src/pathops/SkOpSegment.cpp

/*
 * Copyright 2012 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */
#include "SkOpCoincidence.h"
#include "SkOpContour.h"
#include "SkOpSegment.h"
#include "SkPathWriter.h"
#include "SkPointPriv.h"

#include <utility>

/*
After computing raw intersections, post process all segments to:
- find small collections of points that can be collapsed to a single point
- find missing intersections to resolve differences caused by different algorithms

Consider segments containing tiny or small intervals. Consider coincident segments
because coincidence finds intersections through distance measurement that non-coincident
intersection tests cannot.
 */

#define F (false)      // discard the edge
#define T (true)       // keep the edge

static const bool gUnaryActiveEdge[2][2] = {
//  from=0  from=1
//  to=0,1  to=0,1
    {F, T}, {T, F},
};

static const bool gActiveEdge[kXOR_SkPathOp + 1][2][2][2][2] = {
//                 miFrom=0                              miFrom=1
//         miTo=0             miTo=1             miTo=0             miTo=1
//     suFrom=0    1      suFrom=0    1      suFrom=0    1      suFrom=0    1
//   suTo=0,1 suTo=0,1  suTo=0,1 suTo=0,1  suTo=0,1 suTo=0,1  suTo=0,1 suTo=0,1
    {{{{F, F}, {F, F}}, {{T, F}, {T, F}}}, {{{T, T}, {F, F}}, {{F, T}, {T, F}}}},  // mi - su
    {{{{F, F}, {F, F}}, {{F, T}, {F, T}}}, {{{F, F}, {T, T}}, {{F, T}, {T, F}}}},  // mi & su
    {{{{F, T}, {T, F}}, {{T, T}, {F, F}}}, {{{T, F}, {T, F}}, {{F, F}, {F, F}}}},  // mi | su
    {{{{F, T}, {T, F}}, {{T, F}, {F, T}}}, {{{T, F}, {F, T}}, {{F, T}, {T, F}}}},  // mi ^ su
};

#undef F
#undef T

SkOpAngle* SkOpSegment::activeAngle(SkOpSpanBase* start, SkOpSpanBase** startPtr,
        SkOpSpanBase** endPtr, bool* done) {
    if (SkOpAngle* result = activeAngleInner(start, startPtr, endPtr, done)) {
        return result;
    }
    if (SkOpAngle* result = activeAngleOther(start, startPtr, endPtr, done)) {
        return result;
    }
    return nullptr;
}

SkOpAngle* SkOpSegment::activeAngleInner(SkOpSpanBase* start, SkOpSpanBase** startPtr,
        SkOpSpanBase** endPtr, bool* done) {
    SkOpSpan* upSpan = start->upCastable();
    if (upSpan) {
        if (upSpan->windValue() || upSpan->oppValue()) {
            SkOpSpanBase* next = upSpan->next();
            if (!*endPtr) {
                *startPtr = start;
                *endPtr = next;
            }
            if (!upSpan->done()) {
                if (upSpan->windSum() != SK_MinS32) {
                    return spanToAngle(start, next);
                }
                *done = false;
            }
        } else {
            SkASSERT(upSpan->done());
        }
    }
    SkOpSpan* downSpan = start->prev();
    // edge leading into junction
    if (downSpan) {
        if (downSpan->windValue() || downSpan->oppValue()) {
            if (!*endPtr) {
                *startPtr = start;
                *endPtr = downSpan;
            }
            if (!downSpan->done()) {
                if (downSpan->windSum() != SK_MinS32) {
                    return spanToAngle(start, downSpan);
                }
                *done = false;
            }
        } else {
            SkASSERT(downSpan->done());
        }
    }
    return nullptr;
}

SkOpAngle* SkOpSegment::activeAngleOther(SkOpSpanBase* start, SkOpSpanBase** startPtr,
        SkOpSpanBase** endPtr, bool* done) {
    SkOpPtT* oPtT = start->ptT()->next();
    SkOpSegment* other = oPtT->segment();
    SkOpSpanBase* oSpan = oPtT->span();
    return other->activeAngleInner(oSpan, startPtr, endPtr, done);
}

bool SkOpSegment::activeOp(SkOpSpanBase* start, SkOpSpanBase* end, int xorMiMask, int xorSuMask,
        SkPathOp op) {
    int sumMiWinding = this->updateWinding(end, start);
    int sumSuWinding = this->updateOppWinding(end, start);
#if DEBUG_LIMIT_WIND_SUM
    SkASSERT(abs(sumMiWinding) <= DEBUG_LIMIT_WIND_SUM);
    SkASSERT(abs(sumSuWinding) <= DEBUG_LIMIT_WIND_SUM);
#endif
    if (this->operand()) {
        using std::swap;
        swap(sumMiWinding, sumSuWinding);
    }
    return this->activeOp(xorMiMask, xorSuMask, start, end, op, &sumMiWinding, &sumSuWinding);
}

bool SkOpSegment::activeOp(int xorMiMask, int xorSuMask, SkOpSpanBase* start, SkOpSpanBase* end,
        SkPathOp op, int* sumMiWinding, int* sumSuWinding) {
    int maxWinding, sumWinding, oppMaxWinding, oppSumWinding;
    this->setUpWindings(start, end, sumMiWinding, sumSuWinding,
            &maxWinding, &sumWinding, &oppMaxWinding, &oppSumWinding);
    bool miFrom;
    bool miTo;
    bool suFrom;
    bool suTo;
    if (operand()) {
        miFrom = (oppMaxWinding & xorMiMask) != 0;
        miTo = (oppSumWinding & xorMiMask) != 0;
        suFrom = (maxWinding & xorSuMask) != 0;
        suTo = (sumWinding & xorSuMask) != 0;
    } else {
        miFrom = (maxWinding & xorMiMask) != 0;
        miTo = (sumWinding & xorMiMask) != 0;
        suFrom = (oppMaxWinding & xorSuMask) != 0;
        suTo = (oppSumWinding & xorSuMask) != 0;
    }
    bool result = gActiveEdge[op][miFrom][miTo][suFrom][suTo];
#if DEBUG_ACTIVE_OP
    SkDebugf("%s id=%d t=%1.9g tEnd=%1.9g op=%s miFrom=%d miTo=%d suFrom=%d suTo=%d result=%d\n",
            __FUNCTION__, debugID(), start->t(), end->t(),
            SkPathOpsDebug::kPathOpStr[op], miFrom, miTo, suFrom, suTo, result);
#endif
    return result;
}

bool SkOpSegment::activeWinding(SkOpSpanBase* start, SkOpSpanBase* end) {
    int sumWinding = updateWinding(end, start);
    return activeWinding(start, end, &sumWinding);
}

bool SkOpSegment::activeWinding(SkOpSpanBase* start, SkOpSpanBase* end, int* sumWinding) {
    int maxWinding;
    setUpWinding(start, end, &maxWinding, sumWinding);
    bool from = maxWinding != 0;
    bool to = *sumWinding  != 0;
    bool result = gUnaryActiveEdge[from][to];
    return result;
}

bool SkOpSegment::addCurveTo(const SkOpSpanBase* start, const SkOpSpanBase* end,
        SkPathWriter* path) const {
    FAIL_IF(start->starter(end)->alreadyAdded());
    SkDCurveSweep curvePart;
    start->segment()->subDivide(start, end, &curvePart.fCurve);
    curvePart.setCurveHullSweep(fVerb);
    SkPath::Verb verb = curvePart.isCurve() ? fVerb : SkPath::kLine_Verb;
    path->deferredMove(start->ptT());
    switch (verb) {
        case SkPath::kLine_Verb:
            FAIL_IF(!path->deferredLine(end->ptT()));
            break;
        case SkPath::kQuad_Verb:
            path->quadTo(curvePart.fCurve.fQuad[1].asSkPoint(), end->ptT());
            break;
        case SkPath::kConic_Verb:
            path->conicTo(curvePart.fCurve.fConic[1].asSkPoint(), end->ptT(),
                    curvePart.fCurve.fConic.fWeight);
            break;
        case SkPath::kCubic_Verb:
            path->cubicTo(curvePart.fCurve.fCubic[1].asSkPoint(),
                    curvePart.fCurve.fCubic[2].asSkPoint(), end->ptT());
            break;
        default:
            SkASSERT(0);
    }
    return true;
}

const SkOpPtT* SkOpSegment::existing(double t, const SkOpSegment* opp) const {
    const SkOpSpanBase* test = &fHead;
    const SkOpPtT* testPtT;
    SkPoint pt = this->ptAtT(t);
    do {
        testPtT = test->ptT();
        if (testPtT->fT == t) {
            break;
        }
        if (!this->match(testPtT, this, t, pt)) {
            if (t < testPtT->fT) {
                return nullptr;
            }
            continue;
        }
        if (!opp) {
            return testPtT;
        }
        const SkOpPtT* loop = testPtT->next();
        while (loop != testPtT) {
            if (loop->segment() == this && loop->fT == t && loop->fPt == pt) {
                goto foundMatch;
            }
            loop = loop->next();
        }
        return nullptr;
    } while ((test = test->upCast()->next()));
foundMatch:
    return opp && !test->contains(opp) ? nullptr : testPtT;
}

