shape ops work in progress

git-svn-id: http://skia.googlecode.com/svn/trunk@7898 2bbb7eff-a529-9590-31e7-b0007b416f81

16 files changed, 677 insertions, 319 deletions

diff --git a/experimental/Intersection/CubicIntersection.cpp b/experimental/Intersection/CubicIntersection.cpp
index 0a82866d45..f7b66d540e 100644
--- a/experimental/Intersection/CubicIntersection.cpp
+++ b/experimental/Intersection/CubicIntersection.cpp
@@ -14,7 +14,7 @@
 #include "QuadraticUtilities.h"
 
 #if ONE_OFF_DEBUG
-static const double tLimits[2][2] = {{0.772784538, 0.77278492}, {0.999111748, 0.999112129}};
+static const double tLimits[2][2] = {{0.134, 0.145}, {0.134, 0.136}};
 #endif
 
 #define DEBUG_QUAD_PART 0
@@ -66,217 +66,6 @@ static void intersectWithOrder(const Quadratic& simple1, int order1, const Quadr
     }
 }
 
-static double distanceFromEnd(double t) {
-    return t > 0.5 ? 1 - t : t;
-}
-
-// OPTIMIZATION: this used to try to guess the value for delta, and that may still be worthwhile
-static void bumpForRetry(double t1, double t2, double& s1, double& e1, double& s2, double& e2) {
-    double dt1 = distanceFromEnd(t1);
-    double dt2 = distanceFromEnd(t2);
-    double delta = 1.0 / gPrecisionUnit;
-    if (dt1 < dt2) {
-        if (t1 == dt1) {
-            s1 = SkTMax(s1 - delta, 0.);
-        } else {
-            e1 = SkTMin(e1 + delta, 1.);
-        }
-    } else {
-        if (t2 == dt2) {
-            s2 = SkTMax(s2 - delta, 0.);
-        } else {
-            e2 = SkTMin(e2 + delta, 1.);
-        }
-    }
-}
-
-static bool doIntersect(const Cubic& cubic1, double t1s, double t1m, double t1e,
-        const Cubic& cubic2, double t2s, double t2m, double t2e, Intersections& i) {
-    bool result = false;
-    i.upDepth();
-    // divide the quadratics at the new t value and try again
-    double p1s = t1s;
-    double p1e = t1m;
-    for (int p1 = 0; p1 < 2; ++p1) {
-        Quadratic s1a;
-        int o1a = quadPart(cubic1, p1s, p1e, s1a);
-        double p2s = t2s;
-        double p2e = t2m;
-        for (int p2 = 0; p2 < 2; ++p2) {
-            Quadratic s2a;
-            int o2a = quadPart(cubic2, p2s, p2e, s2a);
-            Intersections locals;
-        #if ONE_OFF_DEBUG
-            if (tLimits[0][0] >= p1s && tLimits[0][1] <= p1e
-                            && tLimits[1][0] >= p2s && tLimits[1][1] <= p2e) {
-                SkDebugf("t1=(%1.9g,%1.9g) o1=%d t2=(%1.9g,%1.9g) o2=%d\n",
-                    p1s, p1e, o1a, p2s, p2e, o2a);
-                if (o1a == 2) {
-                    SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
-                            s1a[0].x, s1a[0].y, s1a[1].x, s1a[1].y);
-                } else {
-                    SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
-                            s1a[0].x, s1a[0].y, s1a[1].x, s1a[1].y, s1a[2].x, s1a[2].y);
-                }
-                if (o2a == 2) {
-                    SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
-                            s2a[0].x, s2a[0].y, s2a[1].x, s2a[1].y);
-                } else {
-                    SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
-                            s2a[0].x, s2a[0].y, s2a[1].x, s2a[1].y, s2a[2].x, s2a[2].y);
-                }
-                Intersections xlocals;
-                intersectWithOrder(s1a, o1a, s2a, o2a, xlocals);
-                SkDebugf("xlocals.fUsed=%d depth=%d\n", xlocals.used(), i.depth());
-            }
-        #endif
-            intersectWithOrder(s1a, o1a, s2a, o2a, locals);
-            for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
-                double to1 = p1s + (p1e - p1s) * locals.fT[0][tIdx];
-                double to2 = p2s + (p2e - p2s) * locals.fT[1][tIdx];
-    // if the computed t is not sufficiently precise, iterate
-                _Point p1, p2;
-                xy_at_t(cubic1, to1, p1.x, p1.y);
-                xy_at_t(cubic2, to2, p2.x, p2.y);
-        #if ONE_OFF_DEBUG
-                SkDebugf("to1=%1.9g p1=(%1.9g,%1.9g) to2=%1.9g p2=(%1.9g,%1.9g) d=%1.9g\n",
-                    to1, p1.x, p1.y, to2, p2.x, p2.y, p1.distance(p2));
-
-        #endif
-                if (p1.approximatelyEqualHalf(p2)) {
-                    i.insertSwap(to1, to2, p1);
-                    result = true;
-                } else {
-                    result = doIntersect(cubic1, p1s, to1, p1e, cubic2, p2s, to2, p2e, i);
-                    if (!result && p1.approximatelyEqual(p2)) {
-                        i.insertSwap(to1, to2, p1);
-        #if SWAP_TOP_DEBUG
-                        SkDebugf("!!!\n");
-        #endif
-                        result = true;
-                    } else
-                    // if both cubics curve in the same direction, the quadratic intersection
-                    // may mark a range that does not contain the cubic intersection. If no
-                    // intersection is found, look again including the t distance of the
-                    // of the quadratic intersection nearest a quadratic end (which in turn is
-                    // nearest the actual cubic)
-                    if (!result) {
-                        double b1s = p1s;
-                        double b1e = p1e;
-                        double b2s = p2s;
-                        double b2e = p2e;
-                        bumpForRetry(locals.fT[0][tIdx], locals.fT[1][tIdx], b1s, b1e, b2s, b2e);
-                        result = doIntersect(cubic1, b1s, to1, b1e, cubic2, b2s, to2, b2e, i);
-                    }
-                }
-            }
-            p2s = p2e;
-            p2e = t2e;
-        }
-        p1s = p1e;
-        p1e = t1e;
-    }
-    i.downDepth();
-    return result;
-}
-
-// this flavor approximates the cubics with quads to find the intersecting ts
-// OPTIMIZE: if this strategy proves successful, the quad approximations, or the ts used
-// to create the approximations, could be stored in the cubic segment
-// FIXME: this strategy needs to intersect the convex hull on either end with the opposite to
-// account for inset quadratics that cause the endpoint intersection to avoid detection
-// the segments can be very short -- the length of the maximum quadratic error (precision)
-static bool intersect2(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
-        double t2s, double t2e, double precisionScale, Intersections& i) {
-    Cubic c1, c2;
-    sub_divide(cubic1, t1s, t1e, c1);
-    sub_divide(cubic2, t2s, t2e, c2);
-    SkTDArray<double> ts1;
-    cubic_to_quadratics(c1, calcPrecision(c1) * precisionScale, ts1);
-    SkTDArray<double> ts2;
-    cubic_to_quadratics(c2, calcPrecision(c2) * precisionScale, ts2);
-    double t1Start = t1s;
-    int ts1Count = ts1.count();
-    for (int i1 = 0; i1 <= ts1Count; ++i1) {
-        const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1;
-        const double t1 = t1s + (t1e - t1s) * tEnd1;
-        Quadratic s1;
-        int o1 = quadPart(cubic1, t1Start, t1, s1);
-        double t2Start = t2s;
-        int ts2Count = ts2.count();
-        for (int i2 = 0; i2 <= ts2Count; ++i2) {
-            const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1;
-            const double t2 = t2s + (t2e - t2s) * tEnd2;
-            Quadratic s2;
-            int o2 = quadPart(cubic2, t2Start, t2, s2);
-        #if ONE_OFF_DEBUG
-                if (tLimits[0][0] >= t1Start && tLimits[0][1] <= t1
-                        && tLimits[1][0] >= t2Start && tLimits[1][1] <= t2) {
-                Cubic cSub1, cSub2;
-                sub_divide(cubic1, t1Start, tEnd1, cSub1);
-                sub_divide(cubic2, t2Start, tEnd2, cSub2);
-                SkDebugf("t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)\n",
-                        t1Start, t1, t2Start, t2);
-                Intersections xlocals;
-                intersectWithOrder(s1, o1, s2, o2, xlocals);
-                SkDebugf("xlocals.fUsed=%d\n", xlocals.used());
-            }
-        #endif
-            Intersections locals;
-            intersectWithOrder(s1, o1, s2, o2, locals);
-
-            for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
-                double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
-                double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
-    // if the computed t is not sufficiently precise, iterate
-                _Point p1, p2;
-                xy_at_t(cubic1, to1, p1.x, p1.y);
-                xy_at_t(cubic2, to2, p2.x, p2.y);
-                if (p1.approximatelyEqual(p2)) {
-                    i.insert(to1, to2, p1);
-                } else {
-                #if ONE_OFF_DEBUG
-                    if (tLimits[0][0] >= t1Start && tLimits[0][1] <= t1
-                            && tLimits[1][0] >= t2Start && tLimits[1][1] <= t2) {
-                        SkDebugf("t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)\n",
-                                t1Start, t1, t2Start, t2);
-                    }
-                #endif
-                    bool found = doIntersect(cubic1, t1Start, to1, t1, cubic2, t2Start, to2, t2, i);
-                    if (!found) {
-                        double b1s = t1Start;
-                        double b1e = t1;
-                        double b2s = t2Start;
-                        double b2e = t2;
-                        bumpForRetry(locals.fT[0][tIdx], locals.fT[1][tIdx], b1s, b1e, b2s, b2e);
-                        doIntersect(cubic1, b1s, to1, b1e, cubic2, b2s, to2, b2e, i);
-                    }
-                }
-            }
-            int coincidentCount = locals.coincidentUsed();
-            if (coincidentCount) {
-                // FIXME: one day, we'll probably need to allow coincident + non-coincident pts
-                SkASSERT(coincidentCount == locals.used());
-                SkASSERT(coincidentCount == 2);
-                double coTs[2][2];
-                for (int tIdx = 0; tIdx < coincidentCount; ++tIdx) {
-                    if (locals.fIsCoincident[0] & (1 << tIdx)) {
-                        coTs[0][tIdx] = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
-                    }
-                    if (locals.fIsCoincident[1] & (1 << tIdx)) {
-                        coTs[1][tIdx] = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
-                    }
-                }
-                i.insertCoincidentPair(coTs[0][0], coTs[0][1], coTs[1][0], coTs[1][1],
-                        locals.fPt[0], locals.fPt[1]);
-            }
-            t2Start = t2;
-        }
-        t1Start = t1;
-    }
-    return i.intersected();
-}
-
 // this flavor centers potential intersections recursively. In contrast, '2' may inadvertently
 // chase intersections near quadratic ends, requiring odd hacks to find them.
 static bool intersect3(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
@@ -325,7 +114,8 @@ static bool intersect3(const Cubic& cubic1, double t1s, double t1e, const Cubic&
             intersectWithOrder(s1, o1, s2, o2, locals);
             double coStart[2] = { -1 };
             _Point coPoint;
-            for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
+            int tCount = locals.used();
+            for (int tIdx = 0; tIdx < tCount; ++tIdx) {
                 double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
                 double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
     // if the computed t is not sufficiently precise, iterate
@@ -353,39 +143,32 @@ static bool intersect3(const Cubic& cubic1, double t1s, double t1e, const Cubic&
                     }
                 } else {
                     double offset = precisionScale / 16; // FIME: const is arbitrary -- test & refine
-                    double c1Min = SkTMax(0., to1 - offset);
-                    double c1Max = SkTMin(1., to1 + offset);
-                    double c2Min = SkTMax(0., to2 - offset);
-                    double c2Max = SkTMin(1., to2 + offset);
-                    bool found = intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
-                    if (false && !found) {
-                        // either offset was overagressive or cubics didn't really intersect
-                        // if they didn't intersect, then quad tangents ought to be nearly parallel
-                        offset = precisionScale / 2; // try much less agressive offset
-                        c1Min = SkTMax(0., to1 - offset);
-                        c1Max = SkTMin(1., to1 + offset);
-                        c2Min = SkTMax(0., to2 - offset);
-                        c2Max = SkTMin(1., to2 + offset);
-                        found = intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
-                        if (found) {
-                            SkDebugf("%s *** over-aggressive? offset=%1.9g depth=%d\n", __FUNCTION__,
-                                    offset, i.depth());
-                        }
-                        // try parallel measure
-                        _Vector d1 = dxdy_at_t(cubic1, to1);
-                        _Vector d2 = dxdy_at_t(cubic2, to2);
-                        double shallow = d1.cross(d2);
-                    #if 1 || ONE_OFF_DEBUG // not sure this is worth debugging
-                        if (!approximately_zero(shallow)) {
-                            SkDebugf("%s *** near-miss? shallow=%1.9g depth=%d\n", __FUNCTION__,
-                                    offset, i.depth());
-                        }
-                    #endif
-                        if (i.depth() == 1 && shallow < 0.6) {
-                            SkDebugf("%s !!! near-miss? shallow=%1.9g depth=%d\n", __FUNCTION__,
-                                    offset, i.depth());
-                        }
+                    double c1Bottom = tIdx == 0 ? 0 :
+                            (t1Start + (t1 - t1Start) * locals.fT[0][tIdx - 1] + to1) / 2;
+                    double c1Min = SkTMax(c1Bottom, to1 - offset);
+                    double c1Top = tIdx == tCount - 1 ? 1 :
+                            (t1Start + (t1 - t1Start) * locals.fT[0][tIdx + 1] + to1) / 2;
+                    double c1Max = SkTMin(c1Top, to1 + offset);
+                    double c2Bottom = tIdx == 0 ? to2 :
+                            (t2Start + (t2 - t2Start) * locals.fT[1][tIdx - 1] + to2) / 2;
+                    double c2Top = tIdx == tCount - 1 ? to2 :
+                            (t2Start + (t2 - t2Start) * locals.fT[1][tIdx + 1] + to2) / 2;
+                    if (c2Bottom > c2Top) {
+                        SkTSwap(c2Bottom, c2Top);
+                    }
+                    if (c2Bottom == to2) {
+                        c2Bottom = 0;
                     }
+                    if (c2Top == to2) {
+                        c2Top = 1;
+                    }
+                    double c2Min = SkTMax(c2Bottom, to2 - offset);
+                    double c2Max = SkTMin(c2Top, to2 + offset);
+                    intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
+                    // TODO: if no intersection is found, either quadratics intersected where
+                    // cubics did not, or the intersection was missed. In the former case, expect
+                    // the quadratics to be nearly parallel at the point of intersection, and check
+                    // for that.
                 }
             }
             SkASSERT(coStart[0] == -1);
@@ -440,25 +223,6 @@ static bool intersectEnd(const Cubic& cubic1, bool start, const Cubic& cubic2, c
     return intersect3(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
 }
 
