cumulative pathops patch

src/pathops/SkOpSegment.cpp

Index: src/pathops/SkOpSegment.cpp
diff --git a/src/pathops/SkOpSegment.cpp b/src/pathops/SkOpSegment.cpp
index 1fb5afa028af33e894a82fe890e8b03af185f52a..c6ccf93003de931ba2fc5f72e58ff379f69b88d3 100644
--- a/src/pathops/SkOpSegment.cpp
+++ b/src/pathops/SkOpSegment.cpp
@@ -4,11 +4,20 @@
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
-#include "SkIntersections.h"
+#include "SkOpCoincidence.h"
 #include "SkOpContour.h"
 #include "SkOpSegment.h"
 #include "SkPathWriter.h"
-#include "SkTSort.h"
+
+/*
+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
@@ -19,7 +28,7 @@ static const bool gUnaryActiveEdge[2][2] = {
     {F, T}, {T, F},
 };
 
-static const bool gActiveEdge[kXOR_PathOp + 1][2][2][2][2] = {
+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
@@ -33,147 +42,125 @@ static const bool gActiveEdge[kXOR_PathOp + 1][2][2][2][2] = {
 #undef F
 #undef T
 
-enum {
-    kOutsideTrackedTCount = 16,  // FIXME: determine what this should be
-    kMissingSpanCount = 4,  // FIXME: determine what this should be
-};
-
-const SkOpAngle* SkOpSegment::activeAngle(int index, int* start, int* end, bool* done,
-        bool* sortable) const {
-    if (const SkOpAngle* result = activeAngleInner(index, start, end, done, sortable)) {
+SkOpAngle* SkOpSegment::activeAngle(SkOpSpanBase* start, SkOpSpanBase** startPtr,
+        SkOpSpanBase** endPtr, bool* done, bool* sortable) {
+    if (SkOpAngle* result = activeAngleInner(start, startPtr, endPtr, done, sortable)) {
         return result;
     }
-    double referenceT = fTs[index].fT;
-    int lesser = index;
-    while (--lesser >= 0
-            && (precisely_negative(referenceT - fTs[lesser].fT) || fTs[lesser].fTiny)) {
-        if (const SkOpAngle* result = activeAngleOther(lesser, start, end, done, sortable)) {
-            return result;
-        }
+    if (SkOpAngle* result = activeAngleOther(start, startPtr, endPtr, done, sortable)) {
+        return result;
     }
-    do {
-        if (const SkOpAngle* result = activeAngleOther(index, start, end, done, sortable)) {
-            return result;
-        }
-        if (++index == fTs.count()) {
-            break;
-        }
-        if (fTs[index - 1].fTiny) {
-            referenceT = fTs[index].fT;
-            continue;
-        }
-    } while (precisely_negative(fTs[index].fT - referenceT));
     return NULL;
 }
 
-const SkOpAngle* SkOpSegment::activeAngleInner(int index, int* start, int* end, bool* done,
-        bool* sortable) const {
-    int next = nextExactSpan(index, 1);
-    if (next > 0) {
-        const SkOpSpan& upSpan = fTs[index];
-        if (upSpan.fWindValue || upSpan.fOppValue) {
-            if (*end < 0) {
-                *start = index;
-                *end = next;
+SkOpAngle* SkOpSegment::activeAngleInner(SkOpSpanBase* start, SkOpSpanBase** startPtr,
+        SkOpSpanBase** endPtr, bool* done, bool* sortable) {
+    SkOpSpan* upSpan = start->upCastable();
+    if (upSpan) {
+        if (upSpan->windValue() || upSpan->oppValue()) {
+            SkOpSpanBase* next = upSpan->next();
+            if (!*endPtr) {
+                *startPtr = start;
+                *endPtr = next;
             }
-            if (!upSpan.fDone) {
-                if (upSpan.fWindSum != SK_MinS32) {
-                    return spanToAngle(index, next);
+            if (!upSpan->done()) {
+                if (upSpan->windSum() != SK_MinS32) {
+                    return spanToAngle(start, next);
                 }
                 *done = false;
             }
         } else {
-            SkASSERT(upSpan.fDone);
+            SkASSERT(upSpan->done());
         }
     }
-    int prev = nextExactSpan(index, -1);
+    SkOpSpan* downSpan = start->prev();
     // edge leading into junction
-    if (prev >= 0) {
-        const SkOpSpan& downSpan = fTs[prev];
-        if (downSpan.fWindValue || downSpan.fOppValue) {
-            if (*end < 0) {
-                *start = index;
-                *end = prev;
-            }
-            if (!downSpan.fDone) {
-                if (downSpan.fWindSum != SK_MinS32) {
-                    return spanToAngle(index, prev);
+    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.fDone);
+            SkASSERT(downSpan->done());
         }
     }
     return NULL;
 }
 
-const SkOpAngle* SkOpSegment::activeAngleOther(int index, int* start, int* end, bool* done,
-        bool* sortable) const {
-    const SkOpSpan* span = &fTs[index];
-    SkOpSegment* other = span->fOther;
-    int oIndex = span->fOtherIndex;
-    return other->activeAngleInner(oIndex, start, end, done, sortable);
+SkOpAngle* SkOpSegment::activeAngleOther(SkOpSpanBase* start, SkOpSpanBase** startPtr,
+        SkOpSpanBase** endPtr, bool* done, bool* sortable) {
+    SkOpPtT* oPtT = start->ptT()->next();
+    SkOpSegment* other = oPtT->segment();
+    SkOpSpanBase* oSpan = oPtT->span();
+    return other->activeAngleInner(oSpan, startPtr, endPtr, done, sortable);
 }
 
-SkPoint SkOpSegment::activeLeftTop(int* firstT) const {
+SkPoint SkOpSegment::activeLeftTop(SkOpSpanBase** firstSpan) {
     SkASSERT(!done());
     SkPoint topPt = {SK_ScalarMax, SK_ScalarMax};
-    int count = fTs.count();
     // see if either end is not done since we want smaller Y of the pair
     bool lastDone = true;
     double lastT = -1;
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (span.fDone && lastDone) {
-            goto next;
-        }
-        if (approximately_negative(span.fT - lastT)) {
+    SkOpSpanBase* span = &fHead;
+    do {
+        if (lastDone && (span->final() || span->upCast()->done())) {
             goto next;
         }
         {
-            const SkPoint& xy = xyAtT(&span);
+            const SkPoint& xy = span->pt();
             if (topPt.fY > xy.fY || (topPt.fY == xy.fY && topPt.fX > xy.fX)) {
                 topPt = xy;
-                if (firstT) {
-                    *firstT = index;
+                if (firstSpan) {
+                    *firstSpan = span;
                 }
             }
             if (fVerb != SkPath::kLine_Verb && !lastDone) {
-                SkPoint curveTop = (*CurveTop[SkPathOpsVerbToPoints(fVerb)])(fPts, lastT, span.fT);
+                SkPoint curveTop = (*CurveTop[SkPathOpsVerbToPoints(fVerb)])(fPts, lastT,
+                        span->t());
                 if (topPt.fY > curveTop.fY || (topPt.fY == curveTop.fY
                         && topPt.fX > curveTop.fX)) {
                     topPt = curveTop;
-                    if (firstT) {
-                        *firstT = index;
+                    if (firstSpan) {
+                        *firstSpan = span;
                     }
                 }
             }
-            lastT = span.fT;
+            lastT = span->t();
         }
 next:
-        lastDone = span.fDone;
-    }
+        if (span->final()) {
+            break;
+        }
+        lastDone = span->upCast()->done();
+    } while ((span = span->upCast()->next()));
     return topPt;
 }
 
-bool SkOpSegment::activeOp(int index, int endIndex, int xorMiMask, int xorSuMask, SkPathOp op) {
-    int sumMiWinding = updateWinding(endIndex, index);
-    int sumSuWinding = updateOppWinding(endIndex, index);
+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 (fOperand) {
+    if (this->operand()) {
         SkTSwap<int>(sumMiWinding, sumSuWinding);
     }
-    return activeOp(xorMiMask, xorSuMask, index, endIndex, op, &sumMiWinding, &sumSuWinding);
+    return this->activeOp(xorMiMask, xorSuMask, start, end, op, &sumMiWinding, &sumSuWinding);
 }
 
-bool SkOpSegment::activeOp(int xorMiMask, int xorSuMask, int index, int endIndex, SkPathOp op,
-        int* sumMiWinding, int* sumSuWinding) {
+bool SkOpSegment::activeOp(int xorMiMask, int xorSuMask, SkOpSpanBase* start, SkOpSpanBase* end,
+        SkPathOp op, int* sumMiWinding, int* sumSuWinding) {
     int maxWinding, sumWinding, oppMaxWinding, oppSumWinding;
-    setUpWindings(index, endIndex, sumMiWinding, sumSuWinding,
+    this->setUpWindings(start, end, sumMiWinding, sumSuWinding,
             &maxWinding, &sumWinding, &oppMaxWinding, &oppSumWinding);
     bool miFrom;
     bool miTo;
@@ -193,178 +180,31 @@ bool SkOpSegment::activeOp(int xorMiMask, int xorSuMask, int index, int endIndex
     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(), span(index).fT, span(endIndex).fT,
+            __FUNCTION__, debugID(), start->t(), end->t(),
             SkPathOpsDebug::kPathOpStr[op], miFrom, miTo, suFrom, suTo, result);
 #endif
     return result;
 }
 
-bool SkOpSegment::activeWinding(int index, int endIndex) {
-    int sumWinding = updateWinding(endIndex, index);
-    return activeWinding(index, endIndex, &sumWinding);
+bool SkOpSegment::activeWinding(SkOpSpanBase* start, SkOpSpanBase* end) {
+    int sumWinding = updateWinding(end, start);
+    return activeWinding(start, end, &sumWinding);
 }
 
-bool SkOpSegment::activeWinding(int index, int endIndex, int* sumWinding) {
+bool SkOpSegment::activeWinding(SkOpSpanBase* start, SkOpSpanBase* end, int* sumWinding) {
     int maxWinding;
-    setUpWinding(index, endIndex, &maxWinding, sumWinding);
+    setUpWinding(start, end, &maxWinding, sumWinding);
     bool from = maxWinding != 0;
     bool to = *sumWinding  != 0;
     bool result = gUnaryActiveEdge[from][to];
     return result;
 }
 
-void SkOpSegment::addCancelOutsides(const SkPoint& startPt, const SkPoint& endPt,
-        SkOpSegment* other) {
-    int tIndex = -1;
-    int tCount = fTs.count();
-    int oIndex = -1;
-    int oCount = other->fTs.count();
-    do {
-        ++tIndex;
-    } while (startPt != fTs[tIndex].fPt && tIndex < tCount);
-    int tIndexStart = tIndex;
-    do {
-        ++oIndex;
-    } while (endPt != other->fTs[oIndex].fPt && oIndex < oCount);
-    int oIndexStart = oIndex;
-    const SkPoint* nextPt;
-    do {
-        nextPt = &fTs[++tIndex].fPt;
-        SkASSERT(fTs[tIndex].fT < 1 || startPt != *nextPt);
-    } while (startPt == *nextPt);
-    double nextT = fTs[tIndex].fT;
-    const SkPoint* oNextPt;
-    do {
-        oNextPt = &other->fTs[++oIndex].fPt;
-        SkASSERT(other->fTs[oIndex].fT < 1 || endPt != *oNextPt);
-    } while (endPt == *oNextPt);
-    double oNextT = other->fTs[oIndex].fT;
-    // at this point, spans before and after are at:
-    //  fTs[tIndexStart - 1], fTs[tIndexStart], fTs[tIndex]
-    // if tIndexStart == 0, no prior span
-    // if nextT == 1, no following span
-
-    // advance the span with zero winding
-    // if the following span exists (not past the end, non-zero winding)
-    // connect the two edges
-    if (!fTs[tIndexStart].fWindValue) {
-        if (tIndexStart > 0 && fTs[tIndexStart - 1].fWindValue) {
-#if DEBUG_CONCIDENT
-            SkDebugf("%s 1 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
-                    __FUNCTION__, fID, other->fID, tIndexStart - 1,
-                    fTs[tIndexStart].fT, xyAtT(tIndexStart).fX,
-                    xyAtT(tIndexStart).fY);
-#endif
-            SkPoint copy = fTs[tIndexStart].fPt;  // add t pair may move the point array
-            addTPair(fTs[tIndexStart].fT, other, other->fTs[oIndex].fT, false, copy);
-        }
-        if (nextT < 1 && fTs[tIndex].fWindValue) {
-#if DEBUG_CONCIDENT
-            SkDebugf("%s 2 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
-                    __FUNCTION__, fID, other->fID, tIndex,
-                    fTs[tIndex].fT, xyAtT(tIndex).fX,
-                    xyAtT(tIndex).fY);
-#endif
-            SkPoint copy = fTs[tIndex].fPt;  // add t pair may move the point array
-            addTPair(fTs[tIndex].fT, other, other->fTs[oIndexStart].fT, false, copy);
-        }
-    } else {
-        SkASSERT(!other->fTs[oIndexStart].fWindValue);
-        if (oIndexStart > 0 && other->fTs[oIndexStart - 1].fWindValue) {
-#if DEBUG_CONCIDENT
-            SkDebugf("%s 3 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
-                    __FUNCTION__, fID, other->fID, oIndexStart - 1,
-                    other->fTs[oIndexStart].fT, other->xyAtT(oIndexStart).fX,
-                    other->xyAtT(oIndexStart).fY);
-            other->debugAddTPair(other->fTs[oIndexStart].fT, *this, fTs[tIndex].fT);
-#endif
-        }
-        if (oNextT < 1 && other->fTs[oIndex].fWindValue) {
-#if DEBUG_CONCIDENT
-            SkDebugf("%s 4 this=%d other=%d t [%d] %1.9g (%1.9g,%1.9g)\n",
-                    __FUNCTION__, fID, other->fID, oIndex,
-                    other->fTs[oIndex].fT, other->xyAtT(oIndex).fX,
-                    other->xyAtT(oIndex).fY);
-            other->debugAddTPair(other->fTs[oIndex].fT, *this, fTs[tIndexStart].fT);
-#endif
-        }
-    }
-}
-
-void SkOpSegment::addCoinOutsides(const SkPoint& startPt, const SkPoint& endPt,
-        SkOpSegment* other) {
-    // walk this to startPt
-    // walk other to startPt
-    // if either is > 0, add a pointer to the other, copying adjacent winding
-    int tIndex = -1;
-    int oIndex = -1;
-    do {
-        ++tIndex;
-    } while (startPt != fTs[tIndex].fPt);
-    int ttIndex = tIndex;
-    bool checkOtherTMatch = false;
-    do {
-        const SkOpSpan& span = fTs[ttIndex];
-        if (startPt != span.fPt) {
-            break;
-        }
-        if (span.fOther == other && span.fPt == startPt) {
-            checkOtherTMatch = true;
-            break;
-        }
-    } while (++ttIndex < count());
-    do {
-        ++oIndex;
-    } while (startPt != other->fTs[oIndex].fPt);
-    bool skipAdd = false;
-    if (checkOtherTMatch) {
-        int ooIndex = oIndex;
-        do {
-            const SkOpSpan& oSpan = other->fTs[ooIndex];
-            if (startPt != oSpan.fPt) {
-                break;
-            }
-            if (oSpan.fT == fTs[ttIndex].fOtherT) {
-                skipAdd = true;
-                break;
-            }
-        } while (++ooIndex < other->count());
-    }
-    if ((tIndex > 0 || oIndex > 0 || fOperand != other->fOperand) && !skipAdd) {
-        addTPair(fTs[tIndex].fT, other, other->fTs[oIndex].fT, false, startPt);
-    }
-    SkPoint nextPt = startPt;
-    do {
-        const SkPoint* workPt;
-        do {
-            workPt = &fTs[++tIndex].fPt;
-        } while (nextPt == *workPt);
-        const SkPoint* oWorkPt;
-        do {
-            oWorkPt = &other->fTs[++oIndex].fPt;
-        } while (nextPt == *oWorkPt);
-        nextPt = *workPt;
-        double tStart = fTs[tIndex].fT;
-        double oStart = other->fTs[oIndex].fT;
-        if (tStart == 1 && oStart == 1 && fOperand == other->fOperand) {
-            break;
-        }
-        if (*workPt == *oWorkPt) {
-            addTPair(tStart, other, oStart, false, nextPt);
-        }
-    } while (endPt != nextPt);
-}
-
-void SkOpSegment::addCubic(const SkPoint pts[4], bool operand, bool evenOdd) {
-    init(pts, SkPath::kCubic_Verb, operand, evenOdd);
-    fBounds.setCubicBounds(pts);
-}
-
-void SkOpSegment::addCurveTo(int start, int end, SkPathWriter* path, bool active) const {
+void SkOpSegment::addCurveTo(const SkOpSpanBase* start, const SkOpSpanBase* end,
+        SkPathWriter* path, bool active) const {
     SkPoint edge[4];
     const SkPoint* ePtr;
-    int lastT = fTs.count() - 1;
-    if (lastT < 0 || (start == 0 && end == lastT) || (start == lastT && end == 0)) {
+    if ((start == &fHead && end == &fTail) || (start == &fTail && end == &fHead)) {
         ePtr = fPts;
     } else {
     // OPTIMIZE? if not active, skip remainder and return xyAtT(end)
@@ -372,7 +212,7 @@ void SkOpSegment::addCurveTo(int start, int end, SkPathWriter* path, bool active
         ePtr = edge;
     }
     if (active) {
-        bool reverse = ePtr == fPts && start != 0;
+        bool reverse = ePtr == fPts && start != &fHead;
         if (reverse) {
             path->deferredMoveLine(ePtr[SkPathOpsVerbToPoints(fVerb)]);
             switch (fVerb) {
@@ -388,7 +228,6 @@ void SkOpSegment::addCurveTo(int start, int end, SkPathWriter* path, bool active
                 default:
                     SkASSERT(0);
             }
-   //         return ePtr[0];
        } else {
             path->deferredMoveLine(ePtr[0]);
             switch (fVerb) {
@@ -406,1473 +245,350 @@ void SkOpSegment::addCurveTo(int start, int end, SkPathWriter* path, bool active
             }
         }
     }
-  //  return ePtr[SkPathOpsVerbToPoints(fVerb)];
 }
 
-void SkOpSegment::addEndSpan(int endIndex) {
-    SkASSERT(span(endIndex).fT == 1 || (span(endIndex).fTiny
-//            && approximately_greater_than_one(span(endIndex).fT)
-    ));
-    int spanCount = fTs.count();
-    int startIndex = endIndex - 1;
-    while (fTs[startIndex].fT == 1 || fTs[startIndex].fTiny) {
-        --startIndex;
-        SkASSERT(startIndex > 0);
-        --endIndex;
-    }
-    SkOpAngle& angle = fAngles.push_back();
-    angle.set(this, spanCount - 1, startIndex);
-#if DEBUG_ANGLE
-    debugCheckPointsEqualish(endIndex, spanCount);
-#endif
-    setFromAngle(endIndex, &angle);
-}
-
-void SkOpSegment::setFromAngle(int endIndex, SkOpAngle* angle) {
-    int spanCount = fTs.count();
+SkOpPtT* SkOpSegment::addMissing(double t, SkOpSegment* opp, SkChunkAlloc* allocator) {
+    SkOpSpanBase* existing = NULL;
+    SkOpSpanBase* test = &fHead;
+    double testT;
     do {
-        fTs[endIndex].fFromAngle = angle;
-    } while (++endIndex < spanCount);
-}
-
-void SkOpSegment::addLine(const SkPoint pts[2], bool operand, bool evenOdd) {
-    init(pts, SkPath::kLine_Verb, operand, evenOdd);
-    fBounds.set(pts, 2);
-}
-
-// add 2 to edge or out of range values to get T extremes
-void SkOpSegment::addOtherT(int index, double otherT, int otherIndex) {
-    SkOpSpan& span = fTs[index];
-    if (precisely_zero(otherT)) {
-        otherT = 0;
-    } else if (precisely_equal(otherT, 1)) {
-        otherT = 1;
+        if ((testT = test->ptT()->fT) >= t) {
+            if (testT == t) {
+                existing = test;
+            }
+            break;
+        }
+    } while ((test = test->upCast()->next()));
+    SkOpPtT* result;
+    if (existing && existing->contains(opp)) {
+        result = existing->ptT();
+    } else {
+        result = this->addT(t, SkOpSegment::kNoAlias, allocator);
     }
-    span.fOtherT = otherT;
-    span.fOtherIndex = otherIndex;
-}
-
-void SkOpSegment::addQuad(const SkPoint pts[3], bool operand, bool evenOdd) {
-    init(pts, SkPath::kQuad_Verb, operand, evenOdd);
-    fBounds.setQuadBounds(pts);
+    SkASSERT(result);
+    return result;
 }
 
-SkOpAngle* SkOpSegment::addSingletonAngleDown(SkOpSegment** otherPtr, SkOpAngle** anglePtr) {
-    int spanIndex = count() - 1;
-    int startIndex = nextExactSpan(spanIndex, -1);
-    SkASSERT(startIndex >= 0);
-    SkOpAngle& angle = fAngles.push_back();
-    *anglePtr = &angle;
-    angle.set(this, spanIndex, startIndex);
-    setFromAngle(spanIndex, &angle);
-    SkOpSegment* other;
-    int oStartIndex, oEndIndex;
-    do {
-        const SkOpSpan& span = fTs[spanIndex];
-        SkASSERT(span.fT > 0);
-        other = span.fOther;
-        oStartIndex = span.fOtherIndex;
-        oEndIndex = other->nextExactSpan(oStartIndex, 1);
-        if (oEndIndex > 0 && other->span(oStartIndex).fWindValue) {
+SkOpAngle* SkOpSegment::addSingletonAngleDown(SkOpSegment** otherPtr, SkOpAngle** anglePtr,
+        SkChunkAlloc* allocator) {
+    SkOpSpan* startSpan = fTail.prev();
+    SkASSERT(startSpan);
+    SkOpAngle* angle = SkOpTAllocator<SkOpAngle>::Allocate(allocator);
+    *anglePtr = angle;
+    angle->set(&fTail, startSpan);
+    fTail.setFromAngle(angle);
+    SkOpSegment* other = NULL;  // these initializations silence a release build warning
+    SkOpSpan* oStartSpan = NULL;
+    SkOpSpanBase* oEndSpan = NULL;
+    SkOpPtT* ptT = fTail.ptT(), * startPtT = ptT;
+    while ((ptT = ptT->next()) != startPtT) {
+        other = ptT->segment();
+        oStartSpan = ptT->span()->upCastable();
+        if (oStartSpan && oStartSpan->windValue()) {
+            oEndSpan = oStartSpan->next();
             break;
         }
-        oEndIndex = oStartIndex;
-        oStartIndex = other->nextExactSpan(oEndIndex, -1);
-        --spanIndex;
-    } while (oStartIndex < 0 || !other->span(oStartIndex).fWindSum);
-    SkOpAngle& oAngle = other->fAngles.push_back();
-    oAngle.set(other, oStartIndex, oEndIndex);
-    other->setToAngle(oEndIndex, &oAngle);
-    *otherPtr = other;
-    return &oAngle;
-}
-
-SkOpAngle* SkOpSegment::addSingletonAngleUp(SkOpSegment** otherPtr, SkOpAngle** anglePtr) {
-    int endIndex = nextExactSpan(0, 1);
-    SkASSERT(endIndex > 0);
-    SkOpAngle& angle = fAngles.push_back();
-    *anglePtr = &angle;
-    angle.set(this, 0, endIndex);
-    setToAngle(endIndex, &angle);
-    int spanIndex = 0;
-    SkOpSegment* other;
-    int oStartIndex, oEndIndex;
-    do {
-        const SkOpSpan& span = fTs[spanIndex];
-        SkASSERT(span.fT < 1);
-        other = span.fOther;
-        oEndIndex = span.fOtherIndex;
-        oStartIndex = other->nextExactSpan(oEndIndex, -1);
-        if (oStartIndex >= 0 && other->span(oStartIndex).fWindValue) {
+        oEndSpan = ptT->span();
+        oStartSpan = oEndSpan->prev();
+        if (oStartSpan && oStartSpan->windValue()) {
             break;
         }
-        oStartIndex = oEndIndex;
-        oEndIndex = other->nextExactSpan(oStartIndex, 1);
-        ++spanIndex;
-    } while (oEndIndex < 0 || !other->span(oStartIndex).fWindValue);
-    SkOpAngle& oAngle = other->fAngles.push_back();
-    oAngle.set(other, oEndIndex, oStartIndex);
-    other->setFromAngle(oEndIndex, &oAngle);
+    }
+    SkOpAngle* oAngle = SkOpTAllocator<SkOpAngle>::Allocate(allocator);
+    oAngle->set(oStartSpan, oEndSpan);
+    oStartSpan->setToAngle(oAngle);
     *otherPtr = other;
-    return &oAngle;
+    return oAngle;
 }
 
-SkOpAngle* SkOpSegment::addSingletonAngles(int step) {
+SkOpAngle* SkOpSegment::addSingletonAngles(int step, SkChunkAlloc* allocator) {
     SkOpSegment* other;
     SkOpAngle* angle, * otherAngle;
     if (step > 0) {
-        otherAngle = addSingletonAngleUp(&other, &angle);
+        otherAngle = addSingletonAngleUp(&other, &angle, allocator);
     } else {
-        otherAngle = addSingletonAngleDown(&other, &angle);
+        otherAngle = addSingletonAngleDown(&other, &angle, allocator);
     }
     angle->insert(otherAngle);
     return angle;
 }
 
-void SkOpSegment::addStartSpan(int endIndex) {
-    int index = 0;
-    SkOpAngle& angle = fAngles.push_back();
-    angle.set(this, index, endIndex);
-#if DEBUG_ANGLE
-    debugCheckPointsEqualish(index, endIndex);
-#endif
-    setToAngle(endIndex, &angle);
+SkOpAngle* SkOpSegment::addSingletonAngleUp(SkOpSegment** otherPtr, SkOpAngle** anglePtr,
+        SkChunkAlloc* allocator) {
+    SkOpSpanBase* endSpan = fHead.next();
+    SkASSERT(endSpan);
+    SkOpAngle* angle = SkOpTAllocator<SkOpAngle>::Allocate(allocator);
+    *anglePtr = angle;
+    angle->set(&fHead, endSpan);
+    fHead.setToAngle(angle);
+    SkOpSegment* other = NULL;  // these initializations silence a release build warning
+    SkOpSpan* oStartSpan = NULL;
+    SkOpSpanBase* oEndSpan = NULL;
+    SkOpPtT* ptT = fHead.ptT(), * startPtT = ptT;
+    while ((ptT = ptT->next()) != startPtT) {
+        other = ptT->segment();
+        oEndSpan = ptT->span();
+        oStartSpan = oEndSpan->prev();
+        if (oStartSpan && oStartSpan->windValue()) {
+            break;
+        }
+        oStartSpan = oEndSpan->upCastable();
+        if (oStartSpan && oStartSpan->windValue()) {
+            oEndSpan = oStartSpan->next();
+            break;
+        }
+    }
+    SkOpAngle* oAngle = SkOpTAllocator<SkOpAngle>::Allocate(allocator);
+    oAngle->set(oEndSpan, oStartSpan);
+    oEndSpan->setFromAngle(oAngle);
+    *otherPtr = other;
+    return oAngle;
 }
 