// break the span so that the coincident part does not change the angle of the remainder
bool SkOpSegment::addExpanded(double newT, const SkOpSpanBase* test, bool* startOver) {
    if (this->contains(newT)) {
        return true;
    }
    this->globalState()->resetAllocatedOpSpan();
    FAIL_IF(!between(0, newT, 1));
    SkOpPtT* newPtT = this->addT(newT);
    *startOver |= this->globalState()->allocatedOpSpan();
    if (!newPtT) {
        return false;
    }
    newPtT->fPt = this->ptAtT(newT);
    SkOpPtT* oppPrev = test->ptT()->oppPrev(newPtT);
    if (oppPrev) {
        // const cast away to change linked list; pt/t values stays unchanged
        SkOpSpanBase* writableTest = const_cast<SkOpSpanBase*>(test);
        writableTest->mergeMatches(newPtT->span());
        writableTest->ptT()->addOpp(newPtT, oppPrev);
        writableTest->checkForCollapsedCoincidence();
    }
    return true;
}

// Please keep this in sync with debugAddT()
SkOpPtT* SkOpSegment::addT(double t, const SkPoint& pt) {
    debugValidate();
    SkOpSpanBase* spanBase = &fHead;
    do {
        SkOpPtT* result = spanBase->ptT();
        if (t == result->fT || (!zero_or_one(t) && this->match(result, this, t, pt))) {
            spanBase->bumpSpanAdds();
            return result;
        }
        if (t < result->fT) {
            SkOpSpan* prev = result->span()->prev();
            FAIL_WITH_NULL_IF(!prev);
            // marks in global state that new op span has been allocated
            SkOpSpan* span = this->insert(prev);
            span->init(this, prev, t, pt);
            this->debugValidate();
#if DEBUG_ADD_T
            SkDebugf("%s insert t=%1.9g segID=%d spanID=%d\n", __FUNCTION__, t,
                    span->segment()->debugID(), span->debugID());
#endif
            span->bumpSpanAdds();
            return span->ptT();
        }
        FAIL_WITH_NULL_IF(spanBase == &fTail);
    } while ((spanBase = spanBase->upCast()->next()));
    SkASSERT(0);
    return nullptr;  // we never get here, but need this to satisfy compiler
}

SkOpPtT* SkOpSegment::addT(double t) {
    return addT(t, this->ptAtT(t));
}

void SkOpSegment::calcAngles() {
    bool activePrior = !fHead.isCanceled();
    if (activePrior && !fHead.simple()) {
        addStartSpan();
    }
    SkOpSpan* prior = &fHead;
    SkOpSpanBase* spanBase = fHead.next();
    while (spanBase != &fTail) {
        if (activePrior) {
            SkOpAngle* priorAngle = this->globalState()->allocator()->make<SkOpAngle>();
            priorAngle->set(spanBase, prior);
            spanBase->setFromAngle(priorAngle);
        }
        SkOpSpan* span = spanBase->upCast();
        bool active = !span->isCanceled();
        SkOpSpanBase* next = span->next();
        if (active) {
            SkOpAngle* angle = this->globalState()->allocator()->make<SkOpAngle>();
            angle->set(span, next);
            span->setToAngle(angle);
        }
        activePrior = active;
        prior = span;
        spanBase = next;
    }
    if (activePrior && !fTail.simple()) {
        addEndSpan();
    }
}

// Please keep this in sync with debugClearAll()
void SkOpSegment::clearAll() {
    SkOpSpan* span = &fHead;
    do {
        this->clearOne(span);
    } while ((span = span->next()->upCastable()));
    this->globalState()->coincidence()->release(this);
}

// Please keep this in sync with debugClearOne()
void SkOpSegment::clearOne(SkOpSpan* span) {
    span->setWindValue(0);
    span->setOppValue(0);
    this->markDone(span);
}

SkOpSpanBase::Collapsed SkOpSegment::collapsed(double s, double e) const {
    const SkOpSpanBase* span = &fHead;
    do {
        SkOpSpanBase::Collapsed result = span->collapsed(s, e);
        if (SkOpSpanBase::Collapsed::kNo != result) {
            return result;
        }
    } while (span->upCastable() && (span = span->upCast()->next()));
    return SkOpSpanBase::Collapsed::kNo;
}

void SkOpSegment::ComputeOneSum(const SkOpAngle* baseAngle, SkOpAngle* nextAngle,
        SkOpAngle::IncludeType includeType) {
    SkOpSegment* baseSegment = baseAngle->segment();
    int sumMiWinding = baseSegment->updateWindingReverse(baseAngle);
    int sumSuWinding;
    bool binary = includeType >= SkOpAngle::kBinarySingle;
    if (binary) {
        sumSuWinding = baseSegment->updateOppWindingReverse(baseAngle);
        if (baseSegment->operand()) {
            using std::swap;
            swap(sumMiWinding, sumSuWinding);
        }
    }
    SkOpSegment* nextSegment = nextAngle->segment();
    int maxWinding, sumWinding;
    SkOpSpanBase* last;
    if (binary) {
        int oppMaxWinding, oppSumWinding;
        nextSegment->setUpWindings(nextAngle->start(), nextAngle->end(), &sumMiWinding,
                &sumSuWinding, &maxWinding, &sumWinding, &oppMaxWinding, &oppSumWinding);
        last = nextSegment->markAngle(maxWinding, sumWinding, oppMaxWinding, oppSumWinding,
                nextAngle);
    } else {
        nextSegment->setUpWindings(nextAngle->start(), nextAngle->end(), &sumMiWinding,
                &maxWinding, &sumWinding);
        last = nextSegment->markAngle(maxWinding, sumWinding, nextAngle);
    }
    nextAngle->setLastMarked(last);
}

void SkOpSegment::ComputeOneSumReverse(SkOpAngle* baseAngle, SkOpAngle* nextAngle,
        SkOpAngle::IncludeType includeType) {
    SkOpSegment* baseSegment = baseAngle->segment();
    int sumMiWinding = baseSegment->updateWinding(baseAngle);
    int sumSuWinding;
    bool binary = includeType >= SkOpAngle::kBinarySingle;
    if (binary) {
        sumSuWinding = baseSegment->updateOppWinding(baseAngle);
        if (baseSegment->operand()) {
            using std::swap;
            swap(sumMiWinding, sumSuWinding);
        }
    }
    SkOpSegment* nextSegment = nextAngle->segment();
    int maxWinding, sumWinding;
    SkOpSpanBase* last;
    if (binary) {
        int oppMaxWinding, oppSumWinding;
        nextSegment->setUpWindings(nextAngle->end(), nextAngle->start(), &sumMiWinding,
                &sumSuWinding, &maxWinding, &sumWinding, &oppMaxWinding, &oppSumWinding);
        last = nextSegment->markAngle(maxWinding, sumWinding, oppMaxWinding, oppSumWinding,
                nextAngle);
    } else {
        nextSegment->setUpWindings(nextAngle->end(), nextAngle->start(), &sumMiWinding,
                &maxWinding, &sumWinding);
        last = nextSegment->markAngle(maxWinding, sumWinding, nextAngle);
    }
    nextAngle->setLastMarked(last);
}

