shape ops work in progress

M    Intersection/DataTypes.cpp
M    Intersection/QuadraticIntersection_Test.cpp
M    Intersection/EdgeWalker.cpp
M    Intersection/LineQuadraticIntersection_Test.cpp
M    Intersection/LineIntersection_Test.cpp
M    Intersection/LineIntersection.cpp
D    Intersection/edge.xcodeproj
M    Intersection/SimplifyFindTop_Test.cpp
M    Intersection/DataTypes.h
A    Intersection/SimplifyRect4x4_Test.cpp
M    Intersection/CubicIntersection_Test.cpp
M    Intersection/QuadraticUtilities.h
M    Intersection/LineCubicIntersection_Test.cpp
A    Intersection/CurveUtilities.h
M    Intersection/QuadraticBezierClip.cpp
M    Intersection/QuadraticBounds.cpp
M    Intersection/LineUtilities.h
M    Intersection/Intersection_Tests.cpp
M    Intersection/Simplify.cpp
M    Intersection/EdgeWalker_TestUtility.cpp
M    Intersection/QuadraticUtilities.cpp
M    Intersection/thingsToDo.txt
M    Intersection/LineUtilities.cpp
M    Intersection/CubicUtilities.h
M    Intersection/SimplifyFindNext_Test.cpp
M    Intersection/Intersection_Tests.h
M    Intersection/CubicBezierClip.cpp
M    Intersection/ActiveEdge_Test.cpp
M    Intersection/CubicBounds.cpp
M    Intersection/Simplify.h
M    Intersection/SimplifyNew_Test.cpp
M    Intersection/EdgeWalker_Test.h
M    Intersection/CubicUtilities.cpp
M    Intersection/op.htm
M    Intersection/ConvexHull.cpp
D    Intersection/RectUtilities.cpp
M    Intersection/SimplifyAddIntersectingTs_Test.cpp



git-svn-id: http://skia.googlecode.com/svn/trunk@4429 2bbb7eff-a529-9590-31e7-b0007b416f81

37 files changed, 2140 insertions, 1763 deletions

diff --git a/experimental/Intersection/ActiveEdge_Test.cpp b/experimental/Intersection/ActiveEdge_Test.cpp
index 3e1b958ab6..5456155abc 100755
--- a/experimental/Intersection/ActiveEdge_Test.cpp
+++ b/experimental/Intersection/ActiveEdge_Test.cpp
@@ -1,12 +1,4 @@
-#include "CurveIntersection.h"
-#include "Intersections.h"
-#include "LineIntersection.h"
-#include "SkPath.h"
-#include "SkRect.h"
-#include "SkTArray.h"
-#include "SkTDArray.h"
-#include "ShapeOps.h"
-#include "TSearch.h"
+#include "Simplify.h"
 
 namespace UnitTest {
 
diff --git a/experimental/Intersection/ConvexHull.cpp b/experimental/Intersection/ConvexHull.cpp
index 6cdbe60995..1551720eef 100644
--- a/experimental/Intersection/ConvexHull.cpp
+++ b/experimental/Intersection/ConvexHull.cpp
@@ -1,4 +1,5 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "IntersectionUtilities.h"
 
 /* Given a cubic, find the convex hull described by the end and control points.
diff --git a/experimental/Intersection/CubicBezierClip.cpp b/experimental/Intersection/CubicBezierClip.cpp
index 4ed1369d1a..4eddc70a42 100644
--- a/experimental/Intersection/CubicBezierClip.cpp
+++ b/experimental/Intersection/CubicBezierClip.cpp
@@ -1,4 +1,5 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "LineParameters.h"
 #include <algorithm> // used for std::swap
 
diff --git a/experimental/Intersection/CubicBounds.cpp b/experimental/Intersection/CubicBounds.cpp
index 8d14ea5a9e..024fb9637f 100644
--- a/experimental/Intersection/CubicBounds.cpp
+++ b/experimental/Intersection/CubicBounds.cpp
@@ -1,4 +1,5 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "Extrema.h"
 
 static int isBoundedByEndPoints(double a, double b, double c, double d)
diff --git a/experimental/Intersection/CubicIntersection_Test.cpp b/experimental/Intersection/CubicIntersection_Test.cpp
index 005e77781c..14b30ed50e 100644
--- a/experimental/Intersection/CubicIntersection_Test.cpp
+++ b/experimental/Intersection/CubicIntersection_Test.cpp
@@ -1,4 +1,5 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "CubicIntersection_TestData.h"
 #include "Intersection_Tests.h"
 #include "Intersections.h"
diff --git a/experimental/Intersection/CubicUtilities.cpp b/experimental/Intersection/CubicUtilities.cpp
index 3fab29ec80..05c00a0d29 100644
--- a/experimental/Intersection/CubicUtilities.cpp
+++ b/experimental/Intersection/CubicUtilities.cpp
@@ -74,3 +74,75 @@ int cubicRoots(double A, double B, double C, double D, double t[3]) {
     }
     return (int)(roots - t);
 }
+
+// from http://www.cs.sunysb.edu/~qin/courses/geometry/4.pdf
+// c(t)  = a(1-t)^3 + 3bt(1-t)^2 + 3c(1-t)t^2 + dt^3
+// c'(t) = -3a(1-t)^2 + 3b((1-t)^2 - 2t(1-t)) + 3c(2t(1-t) - t^2) + 3dt^2
+//       = 3(b-a)(1-t)^2 + 6(c-b)t(1-t) + 3(d-c)t^2
+double derivativeAtT(const double* cubic, double t) {
+    double one_t = 1 - t;
+    double a = cubic[0];
+    double b = cubic[2];
+    double c = cubic[4];
+    double d = cubic[6];
+    return (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
+}
+
+// same as derivativeAtT
+// which is more accurate? which is faster?
+double derivativeAtT_2(const double* cubic, double t) {
+    double a = cubic[2] - cubic[0];
+    double b = cubic[4] - 2 * cubic[2] + cubic[0];
+    double c = cubic[6] + 3 * (cubic[2] - cubic[4]) - cubic[0];
+    return c * c * t * t + 2 * b * t + a;
+}
+
+void dxdy_at_t(const Cubic& cubic, double t, double& dx, double& dy) {
+    if (&dx) {
+        dx = derivativeAtT(&cubic[0].x, t);
+    }
+    if (&dy) {
+        dy = derivativeAtT(&cubic[0].y, t);
+    }
+}
+
+bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath) {
+    double dy = cubic[index].y - cubic[zero].y;
+    double dx = cubic[index].x - cubic[zero].x;
+    if (approximately_equal(dy, 0)) {
+        if (approximately_equal(dx, 0)) {
+            return false;
+        }
+        memcpy(rotPath, cubic, sizeof(Cubic));
+        return true;
+    }
+    for (int index = 0; index < 4; ++index) {
+        rotPath[index].x = cubic[index].x * dx + cubic[index].y * dy;
+        rotPath[index].y = cubic[index].y * dx - cubic[index].x * dy;
+    }
+    return true;
+}
+
+double secondDerivativeAtT(const double* cubic, double t) {
+    double a = cubic[0];
+    double b = cubic[2];
+    double c = cubic[4];
+    double d = cubic[6];
+    return (c - 2 * b + a) * (1 - t) + (d - 2 * c + b) * t;
+}
+
+void xy_at_t(const Cubic& cubic, double t, double& x, double& y) {
+    double one_t = 1 - t;
+    double one_t2 = one_t * one_t;
+    double a = one_t2 * one_t;
+    double b = 3 * one_t2 * t;
+    double t2 = t * t;
+    double c = 3 * one_t * t2;
+    double d = t2 * t;
+    if (&x) {
+        x = a * cubic[0].x + b * cubic[1].x + c * cubic[2].x + d * cubic[3].x;
+    }
+    if (&y) {
+        y = a * cubic[0].y + b * cubic[1].y + c * cubic[2].y + d * cubic[3].y;
+    }
+}
diff --git a/experimental/Intersection/CubicUtilities.h b/experimental/Intersection/CubicUtilities.h
index 7a99c95218..94255ee46c 100644
--- a/experimental/Intersection/CubicUtilities.h
+++ b/experimental/Intersection/CubicUtilities.h
@@ -1,3 +1,12 @@
+#include "DataTypes.h"
+
 double cube_root(double x);
 void coefficients(const double* cubic, double& A, double& B, double& C, double& D);
 int cubicRoots(double A, double B, double C, double D, double t[3]);
+double derivativeAtT(const double* cubic, double t);
+// competing version that should produce same results
+double derivativeAtT_2(const double* cubic, double t);
+void dxdy_at_t(const Cubic& , double t, double& x, double& y);
+bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath);
+double secondDerivativeAtT(const double* cubic, double t);
+void xy_at_t(const Cubic& , double t, double& x, double& y);
diff --git a/experimental/Intersection/CurveUtilities.h b/experimental/Intersection/CurveUtilities.h
new file mode 100644
index 0000000000..4d346327eb
--- /dev/null
+++ b/experimental/Intersection/CurveUtilities.h
@@ -0,0 +1,15 @@
+/*
+ * Copyright 2012 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+#ifndef CurveUtilities_DEFINE
+#define CurveUtilities_DEFINE
+
+#include "CubicUtilities.h"
+#include "LineUtilities.h"
+#include "QuadraticUtilities.h"
+
+#endif
diff --git a/experimental/Intersection/DataTypes.cpp b/experimental/Intersection/DataTypes.cpp
index d4ce962c83..db153f6f9a 100644
--- a/experimental/Intersection/DataTypes.cpp
+++ b/experimental/Intersection/DataTypes.cpp
@@ -21,115 +21,6 @@ const double SquaredEpsilon = PointEpsilon * PointEpsilon;
 
 const int UlpsEpsilon = 16;
 
-bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath) {
-    double dy = cubic[index].y - cubic[zero].y;
-    double dx = cubic[index].x - cubic[zero].x;
-    if (approximately_equal(dy, 0)) {
-        if (approximately_equal(dx, 0)) {
-            return false;
-        }
-        memcpy(rotPath, cubic, sizeof(Cubic));
-        return true;
-    }
-    for (int index = 0; index < 4; ++index) {
-        rotPath[index].x = cubic[index].x * dx + cubic[index].y * dy;
-        rotPath[index].y = cubic[index].y * dx - cubic[index].x * dy;
-    }
-    return true;
-}
-
-double t_at(const _Line& line, const _Point& pt) {
-    double dx = line[1].x - line[0].x;
-    double dy = line[1].y - line[0].y;
-    if (fabs(dx) > fabs(dy)) {
-        if (approximately_zero(dx)) {
-            return 0;
-        }
-        return (pt.x - line[0].x) / dx;
-    }
-    if (approximately_zero(dy)) {
-        return 0;
-    }
-    return (pt.y - line[0].y) / dy;
-}
-
-static void setMinMax(double x, int flags, double& minX, double& maxX) {
-    if (minX > x && (flags & (kFindTopMin | kFindBottomMin))) {
-        minX = x;
-    }
-    if (maxX < x && (flags & (kFindTopMax | kFindBottomMax))) {
-        maxX = x;
-    }
-}
-
-void x_at(const _Point& p1, const _Point& p2, double top, double bottom,
-        int flags, double& minX, double& maxX) {
-    if (approximately_equal(p1.y, p2.y)) {
-        // It should be OK to bail early in this case. There's another edge
-        // which shares this end point which can intersect without failing to 
-        // have a slope ... maybe
-        return;
-    }
-    
-    // p2.x is always greater than p1.x -- the part of points (p1, p2) are
-    // moving from the start of the cubic towards its end.
-    // if p1.y < p2.y, minX can be affected
-    // if p1.y > p2.y, maxX can be affected 
-    double slope = (p2.x - p1.x) / (p2.y - p1.y);
-    int topFlags = flags & (kFindTopMin | kFindTopMax);
-    if (topFlags && (top <= p1.y && top >= p2.y
-            || top >= p1.y && top <= p2.y)) {
-        double x = p1.x + (top - p1.y) * slope;
-        setMinMax(x, topFlags, minX, maxX);
-    }
-    int bottomFlags = flags & (kFindBottomMin | kFindBottomMax);
-    if (bottomFlags && (bottom <= p1.y && bottom >= p2.y
-            || bottom >= p1.y && bottom <= p2.y)) {
-        double x = p1.x + (bottom - p1.y) * slope;
-        setMinMax(x, bottomFlags, minX, maxX);
-    }
-}
-
-void xy_at_t(const Cubic& cubic, double t, double& x, double& y) {
-    double one_t = 1 - t;
-    double one_t2 = one_t * one_t;
-    double a = one_t2 * one_t;
-    double b = 3 * one_t2 * t;
-    double t2 = t * t;
-    double c = 3 * one_t * t2;
-    double d = t2 * t;
-    if (&x) {
-        x = a * cubic[0].x + b * cubic[1].x + c * cubic[2].x + d * cubic[3].x;
-    }
-    if (&y) {
-        y = a * cubic[0].y + b * cubic[1].y + c * cubic[2].y + d * cubic[3].y;
-    }
-}
-
-void xy_at_t(const _Line& line, double t, double& x, double& y) {
-    double one_t = 1 - t;
-    if (&x) {
-        x = one_t * line[0].x + t * line[1].x;
-    }
-    if (&y) {
-        y = one_t * line[0].y + t * line[1].y;
-    }
-}
-
-void xy_at_t(const Quadratic& quad, double t, double& x, double& y) {
-    double one_t = 1 - t;
-    double a = one_t * one_t;
-    double b = 2 * one_t * t;
-    double c = t * t;
-    if (&x) {
-        x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
-    }
-    if (&y) {
-        y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
-    }
-}
-
-
 // from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
 union Float_t
 {
diff --git a/experimental/Intersection/DataTypes.h b/experimental/Intersection/DataTypes.h
index 8b7ff7fb30..6218a65702 100644
--- a/experimental/Intersection/DataTypes.h
+++ b/experimental/Intersection/DataTypes.h
@@ -168,20 +168,4 @@ struct QuadraticPair {
     _Point pts[5];
 };
 