-void SkOpSegment::setToAngle(int endIndex, SkOpAngle* angle) {
-    int index = 0;
+SkOpPtT* SkOpSegment::addT(double t, AllowAlias allowAlias, SkChunkAlloc* allocator) {
+    debugValidate();
+    SkPoint pt = this->ptAtT(t);
+    SkOpSpanBase* span = &fHead;
     do {
-        fTs[index].fToAngle = angle;
-    } while (++index < endIndex);
+        SkOpPtT* result = span->ptT();
+        if (t == result->fT) {
+            return result;
+        }
+        if (this->match(result, this, t, pt)) {
+            // see if any existing alias matches segment, pt, and t
+            SkOpPtT* loop = result->next();
+            bool duplicatePt = false;
+            while (loop != result) {
+                bool ptMatch = loop->fPt == pt;
+                if (loop->segment() == this && loop->fT == t && ptMatch) {
+                    return result;
+                }
+                duplicatePt |= ptMatch;
+                loop = loop->next();
+            }
+            if (kNoAlias == allowAlias) {
+                return result;
+            }
+            SkOpPtT* alias = SkOpTAllocator<SkOpPtT>::Allocate(allocator);
+            alias->init(result->span(), t, pt, duplicatePt);
+            result->insert(alias);
+            result->span()->unaligned();
+            this->debugValidate();
+#if DEBUG_ADD_T
+            SkDebugf("%s alias t=%1.9g segID=%d spanID=%d\n",  __FUNCTION__, t,
+                    alias->segment()->debugID(), alias->span()->debugID());
+#endif
+            return alias;
+        }
+        if (t < result->fT) {
+            SkOpSpan* prev = result->span()->prev();
+            SkOpSpan* span = insert(prev, allocator);
+            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
+            return span->ptT();
+        }
+        SkASSERT(span != &fTail);
+    } while ((span = span->upCast()->next()));
+    SkASSERT(0);
+    return NULL;
 }
 
-    // Defer all coincident edge processing until
-    // after normal intersections have been computed
-
-// no need to be tricky; insert in normal T order
-// resolve overlapping ts when considering coincidence later
-
-    // add non-coincident intersection. Resulting edges are sorted in T.
-int SkOpSegment::addT(SkOpSegment* other, const SkPoint& pt, double newT) {
-    SkASSERT(this != other || fVerb == SkPath::kCubic_Verb);
- #if 0  // this needs an even rougher association to be useful
-    SkASSERT(SkDPoint::RoughlyEqual(ptAtT(newT), pt));
- #endif
-    const SkPoint& firstPt = fPts[0];
-    const SkPoint& lastPt = fPts[SkPathOpsVerbToPoints(fVerb)];
-    SkASSERT(newT == 0 || !precisely_zero(newT));
-    SkASSERT(newT == 1 || !precisely_equal(newT, 1));
-    // FIXME: in the pathological case where there is a ton of intercepts,
-    //  binary search?
-    int insertedAt = -1;
-    int tCount = fTs.count();
-    for (int index = 0; index < tCount; ++index) {
-        // OPTIMIZATION: if there are three or more identical Ts, then
-        // the fourth and following could be further insertion-sorted so
-        // that all the edges are clockwise or counterclockwise.
-        // This could later limit segment tests to the two adjacent
-        // neighbors, although it doesn't help with determining which
-        // circular direction to go in.
-        const SkOpSpan& span = fTs[index];
-        if (newT < span.fT) {
-            insertedAt = index;
+// choose a solitary t and pt value; remove aliases; align the opposite ends
+void SkOpSegment::align() {
+    debugValidate();
+    SkOpSpanBase* span = &fHead;
+    if (!span->aligned()) {
+        span->alignEnd(0, fPts[0]);
+    }
+    while ((span = span->upCast()->next())) {
+        if (span == &fTail) {
             break;
         }
-        if (newT == span.fT) {
-            if (pt == span.fPt) {
-                insertedAt = index;
-                break;
-            }
-            if ((pt == firstPt && newT == 0) || (span.fPt == lastPt && newT == 1)) {
-                insertedAt = index;
-                break;
-            }
-        }
+        span->align();
     }
-    SkOpSpan* span;
-    if (insertedAt >= 0) {
-        span = fTs.insert(insertedAt);
-    } else {
-        insertedAt = tCount;
-        span = fTs.append();
+    if (!span->aligned()) {
+        span->alignEnd(1, fPts[SkPathOpsVerbToPoints(fVerb)]);
     }
-    span->fT = newT;
-    span->fOtherT = -1;
-    span->fOther = other;
-    span->fPt = pt;
-#if 0
-    // cubics, for instance, may not be exact enough to satisfy this check (e.g., cubicOp69d)
-    SkASSERT(approximately_equal(xyAtT(newT).fX, pt.fX)
-            && approximately_equal(xyAtT(newT).fY, pt.fY));
-#endif
-    span->fFromAngle = NULL;
-    span->fToAngle = NULL;
-    span->fWindSum = SK_MinS32;
-    span->fOppSum = SK_MinS32;
-    span->fWindValue = 1;
-    span->fOppValue = 0;
-    span->fChased = false;
-    span->fCoincident = false;
-    span->fLoop = false;
-    span->fNear = false;
-    span->fMultiple = false;
-    span->fSmall = false;
-    span->fTiny = false;
-    if ((span->fDone = newT == 1)) {
-        ++fDoneSpans;
+    debugValidate();
+}
+
+bool SkOpSegment::BetweenTs(const SkOpSpanBase* lesser, double testT,
+        const SkOpSpanBase* greater) {
+    if (lesser->t() > greater->t()) {
+        SkTSwap<const SkOpSpanBase*>(lesser, greater);
     }
-    setSpanFlags(pt, newT, span);
-    return insertedAt;
+    return approximately_between(lesser->t(), testT, greater->t());
 }
 
-void SkOpSegment::setSpanFlags(const SkPoint& pt, double newT, SkOpSpan* span) {
-    int less = -1;
-// FIXME: note that this relies on spans being a continguous array
-// find range of spans with nearly the same point as this one
-    // FIXME: SkDPoint::ApproximatelyEqual is better but breaks tests at the moment
-    while (&span[less + 1] - fTs.begin() > 0 && AlmostEqualUlps(span[less].fPt, pt)) {
-        if (fVerb == SkPath::kCubic_Verb) {
-            double tInterval = newT - span[less].fT;
-            double tMid = newT - tInterval / 2;
-            SkDPoint midPt = dcubic_xy_at_t(fPts, tMid);
-            if (!midPt.approximatelyEqual(xyAtT(span))) {
-                break;
-            }
-        }
-        --less;
+void SkOpSegment::calcAngles(SkChunkAlloc* allocator) {
+    bool activePrior = !fHead.isCanceled();
+    if (activePrior && !fHead.simple()) {
+        addStartSpan(allocator);
     }
-    int more = 1;
-    // FIXME: SkDPoint::ApproximatelyEqual is better but breaks tests at the moment
-    while (fTs.end() - &span[more - 1] > 1 && AlmostEqualUlps(span[more].fPt, pt)) {
-        if (fVerb == SkPath::kCubic_Verb) {
-            double tEndInterval = span[more].fT - newT;
-            double tMid = newT - tEndInterval / 2;
-            SkDPoint midEndPt = dcubic_xy_at_t(fPts, tMid);
-            if (!midEndPt.approximatelyEqual(xyAtT(span))) {
-                break;
-            }
+    SkOpSpan* prior = &fHead;
+    SkOpSpanBase* spanBase = fHead.next();
+    while (spanBase != &fTail) {
+        if (activePrior) {
+            SkOpAngle* priorAngle = SkOpTAllocator<SkOpAngle>::Allocate(allocator);
+            priorAngle->set(spanBase, prior);
+            spanBase->setFromAngle(priorAngle);
         }
-        ++more;
-    }
-    ++less;
-    --more;
-    while (more - 1 > less && span[more].fPt == span[more - 1].fPt
-            && span[more].fT == span[more - 1].fT) {
-        --more;
-    }
-    if (less == more) {
-        return;
+        SkOpSpan* span = spanBase->upCast();
+        bool active = !span->isCanceled();
+        SkOpSpanBase* next = span->next();
+        if (active) {
+            SkOpAngle* angle = SkOpTAllocator<SkOpAngle>::Allocate(allocator);
+            angle->set(span, next);
+            span->setToAngle(angle);
+        }
+        activePrior = active;
+        prior = span;
+        spanBase = next;
     }
-    if (precisely_negative(span[more].fT - span[less].fT)) {
-        return;
+    if (activePrior && !fTail.simple()) {
+        addEndSpan(allocator);
     }
-// if the total range of t values is big enough, mark all tiny
-    bool tiny = span[less].fPt == span[more].fPt;
-    int index = less;
-    do {
-        fSmall = span[index].fSmall = true;
-        fTiny |= span[index].fTiny = tiny;
-        if (!span[index].fDone) {
-            span[index].fDone = true;
-            ++fDoneSpans;
-        }
-    } while (++index < more);
-    return;
 }
 
-void SkOpSegment::resetSpanFlags() {
-    fSmall = fTiny = false;
-    fDoneSpans = 0;
-    int start = 0;
-    int last = this->count() - 1;
+void SkOpSegment::checkAngleCoin(SkOpCoincidence* coincidences, SkChunkAlloc* allocator) {
+    SkOpSpanBase* base = &fHead;
+    SkOpSpan* span;
     do {
-        SkOpSpan* startSpan = &this->fTs[start];
-        double startT = startSpan->fT;
-        startSpan->fSmall = startSpan->fTiny = false;  // sets range initial
-        bool terminus = startT == 1;
-        if ((startSpan->fDone = !startSpan->fWindValue | terminus)) {
-            ++fDoneSpans;
-        }
-        ++start;  // range initial + 1
-        if (terminus) {
-            continue;
-        }
-        const SkPoint& pt = startSpan->fPt;
-        int end = start;  // range initial + 1
-        while (end <= last) {
-            const SkOpSpan& endSpan = this->span(end);
-            if (!AlmostEqualUlps(endSpan.fPt, pt)) {
-                break;
-            }
-            if (fVerb == SkPath::kCubic_Verb) {
-                double tMid = (startSpan->fT + endSpan.fT) / 2;
-                SkDPoint midEndPt = dcubic_xy_at_t(fPts, tMid);
-                if (!midEndPt.approximatelyEqual(xyAtT(startSpan))) {
-                    break;
-                }
-            }
-            ++end;
+        SkOpAngle* angle = base->fromAngle();
+        if (angle && angle->fCheckCoincidence) {
+            angle->checkNearCoincidence();
         }
-        if (start == end) {  // end == range final + 1
-            continue;
-        }
-        while (--end >= start) {  // end == range final
-            const SkOpSpan& endSpan = this->span(end);
-            const SkOpSpan& priorSpan = this->span(end - 1);
-            if (endSpan.fPt != priorSpan.fPt || endSpan.fT != priorSpan.fT) {
-                break;  // end == range final + 1
-            }
-        }
-        if (end < start) {  // end == range final + 1
-            continue;
-        }
-        int index = start - 1;  // index == range initial
-        start = end;  // start = range final + 1
-        const SkOpSpan& nextSpan = this->span(end);
-        if (precisely_negative(nextSpan.fT - startSpan->fT)) {
-            while (++index < end) {
-                startSpan = &this->fTs[index];
-                startSpan->fSmall = startSpan->fTiny = false;  // sets range initial + 1
-                if ((startSpan->fDone = !startSpan->fWindValue)) {
-                    ++fDoneSpans;
-                }
-            }
-            continue;
+        if (base->final()) {
+             break;
         }
-        if (!startSpan->fWindValue) {
-            --fDoneSpans;  // added back below
+        span = base->upCast();
+        angle = span->toAngle();
+        if (angle && angle->fCheckCoincidence) {
+            angle->checkNearCoincidence();
         }
-        bool tiny = nextSpan.fPt == startSpan->fPt;
-        do {
-            fSmall = startSpan->fSmall = true;  // sets range initial
-            fTiny |= startSpan->fTiny = tiny;
-            startSpan->fDone = true;
-            ++fDoneSpans;
-            startSpan = &this->fTs[++index];
-        } while (index < end);  // loop through tiny small range end (last)
-    } while (start <= last);
+    } while ((base = span->next()));
 }
 
-// set spans from start to end to decrement by one
-// note this walks other backwards
-// FIXME: there's probably an edge case that can be constructed where
-// two span in one segment are separated by float epsilon on one span but
-// not the other, if one segment is very small. For this
-// case the counts asserted below may or may not be enough to separate the
-// spans. Even if the counts work out, what if the spans aren't correctly
-// sorted? It feels better in such a case to match the span's other span
-// pointer since both coincident segments must contain the same spans.
-// FIXME? It seems that decrementing by one will fail for complex paths that
-// have three or more coincident edges. Shouldn't this subtract the difference
-// between the winding values?
-/*                                      |-->                           |-->
-this     0>>>>1>>>>2>>>>3>>>4      0>>>>1>>>>2>>>>3>>>4      0>>>>1>>>>2>>>>3>>>4
-other         2<<<<1<<<<0               2<<<<1<<<<0               2<<<<1<<<<0
-              ^         ^                 <--|                           <--|
-           startPt    endPt        test/oTest first pos      test/oTest final pos
-*/
-void SkOpSegment::addTCancel(const SkPoint& startPt, const SkPoint& endPt, SkOpSegment* other) {
-    bool binary = fOperand != other->fOperand;
-    int index = 0;
-    while (startPt != fTs[index].fPt) {
-        SkASSERT(index < fTs.count());
-        ++index;
-    }
-    while (index > 0 && precisely_equal(fTs[index].fT, fTs[index - 1].fT)) {
-        --index;
-    }
-    bool oFoundEnd = false;
-    int oIndex = other->fTs.count();
-    while (startPt != other->fTs[--oIndex].fPt) {  // look for startPt match
-        SkASSERT(oIndex > 0);
-    }
-    double oStartT = other->fTs[oIndex].fT;
-    // look for first point beyond match
-    while (startPt == other->fTs[--oIndex].fPt || precisely_equal(oStartT, other->fTs[oIndex].fT)) {
-        if (!oIndex) {
-            return;  // tiny spans may move in the wrong direction
-        }
-    }
-    SkOpSpan* test = &fTs[index];
-    SkOpSpan* oTest = &other->fTs[oIndex];
-    SkSTArray<kOutsideTrackedTCount, SkPoint, true> outsidePts;
-    SkSTArray<kOutsideTrackedTCount, SkPoint, true> oOutsidePts;
-    bool decrement, track, bigger;
-    int originalWindValue;
-    const SkPoint* testPt;
-    const SkPoint* oTestPt;
-    do {
-        SkASSERT(test->fT < 1);
-        SkASSERT(oTest->fT < 1);
-        decrement = test->fWindValue && oTest->fWindValue;
-        track = test->fWindValue || oTest->fWindValue;
-        bigger = test->fWindValue >= oTest->fWindValue;
-        testPt = &test->fPt;
-        double testT = test->fT;
-        oTestPt = &oTest->fPt;
-        double oTestT = oTest->fT;
-        do {
-            if (decrement) {
-                if (binary && bigger) {
-                    test->fOppValue--;
-                } else {
-                    decrementSpan(test);
-                }
-            } else if (track) {
-                TrackOutsidePair(&outsidePts, *testPt, *oTestPt);
-            }
-            SkASSERT(index < fTs.count() - 1);
-            test = &fTs[++index];
-        } while (*testPt == test->fPt || precisely_equal(testT, test->fT));
-        originalWindValue = oTest->fWindValue;
-        do {
-            SkASSERT(oTest->fT < 1);
-            SkASSERT(originalWindValue == oTest->fWindValue);
-            if (decrement) {
-                if (binary && !bigger) {
-                    oTest->fOppValue--;
+// from http://stackoverflow.com/questions/1165647/how-to-determine-if-a-list-of-polygon-points-are-in-clockwise-order
+bool SkOpSegment::clockwise(const SkOpSpanBase* start, const SkOpSpanBase* end, bool* swap) const {
+    SkASSERT(fVerb != SkPath::kLine_Verb);
+    SkPoint edge[4];
+    if (fVerb == SkPath::kCubic_Verb) {
+        double startT = start->t();
+        double endT = end->t();
+        bool flip = startT > endT;
+        SkDCubic cubic;
+        cubic.set(fPts);
+        double inflectionTs[2];
+        int inflections = cubic.findInflections(inflectionTs);
+        for (int index = 0; index < inflections; ++index) {
+            double inflectionT = inflectionTs[index];
+            if (between(startT, inflectionT, endT)) {
+                if (flip) {
+                    if (inflectionT != endT) {
+                        startT = inflectionT;
+                    }
                 } else {
-                    other->decrementSpan(oTest);
+                    if (inflectionT != startT) {
+                        endT = inflectionT;
+                    }
                 }
-            } else if (track) {
-                TrackOutsidePair(&oOutsidePts, *oTestPt, *testPt);
-            }
-            if (!oIndex) {
-                break;
-            }
-            oFoundEnd |= endPt == oTest->fPt;
-            oTest = &other->fTs[--oIndex];
-        } while (*oTestPt == oTest->fPt || precisely_equal(oTestT, oTest->fT));
-    } while (endPt != test->fPt && test->fT < 1);
-    // FIXME: determine if canceled edges need outside ts added
-    if (!oFoundEnd) {
-        for (int oIdx2 = oIndex; oIdx2 >= 0; --oIdx2) {
-            SkOpSpan* oTst2 = &other->fTs[oIdx2];            
-            if (originalWindValue != oTst2->fWindValue) {
-                goto skipAdvanceOtherCancel;
-            }
-            if (!oTst2->fWindValue) {
-                goto skipAdvanceOtherCancel;
-            }
-            if (endPt == other->fTs[oIdx2].fPt) {
-                break;
             }
         }
-        oFoundEnd = endPt == oTest->fPt;
-        do {
-            SkASSERT(originalWindValue == oTest->fWindValue);
-            if (decrement) {
-                if (binary && !bigger) {
-                    oTest->fOppValue--;
-                } else {
-                    other->decrementSpan(oTest);
-                }
-            } else if (track) {
-                TrackOutsidePair(&oOutsidePts, *oTestPt, *testPt);
-            }
-            if (!oIndex) {
-                break;
-            }
-            oTest = &other->fTs[--oIndex];
-            oFoundEnd |= endPt == oTest->fPt;
-        } while (!oFoundEnd || endPt == oTest->fPt);
+        SkDCubic part = cubic.subDivide(startT, endT);
+        for (int index = 0; index < 4; ++index) {
+            edge[index] = part[index].asSkPoint();
+        }
+    } else {
+    subDivide(start, end, edge);
     }
-skipAdvanceOtherCancel:
-    int outCount = outsidePts.count();
-    if (!done() && outCount) {
-        addCancelOutsides(outsidePts[0], outsidePts[1], other);
-        if (outCount > 2) {
-            addCancelOutsides(outsidePts[outCount - 2], outsidePts[outCount - 1], other);
+    bool sumSet = false;
+    int points = SkPathOpsVerbToPoints(fVerb);
+    double sum = (edge[0].fX - edge[points].fX) * (edge[0].fY + edge[points].fY);
+    if (!sumSet) {
+        for (int idx = 0; idx < points; ++idx){
+            sum += (edge[idx + 1].fX - edge[idx].fX) * (edge[idx + 1].fY + edge[idx].fY);
         }
     }
-    if (!other->done() && oOutsidePts.count()) {
-        other->addCancelOutsides(oOutsidePts[0], oOutsidePts[1], this);
+    if (fVerb == SkPath::kCubic_Verb) {
+        SkDCubic cubic;
+        cubic.set(edge);
+        *swap = sum > 0 && !cubic.monotonicInY();
+    } else {
+        SkDQuad quad;
+        quad.set(edge);
+        *swap = sum > 0 && !quad.monotonicInY();
     }
-    setCoincidentRange(startPt, endPt, other);
-    other->setCoincidentRange(startPt, endPt, this);
-}
-
-int SkOpSegment::addSelfT(const SkPoint& pt, double newT) {
-    // if the tail nearly intersects itself but not quite, the caller records this separately
-    int result = addT(this, pt, newT);
-    SkOpSpan* span = &fTs[result];
-    fLoop = span->fLoop = true;
-    return result;
+    return sum <= 0;
 }
 
-// find the starting or ending span with an existing loop of angles
-// FIXME? replicate for all identical starting/ending spans?
-// OPTIMIZE? remove the spans pointing to windValue==0 here or earlier?
-// FIXME? assert that only one other span has a valid windValue or oppValue
-void SkOpSegment::addSimpleAngle(int index) {
-    SkOpSpan* span = &fTs[index];
-    int idx;
-    int start, end;
-    if (span->fT == 0) {
-        idx = 0;
-        span = &fTs[0];
-        do {
-            if (span->fToAngle) {
-                SkASSERT(span->fToAngle->loopCount() == 2);
-                SkASSERT(!span->fFromAngle);
-                span->fFromAngle = span->fToAngle->next();
-                return;
-            }
-            span = &fTs[++idx];
-        } while (span->fT == 0);
-        SkASSERT(!fTs[0].fTiny && fTs[idx].fT > 0);
-        addStartSpan(idx);
-        start = 0;
-        end = idx;
-    } else {
-        idx = count() - 1;
-        span = &fTs[idx];
-        do {
-            if (span->fFromAngle) {
-                SkASSERT(span->fFromAngle->loopCount() == 2);
-                SkASSERT(!span->fToAngle);
-                span->fToAngle = span->fFromAngle->next();
-                return;
-            }
-            span = &fTs[--idx];
-        } while (span->fT == 1);
-        SkASSERT(!fTs[idx].fTiny && fTs[idx].fT < 1);
-        addEndSpan(++idx);
-        start = idx;
-        end = count();
-    }
-    SkOpSegment* other;
-    SkOpSpan* oSpan;
-    index = start;
-    do {
-        span = &fTs[index];
-        other = span->fOther;
-        int oFrom = span->fOtherIndex;
-        oSpan = &other->fTs[oFrom];
-        if (oSpan->fT < 1 && oSpan->fWindValue) {
-            break;
-        }
-        if (oSpan->fT == 0) {
-            continue;
-        }
-        oFrom = other->nextExactSpan(oFrom, -1);
-        SkOpSpan* oFromSpan = &other->fTs[oFrom];
-        SkASSERT(oFromSpan->fT < 1);
-        if (oFromSpan->fWindValue) {
-            break;
+void SkOpSegment::ComputeOneSum(const SkOpAngle* baseAngle, SkOpAngle* nextAngle,
+        SkOpAngle::IncludeType includeType) {
+    const 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()) {
+            SkTSwap<int>(sumMiWinding, sumSuWinding);
         }
-    } while (++index < end);
-    SkOpAngle* angle, * oAngle;
-    if (span->fT == 0) {
-        SkASSERT(span->fOtherIndex - 1 >= 0);
-        SkASSERT(span->fOtherT == 1);
-        SkDEBUGCODE(int oPriorIndex = other->nextExactSpan(span->fOtherIndex, -1));
-        SkDEBUGCODE(const SkOpSpan& oPrior = other->span(oPriorIndex));
-        SkASSERT(!oPrior.fTiny && oPrior.fT < 1);
-        other->addEndSpan(span->fOtherIndex);
-        angle = span->fToAngle;
-        oAngle = oSpan->fFromAngle;
+    }
+    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 {
-        SkASSERT(span->fOtherIndex + 1 < other->count());
-        SkASSERT(span->fOtherT == 0);
-        SkASSERT(!oSpan->fTiny && (other->fTs[span->fOtherIndex + 1].fT > 0
-                || (other->fTs[span->fOtherIndex + 1].fFromAngle == NULL
-                && other->fTs[span->fOtherIndex + 1].fToAngle == NULL)));
-        int oIndex = 1;
-        do {
-            const SkOpSpan& osSpan = other->span(oIndex);
-            if (osSpan.fFromAngle || osSpan.fT > 0) {
-                break;
-            }
-            ++oIndex;
-            SkASSERT(oIndex < other->count());
-        } while (true);
-        other->addStartSpan(oIndex);
-        angle = span->fFromAngle;
-        oAngle = oSpan->fToAngle;
+        nextSegment->setUpWindings(nextAngle->start(), nextAngle->end(), &sumMiWinding,
+                &maxWinding, &sumWinding);
+        last = nextSegment->markAngle(maxWinding, sumWinding, nextAngle);
     }
-    angle->insert(oAngle);
+    nextAngle->setLastMarked(last);
 }
 