// at this point, the span is already ordered, or unorderable
int SkOpSegment::computeSum(SkOpSpanBase* start, SkOpSpanBase* end,
        SkOpAngle::IncludeType includeType) {
    SkASSERT(includeType != SkOpAngle::kUnaryXor);
    SkOpAngle* firstAngle = this->spanToAngle(end, start);
    if (nullptr == firstAngle || nullptr == firstAngle->next()) {
        return SK_NaN32;
    }
    // if all angles have a computed winding,
    //  or if no adjacent angles are orderable,
    //  or if adjacent orderable angles have no computed winding,
    //  there's nothing to do
    // if two orderable angles are adjacent, and both are next to orderable angles,
    //  and one has winding computed, transfer to the other
    SkOpAngle* baseAngle = nullptr;
    bool tryReverse = false;
    // look for counterclockwise transfers
    SkOpAngle* angle = firstAngle->previous();
    SkOpAngle* next = angle->next();
    firstAngle = next;
    do {
        SkOpAngle* prior = angle;
        angle = next;
        next = angle->next();
        SkASSERT(prior->next() == angle);
        SkASSERT(angle->next() == next);
        if (prior->unorderable() || angle->unorderable() || next->unorderable()) {
            baseAngle = nullptr;
            continue;
        }
        int testWinding = angle->starter()->windSum();
        if (SK_MinS32 != testWinding) {
            baseAngle = angle;
            tryReverse = true;
            continue;
        }
        if (baseAngle) {
            ComputeOneSum(baseAngle, angle, includeType);
            baseAngle = SK_MinS32 != angle->starter()->windSum() ? angle : nullptr;
        }
    } while (next != firstAngle);
    if (baseAngle && SK_MinS32 == firstAngle->starter()->windSum()) {
        firstAngle = baseAngle;
        tryReverse = true;
    }
    if (tryReverse) {
        baseAngle = nullptr;
        SkOpAngle* prior = firstAngle;
        do {
            angle = prior;
            prior = angle->previous();
            SkASSERT(prior->next() == angle);
            next = angle->next();
            if (prior->unorderable() || angle->unorderable() || next->unorderable()) {
                baseAngle = nullptr;
                continue;
            }
            int testWinding = angle->starter()->windSum();
            if (SK_MinS32 != testWinding) {
                baseAngle = angle;
                continue;
            }
            if (baseAngle) {
                ComputeOneSumReverse(baseAngle, angle, includeType);
                baseAngle = SK_MinS32 != angle->starter()->windSum() ? angle : nullptr;
            }
        } while (prior != firstAngle);
    }
    return start->starter(end)->windSum();
}

bool SkOpSegment::contains(double newT) const {
    const SkOpSpanBase* spanBase = &fHead;
    do {
        if (spanBase->ptT()->contains(this, newT)) {
            return true;
        }
        if (spanBase == &fTail) {
            break;
        }
        spanBase = spanBase->upCast()->next();
    } while (true);
    return false;
}

void SkOpSegment::release(const SkOpSpan* span) {
    if (span->done()) {
        --fDoneCount;
    }
    --fCount;
    SkOPASSERT(fCount >= fDoneCount);
}

#if DEBUG_ANGLE
// called only by debugCheckNearCoincidence
double SkOpSegment::distSq(double t, const SkOpAngle* oppAngle) const {
    SkDPoint testPt = this->dPtAtT(t);
    SkDLine testPerp = {{ testPt, testPt }};
    SkDVector slope = this->dSlopeAtT(t);
    testPerp[1].fX += slope.fY;
    testPerp[1].fY -= slope.fX;
    SkIntersections i;
    const SkOpSegment* oppSegment = oppAngle->segment();
    (*CurveIntersectRay[oppSegment->verb()])(oppSegment->pts(), oppSegment->weight(), testPerp, &i);
    double closestDistSq = SK_ScalarInfinity;
    for (int index = 0; index < i.used(); ++index) {
        if (!between(oppAngle->start()->t(), i[0][index], oppAngle->end()->t())) {
            continue;
        }
        double testDistSq = testPt.distanceSquared(i.pt(index));
        if (closestDistSq > testDistSq) {
            closestDistSq = testDistSq;
        }
    }
    return closestDistSq;
}
#endif

/*
 The M and S variable name parts stand for the operators.
   Mi stands for Minuend (see wiki subtraction, analogous to difference)
   Su stands for Subtrahend
 The Opp variable name part designates that the value is for the Opposite operator.
 Opposite values result from combining coincident spans.
 */
SkOpSegment* SkOpSegment::findNextOp(SkTDArray<SkOpSpanBase*>* chase, SkOpSpanBase** nextStart,
        SkOpSpanBase** nextEnd, bool* unsortable, SkPathOp op, int xorMiMask, int xorSuMask) {
    SkOpSpanBase* start = *nextStart;
    SkOpSpanBase* end = *nextEnd;
    SkASSERT(start != end);
    int step = start->step(end);
    SkOpSegment* other = this->isSimple(nextStart, &step);  // advances nextStart
    if (other) {
    // mark the smaller of startIndex, endIndex done, and all adjacent
    // spans with the same T value (but not 'other' spans)
#if DEBUG_WINDING
        SkDebugf("%s simple\n", __FUNCTION__);
#endif
        SkOpSpan* startSpan = start->starter(end);
        if (startSpan->done()) {
            return nullptr;
        }
        markDone(startSpan);
        *nextEnd = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
        return other;
    }
    SkOpSpanBase* endNear = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
    SkASSERT(endNear == end);  // is this ever not end?
    SkASSERT(endNear);
    SkASSERT(start != endNear);
    SkASSERT((start->t() < endNear->t()) ^ (step < 0));
    // more than one viable candidate -- measure angles to find best
    int calcWinding = computeSum(start, endNear, SkOpAngle::kBinaryOpp);
    bool sortable = calcWinding != SK_NaN32;
    if (!sortable) {
        *unsortable = true;
        markDone(start->starter(end));
        return nullptr;
    }
    SkOpAngle* angle = this->spanToAngle(end, start);
    if (angle->unorderable()) {
        *unsortable = true;
        markDone(start->starter(end));
        return nullptr;
    }
#if DEBUG_SORT
    SkDebugf("%s\n", __FUNCTION__);
    angle->debugLoop();
#endif
    int sumMiWinding = updateWinding(end, start);
    if (sumMiWinding == SK_MinS32) {
        *unsortable = true;
        markDone(start->starter(end));
        return nullptr;
    }
    int sumSuWinding = updateOppWinding(end, start);
    if (operand()) {
        using std::swap;
        swap(sumMiWinding, sumSuWinding);
    }
    SkOpAngle* nextAngle = angle->next();
    const SkOpAngle* foundAngle = nullptr;
    bool foundDone = false;
    // iterate through the angle, and compute everyone's winding
    SkOpSegment* nextSegment;
    int activeCount = 0;
    do {
        nextSegment = nextAngle->segment();
        bool activeAngle = nextSegment->activeOp(xorMiMask, xorSuMask, nextAngle->start(),
                nextAngle->end(), op, &sumMiWinding, &sumSuWinding);
        if (activeAngle) {
            ++activeCount;
            if (!foundAngle || (foundDone && activeCount & 1)) {
                foundAngle = nextAngle;
                foundDone = nextSegment->done(nextAngle);
            }
        }
        if (nextSegment->done()) {
            continue;
        }
        if (!activeAngle) {
            (void) nextSegment->markAndChaseDone(nextAngle->start(), nextAngle->end());
        }
        SkOpSpanBase* last = nextAngle->lastMarked();
        if (last) {
            SkASSERT(!SkPathOpsDebug::ChaseContains(*chase, last));
            *chase->append() = last;
#if DEBUG_WINDING
            SkDebugf("%s chase.append segment=%d span=%d", __FUNCTION__,
                    last->segment()->debugID(), last->debugID());
            if (!last->final()) {
                SkDebugf(" windSum=%d", last->upCast()->windSum());
            }
            SkDebugf("\n");
#endif
        }
    } while ((nextAngle = nextAngle->next()) != angle);
    start->segment()->markDone(start->starter(end));
    if (!foundAngle) {
        return nullptr;
    }
    *nextStart = foundAngle->start();
    *nextEnd = foundAngle->end();
    nextSegment = foundAngle->segment();
#if DEBUG_WINDING
    SkDebugf("%s from:[%d] to:[%d] start=%d end=%d\n",
            __FUNCTION__, debugID(), nextSegment->debugID(), *nextStart, *nextEnd);
 #endif
    return nextSegment;
}