-enum x_at_flags {
-    kFindTopMin = 1,
-    kFindTopMax = 2,
-    kFindBottomMin = 4,
-    kFindBottomMax = 8
-};
-
-bool rotate(const Cubic& cubic, int zero, int index, Cubic& rotPath);
-double t_at(const _Line&, const _Point& );
-void x_at(const _Point& p1, const _Point& p2, double minY, double maxY,
-        int flags, double& tMin, double& tMax);
-void xy_at_t(const Cubic& , double t, double& x, double& y);
-void xy_at_t(const _Line& , double t, double& x, double& y);
-void xy_at_t(const Quadratic& , double t, double& x, double& y);
-
-
 #endif // __DataTypes_h__
diff --git a/experimental/Intersection/EdgeWalker.cpp b/experimental/Intersection/EdgeWalker.cpp
index e74689fb41..0f624b5633 100644
--- a/experimental/Intersection/EdgeWalker.cpp
+++ b/experimental/Intersection/EdgeWalker.cpp
@@ -5,15 +5,7 @@
  * found in the LICENSE file.
  */
 
-#include "CurveIntersection.h"
-#include "Intersections.h"
-#include "LineIntersection.h"
-#include "SkPath.h"
-#include "SkRect.h"
-#include "SkTArray.h"
-#include "SkTDArray.h"
-#include "ShapeOps.h"
-#include "TSearch.h"
+#include "Simplify.h"
 
 #undef SkASSERT
 #define SkASSERT(cond) while (!(cond)) { sk_throw(); }
diff --git a/experimental/Intersection/EdgeWalker_Test.h b/experimental/Intersection/EdgeWalker_Test.h
index e8215a369f..b35da6d351 100644
--- a/experimental/Intersection/EdgeWalker_Test.h
+++ b/experimental/Intersection/EdgeWalker_Test.h
@@ -15,6 +15,9 @@ extern bool drawAsciiPaths(const SkPath& one, const SkPath& two,
 extern void showPath(const SkPath& path, const char* str = NULL);
 extern bool testSimplify(const SkPath& path, bool fill, SkPath& out,
         SkBitmap& bitmap, SkCanvas* canvas = 0);
+extern bool testSimplifyx(const SkPath& path, SkPath& out,
+        SkBitmap& bitmap, SkCanvas* canvas = 0);
+extern bool testSimplifyx(const SkPath& path);
 
 struct State4 {
     State4();
diff --git a/experimental/Intersection/EdgeWalker_TestUtility.cpp b/experimental/Intersection/EdgeWalker_TestUtility.cpp
index 2a29648a25..7e65e8f032 100644
--- a/experimental/Intersection/EdgeWalker_TestUtility.cpp
+++ b/experimental/Intersection/EdgeWalker_TestUtility.cpp
@@ -60,7 +60,7 @@ static int pathsDrawTheSame(const SkPath& one, const SkPath& two,
     int bitWidth = SkScalarCeil(larger.width()) + 2;
     int bitHeight = SkScalarCeil(larger.height()) + 2;
     if (bits.width() < bitWidth * 2 || bits.height() < bitHeight) {
-        if (bits.width() >= 200) {
+        if (bits.width() >= 200 && false) {
             SkDebugf("%s bitWidth=%d bitHeight=%d\n", __FUNCTION__, bitWidth, bitHeight);
         }
         bits.setConfig(SkBitmap::kARGB_8888_Config, bitWidth * 2, bitHeight);
@@ -192,10 +192,10 @@ int comparePaths(const SkPath& one, const SkPath& two, SkBitmap& bitmap,
         const SkRect& bounds2 = two.getBounds();
         SkRect larger = bounds1;
         larger.join(bounds2);
-        SkScalar xScale = std::max(80.0f / larger.width(), 1.0f);
-        SkScalar yScale = std::max(60.0f / larger.height(), 1.0f);
+        SkScalar xScale = std::max(32.0f / larger.width(), 1.0f);
+        SkScalar yScale = std::max(24.0f / larger.height(), 1.0f);
         errors = scaledDrawTheSame(one, two, xScale, yScale, false, bitmap, canvas);
-        if (errors > 50) {
+        if (errors > 5) {
             scaledDrawTheSame(one, two, xScale, yScale, true, bitmap, canvas);
         }
     }
@@ -203,7 +203,7 @@ int comparePaths(const SkPath& one, const SkPath& two, SkBitmap& bitmap,
         SkDebugf("\n%s errors=%d\n", __FUNCTION__, errors); 
         max = errors;
     }
-    const int MAX_ERRORS = 100;
+    const int MAX_ERRORS = 20;
     if (errors > MAX_ERRORS) SkDebugf("\n%s errors=%d\n", __FUNCTION__, errors); 
     if (errors > MAX_ERRORS && gComparePathsAssert) {
         showPath(one);
@@ -256,6 +256,31 @@ bool testSimplify(const SkPath& path, bool fill, SkPath& out, SkBitmap& bitmap,
     return comparePaths(path, out, bitmap, canvas) == 0;
 }
 
+bool testSimplifyx(const SkPath& path, SkPath& out, SkBitmap& bitmap,
+        SkCanvas* canvas) {
+    if (gShowPath) {
+        showPath(path);
+    }
+    simplifyx(path, out);
+    if (!gComparePaths) {
+        return true;
+    }
+    return comparePaths(path, out, bitmap, canvas) == 0;
+}
+
+bool testSimplifyx(const SkPath& path) {
+    if (false) {
+        showPath(path);
+    }
+    SkPath out;
+    simplifyx(path, out);
+    if (false) {
+        return true;
+    }
+    SkBitmap bitmap;
+    return comparePaths(path, out, bitmap, 0) == 0;
+}
+
 State4::State4() {
     bitmap.setConfig(SkBitmap::kARGB_8888_Config, 150 * 2, 100);
     bitmap.allocPixels();
diff --git a/experimental/Intersection/Intersection_Tests.cpp b/experimental/Intersection/Intersection_Tests.cpp
index e0b07f9029..017f1d1478 100644
--- a/experimental/Intersection/Intersection_Tests.cpp
+++ b/experimental/Intersection/Intersection_Tests.cpp
@@ -2,12 +2,12 @@
 #include "Intersection_Tests.h"
 
 void cubecode_test(int test);
-void testSimplify();
 
 #define TEST_QUADS_FIRST 0
 
 void Intersection_Tests() {
     SimplifyNew_Test();
+    Simplify4x4RectsThreaded_Test();
     SimplifyFindNext_Test();
     SimplifyFindTop_Test();
     SimplifyAngle_Test();
diff --git a/experimental/Intersection/Intersection_Tests.h b/experimental/Intersection/Intersection_Tests.h
index ca7c359bf0..4873bf9845 100644
--- a/experimental/Intersection/Intersection_Tests.h
+++ b/experimental/Intersection/Intersection_Tests.h
@@ -28,6 +28,7 @@ void SimplifyQuadralateralPaths_Test();
 void SimplifyQuadraticPaths_Test();
 void Simplify4x4QuadralateralsThreaded_Test();
 void Simplify4x4QuadraticsThreaded_Test();
+void Simplify4x4RectsThreaded_Test();
 void SimplifyRectangularPaths_Test();
 void QuadraticBezierClip_Test();
 void QuadraticCoincidence_Test();
diff --git a/experimental/Intersection/LineCubicIntersection_Test.cpp b/experimental/Intersection/LineCubicIntersection_Test.cpp
index f05dbd634f..8492b863e3 100644
--- a/experimental/Intersection/LineCubicIntersection_Test.cpp
+++ b/experimental/Intersection/LineCubicIntersection_Test.cpp
@@ -1,7 +1,7 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "Intersection_Tests.h"
 #include "Intersections.h"
-#include "LineUtilities.h"
 #include "TestUtilities.h"
 
 struct lineCubic {
diff --git a/experimental/Intersection/LineIntersection.cpp b/experimental/Intersection/LineIntersection.cpp
index 31e857ed41..3efa240d83 100644
--- a/experimental/Intersection/LineIntersection.cpp
+++ b/experimental/Intersection/LineIntersection.cpp
@@ -39,6 +39,7 @@ int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]
                 aPtr = &a[0].y;
                 bPtr = &b[0].y;
             }
+        #if 0 // sorting edges fails to preserve original direction
             double aMin = aPtr[0];
             double aMax = aPtr[2];
             double bMin = bPtr[0];
@@ -62,6 +63,27 @@ int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]
                 bRange[!bIn] = aMax >= bMax ? 1 : (aMax - bMin) / (bMax - bMin);
             }
             return 1 + ((aRange[0] != aRange[1]) || (bRange[0] != bRange[1]));
+        #else
+            assert(aRange);
+            assert(bRange);
+            double a0 = aPtr[0];
+            double a1 = aPtr[2];
+            double b0 = bPtr[0];
+            double b1 = bPtr[2];
+            double at0 = (a0 - b0) / (a0 - a1);
+            double at1 = (a0 - b1) / (a0 - a1);
+            if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
+                return 0;
+            }
+            aRange[0] = std::max(std::min(at0, 1.0), 0.0);
+            aRange[1] = std::max(std::min(at1, 1.0), 0.0);
+            int bIn = (a0 - a1) * (b0 - b1) < 0;
+            bRange[bIn] = std::max(std::min((b0 - a0) / (b0 - b1), 1.0), 0.0);
+            bRange[!bIn] = std::max(std::min((b0 - a1) / (b0 - b1), 1.0), 0.0);
+            bool second = fabs(aRange[0] - aRange[1]) > FLT_EPSILON;
+            assert((fabs(bRange[0] - bRange[1]) <= FLT_EPSILON) ^ second);
+            return 1 + second;
+        #endif
         }
     }
     double ab0y = a[0].y - b[0].y;
@@ -140,6 +162,7 @@ int horizontalIntersect(const _Line& line, double left, double right,
             break;
         }
         case 2:
+        #if 0 // sorting edges fails to preserve original direction
             double lineL = line[0].x;
             double lineR = line[1].x;
             if (lineL > lineR) {
@@ -159,6 +182,30 @@ int horizontalIntersect(const _Line& line, double left, double right,
                 intersections.fT[0][1] = (overlapR - line[0].x) / (line[1].x - line[0].x);
                 intersections.fT[1][1] = (overlapR - left) / (right - left);
             }
+        #else
+            double a0 = line[0].x;
+            double a1 = line[1].x;
+            double b0 = flipped ? right : left;
+            double b1 = flipped ? left : right;
+            // FIXME: share common code below
+            double at0 = (a0 - b0) / (a0 - a1);
+            double at1 = (a0 - b1) / (a0 - a1);
+            if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
+                return 0;
+            }
+            intersections.fT[0][0] = std::max(std::min(at0, 1.0), 0.0);
+            intersections.fT[0][1] = std::max(std::min(at1, 1.0), 0.0);
+            int bIn = (a0 - a1) * (b0 - b1) < 0;
+            intersections.fT[1][bIn] = std::max(std::min((b0 - a0) / (b0 - b1),
+                    1.0), 0.0);
+            intersections.fT[1][!bIn] = std::max(std::min((b0 - a1) / (b0 - b1),
+                    1.0), 0.0);
+            bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1])
+                    > FLT_EPSILON;
+            assert((fabs(intersections.fT[1][0] - intersections.fT[1][1])
+                    <= FLT_EPSILON) ^ second);
+            return 1 + second;
+        #endif
             break;
     }
     if (flipped) {
@@ -204,6 +251,7 @@ int verticalIntersect(const _Line& line, double top, double bottom,
             break;
         }
         case 2:
+        #if 0 // sorting edges fails to preserve original direction
             double lineT = line[0].y;
             double lineB = line[1].y;
             if (lineT > lineB) {
@@ -223,6 +271,30 @@ int verticalIntersect(const _Line& line, double top, double bottom,
                 intersections.fT[0][1] = (overlapB - line[0].y) / (line[1].y - line[0].y);
                 intersections.fT[1][1] = (overlapB - top) / (bottom - top);
             }
+        #else
+            double a0 = line[0].y;
+            double a1 = line[1].y;
+            double b0 = flipped ? bottom : top;
+            double b1 = flipped ? top : bottom;
+            // FIXME: share common code above
+            double at0 = (a0 - b0) / (a0 - a1);
+            double at1 = (a0 - b1) / (a0 - a1);
+            if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
+                return 0;
+            }
+            intersections.fT[0][0] = std::max(std::min(at0, 1.0), 0.0);
+            intersections.fT[0][1] = std::max(std::min(at1, 1.0), 0.0);
+            int bIn = (a0 - a1) * (b0 - b1) < 0;
+            intersections.fT[1][bIn] = std::max(std::min((b0 - a0) / (b0 - b1),
+                    1.0), 0.0);
+            intersections.fT[1][!bIn] = std::max(std::min((b0 - a1) / (b0 - b1),
+                    1.0), 0.0);
+            bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1])
+                    > FLT_EPSILON;
+            assert((fabs(intersections.fT[1][0] - intersections.fT[1][1])
+                    <= FLT_EPSILON) ^ second);
+            return 1 + second;
+        #endif
             break;
     }
     if (flipped) {
diff --git a/experimental/Intersection/LineIntersection_Test.cpp b/experimental/Intersection/LineIntersection_Test.cpp
index 04b55be884..c73c9b3f7c 100644
--- a/experimental/Intersection/LineIntersection_Test.cpp
+++ b/experimental/Intersection/LineIntersection_Test.cpp
@@ -1,3 +1,4 @@
+#include "CurveUtilities.h"
 #include "Intersection_Tests.h"
 #include "LineIntersection.h"
 
diff --git a/experimental/Intersection/LineQuadraticIntersection_Test.cpp b/experimental/Intersection/LineQuadraticIntersection_Test.cpp
index a48f0af128..7551dc3df2 100644
--- a/experimental/Intersection/LineQuadraticIntersection_Test.cpp
+++ b/experimental/Intersection/LineQuadraticIntersection_Test.cpp
@@ -1,7 +1,7 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "Intersection_Tests.h"
 #include "Intersections.h"
-#include "LineUtilities.h"
 #include "TestUtilities.h"
 
 struct lineQuad {
diff --git a/experimental/Intersection/LineUtilities.cpp b/experimental/Intersection/LineUtilities.cpp
index ca94544a13..8a1c0d7c62 100644
--- a/experimental/Intersection/LineUtilities.cpp
+++ b/experimental/Intersection/LineUtilities.cpp
@@ -58,3 +58,64 @@ float isLeft( _Point P0, _Point P1, _Point P2 )
 }
 #endif
 
