if (tStart > tEnd) {
        return 0;
    }
    SkDVector perpS, perpE;
    if (tStart == span->fStartT) {
        SkTCoincident coinS;
        coinS.setPerp(fCurve, span->fStartT, span->pointFirst(), opp->fCurve);
        perpS = span->pointFirst() - coinS.perpPt();
    } else if (swap) {
        perpS = oCoinE.perpPt() - oppSpan->pointLast();
    } else {
        perpS = oCoinS.perpPt() - oppSpan->pointFirst();
    }
    if (tEnd == span->fEndT) {
        SkTCoincident coinE;
        coinE.setPerp(fCurve, span->fEndT, span->pointLast(), opp->fCurve);
        perpE = span->pointLast() - coinE.perpPt();
    } else if (swap) {
        perpE = oCoinS.perpPt() - oppSpan->pointFirst();
    } else {
        perpE = oCoinE.perpPt() - oppSpan->pointLast();
    }
    if (perpS.dot(perpE) >= 0) {
        return 0;
    }
    SkTCoincident coinW;
    double workT = tStart;
    double tStep = tEnd - tStart;
    SkDPoint workPt;
    do {
        tStep *= 0.5;
        if (precisely_zero(tStep)) {
            return 0;
        }
        workT += tStep;
        workPt = fCurve.ptAtT(workT);
        coinW.setPerp(fCurve, workT, workPt, opp->fCurve);
        double perpT = coinW.perpT();
        if (coinW.isMatch() ? !between(oppSpan->fStartT, perpT, oppSpan->fEndT) : perpT < 0) {
            continue;
        }
        SkDVector perpW = workPt - coinW.perpPt();
        if ((perpS.dot(perpW) >= 0) == (tStep < 0)) {
            tStep = -tStep;
        }
        if (workPt.approximatelyEqual(coinW.perpPt())) {
            break;
        }
    } while (true);
    double oppTTest = coinW.perpT();
    if (!opp->fHead->contains(oppTTest)) {
        return 0;
    }
    i->setMax(1);
    i->insert(workT, oppTTest, workPt);
    return 1;
}

bool SkTSect::markSpanGone(SkTSpan* span) {
    if (--fActiveCount < 0) {
        return false;
    }
    span->fNext = fDeleted;
    fDeleted = span;
    SkOPASSERT(!span->fDeleted);
    span->fDeleted = true;
    return true;
}

bool SkTSect::matchedDirection(double t, const SkTSect* sect2,
        double t2) const {
    SkDVector dxdy = this->fCurve.dxdyAtT(t);
    SkDVector dxdy2 = sect2->fCurve.dxdyAtT(t2);
    return dxdy.dot(dxdy2) >= 0;
}

void SkTSect::matchedDirCheck(double t, const SkTSect* sect2,
        double t2, bool* calcMatched, bool* oppMatched) const {
    if (*calcMatched) {
        SkASSERT(*oppMatched == this->matchedDirection(t, sect2, t2));
    } else {
        *oppMatched = this->matchedDirection(t, sect2, t2);
        *calcMatched = true;
    }
}

void SkTSect::mergeCoincidence(SkTSect* sect2) {
    double smallLimit = 0;
    do {
        // find the smallest unprocessed span
        SkTSpan* smaller = nullptr;
        SkTSpan* test = fCoincident;
        do {
            if (!test) {
                return;
            }
            if (test->fStartT < smallLimit) {
                continue;
            }
            if (smaller && smaller->fEndT < test->fStartT) {
                continue;
            }
            smaller = test;
        } while ((test = test->fNext));
        if (!smaller) {
            return;
        }
        smallLimit = smaller->fEndT;
        // find next larger span
        SkTSpan* prior = nullptr;
        SkTSpan* larger = nullptr;
        SkTSpan* largerPrior = nullptr;
        test = fCoincident;
        do {
            if (test->fStartT < smaller->fEndT) {
                continue;
            }
            SkOPASSERT(test->fStartT != smaller->fEndT);
            if (larger && larger->fStartT < test->fStartT) {
                continue;
            }
            largerPrior = prior;
            larger = test;
        } while ((void) (prior = test), (test = test->fNext));
        if (!larger) {
            continue;
        }
        // check middle t value to see if it is coincident as well
        double midT = (smaller->fEndT + larger->fStartT) / 2;
        SkDPoint midPt = fCurve.ptAtT(midT);
        SkTCoincident coin;
        coin.setPerp(fCurve, midT, midPt, sect2->fCurve);
        if (coin.isMatch()) {
            smaller->fEndT = larger->fEndT;
            smaller->fCoinEnd = larger->fCoinEnd;
            if (largerPrior) {
                largerPrior->fNext = larger->fNext;
                largerPrior->validate();
            } else {
                fCoincident = larger->fNext;
            }
        }
    } while (true);
}