SkOpSegment* SkOpSegment::findNextWinding(SkTDArray<SkOpSpanBase*>* chase,
        SkOpSpanBase** nextStart, SkOpSpanBase** nextEnd, bool* unsortable) {
    SkOpSpanBase* start = *nextStart;
    SkOpSpanBase* end = *nextEnd;
    SkASSERT(start != end);
    int step = start->step(end);
    SkOpSegment* other = this->isSimple(nextStart, &step);  // advances nextStart
    if (other) {
    // mark the smaller of startIndex, endIndex done, and all adjacent
    // spans with the same T value (but not 'other' spans)
#if DEBUG_WINDING
        SkDebugf("%s simple\n", __FUNCTION__);
#endif
        SkOpSpan* startSpan = start->starter(end);
        if (startSpan->done()) {
            return nullptr;
        }
        markDone(startSpan);
        *nextEnd = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
        return other;
    }
    SkOpSpanBase* endNear = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
    SkASSERT(endNear == end);  // is this ever not end?
    SkASSERT(endNear);
    SkASSERT(start != endNear);
    SkASSERT((start->t() < endNear->t()) ^ (step < 0));
    // more than one viable candidate -- measure angles to find best
    int calcWinding = computeSum(start, endNear, SkOpAngle::kUnaryWinding);
    bool sortable = calcWinding != SK_NaN32;
    if (!sortable) {
        *unsortable = true;
        markDone(start->starter(end));
        return nullptr;
    }
    SkOpAngle* angle = this->spanToAngle(end, start);
    if (angle->unorderable()) {
        *unsortable = true;
        markDone(start->starter(end));
        return nullptr;
    }
#if DEBUG_SORT
    SkDebugf("%s\n", __FUNCTION__);
    angle->debugLoop();
#endif
    int sumWinding = updateWinding(end, start);
    SkOpAngle* nextAngle = angle->next();
    const SkOpAngle* foundAngle = nullptr;
    bool foundDone = false;
    // iterate through the angle, and compute everyone's winding
    SkOpSegment* nextSegment;
    int activeCount = 0;
    do {
        nextSegment = nextAngle->segment();
        bool activeAngle = nextSegment->activeWinding(nextAngle->start(), nextAngle->end(),
                &sumWinding);
        if (activeAngle) {
            ++activeCount;
            if (!foundAngle || (foundDone && activeCount & 1)) {
                foundAngle = nextAngle;
                foundDone = nextSegment->done(nextAngle);
            }
        }
        if (nextSegment->done()) {
            continue;
        }
        if (!activeAngle) {
            (void) nextSegment->markAndChaseDone(nextAngle->start(), nextAngle->end());
        }
        SkOpSpanBase* last = nextAngle->lastMarked();
        if (last) {
            SkASSERT(!SkPathOpsDebug::ChaseContains(*chase, last));
            *chase->append() = last;
#if DEBUG_WINDING
            SkDebugf("%s chase.append segment=%d span=%d", __FUNCTION__,
                    last->segment()->debugID(), last->debugID());
            if (!last->final()) {
                SkDebugf(" windSum=%d", last->upCast()->windSum());
            }
            SkDebugf("\n");
#endif
        }
    } while ((nextAngle = nextAngle->next()) != angle);
    start->segment()->markDone(start->starter(end));
    if (!foundAngle) {
        return nullptr;
    }
    *nextStart = foundAngle->start();
    *nextEnd = foundAngle->end();
    nextSegment = foundAngle->segment();
#if DEBUG_WINDING
    SkDebugf("%s from:[%d] to:[%d] start=%d end=%d\n",
            __FUNCTION__, debugID(), nextSegment->debugID(), *nextStart, *nextEnd);
 #endif
    return nextSegment;
}

SkOpSegment* SkOpSegment::findNextXor(SkOpSpanBase** nextStart, SkOpSpanBase** nextEnd,
        bool* unsortable) {
    SkOpSpanBase* start = *nextStart;
    SkOpSpanBase* end = *nextEnd;
    SkASSERT(start != end);
    int step = start->step(end);
    SkOpSegment* other = this->isSimple(nextStart, &step);  // advances nextStart
    if (other) {
    // mark the smaller of startIndex, endIndex done, and all adjacent
    // spans with the same T value (but not 'other' spans)
#if DEBUG_WINDING
        SkDebugf("%s simple\n", __FUNCTION__);
#endif
        SkOpSpan* startSpan = start->starter(end);
        if (startSpan->done()) {
            return nullptr;
        }
        markDone(startSpan);
        *nextEnd = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
        return other;
    }
    SkDEBUGCODE(SkOpSpanBase* endNear = step > 0 ? (*nextStart)->upCast()->next() \
            : (*nextStart)->prev());
    SkASSERT(endNear == end);  // is this ever not end?
    SkASSERT(endNear);
    SkASSERT(start != endNear);
    SkASSERT((start->t() < endNear->t()) ^ (step < 0));
    SkOpAngle* angle = this->spanToAngle(end, start);
    if (!angle || angle->unorderable()) {
        *unsortable = true;
        markDone(start->starter(end));
        return nullptr;
    }
#if DEBUG_SORT
    SkDebugf("%s\n", __FUNCTION__);
    angle->debugLoop();
#endif
    SkOpAngle* nextAngle = angle->next();
    const SkOpAngle* foundAngle = nullptr;
    bool foundDone = false;
    // iterate through the angle, and compute everyone's winding
    SkOpSegment* nextSegment;
    int activeCount = 0;
    do {
        if (!nextAngle) {
            return nullptr;
        }
        nextSegment = nextAngle->segment();
        ++activeCount;
        if (!foundAngle || (foundDone && activeCount & 1)) {
            foundAngle = nextAngle;
            if (!(foundDone = nextSegment->done(nextAngle))) {
                break;
            }
        }
        nextAngle = nextAngle->next();
    } while (nextAngle != angle);
    start->segment()->markDone(start->starter(end));
    if (!foundAngle) {
        return nullptr;
    }
    *nextStart = foundAngle->start();
    *nextEnd = foundAngle->end();
    nextSegment = foundAngle->segment();
#if DEBUG_WINDING
    SkDebugf("%s from:[%d] to:[%d] start=%d end=%d\n",
            __FUNCTION__, debugID(), nextSegment->debugID(), *nextStart, *nextEnd);
 #endif
    return nextSegment;
}

SkOpGlobalState* SkOpSegment::globalState() const {
    return contour()->globalState();
}

void SkOpSegment::init(SkPoint pts[], SkScalar weight, SkOpContour* contour, SkPath::Verb verb) {
    fContour = contour;
    fNext = nullptr;
    fPts = pts;
    fWeight = weight;
    fVerb = verb;
    fCount = 0;
    fDoneCount = 0;
    fVisited = false;
    SkOpSpan* zeroSpan = &fHead;
    zeroSpan->init(this, nullptr, 0, fPts[0]);
    SkOpSpanBase* oneSpan = &fTail;
    zeroSpan->setNext(oneSpan);
    oneSpan->initBase(this, zeroSpan, 1, fPts[SkPathOpsVerbToPoints(fVerb)]);
    SkDEBUGCODE(fID = globalState()->nextSegmentID());
}

bool SkOpSegment::isClose(double t, const SkOpSegment* opp) const {
    SkDPoint cPt = this->dPtAtT(t);
    SkDVector dxdy = (*CurveDSlopeAtT[this->verb()])(this->pts(), this->weight(), t);
    SkDLine perp = {{ cPt, {cPt.fX + dxdy.fY, cPt.fY - dxdy.fX} }};
    SkIntersections i;
    (*CurveIntersectRay[opp->verb()])(opp->pts(), opp->weight(), perp, &i);
    int used = i.used();
    for (int index = 0; index < used; ++index) {
        if (cPt.roughlyEqual(i.pt(index))) {
            return true;
        }
    }
    return false;
}

bool SkOpSegment::isXor() const {
    return fContour->isXor();
}

void SkOpSegment::markAllDone() {
    SkOpSpan* span = this->head();
    do {
        this->markDone(span);
    } while ((span = span->next()->upCastable()));
}