+double t_at(const _Line& line, const _Point& pt) {
+    double dx = line[1].x - line[0].x;
+    double dy = line[1].y - line[0].y;
+    if (fabs(dx) > fabs(dy)) {
+        if (approximately_zero(dx)) {
+            return 0;
+        }
+        return (pt.x - line[0].x) / dx;
+    }
+    if (approximately_zero(dy)) {
+        return 0;
+    }
+    return (pt.y - line[0].y) / dy;
+}
+
+static void setMinMax(double x, int flags, double& minX, double& maxX) {
+    if (minX > x && (flags & (kFindTopMin | kFindBottomMin))) {
+        minX = x;
+    }
+    if (maxX < x && (flags & (kFindTopMax | kFindBottomMax))) {
+        maxX = x;
+    }
+}
+
+void x_at(const _Point& p1, const _Point& p2, double top, double bottom,
+        int flags, double& minX, double& maxX) {
+    if (approximately_equal(p1.y, p2.y)) {
+        // It should be OK to bail early in this case. There's another edge
+        // which shares this end point which can intersect without failing to 
+        // have a slope ... maybe
+        return;
+    }
+    
+    // p2.x is always greater than p1.x -- the part of points (p1, p2) are
+    // moving from the start of the cubic towards its end.
+    // if p1.y < p2.y, minX can be affected
+    // if p1.y > p2.y, maxX can be affected 
+    double slope = (p2.x - p1.x) / (p2.y - p1.y);
+    int topFlags = flags & (kFindTopMin | kFindTopMax);
+    if (topFlags && (top <= p1.y && top >= p2.y
+            || top >= p1.y && top <= p2.y)) {
+        double x = p1.x + (top - p1.y) * slope;
+        setMinMax(x, topFlags, minX, maxX);
+    }
+    int bottomFlags = flags & (kFindBottomMin | kFindBottomMax);
+    if (bottomFlags && (bottom <= p1.y && bottom >= p2.y
+            || bottom >= p1.y && bottom <= p2.y)) {
+        double x = p1.x + (bottom - p1.y) * slope;
+        setMinMax(x, bottomFlags, minX, maxX);
+    }
+}
+
+void xy_at_t(const _Line& line, double t, double& x, double& y) {
+    double one_t = 1 - t;
+    if (&x) {
+        x = one_t * line[0].x + t * line[1].x;
+    }
+    if (&y) {
+        y = one_t * line[0].y + t * line[1].y;
+    }
+}
diff --git a/experimental/Intersection/LineUtilities.h b/experimental/Intersection/LineUtilities.h
index 4dafc9fdcc..fc55a741aa 100644
--- a/experimental/Intersection/LineUtilities.h
+++ b/experimental/Intersection/LineUtilities.h
@@ -2,3 +2,17 @@
 
 bool implicitLine(const _Line& line, double& slope, double& axisIntercept);
 int reduceOrder(const _Line& line, _Line& reduced);
+
+double t_at(const _Line&, const _Point& );
+void xy_at_t(const _Line& , double t, double& x, double& y);
+
+enum x_at_flags {
+    kFindTopMin = 1,
+    kFindTopMax = 2,
+    kFindBottomMin = 4,
+    kFindBottomMax = 8
+};
+
+void x_at(const _Point& p1, const _Point& p2, double minY, double maxY,
+        int flags, double& tMin, double& tMax);
+
diff --git a/experimental/Intersection/QuadraticBezierClip.cpp b/experimental/Intersection/QuadraticBezierClip.cpp
index d9d984d5dd..e27db7c7eb 100644
--- a/experimental/Intersection/QuadraticBezierClip.cpp
+++ b/experimental/Intersection/QuadraticBezierClip.cpp
@@ -1,4 +1,5 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "LineParameters.h"
 #include <algorithm> // used for std::swap
 
diff --git a/experimental/Intersection/QuadraticBounds.cpp b/experimental/Intersection/QuadraticBounds.cpp
index 813fccc67e..27c170e808 100644
--- a/experimental/Intersection/QuadraticBounds.cpp
+++ b/experimental/Intersection/QuadraticBounds.cpp
@@ -1,4 +1,5 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "Extrema.h"
 
 static int isBoundedByEndPoints(double a, double b, double c)
diff --git a/experimental/Intersection/QuadraticIntersection_Test.cpp b/experimental/Intersection/QuadraticIntersection_Test.cpp
index adf91bde86..7aeb580335 100644
--- a/experimental/Intersection/QuadraticIntersection_Test.cpp
+++ b/experimental/Intersection/QuadraticIntersection_Test.cpp
@@ -1,4 +1,5 @@
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "Intersection_Tests.h"
 #include "Intersections.h"
 #include "QuadraticIntersection_TestData.h"
diff --git a/experimental/Intersection/QuadraticUtilities.cpp b/experimental/Intersection/QuadraticUtilities.cpp
index 4b4d79417e..4b695df7b6 100644
--- a/experimental/Intersection/QuadraticUtilities.cpp
+++ b/experimental/Intersection/QuadraticUtilities.cpp
@@ -25,3 +25,28 @@ int quadraticRoots(double A, double B, double C, double t[2]) {
     }
     return foundRoots;
 }
+
+void dxdy_at_t(const Quadratic& quad, double t, double& x, double& y) {
+    double a = t - 1;
+    double b = 1 - 2 * t;
+    double c = t;
+    if (&x) {
+        x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
+    }
+    if (&y) {
+        y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
+    }
+}
+
+void xy_at_t(const Quadratic& quad, double t, double& x, double& y) {
+    double one_t = 1 - t;
+    double a = one_t * one_t;
+    double b = 2 * one_t * t;
+    double c = t * t;
+    if (&x) {
+        x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
+    }
+    if (&y) {
+        y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
+    }
+}
diff --git a/experimental/Intersection/QuadraticUtilities.h b/experimental/Intersection/QuadraticUtilities.h
index 2b7e34a2a2..7ac48e5f8a 100644
--- a/experimental/Intersection/QuadraticUtilities.h
+++ b/experimental/Intersection/QuadraticUtilities.h
@@ -1,3 +1,7 @@
+#include "DataTypes.h"
+
+void dxdy_at_t(const Quadratic& , double t, double& x, double& y);
+
 /* Parameterization form, given A*t*t + 2*B*t*(1-t) + C*(1-t)*(1-t)
  *
  * a = A - 2*B +   C
@@ -14,3 +18,5 @@ inline void set_abc(const double* quad, double& a, double& b, double& c) {
 }
 
 int quadraticRoots(double A, double B, double C, double t[2]);
+
+void xy_at_t(const Quadratic& , double t, double& x, double& y);
diff --git a/experimental/Intersection/RectUtilities.cpp b/experimental/Intersection/RectUtilities.cpp
deleted file mode 100644
index e69de29bb2..0000000000
--- a/experimental/Intersection/RectUtilities.cpp
+++ /dev/null
diff --git a/experimental/Intersection/Simplify.cpp b/experimental/Intersection/Simplify.cpp
index b57acf341d..23a0a3dc62 100644
--- a/experimental/Intersection/Simplify.cpp
+++ b/experimental/Intersection/Simplify.cpp
@@ -25,9 +25,12 @@
 
 #define DEBUG_ADD_INTERSECTING_TS 0
 #define DEBUG_BRIDGE 0
+#define DEBUG_CROSS 0
 #define DEBUG_DUMP 0
 #define DEBUG_PATH_CONSTRUCTION 0
+#define DEBUG_WINDING 0
 #define DEBUG_UNUSED 0 // set to expose unused functions
+#define DEBUG_MARK_DONE 0
 
 #else
 
@@ -35,9 +38,12 @@
 
 #define DEBUG_ADD_INTERSECTING_TS 0
 #define DEBUG_BRIDGE 1
+#define DEBUG_CROSS 1
 #define DEBUG_DUMP 1
 #define DEBUG_PATH_CONSTRUCTION 1
+#define DEBUG_WINDING 0
 #define DEBUG_UNUSED 0 // set to expose unused functions
+#define DEBUG_MARK_DONE 01
 
 #endif
 
@@ -48,6 +54,10 @@ static int gContourID;
 static int gSegmentID;
 #endif
 
+#ifndef DEBUG_TEST
+#define DEBUG_TEST 0
+#endif
+
 static int LineIntersect(const SkPoint a[2], const SkPoint b[2],
         Intersections& intersections) {
     const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
@@ -95,24 +105,12 @@ static int HLineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
     return horizontalIntersect(aLine, left, right, y, flipped, intersections);
 }
 
-static int VLineIntersect(const SkPoint a[2], SkScalar left, SkScalar right,
-        SkScalar y, bool flipped, Intersections& intersections) {
-    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
-    return verticalIntersect(aLine, left, right, y, flipped, intersections);
-}
-
 static int HQuadIntersect(const SkPoint a[3], SkScalar left, SkScalar right,
         SkScalar y, bool flipped, Intersections& intersections) {
     const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
     return horizontalIntersect(aQuad, left, right, y, flipped, intersections);
 }
 
-static int VQuadIntersect(const SkPoint a[3], SkScalar left, SkScalar right,
-        SkScalar y, bool flipped, Intersections& intersections) {
-    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
-    return verticalIntersect(aQuad, left, right, y, flipped, intersections);
-}
-
 static int HCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
         SkScalar y, bool flipped, Intersections& intersections) {
     const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
@@ -120,13 +118,33 @@ static int HCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
     return horizontalIntersect(aCubic, left, right, y, flipped, intersections);
 }
 
-static int VCubicIntersect(const SkPoint a[4], SkScalar left, SkScalar right,
-        SkScalar y, bool flipped, Intersections& intersections) {
+static int VLineIntersect(const SkPoint a[2], SkScalar top, SkScalar bottom,
+        SkScalar x, bool flipped, Intersections& intersections) {
+    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
+    return verticalIntersect(aLine, top, bottom, x, flipped, intersections);
+}
+
+static int VQuadIntersect(const SkPoint a[3], SkScalar top, SkScalar bottom,
+        SkScalar x, bool flipped, Intersections& intersections) {
+    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
+    return verticalIntersect(aQuad, top, bottom, x, flipped, intersections);
+}
+
+static int VCubicIntersect(const SkPoint a[4], SkScalar top, SkScalar bottom,
+        SkScalar x, bool flipped, Intersections& intersections) {
     const Cubic aCubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
             {a[3].fX, a[3].fY}};
-    return verticalIntersect(aCubic, left, right, y, flipped, intersections);
+    return verticalIntersect(aCubic, top, bottom, x, flipped, intersections);
 }
 
+static int (* const VSegmentIntersect[])(const SkPoint [], SkScalar ,
+        SkScalar , SkScalar , bool , Intersections& ) = {
+    NULL,
+    VLineIntersect,
+    VQuadIntersect,
+    VCubicIntersect
+};
+
 static void LineXYAtT(const SkPoint a[2], double t, SkPoint* out) {
     const _Line line = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
     double x, y;
@@ -217,6 +235,32 @@ static SkScalar (* const SegmentYAtT[])(const SkPoint [], double ) = {
     CubicYAtT
 };
 
+static SkScalar LineDXAtT(const SkPoint a[2], double ) {
+    return a[1].fX - a[0].fX;
+}
+
+static SkScalar QuadDXAtT(const SkPoint a[3], double t) {
+    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
+    double x;
+    dxdy_at_t(quad, t, x, *(double*) 0);
+    return SkDoubleToScalar(x);
+}
+
+static SkScalar CubicDXAtT(const SkPoint a[4], double t) {
+    const Cubic cubic = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY},
+            {a[3].fX, a[3].fY}};
+    double x;
+    dxdy_at_t(cubic, t, x, *(double*) 0);
+    return SkDoubleToScalar(x);
+}
+
+static SkScalar (* const SegmentDXAtT[])(const SkPoint [], double ) = {
+    NULL,
+    LineDXAtT,
+    QuadDXAtT,
+    CubicDXAtT
+};
+
 static void LineSubDivide(const SkPoint a[2], double startT, double endT,
         SkPoint sub[2]) {
     const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
@@ -416,6 +460,10 @@ public:
         return fDDDx * rh.fDDDy < rh.fDDDx * fDDDy;
     }
 
+    bool cancels(const Angle& rh) const {
+        return fDx * rh.fDx < 0 || fDy * rh.fDy < 0;
+    }
+
     int end() const {
         return fEnd;
     }
@@ -427,7 +475,7 @@ public:
     // since all angles share a point, this needs to know which point
     // is the common origin, i.e., whether the center is at pts[0] or pts[verb]
     // practically, this should only be called by addAngle
-    void set(const SkPoint* pts, SkPath::Verb verb, Segment* segment,
+    void set(const SkPoint* pts, SkPath::Verb verb, const Segment* segment,
             int start, int end) {
         SkASSERT(start != end);
         fSegment = segment;
@@ -498,18 +546,13 @@ public:
     }
     
     Segment* segment() const {
-        return fSegment;
+        return const_cast<Segment*>(fSegment);
     }
     
     int sign() const {
         return SkSign32(fStart - fEnd);
     }
     
-    bool slopeEquals(const Angle& rh) const {
-        return fDx == rh.fDx && fDy == rh.fDy;
-
-    }
-
     int start() const {
         return fStart;
     }
@@ -521,7 +564,7 @@ private:
     SkScalar fDDy;
     SkScalar fDDDx;
     SkScalar fDDDy;
-    Segment* fSegment;
+    const Segment* fSegment;
     int fStart;
     int fEnd;
 };
@@ -536,13 +579,32 @@ static void sortAngles(SkTDArray<Angle>& angles, SkTDArray<Angle*>& angleList) {
     QSort<Angle>(angleList.begin(), angleList.end() - 1);
 }
 
-// Bounds, unlike Rect, does not consider a vertical line to be empty.
+// Bounds, unlike Rect, does not consider a line to be empty.
 struct Bounds : public SkRect {
     static bool Intersects(const Bounds& a, const Bounds& b) {
         return a.fLeft <= b.fRight && b.fLeft <= a.fRight &&
                 a.fTop <= b.fBottom && b.fTop <= a.fBottom;
     }
 
