Now, path ops natively intersect conics, quads, and cubics in any combination. There are still a class of cubic tests that fail and a handful of undiagnosed failures from skps and fuzz tests, but things are much better overall.

Extended tests (150M+) run to completion in release in about 6 minutes; the standard test suite exceeds 100K and finishes in a few seconds on desktops.

TBR=reed
BUG=skia:3588

Review URL: https://codereview.chromium.org/1037953004

1 files changed, 546 insertions, 399 deletions

diff --git a/src/pathops/SkPathOpsTSect.h b/src/pathops/SkPathOpsTSect.h
index 9d63433330..ffd69951d3 100644
--- a/src/pathops/SkPathOpsTSect.h
+++ b/src/pathops/SkPathOpsTSect.h
@@ -8,16 +8,15 @@
 #include "SkChunkAlloc.h"
 #include "SkPathOpsBounds.h"
 #include "SkPathOpsRect.h"
-#include "SkPathOpsQuad.h"
 #include "SkIntersections.h"
 #include "SkTSort.h"
 
-/* TCurve is either SkDQuadratic or SkDCubic */
-template<typename TCurve>
+/* TCurve and OppCurve are one of { SkDQuadratic, SkDConic, SkDCubic } */
+template<typename TCurve, typename OppCurve>
 class SkTCoincident {
 public:
     SkTCoincident() {
-        clear();
+        this->clear();
     }
 
     void clear() {
@@ -25,12 +24,19 @@ public:
         fCoincident = false;
     }
 
+    void debugInit() {
+        this->clear();
+        fPerpPt.fX = fPerpPt.fY = SK_ScalarNaN;
+    }
+
+    void dump() const;
+
     bool isCoincident() const {
         return fCoincident;
     }
 
     void init() {
-        clear();
+        this->clear();
         SkDEBUGCODE(fPerpPt.fX = fPerpPt.fY = SK_ScalarNaN);
     }
 
@@ -49,7 +55,7 @@ public:
         return fPerpT;
     }
 
-    void setPerp(const TCurve& c1, double t, const SkDPoint& cPt, const TCurve& );
+    void setPerp(const TCurve& c1, double t, const SkDPoint& cPt, const OppCurve& );
 
 private:
     SkDPoint fPerpPt;
@@ -57,40 +63,51 @@ private:
     bool fCoincident;
 };
 
-template<typename TCurve> class SkTSect;
-template<typename TCurve> class SkTSpan;
+template<typename TCurve, typename OppCurve> class SkTSect;
+template<typename TCurve, typename OppCurve> class SkTSpan;
 
-template<typename TCurve>
+template<typename TCurve, typename OppCurve>
 struct SkTSpanBounded {
-    SkTSpan<TCurve>* fBounded;
+    SkTSpan<TCurve, OppCurve>* fBounded;
     SkTSpanBounded* fNext;
 };
 
 /* Curve is either TCurve or SkDCubic */
-template<typename TCurve>
+template<typename TCurve, typename OppCurve>
 class SkTSpan {
 public:
-    void addBounded(SkTSpan* , SkChunkAlloc* );
+    void addBounded(SkTSpan<OppCurve, TCurve>* , SkChunkAlloc* );
     double closestBoundedT(const SkDPoint& pt) const;
     bool contains(double t) const;
 
-    const SkTSect<TCurve>* debugOpp() const;
+    void debugInit() {
+        TCurve dummy;
+        dummy.debugInit();
+        init(dummy);
+        initBounds(dummy);
+        fCoinStart.debugInit();
+        fCoinEnd.debugInit();
+    }
+
+    const SkTSect<OppCurve, TCurve>* debugOpp() const;
     const SkTSpan* debugSpan(int ) const;
     const SkTSpan* debugT(double t) const;
 #ifdef SK_DEBUG
     bool debugIsBefore(const SkTSpan* span) const;
 #endif
     void dump() const;
-    void dumpBounds(int id) const;
+    void dumpBounded(int id) const;
+    void dumpBounds() const;
+    void dumpCoin() const;
 
     double endT() const {
         return fEndT;
     }
 
-    SkTSpan* findOppSpan(const SkTSpan* opp) const;
+    SkTSpan<OppCurve, TCurve>* findOppSpan(const SkTSpan<OppCurve, TCurve>* opp) const;
 
-    SkTSpan* findOppT(double t) const {
-        SkTSpan* result = oppT(t);
+    SkTSpan<OppCurve, TCurve>* findOppT(double t) const {
+        SkTSpan<OppCurve, TCurve>* result = oppT(t);
         SkASSERT(result);
         return result;
     }
@@ -99,7 +116,7 @@ public:
         return SkToBool(oppT(t));
     }
 
-    int hullsIntersect(SkTSpan* span, bool* start, bool* oppStart);
+    int hullsIntersect(SkTSpan<OppCurve, TCurve>* span, bool* start, bool* oppStart);
     void init(const TCurve& );
     void initBounds(const TCurve& );
 
@@ -107,7 +124,7 @@ public:
         return fBounded != NULL;
     }
 
-    bool linearsIntersect(SkTSpan* span);
+    bool linearsIntersect(SkTSpan<OppCurve, TCurve>* span);
     double linearT(const SkDPoint& ) const;
 
     void markCoincident() {
@@ -119,14 +136,15 @@ public:
         return fNext;
     }
 
-    bool onlyEndPointsInCommon(const SkTSpan* opp, bool* start, bool* oppStart, bool* ptsInCommon);
+    bool onlyEndPointsInCommon(const SkTSpan<OppCurve, TCurve>* opp, bool* start,
+            bool* oppStart, bool* ptsInCommon);
 
     const TCurve& part() const {
         return fPart;
     }
 
     bool removeAllBounded();
-    bool removeBounded(const SkTSpan* opp);
+    bool removeBounded(const SkTSpan<OppCurve, TCurve>* opp);
 
     void reset() {
         fBounded = NULL;
@@ -156,9 +174,9 @@ private:
 
     void dumpID() const;
 
-    int hullCheck(const SkTSpan* opp, bool* start, bool* oppStart);
-    int linearIntersects(const TCurve& ) const;
-    SkTSpan* oppT(double t) const;
+    int hullCheck(const SkTSpan<OppCurve, TCurve>* opp, bool* start, bool* oppStart);
+    int linearIntersects(const OppCurve& ) const;
+    SkTSpan<OppCurve, TCurve>* oppT(double t) const;
 
     void validate() const;
     void validateBounded() const;
@@ -166,9 +184,9 @@ private:
     void validatePerpPt(double t, const SkDPoint& ) const;
 
     TCurve fPart;
-    SkTCoincident<TCurve> fCoinStart;
-    SkTCoincident<TCurve> fCoinEnd;
-    SkTSpanBounded<TCurve>* fBounded;
+    SkTCoincident<TCurve, OppCurve> fCoinStart;
+    SkTCoincident<TCurve, OppCurve> fCoinEnd;
+    SkTSpanBounded<OppCurve, TCurve>* fBounded;
     SkTSpan* fPrev;
     SkTSpan* fNext;
     SkDRect fBounds;
@@ -180,29 +198,33 @@ private:
     bool fIsLinear;
     bool fIsLine;
     bool fDeleted;
-    PATH_OPS_DEBUG_CODE(SkTSect<TCurve>* fDebugSect);
+    SkDEBUGCODE_(SkTSect<TCurve, OppCurve>* fDebugSect);
     PATH_OPS_DEBUG_T_SECT_CODE(int fID);
-    friend class SkTSect<TCurve>;
+    friend class SkTSect<TCurve, OppCurve>;
+    friend class SkTSect<OppCurve, TCurve>;
+    friend class SkTSpan<OppCurve, TCurve>;
 };
 
-template<typename TCurve>
+template<typename TCurve, typename OppCurve>
 class SkTSect {
 public:
     SkTSect(const TCurve& c  PATH_OPS_DEBUG_T_SECT_PARAMS(int id));
-    static void BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersections* intersections);
+    static void BinarySearch(SkTSect* sect1, SkTSect<OppCurve, TCurve>* sect2,
+            SkIntersections* intersections);
 
     // for testing only
-    bool debugHasBounded(const SkTSpan<TCurve>* ) const;
+    bool debugHasBounded(const SkTSpan<OppCurve, TCurve>* ) const;
 
-    const SkTSect* debugOpp() const {
-        return PATH_OPS_DEBUG_RELEASE(fOppSect, NULL);
+    const SkTSect<OppCurve, TCurve>* debugOpp() const {
+        return SkDEBUGRELEASE(fOppSect, NULL);
     }
 
-    const SkTSpan<TCurve>* debugSpan(int id) const;
-    const SkTSpan<TCurve>* debugT(double t) const;
+    const SkTSpan<TCurve, OppCurve>* debugSpan(int id) const;
+    const SkTSpan<TCurve, OppCurve>* debugT(double t) const;
     void dump() const;
-    void dumpBoth(SkTSect* ) const;
-    void dumpBounds(int id) const;
+    void dumpBoth(SkTSect<OppCurve, TCurve>* ) const;
+    void dumpBounded(int id) const;
+    void dumpBounds() const;
     void dumpCoin() const;
     void dumpCoinCurves() const;
     void dumpCurves() const;
@@ -215,82 +237,92 @@ private:
         kOneS2Set = 8
     };
 
-    SkTSpan<TCurve>* addFollowing(SkTSpan<TCurve>* prior);
-    void addForPerp(SkTSpan<TCurve>* span, double t);
-    SkTSpan<TCurve>* addOne();
+    SkTSpan<TCurve, OppCurve>* addFollowing(SkTSpan<TCurve, OppCurve>* prior);
+    void addForPerp(SkTSpan<OppCurve, TCurve>* span, double t);
+    SkTSpan<TCurve, OppCurve>* addOne();
     
-    SkTSpan<TCurve>* addSplitAt(SkTSpan<TCurve>* span, double t) {
-        SkTSpan<TCurve>* result = this->addOne();
+    SkTSpan<TCurve, OppCurve>* addSplitAt(SkTSpan<TCurve, OppCurve>* span, double t) {
+        SkTSpan<TCurve, OppCurve>* result = this->addOne();
         result->splitAt(span, t, &fHeap);
         result->initBounds(fCurve);
         span->initBounds(fCurve);
         return result;
     }
 