SkTSpan* SkTSect::prev(
        SkTSpan* span) const {
    SkTSpan* result = nullptr;
    SkTSpan* test = fHead;
    while (span != test) {
        result = test;
        test = test->fNext;
        SkASSERT(test);
    }
    return result;
}

void SkTSect::recoverCollapsed() {
    SkTSpan* deleted = fDeleted;
    while (deleted) {
        SkTSpan* delNext = deleted->fNext;
        if (deleted->fCollapsed) {
            SkTSpan** spanPtr = &fHead;
            while (*spanPtr && (*spanPtr)->fEndT <= deleted->fStartT) {
                spanPtr = &(*spanPtr)->fNext;
            }
            deleted->fNext = *spanPtr;
            *spanPtr = deleted;
        }
        deleted = delNext;
    }
}

void SkTSect::removeAllBut(const SkTSpan* keep,
        SkTSpan* span, SkTSect* opp) {
    const SkTSpanBounded* testBounded = span->fBounded;
    while (testBounded) {
        SkTSpan* bounded = testBounded->fBounded;
        const SkTSpanBounded* next = testBounded->fNext;
        // may have been deleted when opp did 'remove all but'
        if (bounded != keep && !bounded->fDeleted) {
            SkAssertResult(SkDEBUGCODE(!) span->removeBounded(bounded));
            if (bounded->removeBounded(span)) {
                opp->removeSpan(bounded);
            }
        }
        testBounded = next;
    }
    SkASSERT(!span->fDeleted);
    SkASSERT(span->findOppSpan(keep));
    SkASSERT(keep->findOppSpan(span));
}

bool SkTSect::removeByPerpendicular(SkTSect* opp) {
    SkTSpan* test = fHead;
    SkTSpan* next;
    do {
        next = test->fNext;
        if (test->fCoinStart.perpT() < 0 || test->fCoinEnd.perpT() < 0) {
            continue;
        }
        SkDVector startV = test->fCoinStart.perpPt() - test->pointFirst();
        SkDVector endV = test->fCoinEnd.perpPt() - test->pointLast();
#if DEBUG_T_SECT
        SkDebugf("%s startV=(%1.9g,%1.9g) endV=(%1.9g,%1.9g) dot=%1.9g\n", __FUNCTION__,
                startV.fX, startV.fY, endV.fX, endV.fY, startV.dot(endV));
#endif
        if (startV.dot(endV) <= 0) {
            continue;
        }
        if (!this->removeSpans(test, opp)) {
            return false;
        }
    } while ((test = next));
    return true;
}

bool SkTSect::removeCoincident(SkTSpan* span, bool isBetween) {
    if (!this->unlinkSpan(span)) {
        return false;
    }
    if (isBetween || between(0, span->fCoinStart.perpT(), 1)) {
        --fActiveCount;
        span->fNext = fCoincident;
        fCoincident = span;
    } else {
        this->markSpanGone(span);
    }
    return true;
}

void SkTSect::removedEndCheck(SkTSpan* span) {
    if (!span->fStartT) {
        fRemovedStartT = true;
    }
    if (1 == span->fEndT) {
        fRemovedEndT = true;
    }
}

bool SkTSect::removeSpan(SkTSpan* span) {\
    this->removedEndCheck(span);
    if (!this->unlinkSpan(span)) {
        return false;
    }
    return this->markSpanGone(span);
}

void SkTSect::removeSpanRange(SkTSpan* first,
        SkTSpan* last) {
    if (first == last) {
        return;
    }
    SkTSpan* span = first;
    SkASSERT(span);
    SkTSpan* final = last->fNext;
    SkTSpan* next = span->fNext;
    while ((span = next) && span != final) {
        next = span->fNext;
        this->markSpanGone(span);
    }
    if (final) {
        final->fPrev = first;
    }
    first->fNext = final;
    // world may not be ready for validation here
    first->validate();
}

bool SkTSect::removeSpans(SkTSpan* span,
        SkTSect* opp) {
    SkTSpanBounded* bounded = span->fBounded;
    while (bounded) {
        SkTSpan* spanBounded = bounded->fBounded;
        SkTSpanBounded* next = bounded->fNext;
        if (span->removeBounded(spanBounded)) {  // shuffles last into position 0
            this->removeSpan(span);
        }
        if (spanBounded->removeBounded(span)) {
            opp->removeSpan(spanBounded);
        }
        if (span->fDeleted && opp->hasBounded(span)) {
            return false;
        }
        bounded = next;
    }
    return true;
}