+    void add(SkScalar left, SkScalar top, SkScalar right, SkScalar bottom) {
+        if (left < fLeft) {
+            fLeft = left;
+        }
+        if (top < fTop) {
+            fTop = top;
+        }
+        if (right > fRight) {
+            fRight = right;
+        }
+        if (bottom > fBottom) {
+            fBottom = bottom;
+        }
+    }
+
+    void add(const Bounds& toAdd) {
+        add(toAdd.fLeft, toAdd.fTop, toAdd.fRight, toAdd.fBottom);
+    }
+
     bool isEmpty() {
         return fLeft > fRight || fTop > fBottom
                 || fLeft == fRight && fTop == fBottom
@@ -570,14 +632,13 @@ struct Bounds : public SkRect {
 };
 
 struct Span {
-    double fT;
     Segment* fOther;
+    mutable SkPoint const* fPt; // lazily computed as needed
+    double fT;
     double fOtherT; // value at fOther[fOtherIndex].fT
-    mutable SkPoint const * fPt; // lazily computed as needed
     int fOtherIndex;  // can't be used during intersection
-    int fWinding; // accumulated from contours surrounding this one
-    // OPTIMIZATION: coincident needs only 2 bits (values are -1, 0, 1)
-    int fCoincident; // -1 start of coincidence, 0 no coincidence, 1 end
+    int fWindSum; // accumulated from contours surrounding this one
+    int fWindValue; // 0 == canceled; 1 == normal; >1 == coincident
     bool fDone; // if set, this span to next higher T has been processed
 };
 
@@ -589,7 +650,26 @@ public:
 #endif
     }
     
-    void addAngle(SkTDArray<Angle>& angles, int start, int end) {
+    SkScalar activeTop() const {
+        SkASSERT(!done());
+        int count = fTs.count();
+        SkScalar result = SK_ScalarMax;
+        bool lastDone = true;
+        for (int index = 0; index < count; ++index) {
+            bool done = fTs[index].fDone;
+            if (!done || !lastDone) {
+                SkScalar y = yAtT(index);
+                if (result > y) {
+                    result = y;
+                }
+            }
+            lastDone = done;
+        }
+        SkASSERT(result < SK_ScalarMax);
+        return result;
+    }
+
+    void addAngle(SkTDArray<Angle>& angles, int start, int end) const {
         SkASSERT(start != end);
         SkPoint edge[4];
         (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
@@ -603,31 +683,34 @@ public:
     }
 
     // FIXME: this needs to defer add for aligned consecutive line segments
-    SkPoint addCurveTo(int start, int end, SkPath& path) {
+    SkPoint addCurveTo(int start, int end, SkPath& path, bool active) {
         SkPoint edge[4];
+        // OPTIMIZE? if not active, skip remainder and return xy_at_t(end)
         (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
+        if (active) {
     #if DEBUG_PATH_CONSTRUCTION
-        SkDebugf("%s %s (%1.9g,%1.9g)", __FUNCTION__,
-                kLVerbStr[fVerb], edge[1].fX, edge[1].fY);
-        if (fVerb > 1) {
-            SkDebugf(" (%1.9g,%1.9g)", edge[2].fX, edge[2].fY);
-        }
-        if (fVerb > 2) {
-            SkDebugf(" (%1.9g,%1.9g)", edge[3].fX, edge[3].fY);
-        }
-        SkDebugf("\n");
+            SkDebugf("%s %s (%1.9g,%1.9g)", __FUNCTION__,
+                    kLVerbStr[fVerb], edge[1].fX, edge[1].fY);
+            if (fVerb > 1) {
+                SkDebugf(" (%1.9g,%1.9g)", edge[2].fX, edge[2].fY);
+            }
+            if (fVerb > 2) {
+                SkDebugf(" (%1.9g,%1.9g)", edge[3].fX, edge[3].fY);
+            }
+            SkDebugf("\n");
     #endif
-        switch (fVerb) {
-            case SkPath::kLine_Verb:
-                path.lineTo(edge[1].fX, edge[1].fY);
-                break;
-            case SkPath::kQuad_Verb:
-                path.quadTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY);
-                break;
-            case SkPath::kCubic_Verb:
-                path.cubicTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY,
-                        edge[3].fX, edge[3].fY);
-                break;
+            switch (fVerb) {
+                case SkPath::kLine_Verb:
+                    path.lineTo(edge[1].fX, edge[1].fY);
+                    break;
+                case SkPath::kQuad_Verb:
+                    path.quadTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY);
+                    break;
+                case SkPath::kCubic_Verb:
+                    path.cubicTo(edge[1].fX, edge[1].fY, edge[2].fX, edge[2].fY,
+                            edge[3].fX, edge[3].fY);
+                    break;
+            }
         }
         return edge[fVerb];
     }
@@ -637,12 +720,14 @@ public:
         fBounds.set(pts, 2);
     }
 
-    const SkPoint& addMoveTo(int tIndex, SkPath& path) {
-        const SkPoint& pt = xyAtT(&fTs[tIndex]);
+    const SkPoint& addMoveTo(int tIndex, SkPath& path, bool active) {
+        const SkPoint& pt = xyAtT(tIndex);
+        if (active) {
     #if DEBUG_PATH_CONSTRUCTION
-        SkDebugf("%s (%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY);
+            SkDebugf("%s (%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY);
     #endif
-        path.moveTo(pt.fX, pt.fY);
+            path.moveTo(pt.fX, pt.fY);
+        }
         return pt;
     }
 
@@ -657,50 +742,233 @@ public:
         init(pts, SkPath::kQuad_Verb);
         fBounds.setQuadBounds(pts);
     }
+    
+    // Defer all coincident edge processing until
+    // after normal intersections have been computed
+
+// no need to be tricky; insert in normal T order
+// resolve overlapping ts when considering coincidence later
 
-    // edges are sorted by T, then by coincidence
-    int addT(double newT, Segment& other, int coincident) {
+    // add non-coincident intersection. Resulting edges are sorted in T.
+    int addT(double newT, Segment* other) {
         // FIXME: in the pathological case where there is a ton of intercepts,
         //  binary search?
         int insertedAt = -1;
-        Span* span;
         size_t tCount = fTs.count();
-        for (size_t idx2 = 0; idx2 < tCount; ++idx2) {
+        for (size_t index = 0; index < tCount; ++index) {
             // OPTIMIZATION: if there are three or more identical Ts, then
             // the fourth and following could be further insertion-sorted so
             // that all the edges are clockwise or counterclockwise.
             // This could later limit segment tests to the two adjacent
             // neighbors, although it doesn't help with determining which
             // circular direction to go in.
-            if (newT < fTs[idx2].fT || (newT == fTs[idx2].fT && 
-                    coincident <= fTs[idx2].fCoincident)) {
-                insertedAt = idx2;
-                span = fTs.insert(idx2);
-                goto finish;
+            if (newT < fTs[index].fT) {
+                insertedAt = index;
+                break;
             }
         }
-        insertedAt = tCount;
-        span = fTs.append();
-finish:
+        Span* span;
+        if (insertedAt >= 0) {
+            span = fTs.insert(insertedAt);
+        } else {
+            insertedAt = tCount;
+            span = fTs.append();
+        }
         span->fT = newT;
-        span->fOther = &other;
+        span->fOther = other;
         span->fPt = NULL;
-        span->fWinding = 0;
-        if (span->fDone = newT == 1) {
+        span->fWindSum = SK_MinS32;
+        span->fWindValue = 1;
+        if ((span->fDone = newT == 1)) {
             ++fDoneSpans;
         } 
-        span->fCoincident = coincident;
-        fCoincident |= coincident; // OPTIMIZATION: ever used?
         return insertedAt;
     }
 
-    void addTwoAngles(int start, int end, SkTDArray<Angle>& angles) {
+    // set spans from start to end to decrement by one
+    // note this walks other backwards
+    // FIMXE: there's probably an edge case that can be constructed where
+    // two span in one segment are separated by float epsilon on one span but
+    // not the other, if one segment is very small. For this
+    // case the counts asserted below may or may not be enough to separate the
+    // spans. Even if the counts work out, what if the spanw aren't correctly
+    // sorted? It feels better in such a case to match the span's other span
+    // pointer since both coincident segments must contain the same spans.
+    void addTCancel(double startT, double endT, Segment& other,
+            double oStartT, double oEndT) {
+        SkASSERT(endT - startT >= FLT_EPSILON);
+        SkASSERT(oEndT - oStartT >= FLT_EPSILON);
+        int index = 0;
+        while (startT - fTs[index].fT >= FLT_EPSILON) {
+            ++index;
+        }
+        int oCount = other.fTs.count();
+        while (other.fTs[--oCount].fT - oEndT >= FLT_EPSILON)
+            ;
+        int oIndex = oCount;
+        while (other.fTs[--oIndex].fT - oEndT > -FLT_EPSILON)
+            ;
+        Span* test = &fTs[index];
+        Span* oTest = &other.fTs[oIndex];
+        SkDEBUGCODE(int testWindValue = test->fWindValue);
+        SkDEBUGCODE(int oTestWindValue = oTest->fWindValue);
+        SkDEBUGCODE(int startIndex = index);
+        SkTDArray<double> outsideTs;
+        SkTDArray<double> oOutsideTs;
+        do {
+            bool decrement = test->fWindValue && oTest->fWindValue;
+            Span* end = test;
+            double startT = end->fT;
+            double oStartT = oTest->fT;
+            do {
+                SkASSERT(testWindValue == end->fWindValue);
+                if (decrement) {
+                    if (--(end->fWindValue) == 0) {
+                        end->fDone = true;
+                        ++fDoneSpans;
+                        *outsideTs.append() = end->fT;
+                        *outsideTs.append() = oStartT;
+                    }
+                }
+                end = &fTs[++index];
+            } while (end->fT - test->fT < FLT_EPSILON);
+            SkASSERT(oCount - oIndex == index - startIndex);
+            Span* oTestStart = oTest;
+            SkDEBUGCODE(oCount = oIndex);
+            do {
+                SkASSERT(oTestWindValue == oTestStart->fWindValue);
+                if (decrement) {
+                    if (--(oTestStart->fWindValue) == 0) {
+                        oTestStart->fDone = true;
+                        ++other.fDoneSpans;
+                        *oOutsideTs.append() = oTestStart->fT;
+                        *oOutsideTs.append() = startT;
+                    }
+                }
+                if (!oIndex) {
+                    break;
+                }
+                oTestStart = &other.fTs[--oIndex];
+            } while (oTest->fT - oTestStart->fT < FLT_EPSILON); 
+            test = end;
+            oTest = oTestStart;
+        } while (test->fT < endT - FLT_EPSILON);
+        SkASSERT(!oIndex || oTest->fT <= oStartT - FLT_EPSILON);
+#if 0
+        if (!done() && outsideTs.count()) {
+            addTOutsides(outsideTs, &other, oStartT);
+        }
+        if (!other.done() && oOutsideTs.count()) {
+            other.addTOutsides(oOutsideTs, this, startT);
+        }
+#endif
+    }
+
+    // set spans from start to end to increment the greater by one and decrement
+    // the lesser
+    void addTCoincident(double startT, double endT, Segment& other,
+            double oStartT, double oEndT) {
+        SkASSERT(endT - startT >= FLT_EPSILON);
+        SkASSERT(oEndT - oStartT >= FLT_EPSILON);
+        int index = 0;
+        while (startT - fTs[index].fT >= FLT_EPSILON) {
+            ++index;
+        }
+        int oIndex = 0;
+        while (oStartT - other.fTs[oIndex].fT >= FLT_EPSILON) {
+            ++oIndex;
+        }
+        Span* test = &fTs[index];
+        Span* oTest = &other.fTs[oIndex];
+        SkDEBUGCODE(int testWindValue = test->fWindValue);
+        SkDEBUGCODE(int oTestWindValue = oTest->fWindValue);
+        SkTDArray<double> outsideTs;
+        SkTDArray<double> oOutsideTs;
+        do {
+            bool decrementOther = test->fWindValue >= oTest->fWindValue;
+            Span* end = test;
+            double startT = end->fT;
+            double oStartT = oTest->fT;
+            do {
+                SkASSERT(testWindValue == end->fWindValue);
+                if (decrementOther) {
+                    ++(end->fWindValue);
+                } else {
+                    if (--(end->fWindValue) == 0) {
+                        end->fDone = true;
+                        ++fDoneSpans;
+                        *outsideTs.append() = end->fT;
+                        *outsideTs.append() = oStartT;
+                    }
+                }
+                end = &fTs[++index];
+            } while (end->fT - test->fT < FLT_EPSILON);
+            Span* oEnd = oTest;
+            do {
+                SkASSERT(oTestWindValue == oEnd->fWindValue);
+                if (decrementOther) {
+                    if (--(oEnd->fWindValue) == 0) {
+                        oEnd->fDone = true;
+                        ++other.fDoneSpans;
+                        *oOutsideTs.append() = oEnd->fT;
+                        *oOutsideTs.append() = startT;
+                    }
+                } else {
+                    ++(oEnd->fWindValue);
+                }
+                oEnd = &other.fTs[++oIndex];
+            } while (oEnd->fT - oTest->fT < FLT_EPSILON);
+            test = end;
+            oTest = oEnd;
+        } while (test->fT < endT - FLT_EPSILON);
+        SkASSERT(oTest->fT < oEndT + FLT_EPSILON);
+        SkASSERT(oTest->fT > oEndT - FLT_EPSILON);
+        if (!done() && outsideTs.count()) {
+            addTOutsides(outsideTs, &other, oEndT);
+        }
+        if (!other.done() && oOutsideTs.count()) {
+            other.addTOutsides(oOutsideTs, this, endT);
+        }
+    }
+
+    void addTOutsides(const SkTDArray<double>& outsideTs, Segment* other,
+            double otherEnd) {
+        int count = outsideTs.count();
+        double endT = 0;
+        int endSpan = 0;
+        for (int index = 0; index < count; index += 2) {
+            double t = outsideTs[index];
+            double otherT = outsideTs[index + 1];
+            if (t > 1 - FLT_EPSILON) {
+                return;
+            }
+            if (t - endT > FLT_EPSILON) {
+                endSpan = addTPair(t, other, otherT);
+            }
+            do {
+                endT = fTs[++endSpan].fT;
+            } while (endT - t < FLT_EPSILON);
+        }
+        addTPair(endT, other, otherEnd);
+    }
+    
+    int addTPair(double t, Segment* other, double otherT) {
+        int insertedAt = addT(t, other);
+        int otherInsertedAt = other->addT(otherT, this);
+        addOtherT(insertedAt, otherT, otherInsertedAt);
+        other->addOtherT(otherInsertedAt, t, insertedAt);
+        return insertedAt;
+    }
+
+    void addTwoAngles(int start, int end, SkTDArray<Angle>& angles) const {
         // add edge leading into junction
-        addAngle(angles, end, start);
+        if (fTs[SkMin32(end, start)].fWindValue > 0) {
+            addAngle(angles, end, start);
+        }
         // add edge leading away from junction
         int step = SkSign32(end - start);
         int tIndex = nextSpan(end, step);
-        if (tIndex >= 0) {
+        if (tIndex >= 0 && fTs[SkMin32(end, tIndex)].fWindValue > 0) {
             addAngle(angles, end, tIndex);
         }
     }
@@ -710,15 +978,14 @@ finish:
     }
 
     void buildAngles(int index, SkTDArray<Angle>& angles) const {
-        SkASSERT(!done());
         double referenceT = fTs[index].fT;
         int lesser = index;
-        while (--lesser >= 0 && referenceT == fTs[lesser].fT) {
+        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
             buildAnglesInner(lesser, angles);
         }
         do {
             buildAnglesInner(index, angles);
-        } while (++index < fTs.count() && referenceT == fTs[index].fT);
+        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
     }
 
     void buildAnglesInner(int index, SkTDArray<Angle>& angles) const {
@@ -731,15 +998,22 @@ finish:
         int oIndex = span->fOtherIndex;
         // if done == -1, prior span has already been processed
         int step = 1;
-        int next = other->nextSpanEnd(oIndex, step);
+        int next = other->nextSpan(oIndex, step);
         if (next < 0) {
             step = -step;
-            next = other->nextSpanEnd(oIndex, step);
+            next = other->nextSpan(oIndex, step);
         }
-        oIndex = other->coincidentEnd(oIndex, -step);
         // add candidate into and away from junction
         other->addTwoAngles(next, oIndex, angles);
-    }    
+    }
+
+    // OPTIMIZATION: inefficient, refactor
+    bool cancels(const Segment& other) const {
+        SkTDArray<Angle> angles;
+        addAngle(angles, 0, fTs.count() - 1);
+        other.addAngle(angles, 0, other.fTs.count() - 1);
+        return angles[0].cancels(angles[1]);
+    }
 