-void SkOpSegment::alignMultiples(SkTDArray<AlignedSpan>* alignedArray) {
-    debugValidate();
-    int count = this->count();
-    for (int index = 0; index < count; ++index) {
-        SkOpSpan& span = fTs[index];
-        if (!span.fMultiple) {
-            continue;
-        }
-        int end = nextExactSpan(index, 1);
-        SkASSERT(end > index + 1);
-        const SkPoint& thisPt = span.fPt;
-        while (index < end - 1) {
-            SkOpSegment* other1 = span.fOther;
-            int oCnt = other1->count();
-            for (int idx2 = index + 1; idx2 < end; ++idx2) {
-                SkOpSpan& span2 = fTs[idx2];
-                SkOpSegment* other2 = span2.fOther;
-                for (int oIdx = 0; oIdx < oCnt; ++oIdx) {
-                    SkOpSpan& oSpan = other1->fTs[oIdx];
-                    if (oSpan.fOther != other2) {
-                        continue;
-                    }
-                    if (oSpan.fPt == thisPt) {
-                        goto skipExactMatches;
-                    }
-                }
-                for (int oIdx = 0; oIdx < oCnt; ++oIdx) {
-                    SkOpSpan& oSpan = other1->fTs[oIdx];
-                    if (oSpan.fOther != other2) {
-                        continue;
-                    }
-                    if (SkDPoint::RoughlyEqual(oSpan.fPt, thisPt)) {
-                        SkOpSpan& oSpan2 = other2->fTs[oSpan.fOtherIndex];
-                        if (zero_or_one(span.fOtherT) || zero_or_one(oSpan.fT)
-                                || zero_or_one(span2.fOtherT) || zero_or_one(oSpan2.fT)) {
-                            return;
-                        }
-                        if (!way_roughly_equal(span.fOtherT, oSpan.fT)
-                                || !way_roughly_equal(span2.fOtherT, oSpan2.fT)
-                                || !way_roughly_equal(span2.fOtherT, oSpan.fOtherT)
-                                || !way_roughly_equal(span.fOtherT, oSpan2.fOtherT)) {
-                            return;
-                        }
-                        alignSpan(thisPt, span.fOtherT, other1, span2.fOtherT,
-                                other2, &oSpan, alignedArray);
-                        alignSpan(thisPt, span2.fOtherT, other2, span.fOtherT, 
-                                other1, &oSpan2, alignedArray);
-                        break;
-                    }
-                }
-        skipExactMatches:
-                ;
-            }
-            ++index;
-        }
-    }
-    debugValidate();
-}
-
-void SkOpSegment::alignRange(int lower, int upper,
-        const SkOpSegment* other, int oLower, int oUpper) {
-    for (int oIndex = oLower; oIndex <= oUpper; ++oIndex) {
-        const SkOpSpan& oSpan = other->span(oIndex);
-        const SkOpSegment* oOther = oSpan.fOther;
-        if (oOther == this) {
-            continue;
-        }
-        SkOpSpan* matchSpan;
-        int matchIndex;
-        const SkOpSpan* refSpan;
-        for (int iIndex = lower; iIndex <= upper; ++iIndex) {
-            const SkOpSpan& iSpan = this->span(iIndex);
-            const SkOpSegment* iOther = iSpan.fOther;
-            if (iOther == other) {
-                continue;
-            }
-            if (iOther == oOther) {
-                goto nextI;
-            }
-        }
-        {
-            // oSpan does not have a match in this
-            int iCount = this->count();
-            const SkOpSpan* iMatch = NULL;
-            double iMatchTDiff;
-            matchIndex = -1;
-            for (int iIndex = 0; iIndex < iCount; ++iIndex) {
-                const SkOpSpan& iSpan = this->span(iIndex);
-                const SkOpSegment* iOther = iSpan.fOther;
-                if (iOther != oOther) {
-                    continue;
-                }
-                double testTDiff = fabs(iSpan.fOtherT - oSpan.fOtherT);
-                if (!iMatch || testTDiff < iMatchTDiff) {
-                    matchIndex = iIndex;
-                    iMatch = &iSpan;
-                    iMatchTDiff = testTDiff;
-                }
-            }
-            if (matchIndex < 0) {
-                continue;  // the entry is missing, & will be picked up later (FIXME: fix it here?)
-            }
-            matchSpan = &this->fTs[matchIndex];
-            refSpan = &this->span(lower);
-            if (!SkDPoint::ApproximatelyEqual(matchSpan->fPt, refSpan->fPt)) {
-                goto nextI;
-            }
-            if (matchIndex != lower - 1 && matchIndex != upper + 1) {
-                // the consecutive spans need to be rearranged to get the missing one close 
-                continue;  // FIXME: more work to do
-            }
-        }
-        {
-            this->fixOtherTIndex();
-            SkScalar newT;
-            if (matchSpan->fT != 0 && matchSpan->fT != 1) {
-                newT = matchSpan->fT = refSpan->fT;
-                matchSpan->fOther->fTs[matchSpan->fOtherIndex].fOtherT = refSpan->fT;
-            } else {  // leave span at the start or end there and adjust the neighbors
-                newT = matchSpan->fT;
-                for (int iIndex = lower; iIndex <= upper; ++iIndex) {
-                    matchSpan = &this->fTs[iIndex];
-                    matchSpan->fT = newT;
-                    matchSpan->fOther->fTs[matchSpan->fOtherIndex].fOtherT = newT;
-                }
-            }
-            this->resetSpanFlags();  // fix up small / tiny / done
-            // align ts of other ranges with adjacent spans that match the aligned points
-            lower = SkTMin(lower, matchIndex);
-            while (lower > 0) {
-                const SkOpSpan& span = this->span(lower - 1);
-                if (span.fT != newT) {
-                    break;
-                }
-                --lower;
-            }
-            upper = SkTMax(upper, matchIndex);
-            int last = this->count() - 1;
-            while (upper < last) {
-                const SkOpSpan& span = this->span(upper + 1);
-                if (span.fT != newT) {
-                    break;
-                }
-                ++upper;
-            }
-            for (int iIndex = lower; iIndex <= upper; ++iIndex) {
-                const SkOpSpan& span = this->span(iIndex);
-                SkOpSegment* aOther = span.fOther;
-                int aLower = span.fOtherIndex;
-                SkScalar aT = span.fOtherT;
-                bool aResetFlags = false;
-                while (aLower > 0) {
-                    SkOpSpan* aSpan = &aOther->fTs[aLower - 1];
-                    for (int iIndex = lower; iIndex <= upper; ++iIndex) {
-                        if (aSpan->fPt == this->fTs[iIndex].fPt) {
-                            goto matchFound;
-                        }
-                    }
-                    break;
-            matchFound:
-                    --aLower;
-                }
-                int aUpper = span.fOtherIndex;
-                int aLast = aOther->count() - 1;
-                while (aUpper < aLast) {
-                    SkOpSpan* aSpan = &aOther->fTs[aUpper + 1];
-                    for (int iIndex = lower; iIndex <= upper; ++iIndex) {
-                        if (aSpan->fPt == this->fTs[iIndex].fPt) {
-                            goto matchFound2;
-                        }
-                    }
-                    break;
-            matchFound2:
-                    ++aUpper;
-                }
-                if (aOther->fTs[aLower].fT == 0) {
-                    aT = 0;
-                } else if (aOther->fTs[aUpper].fT == 1) {
-                    aT = 1;
-                }
-                bool aFixed = false;
-                for (int aIndex = aLower; aIndex <= aUpper; ++aIndex) {
-                    SkOpSpan* aSpan = &aOther->fTs[aIndex];
-                    if (aSpan->fT == aT) {
-                        continue;
-                    }
-                    SkASSERT(way_roughly_equal(aSpan->fT, aT));
-                    if (!aFixed) {
-                        aOther->fixOtherTIndex();
-                        aFixed = true;
-                    }
-                    aSpan->fT = aT;
-                    aSpan->fOther->fTs[aSpan->fOtherIndex].fOtherT = aT;
-                    aResetFlags = true;
-                }
-                if (aResetFlags) {
-                    aOther->resetSpanFlags();
-                }
-            }
-        }
-nextI: ;
-    }
-}
-
-void SkOpSegment::alignSpan(const SkPoint& newPt, double newT, const SkOpSegment* other,
-        double otherT, const SkOpSegment* other2, SkOpSpan* oSpan,
-        SkTDArray<AlignedSpan>* alignedArray) {
-    AlignedSpan* aligned = alignedArray->append();
-    aligned->fOldPt = oSpan->fPt;
-    aligned->fPt = newPt;
-    aligned->fOldT = oSpan->fT;
-    aligned->fT = newT;
-    aligned->fSegment = this;  // OPTIMIZE: may be unused, can remove
-    aligned->fOther1 = other;
-    aligned->fOther2 = other2;
-    SkASSERT(SkDPoint::RoughlyEqual(oSpan->fPt, newPt));
-    oSpan->fPt = newPt;
-//    SkASSERT(way_roughly_equal(oSpan->fT, newT));
-    oSpan->fT = newT;
-//    SkASSERT(way_roughly_equal(oSpan->fOtherT, otherT));
-    oSpan->fOtherT = otherT;
-}
-
-bool SkOpSegment::alignSpan(int index, double thisT, const SkPoint& thisPt) {
-    bool aligned = false;
-    SkOpSpan* span = &fTs[index];
-    SkOpSegment* other = span->fOther;
-    int oIndex = span->fOtherIndex;
-    SkOpSpan* oSpan = &other->fTs[oIndex];
-    if (span->fT != thisT) {
-        span->fT = thisT;
-        oSpan->fOtherT = thisT;
-        aligned = true;
-    }
-    if (span->fPt != thisPt) {
-        span->fPt = thisPt;
-        oSpan->fPt = thisPt;
-        aligned = true;
-    }
-    double oT = oSpan->fT;
-    if (oT == 0) {
-        return aligned;
-    }
-    int oStart = other->nextSpan(oIndex, -1) + 1;
-    oSpan = &other->fTs[oStart];
-    int otherIndex = oStart;
-    if (oT == 1) {
-        if (aligned) {
-            while (oSpan->fPt == thisPt && oSpan->fT != 1) {
-                oSpan->fTiny = true;
-                ++oSpan;
-            }
-        }
-        return aligned;
-    }
-    oT = oSpan->fT;
-    int oEnd = other->nextSpan(oIndex, 1);
-    bool oAligned = false;
-    if (oSpan->fPt != thisPt) {
-        oAligned |= other->alignSpan(oStart, oT, thisPt);
-    }
-    while (++otherIndex < oEnd) {
-        SkOpSpan* oNextSpan = &other->fTs[otherIndex];
-        if (oNextSpan->fT != oT || oNextSpan->fPt != thisPt) {
-            oAligned |= other->alignSpan(otherIndex, oT, thisPt);
-        }
-    }
-    if (oAligned) {
-        other->alignSpanState(oStart, oEnd);
-    }
-    return aligned;
-}
-
-void SkOpSegment::alignSpanState(int start, int end) {
-    SkOpSpan* lastSpan = &fTs[--end];
-    bool allSmall = lastSpan->fSmall;
-    bool allTiny = lastSpan->fTiny;
-    bool allDone = lastSpan->fDone;
-    SkDEBUGCODE(int winding = lastSpan->fWindValue);
-    SkDEBUGCODE(int oppWinding = lastSpan->fOppValue);
-    int index = start;
-    while (index < end) {
-        SkOpSpan* span = &fTs[index];
-        span->fSmall = allSmall;
-        span->fTiny = allTiny;
-        if (span->fDone != allDone) {
-            span->fDone = allDone;
-            fDoneSpans += allDone ? 1 : -1;
-        }
-        SkASSERT(span->fWindValue == winding);
-        SkASSERT(span->fOppValue == oppWinding);
-        ++index;
-    }
-}
-
-void SkOpSegment::blindCancel(const SkCoincidence& coincidence, SkOpSegment* other) {
-    bool binary = fOperand != other->fOperand;
-    int index = 0;
-    int last = this->count();
-    do {
-        SkOpSpan& span = this->fTs[--last];
-        if (span.fT != 1 && !span.fSmall) {
-            break;
-        }
-        span.fCoincident = true;
-    } while (true);
-    int oIndex = other->count();
-    do {
-        SkOpSpan& oSpan = other->fTs[--oIndex];
-        if (oSpan.fT != 1 && !oSpan.fSmall) {
-            break;
-        }
-        oSpan.fCoincident = true;
-    } while (true);
-    do {
-        SkOpSpan* test = &this->fTs[index];
-        int baseWind = test->fWindValue;
-        int baseOpp = test->fOppValue;
-        int endIndex = index;
-        while (++endIndex <= last) {
-            SkOpSpan* endSpan = &this->fTs[endIndex];
-            SkASSERT(endSpan->fT < 1);
-            if (endSpan->fWindValue != baseWind || endSpan->fOppValue != baseOpp) {
-                break;
-            }
-            endSpan->fCoincident = true;
-        }
-        SkOpSpan* oTest = &other->fTs[oIndex];
-        int oBaseWind = oTest->fWindValue;
-        int oBaseOpp = oTest->fOppValue;
-        int oStartIndex = oIndex;
-        while (--oStartIndex >= 0) {
-            SkOpSpan* oStartSpan = &other->fTs[oStartIndex];
-            if (oStartSpan->fWindValue != oBaseWind || oStartSpan->fOppValue != oBaseOpp) {
-                break;
-            }
-            oStartSpan->fCoincident = true;
-        }
-        bool decrement = baseWind && oBaseWind;
-        bool bigger = baseWind >= oBaseWind;
-        do {
-            SkASSERT(test->fT < 1);
-            if (decrement) {
-                if (binary && bigger) {
-                    test->fOppValue--;
-                } else {
-                    decrementSpan(test);
-                }
-            }
-            test->fCoincident = true;
-            test = &fTs[++index];
-        } while (index < endIndex);
-        do {
-            SkASSERT(oTest->fT < 1);
-            if (decrement) {
-                if (binary && !bigger) {
-                    oTest->fOppValue--;
-                } else {
-                    other->decrementSpan(oTest);
-                }
-            }
-            oTest->fCoincident = true;
-            oTest = &other->fTs[--oIndex];
-        } while (oIndex > oStartIndex);
-    } while (index <= last && oIndex >= 0);
-    SkASSERT(index > last);
-    SkASSERT(oIndex < 0);
-}
-
-void SkOpSegment::blindCoincident(const SkCoincidence& coincidence, SkOpSegment* other) {
-    bool binary = fOperand != other->fOperand;
-    int index = 0;
-    int last = this->count();
-    do {
-        SkOpSpan& span = this->fTs[--last];
-        if (span.fT != 1 && !span.fSmall) {
-            break;
-        }
-        span.fCoincident = true;
-    } while (true);
-    int oIndex = 0;
-    int oLast = other->count();
-    do {
-        SkOpSpan& oSpan = other->fTs[--oLast];
-        if (oSpan.fT != 1 && !oSpan.fSmall) {
-            break;
-        }
-        oSpan.fCoincident = true;
-    } while (true);
-    do {
-        SkOpSpan* test = &this->fTs[index];
-        int baseWind = test->fWindValue;
-        int baseOpp = test->fOppValue;
-        int endIndex = index;
-        SkOpSpan* endSpan;
-        while (++endIndex <= last) {
-            endSpan = &this->fTs[endIndex];
-            SkASSERT(endSpan->fT < 1);
-            if (endSpan->fWindValue != baseWind || endSpan->fOppValue != baseOpp) {
-                break;
-            }
-            endSpan->fCoincident = true;
-        }
-        SkOpSpan* oTest = &other->fTs[oIndex];
-        int oBaseWind = oTest->fWindValue;
-        int oBaseOpp = oTest->fOppValue;
-        int oEndIndex = oIndex;
-        SkOpSpan* oEndSpan;
-        while (++oEndIndex <= oLast) {
-            oEndSpan = &this->fTs[oEndIndex];
-            SkASSERT(oEndSpan->fT < 1);
-            if (oEndSpan->fWindValue != oBaseWind || oEndSpan->fOppValue != oBaseOpp) {
-                break;
-            }
-            oEndSpan->fCoincident = true;
-        }
-        // consolidate the winding count even if done
-        if ((test->fWindValue || test->fOppValue) && (oTest->fWindValue || oTest->fOppValue)) {
-            if (!binary || test->fWindValue + oTest->fOppValue >= 0) {
-                bumpCoincidentBlind(binary, index, endIndex);
-                other->bumpCoincidentOBlind(oIndex, oEndIndex);
-            } else {
-                other->bumpCoincidentBlind(binary, oIndex, oEndIndex);
-                bumpCoincidentOBlind(index, endIndex);
-            }
-        }
-        index = endIndex;
-        oIndex = oEndIndex;
-    } while (index <= last && oIndex <= oLast);
-    SkASSERT(index > last);
-    SkASSERT(oIndex > oLast);
-}
-
-void SkOpSegment::bumpCoincidentBlind(bool binary, int index, int endIndex) {
-    const SkOpSpan& oTest = fTs[index];
-    int oWindValue = oTest.fWindValue;
-    int oOppValue = oTest.fOppValue;
-    if (binary) {
-        SkTSwap<int>(oWindValue, oOppValue);
-    }
-    do {
-        (void) bumpSpan(&fTs[index], oWindValue, oOppValue);
-    } while (++index < endIndex);
-}
-
-bool SkOpSegment::bumpCoincidentThis(const SkOpSpan& oTest, bool binary, int* indexPtr,
-        SkTArray<SkPoint, true>* outsideTs) {
-    int index = *indexPtr;
-    int oWindValue = oTest.fWindValue;
-    int oOppValue = oTest.fOppValue;
+void SkOpSegment::ComputeOneSumReverse(const SkOpAngle* baseAngle, SkOpAngle* nextAngle,
+        SkOpAngle::IncludeType includeType) {
+    const SkOpSegment* baseSegment = baseAngle->segment();
+    int sumMiWinding = baseSegment->updateWinding(baseAngle);
+    int sumSuWinding;
+    bool binary = includeType >= SkOpAngle::kBinarySingle;
     if (binary) {
-        SkTSwap<int>(oWindValue, oOppValue);
-    }
-    SkOpSpan* const test = &fTs[index];
-    SkOpSpan* end = test;
-    const SkPoint& oStartPt = oTest.fPt;
-    do {
-        if (end->fDone && !end->fTiny && !end->fSmall) {  // extremely large paths trigger this
-            return false;
-        }
-        if (bumpSpan(end, oWindValue, oOppValue)) {
-            TrackOutside(outsideTs, oStartPt);
-        }
-        end = &fTs[++index];
-    } while ((end->fPt == test->fPt || precisely_equal(end->fT, test->fT)) && end->fT < 1);
-    *indexPtr = index;
-    return true;
-}
-
-void SkOpSegment::bumpCoincidentOBlind(int index, int endIndex) {
-    do {
-        zeroSpan(&fTs[index]);
-    } while (++index < endIndex);
-}
-
-// because of the order in which coincidences are resolved, this and other
-// may not have the same intermediate points. Compute the corresponding
-// intermediate T values (using this as the master, other as the follower)
-// and walk other conditionally -- hoping that it catches up in the end
-bool SkOpSegment::bumpCoincidentOther(const SkOpSpan& test, int* oIndexPtr,
-        SkTArray<SkPoint, true>* oOutsidePts, const SkPoint& oEndPt) {
-    int oIndex = *oIndexPtr;
-    SkOpSpan* const oTest = &fTs[oIndex];
-    SkOpSpan* oEnd = oTest;
-    const SkPoint& oStartPt = oTest->fPt;
-    double oStartT = oTest->fT;
-#if 0  // FIXME : figure out what disabling this breaks
-    const SkPoint& startPt = test.fPt;
-    // this is always true since oEnd == oTest && oStartPt == oTest->fPt -- find proper condition
-    if (oStartPt == oEnd->fPt || precisely_equal(oStartT, oEnd->fT)) {
-        TrackOutside(oOutsidePts, startPt);
-    }
-#endif
-    bool foundEnd = false;
-    while (oStartPt == oEnd->fPt || precisely_equal(oStartT, oEnd->fT)) {
-        foundEnd |= oEndPt == oEnd->fPt;
-        zeroSpan(oEnd);
-        oEnd = &fTs[++oIndex];
-    }
-    *oIndexPtr = oIndex;
-    return foundEnd;
-}
-
-// FIXME: need to test this case:
-// contourA has two segments that are coincident
-// contourB has two segments that are coincident in the same place
-// each ends up with +2/0 pairs for winding count
-// since logic below doesn't transfer count (only increments/decrements) can this be
-// resolved to +4/0 ?
-
-// set spans from start to end to increment the greater by one and decrement
-// the lesser
-bool SkOpSegment::addTCoincident(const SkPoint& startPt, const SkPoint& endPt, double endT,
-        SkOpSegment* other) {
-    bool binary = fOperand != other->fOperand;
-    int index = 0;
-    while (startPt != fTs[index].fPt) {
-        SkASSERT(index < fTs.count());
-        ++index;
-    }
-    double startT = fTs[index].fT;
-    while (index > 0 && precisely_equal(fTs[index - 1].fT, startT)) {
-        --index;
-    }
-    int oIndex = 0;
-    while (startPt != other->fTs[oIndex].fPt) {
-        SkASSERT(oIndex < other->fTs.count());
-        ++oIndex;
-    }
-    double oStartT = other->fTs[oIndex].fT;
-    while (oIndex > 0 && precisely_equal(other->fTs[oIndex - 1].fT, oStartT)) {
-        --oIndex;
-    }
-    SkSTArray<kOutsideTrackedTCount, SkPoint, true> outsidePts;
-    SkSTArray<kOutsideTrackedTCount, SkPoint, true> oOutsidePts;
-    SkOpSpan* test = &fTs[index];
-    const SkPoint* testPt = &test->fPt;
-    double testT = test->fT;
-    SkOpSpan* oTest = &other->fTs[oIndex];
-    const SkPoint* oTestPt = &oTest->fPt;
-    // paths with extreme data will fail this test and eject out of pathops altogether later on
-    // SkASSERT(AlmostEqualUlps(*testPt, *oTestPt));
-    do {
-        SkASSERT(test->fT < 1);
-        if (oTest->fT == 1) {
-            // paths with extreme data may be so mismatched that we fail here
-            return false;
-        }
-
-        // consolidate the winding count even if done
-        bool foundEnd = false;
-        if ((test->fWindValue == 0 && test->fOppValue == 0)
-                || (oTest->fWindValue == 0 && oTest->fOppValue == 0)) {
-            SkDEBUGCODE(int firstWind = test->fWindValue);
-            SkDEBUGCODE(int firstOpp = test->fOppValue);
-            do {
-                SkASSERT(firstWind == fTs[index].fWindValue);
-                SkASSERT(firstOpp == fTs[index].fOppValue);
-                ++index;
-                SkASSERT(index < fTs.count());
-            } while (*testPt == fTs[index].fPt);
-            SkDEBUGCODE(firstWind = oTest->fWindValue);
-            SkDEBUGCODE(firstOpp = oTest->fOppValue);
-            do {
-                SkASSERT(firstWind == other->fTs[oIndex].fWindValue);
-                SkASSERT(firstOpp == other->fTs[oIndex].fOppValue);
-                ++oIndex;
-                SkASSERT(oIndex < other->fTs.count());
-            } while (*oTestPt == other->fTs[oIndex].fPt);
-        } else {
-            if (!binary || test->fWindValue + oTest->fOppValue >= 0) {
-                if (!bumpCoincidentThis(*oTest, binary, &index, &outsidePts)) {
-                    return false;
-                }
-                foundEnd = other->bumpCoincidentOther(*test, &oIndex, &oOutsidePts, endPt);
-            } else {
-                if (!other->bumpCoincidentThis(*test, binary, &oIndex, &oOutsidePts)) {
-                    return false;
-                }
-                foundEnd = bumpCoincidentOther(*oTest, &index, &outsidePts, endPt);
-            }
-        }
-        test = &fTs[index];
-        testPt = &test->fPt;
-        testT = test->fT;
-        oTest = &other->fTs[oIndex];
-        oTestPt = &oTest->fPt;
-        if (endPt == *testPt || precisely_equal(endT, testT)) {
-            break;
-        }
-        if (0 && foundEnd) {  // FIXME: this is likely needed but wait until a test case triggers it
-            break;
-        }
-//        SkASSERT(AlmostEqualUlps(*testPt, *oTestPt));
-    } while (endPt != *oTestPt);
-    // in rare cases, one may have ended before the other
-    if (endPt != *testPt && !precisely_equal(endT, testT)) {
-        int lastWind = test[-1].fWindValue;
-        int lastOpp = test[-1].fOppValue;
-        bool zero = lastWind == 0 && lastOpp == 0;
-        do {
-            if (test->fWindValue || test->fOppValue) {
-                test->fWindValue = lastWind;
-                test->fOppValue = lastOpp;
-                if (zero) {
-                    SkASSERT(!test->fDone);
-                    test->fDone = true;
-                    ++fDoneSpans;
-                }
-            }
-            test = &fTs[++index];
-            testPt = &test->fPt;
-        } while (endPt != *testPt);
-    }
-    if (endPt != *oTestPt) {
-        // look ahead to see if zeroing more spans will allows us to catch up
-        int oPeekIndex = oIndex;
-        bool success = true;
-        SkOpSpan* oPeek;
-        int oCount = other->count();
-        do {
-            oPeek = &other->fTs[oPeekIndex];
-            if (++oPeekIndex == oCount) {
-                success = false;
-                break;
-            }
-        } while (endPt != oPeek->fPt);
-        if (success) {
-            // make sure the matching point completes the coincidence span
-            success = false;
-            do {
-                if (oPeek->fOther == this) {
-                    success = true;
-                    break;
-                }
-                if (++oPeekIndex == oCount) {
-                    break;
-                }
-                oPeek = &other->fTs[oPeekIndex];
-            } while (endPt == oPeek->fPt);
-        }
-        if (success) {
-            do {
-                if (!binary || test->fWindValue + oTest->fOppValue >= 0) {
-                    if (other->bumpCoincidentOther(*test, &oIndex, &oOutsidePts, endPt)) {
-                        break;
-                    }
-                } else {
-                    if (!other->bumpCoincidentThis(*test, binary, &oIndex, &oOutsidePts)) {
-                        return false;
-                    }
-                }
-                oTest = &other->fTs[oIndex];
-                oTestPt = &oTest->fPt;
-            } while (endPt != *oTestPt);
-        }
-    }
-    int outCount = outsidePts.count();
-    if (!done() && outCount) {
-        addCoinOutsides(outsidePts[0], endPt, other);
-    }
-    if (!other->done() && oOutsidePts.count()) {
-        other->addCoinOutsides(oOutsidePts[0], endPt, this);
-    }
-    setCoincidentRange(startPt, endPt, other);
-    other->setCoincidentRange(startPt, endPt, this);
-    return true;
-}
-
-// FIXME: this doesn't prevent the same span from being added twice
-// fix in caller, SkASSERT here?
-// FIXME: this may erroneously reject adds for cubic loops
-const SkOpSpan* SkOpSegment::addTPair(double t, SkOpSegment* other, double otherT, bool borrowWind,
-        const SkPoint& pt, const SkPoint& pt2) {
-    int tCount = fTs.count();
-    for (int tIndex = 0; tIndex < tCount; ++tIndex) {
-        const SkOpSpan& span = fTs[tIndex];
-        if (!approximately_negative(span.fT - t)) {
-            break;
-        }
-        if (span.fOther == other) {
-            bool tsMatch = approximately_equal(span.fT, t);
-            bool otherTsMatch = approximately_equal(span.fOtherT, otherT);
-            // FIXME: add cubic loop detecting logic here
-            // if fLoop bit is set on span, that could be enough if addOtherT copies the bit
-            // or if a new bit is added ala fOtherLoop
-            if (tsMatch || otherTsMatch) {
-#if DEBUG_ADD_T_PAIR
-                SkDebugf("%s addTPair duplicate this=%d %1.9g other=%d %1.9g\n",
-                        __FUNCTION__, fID, t, other->fID, otherT);
-#endif
-                return NULL;
-            }
-        }
-    }
-    int oCount = other->count();
-    for (int oIndex = 0; oIndex < oCount; ++oIndex) {
-        const SkOpSpan& oSpan = other->span(oIndex);
-        if (!approximately_negative(oSpan.fT - otherT)) {
-            break;
-        }
-        if (oSpan.fOther == this) {
-            bool otherTsMatch = approximately_equal(oSpan.fT, otherT);
-            bool tsMatch = approximately_equal(oSpan.fOtherT, t);
-            if (otherTsMatch || tsMatch) {
-#if DEBUG_ADD_T_PAIR
-                SkDebugf("%s addTPair other duplicate this=%d %1.9g other=%d %1.9g\n",
-                        __FUNCTION__, fID, t, other->fID, otherT);
-#endif
-                return NULL;
-            }
-        }
-    }
-#if DEBUG_ADD_T_PAIR
-    SkDebugf("%s addTPair this=%d %1.9g other=%d %1.9g\n",
-            __FUNCTION__, fID, t, other->fID, otherT);
-#endif
-    SkASSERT(other != this);
-    int insertedAt = addT(other, pt, t);
-    int otherInsertedAt = other->addT(this, pt2, otherT);
-    this->addOtherT(insertedAt, otherT, otherInsertedAt);
-    other->addOtherT(otherInsertedAt, t, insertedAt);
-    this->matchWindingValue(insertedAt, t, borrowWind);
-    other->matchWindingValue(otherInsertedAt, otherT, borrowWind);
-    SkOpSpan& span = this->fTs[insertedAt];
-    if (pt != pt2) {
-        span.fNear = true;
-        SkOpSpan& oSpan = other->fTs[otherInsertedAt];
-        oSpan.fNear = true;
-    }
-    // if the newly inserted spans match a neighbor on one but not the other, make them agree
-    int lower = this->nextExactSpan(insertedAt, -1) + 1;
-    int upper = this->nextExactSpan(insertedAt, 1) - 1;
-    if (upper < 0) {
-        upper = this->count() - 1;
-    }
-    int oLower = other->nextExactSpan(otherInsertedAt, -1) + 1;
-    int oUpper = other->nextExactSpan(otherInsertedAt, 1) - 1;
-    if (oUpper < 0) {
-        oUpper = other->count() - 1;
-    }
-    if (lower == upper && oLower == oUpper) {
-        return &span;
-    }
-#if DEBUG_CONCIDENT
-    SkDebugf("%s id=%d lower=%d upper=%d other=%d oLower=%d oUpper=%d\n", __FUNCTION__,
-            debugID(), lower, upper, other->debugID(), oLower, oUpper);
-#endif
-    // find the nearby spans in one range missing in the other
-    this->alignRange(lower, upper, other, oLower, oUpper);
-    other->alignRange(oLower, oUpper, this, lower, upper);
-    return &span;
-}
-
-const SkOpSpan* SkOpSegment::addTPair(double t, SkOpSegment* other, double otherT, bool borrowWind,
-                           const SkPoint& pt) {
-    return addTPair(t, other, otherT, borrowWind, pt, pt);
-}
-
-bool SkOpSegment::betweenPoints(double midT, const SkPoint& pt1, const SkPoint& pt2) const {
-    const SkPoint midPt = ptAtT(midT);
-    SkPathOpsBounds bounds;
-    bounds.set(pt1.fX, pt1.fY, pt2.fX, pt2.fY);
-    bounds.sort();
-    return bounds.almostContains(midPt);
-}
-
-bool SkOpSegment::betweenTs(int lesser, double testT, int greater) const {
-    if (lesser > greater) {
-        SkTSwap<int>(lesser, greater);
-    }
-    return approximately_between(fTs[lesser].fT, testT, fTs[greater].fT);
-}
-
-// in extreme cases (like the buffer overflow test) return false to abort
-// for now, if one t value represents two different points, then the values are too extreme
-// to generate meaningful results
-bool SkOpSegment::calcAngles() {
-    int spanCount = fTs.count();
-    if (spanCount <= 2) {
-        return spanCount == 2;
-    }
-    int index = 1;
-    const SkOpSpan* firstSpan = &fTs[index];
-    int activePrior = checkSetAngle(0);
-    const SkOpSpan* span = &fTs[0];
-    if (firstSpan->fT == 0 || span->fTiny || span->fOtherT != 1 || span->fOther->multipleEnds()) {
-        index = findStartSpan(0);  // curve start intersects
-        if (fTs[index].fT == 0) {
-            return false;
-        }
-        SkASSERT(index > 0);
-        if (activePrior >= 0) {
-            addStartSpan(index);
+        sumSuWinding = baseSegment->updateOppWinding(baseAngle);
+        if (baseSegment->operand()) {
+            SkTSwap<int>(sumMiWinding, sumSuWinding);
         }
     }
-    bool addEnd;
-    int endIndex = spanCount - 1;
-    span = &fTs[endIndex - 1];
-    if ((addEnd = span->fT == 1 || span->fTiny)) {  // if curve end intersects
-        endIndex = findEndSpan(endIndex);
-        SkASSERT(endIndex > 0);
+    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 {
-        addEnd = fTs[endIndex].fOtherT != 0 || fTs[endIndex].fOther->multipleStarts();
-    }
-    SkASSERT(endIndex >= index);
-    int prior = 0;
-    while (index < endIndex) {
-        const SkOpSpan& fromSpan = fTs[index];  // for each intermediate intersection
-        const SkOpSpan* lastSpan;
-        span = &fromSpan;
-        int start = index;
-        do {
-            lastSpan = span;
-            span = &fTs[++index];
-            SkASSERT(index < spanCount);
-            if (!precisely_negative(span->fT - lastSpan->fT) && !lastSpan->fTiny) {
-                break;
-            }
-            if (!SkDPoint::ApproximatelyEqual(lastSpan->fPt, span->fPt)) {
-                return false;
-            }
-        } while (true);
-        SkOpAngle* angle = NULL;
-        SkOpAngle* priorAngle;
-        if (activePrior >= 0) {
-            int pActive = firstActive(prior);
-            SkASSERT(pActive < start);
-            priorAngle = &fAngles.push_back();
-            priorAngle->set(this, start, pActive);
-        }
-        int active = checkSetAngle(start);
-        if (active >= 0) {
-            SkASSERT(active < index);
-            angle = &fAngles.push_back();
-            angle->set(this, active, index);
-        }
-    #if DEBUG_ANGLE
-        debugCheckPointsEqualish(start, index);
-    #endif
-        prior = start;
-        do {
-            const SkOpSpan* startSpan = &fTs[start - 1];
-            if (!startSpan->fSmall || isCanceled(start - 1) || startSpan->fFromAngle
-                    || startSpan->fToAngle) {
-                break;
-            }
-            --start;
-        } while (start > 0);
-        do {
-            if (activePrior >= 0) {
-                SkASSERT(fTs[start].fFromAngle == NULL);
-                fTs[start].fFromAngle = priorAngle;
-            }
-            if (active >= 0) {
-                SkASSERT(fTs[start].fToAngle == NULL);
-                fTs[start].fToAngle = angle;
-            }
-        } while (++start < index);
-        activePrior = active;
-    }
-    if (addEnd && activePrior >= 0) {
-        addEndSpan(endIndex);
-    }
-    return true;
-}
-
-int SkOpSegment::checkSetAngle(int tIndex) const {
-    const SkOpSpan* span = &fTs[tIndex];
-    while (span->fTiny /* || span->fSmall */) {
-        span = &fTs[++tIndex];
+        nextSegment->setUpWindings(nextAngle->end(), nextAngle->start(), &sumMiWinding,
+                &maxWinding, &sumWinding);
+        last = nextSegment->markAngle(maxWinding, sumWinding, nextAngle);
     }
-    return isCanceled(tIndex) ? -1 : tIndex;
+    nextAngle->setLastMarked(last);
 }
 