-// FIXME: add intersection of convex hull on cubics' ends with the opposite cubic. The hull line
-// segments can be constructed to be only as long as the calculated precision suggests. If the hull
-// line segments intersect the cubic, then use the intersections to construct a subdivision for
-// quadratic curve fitting.
-bool intersect2(const Cubic& c1, const Cubic& c2, Intersections& i) {
-    bool result = intersect2(c1, 0, 1, c2, 0, 1, 1, i);
-    // FIXME: pass in cached bounds from caller
-    _Rect c1Bounds, c2Bounds;
-    c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ?
-    c2Bounds.setBounds(c2);
-    result |= intersectEnd(c1, false, c2, c2Bounds, i);
-    result |= intersectEnd(c1, true, c2, c2Bounds, i);
-    i.swap();
-    result |= intersectEnd(c2, false, c1, c1Bounds, i);
-    result |= intersectEnd(c2, true, c1, c1Bounds, i);
-    i.swap();
-    return result;
-}
-
 const double CLOSE_ENOUGH = 0.001;
 
 static bool closeStart(const Cubic& cubic, int cubicIndex, Intersections& i, _Point& pt) {
diff --git a/experimental/Intersection/CubicIntersection_Test.cpp b/experimental/Intersection/CubicIntersection_Test.cpp
index 358afcf605..20c7671242 100644
--- a/experimental/Intersection/CubicIntersection_Test.cpp
+++ b/experimental/Intersection/CubicIntersection_Test.cpp
@@ -134,7 +134,10 @@ static const Cubic testSet[] = {
 const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]);
 
 static const Cubic newTestSet[] = {
-{{0,1}, {2,5}, {6,0}, {5,3}},
+{{0,1}, {3,5}, {2,1}, {3,1}},
+{{1,2}, {1,3}, {1,0}, {5,3}},
+
+{{0,1}, {2,5}, {6,0}, {5,3}}, 
 {{0,6}, {3,5}, {1,0}, {5,2}},
 
 {{0,1}, {3,6}, {1,0}, {5,2}},
@@ -152,6 +155,7 @@ static const Cubic newTestSet[] = {
 
 const size_t newTestSetCount = sizeof(newTestSet) / sizeof(newTestSet[0]);
 
+#if 0
 static void oneOff(const Cubic& cubic1, const Cubic& cubic2) {
     SkTDArray<Quadratic> quads1;
     cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1);
@@ -224,7 +228,7 @@ static void oneOff(const Cubic& cubic1, const Cubic& cubic2) {
             tt2 = intersections3.fT[1][pt2];
             xy_at_t(cubic2, tt2, xy2.x, xy2.y);
     #if ONE_OFF_DEBUG
-            SkDebugf("%s t3=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
+            SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
                     __FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt1].x,
                     intersections3.fPt[pt1].y, xy2.x, xy2.y, tt2);
     #endif
@@ -233,6 +237,7 @@ static void oneOff(const Cubic& cubic1, const Cubic& cubic2) {
         }
     }
 }
+#endif
 
 static void oneOff3(const Cubic& cubic1, const Cubic& cubic2) {
     SkTDArray<Quadratic> quads1;
@@ -270,7 +275,7 @@ static void oneOff3(const Cubic& cubic1, const Cubic& cubic2) {
         tt2 = intersections3.fT[1][pt2];
         xy_at_t(cubic2, tt2, xy2.x, xy2.y);
 #if ONE_OFF_DEBUG
-        SkDebugf("%s t3=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
+        SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
                 __FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt3].x,
                 intersections3.fPt[pt3].y, xy2.x, xy2.y, tt2);
 #endif
@@ -278,6 +283,7 @@ static void oneOff3(const Cubic& cubic1, const Cubic& cubic2) {
     }
 }
 
+#if 0
 static int fails[][2] = {   {0, 23}, // fails in intersect2 recursing
                             {2, 7},  // answers differ, but neither is correct ('3' is closer)
                             {3, 26}, // fails in intersect2 recursing
@@ -293,10 +299,12 @@ static int fails[][2] = {   {0, 23}, // fails in intersect2 recursing
 };
 
 static int failCount = sizeof(fails) / sizeof(fails[0]);
+#endif
 
 static void oneOff(int outer, int inner) {
     const Cubic& cubic1 = testSet[outer];
     const Cubic& cubic2 = testSet[inner];
+#if 0
     bool failing = false;
     for (int i = 0; i < failCount; ++i) {
         if ((fails[i][0] == outer && fails[i][1] == inner)
@@ -308,8 +316,9 @@ static void oneOff(int outer, int inner) {
     if (!failing) {
         oneOff(cubic1, cubic2);
     } else {
+#endif
         oneOff3(cubic1, cubic2);
-    }
+//    }
 }
 
 void CubicIntersection_OneOffTest() {
@@ -324,6 +333,7 @@ static void newOneOff(int outer, int inner) {
 
 void CubicIntersection_NewOneOffTest() {
     newOneOff(0, 1);
+    newOneOff(1, 0);
 }
 
 static void oneOffTests() {
@@ -356,7 +366,7 @@ bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
     sub_divide(cubic1, minT1, maxT1, sub1);
     sub_divide(cubic2, minT2, maxT2, sub2);
     Intersections i;
-    intersect2(sub1, sub2, i);
+    intersect3(sub1, sub2, i);
     if (i.used() == 0) {
         return false;
     }
@@ -433,7 +443,7 @@ void CubicIntersection_RandTestOld() {
         if (test == -1) {
             SkDebugf("ready...\n");
         }
-        bool newIntersects = intersect2(cubic1, cubic2, i2);
+        bool newIntersects = intersect3(cubic1, cubic2, i2);
         if (!boundsIntersect && (oldIntersects || newIntersects)) {
     #if DEBUG_CRASH
             SkDebugf("%s %d unexpected intersection boundsIntersect=%d oldIntersects=%d"
@@ -484,7 +494,7 @@ void CubicIntersection_RandTestOld() {
     #if DEBUG_CRASH
             SkDebugf("%s\n", str);
     #endif
-            oneOff(cubic1, cubic2);
+            oneOff3(cubic1, cubic2);
             largestFactor = factor1;
         }
         if (factor2 < largestFactor) {
@@ -492,7 +502,7 @@ void CubicIntersection_RandTestOld() {
     #if DEBUG_CRASH
             SkDebugf("%s\n", str);
     #endif
-            oneOff(cubic1, cubic2);
+            oneOff3(cubic1, cubic2);
             largestFactor = factor2;
         }
     }
@@ -527,7 +537,7 @@ void CubicIntersection_RandTest() {
             SkDebugf("ready...\n");
         }
         Intersections intersections2;
-        bool newIntersects = intersect2(cubic1, cubic2, intersections2);
+        bool newIntersects = intersect3(cubic1, cubic2, intersections2);
         if (!boundsIntersect && newIntersects) {
     #if DEBUG_CRASH
             SkDebugf("%s %d unexpected intersection boundsIntersect=%d "
@@ -556,10 +566,10 @@ void CubicIntersection_IntersectionFinder() {
     const Cubic& cubic1 = newTestSet[0];
     const Cubic& cubic2 = newTestSet[1];
 