     // figure out if the segment's ascending T goes clockwise or not
     // not enough context to write this as shown
@@ -752,45 +1026,41 @@ finish:
         return false;
     }
 
-    static bool Coincident(const Angle* current, const Angle* next) {
-        const Segment* segment = current->segment();
-        const Span& span = segment->fTs[current->start()];
-        if (!span.fCoincident) {
-            return false;
-        }
-        const Segment* nextSegment = next->segment();
-        const Span& nextSpan = nextSegment->fTs[next->start()];
-        if (!nextSpan.fCoincident) {
-            return false;
-        }
-        // use angle dx/dy instead of other since 3 or more may be coincident
-        return current->slopeEquals(*next);
-    }
-
-    static bool CoincidentCancels(const Angle* current, const Angle* next) {
-        return SkSign32(current->start() - current->end())
-                != SkSign32(next->start() - next->end());
-    }
-
-    int coincidentEnd(int from, int step) const {
-        double fromT = fTs[from].fT;
-        int count = fTs.count();
-        int to = from;
-        while (step > 0 ? ++to < count : --to >= 0) {
-            const Span& span = fTs[to];
-            if (fromT != span.fT) {
-                // FIXME: we assume that if the T changes, we don't care about 
-                // coincident -- but in nextSpan, we require that both the T
-                // and actual loc change to represent a span. This asymettry may
-                // be OK or may be trouble -- if trouble, probably will need to
-                // detect coincidence earlier or sort differently 
-                break;
+    int crossedSpan(const SkPoint& basePt, SkScalar& bestY, double& hitT) const {
+        int start = 0;
+        int bestT = -1;
+        SkScalar top = bounds().fTop;
+        SkScalar bottom = bounds().fBottom;
+        int end;
+        do {
+            end = nextSpan(start, 1);
+            SkPoint edge[4];
+            // OPTIMIZE: wrap this so that if start==0 end==fTCount-1 we can 
+            // work with the original data directly
+            (*SegmentSubDivide[fVerb])(fPts, fTs[start].fT, fTs[end].fT, edge);
+            // start here; intersect ray starting at basePt with edge
+            Intersections intersections;
+            int pts = (*VSegmentIntersect[fVerb])(edge, top, bottom, basePt.fX,
+                    false, intersections);
+            if (pts == 0) {
+                continue;
             }
-            if (span.fCoincident == step) {
-                return to;
+            if (pts > 1 && fVerb == SkPath::kLine_Verb) {
+            // if the intersection is edge on, wait for another one
+                continue;
             }
-        }
-        return from;
+            SkASSERT(pts == 1); // FIXME: more code required to disambiguate
+            SkPoint pt;
+            double foundT = intersections.fT[0][0];
+            (*SegmentXYAtT[fVerb])(fPts, foundT, &pt);
+            if (bestY < pt.fY) {
+                bestY = pt.fY;
+                bestT = foundT < 1 ? start : end;
+                hitT = foundT;
+            }
+            start = end;
+        } while (fTs[end].fT != 1);
+        return bestT;
     }
         
     bool done() const {
@@ -798,37 +1068,46 @@ finish:
         return fDoneSpans == fTs.count();
     }
 
+    // so the span needs to contain the pairing info found here
+    // this should include the winding computed for the edge, and
+    //  what edge it connects to, and whether it is discarded
+    //  (maybe discarded == abs(winding) > 1) ?
+    // only need derivatives for duration of sorting, add a new struct
+    // for pairings, remove extra spans that have zero length and
+    //  reference an unused other
+    // for coincident, the last span on the other may be marked done
+    //  (always?)
+    
+    // if loop is exhausted, contour may be closed.
+    // FIXME: pass in close point so we can check for closure
+
+    // given a segment, and a sense of where 'inside' is, return the next
+    // segment. If this segment has an intersection, or ends in multiple
+    // segments, find the mate that continues the outside.
+    // note that if there are multiples, but no coincidence, we can limit
+    // choices to connections in the correct direction
+    
+    // mark found segments as done
+
     // start is the index of the beginning T of this edge
     // it is guaranteed to have an end which describes a non-zero length (?)
     // winding -1 means ccw, 1 means cw
-    // step is in/out -1 or 1
-    // spanIndex is returned
+    // firstFind allows coincident edges to be treated differently
     Segment* findNext(int winding, const int startIndex, const int endIndex,
-            int& nextStart, int& nextEnd) {
+            int& nextStart, int& nextEnd, bool firstFind) {
         SkASSERT(startIndex != endIndex);
         int count = fTs.count();
         SkASSERT(startIndex < endIndex ? startIndex < count - 1
                 : startIndex > 0);
-
         int step = SkSign32(endIndex - startIndex);
-        int end = nextSpanEnd(startIndex, step);
+        int end = nextSpan(startIndex, step);
         SkASSERT(end >= 0);
-
-        // preflight for coincidence -- if present, it may change winding
-        // considerations and whether reversed edges can be followed
-
-        // Discard opposing direction candidates if no coincidence was found.
         Span* endSpan = &fTs[end];
         Segment* other;
-        if (isSimple(end, step)) {
+        if (isSimple(end)) {
         // mark the smaller of startIndex, endIndex done, and all adjacent
         // spans with the same T value (but not 'other' spans)
             markDone(SkMin32(startIndex, endIndex), winding);
-            // move in winding direction until edge in correct direction
-            // balance wrong direction edges before finding correct one
-            // this requres that the intersection is angularly sorted
-            // for a single intersection, special case -- choose the opposite
-            // edge that steps the same
             other = endSpan->fOther;
             nextStart = endSpan->fOtherIndex;
             nextEnd = nextStart + step;
@@ -857,106 +1136,65 @@ finish:
             }
         }
         // back up if prior edge is coincident with firstIndex
-        int prior = firstIndex;
-        do {
-            if (--prior < 0) {
-                prior = angleCount - 1;
-            }
-            SkASSERT(prior != angleIndex);
-            if (!Coincident(sorted[prior], sorted[firstIndex])) {
-                break;
-            }
-            firstIndex = prior;
-            angle = sorted[prior];
-        } while (true);
-        
-    // put some thought into handling coincident edges
-    // 1) defer the initial moveTo/curveTo until we know that firstIndex
-    //    isn't coincident (although maybe findTop could tell us that)
-    // 2) allow the below to mark and skip coincident pairs
-    // 3) return something (null?) if all segments cancel each other out
-    // 4) if coincident edges don't cancel, figure out which to return (follow)   
-    
+   //     adjustFirst(sorted, firstIndex, winding, firstFind);
         SkASSERT(firstIndex >= 0);
         int startWinding = winding;
-        int nextIndex = firstIndex;
-        const Angle* nextAngle;
-        Segment* nextSegment;
+        int nextIndex = firstIndex + 1;
+        int lastIndex = firstIndex != 0 ? firstIndex : angleCount;
+        const Angle* foundAngle = NULL;
+  //      bool alreadyMarked = angle->segment()->fTs[SkMin32(angle->start(),
+  //              angle->end())].fDone;
+        // iterate through the angle, and compute everyone's winding
+        bool firstEdge = true;
         do {
-            if (++nextIndex == angleCount) {
+            if (nextIndex == angleCount) {
                 nextIndex = 0;
             }
-            SkASSERT(nextIndex != firstIndex); // should never wrap around
-            nextAngle = sorted[nextIndex];
+            const Angle* nextAngle = sorted[nextIndex];
             int maxWinding = winding;
-            winding -= nextAngle->sign();
-            nextSegment = nextAngle->segment();
-            if (nextSegment->done()) {
-                if (!winding) {
-                    break;
-                }
-                continue;
-            }
-            bool pairCoincides = Coincident(angle, nextAngle);
-            bool pairCancels = pairCoincides
-                    && CoincidentCancels(angle, nextAngle);
-            if (pairCancels) {
-                angle->segment()->markAndChaseCoincident(angle->start(),
-                        angle->end(), nextSegment);
-                return NULL;
-            }
+            Segment* nextSegment = nextAngle->segment();
+            int windValue = nextSegment->windValue(nextAngle);
+            SkASSERT(windValue > 0);
+            winding -= nextAngle->sign() * windValue;
+            firstEdge = false;
             if (!winding) {
-                break;
-            } 
-            if (pairCoincides) {
-                bool markNext = abs(maxWinding) < abs(winding);
-                if (markNext) {
-                    nextSegment->markDone(SkMin32(nextAngle->start(),
-                            nextAngle->end()), winding);
-                } else {
-                    angle->segment()->markDone(SkMin32(angle->start(),
-                            angle->end()), maxWinding);
+                if (!foundAngle) {
+                    foundAngle = nextAngle;
                 }
+                goto doNext;
+            }
+            if (nextSegment->done()) {
+                goto doNext;
             }
             // if the winding is non-zero, nextAngle does not connect to
             // current chain. If we haven't done so already, mark the angle
             // as done, record the winding value, and mark connected unambiguous
             // segments as well.
-            else if (nextSegment->winding(nextAngle) == 0) {
+            if (nextSegment->winding(nextAngle) == SK_MinS32) {
                 if (abs(maxWinding) < abs(winding)) {
                     maxWinding = winding;
                 }
-                nextSegment->markAndChaseWinding(nextAngle, maxWinding);
+                if (foundAngle) {
+                    nextSegment->markAndChaseWinding(nextAngle, maxWinding);
+                } else {
+                    nextSegment->markAndChaseDone(nextAngle, maxWinding);
+                }
             }
-        } while ((angle = nextAngle)); // always true
-        markDone(SkMin32(startIndex, endIndex), startWinding);
-        nextStart = nextAngle->start();
-        nextEnd = nextAngle->end();
-        return nextSegment;
+    doNext:
+            angle = nextAngle;
+        } while (++nextIndex != lastIndex);
+   //     if (!alreadyMarked) {
+            sorted[firstIndex]->segment()->
+                markDone(SkMin32(startIndex, endIndex), startWinding);
+   //     }
+        if (!foundAngle) {
+            return NULL;
+        }
+        nextStart = foundAngle->start();
+        nextEnd = foundAngle->end();
+        return foundAngle->segment();
     }
     
-    
-        // so the span needs to contain the pairing info found here
-        // this should include the winding computed for the edge, and
-        //  what edge it connects to, and whether it is discarded
-        //  (maybe discarded == abs(winding) > 1) ?
-        // only need derivatives for duration of sorting, add a new struct
-        // for pairings, remove extra spans that have zero length and
-        //  reference an unused other
-        // for coincident, the last span on the other may be marked done
-        //  (always?)
-        
-        // if loop is exhausted, contour may be closed.
-        // FIXME: pass in close point so we can check for closure
-
-        // given a segment, and a sense of where 'inside' is, return the next
-        // segment. If this segment has an intersection, or ends in multiple
-        // segments, find the mate that continues the outside.
-        // note that if there are multiples, but no coincidence, we can limit
-        // choices to connections in the correct direction
-        
-        // mark found segments as done
-
     // FIXME: this is tricky code; needs its own unit test
     void findTooCloseToCall(int /* winding */ ) { // FIXME: winding should be considered
         int count = fTs.count();
@@ -985,7 +1223,7 @@ finish:
         // so, the span from here to there is coincident.
         for (int index = matchIndex + 1; index < count; ++index) {
             Span* test = &fTs[index];
-            if (test->fCoincident) {
+            if (test->fDone) {
                 continue;
             }
             Segment* tOther = test->fOther;
@@ -1007,7 +1245,7 @@ finish:
             double moStartT, moEndT;
             for (int moIndex = 0; moIndex < moCount; ++moIndex) {
                 Span& moSpan = mOther->fTs[moIndex];
-                if (moSpan.fCoincident) {
+                if (moSpan.fDone) {
                     continue;
                 }
                 if (moSpan.fOther == this) {
@@ -1060,11 +1298,16 @@ finish:
                     || !tOther->isLinear(toStart, toEnd)) {
                 continue;
             }
-            // FIXME: may need to resort if we depend on coincidence first, last
-            mOther->fTs[moStart].fCoincident = -1;
-            tOther->fTs[toStart].fCoincident = -1;
-            mOther->fTs[moEnd].fCoincident = 1;
-            tOther->fTs[toEnd].fCoincident = 1;
+            // FIXME: defer implementation until the rest works
+            // this may share code with regular coincident detection
+            SkASSERT(0);
+        #if 0
+            if (flipped) {
+                mOther->addTCancel(moStart, moEnd, tOther, tStart, tEnd);
+            } else {
+                mOther->addTCoincident(moStart, moEnd, tOther, tStart, tEnd);
+            }
+        #endif
         }
     }
 