SkTSpan* SkTSect::spanAtT(double t,
        SkTSpan** priorSpan) {
    SkTSpan* test = fHead;
    SkTSpan* prev = nullptr;
    while (test && test->fEndT < t) {
        prev = test;
        test = test->fNext;
    }
    *priorSpan = prev;
    return test && test->fStartT <= t ? test : nullptr;
}

SkTSpan* SkTSect::tail() {
    SkTSpan* result = fHead;
    SkTSpan* next = fHead;
    int safetyNet = 100000;
    while ((next = next->fNext)) {
        if (!--safetyNet) {
            return nullptr;
        }
        if (next->fEndT > result->fEndT) {
            result = next;
        }
    }
    return result;
}

/* Each span has a range of opposite spans it intersects. After the span is split in two,
    adjust the range to its new size */

bool SkTSect::trim(SkTSpan* span,
        SkTSect* opp) {
    FAIL_IF(!span->initBounds(fCurve));
    const SkTSpanBounded* testBounded = span->fBounded;
    while (testBounded) {
        SkTSpan* test = testBounded->fBounded;
        const SkTSpanBounded* next = testBounded->fNext;
        int oppSects, sects = this->intersects(span, opp, test, &oppSects);
        if (sects >= 1) {
            if (oppSects == 2) {
                test->initBounds(opp->fCurve);
                opp->removeAllBut(span, test, this);
            }
            if (sects == 2) {
                span->initBounds(fCurve);
                this->removeAllBut(test, span, opp);
                return true;
            }
        } else {
            if (span->removeBounded(test)) {
                this->removeSpan(span);
            }
            if (test->removeBounded(span)) {
                opp->removeSpan(test);
            }
        }
        testBounded = next;
    }
    return true;
}

bool SkTSect::unlinkSpan(SkTSpan* span) {
    SkTSpan* prev = span->fPrev;
    SkTSpan* next = span->fNext;
    if (prev) {
        prev->fNext = next;
        if (next) {
            next->fPrev = prev;
            if (next->fStartT > next->fEndT) {
                return false;
            }
            // world may not be ready for validate here
            next->validate();
        }
    } else {
        fHead = next;
        if (next) {
            next->fPrev = nullptr;
        }
    }
    return true;
}

bool SkTSect::updateBounded(SkTSpan* first,
        SkTSpan* last, SkTSpan* oppFirst) {
    SkTSpan* test = first;
    const SkTSpan* final = last->next();
    bool deleteSpan = false;
    do {
        deleteSpan |= test->removeAllBounded();
    } while ((test = test->fNext) != final && test);
    first->fBounded = nullptr;
    first->addBounded(oppFirst, &fHeap);
    // cannot call validate until remove span range is called
    return deleteSpan;
}

void SkTSect::validate() const {
#if DEBUG_VALIDATE
    int count = 0;
    double last = 0;
    if (fHead) {
        const SkTSpan* span = fHead;
        SkASSERT(!span->fPrev);
        const SkTSpan* next;
        do {
            span->validate();
            SkASSERT(span->fStartT >= last);
            last = span->fEndT;
            ++count;
            next = span->fNext;
            SkASSERT(next != span);
        } while ((span = next) != nullptr);
    }
    SkASSERT(count == fActiveCount);
#endif
#if DEBUG_T_SECT
    SkASSERT(fActiveCount <= fDebugAllocatedCount);
    int deletedCount = 0;
    const SkTSpan* deleted = fDeleted;
    while (deleted) {
        ++deletedCount;
        deleted = deleted->fNext;
    }
    const SkTSpan* coincident = fCoincident;
    while (coincident) {
        ++deletedCount;
        coincident = coincident->fNext;
    }
    SkASSERT(fActiveCount + deletedCount == fDebugAllocatedCount);
#endif
}