SkOpSpanBase* SkOpSegment::markAndChaseDone(SkOpSpanBase* start, SkOpSpanBase* end) {
    int step = start->step(end);
    SkOpSpan* minSpan = start->starter(end);
    markDone(minSpan);
    SkOpSpanBase* last = nullptr;
    SkOpSegment* other = this;
    SkOpSpan* priorDone = nullptr;
    SkOpSpan* lastDone = nullptr;
    while ((other = other->nextChase(&start, &step, &minSpan, &last))) {
        if (other->done()) {
            SkASSERT(!last);
            break;
        }
        if (lastDone == minSpan || priorDone == minSpan) {
            return nullptr;
        }
        other->markDone(minSpan);
        priorDone = lastDone;
        lastDone = minSpan;
    }
    return last;
}

bool SkOpSegment::markAndChaseWinding(SkOpSpanBase* start, SkOpSpanBase* end, int winding,
        SkOpSpanBase** lastPtr) {
    SkOpSpan* spanStart = start->starter(end);
    int step = start->step(end);
    bool success = markWinding(spanStart, winding);
    SkOpSpanBase* last = nullptr;
    SkOpSegment* other = this;
    while ((other = other->nextChase(&start, &step, &spanStart, &last))) {
        if (spanStart->windSum() != SK_MinS32) {
//            SkASSERT(spanStart->windSum() == winding);   // FIXME: is this assert too aggressive?
            SkASSERT(!last);
            break;
        }
        (void) other->markWinding(spanStart, winding);
    }
    if (lastPtr) {
        *lastPtr = last;
    }
    return success;
}

bool SkOpSegment::markAndChaseWinding(SkOpSpanBase* start, SkOpSpanBase* end,
        int winding, int oppWinding, SkOpSpanBase** lastPtr) {
    SkOpSpan* spanStart = start->starter(end);
    int step = start->step(end);
    bool success = markWinding(spanStart, winding, oppWinding);
    SkOpSpanBase* last = nullptr;
    SkOpSegment* other = this;
    while ((other = other->nextChase(&start, &step, &spanStart, &last))) {
        if (spanStart->windSum() != SK_MinS32) {
            if (this->operand() == other->operand()) {
                if (spanStart->windSum() != winding || spanStart->oppSum() != oppWinding) {
                    this->globalState()->setWindingFailed();
                    return false;
                }
            } else {
                SkASSERT(spanStart->windSum() == oppWinding);
                SkASSERT(spanStart->oppSum() == winding);
            }
            SkASSERT(!last);
            break;
        }
        if (this->operand() == other->operand()) {
            (void) other->markWinding(spanStart, winding, oppWinding);
        } else {
            (void) other->markWinding(spanStart, oppWinding, winding);
        }
    }
    if (lastPtr) {
        *lastPtr = last;
    }
    return success;
}

SkOpSpanBase* SkOpSegment::markAngle(int maxWinding, int sumWinding, const SkOpAngle* angle) {
    SkASSERT(angle->segment() == this);
    if (UseInnerWinding(maxWinding, sumWinding)) {
        maxWinding = sumWinding;
    }
    SkOpSpanBase* last;
    (void) markAndChaseWinding(angle->start(), angle->end(), maxWinding, &last);
#if DEBUG_WINDING
    if (last) {
        SkDebugf("%s last seg=%d span=%d", __FUNCTION__,
                last->segment()->debugID(), last->debugID());
        if (!last->final()) {
            SkDebugf(" windSum=");
            SkPathOpsDebug::WindingPrintf(last->upCast()->windSum());
        }
        SkDebugf("\n");
    }
#endif
    return last;
}

SkOpSpanBase* SkOpSegment::markAngle(int maxWinding, int sumWinding, int oppMaxWinding,
                                   int oppSumWinding, const SkOpAngle* angle) {
    SkASSERT(angle->segment() == this);
    if (UseInnerWinding(maxWinding, sumWinding)) {
        maxWinding = sumWinding;
    }
    if (oppMaxWinding != oppSumWinding && UseInnerWinding(oppMaxWinding, oppSumWinding)) {
        oppMaxWinding = oppSumWinding;
    }
    SkOpSpanBase* last = nullptr;
    // caller doesn't require that this marks anything
    (void) markAndChaseWinding(angle->start(), angle->end(), maxWinding, oppMaxWinding, &last);
#if DEBUG_WINDING
    if (last) {
        SkDebugf("%s last segment=%d span=%d", __FUNCTION__,
                last->segment()->debugID(), last->debugID());
        if (!last->final()) {
            SkDebugf(" windSum=");
            SkPathOpsDebug::WindingPrintf(last->upCast()->windSum());
        }
        SkDebugf(" \n");
    }
#endif
    return last;
}

void SkOpSegment::markDone(SkOpSpan* span) {
    SkASSERT(this == span->segment());
    if (span->done()) {
        return;
    }
#if DEBUG_MARK_DONE
    debugShowNewWinding(__FUNCTION__, span, span->windSum(), span->oppSum());
#endif
    span->setDone(true);
    ++fDoneCount;
    debugValidate();
}

bool SkOpSegment::markWinding(SkOpSpan* span, int winding) {
    SkASSERT(this == span->segment());
    SkASSERT(winding);
    if (span->done()) {
        return false;
    }
#if DEBUG_MARK_DONE
    debugShowNewWinding(__FUNCTION__, span, winding);
#endif
    span->setWindSum(winding);
    debugValidate();
    return true;
}

bool SkOpSegment::markWinding(SkOpSpan* span, int winding, int oppWinding) {
    SkASSERT(this == span->segment());
    SkASSERT(winding || oppWinding);
    if (span->done()) {
        return false;
    }
#if DEBUG_MARK_DONE
    debugShowNewWinding(__FUNCTION__, span, winding, oppWinding);
#endif
    span->setWindSum(winding);
    span->setOppSum(oppWinding);
    debugValidate();
    return true;
}

bool SkOpSegment::match(const SkOpPtT* base, const SkOpSegment* testParent, double testT,
        const SkPoint& testPt) const {
    SkASSERT(this == base->segment());
    if (this == testParent) {
        if (precisely_equal(base->fT, testT)) {
            return true;
        }
    }
    if (!SkDPoint::ApproximatelyEqual(testPt, base->fPt)) {
        return false;
    }
    return this != testParent || !this->ptsDisjoint(base->fT, base->fPt, testT, testPt);
}

static SkOpSegment* set_last(SkOpSpanBase** last, SkOpSpanBase* endSpan) {
    if (last) {
        *last = endSpan;
    }
    return nullptr;
}

SkOpSegment* SkOpSegment::nextChase(SkOpSpanBase** startPtr, int* stepPtr, SkOpSpan** minPtr,
        SkOpSpanBase** last) const {
    SkOpSpanBase* origStart = *startPtr;
    int step = *stepPtr;
    SkOpSpanBase* endSpan = step > 0 ? origStart->upCast()->next() : origStart->prev();
    SkASSERT(endSpan);
    SkOpAngle* angle = step > 0 ? endSpan->fromAngle() : endSpan->upCast()->toAngle();
    SkOpSpanBase* foundSpan;
    SkOpSpanBase* otherEnd;
    SkOpSegment* other;
    if (angle == nullptr) {
        if (endSpan->t() != 0 && endSpan->t() != 1) {
            return nullptr;
        }
        SkOpPtT* otherPtT = endSpan->ptT()->next();
        other = otherPtT->segment();
        foundSpan = otherPtT->span();
        otherEnd = step > 0
                ? foundSpan->upCastable() ? foundSpan->upCast()->next() : nullptr
                : foundSpan->prev();
    } else {
        int loopCount = angle->loopCount();
        if (loopCount > 2) {
            return set_last(last, endSpan);
        }
        const SkOpAngle* next = angle->next();
        if (nullptr == next) {
            return nullptr;
        }
#if DEBUG_WINDING
        if (angle->debugSign() != next->debugSign() && !angle->segment()->contour()->isXor()
                && !next->segment()->contour()->isXor()) {
            SkDebugf("%s mismatched signs\n", __FUNCTION__);
        }
#endif
        other = next->segment();
        foundSpan = endSpan = next->start();
        otherEnd = next->end();
    }
    if (!otherEnd) {
        return nullptr;
    }
    int foundStep = foundSpan->step(otherEnd);
    if (*stepPtr != foundStep) {
        return set_last(last, endSpan);
    }
    SkASSERT(*startPtr);
//    SkASSERT(otherEnd >= 0);
    SkOpSpan* origMin = step < 0 ? origStart->prev() : origStart->upCast();
    SkOpSpan* foundMin = foundSpan->starter(otherEnd);
    if (foundMin->windValue() != origMin->windValue()
            || foundMin->oppValue() != origMin->oppValue()) {
          return set_last(last, endSpan);
    }
    *startPtr = foundSpan;
    *stepPtr = foundStep;
    if (minPtr) {
        *minPtr = foundMin;
    }
    return other;
}