@@ -1077,10 +1320,10 @@ finish:
         SkASSERT(!done());
         int firstT;
         int lastT;
-        int firstCoinT;
         SkPoint topPt;
         topPt.fY = SK_ScalarMax;
         int count = fTs.count();
+        // see if either end is not done since we want smaller Y of the pair
         bool lastDone = true;
         for (int index = 0; index < count; ++index) {
             const Span& span = fTs[index];
@@ -1089,22 +1332,13 @@ finish:
                 if (topPt.fY > intercept.fY || (topPt.fY == intercept.fY
                         && topPt.fX > intercept.fX)) {
                     topPt = intercept;
-                    firstT = lastT = firstCoinT = index;
+                    firstT = lastT = index;
                 } else if (topPt == intercept) {
                     lastT = index;
-                    if (span.fCoincident) {
-                        firstCoinT = index;
-                    }
                 }
             }
             lastDone = span.fDone;
         }
-        // if there's only a pair of segments, go with the endpoint chosen above
-        if (firstT == lastT) {
-            tIndex = firstT;
-            endIndex = firstT > 0 ? tIndex - 1 : tIndex + 1;
-            return this;
-        }
         // sort the edges to find the leftmost
         int step = 1;
         int end = nextSpan(firstT, step);
@@ -1117,7 +1351,7 @@ finish:
         // look for left-ness from tLeft to firstT (matching y of other)
         SkTDArray<Angle> angles;
         SkASSERT(firstT - end != 0);
-        addTwoAngles(end, firstCoinT, angles);
+        addTwoAngles(end, firstT, angles);
         buildAngles(firstT, angles);
         SkTDArray<Angle*> sorted;
         sortAngles(angles, sorted);
@@ -1150,93 +1384,27 @@ finish:
                 Span& oSpan = other->fTs[o];
                 if (oT == oSpan.fT && this == oSpan.fOther) {
                     iSpan.fOtherIndex = o;
+                    break;
                 }
             }
         }
     }
     
     // OPTIMIZATION: uses tail recursion. Unwise?
-    void innerCoincidentChase(int step, Segment* other) {
-        // find other at index
-        SkASSERT(!done());
-        const Span* start = NULL;
-        const Span* end = NULL;
-        int index, startIndex, endIndex;
-        int count = fTs.count();
-        for (index = 0; index < count; ++index) {
-            const Span& span = fTs[index];
-            if (!span.fCoincident || span.fOther != other) {
-                continue;
-            }
-            if (!start) {
-                if (span.fDone) {
-                    continue;
-                }
-                startIndex = index;
-                start = &span;
-            } else {
-                SkASSERT(!end);
-                endIndex = index;
-                end = &span;
-            }
-        }
-        if (!end) {
+    void innerChaseDone(int index, int step, int winding) {
+        int end = nextSpan(index, step);
+        if (multipleSpans(end, step)) {
             return;
         }
-        Segment* next;
-        Segment* nextOther;
-        if (step < 0) {
-            next = start->fT == 0 ? NULL : this;
-            nextOther = other->fTs[start->fOtherIndex].fT == 1 ? NULL : other;
-        } else {
-            next = end->fT == 1 ? NULL : this;
-            nextOther = other->fTs[end->fOtherIndex].fT == 0 ? NULL : other;
-        }
-        SkASSERT(!next || !nextOther);
-        for (index = 0; index < count; ++index) {
-            const Span& span = fTs[index];
-            if (span.fCoincident || span.fOther == other) {
-                continue;
-            }
-            bool checkNext = !next && (step < 0 ? span.fT == 0
-                && span.fOtherT == 1 : span.fT == 1 && span.fOtherT == 0);
-            bool checkOther = !nextOther && (step < 0 ? span.fT == start->fT
-                && span.fOtherT == 0 : span.fT == end->fT && span.fOtherT == 1);
-            if (!checkNext && !checkOther) {
-                continue;
-            }
-            Segment* oSegment = span.fOther;
-            if (oSegment->done()) {
-                continue;
-            }
-            int oCount = oSegment->fTs.count();
-            for (int oIndex = 0; oIndex < oCount; ++oIndex) {
-                const Span& oSpan = oSegment->fTs[oIndex];
-                if (oSpan.fT > 0 && oSpan.fT < 1) {
-                    continue;
-                }
-                if (!oSpan.fCoincident) {
-                    continue;
-                }
-                if (checkNext && (oSpan.fT == 0 ^ step < 0)) { 
-                    next = oSegment;
-                    checkNext = false;
-                }
-                if (checkOther && (oSpan.fT == 1 ^ step < 0)) {
-                    nextOther = oSegment;
-                    checkOther = false;
-                }
-            }
-        }
-        markDone(SkMin32(startIndex, endIndex), 0);
-        other->markDone(SkMin32(start->fOtherIndex, end->fOtherIndex), 0);
-        if (next && nextOther) {
-            next->innerCoincidentChase(step, nextOther);
-        }
+        const Span& endSpan = fTs[end];
+        Segment* other = endSpan.fOther;
+        index = endSpan.fOtherIndex;
+        int otherEnd = other->nextSpan(index, step);
+        other->innerChaseDone(index, step, winding);
+        other->markDone(SkMin32(index, otherEnd), winding);
     }
     
-    // OPTIMIZATION: uses tail recursion. Unwise?
-    void innerChase(int index, int step, int winding) {
+    void innerChaseWinding(int index, int step, int winding) {
         int end = nextSpan(index, step);
         if (multipleSpans(end, step)) {
             return;
@@ -1245,15 +1413,19 @@ finish:
         Segment* other = endSpan.fOther;
         index = endSpan.fOtherIndex;
         int otherEnd = other->nextSpan(index, step);
-        other->innerChase(index, step, winding);
-        other->markDone(SkMin32(index, otherEnd), winding);
+        int min = SkMin32(index, otherEnd);
+        if (other->fTs[min].fWindSum != SK_MinS32) {
+            SkASSERT(other->fTs[index].fWindSum == winding);
+            return;
+        }
+        other->innerChaseWinding(index, step, winding);
+        other->markWinding(min, winding);
     }
     
     void init(const SkPoint pts[], SkPath::Verb verb) {
         fPts = pts;
         fVerb = verb;
         fDoneSpans = 0;
-        fCoincident = 0;
     }
 
     bool intersected() const {
@@ -1276,27 +1448,19 @@ finish:
         }
     }
     
-    bool isSimple(int index, int step) const {
+    bool isSimple(int end) const {
         int count = fTs.count();
         if (count == 2) {
             return true;
         }
-       double spanT = fTs[index].fT;
-        if (spanT > 0 && spanT < 1) {
-            return false;
-        }
-        if (step < 0) {
-            const Span& secondSpan = fTs[1];
-            if (secondSpan.fT == 0) {
-                return false;
-            }
-            return xyAtT(&fTs[0]) != xyAtT(&secondSpan);
+        double t = fTs[end].fT;
+        if (t < FLT_EPSILON) {
+            return fTs[1].fT >= FLT_EPSILON;
         }
-        const Span& penultimateSpan = fTs[count - 2];
-        if (penultimateSpan.fT == 1) {
-            return false;
+        if (t > 1 - FLT_EPSILON) {
+            return fTs[count - 2].fT <= 1 - FLT_EPSILON;
         }
-        return xyAtT(&fTs[count - 1]) != xyAtT(&penultimateSpan);
+        return false;
     }
 
     bool isHorizontal() const {
@@ -1311,51 +1475,101 @@ finish:
         return (*SegmentLeftMost[fVerb])(fPts, fTs[start].fT, fTs[end].fT);
     }
     
-    void markAndChaseCoincident(int index, int endIndex, Segment* other) {
-        int step = SkSign32(endIndex - index);
-        innerCoincidentChase(step, other);
-    }
-
     // this span is excluded by the winding rule -- chase the ends
     // as long as they are unambiguous to mark connections as done
     // and give them the same winding value
-    void markAndChaseWinding(const Angle* angle, int winding) {
+    void markAndChaseDone(const Angle* angle, int winding) {
         int index = angle->start();
         int endIndex = angle->end();
         int step = SkSign32(endIndex - index);
-        innerChase(index, step, winding);
+        innerChaseDone(index, step, winding);
         markDone(SkMin32(index, endIndex), winding);
     }
     
+    void markAndChaseWinding(const Angle* angle, int winding) {
+        int index = angle->start();
+        int endIndex = angle->end();
+        int min = SkMin32(index, endIndex);
+        int step = SkSign32(endIndex - index);
+        innerChaseWinding(index, step, winding);
+        markWinding(min, winding);
+    }
+    
     // FIXME: this should also mark spans with equal (x,y)
+    // This may be called when the segment is already marked done. While this
+    // wastes time, it shouldn't do any more than spin through the T spans.
+    // OPTIMIZATION: abort on first done found (assuming that this code is 
+    // always called to mark segments done).
     void markDone(int index, int winding) {
-        SkASSERT(!done());
+      //  SkASSERT(!done());
         double referenceT = fTs[index].fT;
         int lesser = index;
-        while (--lesser >= 0 && referenceT == fTs[lesser].fT) {
+        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
             Span& span = fTs[lesser];
-     // FIXME: this needs to assert that all are not done or one or more are
-     // coincident
-     //       SkASSERT(!span.fDone || span.fCoincident);
             if (span.fDone) {
                 continue;
             }
+        #if DEBUG_MARK_DONE
+            const SkPoint& pt = xyAtT(&span);
+            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
+                    __FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
+        #endif
             span.fDone = true;
-            SkASSERT(!span.fWinding || span.fWinding == winding);
-            span.fWinding = winding;
+            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
+            span.fWindSum = winding;
             fDoneSpans++;
         }
         do {
             Span& span = fTs[index];
-     //       SkASSERT(!span.fDone || span.fCoincident);
+     //       SkASSERT(!span.fDone);
             if (span.fDone) {
                 continue;
             }
+        #if DEBUG_MARK_DONE
+            const SkPoint& pt = xyAtT(&span);
+            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
+                    __FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
+        #endif
             span.fDone = true;
-            SkASSERT(!span.fWinding || span.fWinding == winding);
-            span.fWinding = winding;
+            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
+            span.fWindSum = winding;
             fDoneSpans++;
-        } while (++index < fTs.count() && referenceT == fTs[index].fT);
+        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
+    }
+
+    void markWinding(int index, int winding) {
+        SkASSERT(!done());
+        double referenceT = fTs[index].fT;
+        int lesser = index;
+        while (--lesser >= 0 && referenceT - fTs[lesser].fT < FLT_EPSILON) {
+            Span& span = fTs[lesser];
+            if (span.fDone) {
+                continue;
+            }
+            SkASSERT(span.fWindValue == 1 || winding == 0);
+            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
+        #if DEBUG_MARK_DONE
+            const SkPoint& pt = xyAtT(&span);
+            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
+                    __FUNCTION__, fID, lesser, span.fT, pt.fX, pt.fY, winding);
+        #endif
+            span.fWindSum = winding;
+        }
+        do {
+            Span& span = fTs[index];
+     //       SkASSERT(!span.fDone || span.fCoincident);
+            if (span.fDone) {
+                continue;
+            }
+            SkASSERT(span.fWindValue == 1 || winding == 0);
+            SkASSERT(span.fWindSum == SK_MinS32 || span.fWindSum == winding);
+        #if DEBUG_MARK_DONE
+            const SkPoint& pt = xyAtT(&span);
+            SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g) wind=%d\n",
+                    __FUNCTION__, fID, index, span.fT, pt.fX, pt.fY, winding);
+        #endif
+            span.fWindSum = winding;
+        } while (++index < fTs.count() && fTs[index].fT - referenceT < FLT_EPSILON);
     }
 
     bool multipleSpans(int end, int step) const {
@@ -1368,18 +1582,14 @@ finish:
     // coincidence is found when the beginning Ts contain -step and the end
     // contains step. When it is looking for the beginning of the next, the
     // first Ts found can be ignored and the last Ts should contain -step.
+    // OPTIMIZATION: probably should split into two functions
     int nextSpan(int from, int step) const {
         const Span& fromSpan = fTs[from];
         int count = fTs.count();
         int to = from;
         while (step > 0 ? ++to < count : --to >= 0) {
             const Span& span = fTs[to];
-            if (fromSpan.fT == span.fT) {
-                continue;
-            }
-            const SkPoint& loc = xyAtT(&span);
-            const SkPoint& fromLoc = xyAtT(&fromSpan);
-            if (fromLoc == loc) {
+            if ((step > 0 ? span.fT - fromSpan.fT : fromSpan.fT - span.fT) < FLT_EPSILON) {
                 continue;
             }
             return to;
@@ -1387,16 +1597,6 @@ finish:
         return -1;
     }
 
-    // once past current span, if step>0, look for coicident==1
-    // if step<0, look for coincident==-1
-    int nextSpanEnd(int from, int step) const {
-        int result = nextSpan(from, step);
-        if (result < 0) {
-            return result;
-        }
-        return coincidentEnd(result, step);
-    }
-
     const SkPoint* pts() const {
         return fPts;
     }
@@ -1411,6 +1611,11 @@ finish:
     const Span& span(int tIndex) const {
         return fTs[tIndex];
     }
+    
+    int spanSign(int startIndex, int endIndex) const {
+        return startIndex < endIndex ? -fTs[startIndex].fWindValue :
+                fTs[endIndex].fWindValue;
+    }
 
     // OPTIMIZATION: mark as debugging only if used solely by tests
     double t(int tIndex) const {
@@ -1424,18 +1629,64 @@ finish:
     SkPath::Verb verb() const {
         return fVerb;
     }
+
+    // if the only remaining spans are small, ignore them, and mark done
+    bool virtuallyDone() {
+        int count = fTs.count();
+        double previous = 0;
+        bool previousDone = fTs[0].fDone;
+        for (int index = 1; index < count; ++index) {
+            Span& span = fTs[index];
+            double t = span.fT;
+            if (t - previous < FLT_EPSILON) {
+                if (span.fDone && !previousDone) {
+                    int prior = --index;
+                    int winding = span.fWindSum;
+                    do {
+                        Span& priorSpan = fTs[prior];
+                        priorSpan.fDone = true;
+                        priorSpan.fWindSum = winding;
+                        fDoneSpans++;
+                    } while (--prior >= 0 && t - fTs[prior].fT < FLT_EPSILON);
+                }
+            } else if (!previousDone) {
+                return false;
+            }
+            previous = t;
+            previousDone = span.fDone;
+        }
+        SkASSERT(done());
+        return true;
+    }
+
+    int winding(int tIndex) const {
+        return fTs[tIndex].fWindSum;
+    }
     