-    double t1Seed = 0.77;
-    double t2Seed = 0.99;
+    double t1Seed = 0.134792061;
+    double t2Seed = 0.134792094;
     double t1Step = 0.1;
-    double t2Step = 0.01;
+    double t2Step = 0.1;
     _Point t1[3], t2[3];
     bool toggle = true;
     do {
diff --git a/experimental/Intersection/CubicUtilities.cpp b/experimental/Intersection/CubicUtilities.cpp
index 1de2ef75e9..56f1e4548d 100644
--- a/experimental/Intersection/CubicUtilities.cpp
+++ b/experimental/Intersection/CubicUtilities.cpp
@@ -113,7 +113,7 @@ int cubicRootsReal(double A, double B, double C, double D, double s[3]) {
     bzero(str, sizeof(str));
     sprintf(str, "Solve[%1.19g x^3 + %1.19g x^2 + %1.19g x + %1.19g == 0, x]", A, B, C, D);
     mathematica_ize(str, sizeof(str));
-#if ONE_OFF_DEBUG
+#if ONE_OFF_DEBUG && ONE_OFF_DEBUG_MATHEMATICA
     SkDebugf("%s\n", str);
 #endif
 #endif
diff --git a/experimental/Intersection/CurveIntersection.h b/experimental/Intersection/CurveIntersection.h
index d01bb7ddb8..cbcda76452 100644
--- a/experimental/Intersection/CurveIntersection.h
+++ b/experimental/Intersection/CurveIntersection.h
@@ -51,7 +51,7 @@ int horizontalIntersect(const Quadratic& quad, double left, double right,
         double y, bool flipped, Intersections& );
 bool intersect(const Cubic& cubic1, const Cubic& cubic2, Intersections& );
 // the following flavor uses quadratic approximation instead of convex hulls
-bool intersect2(const Cubic& cubic1, const Cubic& cubic2, Intersections& );
+//bool intersect2(const Cubic& cubic1, const Cubic& cubic2, Intersections& );
 // like '2', but iterates on centers instead of possible edges
 bool intersect3(const Cubic& cubic1, const Cubic& cubic2, Intersections& );
 int intersect(const Cubic& cubic, Intersections& i); // return true if cubic self-intersects
diff --git a/experimental/Intersection/DataTypes.h b/experimental/Intersection/DataTypes.h
index 4b682fff63..166ba813c7 100644
--- a/experimental/Intersection/DataTypes.h
+++ b/experimental/Intersection/DataTypes.h
@@ -13,6 +13,7 @@
 #include "SkPoint.h"
 
 #define ONE_OFF_DEBUG 0
+#define ONE_OFF_DEBUG_MATHEMATICA 1
 
 // FIXME: move these into SkTypes.h
 template <typename T> inline T SkTMax(T a, T b) {
diff --git a/experimental/Intersection/EdgeWalker_TestUtility.cpp b/experimental/Intersection/EdgeWalker_TestUtility.cpp
index 8afc09f3cc..9f4aafc14e 100644
--- a/experimental/Intersection/EdgeWalker_TestUtility.cpp
+++ b/experimental/Intersection/EdgeWalker_TestUtility.cpp
@@ -265,7 +265,8 @@ static void showShapeOpPath(const SkPath& one, const SkPath& two, const SkPath&
     showPath(a, "minuend:");
     SkDebugf("op: %s\n", opStrs[shapeOp]);
     showPath(b, "subtrahend:");
-    showPath(scaledOne, "region:", scale);
+    // the region often isn't very helpful since it approximates curves with a lot of line-tos
+    if (0) showPath(scaledOne, "region:", scale);
     showPath(two, "op result:");
     drawAsciiPaths(scaledOne, scaledTwo, true);
 }
diff --git a/experimental/Intersection/Intersection_Tests.cpp b/experimental/Intersection/Intersection_Tests.cpp
index 244f92f187..9e5237cdc3 100644
--- a/experimental/Intersection/Intersection_Tests.cpp
+++ b/experimental/Intersection/Intersection_Tests.cpp
@@ -14,11 +14,11 @@ void parseSVG();
 
 void Intersection_Tests() {
     int testsRun = 0;
+    CubicIntersection_SelfTest();
     QuadraticIntersection_IntersectionFinder();
     QuadraticIntersection_OneOffTest();
     CubicIntersection_IntersectionFinder();
     CubicIntersection_NewOneOffTest();
-    CubicIntersection_SelfTest();
 #if 0
 #endif
     SimplifyNew_Test();
diff --git a/experimental/Intersection/QuadraticIntersection_Test.cpp b/experimental/Intersection/QuadraticIntersection_Test.cpp
index 46cf20ab51..35fda3aae5 100644
--- a/experimental/Intersection/QuadraticIntersection_Test.cpp
+++ b/experimental/Intersection/QuadraticIntersection_Test.cpp
@@ -54,6 +54,9 @@ static void standardTestCases() {
 }
 
 static const Quadratic testSet[] = {
+  {{1,2}, {0.984375,2.3359375}, {1.0625,2.15625}},
+  {{0,1}, {0.983539095,2.30041152}, {1.47325103,2.61316872}},
+
   {{4.09011926,2.20971038}, {4.74608133,1.9335932}, {5.02469918,2.00694987}},
   {{2.79472921,1.73568666}, {3.36246373,1.21251209}, {5,2}},
 
diff --git a/experimental/Intersection/QuarticRoot.cpp b/experimental/Intersection/QuarticRoot.cpp
index 061098a598..039a2c797f 100644
--- a/experimental/Intersection/QuarticRoot.cpp
+++ b/experimental/Intersection/QuarticRoot.cpp
@@ -41,7 +41,7 @@ int reducedQuarticRoots(const double t4, const double t3, const double t2, const
     sprintf(str, "Solve[%1.19g x^4 + %1.19g x^3 + %1.19g x^2 + %1.19g x + %1.19g == 0, x]",
         t4, t3, t2, t1, t0);
     mathematica_ize(str, sizeof(str));
-#if ONE_OFF_DEBUG
+#if ONE_OFF_DEBUG && ONE_OFF_DEBUG_MATHEMATICA
     SkDebugf("%s\n", str);
 #endif
 #endif
diff --git a/experimental/Intersection/ShapeOps.cpp b/experimental/Intersection/ShapeOps.cpp
index f1792a87eb..7c7a205174 100644
--- a/experimental/Intersection/ShapeOps.cpp
+++ b/experimental/Intersection/ShapeOps.cpp
@@ -134,8 +134,6 @@ static bool bridgeOp(SkTDArray<Contour*>& contourList, const ShapeOp op,
     bool firstContour = true;
     bool unsortable = false;
     bool topUnsortable = false;
-    bool firstRetry = false;
-    bool closable = true;
     SkPoint topLeft = {SK_ScalarMin, SK_ScalarMin};
     do {
         int index, endIndex;
@@ -145,8 +143,7 @@ static bool bridgeOp(SkTDArray<Contour*>& contourList, const ShapeOp op,
         if (!current) {
             if (topUnsortable || !done) {
                 topUnsortable = false;
-                SkASSERT(!firstRetry);
-                firstRetry = true;
+                SkASSERT(topLeft.fX != SK_ScalarMin && topLeft.fY != SK_ScalarMin);
                 topLeft.fX = topLeft.fY = SK_ScalarMin;
                 continue;
             }
@@ -155,7 +152,6 @@ static bool bridgeOp(SkTDArray<Contour*>& contourList, const ShapeOp op,
         SkTDArray<Span*> chaseArray;
         do {
             if (current->activeOp(index, endIndex, xorMask, xorOpMask, op)) {
-                bool active = true;
                 do {
             #if DEBUG_ACTIVE_SPANS
                     if (!unsortable && current->done()) {
@@ -168,34 +164,37 @@ static bool bridgeOp(SkTDArray<Contour*>& contourList, const ShapeOp op,
                     Segment* next = current->findNextOp(chaseArray, nextStart, nextEnd,
                             unsortable, op, xorMask, xorOpMask);
                     if (!next) {
-         //               SkASSERT(!unsortable);
                         if (!unsortable && simple.hasMove()
                                 && current->verb() != SkPath::kLine_Verb
                                 && !simple.isClosed()) {
                             current->addCurveTo(index, endIndex, simple, true);
                             SkASSERT(simple.isClosed());
                         }
-                        active = false;
                         break;
                     }
+        #if DEBUG_FLOW
+            SkDebugf("%s current id=%d from=(%1.9g,%1.9g) to=(%1.9g,%1.9g)\n", __FUNCTION__,
+                    current->debugID(), current->xyAtT(index).fX, current->xyAtT(index).fY,
+                    current->xyAtT(endIndex).fX, current->xyAtT(endIndex).fY);
+        #endif
                     current->addCurveTo(index, endIndex, simple, true);
                     current = next;
                     index = nextStart;
                     endIndex = nextEnd;
-                } while (!simple.isClosed() && ((!unsortable) || !current->done()));
-                if (active && !simple.isClosed()) {
+                } while (!simple.isClosed() && ((!unsortable)
+                        || !current->done(SkMin32(index, endIndex))));
+                if (current->activeWinding(index, endIndex) && !simple.isClosed()) {
                     SkASSERT(unsortable);
                     int min = SkMin32(index, endIndex);
                     if (!current->done(min)) {
                         current->addCurveTo(index, endIndex, simple, true);
                         current->markDoneBinary(min);
                     }
-                    closable = false;
                 }
                 simple.close();
             } else {
                 Span* last = current->markAndChaseDoneBinary(index, endIndex);
-                if (last) {
+                if (last && !last->fLoop) {
                     *chaseArray.append() = last;
                 }
             }
@@ -208,7 +207,7 @@ static bool bridgeOp(SkTDArray<Contour*>& contourList, const ShapeOp op,
             }
         } while (true);
     } while (true);
-    return closable;
+    return simple.someAssemblyRequired();
 }
 
 } // end of Op namespace
diff --git a/experimental/Intersection/Simplify.cpp b/experimental/Intersection/Simplify.cpp
index e269ffd782..47ce8f49e9 100644
--- a/experimental/Intersection/Simplify.cpp
+++ b/experimental/Intersection/Simplify.cpp
@@ -69,7 +69,7 @@ const bool gRunTestsInOneThread = true;
 #define DEBUG_ADD_INTERSECTING_TS 1
 #define DEBUG_ADD_T_PAIR 1
 #define DEBUG_ANGLE 1
-#define DEBUG_AS_C_CODE 0
+#define DEBUG_AS_C_CODE 1
 #define DEBUG_ASSEMBLE 1
 #define DEBUG_CONCIDENT 1
 #define DEBUG_CROSS 0
@@ -97,7 +97,7 @@ static int gSegmentID;
 #endif
 
 #if DEBUG_SORT
-static int gDebugSortCountDefault = 3; // SK_MaxS32;
+static int gDebugSortCountDefault = SK_MaxS32;
 static int gDebugSortCount;
 #endif
 
@@ -649,6 +649,7 @@ struct Span {
     bool fUnsortableStart; // set when start is part of an unsortable pair
     bool fUnsortableEnd; // set when end is part of an unsortable pair
     bool fTiny; // if set, span may still be considered once for edge following
+    bool fLoop; // set when a cubic loops back to this point
 };
 