 // at this point, the span is already ordered, or unorderable
-int SkOpSegment::computeSum(int startIndex, int endIndex, SkOpAngle::IncludeType includeType) {
+int SkOpSegment::computeSum(SkOpSpanBase* start, SkOpSpanBase* end,
+        SkOpAngle::IncludeType includeType) {
     SkASSERT(includeType != SkOpAngle::kUnaryXor);
-    SkOpAngle* firstAngle = spanToAngle(endIndex, startIndex);
+    SkOpAngle* firstAngle = this->spanToAngle(end, start);
     if (NULL == firstAngle || NULL == firstAngle->next()) {
         return SK_NaN32;
     }
@@ -1898,7 +614,7 @@ int SkOpSegment::computeSum(int startIndex, int endIndex, SkOpAngle::IncludeType
             baseAngle = NULL;
             continue;
         }
-        int testWinding = angle->segment()->windSum(angle);
+        int testWinding = angle->starter()->windSum();
         if (SK_MinS32 != testWinding) {
             baseAngle = angle;
             tryReverse = true;
@@ -1906,10 +622,10 @@ int SkOpSegment::computeSum(int startIndex, int endIndex, SkOpAngle::IncludeType
         }
         if (baseAngle) {
             ComputeOneSum(baseAngle, angle, includeType);
-            baseAngle = SK_MinS32 != angle->segment()->windSum(angle) ? angle : NULL;
+            baseAngle = SK_MinS32 != angle->starter()->windSum() ? angle : NULL;
         }
     } while (next != firstAngle);
-    if (baseAngle && SK_MinS32 == firstAngle->segment()->windSum(firstAngle)) {
+    if (baseAngle && SK_MinS32 == firstAngle->starter()->windSum()) {
         firstAngle = baseAngle;
         tryReverse = true;
     }
@@ -1925,1101 +641,145 @@ int SkOpSegment::computeSum(int startIndex, int endIndex, SkOpAngle::IncludeType
                 baseAngle = NULL;
                 continue;
             }
-            int testWinding = angle->segment()->windSum(angle);
+            int testWinding = angle->starter()->windSum();
             if (SK_MinS32 != testWinding) {
                 baseAngle = angle;
                 continue;
             }
             if (baseAngle) {
                 ComputeOneSumReverse(baseAngle, angle, includeType);
-                baseAngle = SK_MinS32 != angle->segment()->windSum(angle) ? angle : NULL;
+                baseAngle = SK_MinS32 != angle->starter()->windSum() ? angle : NULL;
             }
         } while (prior != firstAngle);
     }
-    int minIndex = SkMin32(startIndex, endIndex);
-    return windSum(minIndex);
+    return start->starter(end)->windSum();
 }
 
-void SkOpSegment::ComputeOneSum(const SkOpAngle* baseAngle, SkOpAngle* nextAngle,
-        SkOpAngle::IncludeType includeType) {
-    const 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()) {
-            SkTSwap<int>(sumMiWinding, sumSuWinding);
-        }
-    }
-    SkOpSegment* nextSegment = nextAngle->segment();
-    int maxWinding, sumWinding;
-    SkOpSpan* 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(const SkOpAngle* baseAngle, SkOpAngle* nextAngle,
-        SkOpAngle::IncludeType includeType) {
-    const 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()) {
-            SkTSwap<int>(sumMiWinding, sumSuWinding);
-        }
-    }
-    SkOpSegment* nextSegment = nextAngle->segment();
-    int maxWinding, sumWinding;
-    SkOpSpan* 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);
-}
-
-bool SkOpSegment::containsPt(const SkPoint& pt, int index, int endIndex) const {
-    int step = index < endIndex ? 1 : -1;
-    do {
-        const SkOpSpan& span = this->span(index);
-        if (span.fPt == pt) {
-            const SkOpSpan& endSpan = this->span(endIndex);
-            return span.fT == endSpan.fT && pt != endSpan.fPt;
-        }
-        index += step;
-    } while (index != endIndex);
-    return false;
-}
-
-bool SkOpSegment::containsT(double t, const SkOpSegment* other, double otherT) const {
-    int count = this->count();
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (t < span.fT) {
-            return false;
-        }
-        if (t == span.fT) {
-            if (other != span.fOther) {
-                continue;
-            }
-            if (other->fVerb != SkPath::kCubic_Verb) {
-                return true;
-            }
-            if (!other->fLoop) {
-                return true;
-            }
-            double otherMidT = (otherT + span.fOtherT) / 2;
-            SkPoint otherPt = other->ptAtT(otherMidT);
-            return SkDPoint::ApproximatelyEqual(span.fPt, otherPt);
-        }
-    }
-    return false;
-}
-
-int SkOpSegment::crossedSpanY(const SkPoint& basePt, SkScalar* bestY, double* hitT,
-                              bool* hitSomething, double mid, bool opp, bool current) const {
+SkOpSpan* SkOpSegment::crossedSpanY(const SkPoint& basePt, double mid, bool opp, bool current,
+        SkScalar* bestY, double* hitT, bool* hitSomething, bool* vertical) {
     SkScalar bottom = fBounds.fBottom;
-    int bestTIndex = -1;
+    *vertical = false;
     if (bottom <= *bestY) {
-        return bestTIndex;
+        return NULL;
     }
     SkScalar top = fBounds.fTop;
     if (top >= basePt.fY) {
-        return bestTIndex;
+        return NULL;
     }
     if (fBounds.fLeft > basePt.fX) {
-        return bestTIndex;
+        return NULL;
     }
     if (fBounds.fRight < basePt.fX) {
-        return bestTIndex;
+        return NULL;
     }
     if (fBounds.fLeft == fBounds.fRight) {
-        // if vertical, and directly above test point, wait for another one
-        return AlmostEqualUlps(basePt.fX, fBounds.fLeft) ? SK_MinS32 : bestTIndex;
-    }
-    // intersect ray starting at basePt with edge
-    SkIntersections intersections;
-    // OPTIMIZE: use specialty function that intersects ray with curve,
-    // returning t values only for curve (we don't care about t on ray)
-    intersections.allowNear(false);
-    int pts = (intersections.*CurveVertical[SkPathOpsVerbToPoints(fVerb)])
-            (fPts, top, bottom, basePt.fX, false);
-    if (pts == 0 || (current && pts == 1)) {
-        return bestTIndex;
-    }
-    if (current) {
-        SkASSERT(pts > 1);
-        int closestIdx = 0;
-        double closest = fabs(intersections[0][0] - mid);
-        for (int idx = 1; idx < pts; ++idx) {
-            double test = fabs(intersections[0][idx] - mid);
-            if (closest > test) {
-                closestIdx = idx;
-                closest = test;
-            }
-        }
-        intersections.quickRemoveOne(closestIdx, --pts);
-    }
-    double bestT = -1;
-    for (int index = 0; index < pts; ++index) {
-        double foundT = intersections[0][index];
-        if (approximately_less_than_zero(foundT)
-                    || approximately_greater_than_one(foundT)) {
-            continue;
-        }
-        SkScalar testY = (*CurvePointAtT[SkPathOpsVerbToPoints(fVerb)])(fPts, foundT).fY;
-        if (approximately_negative(testY - *bestY)
-                || approximately_negative(basePt.fY - testY)) {
-            continue;
-        }
-        if (pts > 1 && fVerb == SkPath::kLine_Verb) {
-            return SK_MinS32;  // if the intersection is edge on, wait for another one
-        }
-        if (fVerb > SkPath::kLine_Verb) {
-            SkScalar dx = (*CurveSlopeAtT[SkPathOpsVerbToPoints(fVerb)])(fPts, foundT).fX;
-            if (approximately_zero(dx)) {
-                return SK_MinS32;  // hit vertical, wait for another one
-            }
-        }
-        *bestY = testY;
-        bestT = foundT;
-    }
-    if (bestT < 0) {
-        return bestTIndex;
-    }
-    SkASSERT(bestT >= 0);
-    SkASSERT(bestT <= 1);
-    int start;
-    int end = 0;
-    do {
-        start = end;
-        end = nextSpan(start, 1);
-    } while (fTs[end].fT < bestT);
-    // FIXME: see next candidate for a better pattern to find the next start/end pair
-    while (start + 1 < end && fTs[start].fDone) {
-        ++start;
-    }
-    if (!isCanceled(start)) {
-        *hitT = bestT;
-        bestTIndex = start;
-        *hitSomething = true;
-    }
-    return bestTIndex;
-}
-
-bool SkOpSegment::decrementSpan(SkOpSpan* span) {
-    SkASSERT(span->fWindValue > 0);
-    if (--(span->fWindValue) == 0) {
-        if (!span->fOppValue && !span->fDone) {
-            span->fDone = true;
-            ++fDoneSpans;
-            return true;
-        }
-    }
-    return false;
-}
-
-bool SkOpSegment::bumpSpan(SkOpSpan* span, int windDelta, int oppDelta) {
-    SkASSERT(!span->fDone || span->fTiny || span->fSmall);
-    span->fWindValue += windDelta;
-    SkASSERT(span->fWindValue >= 0);
-    span->fOppValue += oppDelta;
-    SkASSERT(span->fOppValue >= 0);
-    if (fXor) {
-        span->fWindValue &= 1;
-    }
-    if (fOppXor) {
-        span->fOppValue &= 1;
-    }
-    if (!span->fWindValue && !span->fOppValue) {
-        if (!span->fDone) {
-            span->fDone = true;
-            ++fDoneSpans;
-        }
-        return true;
-    }
-    return false;
-}
-
-const SkOpSpan& SkOpSegment::firstSpan(const SkOpSpan& thisSpan) const {
-    const SkOpSpan* firstSpan = &thisSpan; // rewind to the start
-    const SkOpSpan* beginSpan = fTs.begin();
-    const SkPoint& testPt = thisSpan.fPt;
-    while (firstSpan > beginSpan && firstSpan[-1].fPt == testPt) {
-        --firstSpan;
-    }
-    return *firstSpan;
-}
-
-const SkOpSpan& SkOpSegment::lastSpan(const SkOpSpan& thisSpan) const {
-    const SkOpSpan* endSpan = fTs.end() - 1;  // last can't be small
-    const SkOpSpan* lastSpan = &thisSpan;  // find the end
-    const SkPoint& testPt = thisSpan.fPt;
-    while (lastSpan < endSpan && lastSpan[1].fPt == testPt) {
-        ++lastSpan;
-    }
-    return *lastSpan;
-}
-
-// with a loop, the comparison is move involved
-// scan backwards and forwards to count all matching points
-// (verify that there are twp scans marked as loops)
-// compare that against 2 matching scans for loop plus other results
-bool SkOpSegment::calcLoopSpanCount(const SkOpSpan& thisSpan, int* smallCounts) {
-    const SkOpSpan& firstSpan = this->firstSpan(thisSpan); // rewind to the start
-    const SkOpSpan& lastSpan = this->lastSpan(thisSpan);  // find the end
-    double firstLoopT = -1, lastLoopT = -1;
-    const SkOpSpan* testSpan = &firstSpan - 1;
-    while (++testSpan <= &lastSpan) {
-        if (testSpan->fLoop) {
-            firstLoopT = testSpan->fT;
-            break;
-        }
-    }
-    testSpan = &lastSpan + 1;
-    while (--testSpan >= &firstSpan) {
-        if (testSpan->fLoop) {
-            lastLoopT = testSpan->fT;
-            break;
-        }
-    }
-    SkASSERT((firstLoopT == -1) == (lastLoopT == -1));
-    if (firstLoopT == -1) {
-        return false;
-    }
-    SkASSERT(firstLoopT < lastLoopT);
-    testSpan = &firstSpan - 1;
-    smallCounts[0] = smallCounts[1] = 0;
-    while (++testSpan <= &lastSpan) {
-        SkASSERT(approximately_equal(testSpan->fT, firstLoopT) +
-                approximately_equal(testSpan->fT, lastLoopT) == 1);
-        smallCounts[approximately_equal(testSpan->fT, lastLoopT)]++;
-    }
-    return true;
-}
-
-double SkOpSegment::calcMissingTEnd(const SkOpSegment* ref, double loEnd, double min, double max,
-        double hiEnd, const SkOpSegment* other, int thisStart) {
-    if (max >= hiEnd) {
-        return -1;
-    }
-    int end = findOtherT(hiEnd, ref);
-    if (end < 0) {
-        return -1;
-    }
-    double tHi = span(end).fT;
-    double tLo, refLo;
-    if (thisStart >= 0) {
-        tLo = span(thisStart).fT;
-        refLo = min;
-    } else {
-        int start1 = findOtherT(loEnd, ref);
-        SkASSERT(start1 >= 0);
-        tLo = span(start1).fT;
-        refLo = loEnd;
-    }
-    double missingT = (max - refLo) / (hiEnd - refLo);
-    missingT = tLo + missingT * (tHi - tLo);
-    return missingT;
-}
-
-double SkOpSegment::calcMissingTStart(const SkOpSegment* ref, double loEnd, double min, double max,
-        double hiEnd, const SkOpSegment* other, int thisEnd) {
-    if (min <= loEnd) {
-        return -1;
-    }
-    int start = findOtherT(loEnd, ref);
-    if (start < 0) {
-        return -1;
-    }
-    double tLo = span(start).fT;
-    double tHi, refHi;
-    if (thisEnd >= 0) {
-        tHi = span(thisEnd).fT;
-        refHi = max;
-    } else {
-        int end1 = findOtherT(hiEnd, ref);
-        if (end1 < 0) {
-            return -1;
-        }
-        tHi = span(end1).fT;
-        refHi = hiEnd;
-    }
-    double missingT = (min - loEnd) / (refHi - loEnd);
-    missingT = tLo + missingT * (tHi - tLo);
-    return missingT;
-}
-
-// see if spans with two or more intersections have the same number on the other end
-void SkOpSegment::checkDuplicates() {
-    debugValidate();
-    SkSTArray<kMissingSpanCount, MissingSpan, true> missingSpans;
-    int index;
-    int endIndex = 0;
-    bool endFound;
-    do {
-        index = endIndex;
-        endIndex = nextExactSpan(index, 1);
-        if ((endFound = endIndex < 0)) {
-            endIndex = count();
-        }
-        int dupCount = endIndex - index;
-        if (dupCount < 2) {
-            continue;
-        }
-        do {
-            const SkOpSpan* thisSpan = &fTs[index];
-            if (thisSpan->fNear) {
-                continue;
-            }
-            SkOpSegment* other = thisSpan->fOther;
-            int oIndex = thisSpan->fOtherIndex;
-            int oStart = other->nextExactSpan(oIndex, -1) + 1;
-            int oEnd = other->nextExactSpan(oIndex, 1);
-            if (oEnd < 0) {
-                oEnd = other->count();
-            }
-            int oCount = oEnd - oStart;
-            // force the other to match its t and this pt if not on an end point
-            if (oCount != dupCount) {
-                MissingSpan& missing = missingSpans.push_back();
-                missing.fOther = NULL;
-                SkDEBUGCODE(sk_bzero(&missing, sizeof(missing)));
-                missing.fPt = thisSpan->fPt;
-                const SkOpSpan& oSpan = other->span(oIndex);
-                if (oCount > dupCount) {
-                    missing.fSegment = this;
-                    missing.fT = thisSpan->fT;
-                    other->checkLinks(&oSpan, &missingSpans);
-                } else {
-                    missing.fSegment = other;
-                    missing.fT = oSpan.fT;
-                    checkLinks(thisSpan, &missingSpans);
-                }
-                if (!missingSpans.back().fOther) {
-                    missingSpans.pop_back();
-                }
-            }
-        } while (++index < endIndex);
-    } while (!endFound);
-    int missingCount = missingSpans.count();
-    if (missingCount == 0) {
-        return;
-    }
-    SkSTArray<kMissingSpanCount, MissingSpan, true> missingCoincidence;
-    for (index = 0; index < missingCount; ++index)  {
-        MissingSpan& missing = missingSpans[index];
-        SkOpSegment* missingOther = missing.fOther;
-        if (missing.fSegment == missing.fOther) {
-            continue;
-        }
-#if 0  // FIXME: this eliminates spurious data from skpwww_argus_presse_fr_41 but breaks
-       // skpwww_fashionscandal_com_94 -- calcAngles complains, but I don't understand why
-        if (missing.fSegment->containsT(missing.fT, missing.fOther, missing.fOtherT)) {
-#if DEBUG_DUPLICATES
-            SkDebugf("skip 1 id=%d t=%1.9g other=%d otherT=%1.9g\n", missing.fSegment->fID,
-                    missing.fT, missing.fOther->fID, missing.fOtherT);
-#endif
-            continue;
-        }
-        if (missing.fOther->containsT(missing.fOtherT, missing.fSegment, missing.fT)) {
-#if DEBUG_DUPLICATES
-            SkDebugf("skip 2 id=%d t=%1.9g other=%d otherT=%1.9g\n", missing.fOther->fID,
-                    missing.fOtherT, missing.fSegment->fID, missing.fT);
-#endif
-            continue;
-        }
-#endif
-        // skip if adding would insert point into an existing coincindent span
-        if (missing.fSegment->inCoincidentSpan(missing.fT, missingOther)
-                && missingOther->inCoincidentSpan(missing.fOtherT, this)) {
-            continue;
-        }
-        // skip if the created coincident spans are small
-        if (missing.fSegment->coincidentSmall(missing.fPt, missing.fT, missingOther)
-                && missingOther->coincidentSmall(missing.fPt, missing.fOtherT, missing.fSegment)) {
-            continue;
-        }
-        const SkOpSpan* added = missing.fSegment->addTPair(missing.fT, missingOther,
-                missing.fOtherT, false, missing.fPt);
-        if (added && added->fSmall) {
-            missing.fSegment->checkSmallCoincidence(*added, &missingCoincidence);
-        }
-    }
-    for (index = 0; index < missingCount; ++index)  {
-        MissingSpan& missing = missingSpans[index];
-        missing.fSegment->fixOtherTIndex();
-        missing.fOther->fixOtherTIndex();
-    }
-    for (index = 0; index < missingCoincidence.count(); ++index) {
-        MissingSpan& missing = missingCoincidence[index];
-        missing.fSegment->fixOtherTIndex();
-    }
-    debugValidate();
-}
-
-// look to see if the curve end intersects an intermediary that intersects the other
-bool SkOpSegment::checkEnds() {
-    debugValidate();
-    SkSTArray<kMissingSpanCount, MissingSpan, true> missingSpans;
-    int count = fTs.count();
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        double otherT = span.fOtherT;
-        if (otherT != 0 && otherT != 1) { // only check ends
-            continue;
-        }
-        const SkOpSegment* other = span.fOther;
-        // peek start/last describe the range of spans that match the other t of this span
-        int peekStart = span.fOtherIndex;
-        while (--peekStart >= 0 && other->fTs[peekStart].fT == otherT)
-            ;
-        int otherCount = other->fTs.count();
-        int peekLast = span.fOtherIndex;
-        while (++peekLast < otherCount && other->fTs[peekLast].fT == otherT)
-            ;
-        if (++peekStart == --peekLast) { // if there isn't a range, there's nothing to do
-            continue;
-        }
-        // t start/last describe the range of spans that match the t of this span
-        double t = span.fT;
-        double tBottom = -1;
-        int tStart = -1;
-        int tLast = count;
-        bool lastSmall = false;
-        double afterT = t;
-        for (int inner = 0; inner < count; ++inner) {
-            double innerT = fTs[inner].fT;
-            if (innerT <= t && innerT > tBottom) {
-                if (innerT < t || !lastSmall) {
-                    tStart = inner - 1;
-                }
-                tBottom = innerT;
-            }
-            if (innerT > afterT) {
-                if (t == afterT && lastSmall) {
-                    afterT = innerT;
-                } else {
-                    tLast = inner;
-                    break;
-                }
-            }
-            lastSmall = innerT <= t ? fTs[inner].fSmall : false;
-        }
-        for (int peekIndex = peekStart; peekIndex <= peekLast; ++peekIndex) {
-            if (peekIndex == span.fOtherIndex) {  // skip the other span pointed to by this span
-                continue;
-            }
-            const SkOpSpan& peekSpan = other->fTs[peekIndex];
-            SkOpSegment* match = peekSpan.fOther;
-            if (match->done()) {
-                continue;  // if the edge has already been eaten (likely coincidence), ignore it
-            }
-            const double matchT = peekSpan.fOtherT;
-            // see if any of the spans match the other spans
-            for (int tIndex = tStart + 1; tIndex < tLast; ++tIndex) {
-                const SkOpSpan& tSpan = fTs[tIndex];
-                if (tSpan.fOther == match) {
-                    if (tSpan.fOtherT == matchT) {
-                        goto nextPeekIndex;
-                    }
-                    double midT = (tSpan.fOtherT + matchT) / 2;
-                    if (match->betweenPoints(midT, tSpan.fPt, peekSpan.fPt)) {
-                        goto nextPeekIndex;
-                    }
-                }
-            }
-            if (missingSpans.count() > 0) {
-                const MissingSpan& lastMissing = missingSpans.back();
-                if (lastMissing.fT == t
-                        && lastMissing.fOther == match
-                        && lastMissing.fOtherT == matchT) {
-                    SkASSERT(SkDPoint::ApproximatelyEqual(lastMissing.fPt, peekSpan.fPt));
-                    continue;
-                }
-            }
-            if (this == match) {
-                return false; // extremely large paths can trigger this
-            }
-#if DEBUG_CHECK_ALIGN
-            SkDebugf("%s id=%d missing t=%1.9g other=%d otherT=%1.9g pt=(%1.9g,%1.9g)\n",
-                    __FUNCTION__, fID, t, match->fID, matchT, peekSpan.fPt.fX, peekSpan.fPt.fY);
-#endif
-            // this segment is missing a entry that the other contains
-            // remember so we can add the missing one and recompute the indices
-            {
-                MissingSpan& missing = missingSpans.push_back();
-                SkDEBUGCODE(sk_bzero(&missing, sizeof(missing)));
-                missing.fT = t;
-                SkASSERT(this != match);
-                missing.fOther = match;
-                missing.fOtherT = matchT;
-                missing.fPt = peekSpan.fPt;
-            }
-            break;
-nextPeekIndex:
-            ;
-        }
-    }
-    if (missingSpans.count() == 0) {
-        debugValidate();
-        return true;
-    }
-    debugValidate();
-    int missingCount = missingSpans.count();
-    for (int index = 0; index < missingCount; ++index)  {
-        MissingSpan& missing = missingSpans[index];
-        if (this != missing.fOther) {
-            addTPair(missing.fT, missing.fOther, missing.fOtherT, false, missing.fPt);
-        }
-    }
-    fixOtherTIndex();
-    // OPTIMIZATION: this may fix indices more than once. Build an array of unique segments to
-    // avoid this
-    for (int index = 0; index < missingCount; ++index)  {
-        missingSpans[index].fOther->fixOtherTIndex();
-    }
-    debugValidate();
-    return true;
-}
-
-void SkOpSegment::checkLinks(const SkOpSpan* base,
-        SkTArray<MissingSpan, true>* missingSpans) const {
-    const SkOpSpan* first = fTs.begin();
-    const SkOpSpan* last = fTs.end() - 1;
-    SkASSERT(base >= first && last >= base);
-    const SkOpSegment* other = base->fOther;
-    const SkOpSpan* oFirst = other->fTs.begin();
-    const SkOpSpan* oLast = other->fTs.end() - 1;
-    const SkOpSpan* oSpan = &other->fTs[base->fOtherIndex];
-    const SkOpSpan* test = base;
-    const SkOpSpan* missing = NULL;
-    while (test > first && (--test)->fPt == base->fPt) {
-        if (this == test->fOther) {
-            continue;
-        }
-        CheckOneLink(test, oSpan, oFirst, oLast, &missing, missingSpans);
-    }
-    test = base;
-    while (test < last && (++test)->fPt == base->fPt) {
-        SkASSERT(this != test->fOther || test->fLoop);
-        CheckOneLink(test, oSpan, oFirst, oLast, &missing, missingSpans);
-    }
-}
-
-// see if spans with two or more intersections all agree on common t and point values
-void SkOpSegment::checkMultiples() {
-    debugValidate();
-    int index;
-    int end = 0;
-    while (fTs[++end].fT == 0)
-        ;
-    while (fTs[end].fT < 1) {
-        int start = index = end;
-        end = nextExactSpan(index, 1);
-        if (end <= index) {
-            return;  // buffer overflow example triggers this
-        }
-        if (index + 1 == end) {
-            continue;
-        }
-        // force the duplicates to agree on t and pt if not on the end
-        SkOpSpan& span = fTs[index];
-        double thisT = span.fT;
-        const SkPoint& thisPt = span.fPt;
-        span.fMultiple = true;
-        bool aligned = false;
-        while (++index < end) {
-            aligned |= alignSpan(index, thisT, thisPt);
-        }
-        if (aligned) {
-            alignSpanState(start, end);
-        }
-        fMultiples = true;
-    }
-    debugValidate();
-}
-
-void SkOpSegment::CheckOneLink(const SkOpSpan* test, const SkOpSpan* oSpan,
-        const SkOpSpan* oFirst, const SkOpSpan* oLast, const SkOpSpan** missingPtr,
-        SkTArray<MissingSpan, true>* missingSpans) {
-    SkASSERT(oSpan->fPt == test->fPt);
-    const SkOpSpan* oTest = oSpan;
-    while (oTest > oFirst && (--oTest)->fPt == test->fPt) {
-        if (oTest->fOther == test->fOther && oTest->fOtherT == test->fOtherT) {
-            return;
-        }
-    }
-    oTest = oSpan;
-    while (oTest < oLast && (++oTest)->fPt == test->fPt) {
-        if (oTest->fOther == test->fOther && oTest->fOtherT == test->fOtherT) {
-            return;
-        }
-    }
-    if (*missingPtr) {
-        missingSpans->push_back();
-    }
-    MissingSpan& lastMissing = missingSpans->back();
-    if (*missingPtr) {
-        lastMissing = missingSpans->end()[-2];
-    }
-    *missingPtr = test;
-    lastMissing.fOther = test->fOther;
-    lastMissing.fOtherT = test->fOtherT;
-}
-
-bool SkOpSegment::checkSmall(int index) const {
-    if (fTs[index].fSmall) {
-        return true;
-    }
-    double tBase = fTs[index].fT;
-    while (index > 0 && precisely_negative(tBase - fTs[--index].fT))
-        ;
-    return fTs[index].fSmall;
-}
-
-// a pair of curves may turn into coincident lines -- small may be a hint that that happened
-// if a cubic contains a loop, the counts must be adjusted
-void SkOpSegment::checkSmall() {
-    SkSTArray<kMissingSpanCount, MissingSpan, true> missingSpans;
-    const SkOpSpan* beginSpan = fTs.begin();
-    const SkOpSpan* thisSpan = beginSpan - 1;
-    const SkOpSpan* endSpan = fTs.end() - 1;  // last can't be small
-    while (++thisSpan < endSpan) {
-        if (!thisSpan->fSmall) {
-            continue;
-        }
-        if (!thisSpan->fWindValue) {
-            continue;
-        }
-        const SkOpSpan& firstSpan = this->firstSpan(*thisSpan);
-        const SkOpSpan& lastSpan = this->lastSpan(*thisSpan);
-        const SkOpSpan* nextSpan = &firstSpan + 1;
-        ptrdiff_t smallCount = &lastSpan - &firstSpan + 1;
-        SkASSERT(1 <= smallCount && smallCount < count());
-        if (smallCount <= 1 && !nextSpan->fSmall) {
-            SkASSERT(1 == smallCount);
-            checkSmallCoincidence(firstSpan, NULL);
-            continue;
-        }
-        // at this point, check for missing computed intersections
-        const SkPoint& testPt = firstSpan.fPt;
-        thisSpan = &firstSpan - 1;
-        SkOpSegment* other = NULL;
-        while (++thisSpan <= &lastSpan) {
-            other = thisSpan->fOther;
-            if (other != this) {
-                break;
-            }
-        }
-        SkASSERT(other != this);
-        int oIndex = thisSpan->fOtherIndex;
-        const SkOpSpan& oSpan = other->span(oIndex);
-        const SkOpSpan& oFirstSpan = other->firstSpan(oSpan);
-        const SkOpSpan& oLastSpan = other->lastSpan(oSpan);
-        ptrdiff_t oCount = &oLastSpan - &oFirstSpan + 1;
-        if (fLoop) {
-            int smallCounts[2];
-            SkASSERT(!other->fLoop);  // FIXME: we need more complicated logic for pair of loops
-            if (calcLoopSpanCount(*thisSpan, smallCounts)) {
-                if (smallCounts[0] && oCount != smallCounts[0]) {
-                    SkASSERT(0);  // FIXME: need a working test case to properly code & debug
-                }
-                if (smallCounts[1] && oCount != smallCounts[1]) {
-                    SkASSERT(0);  // FIXME: need a working test case to properly code & debug
-                }
-                goto nextSmallCheck;
-            }
-        }
-        if (other->fLoop) {
-            int otherCounts[2];
-            if (other->calcLoopSpanCount(other->span(oIndex), otherCounts)) {
-                if (otherCounts[0] && otherCounts[0] != smallCount) {
-                    SkASSERT(0);  // FIXME: need a working test case to properly code & debug
-                }
-                if (otherCounts[1] && otherCounts[1] != smallCount) {
-                    SkASSERT(0);  // FIXME: need a working test case to properly code & debug
-                }
-                goto nextSmallCheck;
-            }
-        }
-        if (oCount != smallCount) {  // check if number of pts in this match other
-            MissingSpan& missing = missingSpans.push_back();
-            missing.fOther = NULL;
-            SkDEBUGCODE(sk_bzero(&missing, sizeof(missing)));
-            missing.fPt = testPt;
-            const SkOpSpan& oSpan = other->span(oIndex);
-            if (oCount > smallCount) {
-                missing.fSegment = this;
-                missing.fT = thisSpan->fT;
-                other->checkLinks(&oSpan, &missingSpans);
-            } else {
-                missing.fSegment = other;
-                missing.fT = oSpan.fT;
-                checkLinks(thisSpan, &missingSpans);
-            }
-            if (!missingSpans.back().fOther || missing.fSegment->done()) {
-                missingSpans.pop_back();
-            }
-        }
-nextSmallCheck:
-        thisSpan = &lastSpan;
-    }
-    int missingCount = missingSpans.count();
-    for (int index = 0; index < missingCount; ++index)  {
-        MissingSpan& missing = missingSpans[index];
-        SkOpSegment* missingOther = missing.fOther;
-        // note that add t pair may edit span arrays, so prior pointers to spans are no longer valid
-        if (!missing.fSegment->addTPair(missing.fT, missingOther, missing.fOtherT, false,
-                missing.fPt)) {
-            continue;
-        }
-        int otherTIndex = missingOther->findT(missing.fOtherT, missing.fPt, missing.fSegment);
-        const SkOpSpan& otherSpan = missingOther->span(otherTIndex);
-        if (otherSpan.fSmall) {
-            const SkOpSpan* nextSpan = &otherSpan;
-            if (nextSpan->fPt == missing.fPt) {
-                continue;
-            }
-            do {
-                ++nextSpan;
-            } while (nextSpan->fSmall);
-            if (nextSpan->fT == 1) {
-                continue;
-            }
-            SkAssertResult(missing.fSegment->addTCoincident(missing.fPt, nextSpan->fPt,
-                    nextSpan->fT, missingOther));
-        } else if (otherSpan.fT > 0) {
-            const SkOpSpan* priorSpan = &otherSpan;
-            do {
-                --priorSpan;
-            } while (priorSpan->fT == otherSpan.fT);
-            if (priorSpan->fSmall) {
-                missing.fSegment->addTCancel(missing.fPt, priorSpan->fPt, missingOther);
-            }
-        }
-    }
-    // OPTIMIZATION: this may fix indices more than once. Build an array of unique segments to
-    // avoid this
-    for (int index = 0; index < missingCount; ++index)  {
-        MissingSpan& missing = missingSpans[index];
-        missing.fSegment->fixOtherTIndex();
-        missing.fOther->fixOtherTIndex();
-    }
-    debugValidate();
-}
-
-void SkOpSegment::checkSmallCoincidence(const SkOpSpan& span,
-        SkTArray<MissingSpan, true>* checkMultiple) {
-    SkASSERT(span.fSmall);
-    if (0 && !span.fWindValue) {
-        return;
-    }
-    SkASSERT(&span < fTs.end() - 1);
-    const SkOpSpan* next = &span + 1;
-    SkASSERT(!next->fSmall || checkMultiple);
-    if (checkMultiple) {
-        while (next->fSmall) {
-            ++next;
-            SkASSERT(next < fTs.end());
-        }
-    }
-    SkOpSegment* other = span.fOther;
-    while (other != next->fOther) {
-        if (!checkMultiple) {
-            return;
-        }
-        const SkOpSpan* test = next + 1;
-        if (test == fTs.end()) {
-            return;
-        }
-        if (test->fPt != next->fPt || !precisely_equal(test->fT, next->fT)) {
-            return;
-        }
-        next = test;
-    }
-    SkASSERT(span.fT < next->fT);
-    int oStartIndex = other->findExactT(span.fOtherT, this);
-    int oEndIndex = other->findExactT(next->fOtherT, this);
-    // FIXME: be overly conservative by limiting this to the caller that allows multiple smalls
-    if (!checkMultiple || fVerb != SkPath::kLine_Verb || other->fVerb != SkPath::kLine_Verb) {
-        SkPoint mid = ptAtT((span.fT + next->fT) / 2);
-        const SkOpSpan& oSpanStart = other->fTs[oStartIndex];
-        const SkOpSpan& oSpanEnd = other->fTs[oEndIndex];
-        SkPoint oMid = other->ptAtT((oSpanStart.fT + oSpanEnd.fT) / 2);
-        if (!SkDPoint::ApproximatelyEqual(mid, oMid)) {
-            return;
-        }
-    }
-    // FIXME: again, be overly conservative to avoid breaking existing tests
-    const SkOpSpan& oSpan = oStartIndex < oEndIndex ? other->fTs[oStartIndex]
-            : other->fTs[oEndIndex];
-    if (checkMultiple && !oSpan.fSmall) {
-        return;
-    }
-//    SkASSERT(oSpan.fSmall);
-    if (oStartIndex < oEndIndex) {
-        SkAssertResult(addTCoincident(span.fPt, next->fPt, next->fT, other));
-    } else {
-        addTCancel(span.fPt, next->fPt, other);
-    }
-    if (!checkMultiple) {
-        return;
+        // if vertical, and directly above test point, wait for another one
+        *vertical = AlmostEqualUlps(basePt.fX, fBounds.fLeft);
+        return NULL;
     }
-    // check to see if either segment is coincident with a third segment -- if it is, and if
-    // the opposite segment is not already coincident with the third, make it so
-    // OPTIMIZE: to make this check easier, add coincident and cancel could set a coincident bit
-    if (span.fWindValue != 1 || span.fOppValue != 0) {
-//        start here;
-        // iterate through the spans, looking for the third coincident case
-        // if we find one, we need to return state to the caller so that the indices can be fixed
-        // this also suggests that all of this function is fragile since it relies on a valid index
+    // intersect ray starting at basePt with edge
+    SkIntersections intersections;
+    // OPTIMIZE: use specialty function that intersects ray with curve,
+    // returning t values only for curve (we don't care about t on ray)
+    intersections.allowNear(false);
+    int pts = (intersections.*CurveVertical[SkPathOpsVerbToPoints(fVerb)])
+            (fPts, top, bottom, basePt.fX, false);
+    if (pts == 0 || (current && pts == 1)) {
+        return NULL;
     }
-    // probably should make this a common function rather than copy/paste code
-    if (oSpan.fWindValue != 1 || oSpan.fOppValue != 0) {
-        const SkOpSpan* oTest = &oSpan;
-        while (--oTest >= other->fTs.begin()) {
-            if (oTest->fPt != oSpan.fPt || !precisely_equal(oTest->fT, oSpan.fT)) {
-                break;
-            }
-            SkOpSegment* testOther = oTest->fOther;
-            SkASSERT(testOther != this);
-            // look in both directions to see if there is a coincident span
-            const SkOpSpan* tTest = testOther->fTs.begin();
-            for (int testIndex = 0; testIndex < testOther->count(); ++testIndex) {
-                if (tTest->fPt != span.fPt) {
-                    ++tTest;
-                    continue;
-                }
-                if (testOther->verb() != SkPath::kLine_Verb
-                        || other->verb() != SkPath::kLine_Verb) {
-                    SkPoint mid = ptAtT((span.fT + next->fT) / 2);
-                    SkPoint oMid = other->ptAtT((oTest->fOtherT + tTest->fT) / 2);
-                    if (!SkDPoint::ApproximatelyEqual(mid, oMid)) {
-                        continue;
-                    }
-                }
-#if DEBUG_CONCIDENT
-                SkDebugf("%s coincident found=%d %1.9g %1.9g\n", __FUNCTION__, testOther->fID,
-                        oTest->fOtherT, tTest->fT);
-#endif
-                if (tTest->fT < oTest->fOtherT) {
-                    SkAssertResult(addTCoincident(span.fPt, next->fPt, next->fT, testOther));
-                } else {
-                    addTCancel(span.fPt, next->fPt, testOther);
-                }
-                MissingSpan missing;
-                missing.fSegment = testOther;
-                checkMultiple->push_back(missing);
-                break;
-            }
-        }
-        oTest = &oSpan;
-        while (++oTest < other->fTs.end()) {
-            if (oTest->fPt != oSpan.fPt || !precisely_equal(oTest->fT, oSpan.fT)) {
-                break;
+    if (current) {
+        SkASSERT(pts > 1);
+        int closestIdx = 0;
+        double closest = fabs(intersections[0][0] - mid);
+        for (int idx = 1; idx < pts; ++idx) {
+            double test = fabs(intersections[0][idx] - mid);
+            if (closest > test) {
+                closestIdx = idx;
+                closest = test;
             }
-
         }
+        intersections.quickRemoveOne(closestIdx, --pts);
     }
-}
-
-// if pair of spans on either side of tiny have the same end point and mid point, mark
-// them as parallel
-void SkOpSegment::checkTiny() {
-    SkSTArray<kMissingSpanCount, MissingSpan, true> missingSpans;
-    SkOpSpan* thisSpan = fTs.begin() - 1;
-    const SkOpSpan* endSpan = fTs.end() - 1;  // last can't be tiny
-    while (++thisSpan < endSpan) {
-        if (!thisSpan->fTiny) {
+    double bestT = -1;
+    for (int index = 0; index < pts; ++index) {
+        double foundT = intersections[0][index];
+        if (approximately_less_than_zero(foundT)
+                    || approximately_greater_than_one(foundT)) {
             continue;
         }
-        SkOpSpan* nextSpan = thisSpan + 1;
-        double thisT = thisSpan->fT;
-        double nextT = nextSpan->fT;
-        if (thisT == nextT) {
+        SkScalar testY = (*CurvePointAtT[SkPathOpsVerbToPoints(fVerb)])(fPts, foundT).fY;
+        if (approximately_negative(testY - *bestY)
+                || approximately_negative(basePt.fY - testY)) {
             continue;
         }
-        SkASSERT(thisT < nextT);
-        SkASSERT(thisSpan->fPt == nextSpan->fPt);
-        SkOpSegment* thisOther = thisSpan->fOther;
-        SkOpSegment* nextOther = nextSpan->fOther;
-        int oIndex = thisSpan->fOtherIndex;
-        for (int oStep = -1; oStep <= 1; oStep += 2) {
-            int oEnd = thisOther->nextExactSpan(oIndex, oStep);
-            if (oEnd < 0) {
-                continue;
-            }
-            const SkOpSpan& oSpan = thisOther->span(oEnd);
-            int nIndex = nextSpan->fOtherIndex;
-            for (int nStep = -1; nStep <= 1; nStep += 2) {
-                int nEnd = nextOther->nextExactSpan(nIndex, nStep);
-                if (nEnd < 0) {
-                    continue;
-                }
-                const SkOpSpan& nSpan = nextOther->span(nEnd);
-                if (oSpan.fPt != nSpan.fPt) {
-                    continue;
-                }
-                double oMidT = (thisSpan->fOtherT + oSpan.fT) / 2;
-                const SkPoint& oPt = thisOther->ptAtT(oMidT);
-                double nMidT = (nextSpan->fOtherT + nSpan.fT) / 2;
-                const SkPoint& nPt = nextOther->ptAtT(nMidT);
-                if (!AlmostEqualUlps(oPt, nPt)) {
-                    continue;
-                }
-#if DEBUG_CHECK_TINY
-                SkDebugf("%s [%d] add coincidence [%d] [%d]\n", __FUNCTION__, fID,
-                    thisOther->fID, nextOther->fID);
-#endif
-                // this segment is missing a entry that the other contains
-                // remember so we can add the missing one and recompute the indices
-                MissingSpan& missing = missingSpans.push_back();
-                SkDEBUGCODE(sk_bzero(&missing, sizeof(missing)));
-                missing.fSegment = thisOther;
-                missing.fT = thisSpan->fOtherT;
-                SkASSERT(this != nextOther);
-                missing.fOther = nextOther;
-                missing.fOtherT = nextSpan->fOtherT;
-                missing.fPt = thisSpan->fPt;
+        if (pts > 1 && fVerb == SkPath::kLine_Verb) {
+            *vertical = true;
+            return NULL;  // if the intersection is edge on, wait for another one
+        }
+        if (fVerb > SkPath::kLine_Verb) {
+            SkScalar dx = (*CurveSlopeAtT[SkPathOpsVerbToPoints(fVerb)])(fPts, foundT).fX;
+            if (approximately_zero(dx)) {
+                *vertical = true;
+                return NULL;  // hit vertical, wait for another one
             }
         }
+        *bestY = testY;
+        bestT = foundT;
     }
-    int missingCount = missingSpans.count();
-    if (!missingCount) {
-        return;
+    if (bestT < 0) {
+        return NULL;
     }
-    for (int index = 0; index < missingCount; ++index)  {
-        MissingSpan& missing = missingSpans[index];
-        if (missing.fSegment != missing.fOther) {
-            missing.fSegment->addTPair(missing.fT, missing.fOther, missing.fOtherT, false,
-                    missing.fPt);
+    SkASSERT(bestT >= 0);
+    SkASSERT(bestT < 1);
+    SkOpSpanBase* testTSpanBase = &this->fHead;
+    SkOpSpanBase* nextTSpan;
+    double endT = 0;
+    do {
+        nextTSpan = testTSpanBase->upCast()->next();
+        endT = nextTSpan->t();
+        if (endT >= bestT) {
+            break;
         }
+        testTSpanBase = nextTSpan;
+    } while (testTSpanBase);
+    SkOpSpan* bestTSpan = NULL;
+    SkOpSpan* testTSpan = testTSpanBase->upCast();
+    if (!testTSpan->isCanceled()) {
+        *hitT = bestT;
+        bestTSpan = testTSpan;
+        *hitSomething = true;
     }
-    // OPTIMIZE: consolidate to avoid multiple calls to fix index
-    for (int index = 0; index < missingCount; ++index)  {
-        MissingSpan& missing = missingSpans[index];
-        missing.fSegment->fixOtherTIndex();
-        missing.fOther->fixOtherTIndex();
-    }
+    return bestTSpan;
 }
 