void SkTSect::validateBounded() const {
#if DEBUG_VALIDATE
    if (!fHead) {
        return;
    }
    const SkTSpan* span = fHead;
    do {
        span->validateBounded();
    } while ((span = span->fNext) != nullptr);
#endif
}

int SkTSect::EndsEqual(const SkTSect* sect1,
        const SkTSect* sect2, SkIntersections* intersections) {
    int zeroOneSet = 0;
    if (sect1->fCurve[0] == sect2->fCurve[0]) {
        zeroOneSet |= kZeroS1Set | kZeroS2Set;
        intersections->insert(0, 0, sect1->fCurve[0]);
    }
    if (sect1->fCurve[0] == sect2->pointLast()) {
        zeroOneSet |= kZeroS1Set | kOneS2Set;
        intersections->insert(0, 1, sect1->fCurve[0]);
    }
    if (sect1->pointLast() == sect2->fCurve[0]) {
        zeroOneSet |= kOneS1Set | kZeroS2Set;
        intersections->insert(1, 0, sect1->pointLast());
    }
    if (sect1->pointLast() == sect2->pointLast()) {
        zeroOneSet |= kOneS1Set | kOneS2Set;
            intersections->insert(1, 1, sect1->pointLast());
    }
    // check for zero
    if (!(zeroOneSet & (kZeroS1Set | kZeroS2Set))
            && sect1->fCurve[0].approximatelyEqual(sect2->fCurve[0])) {
        zeroOneSet |= kZeroS1Set | kZeroS2Set;
        intersections->insertNear(0, 0, sect1->fCurve[0], sect2->fCurve[0]);
    }
    if (!(zeroOneSet & (kZeroS1Set | kOneS2Set))
            && sect1->fCurve[0].approximatelyEqual(sect2->pointLast())) {
        zeroOneSet |= kZeroS1Set | kOneS2Set;
        intersections->insertNear(0, 1, sect1->fCurve[0], sect2->pointLast());
    }
    // check for one
    if (!(zeroOneSet & (kOneS1Set | kZeroS2Set))
            && sect1->pointLast().approximatelyEqual(sect2->fCurve[0])) {
        zeroOneSet |= kOneS1Set | kZeroS2Set;
        intersections->insertNear(1, 0, sect1->pointLast(), sect2->fCurve[0]);
    }
    if (!(zeroOneSet & (kOneS1Set | kOneS2Set))
            && sect1->pointLast().approximatelyEqual(sect2->pointLast())) {
        zeroOneSet |= kOneS1Set | kOneS2Set;
        intersections->insertNear(1, 1, sect1->pointLast(), sect2->pointLast());
    }
    return zeroOneSet;
}

struct SkClosestRecord {
    bool operator<(const SkClosestRecord& rh) const {
        return fClosest < rh.fClosest;
    }

    void addIntersection(SkIntersections* intersections) const {
        double r1t = fC1Index ? fC1Span->endT() : fC1Span->startT();
        double r2t = fC2Index ? fC2Span->endT() : fC2Span->startT();
        intersections->insert(r1t, r2t, fC1Span->part()[fC1Index]);
    }

    void findEnd(const SkTSpan* span1, const SkTSpan* span2,
            int c1Index, int c2Index) {
        const SkTCurve& c1 = span1->part();
        const SkTCurve& c2 = span2->part();
        if (!c1[c1Index].approximatelyEqual(c2[c2Index])) {
            return;
        }
        double dist = c1[c1Index].distanceSquared(c2[c2Index]);
        if (fClosest < dist) {
            return;
        }
        fC1Span = span1;
        fC2Span = span2;
        fC1StartT = span1->startT();
        fC1EndT = span1->endT();
        fC2StartT = span2->startT();
        fC2EndT = span2->endT();
        fC1Index = c1Index;
        fC2Index = c2Index;
        fClosest = dist;
    }

    bool matesWith(const SkClosestRecord& mate  SkDEBUGPARAMS(SkIntersections* i)) const {
        SkOPOBJASSERT(i, fC1Span == mate.fC1Span || fC1Span->endT() <= mate.fC1Span->startT()
                || mate.fC1Span->endT() <= fC1Span->startT());
        SkOPOBJASSERT(i, fC2Span == mate.fC2Span || fC2Span->endT() <= mate.fC2Span->startT()
                || mate.fC2Span->endT() <= fC2Span->startT());
        return fC1Span == mate.fC1Span || fC1Span->endT() == mate.fC1Span->startT()
                || fC1Span->startT() == mate.fC1Span->endT()
                || fC2Span == mate.fC2Span
                || fC2Span->endT() == mate.fC2Span->startT()
                || fC2Span->startT() == mate.fC2Span->endT();
    }