 // sorting angles
@@ -862,12 +863,10 @@ public:
             Quadratic& quad = (Quadratic&)fCurvePart;
             QuadSubDivideHD(fPts, startT, endT, quad);
             fTangent1.quadEndPoints(quad, 0, 1);
-        #if 1 // FIXME: try enabling this and see if a) it's called and b) does it break anything
             if (dx() == 0 && dy() == 0) {
  //               SkDebugf("*** %s quad is line\n", __FUNCTION__);
                 fTangent1.quadEndPoints(quad);
             }
-        #endif
             fSide = -fTangent1.pointDistance(fCurvePart[2]); // not normalized -- compare sign only
             } break;
         case SkPath::kCubic_Verb: {
@@ -877,12 +876,10 @@ public:
             if (dx() == 0 && dy() == 0) {
                 fTangent1.cubicEndPoints(fCurvePart, 0, 2);
                 nextC = 3;
-        #if 1 // FIXME: try enabling this and see if a) it's called and b) does it break anything
                 if (dx() == 0 && dy() == 0) {
-                    SkDebugf("*** %s cubic is line\n", __FUNCTION__);
+ //                   SkDebugf("*** %s cubic is line\n", __FUNCTION__);
                     fTangent1.cubicEndPoints(fCurvePart, 0, 3);
                 }
-        #endif
             }
             fSide = -fTangent1.pointDistance(fCurvePart[nextC]); // compare sign only
             if (nextC == 2 && approximately_zero(fSide)) {
@@ -1686,6 +1683,7 @@ public:
         span->fWindValue = 1;
         span->fOppValue = 0;
         span->fTiny = false;
+        span->fLoop = false;
         if ((span->fDone = newT == 1)) {
             ++fDoneSpans;
         }
@@ -1881,6 +1879,13 @@ public:
             other.addCancelOutsides(tStart, oStart, *this, endT);
         }
     }
+    
+    int addSelfT(Segment* other, const SkPoint& pt, double& newT) {
+        int result = addT(other, pt, newT);
+        Span* span = &fTs[result];
+        span->fLoop = true;
+        return result;
+    }
 
     int addUnsortableT(Segment* other, bool start, const SkPoint& pt, double& newT) {
         int result = addT(other, pt, newT);
@@ -2435,6 +2440,7 @@ public:
         bool foundDone = false;
         // iterate through the angle, and compute everyone's winding
         Segment* nextSegment;
+        int activeCount = 0;
         do {
             SkASSERT(nextIndex != firstIndex);
             if (nextIndex == angleCount) {
@@ -2446,9 +2452,16 @@ public:
             bool activeAngle = nextSegment->activeOp(xorMiMask, xorSuMask, nextAngle->start(),
                     nextAngle->end(), op, sumMiWinding, sumSuWinding,
                     maxWinding, sumWinding, oppMaxWinding, oppSumWinding);
-            if (activeAngle && (!foundAngle || foundDone)) {
-                foundAngle = nextAngle;
-                foundDone = nextSegment->done(nextAngle) && !nextSegment->tiny(nextAngle);
+            if (activeAngle) {
+                ++activeCount;
+                if (!foundAngle || (foundDone && activeCount & 1)) {
+                    if (nextSegment->tiny(nextAngle)) {
+                        unsortable = true;
+                        return NULL;
+                    }
+                    foundAngle = nextAngle;
+                    foundDone = nextSegment->done(nextAngle) && !nextSegment->tiny(nextAngle);
+                }
             }
             if (nextSegment->done()) {
                 continue;
@@ -2909,6 +2922,10 @@ public:
             SkVector dxyS = leftSegment->dxdy(tIndex);
             double cross = dxyE.cross(dxyS);
             bool bumpCheck = bumpsUp && xyE.fY < xyS.fY && dxyE.fX < 0;
+            if (xyE == xyS){
+                SkDebugf("%s ignore loops\n", __FUNCTION__);
+                cross = 0;
+            }
         #if DEBUG_SWAP_TOP
             SkDebugf("%s xyE=(%1.9g,%1.9g) xyS=(%1.9g,%1.9g)\n", __FUNCTION__,
                     xyE.fX, xyE.fY, xyS.fX, xyS.fY);
@@ -3195,7 +3212,7 @@ the same winding is shared by both.
         Segment* other = this;
         while ((other = other->nextChase(index, step, min, last))) {
             if (other->fTs[min].fWindSum != SK_MinS32) {
-                SkASSERT(other->fTs[min].fWindSum == winding);
+                SkASSERT(other->fTs[min].fWindSum == winding || other->fTs[min].fLoop);
                 return NULL;
             }
             other->markWinding(min, winding, oppWinding);
@@ -4442,6 +4459,11 @@ public:
         return fSegments[segIndex].addT(&other->fSegments[otherIndex], pt, newT);
     }
 
+    int addSelfT(int segIndex, Contour* other, int otherIndex, const SkPoint& pt, double& newT) {
+        setContainsIntercepts();
+        return fSegments[segIndex].addSelfT(&other->fSegments[otherIndex], pt, newT);
+    }
+
     int addUnsortableT(int segIndex, Contour* other, int otherIndex, bool start,
             const SkPoint& pt, double& newT) {
         return fSegments[segIndex].addUnsortableT(&other->fSegments[otherIndex], start, pt, newT);
@@ -5133,6 +5155,10 @@ public:
     int addT(const Work& other, const SkPoint& pt, double& newT) {
         return fContour->addT(fIndex, other.fContour, other.fIndex, pt, newT);
     }
+    
+    int addSelfT(const Work& other, const SkPoint& pt, double& newT) {
+        return fContour->addSelfT(fIndex, other.fContour, other.fIndex, pt, newT);
+    }
 
     int addUnsortableT(const Work& other, bool start, const SkPoint& pt, double& newT) {
         return fContour->addUnsortableT(fIndex, other.fContour, other.fIndex, start, pt, newT);
@@ -5694,7 +5720,7 @@ static void addSelfIntersectTs(Contour* test) {
         SkASSERT(ts.fT[0][0] >= 0 && ts.fT[0][0] <= 1);
         SkASSERT(ts.fT[1][0] >= 0 && ts.fT[1][0] <= 1);
         SkPoint point = ts.fPt[0].asSkPoint();
-        int testTAt = wt.addT(wt, point, ts.fT[0][0]);
+        int testTAt = wt.addSelfT(wt, point, ts.fT[0][0]);
         int nextTAt = wt.addT(wt, point, ts.fT[1][0]);
         wt.addOtherT(testTAt, ts.fT[1][0], nextTAt);
         wt.addOtherT(nextTAt, ts.fT[0][0], testTAt);
@@ -6157,7 +6183,7 @@ static bool bridgeWinding(SkTDArray<Contour*>& contourList, PathWrapper& simple)
                 simple.close();
             } else {
                 Span* last = current->markAndChaseDoneUnary(index, endIndex);
-                if (last) {
+                if (last && !last->fLoop) {
                     *chaseArray.append() = last;
                 }
             }
diff --git a/experimental/Intersection/SimplifyAngle_Test.cpp b/experimental/Intersection/SimplifyAngle_Test.cpp
index 9b25851eee..e83a52f650 100644
--- a/experimental/Intersection/SimplifyAngle_Test.cpp
+++ b/experimental/Intersection/SimplifyAngle_Test.cpp
@@ -230,10 +230,19 @@ static const segmentWithT oneOffTest3[] = {
     {SkPath::kMove_Verb }
 };
 
+static const segmentWithT oneOffTest4[] = {
+    {SkPath::kCubic_Verb, {{1,2}, {1,3}, {1,0}, {5,3}}, {0.134792, 0}},
+    {SkPath::kCubic_Verb, {{0,1}, {3,5}, {2,1}, {3,1}}, {0.134792094, 0}},
+    {SkPath::kCubic_Verb, {{0,1}, {3,5}, {2,1}, {3,1}}, {0.134792094, 0.551812363}},
+    {SkPath::kCubic_Verb, {{1,2}, {1,3}, {1,0}, {5,3}}, {0.134792, 0.333333333}},
+    {SkPath::kMove_Verb }
+};
+
 static const segmentWithT* oneOffTests[] = {
     oneOffTest1,
     oneOffTest2,
     oneOffTest3,
+    oneOffTest4,
 };
 
 static const size_t oneOffTestCount = sizeof(oneOffTests) / sizeof(oneOffTests[0]);
@@ -259,6 +268,49 @@ static void oneOffTest(bool testFlat) {
     SkDebugf("%s finished\n", __FUNCTION__);
 }
 
+#if 0 // seems too complicated for this to be useful (didn't finish writing/debugging this)
+// this (trys to) take a pair of curves, construct segments/spans, and verify that they sort correctly
+static void oneOffTestNew() {
+    const segmentWithT* segPtr = oneOffTest4;
+    SimplifyAngleTest::Segment segOne, segTwo;
+    segOne.init(segPtr[0].pts, segPtr[0].verb, false, false);
+    segTwo.init(segPtr[1].pts, segPtr[1].verb, false, false);
+    int index = 0;
+    do {
+        int next = index + 1;
+        if (segPtr[index].verb == SkPath::kMove_Verb) {
+            break;
+        }
+        SkPoint sub[4];
+        (*SegmentSubDivide[segPtr[index].verb])(segPtr[index].pts, segPtr[index].ts[0],
+                segPtr[index].ts[1], sub);
+        if (memcmp(segPtr[index].pts, segPtr[0].pts, sizeof(SkPoint) * (segPtr[index].verb + 1) == 0) {
+            segOne.addT(&segTwo, sub[0], segPtr[index].ts[0]);
+            segOne.addT(&segTwo, sub[segPtr[index].verb], segPtr[index].ts[1]);
+        } else {
+            segTwo.addT(&segOne, sub[0], segPtr[index].ts[0]);
+            segTwo.addT(&v, sub[segPtr[index].verb], segPtr[index].ts[1]);
+        }
+    } while (true);
+    SimplifyAngleTest::Angle lesser, greater;
+    do {
+        int next = index + 1;
+        if (segPtr[next].verb == SkPath::kMove_Verb) {
+            break;
+        }
+        SkPoint one[4], two[4];
+        bool use1 = memcmp(segPtr[index].pts, segPtr[0].pts, sizeof(SkPoint) * (segPtr[index].verb + 1) == 0;
+        lesser.set(segPtr[index].pts, segPtr[index].verb, use1 ? &segOne : &segTwo, index, next, dummy);
+        use1 = memcmp(segPtr[next].pts, segPtr[0].pts, sizeof(SkPoint) * (segPtr[next].verb + 1) == 0;
+        greater.set(segPtr[next].pts, segPtr[next].verb, use1 ? &segOne : &segTwo, index, next, dummy);
+        bool result = lesser < greater;
+        SkASSERT(result);
+        index = next;
+    } while (true);
+    SkDebugf("%s finished\n", __FUNCTION__);
+}
+#endif
+
 static void (*tests[])(bool) = {
     oneOffTest,
     testSegments,
diff --git a/experimental/Intersection/SimplifyNew_Test.cpp b/experimental/Intersection/SimplifyNew_Test.cpp
index ffba8dc6e4..145b856d8e 100644
--- a/experimental/Intersection/SimplifyNew_Test.cpp
+++ b/experimental/Intersection/SimplifyNew_Test.cpp
@@ -4164,6 +4164,19 @@ static void cubicOp31u() {
     testShapeOp(path, pathB, kUnion_Op);
 }
 