-    bool binarySearchCoin(SkTSect* , double tStart, double tStep, double* t, double* oppT);
-    SkTSpan<TCurve>* boundsMax() const;
-    void coincidentCheck(SkTSect* sect2);
+    bool binarySearchCoin(SkTSect<OppCurve, TCurve>* , double tStart, double tStep, double* t,
+                          double* oppT);
+    SkTSpan<TCurve, OppCurve>* boundsMax() const;
+    void coincidentCheck(SkTSect<OppCurve, TCurve>* sect2);
     bool coincidentHasT(double t);
-    void computePerpendiculars(SkTSect* sect2, SkTSpan<TCurve>* first, SkTSpan<TCurve>* last);
-    int countConsecutiveSpans(SkTSpan<TCurve>* first, SkTSpan<TCurve>** last) const;
+    int collapsed() const;
+    void computePerpendiculars(SkTSect<OppCurve, TCurve>* sect2, SkTSpan<TCurve, OppCurve>* first,
+                               SkTSpan<TCurve, OppCurve>* last);
+    int countConsecutiveSpans(SkTSpan<TCurve, OppCurve>* first,
+                              SkTSpan<TCurve, OppCurve>** last) const;
 
     int debugID() const {
         return PATH_OPS_DEBUG_T_SECT_RELEASE(fID, -1);
     }
 
     void deleteEmptySpans();
-    void dumpCommon(const SkTSpan<TCurve>* ) const;
-    void dumpCommonCurves(const SkTSpan<TCurve>* ) const;
-    static int EndsEqual(const SkTSect* sect1, const SkTSect* sect2, SkIntersections* );
-    SkTSpan<TCurve>* extractCoincident(SkTSect* sect2, SkTSpan<TCurve>* first,
-                                       SkTSpan<TCurve>* last);
-    SkTSpan<TCurve>* findCoincidentRun(SkTSpan<TCurve>* first, SkTSpan<TCurve>** lastPtr,
-                                       const SkTSect* sect2);
-    int intersects(SkTSpan<TCurve>* span, const SkTSect* opp,
-                   SkTSpan<TCurve>* oppSpan, int* oppResult) const;
-    int linesIntersect(const SkTSpan<TCurve>* span, const SkTSect* opp,
-                       const SkTSpan<TCurve>* oppSpan, SkIntersections* ) const;
-    void markSpanGone(SkTSpan<TCurve>* span);
-    bool matchedDirection(double t, const SkTSect* sect2, double t2) const;
-    void matchedDirCheck(double t, const SkTSect* sect2, double t2,
+    void dumpCommon(const SkTSpan<TCurve, OppCurve>* ) const;
+    void dumpCommonCurves(const SkTSpan<TCurve, OppCurve>* ) const;
+    static int EndsEqual(const SkTSect* sect1, const SkTSect<OppCurve, TCurve>* sect2,
+                         SkIntersections* );
+    SkTSpan<TCurve, OppCurve>* extractCoincident(SkTSect<OppCurve, TCurve>* sect2,
+                                                  SkTSpan<TCurve, OppCurve>* first,
+                                                  SkTSpan<TCurve, OppCurve>* last);
+    SkTSpan<TCurve, OppCurve>* findCoincidentRun(SkTSpan<TCurve, OppCurve>* first,
+                                                  SkTSpan<TCurve, OppCurve>** lastPtr);
+    int intersects(SkTSpan<TCurve, OppCurve>* span, SkTSect<OppCurve, TCurve>* opp,
+                   SkTSpan<OppCurve, TCurve>* oppSpan, int* oppResult);
+    int linesIntersect(SkTSpan<TCurve, OppCurve>* span, SkTSect<OppCurve, TCurve>* opp,
+                       SkTSpan<OppCurve, TCurve>* oppSpan, SkIntersections* );
+    void markSpanGone(SkTSpan<TCurve, OppCurve>* span);
+    bool matchedDirection(double t, const SkTSect<OppCurve, TCurve>* sect2, double t2) const;
+    void matchedDirCheck(double t, const SkTSect<OppCurve, TCurve>* sect2, double t2,
                          bool* calcMatched, bool* oppMatched) const;
-    void mergeCoincidence(SkTSect* sect2);
-    SkTSpan<TCurve>* prev(SkTSpan<TCurve>* ) const;
-    void removeByPerpendicular(SkTSect* opp);
+    void mergeCoincidence(SkTSect<OppCurve, TCurve>* sect2);
+    SkTSpan<TCurve, OppCurve>* prev(SkTSpan<TCurve, OppCurve>* ) const;
+    void removeByPerpendicular(SkTSect<OppCurve, TCurve>* opp);
     void recoverCollapsed();
-    void removeCoincident(SkTSpan<TCurve>* span, bool isBetween);
-    void removeAllBut(const SkTSpan<TCurve>* keep, SkTSpan<TCurve>* span, SkTSect* opp);
-    void removeSpan(SkTSpan<TCurve>* span);
-    void removeSpanRange(SkTSpan<TCurve>* first, SkTSpan<TCurve>* last);
-    void removeSpans(SkTSpan<TCurve>* span, SkTSect* opp);
-    SkTSpan<TCurve>* spanAtT(double t, SkTSpan<TCurve>** priorSpan);
-    SkTSpan<TCurve>* tail();
-    void trim(SkTSpan<TCurve>* span, SkTSect* opp);
-    void unlinkSpan(SkTSpan<TCurve>* span);
-    bool updateBounded(SkTSpan<TCurve>* first, SkTSpan<TCurve>* last, SkTSpan<TCurve>* oppFirst);
+    void removeCoincident(SkTSpan<TCurve, OppCurve>* span, bool isBetween);
+    void removeAllBut(const SkTSpan<OppCurve, TCurve>* keep, SkTSpan<TCurve, OppCurve>* span,
+                      SkTSect<OppCurve, TCurve>* opp);
+    void removeSpan(SkTSpan<TCurve, OppCurve>* span);
+    void removeSpanRange(SkTSpan<TCurve, OppCurve>* first, SkTSpan<TCurve, OppCurve>* last);
+    void removeSpans(SkTSpan<TCurve, OppCurve>* span, SkTSect<OppCurve, TCurve>* opp);
+    SkTSpan<TCurve, OppCurve>* spanAtT(double t, SkTSpan<TCurve, OppCurve>** priorSpan);
+    SkTSpan<TCurve, OppCurve>* tail();
+    void trim(SkTSpan<TCurve, OppCurve>* span, SkTSect<OppCurve, TCurve>* opp);
+    void unlinkSpan(SkTSpan<TCurve, OppCurve>* span);
+    bool updateBounded(SkTSpan<TCurve, OppCurve>* first, SkTSpan<TCurve, OppCurve>* last,
+                       SkTSpan<OppCurve, TCurve>* oppFirst);
     void validate() const;
     void validateBounded() const;
 
     const TCurve& fCurve;
     SkChunkAlloc fHeap;
-    SkTSpan<TCurve>* fHead;
-    SkTSpan<TCurve>* fCoincident;
-    SkTSpan<TCurve>* fDeleted;
+    SkTSpan<TCurve, OppCurve>* fHead;
+    SkTSpan<TCurve, OppCurve>* fCoincident;
+    SkTSpan<TCurve, OppCurve>* fDeleted;
     int fActiveCount;
-    PATH_OPS_DEBUG_CODE(SkTSect* fOppSect);
+    SkDEBUGCODE_(SkTSect<OppCurve, TCurve>* fOppSect);
     PATH_OPS_DEBUG_T_SECT_CODE(int fID);
     PATH_OPS_DEBUG_T_SECT_CODE(int fDebugCount);
 #if DEBUG_T_SECT
     int fDebugAllocatedCount;
 #endif
-    friend class SkTSpan<TCurve>;  // only used by debug id
+    friend class SkTSpan<TCurve, OppCurve>;
+    friend class SkTSpan<OppCurve, TCurve>;
+    friend class SkTSect<OppCurve, TCurve>;
 };
 
 #define COINCIDENT_SPAN_COUNT 9
 
-template<typename TCurve>
-void SkTCoincident<TCurve>::setPerp(const TCurve& c1, double t,
-        const SkDPoint& cPt, const TCurve& c2) {
+template<typename TCurve, typename OppCurve>
+void SkTCoincident<TCurve, OppCurve>::setPerp(const TCurve& c1, double t,
+        const SkDPoint& cPt, const OppCurve& c2) {
     SkDVector dxdy = c1.dxdyAtT(t);
     SkDLine perp = {{ cPt, {cPt.fX + dxdy.fY, cPt.fY - dxdy.fX} }};
     SkIntersections i;
@@ -312,8 +344,9 @@ void SkTCoincident<TCurve>::setPerp(const TCurve& c1, double t,
         }
     }
 #if DEBUG_T_SECT
-    SkDebugf("%s cPt=(%1.9g,%1.9g) %s fPerpPt=(%1.9g,%1.9g)\n", __FUNCTION__, cPt.fX, cPt.fY,
-            cPt.approximatelyEqual(fPerpPt) ? "==" : "!=", fPerpPt.fX, fPerpPt.fY);
+    SkDebugf("setPerp t=%1.9g cPt=(%1.9g,%1.9g) %s oppT=%1.9g fPerpPt=(%1.9g,%1.9g)\n",
+            t, cPt.fX, cPt.fY,
+            cPt.approximatelyEqual(fPerpPt) ? "==" : "!=", fPerpT, fPerpPt.fX, fPerpPt.fY);
 #endif
     fCoincident = cPt.approximatelyEqual(fPerpPt);
 #if DEBUG_T_SECT
@@ -323,20 +356,21 @@ void SkTCoincident<TCurve>::setPerp(const TCurve& c1, double t,
 #endif
 }
 
-template<typename TCurve>
-void SkTSpan<TCurve>::addBounded(SkTSpan* span, SkChunkAlloc* heap) {
-    SkTSpanBounded<TCurve>* bounded = SkNEW_PLACEMENT(heap->allocThrow(
-            sizeof(SkTSpanBounded<TCurve>)), SkTSpanBounded<TCurve>);
+template<typename TCurve, typename OppCurve>
+void SkTSpan<TCurve, OppCurve>::addBounded(SkTSpan<OppCurve, TCurve>* span, SkChunkAlloc* heap) {
+    SkTSpanBounded<OppCurve, TCurve>* bounded = SkNEW_PLACEMENT(heap->allocThrow(
+            sizeof(SkTSpanBounded<OppCurve, TCurve>)), (SkTSpanBounded<OppCurve, TCurve>));
     bounded->fBounded = span;
     bounded->fNext = fBounded;
     fBounded = bounded;
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::addFollowing(SkTSpan<TCurve>* prior) {
-    SkTSpan<TCurve>* result = this->addOne();
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::addFollowing(
+        SkTSpan<TCurve, OppCurve>* prior) {
+    SkTSpan<TCurve, OppCurve>* result = this->addOne();
     result->fStartT = prior ? prior->fEndT : 0;
-    SkTSpan<TCurve>* next = prior ? prior->fNext : fHead;
+    SkTSpan<TCurve, OppCurve>* next = prior ? prior->fNext : fHead;
     result->fEndT = next ? next->fStartT : 1;
     result->fPrev = prior;
     result->fNext = next;
@@ -352,11 +386,11 @@ SkTSpan<TCurve>* SkTSect<TCurve>::addFollowing(SkTSpan<TCurve>* prior) {
     return result;
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::addForPerp(SkTSpan<TCurve>* span, double t) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::addForPerp(SkTSpan<OppCurve, TCurve>* span, double t) {
     if (!span->hasOppT(t)) {
-        SkTSpan<TCurve>* priorSpan;
-        SkTSpan<TCurve>* opp = this->spanAtT(t, &priorSpan);
+        SkTSpan<TCurve, OppCurve>* priorSpan;
+        SkTSpan<TCurve, OppCurve>* opp = this->spanAtT(t, &priorSpan);
         if (!opp) {
             opp = this->addFollowing(priorSpan);
 #if DEBUG_PERP
@@ -373,22 +407,24 @@ void SkTSect<TCurve>::addForPerp(SkTSpan<TCurve>* span, double t) {
         span->addBounded(opp, &fHeap);
     }
     this->validate();
+#if DEBUG_T_SECT
     span->validatePerpT(t);
+#endif
 }
 
-template<typename TCurve>
-double SkTSpan<TCurve>::closestBoundedT(const SkDPoint& pt) const {
+template<typename TCurve, typename OppCurve>
+double SkTSpan<TCurve, OppCurve>::closestBoundedT(const SkDPoint& pt) const {
     double result = -1;
     double closest = FLT_MAX;
-    const SkTSpanBounded<TCurve>* testBounded = fBounded;
+    const SkTSpanBounded<OppCurve, TCurve>* testBounded = fBounded;
     while (testBounded) {
-        const SkTSpan* test = testBounded->fBounded;
+        const SkTSpan<OppCurve, TCurve>* test = testBounded->fBounded;
         double startDist = test->fPart[0].distanceSquared(pt);
         if (closest > startDist) {
             closest = startDist;
             result = test->fStartT;
         }
-        double endDist = test->fPart[TCurve::kPointLast].distanceSquared(pt);
+        double endDist = test->fPart[OppCurve::kPointLast].distanceSquared(pt);
         if (closest > endDist) {
             closest = endDist;
             result = test->fEndT;
@@ -400,8 +436,8 @@ double SkTSpan<TCurve>::closestBoundedT(const SkDPoint& pt) const {
 }
 
 #ifdef SK_DEBUG
-template<typename TCurve>
-bool SkTSpan<TCurve>::debugIsBefore(const SkTSpan* span) const {
+template<typename TCurve, typename OppCurve>
+bool SkTSpan<TCurve, OppCurve>::debugIsBefore(const SkTSpan* span) const {
     const SkTSpan* work = this;
     do {
         if (span == work) {
@@ -412,8 +448,8 @@ bool SkTSpan<TCurve>::debugIsBefore(const SkTSpan* span) const {
 }
 #endif
 