// Please keep this in sync with DebugClearVisited()
void SkOpSegment::ClearVisited(SkOpSpanBase* span) {
    // reset visited flag back to false
    do {
        SkOpPtT* ptT = span->ptT(), * stopPtT = ptT;
        while ((ptT = ptT->next()) != stopPtT) {
            SkOpSegment* opp = ptT->segment();
            opp->resetVisited();
        }
    } while (!span->final() && (span = span->upCast()->next()));
}

// Please keep this in sync with debugMissingCoincidence()
// look for pairs of undetected coincident curves
// assumes that segments going in have visited flag clear
// Even though pairs of curves correct detect coincident runs, a run may be missed
// if the coincidence is a product of multiple intersections. For instance, given
// curves A, B, and C:
// A-B intersect at a point 1; A-C and B-C intersect at point 2, so near
// the end of C that the intersection is replaced with the end of C.
// Even though A-B correctly do not detect an intersection at point 2,
// the resulting run from point 1 to point 2 is coincident on A and B.
bool SkOpSegment::missingCoincidence() {
    if (this->done()) {
        return false;
    }
    SkOpSpan* prior = nullptr;
    SkOpSpanBase* spanBase = &fHead;
    bool result = false;
    do {
        SkOpPtT* ptT = spanBase->ptT(), * spanStopPtT = ptT;
        SkOPASSERT(ptT->span() == spanBase);
        while ((ptT = ptT->next()) != spanStopPtT) {
            if (ptT->deleted()) {
                continue;
            }
            SkOpSegment* opp = ptT->span()->segment();
            if (opp->done()) {
                continue;
            }
            // when opp is encounted the 1st time, continue; on 2nd encounter, look for coincidence
            if (!opp->visited()) {
                continue;
            }
            if (spanBase == &fHead) {
                continue;
            }
            if (ptT->segment() == this) {
                continue;
            }
            SkOpSpan* span = spanBase->upCastable();
            // FIXME?: this assumes that if the opposite segment is coincident then no more
            // coincidence needs to be detected. This may not be true.
            if (span && span->containsCoincidence(opp)) {
                continue;
            }
            if (spanBase->containsCoinEnd(opp)) {
                continue;
            }
            SkOpPtT* priorPtT = nullptr, * priorStopPtT;
            // find prior span containing opp segment
            SkOpSegment* priorOpp = nullptr;
            SkOpSpan* priorTest = spanBase->prev();
            while (!priorOpp && priorTest) {
                priorStopPtT = priorPtT = priorTest->ptT();
                while ((priorPtT = priorPtT->next()) != priorStopPtT) {
                    if (priorPtT->deleted()) {
                        continue;
                    }
                    SkOpSegment* segment = priorPtT->span()->segment();
                    if (segment == opp) {
                        prior = priorTest;
                        priorOpp = opp;
                        break;
                    }
                }
                priorTest = priorTest->prev();
            }
            if (!priorOpp) {
                continue;
            }
            if (priorPtT == ptT) {
                continue;
            }
            SkOpPtT* oppStart = prior->ptT();
            SkOpPtT* oppEnd = spanBase->ptT();
            bool swapped = priorPtT->fT > ptT->fT;
            if (swapped) {
                using std::swap;
                swap(priorPtT, ptT);
                swap(oppStart, oppEnd);
            }
            SkOpCoincidence* coincidences = this->globalState()->coincidence();
            SkOpPtT* rootPriorPtT = priorPtT->span()->ptT();
            SkOpPtT* rootPtT = ptT->span()->ptT();
            SkOpPtT* rootOppStart = oppStart->span()->ptT();
            SkOpPtT* rootOppEnd = oppEnd->span()->ptT();
            if (coincidences->contains(rootPriorPtT, rootPtT, rootOppStart, rootOppEnd)) {
                goto swapBack;
            }
            if (this->testForCoincidence(rootPriorPtT, rootPtT, prior, spanBase, opp)) {
            // mark coincidence
#if DEBUG_COINCIDENCE_VERBOSE
                SkDebugf("%s coinSpan=%d endSpan=%d oppSpan=%d oppEndSpan=%d\n", __FUNCTION__,
                        rootPriorPtT->debugID(), rootPtT->debugID(), rootOppStart->debugID(),
                        rootOppEnd->debugID());
#endif
                if (!coincidences->extend(rootPriorPtT, rootPtT, rootOppStart, rootOppEnd)) {
                    coincidences->add(rootPriorPtT, rootPtT, rootOppStart, rootOppEnd);
                }
#if DEBUG_COINCIDENCE
                SkASSERT(coincidences->contains(rootPriorPtT, rootPtT, rootOppStart, rootOppEnd));
#endif
                result = true;
            }
    swapBack:
            if (swapped) {
                using std::swap;
                swap(priorPtT, ptT);
            }
        }
    } while ((spanBase = spanBase->final() ? nullptr : spanBase->upCast()->next()));
    ClearVisited(&fHead);
    return result;
}

// please keep this in sync with debugMoveMultiples()
// if a span has more than one intersection, merge the other segments' span as needed
bool SkOpSegment::moveMultiples() {
    debugValidate();
    SkOpSpanBase* test = &fHead;
    do {
        int addCount = test->spanAddsCount();
//        FAIL_IF(addCount < 1);
        if (addCount <= 1) {
            continue;
        }
        SkOpPtT* startPtT = test->ptT();
        SkOpPtT* testPtT = startPtT;
        do {  // iterate through all spans associated with start
            SkOpSpanBase* oppSpan = testPtT->span();
            if (oppSpan->spanAddsCount() == addCount) {
                continue;
            }
            if (oppSpan->deleted()) {
                continue;
            }
            SkOpSegment* oppSegment = oppSpan->segment();
            if (oppSegment == this) {
                continue;
            }
            // find range of spans to consider merging
            SkOpSpanBase* oppPrev = oppSpan;
            SkOpSpanBase* oppFirst = oppSpan;
            while ((oppPrev = oppPrev->prev())) {
                if (!roughly_equal(oppPrev->t(), oppSpan->t())) {
                    break;
                }
                if (oppPrev->spanAddsCount() == addCount) {
                    continue;
                }
                if (oppPrev->deleted()) {
                    continue;
                }
                oppFirst = oppPrev;
            }
            SkOpSpanBase* oppNext = oppSpan;
            SkOpSpanBase* oppLast = oppSpan;
            while ((oppNext = oppNext->final() ? nullptr : oppNext->upCast()->next())) {
                if (!roughly_equal(oppNext->t(), oppSpan->t())) {
                    break;
                }
                if (oppNext->spanAddsCount() == addCount) {
                    continue;
                }
                if (oppNext->deleted()) {
                    continue;
                }
                oppLast = oppNext;
            }
            if (oppFirst == oppLast) {
                continue;
            }
            SkOpSpanBase* oppTest = oppFirst;
            do {
                if (oppTest == oppSpan) {
                    continue;
                }
                // check to see if the candidate meets specific criteria:
                // it contains spans of segments in test's loop but not including 'this'
                SkOpPtT* oppStartPtT = oppTest->ptT();
                SkOpPtT* oppPtT = oppStartPtT;
                while ((oppPtT = oppPtT->next()) != oppStartPtT) {
                    SkOpSegment* oppPtTSegment = oppPtT->segment();
                    if (oppPtTSegment == this) {
                        goto tryNextSpan;
                    }
                    SkOpPtT* matchPtT = startPtT;
                    do {
                        if (matchPtT->segment() == oppPtTSegment) {
                            goto foundMatch;
                        }
                    } while ((matchPtT = matchPtT->next()) != startPtT);
                    goto tryNextSpan;
            foundMatch:  // merge oppTest and oppSpan
                    oppSegment->debugValidate();
                    oppTest->mergeMatches(oppSpan);
                    oppTest->addOpp(oppSpan);
                    oppSegment->debugValidate();
                    goto checkNextSpan;
                }
        tryNextSpan:
                ;
            } while (oppTest != oppLast && (oppTest = oppTest->upCast()->next()));
        } while ((testPtT = testPtT->next()) != startPtT);
checkNextSpan:
        ;
    } while ((test = test->final() ? nullptr : test->upCast()->next()));
    debugValidate();
    return true;
}