+static void cubicOp31x() {
+    SkPath path, pathB;
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,2);
+    path.cubicTo(0,3, 2,1, 4,0);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(1,2);
+    pathB.cubicTo(0,4, 2,0, 3,0);
+    pathB.close();
+    testShapeOp(path, pathB, kXor_Op);
+}
+
 static void testCubic2() {
     SkPath path;
     path.moveTo(0,2);
@@ -4175,15 +4188,72 @@ static void testCubic2() {
     testSimplifyx(path);
 }
 
-static void (*firstTest)() = 0;
+static void cubicOp32d() {
+    SkPath path, pathB;
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(1,2, 6,0, 3,1);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(0,6);
+    pathB.cubicTo(1,3, 1,0, 2,1);
+    pathB.close();
+    testShapeOp(path, pathB, kDifference_Op);
+}
+
+static void cubicOp33i() {
+    SkPath path, pathB;
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(1,2, 6,0, 3,1);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(0,6);
+    pathB.cubicTo(1,3, 1,0, 2,1);
+    pathB.close();
+    testShapeOp(path, pathB, kIntersect_Op);
+}
+
+static void cubicOp34d() {
+    SkPath path, pathB;
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(3,5, 2,1, 3,1);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(1,2);
+    pathB.cubicTo(1,3, 1,0, 5,3);
+    pathB.close();
+    testShapeOp(path, pathB, kDifference_Op);
+}
+
+static void cubicOp35d() {
+    SkPath path, pathB;
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(1,5, 2,1, 4,0);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(1,2);
+    pathB.cubicTo(0,4, 1,0, 5,1);
+    pathB.close();
+    testShapeOp(path, pathB, kDifference_Op);
+}
+
+static void (*firstTest)() = cubicOp35d;
 
 static struct {
     void (*fun)();
     const char* str;
 } tests[] = {
+    TEST(cubicOp35d),
+    TEST(cubicOp34d),
+    TEST(cubicOp33i),
+    TEST(cubicOp32d),
+    TEST(cubicOp31d),
     TEST(testCubic2),
+    TEST(cubicOp31x),
     TEST(cubicOp31u),
-    TEST(cubicOp31d),
     TEST(cubicOp30d),
     TEST(cubicOp29d),
     TEST(cubicOp28u),
@@ -4591,7 +4661,7 @@ static void (*firstSubTest)() = 0;
 
 static bool skipAll = false;
 static bool runSubTestsFirst = false;
-static bool runReverse = false;
+static bool runReverse = true;
 static void (*stopTest)() = 0;
 
 void SimplifyNew_Test() {
diff --git a/experimental/Intersection/as.htm b/experimental/Intersection/as.htm
index 93845cbbc7..c8a50bb3e5 100644
--- a/experimental/Intersection/as.htm
+++ b/experimental/Intersection/as.htm
@@ -60,11 +60,177 @@ debugShowActiveSpans id=4 (3,0 1,2) t=0.5 (2,1) tEnd=0.875 other=2 otherT=0.5 ot
 debugShowActiveSpans id=4 (3,0 1,2) t=0.875 (1.25,1.75) tEnd=1 other=1 otherT=0.5 otherIndex=2 windSum=? windValue=1 oppValue=0
 </div>
 