    void merge(const SkClosestRecord& mate) {
        fC1Span = mate.fC1Span;
        fC2Span = mate.fC2Span;
        fClosest = mate.fClosest;
        fC1Index = mate.fC1Index;
        fC2Index = mate.fC2Index;
    }

    void reset() {
        fClosest = FLT_MAX;
        SkDEBUGCODE(fC1Span = nullptr);
        SkDEBUGCODE(fC2Span = nullptr);
        SkDEBUGCODE(fC1Index = fC2Index = -1);
    }

    void update(const SkClosestRecord& mate) {
        fC1StartT = SkTMin(fC1StartT, mate.fC1StartT);
        fC1EndT = SkTMax(fC1EndT, mate.fC1EndT);
        fC2StartT = SkTMin(fC2StartT, mate.fC2StartT);
        fC2EndT = SkTMax(fC2EndT, mate.fC2EndT);
    }

    const SkTSpan* fC1Span;
    const SkTSpan* fC2Span;
    double fC1StartT;
    double fC1EndT;
    double fC2StartT;
    double fC2EndT;
    double fClosest;
    int fC1Index;
    int fC2Index;
};

struct SkClosestSect {
    SkClosestSect()
        : fUsed(0) {
        fClosest.push_back().reset();
    }

    bool find(const SkTSpan* span1, const SkTSpan* span2
            SkDEBUGPARAMS(SkIntersections* i)) {
        SkClosestRecord* record = &fClosest[fUsed];
        record->findEnd(span1, span2, 0, 0);
        record->findEnd(span1, span2, 0, span2->part().pointLast());
        record->findEnd(span1, span2, span1->part().pointLast(), 0);
        record->findEnd(span1, span2, span1->part().pointLast(), span2->part().pointLast());
        if (record->fClosest == FLT_MAX) {
            return false;
        }
        for (int index = 0; index < fUsed; ++index) {
            SkClosestRecord* test = &fClosest[index];
            if (test->matesWith(*record  SkDEBUGPARAMS(i))) {
                if (test->fClosest > record->fClosest) {
                    test->merge(*record);
                }
                test->update(*record);
                record->reset();
                return false;
            }
        }
        ++fUsed;
        fClosest.push_back().reset();
        return true;
    }

    void finish(SkIntersections* intersections) const {
        SkSTArray<SkDCubic::kMaxIntersections * 3,
                const SkClosestRecord*, true> closestPtrs;
        for (int index = 0; index < fUsed; ++index) {
            closestPtrs.push_back(&fClosest[index]);
        }
        SkTQSort<const SkClosestRecord >(closestPtrs.begin(), closestPtrs.end()
                - 1);
        for (int index = 0; index < fUsed; ++index) {
            const SkClosestRecord* test = closestPtrs[index];
            test->addIntersection(intersections);
        }
    }

    // this is oversized so that an extra records can merge into final one
    SkSTArray<SkDCubic::kMaxIntersections * 2, SkClosestRecord, true> fClosest;
    int fUsed;
};