-bool SkOpSegment::coincidentSmall(const SkPoint& pt, double t, const SkOpSegment* other) const {
-    int count = this->count();
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = this->span(index);
-        if (span.fOther != other) {
-            continue;
-        }
-        if (span.fPt == pt) {
-            continue;
-        }
-        if (!AlmostEqualUlps(span.fPt, pt)) {
-            continue;
-        }
-        if (fVerb != SkPath::kCubic_Verb) {
-            return true;
-        }
-        double tInterval = t - span.fT;
-        double tMid = t - tInterval / 2;
-        SkDPoint midPt = dcubic_xy_at_t(fPts, tMid);
-        return midPt.approximatelyEqual(xyAtT(t));
+void SkOpSegment::detach(const SkOpSpan* span) {
+    if (span->done()) {
+        --this->fDoneCount;
     }
-    return false;
+    --this->fCount;
 }
 
-bool SkOpSegment::findCoincidentMatch(const SkOpSpan* span, const SkOpSegment* other, int oStart,
-        int oEnd, int step, SkPoint* startPt, SkPoint* endPt, double* endT) const {
-    SkASSERT(span->fT == 0 || span->fT == 1);
-    SkASSERT(span->fOtherT == 0 || span->fOtherT == 1);
-    const SkOpSpan* otherSpan = &other->span(oEnd);
-    double refT = otherSpan->fT;
-    const SkPoint& refPt = otherSpan->fPt;
-    const SkOpSpan* lastSpan = &other->span(step > 0 ? other->count() - 1 : 0);
-    do {
-        const SkOpSegment* match = span->fOther;
-        if (match == otherSpan->fOther) {
-            // find start of respective spans and see if both have winding
-            int startIndex, endIndex;
-            if (span->fOtherT == 1) {
-                endIndex = span->fOtherIndex;
-                startIndex = match->nextExactSpan(endIndex, -1);
-            } else {
-                startIndex = span->fOtherIndex;
-                endIndex = match->nextExactSpan(startIndex, 1);
-            }
-            const SkOpSpan& startSpan = match->span(startIndex);
-            if (startSpan.fWindValue != 0) {
-                // draw ray from endSpan.fPt perpendicular to end tangent and measure distance
-                // to other segment.
-                const SkOpSpan& endSpan = match->span(endIndex);
-                SkDLine ray;
-                SkVector dxdy;
-                if (span->fOtherT == 1) {
-                    ray.fPts[0].set(startSpan.fPt);
-                    dxdy = match->dxdy(startIndex);
-                } else {
-                    ray.fPts[0].set(endSpan.fPt);
-                    dxdy = match->dxdy(endIndex);
-                }
-                ray.fPts[1].fX = ray.fPts[0].fX + dxdy.fY;
-                ray.fPts[1].fY = ray.fPts[0].fY - dxdy.fX;
-                SkIntersections i;
-                int roots = (i.*CurveRay[SkPathOpsVerbToPoints(other->verb())])(other->pts(), ray);
-                for (int index = 0; index < roots; ++index) {
-                    if (ray.fPts[0].approximatelyEqual(i.pt(index))) {
-                        double matchMidT = (match->span(startIndex).fT
-                                + match->span(endIndex).fT) / 2;
-                        SkPoint matchMidPt = match->ptAtT(matchMidT);
-                        double otherMidT = (i[0][index] + other->span(oStart).fT) / 2;
-                        SkPoint otherMidPt = other->ptAtT(otherMidT);
-                        if (SkDPoint::ApproximatelyEqual(matchMidPt, otherMidPt)) {
-                            *startPt = startSpan.fPt;
-                            *endPt = endSpan.fPt;
-                            *endT = endSpan.fT;
-                            return true;
-                        }
-                    }
-                }
-            }
-            return false;
+double SkOpSegment::distSq(double t, SkOpAngle* oppAngle) {
+    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;
+    SkOpSegment* oppSegment = oppAngle->segment();
+    int oppPtCount = SkPathOpsVerbToPoints(oppSegment->verb());
+    (*CurveIntersectRay[oppPtCount])(oppSegment->pts(), 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;
         }
-        if (otherSpan == lastSpan) {
-            break;
+        double testDistSq = testPt.distanceSquared(i.pt(index));
+        if (closestDistSq > testDistSq) {
+            closestDistSq = testDistSq;
         }
-        otherSpan += step;
-    } while (otherSpan->fT == refT || otherSpan->fPt == refPt);
-    return false;
-}
-
-int SkOpSegment::findEndSpan(int endIndex) const {
-    const SkOpSpan* span = &fTs[--endIndex];
-    const SkPoint& lastPt = span->fPt;
-    double endT = span->fT;
-    do {
-        span = &fTs[--endIndex];
-    } while (SkDPoint::ApproximatelyEqual(span->fPt, lastPt) && (span->fT == endT || span->fTiny));
-    return endIndex + 1;
+    }
+    return closestDistSq;
 }
 
 /*
@@ -3029,71 +789,57 @@ int SkOpSegment::findEndSpan(int endIndex) const {
  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<SkOpSpan*>* chase, int* nextStart, int* nextEnd,
-                                     bool* unsortable, SkPathOp op, const int xorMiMask,
-                                     const int xorSuMask) {
-    const int startIndex = *nextStart;
-    const int endIndex = *nextEnd;
-    SkASSERT(startIndex != endIndex);
-    SkDEBUGCODE(const int count = fTs.count());
-    SkASSERT(startIndex < endIndex ? startIndex < count - 1 : startIndex > 0);
-    int step = SkSign32(endIndex - startIndex);
-    *nextStart = startIndex;
-    SkOpSegment* other = isSimple(nextStart, &step);
-    if (other) 
-    {
+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
-        int min = SkMin32(startIndex, endIndex);
-        if (fTs[min].fDone) {
-            return NULL;
-        }
-        markDoneBinary(min);
-        double startT = other->fTs[*nextStart].fT;
-        *nextEnd = *nextStart;
-        do {
-            *nextEnd += step;
-        } while (precisely_zero(startT - other->fTs[*nextEnd].fT));
-        SkASSERT(step < 0 ? *nextEnd >= 0 : *nextEnd < other->fTs.count());
-        if (other->isTiny(SkMin32(*nextStart, *nextEnd))) {
-            *unsortable = true;
+        SkOpSpan* startSpan = start->starter(end);
+        if (startSpan->done()) {
             return NULL;
         }
+        markDone(startSpan);
+        *nextEnd = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
         return other;
     }
-    const int end = nextExactSpan(startIndex, step);
-    SkASSERT(end >= 0);
-    SkASSERT(startIndex - endIndex != 0);
-    SkASSERT((startIndex - endIndex < 0) ^ (step < 0));
+    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(startIndex, end, SkOpAngle::kBinaryOpp);
+    int calcWinding = computeSum(start, endNear, SkOpAngle::kBinaryOpp);
     bool sortable = calcWinding != SK_NaN32;
     if (!sortable) {
         *unsortable = true;
-        markDoneBinary(SkMin32(startIndex, endIndex));
+        markDone(start->starter(end));
         return NULL;
     }
-    SkOpAngle* angle = spanToAngle(end, startIndex);
+    SkOpAngle* angle = this->spanToAngle(end, start);
     if (angle->unorderable()) {
         *unsortable = true;
-        markDoneBinary(SkMin32(startIndex, endIndex));
+        markDone(start->starter(end));
         return NULL;
     }
 #if DEBUG_SORT
     SkDebugf("%s\n", __FUNCTION__);
     angle->debugLoop();
 #endif
-    int sumMiWinding = updateWinding(endIndex, startIndex);
+    int sumMiWinding = updateWinding(end, start);
     if (sumMiWinding == SK_MinS32) {
         *unsortable = true;
-        markDoneBinary(SkMin32(startIndex, endIndex));
+        markDone(start->starter(end));
         return NULL;
     }
-    int sumSuWinding = updateOppWinding(endIndex, startIndex);
+    int sumSuWinding = updateOppWinding(end, start);
     if (operand()) {
         SkTSwap<int>(sumMiWinding, sumSuWinding);
     }
@@ -3110,11 +856,6 @@ SkOpSegment* SkOpSegment::findNextOp(SkTDArray<SkOpSpan*>* chase, int* nextStart
         if (activeAngle) {
             ++activeCount;
             if (!foundAngle || (foundDone && activeCount & 1)) {
-                if (nextSegment->isTiny(nextAngle)) {
-                    *unsortable = true;
-                    markDoneBinary(SkMin32(startIndex, endIndex));
-                    return NULL;
-                }
                 foundAngle = nextAngle;
                 foundDone = nextSegment->done(nextAngle);
             }
@@ -3122,30 +863,24 @@ SkOpSegment* SkOpSegment::findNextOp(SkTDArray<SkOpSpan*>* chase, int* nextStart
         if (nextSegment->done()) {
             continue;
         }
-        if (nextSegment->isTiny(nextAngle)) {
-            continue;
-        }
         if (!activeAngle) {
-            (void) nextSegment->markAndChaseDoneBinary(nextAngle->start(), nextAngle->end());
+            (void) nextSegment->markAndChaseDone(nextAngle->start(), nextAngle->end());
         }
-        SkOpSpan* last = nextAngle->lastMarked();
+        SkOpSpanBase* last = nextAngle->lastMarked();
         if (last) {
             SkASSERT(!SkPathOpsDebug::ChaseContains(*chase, last));
             *chase->append() = last;
 #if DEBUG_WINDING
-            SkDebugf("%s chase.append id=%d windSum=%d small=%d\n", __FUNCTION__,
-                    last->fOther->fTs[last->fOtherIndex].fOther->debugID(), last->fWindSum,
-                    last->fSmall);
+            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);
-#if DEBUG_ANGLE
-    if (foundAngle) {
-        foundAngle->debugSameAs(foundAngle);
-    }
-#endif
-
-    markDoneBinary(SkMin32(startIndex, endIndex));
+    start->segment()->markDone(start->starter(end));
     if (!foundAngle) {
         return NULL;
     }
@@ -3159,62 +894,55 @@ SkOpSegment* SkOpSegment::findNextOp(SkTDArray<SkOpSpan*>* chase, int* nextStart
     return nextSegment;
 }
 