// adjacent spans may have points close by
bool SkOpSegment::spansNearby(const SkOpSpanBase* refSpan, const SkOpSpanBase* checkSpan,
        bool* found) const {
    const SkOpPtT* refHead = refSpan->ptT();
    const SkOpPtT* checkHead = checkSpan->ptT();
// if the first pt pair from adjacent spans are far apart, assume that all are far enough apart
    if (!SkDPoint::WayRoughlyEqual(refHead->fPt, checkHead->fPt)) {
#if DEBUG_COINCIDENCE
        // verify that no combination of points are close
        const SkOpPtT* dBugRef = refHead;
        do {
            const SkOpPtT* dBugCheck = checkHead;
            do {
                SkOPASSERT(!SkDPoint::ApproximatelyEqual(dBugRef->fPt, dBugCheck->fPt));
                dBugCheck = dBugCheck->next();
            } while (dBugCheck != checkHead);
            dBugRef = dBugRef->next();
        } while (dBugRef != refHead);
#endif
        *found = false;
        return true;
    }
    // check only unique points
    SkScalar distSqBest = SK_ScalarMax;
    const SkOpPtT* refBest = nullptr;
    const SkOpPtT* checkBest = nullptr;
    const SkOpPtT* ref = refHead;
    do {
        if (ref->deleted()) {
            continue;
        }
        while (ref->ptAlreadySeen(refHead)) {
            ref = ref->next();
            if (ref == refHead) {
                goto doneCheckingDistance;
            }
        }
        const SkOpPtT* check = checkHead;
        const SkOpSegment* refSeg = ref->segment();
        int escapeHatch = 100000;  // defend against infinite loops
        do {
            if (check->deleted()) {
                continue;
            }
            while (check->ptAlreadySeen(checkHead)) {
                check = check->next();
                if (check == checkHead) {
                    goto nextRef;
                }
            }
            SkScalar distSq = SkPointPriv::DistanceToSqd(ref->fPt, check->fPt);
            if (distSqBest > distSq && (refSeg != check->segment()
                    || !refSeg->ptsDisjoint(*ref, *check))) {
                distSqBest = distSq;
                refBest = ref;
                checkBest = check;
            }
            if (--escapeHatch <= 0) {
                return false;
            }
        } while ((check = check->next()) != checkHead);
    nextRef:
        ;
   } while ((ref = ref->next()) != refHead);
doneCheckingDistance:
    *found = checkBest && refBest->segment()->match(refBest, checkBest->segment(), checkBest->fT,
            checkBest->fPt);
    return true;
}

// Please keep this function in sync with debugMoveNearby()
// Move nearby t values and pts so they all hang off the same span. Alignment happens later.
bool SkOpSegment::moveNearby() {
    debugValidate();
    // release undeleted spans pointing to this seg that are linked to the primary span
    SkOpSpanBase* spanBase = &fHead;
    int escapeHatch = 9999;  // the largest count for a regular test is 50; for a fuzzer, 500
    do {
        SkOpPtT* ptT = spanBase->ptT();
        const SkOpPtT* headPtT = ptT;
        while ((ptT = ptT->next()) != headPtT) {
            if (!--escapeHatch) {
                return false;
            }
            SkOpSpanBase* test = ptT->span();
            if (ptT->segment() == this && !ptT->deleted() && test != spanBase
                    && test->ptT() == ptT) {
                if (test->final()) {
                    if (spanBase == &fHead) {
                        this->clearAll();
                        return true;
                    }
                    spanBase->upCast()->release(ptT);
                } else if (test->prev()) {
                    test->upCast()->release(headPtT);
                }
                break;
            }
        }
        spanBase = spanBase->upCast()->next();
    } while (!spanBase->final());
    // This loop looks for adjacent spans which are near by
    spanBase = &fHead;
    do {  // iterate through all spans associated with start
        SkOpSpanBase* test = spanBase->upCast()->next();
        bool found;
        if (!this->spansNearby(spanBase, test, &found)) {
            return false;
        }
        if (found) {
            if (test->final()) {
                if (spanBase->prev()) {
                    test->merge(spanBase->upCast());
                } else {
                    this->clearAll();
                    return true;
                }
            } else {
                spanBase->merge(test->upCast());
            }
        }
        spanBase = test;
    } while (!spanBase->final());
    debugValidate();
    return true;
}

bool SkOpSegment::operand() const {
    return fContour->operand();
}

bool SkOpSegment::oppXor() const {
    return fContour->oppXor();
}

bool SkOpSegment::ptsDisjoint(double t1, const SkPoint& pt1, double t2, const SkPoint& pt2) const {
    if (fVerb == SkPath::kLine_Verb) {
        return false;
    }
    // quads (and cubics) can loop back to nearly a line so that an opposite curve
    // hits in two places with very different t values.
    // OPTIMIZATION: curves could be preflighted so that, for example, something like
    // 'controls contained by ends' could avoid this check for common curves
    // 'ends are extremes in x or y' is cheaper to compute and real-world common
    // on the other hand, the below check is relatively inexpensive
    double midT = (t1 + t2) / 2;
    SkPoint midPt = this->ptAtT(midT);
    double seDistSq = SkTMax(SkPointPriv::DistanceToSqd(pt1, pt2) * 2, FLT_EPSILON * 2);
    return SkPointPriv::DistanceToSqd(midPt, pt1) > seDistSq ||
           SkPointPriv::DistanceToSqd(midPt, pt2) > seDistSq;
}

void SkOpSegment::setUpWindings(SkOpSpanBase* start, SkOpSpanBase* end, int* sumMiWinding,
        int* maxWinding, int* sumWinding) {
    int deltaSum = SpanSign(start, end);
    *maxWinding = *sumMiWinding;
    *sumWinding = *sumMiWinding -= deltaSum;
    SkASSERT(!DEBUG_LIMIT_WIND_SUM || SkTAbs(*sumWinding) <= DEBUG_LIMIT_WIND_SUM);
}

void SkOpSegment::setUpWindings(SkOpSpanBase* start, SkOpSpanBase* end, int* sumMiWinding,
        int* sumSuWinding, int* maxWinding, int* sumWinding, int* oppMaxWinding,
        int* oppSumWinding) {
    int deltaSum = SpanSign(start, end);
    int oppDeltaSum = OppSign(start, end);
    if (operand()) {
        *maxWinding = *sumSuWinding;
        *sumWinding = *sumSuWinding -= deltaSum;
        *oppMaxWinding = *sumMiWinding;
        *oppSumWinding = *sumMiWinding -= oppDeltaSum;
    } else {
        *maxWinding = *sumMiWinding;
        *sumWinding = *sumMiWinding -= deltaSum;
        *oppMaxWinding = *sumSuWinding;
        *oppSumWinding = *sumSuWinding -= oppDeltaSum;
    }
    SkASSERT(!DEBUG_LIMIT_WIND_SUM || SkTAbs(*sumWinding) <= DEBUG_LIMIT_WIND_SUM);
    SkASSERT(!DEBUG_LIMIT_WIND_SUM || SkTAbs(*oppSumWinding) <= DEBUG_LIMIT_WIND_SUM);
}

bool SkOpSegment::sortAngles() {
    SkOpSpanBase* span = &this->fHead;
    do {
        SkOpAngle* fromAngle = span->fromAngle();
        SkOpAngle* toAngle = span->final() ? nullptr : span->upCast()->toAngle();
        if (!fromAngle && !toAngle) {
            continue;
        }
#if DEBUG_ANGLE
        bool wroteAfterHeader = false;
#endif
        SkOpAngle* baseAngle = fromAngle;
        if (fromAngle && toAngle) {
#if DEBUG_ANGLE
            SkDebugf("%s [%d] tStart=%1.9g [%d]\n", __FUNCTION__, debugID(), span->t(),
                    span->debugID());
            wroteAfterHeader = true;
#endif
            FAIL_IF(!fromAngle->insert(toAngle));
        } else if (!fromAngle) {
            baseAngle = toAngle;
        }
        SkOpPtT* ptT = span->ptT(), * stopPtT = ptT;
        do {
            SkOpSpanBase* oSpan = ptT->span();
            if (oSpan == span) {
                continue;
            }
            SkOpAngle* oAngle = oSpan->fromAngle();
            if (oAngle) {
#if DEBUG_ANGLE
                if (!wroteAfterHeader) {
                    SkDebugf("%s [%d] tStart=%1.9g [%d]\n", __FUNCTION__, debugID(),
                            span->t(), span->debugID());
                    wroteAfterHeader = true;
                }
#endif
                if (!oAngle->loopContains(baseAngle)) {
                    baseAngle->insert(oAngle);
                }
            }
            if (!oSpan->final()) {
                oAngle = oSpan->upCast()->toAngle();
                if (oAngle) {
#if DEBUG_ANGLE
                    if (!wroteAfterHeader) {
                        SkDebugf("%s [%d] tStart=%1.9g [%d]\n", __FUNCTION__, debugID(),
                                span->t(), span->debugID());
                        wroteAfterHeader = true;
                    }
#endif
                    if (!oAngle->loopContains(baseAngle)) {
                        baseAngle->insert(oAngle);
                    }
                }
            }
        } while ((ptT = ptT->next()) != stopPtT);
        if (baseAngle->loopCount() == 1) {
            span->setFromAngle(nullptr);
            if (toAngle) {
                span->upCast()->setToAngle(nullptr);
            }
            baseAngle = nullptr;
        }
#if DEBUG_SORT
        SkASSERT(!baseAngle || baseAngle->loopCount() > 1);
#endif
    } while (!span->final() && (span = span->upCast()->next()));
    return true;
}