-template<typename TCurve>
-bool SkTSpan<TCurve>::contains(double t) const {
+template<typename TCurve, typename OppCurve>
+bool SkTSpan<TCurve, OppCurve>::contains(double t) const {
     const SkTSpan* work = this;
     do {
         if (between(work->fStartT, t, work->fEndT)) {
@@ -423,16 +459,17 @@ bool SkTSpan<TCurve>::contains(double t) const {
     return false;
 }
 
-template<typename TCurve>
-const SkTSect<TCurve>* SkTSpan<TCurve>::debugOpp() const {
-    return PATH_OPS_DEBUG_RELEASE(fDebugSect->debugOpp(), NULL);
+template<typename TCurve, typename OppCurve>
+const SkTSect<OppCurve, TCurve>* SkTSpan<TCurve, OppCurve>::debugOpp() const {
+    return SkDEBUGRELEASE(fDebugSect->debugOpp(), NULL);
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSpan<TCurve>::findOppSpan(const SkTSpan* opp) const {
-    SkTSpanBounded<TCurve>* bounded = fBounded;
+template<typename TCurve, typename OppCurve>
+SkTSpan<OppCurve, TCurve>* SkTSpan<TCurve, OppCurve>::findOppSpan(
+        const SkTSpan<OppCurve, TCurve>* opp) const {
+    SkTSpanBounded<OppCurve, TCurve>* bounded = fBounded;
     while (bounded) {
-        SkTSpan* test = bounded->fBounded;
+        SkTSpan<OppCurve, TCurve>* test = bounded->fBounded;
         if (opp == test) {
             return test;
         }
@@ -445,8 +482,9 @@ SkTSpan<TCurve>* SkTSpan<TCurve>::findOppSpan(const SkTSpan* opp) const {
 //         1 if hulls intersect
 //         2 if hulls only share a common endpoint
 //        -1 if linear and further checking is required
-template<typename TCurve>
-int SkTSpan<TCurve>::hullCheck(const SkTSpan* opp, bool* start, bool* oppStart) {
+template<typename TCurve, typename OppCurve>
+int SkTSpan<TCurve, OppCurve>::hullCheck(const SkTSpan<OppCurve, TCurve>* opp,
+        bool* start, bool* oppStart) {
     if (fIsLinear) {
         return -1;
     }
@@ -472,8 +510,9 @@ int SkTSpan<TCurve>::hullCheck(const SkTSpan* opp, bool* start, bool* oppStart)
 // OPTIMIZE ? If at_most_end_pts_in_common detects that one quad is near linear,
 // use line intersection to guess a better split than 0.5
 // OPTIMIZE Once at_most_end_pts_in_common detects linear, mark span so all future splits are linear
-template<typename TCurve>
-int SkTSpan<TCurve>::hullsIntersect(SkTSpan* opp, bool* start, bool* oppStart) {
+template<typename TCurve, typename OppCurve>
+int SkTSpan<TCurve, OppCurve>::hullsIntersect(SkTSpan<OppCurve, TCurve>* opp,
+        bool* start, bool* oppStart) {
     if (!fBounds.intersects(opp->fBounds)) {
         return 0;
     }
@@ -488,8 +527,8 @@ int SkTSpan<TCurve>::hullsIntersect(SkTSpan* opp, bool* start, bool* oppStart) {
     return -1;
 }
 
-template<typename TCurve>
-void SkTSpan<TCurve>::init(const TCurve& c) {
+template<typename TCurve, typename OppCurve>
+void SkTSpan<TCurve, OppCurve>::init(const TCurve& c) {
     fPrev = fNext = NULL;
     fStartT = 0;
     fEndT = 1;
@@ -497,8 +536,8 @@ void SkTSpan<TCurve>::init(const TCurve& c) {
     resetBounds(c);
 }
 
-template<typename TCurve>
-void SkTSpan<TCurve>::initBounds(const TCurve& c) {
+template<typename TCurve, typename OppCurve>
+void SkTSpan<TCurve, OppCurve>::initBounds(const TCurve& c) {
     fPart = c.subDivide(fStartT, fEndT);
     fBounds.setBounds(fPart);
     fCoinStart.init();
@@ -514,8 +553,8 @@ void SkTSpan<TCurve>::initBounds(const TCurve& c) {
 #endif
 }
 
-template<typename TCurve>
-bool SkTSpan<TCurve>::linearsIntersect(SkTSpan* span) {
+template<typename TCurve, typename OppCurve>
+bool SkTSpan<TCurve, OppCurve>::linearsIntersect(SkTSpan<OppCurve, TCurve>* span) {
     int result = this->linearIntersects(span->fPart);
     if (result <= 1) {
         return SkToBool(result);
@@ -526,16 +565,16 @@ bool SkTSpan<TCurve>::linearsIntersect(SkTSpan* span) {
     return SkToBool(result);
 }
 
-template<typename TCurve>
-double SkTSpan<TCurve>::linearT(const SkDPoint& pt) const {
+template<typename TCurve, typename OppCurve>
+double SkTSpan<TCurve, OppCurve>::linearT(const SkDPoint& pt) const {
     SkDVector len = fPart[TCurve::kPointLast] - fPart[0];
     return fabs(len.fX) > fabs(len.fY)
             ? (pt.fX - fPart[0].fX) / len.fX
             : (pt.fY - fPart[0].fY) / len.fY;
 }
 
-template<typename TCurve>
-int SkTSpan<TCurve>::linearIntersects(const TCurve& q2) const {
+template<typename TCurve, typename OppCurve>
+int SkTSpan<TCurve, OppCurve>::linearIntersects(const OppCurve& q2) const {
     // looks like q1 is near-linear
     int start = 0, end = TCurve::kPointLast;  // the outside points are usually the extremes
     if (!fPart.controlsInside()) {
@@ -559,7 +598,7 @@ int SkTSpan<TCurve>::linearIntersects(const TCurve& q2) const {
     double opp = fPart[end].fY - origY;
     double maxPart = SkTMax(fabs(adj), fabs(opp));
     double sign = 0;  // initialization to shut up warning in release build
-    for (int n = 0; n < TCurve::kPointCount; ++n) {
+    for (int n = 0; n < OppCurve::kPointCount; ++n) {
         double dx = q2[n].fY - origY;
         double dy = q2[n].fX - origX;
         double maxVal = SkTMax(maxPart, SkTMax(fabs(dx), fabs(dy)));
@@ -581,33 +620,33 @@ int SkTSpan<TCurve>::linearIntersects(const TCurve& q2) const {
     return 0;
 }
 
-template<typename TCurve>
-bool SkTSpan<TCurve>::onlyEndPointsInCommon(const SkTSpan* opp, bool* start, bool* oppStart,
-        bool* ptsInCommon) {
+template<typename TCurve, typename OppCurve>
+bool SkTSpan<TCurve, OppCurve>::onlyEndPointsInCommon(const SkTSpan<OppCurve, TCurve>* opp,
+        bool* start, bool* oppStart, bool* ptsInCommon) {
     if (opp->fPart[0] == fPart[0]) {
         *start = *oppStart = true;
     } else if (opp->fPart[0] == fPart[TCurve::kPointLast]) {
         *start = false;
         *oppStart = true;
-    } else if (opp->fPart[TCurve::kPointLast] == fPart[0]) {
+    } else if (opp->fPart[OppCurve::kPointLast] == fPart[0]) {
         *start = true;
         *oppStart = false;
-    } else if (opp->fPart[TCurve::kPointLast] == fPart[TCurve::kPointLast]) {
+    } else if (opp->fPart[OppCurve::kPointLast] == fPart[TCurve::kPointLast]) {
         *start = *oppStart = false;
     } else {
         *ptsInCommon = false;
         return false;
     }
     *ptsInCommon = true;
-    const SkDPoint* o1Pts[TCurve::kPointCount - 1], * o2Pts[TCurve::kPointCount - 1];
+    const SkDPoint* otherPts[TCurve::kPointCount - 1], * oppOtherPts[OppCurve::kPointCount - 1];
     int baseIndex = *start ? 0 : TCurve::kPointLast;
-    fPart.otherPts(baseIndex, o1Pts);
-    opp->fPart.otherPts(*oppStart ? 0 : TCurve::kPointLast, o2Pts);
+    fPart.otherPts(baseIndex, otherPts);
+    opp->fPart.otherPts(*oppStart ? 0 : OppCurve::kPointLast, oppOtherPts);
     const SkDPoint& base = fPart[baseIndex];
-    for (int o1 = 0; o1 < (int) SK_ARRAY_COUNT(o1Pts); ++o1) {
-        SkDVector v1 = *o1Pts[o1] - base;
-        for (int o2 = 0; o2 < (int) SK_ARRAY_COUNT(o2Pts); ++o2) {
-            SkDVector v2 = *o2Pts[o2] - base;
+    for (int o1 = 0; o1 < (int) SK_ARRAY_COUNT(otherPts); ++o1) {
+        SkDVector v1 = *otherPts[o1] - base;
+        for (int o2 = 0; o2 < (int) SK_ARRAY_COUNT(oppOtherPts); ++o2) {
+            SkDVector v2 = *oppOtherPts[o2] - base;
             if (v2.dot(v1) >= 0) {
                 return false;
             }
@@ -616,11 +655,11 @@ bool SkTSpan<TCurve>::onlyEndPointsInCommon(const SkTSpan* opp, bool* start, boo
     return true;
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSpan<TCurve>::oppT(double t) const {
-    SkTSpanBounded<TCurve>* bounded = fBounded;
+template<typename TCurve, typename OppCurve>
+SkTSpan<OppCurve, TCurve>* SkTSpan<TCurve, OppCurve>::oppT(double t) const {
+    SkTSpanBounded<OppCurve, TCurve>* bounded = fBounded;
     while (bounded) {
-        SkTSpan* test = bounded->fBounded;
+        SkTSpan<OppCurve, TCurve>* test = bounded->fBounded;
         if (between(test->fStartT, t, test->fEndT)) {
             return test;
         }
@@ -629,26 +668,26 @@ SkTSpan<TCurve>* SkTSpan<TCurve>::oppT(double t) const {
     return NULL;
 }
 
-template<typename TCurve>
-bool SkTSpan<TCurve>::removeAllBounded() {
+template<typename TCurve, typename OppCurve>
+bool SkTSpan<TCurve, OppCurve>::removeAllBounded() {
     bool deleteSpan = false;
-    SkTSpanBounded<TCurve>* bounded = fBounded;
+    SkTSpanBounded<OppCurve, TCurve>* bounded = fBounded;
     while (bounded) {
-        SkTSpan* opp = bounded->fBounded;
+        SkTSpan<OppCurve, TCurve>* opp = bounded->fBounded;
         deleteSpan |= opp->removeBounded(this);
         bounded = bounded->fNext;
     }
     return deleteSpan;
 }
 
-template<typename TCurve>
-bool SkTSpan<TCurve>::removeBounded(const SkTSpan* opp) {
+template<typename TCurve, typename OppCurve>
+bool SkTSpan<TCurve, OppCurve>::removeBounded(const SkTSpan<OppCurve, TCurve>* opp) {
     if (fHasPerp) {
         bool foundStart = false;
         bool foundEnd = false;
-        SkTSpanBounded<TCurve>* bounded = fBounded;
+        SkTSpanBounded<OppCurve, TCurve>* bounded = fBounded;
         while (bounded) {
-            SkTSpan* test = bounded->fBounded;
+            SkTSpan<OppCurve, TCurve>* test = bounded->fBounded;
             if (opp != test) {
                 foundStart |= between(test->fStartT, fCoinStart.perpT(), test->fEndT);
                 foundEnd |= between(test->fStartT, fCoinEnd.perpT(), test->fEndT);
@@ -661,10 +700,10 @@ bool SkTSpan<TCurve>::removeBounded(const SkTSpan* opp) {
             fCoinEnd.init();
         }
     }
-    SkTSpanBounded<TCurve>* bounded = fBounded;
-    SkTSpanBounded<TCurve>* prev = NULL;
+    SkTSpanBounded<OppCurve, TCurve>* bounded = fBounded;
+    SkTSpanBounded<OppCurve, TCurve>* prev = NULL;
     while (bounded) {
-        SkTSpanBounded<TCurve>* boundedNext = bounded->fNext;
+        SkTSpanBounded<OppCurve, TCurve>* boundedNext = bounded->fNext;
         if (opp == bounded->fBounded) {
             if (prev) {
                 prev->fNext = boundedNext;
@@ -681,8 +720,8 @@ bool SkTSpan<TCurve>::removeBounded(const SkTSpan* opp) {
     return false;
 }
 