-SkOpSegment* SkOpSegment::findNextWinding(SkTDArray<SkOpSpan*>* chase, int* nextStart,
-                                          int* nextEnd, bool* unsortable) {
-    const int startIndex = *nextStart;
-    const int endIndex = *nextEnd;
-    SkASSERT(startIndex != endIndex);
-    SkDEBUGCODE(const int count = fTs.count());
-    SkASSERT(startIndex < endIndex ? startIndex < count - 1 : startIndex > 0);
-    int step = SkSign32(endIndex - startIndex);
-    *nextStart = startIndex;
-    SkOpSegment* other = isSimple(nextStart, &step);
-    if (other) 
-    {
+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
-        int min = SkMin32(startIndex, endIndex);
-        if (fTs[min].fDone) {
-            return NULL;
-        }
-        markDoneUnary(min);
-        double startT = other->fTs[*nextStart].fT;
-        *nextEnd = *nextStart;
-        do {
-            *nextEnd += step;
-        } while (precisely_zero(startT - other->fTs[*nextEnd].fT));
-        SkASSERT(step < 0 ? *nextEnd >= 0 : *nextEnd < other->fTs.count());
-        if (other->isTiny(SkMin32(*nextStart, *nextEnd))) {
-            *unsortable = true;
+        SkOpSpan* startSpan = start->starter(end);
+        if (startSpan->done()) {
             return NULL;
         }
+        markDone(startSpan);
+        *nextEnd = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
         return other;
     }
-    const int end = nextExactSpan(startIndex, step);
-    SkASSERT(end >= 0);
-    SkASSERT(startIndex - endIndex != 0);
-    SkASSERT((startIndex - endIndex < 0) ^ (step < 0));
+    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(startIndex, end, SkOpAngle::kUnaryWinding);
+    int calcWinding = computeSum(start, endNear, SkOpAngle::kUnaryWinding);
     bool sortable = calcWinding != SK_NaN32;
     if (!sortable) {
         *unsortable = true;
-        markDoneUnary(SkMin32(startIndex, endIndex));
+        markDone(start->starter(end));
+        return NULL;
+    }
+    SkOpAngle* angle = this->spanToAngle(end, start);
+    if (angle->unorderable()) {
+        *unsortable = true;
+        markDone(start->starter(end));
         return NULL;
     }
-    SkOpAngle* angle = spanToAngle(end, startIndex);
 #if DEBUG_SORT
     SkDebugf("%s\n", __FUNCTION__);
     angle->debugLoop();
 #endif
-    int sumWinding = updateWinding(endIndex, startIndex);
+    int sumWinding = updateWinding(end, start);
     SkOpAngle* nextAngle = angle->next();
     const SkOpAngle* foundAngle = NULL;
     bool foundDone = false;
+    // iterate through the angle, and compute everyone's winding
     SkOpSegment* nextSegment;
     int activeCount = 0;
     do {
@@ -3224,11 +952,6 @@ SkOpSegment* SkOpSegment::findNextWinding(SkTDArray<SkOpSpan*>* chase, int* next
         if (activeAngle) {
             ++activeCount;
             if (!foundAngle || (foundDone && activeCount & 1)) {
-                if (nextSegment->isTiny(nextAngle)) {
-                    *unsortable = true;
-                    markDoneUnary(SkMin32(startIndex, endIndex));
-                    return NULL;
-                }
                 foundAngle = nextAngle;
                 foundDone = nextSegment->done(nextAngle);
             }
@@ -3236,24 +959,24 @@ SkOpSegment* SkOpSegment::findNextWinding(SkTDArray<SkOpSpan*>* chase, int* next
         if (nextSegment->done()) {
             continue;
         }
-        if (nextSegment->isTiny(nextAngle)) {
-            continue;
-        }
         if (!activeAngle) {
-            nextSegment->markAndChaseDoneUnary(nextAngle->start(), nextAngle->end());
+            (void) nextSegment->markAndChaseDone(nextAngle->start(), nextAngle->end());
         }
-        SkOpSpan* last = nextAngle->lastMarked();
+        SkOpSpanBase* last = nextAngle->lastMarked();
         if (last) {
             SkASSERT(!SkPathOpsDebug::ChaseContains(*chase, last));
             *chase->append() = last;
 #if DEBUG_WINDING
-            SkDebugf("%s chase.append id=%d windSum=%d small=%d\n", __FUNCTION__,
-                    last->fOther->fTs[last->fOtherIndex].fOther->debugID(), last->fWindSum,
-                    last->fSmall);
+            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);
-    markDoneUnary(SkMin32(startIndex, endIndex));
+    start->segment()->markDone(start->starter(end));
     if (!foundAngle) {
         return NULL;
     }
@@ -3267,57 +990,39 @@ SkOpSegment* SkOpSegment::findNextWinding(SkTDArray<SkOpSpan*>* chase, int* next
     return nextSegment;
 }
 
-SkOpSegment* SkOpSegment::findNextXor(int* nextStart, int* nextEnd, bool* unsortable) {
-    const int startIndex = *nextStart;
-    const int endIndex = *nextEnd;
-    SkASSERT(startIndex != endIndex);
-    SkDEBUGCODE(int count = fTs.count());
-    SkASSERT(startIndex < endIndex ? startIndex < count - 1 : startIndex > 0);
-    int step = SkSign32(endIndex - startIndex);
-// Detect cases where all the ends canceled out (e.g.,
-// there is no angle) and therefore there's only one valid connection 
-    *nextStart = startIndex;
-    SkOpSegment* other = isSimple(nextStart, &step);
-    if (other)
-    {
+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
-        int min = SkMin32(startIndex, endIndex);
-        if (fTs[min].fDone) {
+        SkOpSpan* startSpan = start->starter(end);
+        if (startSpan->done()) {
             return NULL;
         }
-        markDone(min, 1);
-        double startT = other->fTs[*nextStart].fT;
-        // FIXME: I don't know why the logic here is difference from the winding case
-        SkDEBUGCODE(bool firstLoop = true;)
-        if ((approximately_less_than_zero(startT) && step < 0)
-                || (approximately_greater_than_one(startT) && step > 0)) {
-            step = -step;
-            SkDEBUGCODE(firstLoop = false;)
-        }
-        do {
-            *nextEnd = *nextStart;
-            do {
-                *nextEnd += step;
-            } while (precisely_zero(startT - other->fTs[*nextEnd].fT));
-            if (other->fTs[SkMin32(*nextStart, *nextEnd)].fWindValue) {
-                break;
-            }
-            SkASSERT(firstLoop);
-            SkDEBUGCODE(firstLoop = false;)
-            step = -step;
-        } while (true);
-        SkASSERT(step < 0 ? *nextEnd >= 0 : *nextEnd < other->fTs.count());
+        markDone(startSpan);
+        *nextEnd = step > 0 ? (*nextStart)->upCast()->next() : (*nextStart)->prev();
         return other;
     }
-    SkASSERT(startIndex - endIndex != 0);
-    SkASSERT((startIndex - endIndex < 0) ^ (step < 0));
-    // parallel block above with presorted version
-    int end = nextExactSpan(startIndex, step);
-    SkASSERT(end >= 0);
-    SkOpAngle* angle = spanToAngle(end, startIndex);
-    SkASSERT(angle);
+    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->unorderable()) {
+        *unsortable = true;
+        markDone(start->starter(end));
+        return NULL;
+    }
 #if DEBUG_SORT
     SkDebugf("%s\n", __FUNCTION__);
     angle->debugLoop();
@@ -3325,16 +1030,13 @@ SkOpSegment* SkOpSegment::findNextXor(int* nextStart, int* nextEnd, bool* unsort
     SkOpAngle* nextAngle = angle->next();
     const SkOpAngle* foundAngle = NULL;
     bool foundDone = false;
+    // iterate through the angle, and compute everyone's winding
     SkOpSegment* nextSegment;
     int activeCount = 0;
     do {
         nextSegment = nextAngle->segment();
         ++activeCount;
         if (!foundAngle || (foundDone && activeCount & 1)) {
-            if (nextSegment->isTiny(nextAngle)) {
-                *unsortable = true;
-                return NULL;
-            }
             foundAngle = nextAngle;
             if (!(foundDone = nextSegment->done(nextAngle))) {
                 break;
@@ -3342,7 +1044,7 @@ SkOpSegment* SkOpSegment::findNextXor(int* nextStart, int* nextEnd, bool* unsort
         }
         nextAngle = nextAngle->next();
     } while (nextAngle != angle);
-    markDone(SkMin32(startIndex, endIndex), 1);
+    start->segment()->markDone(start->starter(end));
     if (!foundAngle) {
         return NULL;
     }
@@ -3356,105 +1058,39 @@ SkOpSegment* SkOpSegment::findNextXor(int* nextStart, int* nextEnd, bool* unsort
     return nextSegment;
 }
 
-int SkOpSegment::findStartSpan(int startIndex) const {
-    int index = startIndex;
-    const SkOpSpan* span = &fTs[index];
-    const SkPoint& firstPt = span->fPt;
-    double firstT = span->fT;
-    const SkOpSpan* prior;
-    do {
-        prior = span;
-        span = &fTs[++index];
-    } while (SkDPoint::ApproximatelyEqual(span->fPt, firstPt)
-            && (span->fT == firstT || prior->fTiny));
-    return index;
-}
-
-int SkOpSegment::findExactT(double t, const SkOpSegment* match) const {
-    int count = this->count();
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (span.fT == t && span.fOther == match) {
-            return index;
-        }
-    }
-    SkASSERT(0);
-    return -1;
-}
-
-
-
-int SkOpSegment::findOtherT(double t, const SkOpSegment* match) const {
-    int count = this->count();
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (span.fOtherT == t && span.fOther == match) {
-            return index;
-        }
-    }
-    return -1;
-}
-
-int SkOpSegment::findT(double t, const SkPoint& pt, const SkOpSegment* match) const {
-    int count = this->count();
-    // prefer exact matches over approximate matches
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (span.fT == t && span.fOther == match) {
-            return index;
-        }
-    }
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (approximately_equal_orderable(span.fT, t) && span.fOther == match) {
-            return index;
-        }
-    }
-    // Usually, the pair of ts are an exact match. It's possible that the t values have
-    // been adjusted to make multiple intersections align. In this rare case, look for a
-    // matching point / match pair instead.
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (span.fPt == pt && span.fOther == match) {
-            return index;
-        }
-    }
-    SkASSERT(0);
-    return -1;
-}
-
-SkOpSegment* SkOpSegment::findTop(int* tIndexPtr, int* endIndexPtr, bool* unsortable,
-        bool firstPass) {
+SkOpSegment* SkOpSegment::findTop(bool firstPass, SkOpSpanBase** startPtr, SkOpSpanBase** endPtr,
+        bool* unsortable, SkChunkAlloc* allocator) {
     // iterate through T intersections and return topmost
     // topmost tangent from y-min to first pt is closer to horizontal
     SkASSERT(!done());
-    int firstT = -1;
-    /* SkPoint topPt = */ activeLeftTop(&firstT);
-    if (firstT < 0) {
+    SkOpSpanBase* firstT = NULL;
+    (void) this->activeLeftTop(&firstT);
+    if (!firstT) {
         *unsortable = !firstPass;
-        firstT = 0;
-        while (fTs[firstT].fDone) {
-            SkASSERT(firstT < fTs.count());
-            ++firstT;
+        firstT = &fHead;
+        while (firstT->upCast()->done()) {
+            firstT = firstT->upCast()->next();
         }
-        *tIndexPtr = firstT;
-        *endIndexPtr = nextExactSpan(firstT, 1);
+        *startPtr = firstT;
+        *endPtr = firstT->upCast()->next();
         return this;
     }
     // sort the edges to find the leftmost
     int step = 1;
-    int end;
-    if (span(firstT).fDone || (end = nextSpan(firstT, step)) == -1) {
+    SkOpSpanBase* end;
+    if (firstT->final() || firstT->upCast()->done()) {
         step = -1;
-        end = nextSpan(firstT, step);
-        SkASSERT(end != -1);
+        end = firstT->prev();
+        SkASSERT(end);
+    } else {
+        end = firstT->upCast()->next();
     }
     // if the topmost T is not on end, or is three-way or more, find left
     // look for left-ness from tLeft to firstT (matching y of other)
-    SkASSERT(firstT - end != 0);
+    SkASSERT(firstT != end);
     SkOpAngle* markAngle = spanToAngle(firstT, end);
     if (!markAngle) {
-        markAngle = addSingletonAngles(step);
+        markAngle = addSingletonAngles(step, allocator);
     }
     markAngle->markStops();
     const SkOpAngle* baseAngle = markAngle->next() == markAngle && !isVertical() ? markAngle
@@ -3467,7 +1103,7 @@ SkOpSegment* SkOpSegment::findTop(int* tIndexPtr, int* endIndexPtr, bool* unsort
     const SkOpAngle* angle = baseAngle;
     do {
         if (!angle->unorderable()) {
-            SkOpSegment* next = angle->segment();
+            const SkOpSegment* next = angle->segment();
             SkPathOpsBounds bounds;
             next->subDivideBounds(angle->end(), angle->start(), &bounds);
             bool nearSame = AlmostEqualUlps(top, bounds.top());
@@ -3495,9 +1131,10 @@ SkOpSegment* SkOpSegment::findTop(int* tIndexPtr, int* endIndexPtr, bool* unsort
         *unsortable = angle->unorderable();
         if (firstPass || !*unsortable) {
             leftSegment = angle->segment();
-            *tIndexPtr = angle->end();
-            *endIndexPtr = angle->start();
-            if (!leftSegment->fTs[SkMin32(*tIndexPtr, *endIndexPtr)].fDone) {
+            *startPtr = angle->end();
+            *endPtr = angle->start();
+            const SkOpSpan* firstSpan = (*startPtr)->starter(*endPtr);
+            if (!firstSpan->done()) {
                 break;
             }
         }
@@ -3508,157 +1145,52 @@ SkOpSegment* SkOpSegment::findTop(int* tIndexPtr, int* endIndexPtr, bool* unsort
         return NULL;
     }
     if (leftSegment->verb() >= SkPath::kQuad_Verb) {
-        const int tIndex = *tIndexPtr;
-        const int endIndex = *endIndexPtr;
+        SkOpSpanBase* start = *startPtr;
+        SkOpSpanBase* end = *endPtr;
         bool swap;
-        if (!leftSegment->clockwise(tIndex, endIndex, &swap)) {
+        if (!leftSegment->clockwise(start, end, &swap)) {
     #if DEBUG_SWAP_TOP
-            SkDebugf("%s swap=%d inflections=%d serpentine=%d controlledbyends=%d monotonic=%d\n",
+            SkDebugf("%s swap=%d inflections=%d monotonic=%d\n",
                     __FUNCTION__,
-                    swap, leftSegment->debugInflections(tIndex, endIndex),
-                    leftSegment->serpentine(tIndex, endIndex),
-                    leftSegment->controlsContainedByEnds(tIndex, endIndex),
-                    leftSegment->monotonicInY(tIndex, endIndex));
+                    swap, leftSegment->debugInflections(start, end),
+                    leftSegment->monotonicInY(start, end));
     #endif
             if (swap) {
     // FIXME: I doubt it makes sense to (necessarily) swap if the edge was not the first
     // sorted but merely the first not already processed (i.e., not done)
-                SkTSwap(*tIndexPtr, *endIndexPtr);
+                SkTSwap(*startPtr, *endPtr);
             }
         }
     }
-    SkASSERT(!leftSegment->fTs[SkMin32(*tIndexPtr, *endIndexPtr)].fTiny);
     return leftSegment;
 }
 
-int SkOpSegment::firstActive(int tIndex) const {
-    while (fTs[tIndex].fTiny) {
-        SkASSERT(!isCanceled(tIndex));
-        ++tIndex;
-    }
-    return tIndex;
-}
-
-// FIXME: not crazy about this
-// when the intersections are performed, the other index is into an
-// incomplete array. As the array grows, the indices become incorrect
-// while the following fixes the indices up again, it isn't smart about
-// skipping segments whose indices are already correct
-// assuming we leave the code that wrote the index in the first place
-// FIXME: if called after remove, this needs to correct tiny
-void SkOpSegment::fixOtherTIndex() {
-    int iCount = fTs.count();
-    for (int i = 0; i < iCount; ++i) {
-        SkOpSpan& iSpan = fTs[i];
-        double oT = iSpan.fOtherT;
-        SkOpSegment* other = iSpan.fOther;
-        int oCount = other->fTs.count();
-        SkDEBUGCODE(iSpan.fOtherIndex = -1);
-        for (int o = 0; o < oCount; ++o) {
-            SkOpSpan& oSpan = other->fTs[o];
-            if (oT == oSpan.fT && this == oSpan.fOther && oSpan.fOtherT == iSpan.fT) {
-                iSpan.fOtherIndex = o;
-                oSpan.fOtherIndex = i;
-                break;
-            }
-        }
-        SkASSERT(iSpan.fOtherIndex >= 0);
-    }
-}
-
-bool SkOpSegment::inCoincidentSpan(double t, const SkOpSegment* other) const {
-    int foundEnds = 0;
-    int count = this->count();
-    for (int index = 0; index < count; ++index) {
-        const SkOpSpan& span = this->span(index);
-        if (span.fCoincident) {
-            foundEnds |= (span.fOther == other) << ((t > span.fT) + (t >= span.fT));
-        }
-    }
-    SkASSERT(foundEnds != 7);
-    return foundEnds == 0x3 || foundEnds == 0x5 || foundEnds == 0x6;  // two bits set
-}
-
-bool SkOpSegment::inconsistentAngle(int maxWinding, int sumWinding, int oppMaxWinding,
-        int oppSumWinding, const SkOpAngle* angle) const {
-    SkASSERT(angle->segment() == this);
-    if (UseInnerWinding(maxWinding, sumWinding)) {
-        maxWinding = sumWinding;
-    }
-    if (oppMaxWinding != oppSumWinding && UseInnerWinding(oppMaxWinding, oppSumWinding)) {
-        oppMaxWinding = oppSumWinding;
-    }
-    return inconsistentWinding(angle, maxWinding, oppMaxWinding);
-}
-
-bool SkOpSegment::inconsistentWinding(const SkOpAngle* angle, int winding,
-        int oppWinding) const {
-    int index = angle->start();
-    int endIndex = angle->end();
-    int min = SkMin32(index, endIndex);
-    int step = SkSign32(endIndex - index);
-    if (inconsistentWinding(min, winding, oppWinding)) {
-        return true;
-    }
-    const SkOpSegment* other = this;
-    while ((other = other->nextChase(&index, &step, &min, NULL))) {
-        if (other->fTs[min].fWindSum != SK_MinS32) {
-            break;
-        }
-        if (fOperand == other->fOperand) {
-            if (other->inconsistentWinding(min, winding, oppWinding)) {
-                return true;
-            }
-        } else {
-            if (other->inconsistentWinding(min, oppWinding, winding)) {
-                return true;
-            }
-        }
-    }
-    return false;
-}
-
-bool SkOpSegment::inconsistentWinding(int index, int winding, int oppWinding) const {
-    SkASSERT(winding || oppWinding);
-    double referenceT = this->span(index).fT;
-    int lesser = index;
-    while (--lesser >= 0 && precisely_negative(referenceT - fTs[lesser].fT)) {
-        if (inconsistentWinding(__FUNCTION__, lesser, winding, oppWinding)) {
-            return true;
-        }
-    }
-    do {
-        if (inconsistentWinding(__FUNCTION__, index, winding, oppWinding)) {
-            return true;
-        }
-   } while (++index < fTs.count() && precisely_negative(fTs[index].fT - referenceT));
-    return false;
-}
-
-bool SkOpSegment::inconsistentWinding(const char* funName, int tIndex, int winding,
-        int oppWinding) const {
-    const SkOpSpan& span = this->span(tIndex);
-    if (span.fDone && !span.fSmall) {
-        return false;
-    }
-    return (span.fWindSum != SK_MinS32 && span.fWindSum != winding)
-            || (span.fOppSum != SK_MinS32 && span.fOppSum != oppWinding);
+SkOpGlobalState* SkOpSegment::globalState() const {
+    return contour()->globalState(); 
 }
 
-void SkOpSegment::init(const SkPoint pts[], SkPath::Verb verb, bool operand, bool evenOdd) {
-    fDoneSpans = 0;
-    fOperand = operand;
-    fXor = evenOdd;
+void SkOpSegment::init(SkPoint pts[], SkOpContour* contour, SkPath::Verb verb) {
+    fContour = contour;
+    fNext = NULL;
     fPts = pts;
     fVerb = verb;
-    fLoop = fMultiples = fSmall = fTiny = false;
-}
-
-void SkOpSegment::initWinding(int start, int end, SkOpAngle::IncludeType angleIncludeType) {
-    int local = spanSign(start, end);
+    fCount = 0;
+    fDoneCount = 0;
+    fVisited = false;
+    SkOpSpan* zeroSpan = &fHead;
+    zeroSpan->init(this, NULL, 0, fPts[0]);
+    SkOpSpanBase* oneSpan = &fTail;
+    zeroSpan->setNext(oneSpan);
+    oneSpan->initBase(this, zeroSpan, 1, fPts[SkPathOpsVerbToPoints(fVerb)]);
+    PATH_OPS_DEBUG_CODE(fID = globalState()->nextSegmentID());
+}
+
+void SkOpSegment::initWinding(SkOpSpanBase* start, SkOpSpanBase* end,
+        SkOpAngle::IncludeType angleIncludeType) {
+    int local = SkOpSegment::SpanSign(start, end);
     SkDEBUGCODE(bool success);
     if (angleIncludeType == SkOpAngle::kBinarySingle) {
-        int oppLocal = oppSign(start, end);
+        int oppLocal = SkOpSegment::OppSign(start, end);
         SkDEBUGCODE(success =) markAndChaseWinding(start, end, local, oppLocal, NULL);
     // OPTIMIZATION: the reverse mark and chase could skip the first marking
         SkDEBUGCODE(success |=) markAndChaseWinding(end, start, local, oppLocal, NULL);
@@ -3679,12 +1211,13 @@ If there was a winding, then it may or may not need adjusting. If the span the w
 from has the same x direction as this span, the winding should change. If the dx is opposite, then
 the same winding is shared by both.
 */
-bool SkOpSegment::initWinding(int start, int end, double tHit, int winding, SkScalar hitDx,
-                              int oppWind, SkScalar hitOppDx) {
+bool SkOpSegment::initWinding(SkOpSpanBase* start, SkOpSpanBase* end, double tHit,
+        int winding, SkScalar hitDx, int oppWind, SkScalar hitOppDx) {
+    SkASSERT(this == start->segment());
     SkASSERT(hitDx || !winding);
     SkScalar dx = (*CurveSlopeAtT[SkPathOpsVerbToPoints(fVerb)])(fPts, tHit).fX;
-    SkASSERT(dx);
-    int windVal = windValue(SkMin32(start, end));
+//    SkASSERT(dx);
+    int windVal = start->starter(end)->windValue();
 #if DEBUG_WINDING_AT_T
     SkDebugf("%s id=%d oldWinding=%d hitDx=%c dx=%c windVal=%d", __FUNCTION__, debugID(), winding,
             hitDx ? hitDx > 0 ? '+' : '-' : '0', dx > 0 ? '+' : '-', windVal);
@@ -3693,9 +1226,9 @@ bool SkOpSegment::initWinding(int start, int end, double tHit, int winding, SkSc
     if (abs(winding) < abs(sideWind)) {
         winding = sideWind;
     }
-    SkDEBUGCODE(int oppLocal = oppSign(start, end));
+    SkDEBUGCODE(int oppLocal = SkOpSegment::OppSign(start, end));
     SkASSERT(hitOppDx || !oppWind || !oppLocal);
-    int oppWindVal = oppValue(SkMin32(start, end));
+    int oppWindVal = start->starter(end)->oppValue();
     if (!oppWind) {
         oppWind = dx < 0 ? oppWindVal : -oppWindVal;
     } else if (hitOppDx * dx >= 0) {
@@ -3714,149 +1247,57 @@ bool SkOpSegment::initWinding(int start, int end, double tHit, int winding, SkSc
     return success;
 }
 
-bool SkOpSegment::inLoop(const SkOpAngle* baseAngle, int spanCount, int* indexPtr) const {
-    if (!baseAngle->inLoop()) {
-        return false;
-    }
-    int index = *indexPtr;
-    SkOpAngle* from = fTs[index].fFromAngle;
-    SkOpAngle* to = fTs[index].fToAngle;
-    while (++index < spanCount) {
-        SkOpAngle* nextFrom = fTs[index].fFromAngle;
-        SkOpAngle* nextTo = fTs[index].fToAngle;
-        if (from != nextFrom || to != nextTo) {
-            break;
-        }
-    }
-    *indexPtr = index;
-    return true;
-}
-
-// OPTIMIZE: successive calls could start were the last leaves off
-// or calls could specialize to walk forwards or backwards
-bool SkOpSegment::isMissing(double startT, const SkPoint& pt) const {
-    int tCount = fTs.count();
-    for (int index = 0; index < tCount; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (approximately_zero(startT - span.fT) && pt == span.fPt) {
-            return false;
-        }
-    }
-    return true;
-}
-
-
-SkOpSegment* SkOpSegment::isSimple(int* end, int* step) {
-    return nextChase(end, step, NULL, NULL);
-}
-
-bool SkOpSegment::isTiny(const SkOpAngle* angle) const {
-    int start = angle->start();
-    int end = angle->end();
-    const SkOpSpan& mSpan = fTs[SkMin32(start, end)];
-    return mSpan.fTiny;
-}
-
-bool SkOpSegment::isTiny(int index) const {
-    return fTs[index].fTiny;
-}
-
-// look pair of active edges going away from coincident edge
-// one of them should be the continuation of other
-// if both are active, look to see if they both the connect to another coincident pair
-// if at least one is a line, then make the pair coincident
-// if neither is a line, test for coincidence
-bool SkOpSegment::joinCoincidence(SkOpSegment* other, double otherT, const SkPoint& otherPt,
-        int step, bool cancel) {
-    int otherTIndex = other->findT(otherT, otherPt, this);
-    int next = other->nextExactSpan(otherTIndex, step);
-    int otherMin = SkMin32(otherTIndex, next);
-    int otherWind = other->span(otherMin).fWindValue;
-    if (otherWind == 0) {
-        return false;
-    }
-    if (next < 0) {
-        return false;  // can happen if t values were adjusted but coincident ts were not
-    }
-    int tIndex = 0;
-    do {
-        SkOpSpan* test = &fTs[tIndex];
-        SkASSERT(test->fT == 0);
-        if (test->fOther == other || test->fOtherT != 1) {
-            continue;
-        }
-        SkPoint startPt, endPt;
-        double endT;
-        if (findCoincidentMatch(test, other, otherTIndex, next, step, &startPt, &endPt, &endT)) {
-            SkOpSegment* match = test->fOther;
-            if (cancel) {
-                match->addTCancel(startPt, endPt, other);
-            } else {
-                if (!match->addTCoincident(startPt, endPt, endT, other)) {
-                    return false;
-                }
-            }
+bool SkOpSegment::isClose(double t, const SkOpSegment* opp) const {
+    SkDPoint cPt = this->dPtAtT(t);
+    int pts = SkPathOpsVerbToPoints(this->verb());
+    SkDVector dxdy = (*CurveDSlopeAtT[pts])(this->pts(), t);
+    SkDLine perp = {{ cPt, {cPt.fX + dxdy.fY, cPt.fY - dxdy.fX} }};
+    SkIntersections i;
+    int oppPts = SkPathOpsVerbToPoints(opp->verb());
+    (*CurveIntersectRay[oppPts])(opp->pts(), perp, &i);
+    int used = i.used();
+    for (int index = 0; index < used; ++index) {
+        if (cPt.roughlyEqual(i.pt(index))) {
             return true;
         }
-    } while (fTs[++tIndex].fT == 0);
+    }
     return false;
 }
 