-    bool winding(const Angle* angle) {
+    int winding(const Angle* angle) const {
         int start = angle->start();
         int end = angle->end();
         int index = SkMin32(start, end);
-        Span& span = fTs[index];
-        return span.fWinding;
+        return winding(index);
+    }
+
+    int windValue(int tIndex) const {
+        return fTs[tIndex].fWindValue;
+    }
+    
+    int windValue(const Angle* angle) const {
+        int start = angle->start();
+        int end = angle->end();
+        int index = SkMin32(start, end);
+        return windValue(index);
+    }
+
+    SkScalar xAtT(const Span* span) const {
+        return xyAtT(span).fX;
     }
 
-    SkScalar xAtT(double t) const {
-        SkASSERT(t >= 0 && t <= 1);
-        return (*SegmentXAtT[fVerb])(fPts, t);
+    const SkPoint& xyAtT(int index) const {
+        return xyAtT(&fTs[index]);
     }
 
     const SkPoint& xyAtT(const Span* span) const {
@@ -1452,10 +1703,13 @@ finish:
         }
         return *span->fPt;
     }
+    
+    SkScalar yAtT(int index) const {
+        return yAtT(&fTs[index]);
+    }
 
-    SkScalar yAtT(double t) const {
-        SkASSERT(t >= 0 && t <= 1);
-        return (*SegmentYAtT[fVerb])(fPts, t);
+    SkScalar yAtT(const Span* span) const {
+        return xyAtT(span).fY;
     }
 
 #if DEBUG_DUMP
@@ -1466,10 +1720,10 @@ finish:
             SkPoint out;
             (*SegmentXYAtT[fVerb])(fPts, t(i), &out);
             SkDebugf("%*s [%d] %s.fTs[%d]=%1.9g (%1.9g,%1.9g) other=%d"
-                    " otherT=%1.9g winding=%d\n",
+                    " otherT=%1.9g windSum=%d\n",
                     tab + sizeof(className), className, fID,
                     kLVerbStr[fVerb], i, fTs[i].fT, out.fX, out.fY,
-                    fTs[i].fOther->fID, fTs[i].fOtherT, fTs[i].fWinding);
+                    fTs[i].fOther->fID, fTs[i].fOtherT, fTs[i].fWindSum);
         }
         SkDebugf("%*s [%d] fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)",
                 tab + sizeof(className), className, fID,
@@ -1486,14 +1740,17 @@ private:
     // be allocated as needed instead of always initialized -- though maybe
     // the initialization is lightweight enough that it hardly matters
     mutable SkTDArray<SkPoint> fIntersections;
-    // FIXME: coincident only needs two bits (-1, 0, 1)
-    int fCoincident; // non-zero if some coincident span inside 
     int fDoneSpans; // used for quick check that segment is finished
 #if DEBUG_DUMP
     int fID;
 #endif
 };
 
+struct Coincidence {
+    Segment* fSegments[2];
+    double fTs[2][2];
+};
+
 class Contour {
 public:
     Contour() {
@@ -1509,6 +1766,26 @@ public:
                 : fBounds.fTop < rh.fBounds.fTop;
     }
 
+    void addCoincident(int index, Contour* other, int otherIndex,
+            const Intersections& ts, bool swap) {
+        Coincidence& coincidence = *fCoincidences.append();
+        coincidence.fSegments[0] = &fSegments[index];
+        coincidence.fSegments[1] = &other->fSegments[otherIndex];
+        coincidence.fTs[swap][0] = ts.fT[0][0];
+        coincidence.fTs[swap][1] = ts.fT[0][1];
+        coincidence.fTs[!swap][0] = ts.fT[1][0];
+        coincidence.fTs[!swap][1] = ts.fT[1][1];
+    }
+
+    void addCross(const Contour* crosser) {
+#ifdef DEBUG_CROSS
+        for (int index = 0; index < fCrosses.count(); ++index) {
+            SkASSERT(fCrosses[index] != crosser);
+        }
+#endif
+        *fCrosses.append() = crosser;
+    }
+
     void addCubic(const SkPoint pts[4]) {
         fSegments.push_back().addCubic(pts);
         fContainsCurves = true;
@@ -1518,6 +1795,10 @@ public:
         fSegments.push_back().addLine(pts);
         return fSegments.count();
     }
+    
+    void addOtherT(int segIndex, int tIndex, double otherT, int otherIndex) {
+        fSegments[segIndex].addOtherT(tIndex, otherT, otherIndex);
+    }
 
     int addQuad(const SkPoint pts[3]) {
         fSegments.push_back().addQuad(pts);
@@ -1525,6 +1806,11 @@ public:
         return fSegments.count();
     }
 
+    int addT(int segIndex, double newT, Contour* other, int otherIndex) {
+        containsIntercepts();
+        return fSegments[segIndex].addT(newT, &other->fSegments[otherIndex]);
+    }
+
     const Bounds& bounds() const {
         return fBounds;
     }
@@ -1538,6 +1824,48 @@ public:
         fContainsIntercepts = true;
     }
 
+    const Segment* crossedSegment(const SkPoint& basePt, SkScalar& bestY, 
+            int &tIndex, double& hitT) {
+        int segmentCount = fSegments.count();
+        const Segment* bestSegment = NULL;
+        for (int test = 0; test < segmentCount; ++test) {
+            Segment* testSegment = &fSegments[test];
+            const SkRect& bounds = testSegment->bounds();
+            if (bounds.fTop < bestY) {
+                continue;
+            }
+            if (bounds.fTop > basePt.fY) {
+                continue;
+            }
+            if (bounds.fLeft > basePt.fX) {
+                continue;
+            }
+            if (bounds.fRight < basePt.fX) {
+                continue;
+            }
+            double testHitT;
+            int testT = testSegment->crossedSpan(basePt, bestY, testHitT);
+            if (testT >= 0) {
+                bestSegment = testSegment;
+                tIndex = testT;
+                hitT = testHitT;
+            }
+        }
+        return bestSegment;
+    }
+    
+    bool crosses(const Contour* crosser) const {
+        if (this == crosser) {
+            return true;
+        }
+        for (int index = 0; index < fCrosses.count(); ++index) {
+            if (fCrosses[index] == crosser) {
+                return true;
+            }
+        }
+        return false;
+    }
+
     void findTooCloseToCall(int winding) {
         int segmentCount = fSegments.count();
         for (int sIndex = 0; sIndex < segmentCount; ++sIndex) {
@@ -1556,44 +1884,118 @@ public:
         fSegments.reset();
         fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
         fContainsCurves = fContainsIntercepts = false;
+        fWindingSum = -1;
     }
     
+    void resolveCoincidence(int winding) {
+        int count = fCoincidences.count();
+        for (int index = 0; index < count; ++index) {
+            Coincidence& coincidence = fCoincidences[index];
+            Segment* thisOne = coincidence.fSegments[0];
+            Segment* other = coincidence.fSegments[1];
+            double startT = coincidence.fTs[0][0];
+            double endT = coincidence.fTs[0][1];
+            if (startT > endT) {
+                SkTSwap<double>(startT, endT);
+            }
+            SkASSERT(endT - startT >= FLT_EPSILON);
+            double oStartT = coincidence.fTs[1][0];
+            double oEndT = coincidence.fTs[1][1];
+            if (oStartT > oEndT) {
+                SkTSwap<double>(oStartT, oEndT);
+            }
+            SkASSERT(oEndT - oStartT >= FLT_EPSILON);
+            if (winding > 0 || thisOne->cancels(*other)) {
+                thisOne->addTCancel(startT, endT, *other, oStartT, oEndT);
+            } else {
+                thisOne->addTCoincident(startT, endT, *other, oStartT, oEndT);
+            }
+        }
+    }
+    
+    const SkTArray<Segment>& segments() {
+        return fSegments;
+    }
+    
+    void setWinding(int winding) {
+        SkASSERT(fWindingSum < 0);
+        fWindingSum = winding;
+    }
+
     // OPTIMIZATION: feel pretty uneasy about this. It seems like once again
     // we need to sort and walk edges in y, but that on the surface opens the
     // same can of worms as before. But then, this is a rough sort based on 
     // segments' top, and not a true sort, so it could be ameniable to regular
     // sorting instead of linear searching. Still feel like I'm missing something
-    Segment* topSegment() {
+    Segment* topSegment(SkScalar& bestY) {
         int segmentCount = fSegments.count();
         SkASSERT(segmentCount > 0);
         int best = -1;
         Segment* bestSegment = NULL;
         while (++best < segmentCount) {
             Segment* testSegment = &fSegments[best];
+        #if 0 // FIXME: remove if not needed
+            if (testSegment->virtuallyDone()) {
+                continue;
+            }
+        #else
             if (testSegment->done()) {
                 continue;
             }
+        #endif
             bestSegment = testSegment;
             break;
         }
         if (!bestSegment) {
             return NULL;
         }
-        SkScalar bestTop = bestSegment->bounds().fTop;
+        SkScalar bestTop = bestSegment->activeTop();
         for (int test = best + 1; test < segmentCount; ++test) {
             Segment* testSegment = &fSegments[test];
             if (testSegment->done()) {
                 continue;
             }
-            SkScalar testTop = testSegment->bounds().fTop;
+            if (testSegment->bounds().fTop > bestTop) {
+                continue;
+            }
+            SkScalar testTop = testSegment->activeTop();
             if (bestTop > testTop) {
                 bestTop = testTop;
                 bestSegment = testSegment;
             }
         }
+        bestY = bestTop;
         return bestSegment;
     }
 
+    int updateSegment(int index, const SkPoint* pts) {
+        Segment& segment = fSegments[index];
+        segment.updatePts(pts);
+        return segment.verb() + 1;
+    }
+
+    int winding() {
+        if (fWindingSum >= 0) {
+            return fWindingSum;
+        }
+        // check peers
+        int count = fCrosses.count();
+        for (int index = 0; index < count; ++index) {
+            const Contour* crosser = fCrosses[index];
+            if (0 <= crosser->fWindingSum) {
+                fWindingSum = crosser->fWindingSum;
+                break;
+            }
+        }
+        return fWindingSum;
+    }
+
+#if DEBUG_TEST
+    SkTArray<Segment>& debugSegments() {
+        return fSegments;
+    }
+#endif
+
 #if DEBUG_DUMP
     void dump() {
         int i;
@@ -1627,17 +2029,18 @@ protected:
         }
         fBounds = fSegments.front().bounds();
         for (int index = 1; index < count; ++index) {
-            fBounds.growToInclude(fSegments[index].bounds());
+            fBounds.add(fSegments[index].bounds());
         }
     }
 
-public:
-    SkTArray<Segment> fSegments; // not worth accessor functions?
-
 private:
+    SkTArray<Segment> fSegments;
+    SkTDArray<Coincidence> fCoincidences;
+    SkTDArray<const Contour*> fCrosses;
     Bounds fBounds;
     bool fContainsIntercepts;
     bool fContainsCurves;
+    int fWindingSum; // initial winding number outside
 #if DEBUG_DUMP
     int fID;
 #endif
@@ -1661,7 +2064,7 @@ EdgeBuilder(const SkPath& path, SkTArray<Contour>& contours)
 protected:
 
 void complete() {
-    if (fCurrentContour && fCurrentContour->fSegments.count()) {
+    if (fCurrentContour && fCurrentContour->segments().count()) {
         fCurrentContour->complete();
         fCurrentContour = NULL;
     }
@@ -1755,25 +2158,24 @@ void walk() {
         SkASSERT(fCurrentContour);
     }
     complete();
-    if (fCurrentContour && !fCurrentContour->fSegments.count()) {
+    if (fCurrentContour && !fCurrentContour->segments().count()) {
         fContours.pop_back();
     }
     // correct pointers in contours since fReducePts may have moved as it grew
     int cIndex = 0;
-    fCurrentContour = &fContours[0];
     int extraCount = fExtra.count();
-    SkASSERT(fExtra[0] == -1);
+    SkASSERT(extraCount == 0 || fExtra[0] == -1);
     int eIndex = 0;
     int rIndex = 0;
     while (++eIndex < extraCount) {
         int offset = fExtra[eIndex];
         if (offset < 0) {
-            fCurrentContour = &fContours[++cIndex];
+            ++cIndex;
             continue;
         }
-        Segment& segment = fCurrentContour->fSegments[offset - 1];
-        segment.updatePts(&fReducePts[rIndex]);
-        rIndex += segment.verb() + 1;
+        fCurrentContour = &fContours[cIndex];
+        rIndex += fCurrentContour->updateSegment(offset - 1,
+                &fReducePts[rIndex]);
     }
     fExtra.reset(); // we're done with this
 }
@@ -1797,11 +2199,15 @@ public:
         kQuad_Segment = SkPath::kQuad_Verb,
         kCubic_Segment = SkPath::kCubic_Verb,
     };
+    
+    void addCoincident(Work& other, const Intersections& ts, bool swap) {
+        fContour->addCoincident(fIndex, other.fContour, other.fIndex, ts, swap);
+    }
 
     // FIXME: does it make sense to write otherIndex now if we're going to
     // fix it up later?
     void addOtherT(int index, double otherT, int otherIndex) {
-        fContour->fSegments[fIndex].addOtherT(index, otherT, otherIndex);
+        fContour->addOtherT(fIndex, index, otherT, otherIndex);
     }
 
     // Avoid collapsing t values that are close to the same since
@@ -1809,10 +2215,8 @@ public:
     // be nearly equal, any problems caused by this should be taken care
     // of later.
     // On the edge or out of range values are negative; add 2 to get end
-    int addT(double newT, const Work& other, int coincident) {
-        fContour->containsIntercepts();
-        return fContour->fSegments[fIndex].addT(newT,
-                other.fContour->fSegments[other.fIndex], coincident);
+    int addT(double newT, const Work& other) {
+        return fContour->addT(fIndex, newT, other.fContour, other.fIndex);
     }
 
     bool advance() {
@@ -1824,7 +2228,7 @@ public:
     }
 
     const Bounds& bounds() const {
-        return fContour->fSegments[fIndex].bounds();
+        return fContour->segments()[fIndex].bounds();
     }
     
     const SkPoint* cubic() const {
@@ -1834,7 +2238,7 @@ public:
     void init(Contour* contour) {
         fContour = contour;
         fIndex = 0;
-        fLast = contour->fSegments.count();
+        fLast = contour->segments().count();
     }
 
     SkScalar left() const {
@@ -1852,7 +2256,7 @@ public:
     }
 
     const SkPoint* pts() const {
-        return fContour->fSegments[fIndex].pts();
+        return fContour->segments()[fIndex].pts();
     }
 