-template<typename TCurve>
-bool SkTSpan<TCurve>::splitAt(SkTSpan* work, double t, SkChunkAlloc* heap) {
+template<typename TCurve, typename OppCurve>
+bool SkTSpan<TCurve, OppCurve>::splitAt(SkTSpan* work, double t, SkChunkAlloc* heap) {
     fStartT = t;
     fEndT = work->fEndT;
     if (fStartT == fEndT) {
@@ -703,7 +742,7 @@ bool SkTSpan<TCurve>::splitAt(SkTSpan* work, double t, SkChunkAlloc* heap) {
     if (fNext) {
         fNext->fPrev = this;
     }
-    SkTSpanBounded<TCurve>* bounded = work->fBounded;
+    SkTSpanBounded<OppCurve, TCurve>* bounded = work->fBounded;
     fBounded = NULL;
     while (bounded) {
         this->addBounded(bounded->fBounded, heap);
@@ -717,8 +756,8 @@ bool SkTSpan<TCurve>::splitAt(SkTSpan* work, double t, SkChunkAlloc* heap) {
     return true;
 }
 
-template<typename TCurve>
-void SkTSpan<TCurve>::validate() const {
+template<typename TCurve, typename OppCurve>
+void SkTSpan<TCurve, OppCurve>::validate() const {
 #if DEBUG_T_SECT
     SkASSERT(fNext == NULL || fNext != fPrev);
     SkASSERT(fNext == NULL || this == fNext->fPrev);
@@ -743,12 +782,12 @@ void SkTSpan<TCurve>::validate() const {
 #endif
 }
 
-template<typename TCurve>
-void SkTSpan<TCurve>::validateBounded() const {
+template<typename TCurve, typename OppCurve>
+void SkTSpan<TCurve, OppCurve>::validateBounded() const {
 #if DEBUG_VALIDATE
-    const SkTSpanBounded<TCurve>* testBounded = fBounded;
+    const SkTSpanBounded<OppCurve, TCurve>* testBounded = fBounded;
     while (testBounded) {
-        const SkTSpan* overlap = testBounded->fBounded;
+        SkDEBUGCODE_(const SkTSpan<OppCurve, TCurve>* overlap = testBounded->fBounded);
         SkASSERT(!overlap->fDeleted);
         SkASSERT(((this->debugID() ^ overlap->debugID()) & 1) == 1);
         SkASSERT(overlap->findOppSpan(this));
@@ -757,33 +796,29 @@ void SkTSpan<TCurve>::validateBounded() const {
 #endif
 }
 
-template<typename TCurve>
-void SkTSpan<TCurve>::validatePerpT(double oppT) const {
-#if DEBUG_VALIDATE
-    const SkTSpanBounded<TCurve>* testBounded = fBounded;
+template<typename TCurve, typename OppCurve>
+void SkTSpan<TCurve, OppCurve>::validatePerpT(double oppT) const {
+    const SkTSpanBounded<OppCurve, TCurve>* testBounded = fBounded;
     while (testBounded) {
-        const SkTSpan* overlap = testBounded->fBounded;
+        const SkTSpan<OppCurve, TCurve>* overlap = testBounded->fBounded;
         if (between(overlap->fStartT, oppT, overlap->fEndT)) {
             return;
         }
         testBounded = testBounded->fNext;
     }
     SkASSERT(0);
-#endif
 }
 
-template<typename TCurve>
-void SkTSpan<TCurve>::validatePerpPt(double t, const SkDPoint& pt) const {
-#if DEBUG_T_SECT
-    PATH_OPS_DEBUG_CODE(SkASSERT(fDebugSect->fOppSect->fCurve.ptAtT(t) == pt));
-#endif
+template<typename TCurve, typename OppCurve>
+void SkTSpan<TCurve, OppCurve>::validatePerpPt(double t, const SkDPoint& pt) const {
+    SkASSERT(fDebugSect->fOppSect->fCurve.ptAtT(t) == pt);
 }
 
 
-template<typename TCurve>
-SkTSect<TCurve>::SkTSect(const TCurve& c PATH_OPS_DEBUG_T_SECT_PARAMS(int id))
+template<typename TCurve, typename OppCurve>
+SkTSect<TCurve, OppCurve>::SkTSect(const TCurve& c PATH_OPS_DEBUG_T_SECT_PARAMS(int id))
     : fCurve(c)
-    , fHeap(sizeof(SkTSpan<TCurve>) * 4)
+    , fHeap(sizeof(SkTSpan<TCurve, OppCurve>) * 4)
     , fCoincident(NULL)
     , fDeleted(NULL)
     , fActiveCount(0)
@@ -795,15 +830,16 @@ SkTSect<TCurve>::SkTSect(const TCurve& c PATH_OPS_DEBUG_T_SECT_PARAMS(int id))
     fHead->init(c);
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::addOne() {
-    SkTSpan<TCurve>* result;
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::addOne() {
+    SkTSpan<TCurve, OppCurve>* result;
     if (fDeleted) {
         result = fDeleted;
         result->reset();
         fDeleted = result->fNext;
     } else {
-        result = SkNEW_PLACEMENT(fHeap.allocThrow(sizeof(SkTSpan<TCurve>)), SkTSpan<TCurve>);
+        result = SkNEW_PLACEMENT(fHeap.allocThrow(sizeof(SkTSpan<TCurve, OppCurve>)),
+                (SkTSpan<TCurve, OppCurve>));
         result->fBounded = NULL;
 #if DEBUG_T_SECT
         ++fDebugAllocatedCount;
@@ -813,21 +849,21 @@ SkTSpan<TCurve>* SkTSect<TCurve>::addOne() {
     result->fDeleted = false;
     ++fActiveCount; 
     PATH_OPS_DEBUG_T_SECT_CODE(result->fID = fDebugCount++ * 2 + fID);
-    PATH_OPS_DEBUG_CODE(result->fDebugSect = this);
+    SkDEBUGCODE(result->fDebugSect = this);
     return result;
 }
 
-template<typename TCurve>
-bool SkTSect<TCurve>::binarySearchCoin(SkTSect* sect2, double tStart, double tStep,
-        double* resultT, double* oppT) {
-    SkTSpan<TCurve> work;
+template<typename TCurve, typename OppCurve>
+bool SkTSect<TCurve, OppCurve>::binarySearchCoin(SkTSect<OppCurve, TCurve>* sect2, double tStart,
+        double tStep, double* resultT, double* oppT) {
+    SkTSpan<TCurve, OppCurve> work;
     double result = work.fStartT = work.fEndT = tStart;
-    PATH_OPS_DEBUG_CODE(work.fDebugSect = this);
+    SkDEBUGCODE(work.fDebugSect = this);
     SkDPoint last = fCurve.ptAtT(tStart);
     SkDPoint oppPt;
     bool flip = false;
     SkDEBUGCODE(bool down = tStep < 0);
-    const TCurve& opp = sect2->fCurve;
+    const OppCurve& opp = sect2->fCurve;
     do {
         tStep *= 0.5;
         work.fStartT += tStep;
@@ -867,7 +903,7 @@ bool SkTSect<TCurve>::binarySearchCoin(SkTSect* sect2, double tStart, double tSt
     }
     if (oppPt.approximatelyEqual(opp[0])) {
         *oppT = 0;
-    } else if (oppPt.approximatelyEqual(opp[TCurve::kPointLast])) {
+    } else if (oppPt.approximatelyEqual(opp[OppCurve::kPointLast])) {
         *oppT = 1;
     }
     *resultT = result;
@@ -877,25 +913,26 @@ bool SkTSect<TCurve>::binarySearchCoin(SkTSect* sect2, double tStart, double tSt
 // OPTIMIZE ? keep a sorted list of sizes in the form of a doubly-linked list in quad span
 //            so that each quad sect has a pointer to the largest, and can update it as spans
 //            are split
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::boundsMax() const {
-    SkTSpan<TCurve>* test = fHead;
-    SkTSpan<TCurve>* largest = fHead;
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::boundsMax() const {
+    SkTSpan<TCurve, OppCurve>* test = fHead;
+    SkTSpan<TCurve, OppCurve>* largest = fHead;
     bool lCollapsed = largest->fCollapsed;
     while ((test = test->fNext)) {
         bool tCollapsed = test->fCollapsed;
         if ((lCollapsed && !tCollapsed) || (lCollapsed == tCollapsed &&
                 largest->fBoundsMax < test->fBoundsMax)) {
             largest = test;
+            lCollapsed = test->fCollapsed;
         }
     }
     return largest;
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::coincidentCheck(SkTSect* sect2) {
-    SkTSpan<TCurve>* first = fHead;
-    SkTSpan<TCurve>* last, * next;
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::coincidentCheck(SkTSect<OppCurve, TCurve>* sect2) {
+    SkTSpan<TCurve, OppCurve>* first = fHead;
+    SkTSpan<TCurve, OppCurve>* last, * next;
     do {
         int consecutive = this->countConsecutiveSpans(first, &last);
         next = last->fNext;
@@ -908,16 +945,16 @@ void SkTSect<TCurve>::coincidentCheck(SkTSect* sect2) {
         this->validate();
         sect2->validate();
         // check to see if a range of points are on the curve
-        SkTSpan<TCurve>* coinStart = first;
+        SkTSpan<TCurve, OppCurve>* coinStart = first;
         do {
             coinStart = this->extractCoincident(sect2, coinStart, last);
         } while (coinStart && !last->fDeleted);
     } while ((first = next));
 }
 
-template<typename TCurve>
-bool SkTSect<TCurve>::coincidentHasT(double t) {
-    SkTSpan<TCurve>* test = fCoincident;
+template<typename TCurve, typename OppCurve>
+bool SkTSect<TCurve, OppCurve>::coincidentHasT(double t) {
+    SkTSpan<TCurve, OppCurve>* test = fCoincident;
     while (test) {
         if (between(test->fStartT, t, test->fEndT)) {
             return true;
@@ -927,12 +964,25 @@ bool SkTSect<TCurve>::coincidentHasT(double t) {
     return false;
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::computePerpendiculars(SkTSect* sect2, SkTSpan<TCurve>* first,
-        SkTSpan<TCurve>* last) {
-    const TCurve& opp = sect2->fCurve;
-        SkTSpan<TCurve>* work = first;
-    SkTSpan<TCurve>* prior = NULL;
+template<typename TCurve, typename OppCurve>
+int SkTSect<TCurve, OppCurve>::collapsed() const {
+    int result = 0;
+    const SkTSpan<TCurve, OppCurve>* test = fHead;
+    while (test) {
+        if (test->fCollapsed) {
+            ++result;
+        }
+        test = test->next();
+    }
+    return result;
+}
+
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::computePerpendiculars(SkTSect<OppCurve, TCurve>* sect2,
+        SkTSpan<TCurve, OppCurve>* first, SkTSpan<TCurve, OppCurve>* last) {
+    const OppCurve& opp = sect2->fCurve;
+    SkTSpan<TCurve, OppCurve>* work = first;
+    SkTSpan<TCurve, OppCurve>* prior = NULL;
     do {
         if (!work->fHasPerp && !work->fCollapsed) {
             if (prior) {
@@ -968,13 +1018,13 @@ void SkTSect<TCurve>::computePerpendiculars(SkTSect* sect2, SkTSpan<TCurve>* fir
     } while (true);
 }
 