-// this span is excluded by the winding rule -- chase the ends
-// as long as they are unambiguous to mark connections as done
-// and give them the same winding value
-
-SkOpSpan* SkOpSegment::markAndChaseDoneBinary(int index, int endIndex) {
-    int step = SkSign32(endIndex - index);
-    int min = SkMin32(index, endIndex);
-    markDoneBinary(min);
-    SkOpSpan* last = NULL;
-    SkOpSegment* other = this;
-    while ((other = other->nextChase(&index, &step, &min, &last))) {
-        if (other->done()) {
-            SkASSERT(!last);
-            break;
-        }
-        other->markDoneBinary(min);
-    }
-    return last;
+bool SkOpSegment::isXor() const {
+    return fContour->isXor();
 }
 
-SkOpSpan* SkOpSegment::markAndChaseDoneUnary(int index, int endIndex) {
-    int step = SkSign32(endIndex - index);
-    int min = SkMin32(index, endIndex);
-    markDoneUnary(min);
-    SkOpSpan* last = NULL;
+SkOpSpanBase* SkOpSegment::markAndChaseDone(SkOpSpanBase* start, SkOpSpanBase* end) {
+    int step = start->step(end);
+    SkOpSpan* minSpan = start->starter(end);
+    markDone(minSpan);
+    SkOpSpanBase* last = NULL;
     SkOpSegment* other = this;
-    while ((other = other->nextChase(&index, &step, &min, &last))) {
+    while ((other = other->nextChase(&start, &step, &minSpan, &last))) {
         if (other->done()) {
             SkASSERT(!last);
             break;
         }
-        other->markDoneUnary(min);
+        other->markDone(minSpan);
     }
     return last;
 }
 
-bool SkOpSegment::markAndChaseWinding(const SkOpAngle* angle, int winding, SkOpSpan** lastPtr) {
-    int index = angle->start();
-    int endIndex = angle->end();
-    return markAndChaseWinding(index, endIndex, winding, lastPtr);
-}
-
-bool SkOpSegment::markAndChaseWinding(int index, int endIndex, int winding, SkOpSpan** lastPtr) {
-    int min = SkMin32(index, endIndex);
-    int step = SkSign32(endIndex - index);
-    bool success = markWinding(min, winding);
-    SkOpSpan* last = NULL;
+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 = NULL;
     SkOpSegment* other = this;
-    while ((other = other->nextChase(&index, &step, &min, &last))) {
-        if (other->fTs[min].fWindSum != SK_MinS32) {
-            SkASSERT(other->fTs[min].fWindSum == winding || other->fTs[min].fLoop);
+    while ((other = other->nextChase(&start, &step, &spanStart, &last))) {
+        if (spanStart->windSum() != SK_MinS32) {
+            SkASSERT(spanStart->windSum() == winding);
             SkASSERT(!last);
             break;
         }
-        (void) other->markWinding(min, winding);
+        (void) other->markWinding(spanStart, winding);
     }
     if (lastPtr) {
         *lastPtr = last;
@@ -3864,37 +1305,32 @@ bool SkOpSegment::markAndChaseWinding(int index, int endIndex, int winding, SkOp
     return success;
 }
 
-bool SkOpSegment::markAndChaseWinding(int index, int endIndex, int winding, int oppWinding,
-        SkOpSpan** lastPtr) {
-    int min = SkMin32(index, endIndex);
-    int step = SkSign32(endIndex - index);
-    bool success = markWinding(min, winding, oppWinding);
-    SkOpSpan* last = NULL;
+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 = NULL;
     SkOpSegment* other = this;
-    while ((other = other->nextChase(&index, &step, &min, &last))) {
-        if (other->fTs[min].fWindSum != SK_MinS32) {
-#ifdef SK_DEBUG
-            if (!other->fTs[min].fLoop) {
-                if (fOperand == other->fOperand) {
-// FIXME: this is probably a bug -- rects4 asserts here
-//                    SkASSERT(other->fTs[min].fWindSum == winding);
-// FIXME: this is probably a bug -- rects3 asserts here
-//                    SkASSERT(other->fTs[min].fOppSum == oppWinding);
-                } else {
-// FIXME: this is probably a bug -- issue414409b asserts here
-//                    SkASSERT(other->fTs[min].fWindSum == oppWinding);
-// FIXME: this is probably a bug -- skpwww_joomla_org_23 asserts here
-//                    SkASSERT(other->fTs[min].fOppSum == winding);
+    while ((other = other->nextChase(&start, &step, &spanStart, &last))) {
+        if (spanStart->windSum() != SK_MinS32) {
+            if (this->operand() == other->operand()) {
+                SkASSERT(spanStart->windSum() == winding);
+                if (spanStart->oppSum() != oppWinding) {
+                    this->globalState()->setWindingFailed();
+                    return false;
                 }
+            } else {
+                SkASSERT(spanStart->windSum() == oppWinding);
+                SkASSERT(spanStart->oppSum() == winding);
             }
             SkASSERT(!last);
-#endif
             break;
         }
-        if (fOperand == other->fOperand) {
-            (void) other->markWinding(min, winding, oppWinding);
+        if (this->operand() == other->operand()) {
+            (void) other->markWinding(spanStart, winding, oppWinding);
         } else {
-            (void) other->markWinding(min, oppWinding, winding);
+            (void) other->markWinding(spanStart, oppWinding, winding);
         }
     }
     if (lastPtr) {
@@ -3903,33 +1339,29 @@ bool SkOpSegment::markAndChaseWinding(int index, int endIndex, int winding, int
     return success;
 }
 
-bool SkOpSegment::markAndChaseWinding(const SkOpAngle* angle, int winding, int oppWinding,
-        SkOpSpan** lastPtr) {
-    int start = angle->start();
-    int end = angle->end();
-    return markAndChaseWinding(start, end, winding, oppWinding, lastPtr);
-}
-
-SkOpSpan* SkOpSegment::markAngle(int maxWinding, int sumWinding, const SkOpAngle* angle) {
+SkOpSpanBase* SkOpSegment::markAngle(int maxWinding, int sumWinding, const SkOpAngle* angle) {
     SkASSERT(angle->segment() == this);
     if (UseInnerWinding(maxWinding, sumWinding)) {
         maxWinding = sumWinding;
     }
-    SkOpSpan* last;
-    SkAssertResult(markAndChaseWinding(angle, maxWinding, &last));
+    SkOpSpanBase* last;
+    (void) markAndChaseWinding(angle->start(), angle->end(), maxWinding, &last);
 #if DEBUG_WINDING
     if (last) {
-        SkDebugf("%s last id=%d windSum=", __FUNCTION__,
-                last->fOther->fTs[last->fOtherIndex].fOther->debugID());
-        SkPathOpsDebug::WindingPrintf(last->fWindSum);
-        SkDebugf(" small=%d\n", last->fSmall);
+        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;
 }
 
-SkOpSpan* SkOpSegment::markAngle(int maxWinding, int sumWinding, int oppMaxWinding,
-                                 int oppSumWinding, const SkOpAngle* angle) {
+SkOpSpanBase* SkOpSegment::markAngle(int maxWinding, int sumWinding, int oppMaxWinding,
+                                   int oppSumWinding, const SkOpAngle* angle) {
     SkASSERT(angle->segment() == this);
     if (UseInnerWinding(maxWinding, sumWinding)) {
         maxWinding = sumWinding;
@@ -3937,440 +1369,161 @@ SkOpSpan* SkOpSegment::markAngle(int maxWinding, int sumWinding, int oppMaxWindi
     if (oppMaxWinding != oppSumWinding && UseInnerWinding(oppMaxWinding, oppSumWinding)) {
         oppMaxWinding = oppSumWinding;
     }
-    SkOpSpan* last;
+    SkOpSpanBase* last = NULL;
     // caller doesn't require that this marks anything
-    (void) markAndChaseWinding(angle, maxWinding, oppMaxWinding, &last);
+    (void) markAndChaseWinding(angle->start(), angle->end(), maxWinding, oppMaxWinding, &last);
 #if DEBUG_WINDING
     if (last) {
-        SkDebugf("%s last id=%d windSum=", __FUNCTION__,
-                last->fOther->fTs[last->fOtherIndex].fOther->debugID());
-        SkPathOpsDebug::WindingPrintf(last->fWindSum);
-        SkDebugf(" small=%d\n", last->fSmall);
+        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;
 }
 
-// FIXME: this should also mark spans with equal (x,y)
-// This may be called when the segment is already marked done. While this
-// wastes time, it shouldn't do any more than spin through the T spans.
-// OPTIMIZATION: abort on first done found (assuming that this code is
-// always called to mark segments done).
-void SkOpSegment::markDone(int index, int winding) {
-  //  SkASSERT(!done());
-    SkASSERT(winding);
-    double referenceT = fTs[index].fT;
-    int lesser = index;
-    while (--lesser >= 0 && precisely_negative(referenceT - fTs[lesser].fT)) {
-        markOneDone(__FUNCTION__, lesser, winding);
-    }
-    do {
-        markOneDone(__FUNCTION__, index, winding);
-    } while (++index < fTs.count() && precisely_negative(fTs[index].fT - referenceT));
-    debugValidate();
-}
-
-void SkOpSegment::markDoneBinary(int index) {
-    double referenceT = fTs[index].fT;
-    int lesser = index;
-    while (--lesser >= 0 && precisely_negative(referenceT - fTs[lesser].fT)) {
-        markOneDoneBinary(__FUNCTION__, lesser);
-    }
-    do {
-        markOneDoneBinary(__FUNCTION__, index);
-    } while (++index < fTs.count() && precisely_negative(fTs[index].fT - referenceT));
-    debugValidate();
-}
-
-void SkOpSegment::markDoneFinal(int index) {
-    double referenceT = fTs[index].fT;
-    int lesser = index;
-    while (--lesser >= 0 && precisely_negative(referenceT - fTs[lesser].fT)) {
-        markOneDoneFinal(__FUNCTION__, lesser);
-    }
-    do {
-        markOneDoneFinal(__FUNCTION__, index);
-    } while (++index < fTs.count() && precisely_negative(fTs[index].fT - referenceT));
-    debugValidate();
-}
-
-void SkOpSegment::markDoneUnary(int index) {
-    double referenceT = fTs[index].fT;
-    int lesser = index;
-    while (--lesser >= 0 && precisely_negative(referenceT - fTs[lesser].fT)) {
-        markOneDoneUnary(__FUNCTION__, lesser);
-    }
-    do {
-        markOneDoneUnary(__FUNCTION__, index);
-    } while (++index < fTs.count() && precisely_negative(fTs[index].fT - referenceT));
-    debugValidate();
-}
-
-void SkOpSegment::markOneDone(const char* funName, int tIndex, int winding) {
-    SkOpSpan* span;
-    (void) markOneWinding(funName, tIndex, winding, &span);  // allowed to do nothing
-    if (span->fDone) {
-        return;
-    }
-    span->fDone = true;
-    ++fDoneSpans;
-}
-
-void SkOpSegment::markOneDoneFinal(const char* funName, int tIndex) {
-    SkOpSpan* span = &fTs[tIndex];
-    if (span->fDone) {
-        return;
-    }
-    span->fDone = true;
-    ++fDoneSpans;
-}
-
-void SkOpSegment::markOneDoneBinary(const char* funName, int tIndex) {
-    SkOpSpan* span = verifyOneWinding(funName, tIndex);
-    if (!span) {
+void SkOpSegment::markDone(SkOpSpan* span) {
+    SkASSERT(this == span->segment());
+    if (span->done()) {
         return;
     }
-    SkASSERT(!span->fDone);
-    span->fDone = true;
-    ++fDoneSpans;
-}
-
-void SkOpSegment::markOneDoneUnary(const char* funName, int tIndex) {
-    SkOpSpan* span = verifyOneWindingU(funName, tIndex);
-    if (!span) {
-        return;
-    }
-    if (span->fWindSum == SK_MinS32) {
-        SkDebugf("%s uncomputed\n", __FUNCTION__);
-    }
-    SkASSERT(!span->fDone);
-    span->fDone = true;
-    ++fDoneSpans;
+#if DEBUG_MARK_DONE
+    debugShowNewWinding(__FUNCTION__, span, span->windSum(), span->oppSum());
+#endif
+    span->setDone(true);
+    ++fDoneCount;
+    debugValidate();
 }
 
-bool SkOpSegment::markOneWinding(const char* funName, int tIndex, int winding, SkOpSpan** lastPtr) {
-    SkOpSpan* span = &fTs[tIndex];
-    if (lastPtr) {
-        *lastPtr = span;
-    }
-    if (span->fDone && !span->fSmall) {
+bool SkOpSegment::markWinding(SkOpSpan* span, int winding) {
+    SkASSERT(this == span->segment());
+    SkASSERT(winding);
+    if (span->done()) {
         return false;
     }
 #if DEBUG_MARK_DONE
-    debugShowNewWinding(funName, *span, winding);
-#endif
-    SkASSERT(span->fWindSum == SK_MinS32 || span->fWindSum == winding);
-#if DEBUG_LIMIT_WIND_SUM
-    SkASSERT(abs(winding) <= DEBUG_LIMIT_WIND_SUM);
+    debugShowNewWinding(__FUNCTION__, span, winding);
 #endif
-    span->fWindSum = winding;
+    span->setWindSum(winding);
+    debugValidate();
     return true;
 }
 
-bool SkOpSegment::markOneWinding(const char* funName, int tIndex, int winding,
-        int oppWinding, SkOpSpan** lastPtr) {
-    SkOpSpan* span = &fTs[tIndex];
-    if (span->fDone && !span->fSmall) {
+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(funName, *span, winding, oppWinding);
-#endif
-    SkASSERT(span->fWindSum == SK_MinS32 || span->fWindSum == winding);
-#if DEBUG_LIMIT_WIND_SUM
-    SkASSERT(abs(winding) <= DEBUG_LIMIT_WIND_SUM);
-#endif
-    span->fWindSum = winding;
-    SkASSERT(span->fOppSum == SK_MinS32 || span->fOppSum == oppWinding);
-#if DEBUG_LIMIT_WIND_SUM
-    SkASSERT(abs(oppWinding) <= DEBUG_LIMIT_WIND_SUM);
+    debugShowNewWinding(__FUNCTION__, span, winding, oppWinding);
 #endif
-    span->fOppSum = oppWinding;
+    span->setWindSum(winding);
+    span->setOppSum(oppWinding);
     debugValidate();
-    if (lastPtr) {
-        *lastPtr = span;
-    }
     return true;
 }
 
-// from http://stackoverflow.com/questions/1165647/how-to-determine-if-a-list-of-polygon-points-are-in-clockwise-order
-bool SkOpSegment::clockwise(int tStart, int tEnd, bool* swap) const {
-    SkASSERT(fVerb != SkPath::kLine_Verb);
-    SkPoint edge[4];
-    subDivide(tStart, tEnd, edge);
-    int points = SkPathOpsVerbToPoints(fVerb);
-    double sum = (edge[0].fX - edge[points].fX) * (edge[0].fY + edge[points].fY);
-    bool sumSet = false;
-    if (fVerb == SkPath::kCubic_Verb) {
-        SkDCubic cubic;
-        cubic.set(edge);
-        double inflectionTs[2];
-        int inflections = cubic.findInflections(inflectionTs);
-        // FIXME: this fixes cubicOp114 and breaks cubicOp58d
-        // the trouble is that cubics with inflections confuse whether the curve breaks towards
-        // or away, which in turn is used to determine if it is on the far right or left.
-        // Probably a totally different approach is in order. At one time I tried to project a
-        // horizontal ray to determine winding, but was confused by how to map the vertically
-        // oriented winding computation over. 
-        if (0 && inflections) {
-            double tLo = this->span(tStart).fT;
-            double tHi = this->span(tEnd).fT;
-            double tLoStart = tLo;
-            for (int index = 0; index < inflections; ++index) {
-                if (between(tLo, inflectionTs[index], tHi)) {
-                    tLo = inflectionTs[index];
-                }
-            }
-            if (tLo != tLoStart && tLo != tHi) {
-                SkDPoint sub[2];
-                sub[0] = cubic.ptAtT(tLo);
-                sub[1].set(edge[3]);
-                SkDPoint ctrl[2];
-                SkDCubic::SubDivide(fPts, sub[0], sub[1], tLo, tHi, ctrl);
-                edge[0] = sub[0].asSkPoint();
-                edge[1] = ctrl[0].asSkPoint();
-                edge[2] = ctrl[1].asSkPoint();
-                sum = (edge[0].fX - edge[3].fX) * (edge[0].fY + edge[3].fY);
-            }
-        }
-        SkScalar lesser = SkTMin<SkScalar>(edge[0].fY, edge[3].fY);
-        if (edge[1].fY < lesser && edge[2].fY < lesser) {
-            SkDLine tangent1 = {{ {edge[0].fX, edge[0].fY}, {edge[1].fX, edge[1].fY} }};
-            SkDLine tangent2 = {{ {edge[2].fX, edge[2].fY}, {edge[3].fX, edge[3].fY} }};
-            if (SkIntersections::Test(tangent1, tangent2)) {
-                SkPoint topPt = cubic_top(fPts, fTs[tStart].fT, fTs[tEnd].fT);
-                sum += (topPt.fX - edge[0].fX) * (topPt.fY + edge[0].fY);
-                sum += (edge[3].fX - topPt.fX) * (edge[3].fY + topPt.fY);
-                sumSet = true;
-            }
-        }
+bool SkOpSegment::match(const SkOpPtT* base, const SkOpSegment* testParent, double testT,
+        const SkPoint& testPt) const {
+    const SkOpSegment* baseParent = base->segment();
+    if (this == baseParent && this == testParent && precisely_equal(base->fT, testT)) {
+        return true;
     }
-    if (!sumSet) {
-        for (int idx = 0; idx < points; ++idx){
-            sum += (edge[idx + 1].fX - edge[idx].fX) * (edge[idx + 1].fY + edge[idx].fY);
-        }
+    if (!SkDPoint::ApproximatelyEqual(testPt, base->fPt)) {
+        return false;
     }
-    if (fVerb == SkPath::kCubic_Verb) {
-        SkDCubic cubic;
-        cubic.set(edge);
-         *swap = sum > 0 && !cubic.monotonicInY() && !cubic.serpentine();
-    } else {
-        SkDQuad quad;
-        quad.set(edge);
-        *swap = sum > 0 && !quad.monotonicInY();
+    return !ptsDisjoint(base->fT, base->fPt, testT, testPt);
+}
+
+static SkOpSegment* set_last(SkOpSpanBase** last, SkOpSpanBase* endSpan) {
+    if (last) {
+        *last = endSpan;
     }
-    return sum <= 0;
+    return NULL;
 }
 
-bool SkOpSegment::monotonicInY(int tStart, int tEnd) const {
+bool SkOpSegment::monotonicInY(const SkOpSpanBase* start, const SkOpSpanBase* end) const {
     SkASSERT(fVerb != SkPath::kLine_Verb);
     if (fVerb == SkPath::kQuad_Verb) {
-        SkDQuad dst = SkDQuad::SubDivide(fPts, fTs[tStart].fT, fTs[tEnd].fT);
+        SkDQuad dst = SkDQuad::SubDivide(fPts, start->t(), end->t());
         return dst.monotonicInY();
     }
     SkASSERT(fVerb == SkPath::kCubic_Verb);
-    SkDCubic dst = SkDCubic::SubDivide(fPts, fTs[tStart].fT, fTs[tEnd].fT);
+    SkDCubic dst = SkDCubic::SubDivide(fPts, start->t(), end->t());
     return dst.monotonicInY();
 }
 
-bool SkOpSegment::serpentine(int tStart, int tEnd) const {
-    if (fVerb != SkPath::kCubic_Verb) {
-        return false;
-    }
-    SkDCubic dst = SkDCubic::SubDivide(fPts, fTs[tStart].fT, fTs[tEnd].fT);
-    return dst.serpentine();
-}
-
-SkOpSpan* SkOpSegment::verifyOneWinding(const char* funName, int tIndex) {
-    SkOpSpan& span = fTs[tIndex];
-    if (span.fDone) {
-        return NULL;
-    }
-#if DEBUG_MARK_DONE
-    debugShowNewWinding(funName, span, span.fWindSum, span.fOppSum);
-#endif
-// If the prior angle in the sort is unorderable, the winding sum may not be computable.
-// To enable the assert, the 'prior is unorderable' state could be
-// piped down to this test, but not sure it's worth it.
-// (Once the sort order is stored in the span, this test may be feasible.)
-//    SkASSERT(span.fWindSum != SK_MinS32);
-//    SkASSERT(span.fOppSum != SK_MinS32);
-    return &span;
-}
-
-SkOpSpan* SkOpSegment::verifyOneWindingU(const char* funName, int tIndex) {
-    SkOpSpan& span = fTs[tIndex];
-    if (span.fDone) {
-        return NULL;
-    }
-#if DEBUG_MARK_DONE
-    debugShowNewWinding(funName, span, span.fWindSum);
-#endif
-// If the prior angle in the sort is unorderable, the winding sum may not be computable.
-// To enable the assert, the 'prior is unorderable' state could be
-// piped down to this test, but not sure it's worth it.
-// (Once the sort order is stored in the span, this test may be feasible.)
-//    SkASSERT(span.fWindSum != SK_MinS32);
-    return &span;
-}
-
-bool SkOpSegment::markWinding(int index, int winding) {
-//    SkASSERT(!done());
-    SkASSERT(winding);
-    double referenceT = fTs[index].fT;
-    int lesser = index;
-    bool success = false;
-    while (--lesser >= 0 && precisely_negative(referenceT - fTs[lesser].fT)) {
-        success |= markOneWinding(__FUNCTION__, lesser, winding, NULL);
-    }
-    do {
-        success |= markOneWinding(__FUNCTION__, index, winding, NULL);
-   } while (++index < fTs.count() && precisely_negative(fTs[index].fT - referenceT));
-    debugValidate();
-    return success;
-}
-
-bool SkOpSegment::markWinding(int index, int winding, int oppWinding) {
-//    SkASSERT(!done());
-    SkASSERT(winding || oppWinding);
-    double referenceT = fTs[index].fT;
-    int lesser = index;
-    bool success = false;
-    while (--lesser >= 0 && precisely_negative(referenceT - fTs[lesser].fT)) {
-        success |= markOneWinding(__FUNCTION__, lesser, winding, oppWinding, NULL);
-    }
-    do {
-        success |= markOneWinding(__FUNCTION__, index, winding, oppWinding, NULL);
-   } while (++index < fTs.count() && precisely_negative(fTs[index].fT - referenceT));
-    debugValidate();
-    return success;
-}
-
-void SkOpSegment::matchWindingValue(int tIndex, double t, bool borrowWind) {
-    int nextDoorWind = SK_MaxS32;
-    int nextOppWind = SK_MaxS32;
-    // prefer exact matches
-    if (tIndex > 0) {
-        const SkOpSpan& below = fTs[tIndex - 1];
-        if (below.fT == t) {
-            nextDoorWind = below.fWindValue;
-            nextOppWind = below.fOppValue;
-        }
-    }
-    if (nextDoorWind == SK_MaxS32 && tIndex + 1 < fTs.count()) {
-        const SkOpSpan& above = fTs[tIndex + 1];
-        if (above.fT == t) {
-            nextDoorWind = above.fWindValue;
-            nextOppWind = above.fOppValue;
-        }
-    }
-    if (nextDoorWind == SK_MaxS32 && tIndex > 0) {
-        const SkOpSpan& below = fTs[tIndex - 1];
-        if (approximately_negative(t - below.fT)) {
-            nextDoorWind = below.fWindValue;
-            nextOppWind = below.fOppValue;
-        }
-    }
-    if (nextDoorWind == SK_MaxS32 && tIndex + 1 < fTs.count()) {
-        const SkOpSpan& above = fTs[tIndex + 1];
-        if (approximately_negative(above.fT - t)) {
-            nextDoorWind = above.fWindValue;
-            nextOppWind = above.fOppValue;
-        }
-    }
-    if (nextDoorWind == SK_MaxS32 && borrowWind && tIndex > 0 && t < 1) {
-        const SkOpSpan& below = fTs[tIndex - 1];
-        nextDoorWind = below.fWindValue;
-        nextOppWind = below.fOppValue;
-    }
-    if (nextDoorWind != SK_MaxS32) {
-        SkOpSpan& newSpan = fTs[tIndex];
-        newSpan.fWindValue = nextDoorWind;
-        newSpan.fOppValue = nextOppWind;
-        if (!nextDoorWind && !nextOppWind && !newSpan.fDone) {
-            newSpan.fDone = true;
-            ++fDoneSpans;
-        }
-    }
-}
-
-bool SkOpSegment::nextCandidate(int* start, int* end) const {
-    while (fTs[*end].fDone) {
-        if (fTs[*end].fT == 1) {
+bool SkOpSegment::NextCandidate(SkOpSpanBase* span, SkOpSpanBase** start,
+        SkOpSpanBase** end) {
+    while (span->final() || span->upCast()->done()) {
+        if (span->final()) {
             return false;
         }
-        ++(*end);
+        span = span->upCast()->next();
     }
-    *start = *end;
-    *end = nextExactSpan(*start, 1);
+    *start = span;
+    *end = span->upCast()->next();
     return true;
 }
 