// returns true if the rect is too small to consider

void SkTSect::BinarySearch(SkTSect* sect1,
        SkTSect* sect2, SkIntersections* intersections) {
#if DEBUG_T_SECT_DUMP > 1
    gDumpTSectNum = 0;
#endif
    SkDEBUGCODE(sect1->fOppSect = sect2);
    SkDEBUGCODE(sect2->fOppSect = sect1);
    intersections->reset();
    intersections->setMax(sect1->fCurve.maxIntersections() + 4);  // give extra for slop
    SkTSpan* span1 = sect1->fHead;
    SkTSpan* span2 = sect2->fHead;
    int oppSect, sect = sect1->intersects(span1, sect2, span2, &oppSect);
//    SkASSERT(between(0, sect, 2));
    if (!sect) {
        return;
    }
    if (sect == 2 && oppSect == 2) {
        (void) EndsEqual(sect1, sect2, intersections);
        return;
    }
    span1->addBounded(span2, &sect1->fHeap);
    span2->addBounded(span1, &sect2->fHeap);
    const int kMaxCoinLoopCount = 8;
    int coinLoopCount = kMaxCoinLoopCount;
    double start1s SK_INIT_TO_AVOID_WARNING;
    double start1e SK_INIT_TO_AVOID_WARNING;
    do {
        // find the largest bounds
        SkTSpan* largest1 = sect1->boundsMax();
        if (!largest1) {
            if (sect1->fHung) {
                return;
            }
            break;
        }
        SkTSpan* largest2 = sect2->boundsMax();
        // split it
        if (!largest2 || (largest1 && (largest1->fBoundsMax > largest2->fBoundsMax
                || (!largest1->fCollapsed && largest2->fCollapsed)))) {
            if (sect2->fHung) {
                return;
            }
            if (largest1->fCollapsed) {
                break;
            }
            sect1->resetRemovedEnds();
            sect2->resetRemovedEnds();
            // trim parts that don't intersect the opposite
            SkTSpan* half1 = sect1->addOne();
            SkDEBUGCODE(half1->debugSetGlobalState(sect1->globalState()));
            if (!half1->split(largest1, &sect1->fHeap)) {
                break;
            }
            if (!sect1->trim(largest1, sect2)) {
                SkOPOBJASSERT(intersections, 0);
                return;
            }
            if (!sect1->trim(half1, sect2)) {
                SkOPOBJASSERT(intersections, 0);
                return;
            }
        } else {
            if (largest2->fCollapsed) {
                break;
            }
            sect1->resetRemovedEnds();
            sect2->resetRemovedEnds();
            // trim parts that don't intersect the opposite
            SkTSpan* half2 = sect2->addOne();
            SkDEBUGCODE(half2->debugSetGlobalState(sect2->globalState()));
            if (!half2->split(largest2, &sect2->fHeap)) {
                break;
            }
            if (!sect2->trim(largest2, sect1)) {
                SkOPOBJASSERT(intersections, 0);
                return;
            }
            if (!sect2->trim(half2, sect1)) {
                SkOPOBJASSERT(intersections, 0);
                return;
            }
        }
        sect1->validate();
        sect2->validate();
#if DEBUG_T_SECT_LOOP_COUNT
        intersections->debugBumpLoopCount(SkIntersections::kIterations_DebugLoop);
#endif
        // if there are 9 or more continuous spans on both sects, suspect coincidence
        if (sect1->fActiveCount >= COINCIDENT_SPAN_COUNT
                && sect2->fActiveCount >= COINCIDENT_SPAN_COUNT) {
            if (coinLoopCount == kMaxCoinLoopCount) {
                start1s = sect1->fHead->fStartT;
                start1e = sect1->tail()->fEndT;
            }
            if (!sect1->coincidentCheck(sect2)) {
                return;
            }
            sect1->validate();
            sect2->validate();
#if DEBUG_T_SECT_LOOP_COUNT
            intersections->debugBumpLoopCount(SkIntersections::kCoinCheck_DebugLoop);
#endif
            if (!--coinLoopCount && sect1->fHead && sect2->fHead) {
                /* All known working cases resolve in two tries. Sadly, cubicConicTests[0]
                   gets stuck in a loop. It adds an extension to allow a coincident end
                   perpendicular to track its intersection in the opposite curve. However,
                   the bounding box of the extension does not intersect the original curve,
                   so the extension is discarded, only to be added again the next time around. */
                sect1->coincidentForce(sect2, start1s, start1e);
                sect1->validate();
                sect2->validate();
            }
        }
        if (sect1->fActiveCount >= COINCIDENT_SPAN_COUNT
                && sect2->fActiveCount >= COINCIDENT_SPAN_COUNT) {
            if (!sect1->fHead) {
                return;
            }
            sect1->computePerpendiculars(sect2, sect1->fHead, sect1->tail());
            if (!sect2->fHead) {
                return;
            }
            sect2->computePerpendiculars(sect1, sect2->fHead, sect2->tail());
            if (!sect1->removeByPerpendicular(sect2)) {
                return;
            }
            sect1->validate();
            sect2->validate();
#if DEBUG_T_SECT_LOOP_COUNT
            intersections->debugBumpLoopCount(SkIntersections::kComputePerp_DebugLoop);
#endif
            if (sect1->collapsed() > sect1->fCurve.maxIntersections()) {
                break;
            }
        }
#if DEBUG_T_SECT_DUMP
        sect1->dumpBoth(sect2);
#endif
        if (!sect1->fHead || !sect2->fHead) {
            break;
        }
    } while (true);
    SkTSpan* coincident = sect1->fCoincident;
    if (coincident) {
        // if there is more than one coincident span, check loosely to see if they should be joined
        if (coincident->fNext) {
            sect1->mergeCoincidence(sect2);
            coincident = sect1->fCoincident;
        }
        SkASSERT(sect2->fCoincident);  // courtesy check : coincidence only looks at sect 1
        do {
            if (!coincident) {
                return;
            }
            if (!coincident->fCoinStart.isMatch()) {