-template<typename TCurve>
-int SkTSect<TCurve>::countConsecutiveSpans(SkTSpan<TCurve>* first,
-        SkTSpan<TCurve>** lastPtr) const {
+template<typename TCurve, typename OppCurve>
+int SkTSect<TCurve, OppCurve>::countConsecutiveSpans(SkTSpan<TCurve, OppCurve>* first,
+        SkTSpan<TCurve, OppCurve>** lastPtr) const {
     int consecutive = 1;
-    SkTSpan<TCurve>* last = first;
+    SkTSpan<TCurve, OppCurve>* last = first;
     do {
-        SkTSpan<TCurve>* next = last->fNext;
+        SkTSpan<TCurve, OppCurve>* next = last->fNext;
         if (!next) {
             break;
         }
@@ -988,9 +1038,9 @@ int SkTSect<TCurve>::countConsecutiveSpans(SkTSpan<TCurve>* first,
     return consecutive;
 }
 
-template<typename TCurve>
-bool SkTSect<TCurve>::debugHasBounded(const SkTSpan<TCurve>* span) const {
-    const SkTSpan<TCurve>* test = fHead;
+template<typename TCurve, typename OppCurve>
+bool SkTSect<TCurve, OppCurve>::debugHasBounded(const SkTSpan<OppCurve, TCurve>* span) const {
+    const SkTSpan<TCurve, OppCurve>* test = fHead;
     if (!test) {
         return false;
     }
@@ -1002,10 +1052,10 @@ bool SkTSect<TCurve>::debugHasBounded(const SkTSpan<TCurve>* span) const {
     return false;
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::deleteEmptySpans() {
-    SkTSpan<TCurve>* test;
-    SkTSpan<TCurve>* next = fHead;
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::deleteEmptySpans() {
+    SkTSpan<TCurve, OppCurve>* test;
+    SkTSpan<TCurve, OppCurve>* next = fHead;
     while ((test = next)) {
         next = test->fNext;
         if (!test->fBounded) {
@@ -1014,10 +1064,11 @@ void SkTSect<TCurve>::deleteEmptySpans() {
     }
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::extractCoincident(SkTSect* sect2, SkTSpan<TCurve>* first,
-        SkTSpan<TCurve>* last) {
-    first = findCoincidentRun(first, &last, sect2);
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::extractCoincident(
+        SkTSect<OppCurve, TCurve>* sect2,
+        SkTSpan<TCurve, OppCurve>* first, SkTSpan<TCurve, OppCurve>* last) {
+    first = findCoincidentRun(first, &last);
     if (!first) {
         return NULL;
     }
@@ -1025,24 +1076,25 @@ SkTSpan<TCurve>* SkTSect<TCurve>::extractCoincident(SkTSect* sect2, SkTSpan<TCur
     double startT = first->fStartT;
     double oppStartT SK_INIT_TO_AVOID_WARNING;
     double oppEndT SK_INIT_TO_AVOID_WARNING;
-    SkTSpan<TCurve>* prev = first->fPrev;
+    SkTSpan<TCurve, OppCurve>* prev = first->fPrev;
     SkASSERT(first->fCoinStart.isCoincident());
-    SkTSpan<TCurve>* oppFirst = first->findOppT(first->fCoinStart.perpT());
+    SkTSpan<OppCurve, TCurve>* oppFirst = first->findOppT(first->fCoinStart.perpT());
     SkASSERT(last->fCoinEnd.isCoincident());
     bool oppMatched = first->fCoinStart.perpT() < first->fCoinEnd.perpT();
     double coinStart;
     SkDEBUGCODE(double coinEnd);
+    SkTSpan<OppCurve, TCurve>* cutFirst;
     if (prev && prev->fEndT == startT
             && this->binarySearchCoin(sect2, startT, prev->fStartT - startT, &coinStart,
                                       &oppStartT)
-            && prev->fStartT < coinStart && coinStart < startT) {
-        oppFirst = prev->findOppT(oppStartT);  // find opp start before splitting prev
-        SkASSERT(oppFirst);
+            && prev->fStartT < coinStart && coinStart < startT
+            && (cutFirst = prev->oppT(oppStartT))) {
+        oppFirst = cutFirst;
         first = this->addSplitAt(prev, coinStart);
         first->markCoincident();
         prev->fCoinEnd.markCoincident();
         if (oppFirst->fStartT < oppStartT && oppStartT < oppFirst->fEndT) {
-            SkTSpan<TCurve>* oppHalf = sect2->addSplitAt(oppFirst, oppStartT);
+            SkTSpan<OppCurve, TCurve>* oppHalf = sect2->addSplitAt(oppFirst, oppStartT);
             if (oppMatched) {
                 oppFirst->fCoinEnd.markCoincident();
                 oppHalf->markCoincident();
@@ -1056,7 +1108,8 @@ SkTSpan<TCurve>* SkTSect<TCurve>::extractCoincident(SkTSect* sect2, SkTSpan<TCur
         SkDEBUGCODE(coinStart = first->fStartT);
         SkDEBUGCODE(oppStartT = oppMatched ? oppFirst->fStartT : oppFirst->fEndT);
     }
-    SkTSpan<TCurve>* oppLast;
+    // FIXME: incomplete : if we're not at the end, find end of coin
+    SkTSpan<OppCurve, TCurve>* oppLast;
     SkASSERT(last->fCoinEnd.isCoincident());
     oppLast = last->findOppT(last->fCoinEnd.perpT());
     SkDEBUGCODE(coinEnd = last->fEndT);
@@ -1073,8 +1126,8 @@ SkTSpan<TCurve>* SkTSect<TCurve>::extractCoincident(SkTSect* sect2, SkTSpan<TCur
     // reduce coincident runs to single entries
     this->validate();
     sect2->validate();
-    bool deleteThisSpan = this->updateBounded(first, last, oppFirst);
-    bool deleteSect2Span = sect2->updateBounded(oppFirst, oppLast, first);
+    bool deleteEmptySpans = this->updateBounded(first, last, oppFirst);
+    deleteEmptySpans |= sect2->updateBounded(oppFirst, oppLast, first);
     this->removeSpanRange(first, last);
     sect2->removeSpanRange(oppFirst, oppLast);
     first->fEndT = last->fEndT;
@@ -1096,10 +1149,8 @@ SkTSpan<TCurve>* SkTSect<TCurve>::extractCoincident(SkTSect* sect2, SkTSpan<TCur
     last = first->fNext;
     this->removeCoincident(first, false);
     sect2->removeCoincident(oppFirst, true);
-    if (deleteThisSpan) {
+    if (deleteEmptySpans) {
         this->deleteEmptySpans();
-    }
-    if (deleteSect2Span) {
         sect2->deleteEmptySpans();
     }
     this->validate();
@@ -1107,17 +1158,19 @@ SkTSpan<TCurve>* SkTSect<TCurve>::extractCoincident(SkTSect* sect2, SkTSpan<TCur
     return last && !last->fDeleted ? last : NULL;
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::findCoincidentRun(SkTSpan<TCurve>* first,
-        SkTSpan<TCurve>** lastPtr, const SkTSect* sect2) {
-    SkTSpan<TCurve>* work = first;
-    SkTSpan<TCurve>* lastCandidate = NULL;
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::findCoincidentRun(
+        SkTSpan<TCurve, OppCurve>* first, SkTSpan<TCurve, OppCurve>** lastPtr) {
+    SkTSpan<TCurve, OppCurve>* work = first;
+    SkTSpan<TCurve, OppCurve>* lastCandidate = NULL;
     first = NULL;
     // find the first fully coincident span
     do {
         if (work->fCoinStart.isCoincident()) {
+#if DEBUG_T_SECT
             work->validatePerpT(work->fCoinStart.perpT());
             work->validatePerpPt(work->fCoinStart.perpT(), work->fCoinStart.perpPt());
+#endif
             SkASSERT(work->hasOppT(work->fCoinStart.perpT()));
             if (!work->fCoinEnd.isCoincident()) {
                 break;
@@ -1126,6 +1179,9 @@ SkTSpan<TCurve>* SkTSect<TCurve>::findCoincidentRun(SkTSpan<TCurve>* first,
             if (!first) {
                 first = work;
             }
+        } else if (first && work->fCollapsed) {
+            *lastPtr = lastCandidate;
+            return first;
         } else {
             lastCandidate = NULL;
             SkASSERT(!first);
@@ -1142,9 +1198,10 @@ SkTSpan<TCurve>* SkTSect<TCurve>::findCoincidentRun(SkTSpan<TCurve>* first,
     return first;
 }
 