+<div id="cubicOp35d">
+  SimplifyNew_Test [cubicOp35d]
+debugShowCubicIntersection no self intersect {{0,1}, {1,5}, {2,1}, {4,0}}
+debugShowCubicLineIntersection wtTs[0]=0 {{0,1}, {1,5}, {2,1}, {4,0}} {{0,1}} wtTs[1]=1 {{4,0}} wnTs[0]=1 {{4,0}, {0,1}} wnTs[1]=0
+debugShowCubicIntersection wtTs[0]=0.210357794 {{0,1}, {1,5}, {2,1}, {4,0}} {{0.64038179843233178,2.5646764769093426}} wtTs[1]=0.788675135 {{2.8565880156561105,0.93208711896642604}} wnTs[0]=0.223476 {{1,2}, {0,4}, {1,0}, {5,1}} wnTs[1]=0.788675135
+debugShowCubicLineIntersection wtTs[0]=0.646900486 {{0,1}, {1,5}, {2,1}, {4,0}} {{2.2114165293341985,1.6971458676664504}} wnTs[0]=0.697146 {{5,1}, {1,2}}
+debugShowCubicLineIntersection no intersect {{1,2}, {0,4}, {1,0}, {5,1}} {{4,0}, {0,1}}
+debugShowLineIntersection no intersect {{4,0}, {0,1}} {{5,1}, {1,2}}
+debugShowCubicIntersection wtTs[0]=0.002763735 {{1,2}, {0,4}, {1,0}, {5,1}} {{0.9917546455060533,2.0164451540317003}} wtTs[1]=0.461521979
+debugShowCubicLineIntersection wtTs[0]=0 {{1,2}, {0,4}, {1,0}, {5,1}} {{1,2}} wtTs[1]=0.466666667 {{1.0082962962962965,1.9979259259259259}} wtTs[2]=1 {{5,1}} wnTs[0]=1 {{5,1}, {1,2}} wnTs[1]=0.997925926 wnTs[2]=0
+debugShowActiveSpans id=1 (0,1 1,5 2,1 4,0) t=0 (0,1) tEnd=0.210357794 other=2 otherT=1 otherIndex=1 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=1 (0,1 1,5 2,1 4,0) t=0.210357794 (0.640381813,2.56467652) tEnd=0.646900486 other=3 otherT=0.223476406 otherIndex=2 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=1 (0,1 1,5 2,1 4,0) t=0.646900486 (2.21141648,1.69714582) tEnd=0.788675135 other=4 otherT=0.697145868 otherIndex=1 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=1 (0,1 1,5 2,1 4,0) t=0.788675135 (2.85658813,0.932087123) tEnd=1 other=3 otherT=0.788675135 otherIndex=5 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=2 (4,0 0,1) t=0 (4,0) tEnd=1 other=1 otherT=1 otherIndex=4 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0 (1,2) tEnd=0.002763735 other=4 otherT=1 otherIndex=3 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0.002763735 (0.991754651,2.01644516) tEnd=0.223476406 other=3 otherT=0.461521979 otherIndex=3 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0.223476406 (0.640381813,2.56467652) tEnd=0.461521979 other=1 otherT=0.210357794 otherIndex=1 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0.461521979 (0.991754651,2.01644516) tEnd=0.466666667 other=3 otherT=0.002763735 otherIndex=1 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0.466666667 (1.00829625,1.99792588) tEnd=0.788675135 other=4 otherT=0.997925926 otherIndex=2 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0.788675135 (2.85658813,0.932087123) tEnd=1 other=1 otherT=0.788675135 otherIndex=3 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=4 (5,1 1,2) t=0 (5,1) tEnd=0.697145868 other=3 otherT=1 otherIndex=6 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=4 (5,1 1,2) t=0.697145868 (2.21141648,1.69714582) tEnd=0.997925926 other=1 otherT=0.646900486 otherIndex=2 windSum=? windValue=1 oppValue=0
+debugShowActiveSpans id=4 (5,1 1,2) t=0.997925926 (1.00829625,1.99792588) tEnd=1 other=3 otherT=0.466666667 otherIndex=4 windSum=? windValue=1 oppValue=0
+findTop debugShowSort contourWinding=0 oppContourWinding=0 sign=-1
+debugShowSort [0] id=2 line start=0 (4,0) end=1 (0,1) sign=-1 windValue=1 windSum=? 0->1 (max=1) done=0 tiny=0 opp=0
+debugShowSort [1] id=1 cubic start=4 (4,0) end=3 (2.85658813,0.932087123) sign=1 windValue=1 windSum=? 1->0 (max=1) done=0 tiny=0 opp=0
+markWinding id=2 (4,0 0,1) t=0 [0] (4,0) newWindSum=1 newOppSum=0 oppSum=? windSum=? windValue=1
+markWinding id=1 (0,1 1,5 2,1 4,0) t=0.788675135 [3] (2.85658813,0.932087123) newWindSum=1 newOppSum=0 oppSum=? windSum=? windValue=1
+markWinding id=2 (4,0 0,1) t=0 [0] (4,0) newWindSum=1 newOppSum=0 oppSum=0 windSum=1 windValue=1
+markWinding id=1 (0,1 1,5 2,1 4,0) t=0 [0] (0,1) newWindSum=1 newOppSum=0 oppSum=? windSum=? windValue=1
+activeOp op=diff miFrom=1 miTo=0 suFrom=0 suTo=0 result=1
+findNextOp simple
+markDoneBinary id=2 (4,0 0,1) t=0 [0] (4,0) newWindSum=1 newOppSum=0 oppSum=0 windSum=1 windValue=1
+bridgeOp current id=2 from=(0,1) to=(4,0)
+findNextOp debugShowSort contourWinding=0 oppContourWinding=0 sign=-1
+debugShowSort [1] id=1 cubic start=3 (2.85658813,0.932087123) end=4 (4,0) sign=-1 windValue=1 windSum=1 0->1 (max=1) done=0 tiny=0 opp=0
+debugShowSort [2] id=3 cubic start=5 (2.85658813,0.932087123) end=4 (1.00829625,1.99792588) sign=1 windValue=1 windSum=? 0->-1 (max=-1) done=0 tiny=0 opp=1
+debugShowSort [3] id=1 cubic start=3 (2.85658813,0.932087123) end=2 (2.21141648,1.69714582) sign=1 windValue=1 windSum=? 1->0 (max=1) done=0 tiny=0 opp=0
+debugShowSort [0] id=3 cubic start=5 (2.85658813,0.932087123) end=6 (5,1) sign=-1 windValue=1 windSum=? -1->0 (max=-1) done=0 tiny=0 opp=1
+findNextOp firstIndex=[1] sign=-1
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=1 result=1
+markWinding id=3 (1,2 0,4 1,0 5,1) t=0.466666667 [4] (1.00829625,1.99792588) newWindSum=-1 newOppSum=1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=3
+activeOp op=diff miFrom=1 miTo=0 suFrom=1 suTo=1 result=0
+markDoneBinary id=1 (0,1 1,5 2,1 4,0) t=0.646900486 [2] (2.21141648,1.69714582) newWindSum=1 newOppSum=-1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=1
+activeOp op=diff miFrom=0 miTo=0 suFrom=1 suTo=0 result=0
+markDoneBinary id=3 (1,2 0,4 1,0 5,1) t=0.788675135 [5] (2.85658813,0.932087123) newWindSum=-1 newOppSum=0 oppSum=? windSum=? windValue=1
+markDoneBinary id=4 (5,1 1,2) t=0 [0] (5,1) newWindSum=-1 newOppSum=0 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=4
+markDoneBinary id=1 (0,1 1,5 2,1 4,0) t=0.788675135 [3] (2.85658813,0.932087123) newWindSum=1 newOppSum=0 oppSum=0 windSum=1 windValue=1
+findNextOp from:[1] to:[3] start=5 end=4
+bridgeOp current id=1 from=(4,0) to=(2.85658813,0.932087123)
+path.moveTo(0,1);
+path.lineTo(4,0);
+path.cubicTo(3.57735038,0.211324871, 3.1993587,0.556624353, 2.85658813,0.932087123);
+findNextOp debugShowSort contourWinding=-1 oppContourWinding=1 sign=-1
+debugShowSort [1] id=3 cubic start=4 (1.00829625,1.99792588) end=5 (2.85658813,0.932087123) sign=-1 windValue=1 windSum=-1 -1->0 (max=-1) done=0 tiny=0 opp=0
+debugShowSort [2] id=4 line start=2 (1.00829625,1.99792588) end=3 (1,2) sign=-1 windValue=1 windSum=? 0->1 (max=1) done=0 tiny=0 opp=0
+debugShowSort [3] id=3 cubic start=4 (1.00829625,1.99792588) end=3 (0.991754651,2.01644516) sign=1 windValue=1 windSum=? 1->0 (max=1) done=0 tiny=0 opp=0
+debugShowSort [0] id=4 line start=2 (1.00829625,1.99792588) end=1 (2.21141648,1.69714582) sign=1 windValue=1 windSum=? 0->-1 (max=-1) done=0 tiny=0 opp=0
+findNextOp firstIndex=[1] sign=-1
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=1 result=1
+markWinding id=4 (5,1 1,2) t=0.997925926 [2] (1.00829625,1.99792588) newWindSum=1 newOppSum=1 oppSum=? windSum=? windValue=1
+markWinding id=3 (1,2 0,4 1,0 5,1) t=0 [0] (1,2) newWindSum=1 newOppSum=1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=3
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+markWinding id=3 (1,2 0,4 1,0 5,1) t=0.461521979 [3] (0.991754651,2.01644516) newWindSum=1 newOppSum=1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=3
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=1 result=1
+markWinding id=4 (5,1 1,2) t=0.697145868 [1] (2.21141648,1.69714582) newWindSum=-1 newOppSum=1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=4
+markDoneBinary id=3 (1,2 0,4 1,0 5,1) t=0.466666667 [4] (1.00829625,1.99792588) newWindSum=-1 newOppSum=1 oppSum=1 windSum=-1 windValue=1
+findNextOp from:[3] to:[4] start=2 end=3
+bridgeOp current id=3 from=(2.85658813,0.932087123) to=(1.00829625,1.99792588)
+path.cubicTo(1.96246409,1.13237906, 1.35749662,1.61008465, 1.00829625,1.99792588);
+findNextOp simple
+markDoneBinary id=4 (5,1 1,2) t=0.997925926 [2] (1.00829625,1.99792588) newWindSum=1 newOppSum=1 oppSum=1 windSum=1 windValue=1
+bridgeOp current id=4 from=(1.00829625,1.99792588) to=(1,2)
+Program received signal:  “EXC_BAD_ACCESS”.
+findNextOp debugShowSort contourWinding=1 oppContourWinding=1 sign=1
+debugShowSort [1] id=3 cubic start=1 (0.991754651,2.01644516) end=0 (1,2) sign=1 windValue=1 windSum=1 1->0 (max=1) done=0 tiny=0 opp=0
+debugShowSort [2] id=3 cubic start=3 (0.991754651,2.01644516) end=2 (0.640381813,2.56467652) sign=1 windValue=1 windSum=? 0->-1 (max=-1) done=0 tiny=0 opp=0
+debugShowSort [3] id=3 cubic start=1 (0.991754651,2.01644516) end=2 (0.640381813,2.56467652) sign=-1 windValue=1 windSum=? -1->0 (max=-1) done=0 tiny=0 opp=0
+debugShowSort [0] id=3 cubic start=3 (0.991754651,2.01644516) end=4 (1.00829625,1.99792588) sign=-1 windValue=1 windSum=1 0->1 (max=1) done=0 tiny=0 opp=0
+findNextOp firstIndex=[1] sign=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=1 result=1
+markWinding id=3 (1,2 0,4 1,0 5,1) t=0.223476406 [2] (0.640381813,2.56467652) newWindSum=-1 newOppSum=1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=3
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+markWinding id=3 (1,2 0,4 1,0 5,1) t=0.002763735 [1] (0.991754651,2.01644516) newWindSum=-1 newOppSum=1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=3
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=1 result=1
+markDoneBinary id=3 (1,2 0,4 1,0 5,1) t=0 [0] (1,2) newWindSum=1 newOppSum=1 oppSum=1 windSum=1 windValue=1
+findNextOp from:[3] to:[3] start=3 end=2
+bridgeOp current id=3 from=(1,2) to=(0.991754651,2.01644516)
+path.lineTo(1,2);
+path.cubicTo(0.997236252,2.0055275, 0.994487822,2.01100922, 0.991754651,2.01644516);
+findNextOp debugShowSort contourWinding=-1 oppContourWinding=1 sign=-1
+debugShowSort [0] id=3 cubic start=2 (0.640381813,2.56467652) end=3 (0.991754651,2.01644516) sign=-1 windValue=1 windSum=-1 -1->0 (max=-1) done=0 tiny=0 opp=0
+debugShowSort [1] id=1 cubic start=1 (0.640381813,2.56467652) end=0 (0,1) sign=1 windValue=1 windSum=1 1->0 (max=1) done=0 tiny=0 opp=1
+debugShowSort [2] id=3 cubic start=2 (0.640381813,2.56467652) end=1 (0.991754651,2.01644516) sign=1 windValue=1 windSum=-1 0->-1 (max=-1) done=0 tiny=0 opp=0
+debugShowSort [3] id=1 cubic start=1 (0.640381813,2.56467652) end=2 (2.21141648,1.69714582) sign=-1 windValue=1 windSum=? 0->1 (max=1) done=0 tiny=0 opp=1
+findNextOp firstIndex=[0] sign=-1
+activeOp op=diff miFrom=1 miTo=0 suFrom=0 suTo=0 result=1
+activeOp op=diff miFrom=0 miTo=0 suFrom=0 suTo=1 result=0
+activeOp op=diff miFrom=0 miTo=1 suFrom=1 suTo=1 result=0
+markDoneBinary id=1 (0,1 1,5 2,1 4,0) t=0.210357794 [1] (0.640381813,2.56467652) newWindSum=1 newOppSum=-1 oppSum=? windSum=? windValue=1
+findNextOp chase.append id=1
+markDoneBinary id=3 (1,2 0,4 1,0 5,1) t=0.223476406 [2] (0.640381813,2.56467652) newWindSum=-1 newOppSum=1 oppSum=1 windSum=-1 windValue=1
+findNextOp from:[3] to:[1] start=1 end=0
+bridgeOp current id=3 from=(0.991754651,2.01644516) to=(0.640381813,2.56467652)
+path.cubicTo(0.739642859,2.30096555, 0.627014875,2.53316927, 0.640381813,2.56467652);
+findNextOp simple
+markDoneBinary id=1 (0,1 1,5 2,1 4,0) t=0 [0] (0,1) newWindSum=1 newOppSum=0 oppSum=0 windSum=1 windValue=1
+bridgeOp current id=1 from=(0.640381813,2.56467652) to=(0,1)
+path.cubicTo(0.42071557,2.32885909, 0.2103578,1.84143114, 0,1);
+path.close();
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0.002763735 (0.991754651,2.01644516) tEnd=0.223476406 other=3 otherT=0.461521979 otherIndex=3 windSum=-1 windValue=1 oppValue=0
+debugShowActiveSpans id=3 (1,2 0,4 1,0 5,1) t=0.461521979 (0.991754651,2.01644516) tEnd=0.466666667 other=3 otherT=0.002763735 otherIndex=1 windSum=1 windValue=1 oppValue=0
+debugShowActiveSpans id=4 (5,1 1,2) t=0.697145868 (2.21141648,1.69714582) tEnd=0.997925926 other=1 otherT=0.646900486 otherIndex=2 windSum=-1 windValue=1 oppValue=0
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+findNextOp debugShowSort contourWinding=0 oppContourWinding=1 sign=1
+debugShowSort [0] id=4 line start=2 (1.00829625,1.99792588) end=1 (2.21141648,1.69714582) sign=1 windValue=1 windSum=-1 0->-1 (max=-1) done=0 tiny=0 opp=0
+debugShowSort [1] id=3 cubic start=4 (1.00829625,1.99792588) end=5 (2.85658813,0.932087123) sign=-1 windValue=1 windSum=-1 -1->0 (max=-1) done=1 tiny=0 opp=0
+debugShowSort [2] id=4 line start=2 (1.00829625,1.99792588) end=3 (1,2) sign=-1 windValue=1 windSum=1 0->1 (max=1) done=1 tiny=0 opp=0
+debugShowSort [3] id=3 cubic start=4 (1.00829625,1.99792588) end=3 (0.991754651,2.01644516) sign=1 windValue=1 windSum=1 1->0 (max=1) done=0 tiny=0 opp=0
+findNextOp firstIndex=[0] sign=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=1 result=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+markDoneBinary id=4 (5,1 1,2) t=0.697145868 [1] (2.21141648,1.69714582) newWindSum=-1 newOppSum=1 oppSum=1 windSum=-1 windValue=1
+findNextOp from:[4] to:[3] start=4 end=3
+bridgeOp current id=4 from=(2.21141648,1.69714582) to=(1.00829625,1.99792588)
+findNextOp debugShowSort contourWinding=0 oppContourWinding=1 sign=-1
+debugShowSort [0] id=3 cubic start=3 (0.991754651,2.01644516) end=4 (1.00829625,1.99792588) sign=-1 windValue=1 windSum=1 0->1 (max=1) done=0 tiny=0 opp=0
+debugShowSort [1] id=3 cubic start=1 (0.991754651,2.01644516) end=0 (1,2) sign=1 windValue=1 windSum=1 1->0 (max=1) done=1 tiny=0 opp=0
+debugShowSort [2] id=3 cubic start=3 (0.991754651,2.01644516) end=2 (0.640381813,2.56467652) sign=1 windValue=1 windSum=-1 0->-1 (max=-1) done=1 tiny=0 opp=0
+debugShowSort [3] id=3 cubic start=1 (0.991754651,2.01644516) end=2 (0.640381813,2.56467652) sign=-1 windValue=1 windSum=-1 -1->0 (max=-1) done=0 tiny=0 opp=0
+findNextOp firstIndex=[0] sign=-1
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=1 result=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+markDoneBinary id=3 (1,2 0,4 1,0 5,1) t=0.461521979 [3] (0.991754651,2.01644516) newWindSum=1 newOppSum=1 oppSum=1 windSum=1 windValue=1
+findNextOp from:[3] to:[3] start=1 end=2
+bridgeOp current id=3 from=(1.00829625,1.99792588) to=(0.991754651,2.01644516)
+path.moveTo(2.21141648,1.69714582);
+path.lineTo(1.00829625,1.99792588);
+path.cubicTo(1.00271726,2.0041225, 0.99720329,2.01029587, 0.991754651,2.01644516);
+findNextOp debugShowSort contourWinding=0 oppContourWinding=1 sign=1
+debugShowSort [2] id=3 cubic start=2 (0.640381813,2.56467652) end=1 (0.991754651,2.01644516) sign=1 windValue=1 windSum=-1 0->-1 (max=-1) done=0 tiny=0 opp=0
+debugShowSort [3] id=1 cubic start=1 (0.640381813,2.56467652) end=2 (2.21141648,1.69714582) sign=-1 windValue=1 windSum=1 1->2 (max=2) done=1 tiny=0 opp=1
+debugShowSort [0] id=3 cubic start=2 (0.640381813,2.56467652) end=3 (0.991754651,2.01644516) sign=-1 windValue=1 windSum=-1 -1->0 (max=-1) done=1 tiny=0 opp=0
+debugShowSort [1] id=1 cubic start=1 (0.640381813,2.56467652) end=0 (0,1) sign=1 windValue=1 windSum=1 2->1 (max=2) done=1 tiny=0 opp=1
+findNextOp firstIndex=[2] sign=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=1 result=0
+activeOp op=diff miFrom=1 miTo=1 suFrom=1 suTo=0 result=1
+activeOp op=diff miFrom=1 miTo=1 suFrom=0 suTo=0 result=0
+markDoneBinary id=3 (1,2 0,4 1,0 5,1) t=0.002763735 [1] (0.991754651,2.01644516) newWindSum=-1 newOppSum=1 oppSum=1 windSum=-1 windValue=1
+findNextOp from:[3] to:[3] start=2 end=3
+bridgeOp current id=3 from=(0.991754651,2.01644516) to=(0.640381813,2.56467652)
+path.cubicTo(0.773483634,2.45056915, 0.652775407,2.59388947, 0.640381813,2.56467652);
+</div>
+
 </div>
 