bool SkOpSegment::subDivide(const SkOpSpanBase* start, const SkOpSpanBase* end,
        SkDCurve* edge) const {
    SkASSERT(start != end);
    const SkOpPtT& startPtT = *start->ptT();
    const SkOpPtT& endPtT = *end->ptT();
    SkDEBUGCODE(edge->fVerb = fVerb);
    edge->fCubic[0].set(startPtT.fPt);
    int points = SkPathOpsVerbToPoints(fVerb);
    edge->fCubic[points].set(endPtT.fPt);
    if (fVerb == SkPath::kLine_Verb) {
        return false;
    }
    double startT = startPtT.fT;
    double endT = endPtT.fT;
    if ((startT == 0 || endT == 0) && (startT == 1 || endT == 1)) {
        // don't compute midpoints if we already have them
        if (fVerb == SkPath::kQuad_Verb) {
            edge->fLine[1].set(fPts[1]);
            return false;
        }
        if (fVerb == SkPath::kConic_Verb) {
            edge->fConic[1].set(fPts[1]);
            edge->fConic.fWeight = fWeight;
            return false;
        }
        SkASSERT(fVerb == SkPath::kCubic_Verb);
        if (startT == 0) {
            edge->fCubic[1].set(fPts[1]);
            edge->fCubic[2].set(fPts[2]);
            return false;
        }
        edge->fCubic[1].set(fPts[2]);
        edge->fCubic[2].set(fPts[1]);
        return false;
    }
    if (fVerb == SkPath::kQuad_Verb) {
        edge->fQuad[1] = SkDQuad::SubDivide(fPts, edge->fQuad[0], edge->fQuad[2], startT, endT);
    } else if (fVerb == SkPath::kConic_Verb) {
        edge->fConic[1] = SkDConic::SubDivide(fPts, fWeight, edge->fQuad[0], edge->fQuad[2],
            startT, endT, &edge->fConic.fWeight);
    } else {
        SkASSERT(fVerb == SkPath::kCubic_Verb);
        SkDCubic::SubDivide(fPts, edge->fCubic[0], edge->fCubic[3], startT, endT, &edge->fCubic[1]);
    }
    return true;
}

bool SkOpSegment::testForCoincidence(const SkOpPtT* priorPtT, const SkOpPtT* ptT,
        const SkOpSpanBase* prior, const SkOpSpanBase* spanBase, const SkOpSegment* opp) const {
    // average t, find mid pt
    double midT = (prior->t() + spanBase->t()) / 2;
    SkPoint midPt = this->ptAtT(midT);
    bool coincident = true;
    // if the mid pt is not near either end pt, project perpendicular through opp seg
    if (!SkDPoint::ApproximatelyEqual(priorPtT->fPt, midPt)
            && !SkDPoint::ApproximatelyEqual(ptT->fPt, midPt)) {
        if (priorPtT->span() == ptT->span()) {
          return false;
        }
        coincident = false;
        SkIntersections i;
        SkDCurve curvePart;
        this->subDivide(prior, spanBase, &curvePart);
        SkDVector dxdy = (*CurveDDSlopeAtT[fVerb])(curvePart, 0.5f);
        SkDPoint partMidPt = (*CurveDDPointAtT[fVerb])(curvePart, 0.5f);
        SkDLine ray = {{{midPt.fX, midPt.fY}, {partMidPt.fX + dxdy.fY, partMidPt.fY - dxdy.fX}}};
        SkDCurve oppPart;
        opp->subDivide(priorPtT->span(), ptT->span(), &oppPart);
        (*CurveDIntersectRay[opp->verb()])(oppPart, ray, &i);
        // measure distance and see if it's small enough to denote coincidence
        for (int index = 0; index < i.used(); ++index) {
            if (!between(0, i[0][index], 1)) {
                continue;
            }
            SkDPoint oppPt = i.pt(index);
            if (oppPt.approximatelyDEqual(midPt)) {
                // the coincidence can occur at almost any angle
                coincident = true;
            }
        }
    }
    return coincident;
}

SkOpSpan* SkOpSegment::undoneSpan() {
    SkOpSpan* span = &fHead;
    SkOpSpanBase* next;
    do {
        next = span->next();
        if (!span->done()) {
            return span;
        }
    } while (!next->final() && (span = next->upCast()));
    return nullptr;
}

int SkOpSegment::updateOppWinding(const SkOpSpanBase* start, const SkOpSpanBase* end) const {
    const SkOpSpan* lesser = start->starter(end);
    int oppWinding = lesser->oppSum();
    int oppSpanWinding = SkOpSegment::OppSign(start, end);
    if (oppSpanWinding && UseInnerWinding(oppWinding - oppSpanWinding, oppWinding)
            && oppWinding != SK_MaxS32) {
        oppWinding -= oppSpanWinding;
    }
    return oppWinding;
}

int SkOpSegment::updateOppWinding(const SkOpAngle* angle) const {
    const SkOpSpanBase* startSpan = angle->start();
    const SkOpSpanBase* endSpan = angle->end();
    return updateOppWinding(endSpan, startSpan);
}

int SkOpSegment::updateOppWindingReverse(const SkOpAngle* angle) const {
    const SkOpSpanBase* startSpan = angle->start();
    const SkOpSpanBase* endSpan = angle->end();
    return updateOppWinding(startSpan, endSpan);
}

int SkOpSegment::updateWinding(SkOpSpanBase* start, SkOpSpanBase* end) {
    SkOpSpan* lesser = start->starter(end);
    int winding = lesser->windSum();
    if (winding == SK_MinS32) {
        winding = lesser->computeWindSum();
    }
    if (winding == SK_MinS32) {
        return winding;
    }
    int spanWinding = SkOpSegment::SpanSign(start, end);
    if (winding && UseInnerWinding(winding - spanWinding, winding)
            && winding != SK_MaxS32) {
        winding -= spanWinding;
    }
    return winding;
}

int SkOpSegment::updateWinding(SkOpAngle* angle) {
    SkOpSpanBase* startSpan = angle->start();
    SkOpSpanBase* endSpan = angle->end();
    return updateWinding(endSpan, startSpan);
}

int SkOpSegment::updateWindingReverse(const SkOpAngle* angle) {
    SkOpSpanBase* startSpan = angle->start();
    SkOpSpanBase* endSpan = angle->end();
    return updateWinding(startSpan, endSpan);
}

// OPTIMIZATION: does the following also work, and is it any faster?
// return outerWinding * innerWinding > 0
//      || ((outerWinding + innerWinding < 0) ^ ((outerWinding - innerWinding) < 0)))
bool SkOpSegment::UseInnerWinding(int outerWinding, int innerWinding) {
    SkASSERT(outerWinding != SK_MaxS32);
    SkASSERT(innerWinding != SK_MaxS32);
    int absOut = SkTAbs(outerWinding);
    int absIn = SkTAbs(innerWinding);
    bool result = absOut == absIn ? outerWinding < 0 : absOut < absIn;
    return result;
}

int SkOpSegment::windSum(const SkOpAngle* angle) const {
    const SkOpSpan* minSpan = angle->start()->starter(angle->end());
    return minSpan->windSum();
}