-template<typename TCurve>
-int SkTSect<TCurve>::intersects(SkTSpan<TCurve>* span, const SkTSect* opp,
-        SkTSpan<TCurve>* oppSpan, int* oppResult) const {
+template<typename TCurve, typename OppCurve>
+int SkTSect<TCurve, OppCurve>::intersects(SkTSpan<TCurve, OppCurve>* span,
+        SkTSect<OppCurve, TCurve>* opp,
+        SkTSpan<OppCurve, TCurve>* oppSpan, int* oppResult) {
     bool spanStart, oppStart;
     int hullResult = span->hullsIntersect(oppSpan, &spanStart, &oppStart);
     if (hullResult >= 0) {
@@ -1194,21 +1251,22 @@ int SkTSect<TCurve>::intersects(SkTSpan<TCurve>* span, const SkTSect* opp,
 // while the intersection points are sufficiently far apart:
 // construct the tangent lines from the intersections
 // find the point where the tangent line intersects the opposite curve
-template<typename TCurve>
-int SkTSect<TCurve>::linesIntersect(const SkTSpan<TCurve>* span, const SkTSect* opp,
-            const SkTSpan<TCurve>* oppSpan, SkIntersections* i) const {
+template<typename TCurve, typename OppCurve>
+int SkTSect<TCurve, OppCurve>::linesIntersect(SkTSpan<TCurve, OppCurve>* span,
+        SkTSect<OppCurve, TCurve>* opp,
+        SkTSpan<OppCurve, TCurve>* oppSpan, SkIntersections* i) {
     SkIntersections thisRayI, oppRayI;
     SkDLine thisLine = {{ span->fPart[0], span->fPart[TCurve::kPointLast] }};
-    SkDLine oppLine = {{ oppSpan->fPart[0], oppSpan->fPart[TCurve::kPointLast] }};
+    SkDLine oppLine = {{ oppSpan->fPart[0], oppSpan->fPart[OppCurve::kPointLast] }};
     int loopCount = 0;
     double bestDistSq = DBL_MAX;
+    if (!thisRayI.intersectRay(opp->fCurve, thisLine)) {
+        return 0;
+    }
+    if (!oppRayI.intersectRay(this->fCurve, oppLine)) {
+        return 0;
+    }
     do {
-        if (!thisRayI.intersectRay(opp->fCurve, thisLine)) {
-            return 0;
-        }
-        if (!oppRayI.intersectRay(this->fCurve, oppLine)) {
-            return 0;
-        }
         // pick the closest pair of points
         double closest = DBL_MAX;
         int closeIndex SK_INIT_TO_AVOID_WARNING;
@@ -1230,7 +1288,7 @@ int SkTSect<TCurve>::linesIntersect(const SkTSpan<TCurve>* span, const SkTSect*
             }
         }
         if (closest == DBL_MAX) {
-            return 0;
+            break;
         }
         const SkDPoint& oppIPt = thisRayI.pt(oppCloseIndex);
         const SkDPoint& iPt = oppRayI.pt(closeIndex);
@@ -1242,20 +1300,88 @@ int SkTSect<TCurve>::linesIntersect(const SkTSpan<TCurve>* span, const SkTSect*
         }
         double distSq = oppIPt.distanceSquared(iPt);
         if (bestDistSq < distSq || ++loopCount > 5) {
-            break;
+            return 0;
         }
         bestDistSq = distSq;
-        thisLine[0] = fCurve.ptAtT(oppRayI[0][closeIndex]);
-        thisLine[1] = thisLine[0] + fCurve.dxdyAtT(oppRayI[0][closeIndex]);
-        oppLine[0] = opp->fCurve.ptAtT(thisRayI[0][oppCloseIndex]);
-        oppLine[1] = oppLine[0] + opp->fCurve.dxdyAtT(thisRayI[0][oppCloseIndex]);
+        double oppStart = oppRayI[0][closeIndex];
+        thisLine[0] = fCurve.ptAtT(oppStart);
+        thisLine[1] = thisLine[0] + fCurve.dxdyAtT(oppStart);
+        if (!thisRayI.intersectRay(opp->fCurve, thisLine)) {
+            break;
+        }
+        double start = thisRayI[0][oppCloseIndex];
+        oppLine[0] = opp->fCurve.ptAtT(start);
+        oppLine[1] = oppLine[0] + opp->fCurve.dxdyAtT(start);
+        if (!oppRayI.intersectRay(this->fCurve, oppLine)) {
+            break;
+        }
     } while (true);
-    return false;
+    // convergence may fail if the curves are nearly coincident
+    SkTCoincident<OppCurve, TCurve> oCoinS, oCoinE;
+    oCoinS.setPerp(opp->fCurve, oppSpan->fStartT, oppSpan->fPart[0], fCurve);
+    oCoinE.setPerp(opp->fCurve, oppSpan->fEndT, oppSpan->fPart[OppCurve::kPointLast], fCurve);
+    double tStart = oCoinS.perpT();
+    double tEnd = oCoinE.perpT();
+    bool swap = tStart > tEnd;
+    if (swap) {
+        SkTSwap(tStart, tEnd);
+    }
+    tStart = SkTMax(tStart, span->fStartT);
+    tEnd = SkTMin(tEnd, span->fEndT);
+    if (tStart > tEnd) {
+        return 0;
+    }
+    SkDVector perpS, perpE;
+    if (tStart == span->fStartT) {
+        SkTCoincident<TCurve, OppCurve> coinS;
+        coinS.setPerp(fCurve, span->fStartT, span->fPart[0], opp->fCurve);
+        perpS = span->fPart[0] - coinS.perpPt();
+    } else if (swap) {
+        perpS = oCoinE.perpPt() - oppSpan->fPart[OppCurve::kPointLast];
+    } else {
+        perpS = oCoinS.perpPt() - oppSpan->fPart[0];
+    }
+    if (tEnd == span->fEndT) {
+        SkTCoincident<TCurve, OppCurve> coinE;
+        coinE.setPerp(fCurve, span->fEndT, span->fPart[TCurve::kPointLast], opp->fCurve);
+        perpE = span->fPart[TCurve::kPointLast] - coinE.perpPt();
+    } else if (swap) {
+        perpE = oCoinS.perpPt() - oppSpan->fPart[0];
+    } else {
+        perpE = oCoinE.perpPt() - oppSpan->fPart[OppCurve::kPointLast];
+    }
+    if (perpS.dot(perpE) >= 0) {
+        return 0;
+    }
+    SkTCoincident<TCurve, OppCurve> coinW;
+    double workT = tStart;
+    double tStep = tEnd - tStart;
+    SkDPoint workPt;
+    do {
+        tStep *= 0.5;
+        if (precisely_zero(tStep)) {
+            return 0;
+        }
+        workT += tStep;
+        workPt = fCurve.ptAtT(workT);
+        coinW.setPerp(fCurve, workT, workPt, opp->fCurve);
+        SkDVector perpW = workPt - coinW.perpPt();
+        if ((perpS.dot(perpW) >= 0) == (tStep < 0)) {
+            tStep = -tStep;
+        }
+    } while (!workPt.approximatelyEqual(coinW.perpPt()));
+    double oppTTest = coinW.perpT();
+    if (!opp->fHead->contains(oppTTest)) {
+        return 0;
+    }
+    i->setMax(1);
+    i->insert(workT, oppTTest, workPt);
+    return 1;
 }
 
 
-template<typename TCurve>
-void SkTSect<TCurve>::markSpanGone(SkTSpan<TCurve>* span) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::markSpanGone(SkTSpan<TCurve, OppCurve>* span) {
     --fActiveCount;
     span->fNext = fDeleted;
     fDeleted = span;
@@ -1263,16 +1389,17 @@ void SkTSect<TCurve>::markSpanGone(SkTSpan<TCurve>* span) {
     span->fDeleted = true;
 }
 
-template<typename TCurve>
-bool SkTSect<TCurve>::matchedDirection(double t, const SkTSect* sect2, double t2) const {
+template<typename TCurve, typename OppCurve>
+bool SkTSect<TCurve, OppCurve>::matchedDirection(double t, const SkTSect<OppCurve, TCurve>* sect2,
+        double t2) const {
     SkDVector dxdy = this->fCurve.dxdyAtT(t);
     SkDVector dxdy2 = sect2->fCurve.dxdyAtT(t2);
     return dxdy.dot(dxdy2) >= 0;
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::matchedDirCheck(double t, const SkTSect* sect2, double t2,
-        bool* calcMatched, bool* oppMatched) const {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::matchedDirCheck(double t, const SkTSect<OppCurve, TCurve>* sect2,
+        double t2, bool* calcMatched, bool* oppMatched) const {
     if (*calcMatched) {
         SkASSERT(*oppMatched == this->matchedDirection(t, sect2, t2)); 
     } else {
@@ -1281,13 +1408,13 @@ void SkTSect<TCurve>::matchedDirCheck(double t, const SkTSect* sect2, double t2,
     }
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::mergeCoincidence(SkTSect* sect2) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::mergeCoincidence(SkTSect<OppCurve, TCurve>* sect2) {
     double smallLimit = 0;
     do {
         // find the smallest unprocessed span
-        SkTSpan<TCurve>* smaller = NULL;
-        SkTSpan<TCurve>* test = fCoincident;
+        SkTSpan<TCurve, OppCurve>* smaller = NULL;
+        SkTSpan<TCurve, OppCurve>* test = fCoincident;
         do {
             if (test->fStartT < smallLimit) {
                 continue;
@@ -1302,9 +1429,9 @@ void SkTSect<TCurve>::mergeCoincidence(SkTSect* sect2) {
         }
         smallLimit = smaller->fEndT;
         // find next larger span
-        SkTSpan<TCurve>* prior = NULL;
-        SkTSpan<TCurve>* larger = NULL;
-        SkTSpan<TCurve>* largerPrior = NULL;
+        SkTSpan<TCurve, OppCurve>* prior = NULL;
+        SkTSpan<TCurve, OppCurve>* larger = NULL;
+        SkTSpan<TCurve, OppCurve>* largerPrior = NULL;
         test = fCoincident;
         do {
             if (test->fStartT < smaller->fEndT) {
@@ -1323,7 +1450,7 @@ void SkTSect<TCurve>::mergeCoincidence(SkTSect* sect2) {
         // check middle t value to see if it is coincident as well
         double midT = (smaller->fEndT + larger->fStartT) / 2;
         SkDPoint midPt = fCurve.ptAtT(midT);
-        SkTCoincident<TCurve> coin;
+        SkTCoincident<TCurve, OppCurve> coin;
         coin.setPerp(fCurve, midT, midPt, sect2->fCurve);
         if (coin.isCoincident()) {
             smaller->fEndT = larger->fEndT;
@@ -1337,10 +1464,11 @@ void SkTSect<TCurve>::mergeCoincidence(SkTSect* sect2) {
     } while (true);
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::prev(SkTSpan<TCurve>* span) const {
-    SkTSpan<TCurve>* result = NULL;
-    SkTSpan<TCurve>* test = fHead;
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::prev(
+        SkTSpan<TCurve, OppCurve>* span) const {
+    SkTSpan<TCurve, OppCurve>* result = NULL;
+    SkTSpan<TCurve, OppCurve>* test = fHead;
     while (span != test) {
         result = test;
         test = test->fNext;
@@ -1349,13 +1477,13 @@ SkTSpan<TCurve>* SkTSect<TCurve>::prev(SkTSpan<TCurve>* span) const {
     return result; 
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::recoverCollapsed() {
-    SkTSpan<TCurve>* deleted = fDeleted;
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::recoverCollapsed() {
+    SkTSpan<TCurve, OppCurve>* deleted = fDeleted;
     while (deleted) {
-        SkTSpan<TCurve>* delNext = deleted->fNext;
+        SkTSpan<TCurve, OppCurve>* delNext = deleted->fNext;
         if (deleted->fCollapsed) {
-            SkTSpan<TCurve>** spanPtr = &fHead;
+            SkTSpan<TCurve, OppCurve>** spanPtr = &fHead;
             while (*spanPtr && (*spanPtr)->fEndT <= deleted->fStartT) {
                 spanPtr = &(*spanPtr)->fNext;
             }
@@ -1366,13 +1494,13 @@ void SkTSect<TCurve>::recoverCollapsed() {
     }
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::removeAllBut(const SkTSpan<TCurve>* keep, SkTSpan<TCurve>* span,
-        SkTSect* opp) {
-    const SkTSpanBounded<TCurve>* testBounded = span->fBounded;
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::removeAllBut(const SkTSpan<OppCurve, TCurve>* keep,
+        SkTSpan<TCurve, OppCurve>* span, SkTSect<OppCurve, TCurve>* opp) {
+    const SkTSpanBounded<OppCurve, TCurve>* testBounded = span->fBounded;
     while (testBounded) {
-        SkTSpan<TCurve>* bounded = testBounded->fBounded;
-        const SkTSpanBounded<TCurve>* next = testBounded->fNext;
+        SkTSpan<OppCurve, TCurve>* bounded = testBounded->fBounded;
+        const SkTSpanBounded<OppCurve, TCurve>* next = testBounded->fNext;
         // may have been deleted when opp did 'remove all but'
         if (bounded != keep && !bounded->fDeleted) {
             SkAssertResult(SkDEBUGCODE(!) span->removeBounded(bounded));
@@ -1387,10 +1515,10 @@ void SkTSect<TCurve>::removeAllBut(const SkTSpan<TCurve>* keep, SkTSpan<TCurve>*
     SkASSERT(keep->findOppSpan(span));
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::removeByPerpendicular(SkTSect<TCurve>* opp) {
-    SkTSpan<TCurve>* test = fHead;
-    SkTSpan<TCurve>* next;
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::removeByPerpendicular(SkTSect<OppCurve, TCurve>* opp) {
+    SkTSpan<TCurve, OppCurve>* test = fHead;
+    SkTSpan<TCurve, OppCurve>* next;
     do {
         next = test->fNext;
         if (test->fCoinStart.perpT() < 0 || test->fCoinEnd.perpT() < 0) {
@@ -1409,8 +1537,8 @@ void SkTSect<TCurve>::removeByPerpendicular(SkTSect<TCurve>* opp) {
     } while ((test = next));
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::removeCoincident(SkTSpan<TCurve>* span, bool isBetween) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::removeCoincident(SkTSpan<TCurve, OppCurve>* span, bool isBetween) {
     this->unlinkSpan(span);
     if (isBetween || between(0, span->fCoinStart.perpT(), 1)) {
         --fActiveCount;
@@ -1421,21 +1549,22 @@ void SkTSect<TCurve>::removeCoincident(SkTSpan<TCurve>* span, bool isBetween) {
     }
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::removeSpan(SkTSpan<TCurve>* span) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::removeSpan(SkTSpan<TCurve, OppCurve>* span) {
     this->unlinkSpan(span);
     this->markSpanGone(span);
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::removeSpanRange(SkTSpan<TCurve>* first, SkTSpan<TCurve>* last) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::removeSpanRange(SkTSpan<TCurve, OppCurve>* first,
+        SkTSpan<TCurve, OppCurve>* last) {
     if (first == last) {
         return;
     }
-    SkTSpan<TCurve>* span = first;
+    SkTSpan<TCurve, OppCurve>* span = first;
     SkASSERT(span);
-    SkTSpan<TCurve>* final = last->fNext;
-    SkTSpan<TCurve>* next = span->fNext;
+    SkTSpan<TCurve, OppCurve>* final = last->fNext;
+    SkTSpan<TCurve, OppCurve>* next = span->fNext;
     while ((span = next) && span != final) {
         next = span->fNext;
         this->markSpanGone(span);
@@ -1446,12 +1575,13 @@ void SkTSect<TCurve>::removeSpanRange(SkTSpan<TCurve>* first, SkTSpan<TCurve>* l
     first->fNext = final;
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::removeSpans(SkTSpan<TCurve>* span, SkTSect<TCurve>* opp) {
-    SkTSpanBounded<TCurve>* bounded = span->fBounded;
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::removeSpans(SkTSpan<TCurve, OppCurve>* span,
+        SkTSect<OppCurve, TCurve>* opp) {
+    SkTSpanBounded<OppCurve, TCurve>* bounded = span->fBounded;
     while (bounded) {
-        SkTSpan<TCurve>* spanBounded = bounded->fBounded;
-        SkTSpanBounded<TCurve>* next = bounded->fNext;
+        SkTSpan<OppCurve, TCurve>* spanBounded = bounded->fBounded;
+        SkTSpanBounded<OppCurve, TCurve>* next = bounded->fNext;
         if (span->removeBounded(spanBounded)) {  // shuffles last into position 0
             this->removeSpan(span);
         }
@@ -1463,10 +1593,11 @@ void SkTSect<TCurve>::removeSpans(SkTSpan<TCurve>* span, SkTSect<TCurve>* opp) {
     }
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::spanAtT(double t, SkTSpan<TCurve>** priorSpan) {
-    SkTSpan<TCurve>* test = fHead;
-    SkTSpan<TCurve>* prev = NULL;
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::spanAtT(double t,
+        SkTSpan<TCurve, OppCurve>** priorSpan) {
+    SkTSpan<TCurve, OppCurve>* test = fHead;
+    SkTSpan<TCurve, OppCurve>* prev = NULL;
     while (test && test->fEndT < t) {
         prev = test;
         test = test->fNext;
@@ -1475,10 +1606,10 @@ SkTSpan<TCurve>* SkTSect<TCurve>::spanAtT(double t, SkTSpan<TCurve>** priorSpan)
     return test && test->fStartT <= t ? test : NULL;
 }
 