 <script type="text/javascript">
 
 var testDivs = [
+    cubicOp35d,
     cubicOp31da,
     cubicOp31d,
     cubicOp28u,
@@ -140,14 +306,48 @@ var SPAN_C_VAL = 18;
 var SPAN_C_OPP = 19;
 
 var ACTIVE_LINE_SPAN = 1;
-var ACTIVE_QUAD_SPAN = 2;
-var ACTIVE_CUBIC_SPAN = 3;
-var INTERSECT_QUAD_LINE = 4;
-var INTERSECT_QUAD_LINE_2 = 5;
-var INTERSECT_QUAD_LINE_NO = 6;
-var INTERSECT_QUAD = 7;
-var INTERSECT_QUAD_2 = 8;
-var INTERSECT_QUAD_NO = 9;
+var ACTIVE_QUAD_SPAN =        ACTIVE_LINE_SPAN + 1;
+var ACTIVE_CUBIC_SPAN =       ACTIVE_QUAD_SPAN + 1;
+
+var PATH_MOVETO =             ACTIVE_CUBIC_SPAN + 1;
+var PATH_LINETO =             PATH_MOVETO + 1;
+var PATH_QUADTO =             PATH_LINETO + 1;
+var PATH_CUBICTO =            PATH_QUADTO + 1;
+var PATH_CLOSE =              PATH_CUBICTO + 1;
+
+var INTERSECT_LINE =          PATH_CLOSE + 1;
+var INTERSECT_LINE_2 =        INTERSECT_LINE + 1;
+var INTERSECT_LINE_NO =       INTERSECT_LINE_2 + 1;
+var INTERSECT_QUAD_LINE =     INTERSECT_LINE_NO + 1;
+var INTERSECT_QUAD_LINE_2 =   INTERSECT_QUAD_LINE + 1;
+var INTERSECT_QUAD_LINE_NO =  INTERSECT_QUAD_LINE_2 + 1;
+var INTERSECT_QUAD =          INTERSECT_QUAD_LINE_NO + 1;
+var INTERSECT_QUAD_2 =        INTERSECT_QUAD + 1;
+var INTERSECT_QUAD_NO =       INTERSECT_QUAD_2 + 1;
+var INTERSECT_SELF_CUBIC =    INTERSECT_QUAD_NO + 1;
+var INTERSECT_SELF_CUBIC_NO = INTERSECT_SELF_CUBIC + 1;
+var INTERSECT_CUBIC_LINE =    INTERSECT_SELF_CUBIC_NO + 1;
+var INTERSECT_CUBIC_LINE_2 =  INTERSECT_CUBIC_LINE + 1;
+var INTERSECT_CUBIC_LINE_3 =  INTERSECT_CUBIC_LINE_2 + 1;
+var INTERSECT_CUBIC_LINE_NO = INTERSECT_CUBIC_LINE_3 + 1;
+// FIXME: add cubic/quad
+var INTERSECT_CUBIC =         INTERSECT_CUBIC_LINE_NO + 1;
+var INTERSECT_CUBIC_2 =       INTERSECT_CUBIC + 1;
+var INTERSECT_CUBIC_3 =       INTERSECT_CUBIC_2 + 1;
+var INTERSECT_CUBIC_4 =       INTERSECT_CUBIC_3 + 1;
+// FIXME: add cubic 5- 9
+var INTERSECT_CUBIC_NO =      INTERSECT_CUBIC_4 + 1;
+
+var SORT_LINE =               INTERSECT_CUBIC_NO + 1;
+var SORT_QUAD =               SORT_LINE + 1;
+var SORT_CUBIC =              SORT_QUAD + 1;
+
+var REC_TYPE_UNKNOWN = -1;
+var REC_TYPE_PATH = 0;
+var REC_TYPE_SECT = 1;
+var REC_TYPE_ACTIVE = 2;
+var REC_TYPE_ADD = 3;
+var REC_TYPE_SORT = 4;
 
 function strs_to_nums(strs) {
     var result = [];
@@ -215,7 +415,9 @@ function filter_str_by(id, str, regex, array) {
         var result = strs_to_nums(strs);
         array.push(id);
         array.push(result);
+        return true;
     }
+    return false;
 }
 
 // FIXME: add cubic support
@@ -249,6 +451,150 @@ function parse_intersections(test, title) {
     }
 }
 