                continue;
            }
            if (!coincident->fCoinEnd.isMatch()) {
                continue;
            }
            double perpT = coincident->fCoinStart.perpT();
            if (perpT < 0) {
                return;
            }
            int index = intersections->insertCoincident(coincident->fStartT,
                    perpT, coincident->pointFirst());
            if ((intersections->insertCoincident(coincident->fEndT,
                    coincident->fCoinEnd.perpT(),
                    coincident->pointLast()) < 0) && index >= 0) {
                intersections->clearCoincidence(index);
            }
        } while ((coincident = coincident->fNext));
    }
    int zeroOneSet = EndsEqual(sect1, sect2, intersections);
//    if (!sect1->fHead || !sect2->fHead) {
        // if the final iteration contains an end (0 or 1),
        if (sect1->fRemovedStartT && !(zeroOneSet & kZeroS1Set)) {
            SkTCoincident perp;   // intersect perpendicular with opposite curve
            perp.setPerp(sect1->fCurve, 0, sect1->fCurve[0], sect2->fCurve);
            if (perp.isMatch()) {
                intersections->insert(0, perp.perpT(), perp.perpPt());
            }
        }
        if (sect1->fRemovedEndT && !(zeroOneSet & kOneS1Set)) {
            SkTCoincident perp;
            perp.setPerp(sect1->fCurve, 1, sect1->pointLast(), sect2->fCurve);
            if (perp.isMatch()) {
                intersections->insert(1, perp.perpT(), perp.perpPt());
            }
        }
        if (sect2->fRemovedStartT && !(zeroOneSet & kZeroS2Set)) {
            SkTCoincident perp;
            perp.setPerp(sect2->fCurve, 0, sect2->fCurve[0], sect1->fCurve);
            if (perp.isMatch()) {
                intersections->insert(perp.perpT(), 0, perp.perpPt());
            }
        }
        if (sect2->fRemovedEndT && !(zeroOneSet & kOneS2Set)) {
            SkTCoincident perp;
            perp.setPerp(sect2->fCurve, 1, sect2->pointLast(), sect1->fCurve);
            if (perp.isMatch()) {
                intersections->insert(perp.perpT(), 1, perp.perpPt());
            }
        }
//    }
    if (!sect1->fHead || !sect2->fHead) {
        return;
    }
    sect1->recoverCollapsed();
    sect2->recoverCollapsed();
    SkTSpan* result1 = sect1->fHead;
    // check heads and tails for zero and ones and insert them if we haven't already done so
    const SkTSpan* head1 = result1;
    if (!(zeroOneSet & kZeroS1Set) && approximately_less_than_zero(head1->fStartT)) {
        const SkDPoint& start1 = sect1->fCurve[0];
        if (head1->isBounded()) {
            double t = head1->closestBoundedT(start1);
            if (sect2->fCurve.ptAtT(t).approximatelyEqual(start1)) {
                intersections->insert(0, t, start1);
            }
        }
    }
    const SkTSpan* head2 = sect2->fHead;
    if (!(zeroOneSet & kZeroS2Set) && approximately_less_than_zero(head2->fStartT)) {
        const SkDPoint& start2 = sect2->fCurve[0];
        if (head2->isBounded()) {
            double t = head2->closestBoundedT(start2);
            if (sect1->fCurve.ptAtT(t).approximatelyEqual(start2)) {
                intersections->insert(t, 0, start2);
            }
        }
    }
    if (!(zeroOneSet & kOneS1Set)) {
        const SkTSpan* tail1 = sect1->tail();
        if (!tail1) {
            return;
        }
        if (approximately_greater_than_one(tail1->fEndT)) {
            const SkDPoint& end1 = sect1->pointLast();
            if (tail1->isBounded()) {
                double t = tail1->closestBoundedT(end1);
                if (sect2->fCurve.ptAtT(t).approximatelyEqual(end1)) {
                    intersections->insert(1, t, end1);
                }
            }
        }
    }
    if (!(zeroOneSet & kOneS2Set)) {
        const SkTSpan* tail2 = sect2->tail();
        if (!tail2) {
            return;
        }
        if (approximately_greater_than_one(tail2->fEndT)) {
            const SkDPoint& end2 = sect2->pointLast();
            if (tail2->isBounded()) {
                double t = tail2->closestBoundedT(end2);
                if (sect1->fCurve.ptAtT(t).approximatelyEqual(end2)) {
                    intersections->insert(t, 1, end2);
                }
            }
        }
    }
    SkClosestSect closest;
    do {
        while (result1 && result1->fCoinStart.isMatch() && result1->fCoinEnd.isMatch()) {
            result1 = result1->fNext;
        }
        if (!result1) {
            break;
        }
        SkTSpan* result2 = sect2->fHead;
        bool found = false;
        while (result2) {
            found |= closest.find(result1, result2  SkDEBUGPARAMS(intersections));
            result2 = result2->fNext;
        }
    } while ((result1 = result1->fNext));
    closest.finish(intersections);
    // if there is more than one intersection and it isn't already coincident, check
    int last = intersections->used() - 1;
    for (int index = 0; index < last; ) {
        if (intersections->isCoincident(index) && intersections->isCoincident(index + 1)) {
            ++index;
            continue;
        }
        double midT = ((*intersections)[0][index] + (*intersections)[0][index + 1]) / 2;
        SkDPoint midPt = sect1->fCurve.ptAtT(midT);
        // intersect perpendicular with opposite curve
        SkTCoincident perp;
        perp.setPerp(sect1->fCurve, midT, midPt, sect2->fCurve);
        if (!perp.isMatch()) {
            ++index;
            continue;
        }
        if (intersections->isCoincident(index)) {
            intersections->removeOne(index);
            --last;
        } else if (intersections->isCoincident(index + 1)) {
            intersections->removeOne(index + 1);
            --last;
        } else {
            intersections->setCoincident(index++);
        }
        intersections->setCoincident(index);
    }
    SkOPOBJASSERT(intersections, intersections->used() <= sect1->fCurve.maxIntersections());
}