-template<typename TCurve>
-SkTSpan<TCurve>* SkTSect<TCurve>::tail() {
-    SkTSpan<TCurve>* result = fHead;
-    SkTSpan<TCurve>* next = fHead;
+template<typename TCurve, typename OppCurve>
+SkTSpan<TCurve, OppCurve>* SkTSect<TCurve, OppCurve>::tail() {
+    SkTSpan<TCurve, OppCurve>* result = fHead;
+    SkTSpan<TCurve, OppCurve>* next = fHead;
     while ((next = next->fNext)) {
         if (next->fEndT > result->fEndT) {
             result = next;
@@ -1489,13 +1620,14 @@ SkTSpan<TCurve>* SkTSect<TCurve>::tail() {
 
 /* Each span has a range of opposite spans it intersects. After the span is split in two,
     adjust the range to its new size */
-template<typename TCurve>
-void SkTSect<TCurve>::trim(SkTSpan<TCurve>* span, SkTSect* opp) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::trim(SkTSpan<TCurve, OppCurve>* span,
+        SkTSect<OppCurve, TCurve>* opp) {
     span->initBounds(fCurve);
-    const SkTSpanBounded<TCurve>* testBounded = span->fBounded;
+    const SkTSpanBounded<OppCurve, TCurve>* testBounded = span->fBounded;
     while (testBounded) {
-        SkTSpan<TCurve>* test = testBounded->fBounded;
-        const SkTSpanBounded<TCurve>* next = testBounded->fNext;
+        SkTSpan<OppCurve, TCurve>* test = testBounded->fBounded;
+        const SkTSpanBounded<OppCurve, TCurve>* next = testBounded->fNext;
         int oppSects, sects = this->intersects(span, opp, test, &oppSects);
         if (sects >= 1) {
             if (oppSects == 2) {
@@ -1519,10 +1651,10 @@ void SkTSect<TCurve>::trim(SkTSpan<TCurve>* span, SkTSect* opp) {
     }
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::unlinkSpan(SkTSpan<TCurve>* span) {
-    SkTSpan<TCurve>* prev = span->fPrev;
-    SkTSpan<TCurve>* next = span->fNext;
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::unlinkSpan(SkTSpan<TCurve, OppCurve>* span) {
+    SkTSpan<TCurve, OppCurve>* prev = span->fPrev;
+    SkTSpan<TCurve, OppCurve>* next = span->fNext;
     if (prev) {
         prev->fNext = next;
         if (next) {
@@ -1536,11 +1668,11 @@ void SkTSect<TCurve>::unlinkSpan(SkTSpan<TCurve>* span) {
     }
 }
 
-template<typename TCurve>
-bool SkTSect<TCurve>::updateBounded(SkTSpan<TCurve>* first, SkTSpan<TCurve>* last,
-        SkTSpan<TCurve>* oppFirst) {
-    SkTSpan<TCurve>* test = first;
-    const SkTSpan<TCurve>* final = last->next();
+template<typename TCurve, typename OppCurve>
+bool SkTSect<TCurve, OppCurve>::updateBounded(SkTSpan<TCurve, OppCurve>* first,
+        SkTSpan<TCurve, OppCurve>* last, SkTSpan<OppCurve, TCurve>* oppFirst) {
+    SkTSpan<TCurve, OppCurve>* test = first;
+    const SkTSpan<TCurve, OppCurve>* final = last->next();
     bool deleteSpan = false;
     do {
         deleteSpan |= test->removeAllBounded();
@@ -1552,12 +1684,12 @@ bool SkTSect<TCurve>::updateBounded(SkTSpan<TCurve>* first, SkTSpan<TCurve>* las
 }
 
 
-template<typename TCurve>
-void SkTSect<TCurve>::validate() const {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::validate() const {
 #if DEBUG_T_SECT
     int count = 0;
     if (fHead) {
-        const SkTSpan<TCurve>* span = fHead;
+        const SkTSpan<TCurve, OppCurve>* span = fHead;
         SkASSERT(!span->fPrev);
         SkDEBUGCODE(double last = 0);
         do {
@@ -1570,12 +1702,12 @@ void SkTSect<TCurve>::validate() const {
     SkASSERT(count == fActiveCount);
     SkASSERT(fActiveCount <= fDebugAllocatedCount);
     int deletedCount = 0;
-    const SkTSpan<TCurve>* deleted = fDeleted;
+    const SkTSpan<TCurve, OppCurve>* deleted = fDeleted;
     while (deleted) {
         ++deletedCount;
         deleted = deleted->fNext;
     }
-    const SkTSpan<TCurve>* coincident = fCoincident;
+    const SkTSpan<TCurve, OppCurve>* coincident = fCoincident;
     while (coincident) {
         ++deletedCount;
         coincident = coincident->fNext;
@@ -1584,28 +1716,28 @@ void SkTSect<TCurve>::validate() const {
 #endif
 }
 
-template<typename TCurve>
-void SkTSect<TCurve>::validateBounded() const {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::validateBounded() const {
 #if DEBUG_T_SECT
     if (!fHead) {
         return;
     }
-    const SkTSpan<TCurve>* span = fHead;
+    const SkTSpan<TCurve, OppCurve>* span = fHead;
     do {
         span->validateBounded();
     } while ((span = span->fNext) != NULL);
 #endif
 }
 
-template<typename TCurve>
-int SkTSect<TCurve>::EndsEqual(const SkTSect* sect1, const SkTSect* sect2,
-        SkIntersections* intersections) {
+template<typename TCurve, typename OppCurve>
+int SkTSect<TCurve, OppCurve>::EndsEqual(const SkTSect<TCurve, OppCurve>* sect1,
+        const SkTSect<OppCurve, TCurve>* sect2, SkIntersections* intersections) {
     int zeroOneSet = 0;
     if (sect1->fCurve[0] == sect2->fCurve[0]) {
         zeroOneSet |= kZeroS1Set | kZeroS2Set;
         intersections->insert(0, 0, sect1->fCurve[0]);
     }
-    if (sect1->fCurve[0] == sect2->fCurve[TCurve::kPointLast]) {
+    if (sect1->fCurve[0] == sect2->fCurve[OppCurve::kPointLast]) {
         zeroOneSet |= kZeroS1Set | kOneS2Set;
         intersections->insert(0, 1, sect1->fCurve[0]);
     }
@@ -1613,7 +1745,7 @@ int SkTSect<TCurve>::EndsEqual(const SkTSect* sect1, const SkTSect* sect2,
         zeroOneSet |= kOneS1Set | kZeroS2Set;
         intersections->insert(1, 0, sect1->fCurve[TCurve::kPointLast]);
     }
-    if (sect1->fCurve[TCurve::kPointLast] == sect2->fCurve[TCurve::kPointLast]) {
+    if (sect1->fCurve[TCurve::kPointLast] == sect2->fCurve[OppCurve::kPointLast]) {
         zeroOneSet |= kOneS1Set | kOneS2Set;
             intersections->insert(1, 1, sect1->fCurve[TCurve::kPointLast]);
     }
@@ -1624,9 +1756,9 @@ int SkTSect<TCurve>::EndsEqual(const SkTSect* sect1, const SkTSect* sect2,
         intersections->insertNear(0, 0, sect1->fCurve[0], sect2->fCurve[0]);
     }
     if (!(zeroOneSet & (kZeroS1Set | kOneS2Set))
-            && sect1->fCurve[0].approximatelyEqual(sect2->fCurve[TCurve::kPointLast])) {
+            && sect1->fCurve[0].approximatelyEqual(sect2->fCurve[OppCurve::kPointLast])) {
         zeroOneSet |= kZeroS1Set | kOneS2Set;
-        intersections->insertNear(0, 1, sect1->fCurve[0], sect2->fCurve[TCurve::kPointLast]);
+        intersections->insertNear(0, 1, sect1->fCurve[0], sect2->fCurve[OppCurve::kPointLast]);
     }
     // check for one
     if (!(zeroOneSet & (kOneS1Set | kZeroS2Set))
@@ -1636,15 +1768,15 @@ int SkTSect<TCurve>::EndsEqual(const SkTSect* sect1, const SkTSect* sect2,
     }
     if (!(zeroOneSet & (kOneS1Set | kOneS2Set))
             && sect1->fCurve[TCurve::kPointLast].approximatelyEqual(sect2->fCurve[
-            TCurve::kPointLast])) {
+            OppCurve::kPointLast])) {
         zeroOneSet |= kOneS1Set | kOneS2Set;
         intersections->insertNear(1, 1, sect1->fCurve[TCurve::kPointLast],
-                sect2->fCurve[TCurve::kPointLast]);
+                sect2->fCurve[OppCurve::kPointLast]);
     }
     return zeroOneSet;
 }
 
-template<typename TCurve>
+template<typename TCurve, typename OppCurve>
 struct SkClosestRecord {
     bool operator<(const SkClosestRecord& rh) const {
         return fClosest < rh.fClosest;
@@ -1656,10 +1788,10 @@ struct SkClosestRecord {
         intersections->insert(r1t, r2t, fC1Span->part()[fC1Index]);
     }
 
-    void findEnd(const SkTSpan<TCurve>* span1, const SkTSpan<TCurve>* span2,
+    void findEnd(const SkTSpan<TCurve, OppCurve>* span1, const SkTSpan<OppCurve, TCurve>* span2,
             int c1Index, int c2Index) {
         const TCurve& c1 = span1->part();
-        const TCurve& c2 = span2->part();
+        const OppCurve& c2 = span2->part();
         if (!c1[c1Index].approximatelyEqual(c2[c2Index])) {
             return;
         }
@@ -1700,7 +1832,8 @@ struct SkClosestRecord {
     
     void reset() {
         fClosest = FLT_MAX;
-        SkDEBUGCODE(fC1Span = fC2Span = NULL);
+        SkDEBUGCODE(fC1Span = NULL);
+        SkDEBUGCODE(fC2Span = NULL);
         SkDEBUGCODE(fC1Index = fC2Index = -1);
     }
 