-static SkOpSegment* set_last(SkOpSpan** last, const SkOpSpan* endSpan) {
-    if (last && !endSpan->fSmall) {
-        *last = const_cast<SkOpSpan*>(endSpan);  // FIXME: get rid of cast
-    }
-    return NULL;
-}
-
-SkOpSegment* SkOpSegment::nextChase(int* indexPtr, int* stepPtr, int* minPtr,
-        SkOpSpan** last) const {
-    int origIndex = *indexPtr;
+SkOpSegment* SkOpSegment::nextChase(SkOpSpanBase** startPtr, int* stepPtr, SkOpSpan** minPtr,
+        SkOpSpanBase** last) const {
+    SkOpSpanBase* origStart = *startPtr;
     int step = *stepPtr;
-    int end = nextExactSpan(origIndex, step);
-    SkASSERT(end >= 0);
-    const SkOpSpan& endSpan = this->span(end);
-    SkOpAngle* angle = step > 0 ? endSpan.fFromAngle : endSpan.fToAngle;
-    int foundIndex;
-    int otherEnd;
+    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 == NULL) {
-        if (endSpan.fT != 0 && endSpan.fT != 1) {
+        if (endSpan->t() != 0 && endSpan->t() != 1) {
             return NULL;
         }
-        other = endSpan.fOther;
-        foundIndex = endSpan.fOtherIndex;
-        otherEnd = other->nextExactSpan(foundIndex, step);
+        SkOpPtT* otherPtT = endSpan->ptT()->next();
+        other = otherPtT->segment();
+        foundSpan = otherPtT->span();
+        otherEnd = step > 0 ? foundSpan->upCast()->next() : foundSpan->prev();
     } else {
         int loopCount = angle->loopCount();
         if (loopCount > 2) {
-            return set_last(last, &endSpan);
+            return set_last(last, endSpan);
         }
         const SkOpAngle* next = angle->next();
         if (NULL == next) {
             return NULL;
         }
-        if (angle->sign() != next->sign()) {
 #if DEBUG_WINDING
+        if (angle->sign() != next->sign() && !angle->segment()->contour()->isXor()
+                && !next->segment()->contour()->isXor()) {
             SkDebugf("%s mismatched signs\n", __FUNCTION__);
-#endif
-        //    return set_last(last, &endSpan);
         }
+#endif
         other = next->segment();
-        foundIndex = end = next->start();
+        foundSpan = endSpan = next->start();
         otherEnd = next->end();
     }
-    int foundStep = foundIndex < otherEnd ? 1 : -1;
+    int foundStep = foundSpan->step(otherEnd);
     if (*stepPtr != foundStep) {
-        return set_last(last, &endSpan);
+        return set_last(last, endSpan);
     }
-    SkASSERT(*indexPtr >= 0);
-    if (otherEnd < 0) {
+    SkASSERT(*startPtr);
+    if (!otherEnd) {
         return NULL;
     }
 //    SkASSERT(otherEnd >= 0);
-#if 1
-    int origMin = origIndex + (step < 0 ? step : 0);
-    const SkOpSpan& orig = this->span(origMin);
-#endif
-    int foundMin = SkMin32(foundIndex, otherEnd);
-#if 1
-    const SkOpSpan& found = other->span(foundMin);
-    if (found.fWindValue != orig.fWindValue || found.fOppValue != orig.fOppValue) {
-          return set_last(last, &endSpan);
+    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);
     }
-#endif
-    *indexPtr = foundIndex;
+    *startPtr = foundSpan;
     *stepPtr = foundStep;
     if (minPtr) {
         *minPtr = foundMin;
@@ -4378,101 +1531,217 @@ SkOpSegment* SkOpSegment::nextChase(int* indexPtr, int* stepPtr, int* minPtr,
     return other;
 }
 
-// This has callers for two different situations: one establishes the end
-// of the current span, and one establishes the beginning of the next span
-// (thus the name). When this is looking for the end of the current span,
-// coincidence is found when the beginning Ts contain -step and the end
-// contains step. When it is looking for the beginning of the next, the
-// first Ts found can be ignored and the last Ts should contain -step.
-// OPTIMIZATION: probably should split into two functions
-int SkOpSegment::nextSpan(int from, int step) const {
-    const SkOpSpan& fromSpan = fTs[from];
-    int count = fTs.count();
-    int to = from;
-    while (step > 0 ? ++to < count : --to >= 0) {
-        const SkOpSpan& span = fTs[to];
-        if (approximately_zero(span.fT - fromSpan.fT)) {
-            continue;
+static void clear_visited(SkOpSpan* 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();
         }
-        return to;
-    }
-    return -1;
+    } while ((span = span->next()->upCastable()));
 }
 
-// FIXME
-// this returns at any difference in T, vs. a preset minimum. It may be
-// that all callers to nextSpan should use this instead.
-int SkOpSegment::nextExactSpan(int from, int step) const {
-    int to = from;
-    if (step < 0) {
-        const SkOpSpan& fromSpan = fTs[from];
-        while (--to >= 0) {
-            const SkOpSpan& span = fTs[to];
-            if (precisely_negative(fromSpan.fT - span.fT) || span.fTiny) {
+// look for pairs of undetected coincident curves
+// assumes that segments going in have visited flag clear
+// curve/curve intersection should now do a pretty good job of finding coincident runs so 
+// this may be only be necessary for line/curve pairs -- so skip unless this is a line and the
+// the opp is not a line
+void SkOpSegment::missingCoincidence(SkOpCoincidence* coincidences, SkChunkAlloc* allocator) {
+    if (this->verb() != SkPath::kLine_Verb) {
+        return;
+    }
+    SkOpSpan* prior = NULL;
+    SkOpSpan* span = &fHead;
+    do {
+        SkOpPtT* ptT = span->ptT(), * spanStopPtT = ptT;
+        SkASSERT(ptT->span() == span);
+        while ((ptT = ptT->next()) != spanStopPtT) {
+            SkOpSegment* opp = ptT->span()->segment();
+            if (opp->setVisited()) {
                 continue;
             }
-            return to;
-        }
-    } else {
-        while (fTs[from].fTiny) {
-            from++;
+            if (opp->verb() == SkPath::kLine_Verb) {
+                continue;
+            }
+            if (span->containsCoincidence(opp)) { // FIXME: this assumes that if the opposite
+                                                  // segment is coincident then no more coincidence
+                                                  // needs to be detected. This may not be true. 
+                continue;
+            }
+            if (span->containsCoinEnd(opp)) {
+                continue;
+            } 
+            // if already visited and visited again, check for coin
+            if (span == &fHead) {
+                continue;
+            }
+            SkOpPtT* priorPtT = NULL, * priorStopPtT;
+            // find prior span containing opp segment
+            SkOpSegment* priorOpp = NULL;
+            prior = span;
+            while (!priorOpp && (prior = prior->prev())) {
+                priorStopPtT = priorPtT = prior->ptT();
+                while ((priorPtT = priorPtT->next()) != priorStopPtT) {
+                    SkOpSegment* segment = priorPtT->span()->segment();
+                    if (segment == opp) {
+                        priorOpp = opp;
+                        break;
+                    }
+                }
+            }
+            if (!priorOpp) {
+                continue;
+            }
+            SkOpPtT* oppStart = prior->ptT();
+            SkOpPtT* oppEnd = span->ptT();
+            bool swapped = priorPtT->fT > ptT->fT;
+            if (swapped) {
+                SkTSwap(priorPtT, ptT);
+                SkTSwap(oppStart, oppEnd);
+            }
+            bool flipped = oppStart->fT > oppEnd->fT;
+            bool coincident;
+            if (coincidences->contains(priorPtT, ptT, oppStart, oppEnd, flipped)) {
+                goto swapBack;
+            }
+            {
+                // average t, find mid pt
+                double midT = (prior->t() + span->t()) / 2;
+                SkPoint midPt = this->ptAtT(midT);
+                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)) {
+                    coincident = false;
+                    SkIntersections i;
+                    int ptCount = SkPathOpsVerbToPoints(this->verb());
+                    SkVector dxdy = (*CurveSlopeAtT[ptCount])(pts(), midT);
+                    SkDLine ray = {{{midPt.fX, midPt.fY},
+                            {midPt.fX + dxdy.fY, midPt.fY - dxdy.fX}}};
+                    int oppPtCount = SkPathOpsVerbToPoints(opp->verb());
+                    (*CurveIntersectRay[oppPtCount])(opp->pts(), ray, &i);
+                    // measure distance and see if it's small enough to denote coincidence
+                    for (int index = 0; index < i.used(); ++index) {
+                        SkDPoint oppPt = i.pt(index);
+                        if (oppPt.approximatelyEqual(midPt)) {
+                            SkVector oppDxdy = (*CurveSlopeAtT[oppPtCount])(opp->pts(),
+                                    i[index][0]);
+                            oppDxdy.normalize();
+                            dxdy.normalize();
+                            SkScalar flatness = SkScalarAbs(dxdy.cross(oppDxdy) / FLT_EPSILON);
+                            coincident |= flatness < 5000;  // FIXME: replace with tuned value
+                        }
+                    }
+                }
+            }
+            if (coincident) {
+            // mark coincidence
+                coincidences->add(priorPtT, ptT, oppStart, oppEnd, allocator);
+                clear_visited(&fHead);
+                missingCoincidence(coincidences, allocator);
+                return;
+            }
+    swapBack:
+            if (swapped) {
+                SkTSwap(priorPtT, ptT);
+            }
         }
-        const SkOpSpan& fromSpan = fTs[from];
-        int count = fTs.count();
-        while (++to < count) {
-            const SkOpSpan& span = fTs[to];
-            if (precisely_negative(span.fT - fromSpan.fT)) {
+    } while ((span = span->next()->upCastable()));
+    clear_visited(&fHead);
+}
+
+// Move nearby t values and pts so they all hang off the same span. Alignment happens later.
+bool SkOpSegment::moveNearby() {
+    debugValidate();
+    SkOpSpanBase* spanS = &fHead;
+    do {
+        SkOpSpanBase* test = spanS->upCast()->next();
+        SkOpSpanBase* next;
+        if (spanS->contains(test)) {
+            if (!test->final()) {
+                test->upCast()->detach(spanS->ptT());
+                continue;
+            } else if (spanS != &fHead) {
+                spanS->upCast()->detach(test->ptT());
+                spanS = test;
                 continue;
             }
-            return to;
         }
-    }
-    return -1;
+        do {  // iterate through all spans associated with start
+            SkOpPtT* startBase = spanS->ptT();
+            next = test->final() ? NULL : test->upCast()->next();
+            do {
+                SkOpPtT* testBase = test->ptT();
+                do {
+                    if (startBase == testBase) {
+                        goto checkNextSpan;
+                    }
+                    if (testBase->duplicate()) {
+                        continue;
+                    }
+                    if (this->match(startBase, testBase->segment(), testBase->fT, testBase->fPt)) {
+                        if (test == &this->fTail) {
+                            if (spanS == &fHead) {
+                                debugValidate();
+                                return true;  // if this span has collapsed, remove it from parent
+                            }
+                            this->fTail.merge(spanS->upCast());
+                            debugValidate();
+                            return true;
+                        }
+                        spanS->merge(test->upCast());
+                        spanS->upCast()->setNext(next);
+                        goto checkNextSpan;
+                    }
+                } while ((testBase = testBase->next()) != test->ptT());
+            } while ((startBase = startBase->next()) != spanS->ptT());
+    checkNextSpan:
+            ;
+        } while ((test = next));
+        spanS = spanS->upCast()->next();
+    } while (!spanS->final());
+    debugValidate();
+    return true;
 }
 
-void SkOpSegment::pinT(const SkPoint& pt, double* t) {
-    if (pt == fPts[0]) {
-        *t = 0;
-    }
-    int count = SkPathOpsVerbToPoints(fVerb);
-    if (pt == fPts[count]) {
-        *t = 1;
-    }
+bool SkOpSegment::operand() const {
+    return fContour->operand();
 }
 
-bool SkOpSegment::reversePoints(const SkPoint& p1, const SkPoint& p2) const {
-    SkASSERT(p1 != p2);
-    int spanCount = count();
-    int p1IndexMin = -1;
-    int p2IndexMax = spanCount;
-    for (int index = 0; index < spanCount; ++index) {
-        const SkOpSpan& span = fTs[index];
-        if (span.fPt == p1) {
-            if (p1IndexMin < 0) {
-                p1IndexMin = index;
-            }
-        } else if (span.fPt == p2) {
-            p2IndexMax = index;
-        }
-    }
-    return p1IndexMin > p2IndexMax;
+bool SkOpSegment::oppXor() const {
+    return fContour->oppXor();
 }
 
-void SkOpSegment::setCoincidentRange(const SkPoint& startPt, const SkPoint& endPt, 
-        SkOpSegment* other) {
-    int count = this->count();
-    for (int index = 0; index < count; ++index) {
-        SkOpSpan &span = fTs[index];
-        if ((startPt == span.fPt || endPt == span.fPt) && other == span.fOther) {
-            span.fCoincident = true;
-        }
+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(pt1.distanceToSqd(pt2) * 2, FLT_EPSILON * 2);
+    return midPt.distanceToSqd(pt1) > seDistSq || midPt.distanceToSqd(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 || abs(*sumWinding) <= DEBUG_LIMIT_WIND_SUM);
 }
 
-void SkOpSegment::setUpWindings(int index, int endIndex, int* sumMiWinding, int* sumSuWinding,
-        int* maxWinding, int* sumWinding, int* oppMaxWinding, int* oppSumWinding) {
-    int deltaSum = spanSign(index, endIndex);
-    int oppDeltaSum = oppSign(index, endIndex);
+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;
@@ -4484,130 +1753,94 @@ void SkOpSegment::setUpWindings(int index, int endIndex, int* sumMiWinding, int*
         *oppMaxWinding = *sumSuWinding;
         *oppSumWinding = *sumSuWinding -= oppDeltaSum;
     }
-#if DEBUG_LIMIT_WIND_SUM
-    SkASSERT(abs(*sumWinding) <= DEBUG_LIMIT_WIND_SUM);
-    SkASSERT(abs(*oppSumWinding) <= DEBUG_LIMIT_WIND_SUM);
-#endif
-}
-
-void SkOpSegment::setUpWindings(int index, int endIndex, int* sumMiWinding,
-        int* maxWinding, int* sumWinding) {
-    int deltaSum = spanSign(index, endIndex);
-    *maxWinding = *sumMiWinding;
-    *sumWinding = *sumMiWinding -= deltaSum;
-#if DEBUG_LIMIT_WIND_SUM
-    SkASSERT(abs(*sumWinding) <= DEBUG_LIMIT_WIND_SUM);
-#endif
+    SkASSERT(!DEBUG_LIMIT_WIND_SUM || abs(*sumWinding) <= DEBUG_LIMIT_WIND_SUM);
+    SkASSERT(!DEBUG_LIMIT_WIND_SUM || abs(*oppSumWinding) <= DEBUG_LIMIT_WIND_SUM);
 }
 
 void SkOpSegment::sortAngles() {
-    int spanCount = fTs.count();
-    if (spanCount <= 2) {
-        return;
-    }
-    int index = 0;
+    SkOpSpanBase* span = &this->fHead;
     do {
-        SkOpAngle* fromAngle = fTs[index].fFromAngle;
-        SkOpAngle* toAngle = fTs[index].fToAngle;
+        SkOpAngle* fromAngle = span->fromAngle();
+        SkOpAngle* toAngle = span->final() ? NULL : span->upCast()->toAngle();
         if (!fromAngle && !toAngle) {
-            index += 1;
             continue;
         }
-        SkOpAngle* baseAngle = NULL;
-        if (fromAngle) {
-            baseAngle = fromAngle;
-            if (inLoop(baseAngle, spanCount, &index)) {
-                continue;
-            }
-        }
 #if DEBUG_ANGLE
         bool wroteAfterHeader = false;
 #endif
-        if (toAngle) {
-            if (!baseAngle) {
-                baseAngle = toAngle;
-                if (inLoop(baseAngle, spanCount, &index)) {
-                    continue;
-                }
-            } else {
-                SkDEBUGCODE(int newIndex = index);
-                SkASSERT(!inLoop(baseAngle, spanCount, &newIndex) && newIndex == index);
+        SkOpAngle* baseAngle = fromAngle;
+        if (fromAngle && toAngle) {
 #if DEBUG_ANGLE
-                SkDebugf("%s [%d] tStart=%1.9g [%d]\n", __FUNCTION__, debugID(), fTs[index].fT,
-                        index);
-                wroteAfterHeader = true;
+            SkDebugf("%s [%d] tStart=%1.9g [%d]\n", __FUNCTION__, debugID(), span->t(),
+                    span->debugID());
+            wroteAfterHeader = true;
 #endif
-                baseAngle->insert(toAngle);
-            }
+            fromAngle->insert(toAngle);
+        } else if (!fromAngle) {
+            baseAngle = toAngle;
         }
-        SkOpAngle* nextFrom, * nextTo;
-        int firstIndex = index;
+        SkOpPtT* ptT = span->ptT(), * stopPtT = ptT;
         do {
-            SkOpSpan& span = fTs[index];
-            SkOpSegment* other = span.fOther;
-            SkOpSpan& oSpan = other->fTs[span.fOtherIndex];
-            SkOpAngle* oAngle = oSpan.fFromAngle;
+            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(), fTs[index].fT,
-                            index);
+                    SkDebugf("%s [%d] tStart=%1.9g [%d]\n", __FUNCTION__, debugID(),
+                            span->t(), span->debugID());
                     wroteAfterHeader = true;
                 }
 #endif
-                if (!oAngle->loopContains(*baseAngle)) {
+                if (!oAngle->loopContains(baseAngle)) {
                     baseAngle->insert(oAngle);
                 }
             }
-            oAngle = oSpan.fToAngle;
-            if (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(), fTs[index].fT,
-                            index);
-                    wroteAfterHeader = true;
-                }
+                    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 (!oAngle->loopContains(baseAngle)) {
+                        baseAngle->insert(oAngle);
+                    }
                 }
             }
-            if (++index == spanCount) {
-                break;
+        } while ((ptT = ptT->next()) != stopPtT);
+        if (baseAngle->loopCount() == 1) {
+            span->setFromAngle(NULL);
+            if (toAngle) {
+                span->upCast()->setToAngle(NULL);
             }
-            nextFrom = fTs[index].fFromAngle;
-            nextTo = fTs[index].fToAngle;
-        } while (fromAngle == nextFrom && toAngle == nextTo);
-        if (baseAngle && baseAngle->loopCount() == 1) {
-            index = firstIndex;
-            do {
-                SkOpSpan& span = fTs[index];
-                span.fFromAngle = span.fToAngle = NULL;
-                if (++index == spanCount) {
-                    break;
-                }
-                nextFrom = fTs[index].fFromAngle;
-                nextTo = fTs[index].fToAngle;
-            } while (fromAngle == nextFrom && toAngle == nextTo);
             baseAngle = NULL;
         }
 #if DEBUG_SORT
         SkASSERT(!baseAngle || baseAngle->loopCount() > 1);
 #endif
-    } while (index < spanCount);
+    } while (!span->final() && (span = span->upCast()->next()));
 }
 
 // return true if midpoints were computed
-bool SkOpSegment::subDivide(int start, int end, SkPoint edge[4]) const {
+bool SkOpSegment::subDivide(const SkOpSpanBase* start, const SkOpSpanBase* end,
+        SkPoint edge[4]) const {
     SkASSERT(start != end);
-    edge[0] = fTs[start].fPt;
+    const SkOpPtT& startPtT = *start->ptT();
+    const SkOpPtT& endPtT = *end->ptT();
+    edge[0] = startPtT.fPt;
     int points = SkPathOpsVerbToPoints(fVerb);
-    edge[points] = fTs[end].fPt;
+    edge[points] = endPtT.fPt;
     if (fVerb == SkPath::kLine_Verb) {
         return false;
     }
-    double startT = fTs[start].fT;
-    double endT = fTs[end].fT;
+    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) {
@@ -4637,17 +1870,19 @@ bool SkOpSegment::subDivide(int start, int end, SkPoint edge[4]) const {
     return true;
 }
 
-// return true if midpoints were computed
-bool SkOpSegment::subDivide(int start, int end, SkDCubic* result) const {
+bool SkOpSegment::subDivide(const SkOpSpanBase* start, const SkOpSpanBase* end,
+        SkDCubic* result) const {
     SkASSERT(start != end);
-    (*result)[0].set(fTs[start].fPt);
+    const SkOpPtT& startPtT = *start->ptT();
+    const SkOpPtT& endPtT = *end->ptT();
+    (*result)[0].set(startPtT.fPt);
     int points = SkPathOpsVerbToPoints(fVerb);
-    (*result)[points].set(fTs[end].fPt);
+    (*result)[points].set(endPtT.fPt);
     if (fVerb == SkPath::kLine_Verb) {
         return false;
     }
-    double startT = fTs[start].fT;
-    double endT = fTs[end].fT;
+    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) {
@@ -4655,7 +1890,7 @@ bool SkOpSegment::subDivide(int start, int end, SkDCubic* result) const {
             return false;
         }
         SkASSERT(fVerb == SkPath::kCubic_Verb);
-        if (start < end) {
+        if (startT == 0) {
             (*result)[1].set(fPts[1]);
             (*result)[2].set(fPts[2]);
             return false;
@@ -4673,49 +1908,29 @@ bool SkOpSegment::subDivide(int start, int end, SkDCubic* result) const {
     return true;
 }
 
-void SkOpSegment::subDivideBounds(int start, int end, SkPathOpsBounds* bounds) const {
+void SkOpSegment::subDivideBounds(const SkOpSpanBase* start, const SkOpSpanBase* end,
+        SkPathOpsBounds* bounds) const {
     SkPoint edge[4];
     subDivide(start, end, edge);
     (bounds->*SetCurveBounds[SkPathOpsVerbToPoints(fVerb)])(edge);
 }
 
-void SkOpSegment::TrackOutsidePair(SkTArray<SkPoint, true>* outsidePts, const SkPoint& endPt,
-        const SkPoint& startPt) {
-    int outCount = outsidePts->count();
-    if (outCount == 0 || endPt != (*outsidePts)[outCount - 2]) {
-        outsidePts->push_back(endPt);
-        outsidePts->push_back(startPt);
-    }
-}
-
-void SkOpSegment::TrackOutside(SkTArray<SkPoint, true>* outsidePts, const SkPoint& startPt) {
-    int outCount = outsidePts->count();
-    if (outCount == 0 || startPt != (*outsidePts)[outCount - 1]) {
-        outsidePts->push_back(startPt);
-    }
-}
-
-void SkOpSegment::undoneSpan(int* start, int* end) {
-    int tCount = fTs.count();
-    int index;
-    for (index = 0; index < tCount; ++index) {
-        if (!fTs[index].fDone) {
+void SkOpSegment::undoneSpan(SkOpSpanBase** start, SkOpSpanBase** end) {
+    SkOpSpan* span = this->head();
+    do {
+        if (!span->done()) {
             break;
         }
-    }
-    SkASSERT(index < tCount - 1);
-    *start = index;
-    double startT = fTs[index].fT;
-    while (approximately_negative(fTs[++index].fT - startT))
-        SkASSERT(index < tCount);
-    SkASSERT(index < tCount);
-    *end = index;
+    } while ((span = span->next()->upCastable()));
+    SkASSERT(span);
+    *start = span;
+    *end = span->next();
 }
 
-int SkOpSegment::updateOppWinding(int index, int endIndex) const {
-    int lesser = SkMin32(index, endIndex);
-    int oppWinding = oppSum(lesser);
-    int oppSpanWinding = oppSign(index, endIndex);
+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;
@@ -4724,24 +1939,24 @@ int SkOpSegment::updateOppWinding(int index, int endIndex) const {
 }
 
 int SkOpSegment::updateOppWinding(const SkOpAngle* angle) const {
-    int startIndex = angle->start();
-    int endIndex = angle->end();
-    return updateOppWinding(endIndex, startIndex);
+    const SkOpSpanBase* startSpan = angle->start();
+    const SkOpSpanBase* endSpan = angle->end();
+    return updateOppWinding(endSpan, startSpan);
 }
 
 int SkOpSegment::updateOppWindingReverse(const SkOpAngle* angle) const {
-    int startIndex = angle->start();
-    int endIndex = angle->end();
-    return updateOppWinding(startIndex, endIndex);
+    const SkOpSpanBase* startSpan = angle->start();
+    const SkOpSpanBase* endSpan = angle->end();
+    return updateOppWinding(startSpan, endSpan);
 }
 
-int SkOpSegment::updateWinding(int index, int endIndex) const {
-    int lesser = SkMin32(index, endIndex);
-    int winding = windSum(lesser);
+int SkOpSegment::updateWinding(const SkOpSpanBase* start, const SkOpSpanBase* end) const {
+    const SkOpSpan* lesser = start->starter(end);
+    int winding = lesser->windSum();
     if (winding == SK_MinS32) {
         return winding;
     }
-    int spanWinding = spanSign(index, endIndex);
+    int spanWinding = SkOpSegment::SpanSign(start, end);
     if (winding && UseInnerWinding(winding - spanWinding, winding)
             && winding != SK_MaxS32) {
         winding -= spanWinding;
@@ -4750,26 +1965,15 @@ int SkOpSegment::updateWinding(int index, int endIndex) const {
 }
 
 int SkOpSegment::updateWinding(const SkOpAngle* angle) const {
-    int startIndex = angle->start();
-    int endIndex = angle->end();
-    return updateWinding(endIndex, startIndex);
-}
-
-int SkOpSegment::updateWindingReverse(int index, int endIndex) const {
-    int lesser = SkMin32(index, endIndex);
-    int winding = windSum(lesser);
-    int spanWinding = spanSign(endIndex, index);
-    if (winding && UseInnerWindingReverse(winding - spanWinding, winding)
-            && winding != SK_MaxS32) {
-        winding -= spanWinding;
-    }
-    return winding;
+    const SkOpSpanBase* startSpan = angle->start();
+    const SkOpSpanBase* endSpan = angle->end();
+    return updateWinding(endSpan, startSpan);
 }
 
 int SkOpSegment::updateWindingReverse(const SkOpAngle* angle) const {
-    int startIndex = angle->start();
-    int endIndex = angle->end();
-    return updateWindingReverse(endIndex, startIndex);
+    const SkOpSpanBase* startSpan = angle->start();
+    const SkOpSpanBase* endSpan = angle->end();
+    return updateWinding(startSpan, endSpan);
 }
 
 // OPTIMIZATION: does the following also work, and is it any faster?
@@ -4784,25 +1988,17 @@ bool SkOpSegment::UseInnerWinding(int outerWinding, int innerWinding) {
     return result;
 }
 
-bool SkOpSegment::UseInnerWindingReverse(int outerWinding, int innerWinding) {
-    SkASSERT(outerWinding != SK_MaxS32);
-    SkASSERT(innerWinding != SK_MaxS32);
-    int absOut = abs(outerWinding);
-    int absIn = abs(innerWinding);
-    bool result = absOut == absIn ? true : absOut < absIn;
-    return result;
-}
-
-int SkOpSegment::windingAtT(double tHit, int tIndex, bool crossOpp, SkScalar* dx) const {
-    if (approximately_zero(tHit - t(tIndex))) {  // if we hit the end of a span, disregard
+int SkOpSegment::windingAtT(double tHit, const SkOpSpan* span, bool crossOpp,
+        SkScalar* dx) const {
+    if (approximately_zero(tHit - span->t())) {  // if we hit the end of a span, disregard
         return SK_MinS32;
     }
-    int winding = crossOpp ? oppSum(tIndex) : windSum(tIndex);
+    int winding = crossOpp ? span->oppSum() : span->windSum();
     SkASSERT(winding != SK_MinS32);
-    int windVal = crossOpp ? oppValue(tIndex) : windValue(tIndex);
+    int windVal = crossOpp ? span->oppValue() : span->windValue();
 #if DEBUG_WINDING_AT_T
     SkDebugf("%s id=%d opp=%d tHit=%1.9g t=%1.9g oldWinding=%d windValue=%d", __FUNCTION__,
-            debugID(), crossOpp, tHit, t(tIndex), winding, windVal);
+            debugID(), crossOpp, tHit, span->t(), winding, windVal);
 #endif
     // see if a + change in T results in a +/- change in X (compute x'(T))
     *dx = (*CurveSlopeAtT[SkPathOpsVerbToPoints(fVerb)])(fPts, tHit).fX;
@@ -4828,20 +2024,6 @@ int SkOpSegment::windingAtT(double tHit, int tIndex, bool crossOpp, SkScalar* dx
 }
 
 int SkOpSegment::windSum(const SkOpAngle* angle) const {
-    int start = angle->start();
-    int end = angle->end();
-    int index = SkMin32(start, end);
-    return windSum(index);
-}
-
-void SkOpSegment::zeroSpan(SkOpSpan* span) {
-    SkASSERT(span->fWindValue > 0 || span->fOppValue != 0);
-    span->fWindValue = 0;
-    span->fOppValue = 0;
-    if (span->fTiny || span->fSmall) {
-        return;
-    }
-    SkASSERT(!span->fDone);
-    span->fDone = true;
-    ++fDoneSpans;
+    const SkOpSpan* minSpan = angle->start()->starter(angle->end());
+    return minSpan->windSum();
 }