+function construct_regexp2(pattern) {
+    var escape = pattern.replace(/[-/\\^$*+?.()|[\]{}]/g, '\\$&');
+    escape = escape.replace(/CUBIC_VAL/g, "\\(P_VAL P_VAL P_VAL P_VAL\\)");
+    escape = escape.replace(/QUAD_VAL/g, "\\(P_VAL P_VAL P_VAL\\)");
+    escape = escape.replace(/LINE_VAL/g, "\\(P_VAL P_VAL\\)");
+    escape = escape.replace(/PT_VAL/g, "\\(P_VAL\\)");
+    escape = escape.replace(/P_VAL/g, "(\\d+\\.?\\d*),(\\d+\\.?\\d*)");
+    escape = escape.replace(/T_VAL/g, "(\\d+\\.?\\d*e?-?\\d*)");
+    escape = escape.replace(/IDX/g, "(\\d+)");
+    escape = escape.replace(/NUM/g, "(-?\\d+)");
+    escape = escape.replace(/OPT/g, "(\\?|-?\\d+)");
+    return new RegExp(escape, 'i');
+}
+
+function construct_regexp2c(pattern) {
+    var escape = pattern.replace(/[-/\\^$*+?.()|[\]{}]/g, '\\$&');
+    escape = escape.replace(/CUBIC_VAL/g, "\\{\\{P_VAL\\}, \\{P_VAL\\}, \\{P_VAL\\}, \\{P_VAL\\}\\}");
+    escape = escape.replace(/QUAD_VAL/g, "\\{\\{P_VAL\\}, \\{P_VAL\\}, \\{P_VAL\\}\\}");
+    escape = escape.replace(/LINE_VAL/g, "\\{\\{P_VAL\\}, \\{P_VAL\\}\\}");
+    escape = escape.replace(/PT_VAL/g, "\\{\\{P_VAL\\}\\}");
+    escape = escape.replace(/P_VAL/g, "(\\d+\\.?\\d*),(\\d+\\.?\\d*)");
+    escape = escape.replace(/T_VAL/g, "(\\d+\\.?\\d*e?-?\\d*)");
+    escape = escape.replace(/IDX/g, "(\\d+)");
+    escape = escape.replace(/NUM/g, "(-?\\d+)");
+    escape = escape.replace(/OPT/g, "(\\?|-?\\d+)");
+    return new RegExp(escape, 'i');
+}
+
+function match_regexp(str, lineNo, array, id, pattern) {
+    var regex = construct_regexp2(pattern);
+    if (filter_str_by(id, str, regex, array)) {
+        return true;
+    }
+    regex = construct_regexp2c(pattern);
+    return filter_str_by(id, str, regex, array);
+}
+
+function parse_all(test, title) {
+    var lines = test.match(/[^\r\n]+/g);
+    var records = []; // a rec can be the original paths, a set of intersections, a set of active spans, a sort, or a path add
+    var record = [];
+    var recType = REC_TYPE_UNKNOWN;
+    for (var lineNo in lines) {
+        var line = lines[lineNo];
+        var type = line.lastIndexOf("debugShowSort", 0) === 0 ? REC_TYPE_SORT
+                : line.lastIndexOf("debugShowActiveSpans", 0) === 0 ? REC_TYPE_ACTIVE 
+                : line.lastIndexOf("debugShow", 0) === 0 ? REC_TYPE_SECT 
+                : line.lastIndexOf("path.", 0) === 0 ? REC_TYPE_ADD
+                : line.lastIndexOf("{{", 0) === 0 ? REC_TYPE_PATH
+                : REC_TYPE_UNKNOWN;
+        if (recType != type) {
+            if (recType != REC_TYPE_UNKNOWN) {
+                records.push(recType);
+                records.push(lineNo);
+                records.push(record);
+            }
+            record = [];
+            recType = type;
+        }
+        var found = false;
+        switch (recType) {
+            case REC_TYPE_ACTIVE:
+                found = match_regexp(line, lineNo, record, ACTIVE_LINE_SPAN, "debugShowActiveSpans" +
+" id=IDX LINE_VAL t=T_VAL PT_VAL tEnd=T_VAL other=IDX otherT=T_VAL otherIndex=IDX windSum=OPT windValue=IDX oppValue=IDX"
+                ) || match_regexp(line, lineNo, record, ACTIVE_QUAD_SPAN, "debugShowActiveSpans" +
+" id=IDX QUAD_VAL t=T_VAL PT_VAL tEnd=T_VAL other=IDX otherT=T_VAL otherIndex=IDX windSum=OPT windValue=IDX oppValue=IDX"
+                ) || match_regexp(line, lineNo, record, ACTIVE_CUBIC_SPAN, "debugShowActiveSpans" +
+" id=IDX CUBIC_VAL t=T_VAL PT_VAL tEnd=T_VAL other=IDX otherT=T_VAL otherIndex=IDX windSum=OPT windValue=IDX oppValue=IDX"
+                );
+                break;
+            case REC_TYPE_ADD:
+                found = match_regexp(line, lineNo, record, PATH_MOVETO, "path.moveToPT_VAL;"
+                ) || match_regexp(line, lineNo, record, PATH_LINETO, "path.lineTo(P_VAL);"
+                ) || match_regexp(line, lineNo, record, PATH_QUADTO, "path.quadTo(P_VAL, P_VAL);"
+                ) || match_regexp(line, lineNo, record, PATH_CUBICTO, "path.cubicTo(P_VAL, P_VAL, P_VAL);"
+                ) || match_regexp(line, lineNo, record, PATH_CLOSE, "path.close();"
+                );
+                break;
+            case REC_TYPE_SECT:
+                found = match_regexp(line, lineNo, record, INTERSECT_LINE, "debugShowLineIntersection" +
+" wtTs[0]=T_VAL LINE_VAL PT_VAL wnTs[0]=T_VAL LINE_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_LINE_2, "debugShowLineIntersection" +
+" wtTs[0]=T_VAL LINE_VAL PT_VAL wtTs[1]=T_VAL PT_VAL wnTs[0]=T_VAL LINE_VAL wnTs[1]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_LINE_NO, "debugShowLineIntersection" +
+" no intersect LINE_VAL LINE_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_QUAD_LINE, "debugShowQuadLineIntersection" +
+" wtTs[0]=T_VAL QUAD_VAL PT_VAL wnTs[0]=T_VAL LINE_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_QUAD_LINE_2, "debugShowQuadLineIntersection" +
+" wtTs[0]=T_VAL QUAD_VAL PT_VAL wtTs[1]=T_VAL PT_VAL wnTs[0]=T_VAL LINE_VAL wnTs[1]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_QUAD_LINE_NO, "debugShowQuadLineIntersection" +
+" no intersect QUAD_VAL LINE_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_QUAD, "debugShowQuadIntersection" +
+" wtTs[0]=T_VAL QUAD_VAL PT_VAL wnTs[0]=T_VAL QUAD_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_QUAD_2, "debugShowQuadIntersection" +
+" wtTs[0]=T_VAL QUAD_VAL PT_VAL wtTs[1]=T_VAL wnTs[0]=T_VAL QUAD_VAL wnTs[1]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_QUAD_NO, "debugShowQuadIntersection" +
+" no intersect QUAD_VAL QUAD_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_SELF_CUBIC, "debugShowCubicIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wtTs[1]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_SELF_CUBIC_NO, "debugShowCubicIntersection" +
+" no self intersect CUBIC_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_LINE, "debugShowCubicLineIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wnTs[0]=T_VAL LINE_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_LINE_2, "debugShowCubicLineIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wtTs[1]=T_VAL PT_VAL wnTs[0]=T_VAL LINE_VAL wnTs[1]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_LINE_3, "debugShowCubicLineIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wtTs[1]=T_VAL PT_VAL wtTs[2]=T_VAL PT_VAL wnTs[0]=T_VAL LINE_VAL wnTs[1]=T_VAL wnTs[2]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_LINE_NO, "debugShowCubicLineIntersection" +
+" no intersect CUBIC_VAL LINE_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC, "debugShowCubicIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wnTs[0]=T_VAL CUBIC_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_2, "debugShowCubicIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wtTs[1]=T_VAL PT_VAL wnTs[0]=T_VAL CUBIC_VAL wnTs[1]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_3, "debugShowCubicIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wtTs[1]=T_VAL PT_VAL wtTs[2]=T_VAL PT_VAL wnTs[0]=T_VAL CUBIC_VAL wnTs[1]=T_VAL wnTs[2]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_4, "debugShowCubicIntersection" +
+" wtTs[0]=T_VAL CUBIC_VAL PT_VAL wtTs[1]=T_VAL PT_VAL wtTs[2]=T_VAL PT_VAL wtTs[3]=T_VAL PT_VAL wnTs[0]=T_VAL CUBIC_VAL wnTs[1]=T_VAL wnTs[2]=T_VAL wnTs[3]=T_VAL"
+                ) || match_regexp(line, lineNo, record, INTERSECT_CUBIC_NO, "debugShowCubicIntersection" +
+" no intersect CUBIC_VAL CUBIC_VAL"
+                );
+                break;
+            case REC_TYPE_SORT:
+                found = match_regexp(line, lineNo, record, SORT_LINE, "debugShowSort" +
+" [IDX] id=IDX line start=IDX PT_VAL end=IDX PT_VAL sign=NUM windValue=IDX windSum=OPT NUM->NUM (max=NUM) done=IDX tiny=IDX opp=IDX"
+                ) || match_regexp(line, lineNo, record, SORT_QUAD, "debugShowSort" +
+" [IDX] id=IDX quad start=IDX PT_VAL end=IDX PT_VAL sign=NUM windValue=IDX windSum=OPT NUM->NUM (max=NUM) done=IDX tiny=IDX opp=IDX"
+                ) || match_regexp(line, lineNo, record, SORT_CUBIC, "debugShowSort" +
+" [IDX] id=IDX cubic start=IDX PT_VAL end=IDX PT_VAL sign=NUM windValue=IDX windSum=OPT NUM->NUM (max=NUM) done=IDX tiny=IDX opp=IDX"
+                );
+                break;
+            case REC_TYPE_UNKNOWN:
+                found = true;
+                break;
+        }
+        if (!found) {
+            console.log(line + " [" + lineNo + "] of type " + type + " not found");
+        }
+    }
+    if (records.length >= 1) {
+        tests.push(records);
+        testTitles.push(title);
+    }
+}
+
 function init(test) {
     var canvas = document.getElementById('canvas');
     if (!canvas.getContext) return;
@@ -902,6 +1248,7 @@ function start() {
     for (i = 0; i < testDivs.length; ++i) {
         var title = testDivs[i].id.toString();
         var str = testDivs[i].firstChild.data;
+        parse_all(str, title);
         parse_debugShowActiveSpans(str, title);
         parse_intersections(str, title);
     }
diff --git a/experimental/Intersection/op.htm b/experimental/Intersection/op.htm
index 199a9df076..267fbec338 100644
--- a/experimental/Intersection/op.htm
+++ b/experimental/Intersection/op.htm
@@ -3721,11 +3721,59 @@ path.addRect(4, 13, 13, 16, SkPath::kCCW_Direction);
     pathB.close();
 </div>
 
+<div id="cubicOp32d">
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(1,2, 6,0, 3,1);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(0,6);
+    pathB.cubicTo(1,3, 1,0, 2,1);
+    pathB.close();
+</div>
+
+<div id="cubicOp33i">
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(1,2, 6,0, 3,1);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(0,6);
+    pathB.cubicTo(1,3, 1,0, 2,1);
+    pathB.close();
+</div>
+
+<div id="cubicOp34d">
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(3,5, 2,1, 3,1);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(1,2);
+    pathB.cubicTo(1,3, 1,0, 5,3);
+    pathB.close();
+</div>
+
+<div id="cubicOp35d">
+    path.setFillType(SkPath::kWinding_FillType);
+    path.moveTo(0,1);
+    path.cubicTo(1,5, 2,1, 4,0);
+    path.close();
+    pathB.setFillType(SkPath::kWinding_FillType);
+    pathB.moveTo(1,2);
+    pathB.cubicTo(0,4, 1,0, 5,1);
+    pathB.close();
+</div>
+
 </div>
 
 <script type="text/javascript">
 
 var testDivs = [
+    cubicOp35d,
+    cubicOp34d,
+    cubicOp33i,
+    cubicOp32d,
     cubicOp31d,
     cubicOp30d,
     cubicOp29d,
@@ -4267,11 +4315,11 @@ function handleMouseOver() {
     calcXY();
     var num = mouseX.toFixed(3) + ", " + mouseY.toFixed(3);
     ctx.beginPath();
-    ctx.rect(300,100,200,10);
+    ctx.rect(300,0,72,9);
     ctx.fillStyle="white";
     ctx.fill();
     ctx.fillStyle="black";
-    ctx.fillText(num, 300, 108);
+    ctx.fillText(num, 300, 7);
 }
 
 function handleMouseClick() {
diff --git a/experimental/Intersection/qc.htm b/experimental/Intersection/qc.htm
index db77fa4d70..e3075d1e79 100644
--- a/experimental/Intersection/qc.htm
+++ b/experimental/Intersection/qc.htm
@@ -2086,11 +2086,48 @@ quad=(1.20573276,0.813456177 1.2679289,0.830085346 1.33333333,0.851851852)
   {{2.79472921,1.73568666}, {3.36246373,1.21251209}, {5,2}},
 </div>
 
+<div id="cubicOp34d">
+{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1, y = 2.1969085233712229}, {x = 1, y = 2.1347920612232207}, {x = 1, y = 2}}
+{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1.0242251996917398, y = 2.2313593593386498}, {x = 1.0599075827658746, y = 2.1473377437648784}, {x = 1.1481481481481481, y = 2.0370370370370372}}
+{{x = 1.0097960958786989, y = 2.2108396260650962}, {x = 0.73607693096853644, y = 1.9329854848088734}, {x = 0.40437628284615079, y = 1.5391683771282005}, {x = 0, y = 1}}
+{{x = 1.0097960958786989, y = 2.2108396260650962}, {x = 1.8566294376993437, y = 3.0704657726520206}, {x = 2.1484860084122528, y = 2.8201383770234716}, {x = 2.320499529631658, y = 2.3301248824079162}}
+</div>
+
+<div id="cubicOp34da">
+{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1, y = 2.1969085233712229}, {x = 1, y = 2.1347920612232207}, {x = 1, y = 2}}
+{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1.0242251996917398, y = 2.2313593593386498}, {x = 1.0599075827658746, y = 2.1473377437648784}, {x = 1.1481481481481481, y = 2.0370370370370372}}
+</div>
+
+<div id="cubicOp34db">
+{{1,2}, {1,3}, {1,0}, {5,3}},
+{{0,1}, {3,5}, {2,1}, {3,1}},
+
+  {{1,2}, {0.984375,2.3359375}, {1.0625,2.15625}},
+  {{1.0625,2.15625}, {1.140625,1.9765625}, {1.5,1.75}},
+  {{1.5,1.75}, {1.859375,1.5234375}, {2.6875,1.71875}},
+  {{2.6875,1.71875}, {3.515625,1.9140625}, {5,3}},
+
+  {{0,1}, {0.983539095,2.30041152}, {1.47325103,2.61316872}},
+  {{1.47325103,2.61316872}, {1.96296296,2.92592593}, {2.1563786,2.64609053}},
+  {{2.1563786,2.64609053}, {2.34979424,2.36625514}, {2.44444444,1.88888889}},
+  {{2.44444444,1.88888889}, {2.52083333,1.54166667}, {2.63888889,1.27777778}},
+  {{2.63888889,1.27777778}, {2.75694444,1.01388889}, {3,1}},
+</div>
+
+<div id="quadOp34d">
+  {{1,2}, {0.984375,2.3359375}, {1.0625,2.15625}},
+  {{0,1}, {0.983539095,2.30041152}, {1.47325103,2.61316872}},
+</div>
+
 </div>
 
 <script type="text/javascript">
 
 var testDivs = [
+    quadOp34d,
+    cubicOp34db,
+    cubicOp34d,
+    cubicOp34da,
     quadOp30d,
     cubicOp30d,
     quadOp27d,