@@ -1711,8 +1844,8 @@ struct SkClosestRecord {
         fC2EndT = SkTMax(fC2EndT, mate.fC2EndT);
     }
 
-    const SkTSpan<TCurve>* fC1Span;
-    const SkTSpan<TCurve>* fC2Span;
+    const SkTSpan<TCurve, OppCurve>* fC1Span;
+    const SkTSpan<OppCurve, TCurve>* fC2Span;
     double fC1StartT;
     double fC1EndT;
     double fC2StartT;
@@ -1722,24 +1855,24 @@ struct SkClosestRecord {
     int fC2Index;
 };
 
-template<typename TCurve>
+template<typename TCurve, typename OppCurve>
 struct SkClosestSect {
     SkClosestSect()
         : fUsed(0) {
         fClosest.push_back().reset();
     }
 
-    bool find(const SkTSpan<TCurve>* span1, const SkTSpan<TCurve>* span2) {
-        SkClosestRecord<TCurve>* record = &fClosest[fUsed];
+    bool find(const SkTSpan<TCurve, OppCurve>* span1, const SkTSpan<OppCurve, TCurve>* span2) {
+        SkClosestRecord<TCurve, OppCurve>* record = &fClosest[fUsed];
         record->findEnd(span1, span2, 0, 0);
-        record->findEnd(span1, span2, 0, TCurve::kPointLast);
+        record->findEnd(span1, span2, 0, OppCurve::kPointLast);
         record->findEnd(span1, span2, TCurve::kPointLast, 0);
-        record->findEnd(span1, span2, TCurve::kPointLast, TCurve::kPointLast);
+        record->findEnd(span1, span2, TCurve::kPointLast, OppCurve::kPointLast);
         if (record->fClosest == FLT_MAX) {
             return false;
         }
         for (int index = 0; index < fUsed; ++index) {
-            SkClosestRecord<TCurve>* test = &fClosest[index];
+            SkClosestRecord<TCurve, OppCurve>* test = &fClosest[index];
             if (test->matesWith(*record)) {
                 if (test->fClosest > record->fClosest) {
                     test->merge(*record);
@@ -1755,34 +1888,37 @@ struct SkClosestSect {
     }
 
     void finish(SkIntersections* intersections) const {
-        SkSTArray<TCurve::kMaxIntersections * 2, const SkClosestRecord<TCurve>*, true> closestPtrs;
+        SkSTArray<TCurve::kMaxIntersections * 3,
+                const SkClosestRecord<TCurve, OppCurve>*, true> closestPtrs;
         for (int index = 0; index < fUsed; ++index) {
             closestPtrs.push_back(&fClosest[index]);
         }
-        SkTQSort<const SkClosestRecord<TCurve> >(closestPtrs.begin(), closestPtrs.end() - 1);
+        SkTQSort<const SkClosestRecord<TCurve, OppCurve> >(closestPtrs.begin(), closestPtrs.end()
+                - 1);
         for (int index = 0; index < fUsed; ++index) {
-            const SkClosestRecord<TCurve>* test = closestPtrs[index];
+            const SkClosestRecord<TCurve, OppCurve>* test = closestPtrs[index];
             test->addIntersection(intersections);
         }
     }
 
     // this is oversized so that an extra records can merge into final one
-    SkSTArray<TCurve::kMaxIntersections * 2, SkClosestRecord<TCurve>, true> fClosest;
+    SkSTArray<TCurve::kMaxIntersections * 2, SkClosestRecord<TCurve, OppCurve>, true> fClosest;
     int fUsed;
 };
 
 // returns true if the rect is too small to consider
-template<typename TCurve>
-void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersections* intersections) {
+template<typename TCurve, typename OppCurve>
+void SkTSect<TCurve, OppCurve>::BinarySearch(SkTSect<TCurve, OppCurve>* sect1,
+        SkTSect<OppCurve, TCurve>* sect2, SkIntersections* intersections) {
 #if DEBUG_T_SECT_DUMP > 1
     gDumpTSectNum = 0;
 #endif
-    PATH_OPS_DEBUG_CODE(sect1->fOppSect = sect2);
-    PATH_OPS_DEBUG_CODE(sect2->fOppSect = sect1);
+    SkDEBUGCODE(sect1->fOppSect = sect2);
+    SkDEBUGCODE(sect2->fOppSect = sect1);
     intersections->reset();
-    intersections->setMax(TCurve::kMaxIntersections * 2);  // give extra for slop
-    SkTSpan<TCurve>* span1 = sect1->fHead;
-    SkTSpan<TCurve>* span2 = sect2->fHead;
+    intersections->setMax(TCurve::kMaxIntersections * 3);  // give extra for slop
+    SkTSpan<TCurve, OppCurve>* span1 = sect1->fHead;
+    SkTSpan<OppCurve, TCurve>* span2 = sect2->fHead;
     int oppSect, sect = sect1->intersects(span1, sect2, span2, &oppSect);
 //    SkASSERT(between(0, sect, 2));
     if (!sect) {
@@ -1796,28 +1932,36 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
     span2->addBounded(span1, &sect2->fHeap);
     do {
         // find the largest bounds
-        SkTSpan<TCurve>* largest1 = sect1->boundsMax();
+        SkTSpan<TCurve, OppCurve>* largest1 = sect1->boundsMax();
         if (!largest1) {
             break;
         }
-        SkTSpan<TCurve>* largest2 = sect2->boundsMax();
-        bool split1 = !largest2 || (largest1 && (largest1->fBoundsMax > largest2->fBoundsMax
-            || (!largest1->fCollapsed && largest2->fCollapsed)));
+        SkTSpan<OppCurve, TCurve>* largest2 = sect2->boundsMax();
         // split it
-        SkTSpan<TCurve>* half1 = split1 ? largest1 : largest2;
-        SkASSERT(half1);
-        if (half1->fCollapsed) {
-            break;
-        }
-        SkTSect* splitSect = split1 ? sect1 : sect2;
-        // trim parts that don't intersect the opposite
-        SkTSpan<TCurve>* half2 = splitSect->addOne();
-        SkTSect* unsplitSect = split1 ? sect2 : sect1;
-        if (!half2->split(half1, &splitSect->fHeap)) {
-            break;
+        if (!largest2 || (largest1 && (largest1->fBoundsMax > largest2->fBoundsMax
+                || (!largest1->fCollapsed && largest2->fCollapsed)))) {
+            if (largest1->fCollapsed) {
+                break;
+            }
+            // trim parts that don't intersect the opposite
+            SkTSpan<TCurve, OppCurve>* half1 = sect1->addOne();
+            if (!half1->split(largest1, &sect1->fHeap)) {
+                break;
+            }
+            sect1->trim(largest1, sect2);
+            sect1->trim(half1, sect2);
+        } else {
+            if (largest2->fCollapsed) {
+                break;
+            }
+            // trim parts that don't intersect the opposite
+            SkTSpan<OppCurve, TCurve>* half2 = sect2->addOne();
+            if (!half2->split(largest2, &sect2->fHeap)) {
+                break;
+            }
+            sect2->trim(largest2, sect1);
+            sect2->trim(half2, sect1);
         }
-        splitSect->trim(half1, unsplitSect);
-        splitSect->trim(half2, unsplitSect);
         sect1->validate();
         sect2->validate();
         // if there are 9 or more continuous spans on both sects, suspect coincidence
@@ -1834,6 +1978,9 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
             sect1->removeByPerpendicular(sect2);
             sect1->validate();
             sect2->validate();
+            if (sect1->collapsed() > TCurve::kMaxIntersections) {
+                break;
+            }
         }
 #if DEBUG_T_SECT_DUMP
         sect1->dumpBoth(sect2);
@@ -1842,7 +1989,7 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
             break;
         }
     } while (true);
-    SkTSpan<TCurve>* coincident = sect1->fCoincident;
+    SkTSpan<TCurve, OppCurve>* coincident = sect1->fCoincident;
     if (coincident) {
         // if there is more than one coincident span, check loosely to see if they should be joined
         if (coincident->fNext) {
@@ -1862,15 +2009,15 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
             }
         } while ((coincident = coincident->fNext));
     }
+    int zeroOneSet = EndsEqual(sect1, sect2, intersections);
     if (!sect1->fHead || !sect2->fHead) {
         return;
     }
-    int zeroOneSet = EndsEqual(sect1, sect2, intersections);
     sect1->recoverCollapsed();
     sect2->recoverCollapsed();
-    SkTSpan<TCurve>* result1 = sect1->fHead;
+    SkTSpan<TCurve, OppCurve>* result1 = sect1->fHead;
     // check heads and tails for zero and ones and insert them if we haven't already done so
-    const SkTSpan<TCurve>* head1 = result1;
+    const SkTSpan<TCurve, OppCurve>* head1 = result1;
     if (!(zeroOneSet & kZeroS1Set) && approximately_less_than_zero(head1->fStartT)) {
         const SkDPoint& start1 = sect1->fCurve[0];
         if (head1->isBounded()) {
@@ -1880,7 +2027,7 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
             }
         }
     }
-    const SkTSpan<TCurve>* head2 = sect2->fHead;
+    const SkTSpan<OppCurve, TCurve>* head2 = sect2->fHead;
     if (!(zeroOneSet & kZeroS2Set) && approximately_less_than_zero(head2->fStartT)) {
         const SkDPoint& start2 = sect2->fCurve[0];
         if (head2->isBounded()) {
@@ -1890,7 +2037,7 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
             }
         }
     }
-    const SkTSpan<TCurve>* tail1 = sect1->tail();
+    const SkTSpan<TCurve, OppCurve>* tail1 = sect1->tail();
     if (!(zeroOneSet & kOneS1Set) && approximately_greater_than_one(tail1->fEndT)) {
         const SkDPoint& end1 = sect1->fCurve[TCurve::kPointLast];
         if (tail1->isBounded()) {
@@ -1900,9 +2047,9 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
             }
         }
     }
-    const SkTSpan<TCurve>* tail2 = sect2->tail();
+    const SkTSpan<OppCurve, TCurve>* tail2 = sect2->tail();
     if (!(zeroOneSet & kOneS2Set) && approximately_greater_than_one(tail2->fEndT)) {
-        const SkDPoint& end2 = sect2->fCurve[TCurve::kPointLast];
+        const SkDPoint& end2 = sect2->fCurve[OppCurve::kPointLast];
         if (tail2->isBounded()) {
             double t = tail2->closestBoundedT(end2);
             if (sect1->fCurve.ptAtT(t).approximatelyEqual(end2)) {
@@ -1910,7 +2057,7 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
             }
         }
     }
-    SkClosestSect<TCurve> closest;
+    SkClosestSect<TCurve, OppCurve> closest;
     do {
         while (result1 && result1->fCoinStart.isCoincident() && result1->fCoinEnd.isCoincident()) {
             result1 = result1->fNext;
@@ -1918,7 +2065,7 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
         if (!result1) {
             break;
         }
-        SkTSpan<TCurve>* result2 = sect2->fHead;
+        SkTSpan<OppCurve, TCurve>* result2 = sect2->fHead;
         bool found = false;
         while (result2) {
             found |= closest.find(result1, result2);
@@ -1936,7 +2083,7 @@ void SkTSect<TCurve>::BinarySearch(SkTSect* sect1, SkTSect* sect2, SkIntersectio
         double midT = ((*intersections)[0][index] + (*intersections)[0][index + 1]) / 2;
         SkDPoint midPt = sect1->fCurve.ptAtT(midT);
         // intersect perpendicular with opposite curve
-        SkTCoincident<TCurve> perp;
+        SkTCoincident<TCurve, OppCurve> perp;
         perp.setPerp(sect1->fCurve, midT, midPt, sect2->fCurve);
         if (!perp.isCoincident()) {
             ++index;