int SkIntersections::intersect(const SkDQuad& q1, const SkDQuad& q2) {
    SkTQuad quad1(q1);
    SkTQuad quad2(q2);
    SkTSect sect1(quad1  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(1));
    SkTSect sect2(quad2  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(2));
    SkTSect::BinarySearch(&sect1, &sect2, this);
    return used();
}

int SkIntersections::intersect(const SkDConic& c, const SkDQuad& q) {
    SkTConic conic(c);
    SkTQuad quad(q);
    SkTSect sect1(conic  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(1));
    SkTSect sect2(quad  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(2));
    SkTSect::BinarySearch(&sect1, &sect2, this);
    return used();
}

int SkIntersections::intersect(const SkDConic& c1, const SkDConic& c2) {
    SkTConic conic1(c1);
    SkTConic conic2(c2);
    SkTSect sect1(conic1  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(1));
    SkTSect sect2(conic2  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(2));
    SkTSect::BinarySearch(&sect1, &sect2, this);
    return used();
}

int SkIntersections::intersect(const SkDCubic& c, const SkDQuad& q) {
    SkTCubic cubic(c);
    SkTQuad quad(q);
    SkTSect sect1(cubic  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(1));
    SkTSect sect2(quad  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(2));
    SkTSect::BinarySearch(&sect1, &sect2, this);
    return used();
}

int SkIntersections::intersect(const SkDCubic& cu, const SkDConic& co) {
    SkTCubic cubic(cu);
    SkTConic conic(co);
    SkTSect sect1(cubic  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(1));
    SkTSect sect2(conic  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(2));
    SkTSect::BinarySearch(&sect1, &sect2, this);
    return used();

}

int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) {
    SkTCubic cubic1(c1);
    SkTCubic cubic2(c2);
    SkTSect sect1(cubic1  SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(1));
    SkTSect sect2(cubic2   SkDEBUGPARAMS(globalState())  PATH_OPS_DEBUG_T_SECT_PARAMS(2));
    SkTSect::BinarySearch(&sect1, &sect2, this);
    return used();
}