     SkScalar right() const {
@@ -1864,7 +2268,7 @@ public:
     }
 
     SegmentType segmentType() const {
-        const Segment& segment = fContour->fSegments[fIndex];
+        const Segment& segment = fContour->segments()[fIndex];
         SegmentType type = (SegmentType) segment.verb();
         if (type != kLine_Segment) {
             return type;
@@ -1888,7 +2292,7 @@ public:
     }
 
     SkPath::Verb verb() const {
-        return fContour->fSegments[fIndex].verb();
+        return fContour->segments()[fIndex].verb();
     }
 
     SkScalar x() const {
@@ -1904,7 +2308,7 @@ public:
     }
 
     bool yFlipped() const {
-        return y() != pts()[0].fX;
+        return y() != pts()[0].fY;
     }
 
 protected:
@@ -1959,6 +2363,7 @@ static bool addIntersectTs(Contour* test, Contour* next) {
     }
     Work wt;
     wt.init(test);
+    bool foundCommonContour = test == next;
     do {
         Work wn;
         wn.init(next);
@@ -2116,70 +2521,155 @@ static bool addIntersectTs(Contour* test, Contour* next) {
                 default:
                     SkASSERT(0);
             }
+            if (!foundCommonContour && pts > 0) {
+                test->addCross(next);
+                next->addCross(test);
+                foundCommonContour = true;
+            }
             // in addition to recording T values, record matching segment
-            int testCoin;
-            int nextCoin;
             if (pts == 2 && wn.segmentType() <= Work::kLine_Segment
                     && wt.segmentType() <= Work::kLine_Segment) {
-                // pass coincident so that smaller T is -1, larger T is 1
-                testCoin = ts.fT[swap][0] < ts.fT[swap][1] ? -1 : 1;
-                nextCoin = ts.fT[!swap][0] < ts.fT[!swap][1] ? -1 : 1;
-            } else {
-                testCoin = nextCoin = 0;
+                wt.addCoincident(wn, ts, swap);
+                continue;
             }
             for (int pt = 0; pt < pts; ++pt) {
                 SkASSERT(ts.fT[0][pt] >= 0 && ts.fT[0][pt] <= 1);
                 SkASSERT(ts.fT[1][pt] >= 0 && ts.fT[1][pt] <= 1);
-                int testTAt = wt.addT(ts.fT[swap][pt], wn, testCoin);
-                int nextTAt = wn.addT(ts.fT[!swap][pt], wt, nextCoin);
+                int testTAt = wt.addT(ts.fT[swap][pt], wn);
+                int nextTAt = wn.addT(ts.fT[!swap][pt], wt);
                 wt.addOtherT(testTAt, ts.fT[!swap][pt], nextTAt);
                 wn.addOtherT(nextTAt, ts.fT[swap][pt], testTAt);
-                testCoin = -testCoin;
-                nextCoin = -nextCoin;
             }
         } while (wn.advance());
     } while (wt.advance());
     return true;
 }
 
+// resolve any coincident pairs found while intersecting, and
 // see if coincidence is formed by clipping non-concident segments
 static void coincidenceCheck(SkTDArray<Contour*>& contourList, int winding) {
     int contourCount = contourList.count();
     for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
         Contour* contour = contourList[cIndex];
+        contour->resolveCoincidence(winding);
+    }
+    for (int cIndex = 0; cIndex < contourCount; ++cIndex) {
+        Contour* contour = contourList[cIndex];
         contour->findTooCloseToCall(winding);
     }
 }
 
+// project a ray from the top of the contour up and see if it hits anything
+// note: when we compute line intersections, we keep track of whether
+// two contours touch, so we need only look at contours not touching this one.
+// OPTIMIZATION: sort contourList vertically to avoid linear walk
+static int innerContourCheck(SkTDArray<Contour*>& contourList,
+        Contour* baseContour, const SkPoint& basePt) {
+    int contourCount = contourList.count();
+    int winding = 0;
+    SkScalar bestY = SK_ScalarMin;
+    for (int cTest = 0; cTest < contourCount; ++cTest) {
+        Contour* contour = contourList[cTest];
+        if (basePt.fY < contour->bounds().fTop) {
+            continue;
+        }
+        if (bestY > contour->bounds().fBottom) {
+            continue;
+        }
+        if (baseContour->crosses(contour)) {
+           continue;
+        }
+        int tIndex;
+        double tHit;
+        const Segment* test = contour->crossedSegment(basePt, bestY, tIndex,
+            tHit);
+        if (!test) {
+            continue;
+        }
+        // If the ray hit the end of a span, we need to construct the wheel of
+        // angles to find the span closest to the ray -- even if there are just
+        // two spokes on the wheel.
+        if (tHit == test->t(tIndex)) {
+            SkTDArray<Angle> angles;
+            int end = test->nextSpan(tIndex, 1);
+            if (end < 0) {
+                end = test->nextSpan(tIndex, -1);
+            }
+            test->addTwoAngles(tIndex, end, angles);
+     //       test->buildAnglesInner(tIndex, angles);
+            test->buildAngles(tIndex, angles);
+            SkTDArray<Angle*> sorted;
+            sortAngles(angles, sorted);
+            const Angle* angle = sorted[0];
+            test = angle->segment();
+            SkScalar testDx = (*SegmentDXAtT[test->verb()])(test->pts(), tHit);
+            if (testDx == 0) {
+                angle = *(sorted.end() - 1);
+                test = angle->segment();
+                SkASSERT((*SegmentDXAtT[test->verb()])(test->pts(), tHit) != 0);
+            }
+            tIndex = angle->start(); // lesser Y
+            winding = test->winding(SkMin32(tIndex, angle->end()));
+    #if DEBUG_WINDING
+           SkDebugf("%s 1 winding=%d\n", __FUNCTION__, winding);
+    #endif
+        } else {
+            winding = test->winding(tIndex);
+    #if DEBUG_WINDING
+            SkDebugf("%s 2 winding=%d\n", __FUNCTION__, winding);
+    #endif
+        }
+        // see if a + change in T results in a +/- change in X (compute x'(T))
+        SkScalar dx = (*SegmentDXAtT[test->verb()])(test->pts(), tHit);
+    #if DEBUG_WINDING
+        SkDebugf("%s dx=%1.9g\n", __FUNCTION__, dx);
+    #endif
+        SkASSERT(dx != 0);
+        if (winding * dx > 0) { // if same signs, result is negative
+            winding += dx > 0 ? -1 : 1;
+    #if DEBUG_WINDING
+            SkDebugf("%s 3 winding=%d\n", __FUNCTION__, winding);
+    #endif
+        }
+    }
+    baseContour->setWinding(winding);
+    return winding;
+}
     
 // OPTIMIZATION: not crazy about linear search here to find top active y.
 // seems like we should break down and do the sort, or maybe sort each
 // contours' segments? 
 // Once the segment array is built, there's no reason I can think of not to
 // sort it in Y. hmmm
+// FIXME: return the contour found to pass to inner contour check
 static Segment* findTopContour(SkTDArray<Contour*>& contourList,
-        int contourCount) {
+        Contour*& topContour) {
+    int contourCount = contourList.count();
     int cIndex = 0;
     Segment* topStart;
+    SkScalar bestY = SK_ScalarMax;
+    Contour* contour;
     do {
-        Contour* topContour = contourList[cIndex];
-        topStart = topContour->topSegment();
+        contour = contourList[cIndex];
+        topStart = contour->topSegment(bestY);
     } while (!topStart && ++cIndex < contourCount);
     if (!topStart) {
         return NULL;
     }
-    SkScalar top = topStart->bounds().fTop;
-    for (int cTest = cIndex + 1; cTest < contourCount; ++cTest) {
-        Contour* contour = contourList[cTest];
-        if (top < contour->bounds().fTop) {
+    topContour = contour;
+    while (++cIndex < contourCount) {
+        contour = contourList[cIndex];
+        if (bestY < contour->bounds().fTop) {
             continue;
         }
-        Segment* test = contour->topSegment();
-        if (top > test->bounds().fTop) {
-            cIndex = cTest;
-            topStart = test;
-            top = test->bounds().fTop;
+        SkScalar testY = SK_ScalarMax;
+        Segment* test = contour->topSegment(testY);
+        if (!test || bestY <= testY) {
+            continue;
         }
+        topContour = contour;
+        topStart = test;
+        bestY = testY;
     }
     return topStart;
 }
@@ -2194,36 +2684,65 @@ static Segment* findTopContour(SkTDArray<Contour*>& contourList,
     // since we start with leftmost top edge, we'll traverse through a
     // smaller angle counterclockwise to get to the next edge.  
 static void bridge(SkTDArray<Contour*>& contourList, SkPath& simple) {
-    int contourCount = contourList.count();
+    // after findTopContour has already been called once, check if
+    // result of subsequent findTopContour has no winding set
+    bool firstContour = true;
     do {
-        Segment* topStart = findTopContour(contourList, contourCount);
+        Contour* topContour;
+        Segment* topStart = findTopContour(contourList, topContour);
         if (!topStart) {
             break;
         }
-        // FIXME: if this contour is inside others, winding will not be zero initially
-        int winding = 0; // zero says there are no contours outside this one
         // Start at the top. Above the top is outside, below is inside.
         // follow edges to intersection by changing the index by direction.
         int index, endIndex;
         Segment* current = topStart->findTop(index, endIndex);
-        winding += SkSign32(index - endIndex);
+        int winding;
+        int contourWinding;
+        if (firstContour) {
+            topContour->setWinding(0);
+            contourWinding = 0;
+            firstContour = false;
+            winding = 0;
+        } else {
+            winding = topContour->winding();
+    #if DEBUG_WINDING
+            SkDebugf("%s 1 winding=%d\n", __FUNCTION__, winding);
+    #endif
+            if (!winding) {
+                const SkPoint& topPoint = current->xyAtT(endIndex);
+                winding = innerContourCheck(contourList, topContour, topPoint);
+    #if DEBUG_WINDING
+                SkDebugf("%s 2 winding=%d\n", __FUNCTION__, winding);
+    #endif
+            }
+        }
         const SkPoint* firstPt = NULL;
         SkPoint lastPt;
+        bool active = winding >= -1 && winding <= 1;
+        bool firstTime = true;
+        int spanWinding = current->spanSign(index, endIndex);
+    #if DEBUG_WINDING
+        SkDebugf("%s spanWinding=%d\n", __FUNCTION__, startWinding);
+    #endif
         do {
             SkASSERT(!current->done());
             int nextStart, nextEnd;
-            Segment* next = current->findNext(winding, index, endIndex,
-                    nextStart, nextEnd);
+            Segment* next = current->findNext(winding + spanWinding, index,
+                    endIndex, nextStart, nextEnd, firstTime);
             if (!next) {
                 break;
             }
             if (!firstPt) {
-                firstPt = &current->addMoveTo(index, simple);
+                firstPt = &current->addMoveTo(index, simple, active);
             }
-            lastPt = current->addCurveTo(index, endIndex, simple);
+            lastPt = current->addCurveTo(index, endIndex, simple, active);
             current = next;
             index = nextStart;
             endIndex = nextEnd;
+            spanWinding = SkSign32(spanWinding) * next->windValue(
+                    SkMin32(nextStart, nextEnd));
+            firstTime = false;
         } while (*firstPt != lastPt);
         if (firstPt) {
     #if DEBUG_PATH_CONSTRUCTION
@@ -2232,8 +2751,6 @@ static void bridge(SkTDArray<Contour*>& contourList, SkPath& simple) {
             simple.close();
         }
     } while (true);
-    // FIXME: more work to be done for contained (but not intersecting)
-    //  segments
 }
 
 static void fixOtherTIndex(SkTDArray<Contour*>& contourList) {
diff --git a/experimental/Intersection/Simplify.h b/experimental/Intersection/Simplify.h
index ae338eedeb..a0b936abf0 100644
--- a/experimental/Intersection/Simplify.h
+++ b/experimental/Intersection/Simplify.h
@@ -5,6 +5,7 @@
  * found in the LICENSE file.
  */
 #include "CurveIntersection.h"
+#include "CurveUtilities.h"
 #include "Intersections.h"
 #include "LineIntersection.h"
 #include "LineParameters.h"
diff --git a/experimental/Intersection/SimplifyAddIntersectingTs_Test.cpp b/experimental/Intersection/SimplifyAddIntersectingTs_Test.cpp
index da2569c5e0..09481c385a 100644
--- a/experimental/Intersection/SimplifyAddIntersectingTs_Test.cpp
+++ b/experimental/Intersection/SimplifyAddIntersectingTs_Test.cpp
@@ -87,7 +87,7 @@ static void testPath(const SkPath& path, const SkPoint* pts1, SkPath::Verb c1Typ
     SimplifyAddIntersectingTsTest::Contour& c1 = contour[0];
     SimplifyAddIntersectingTsTest::Contour& c2 = contour[1];
     addIntersectTs(&c1, &c2);
-    bool c1Intersected = c1.fSegments[0].intersected();
+    bool c1Intersected = c1.segments()[0].intersected();
     // bool c2Intersected = c2.fSegments[0].intersected();
 #if DEBUG_DUMP
     SkDebugf("%s %s (%1.9g,%1.9g %1.9g,%1.9g) %s %s (%1.9g,%1.9g %1.9g,%1.9g)\n",
diff --git a/experimental/Intersection/SimplifyFindNext_Test.cpp b/experimental/Intersection/SimplifyFindNext_Test.cpp
index 66af15bb0a..c8ca984c8d 100644
--- a/experimental/Intersection/SimplifyFindNext_Test.cpp
+++ b/experimental/Intersection/SimplifyFindNext_Test.cpp
@@ -5,6 +5,8 @@
  * found in the LICENSE file.
  */
  
+#define DEBUG_TEST 1
+ 
 #include "Simplify.h"
 
 namespace SimplifyFindNextTest {
@@ -27,12 +29,12 @@ static const SimplifyFindNextTest::Segment* testCommon(
         addIntersectTs(contourList[1], contourList[1]);
     }
     fixOtherTIndex(contourList);
-    SimplifyFindNextTest::Segment& segment = contours[0].fSegments[0];
+    SimplifyFindNextTest::Segment& segment = contours[0].debugSegments()[0];
     SkPoint pts[2];
     pts[0] = segment.xyAtT(&segment.span(endIndex));
     int nextStart, nextEnd;
     SimplifyFindNextTest::Segment* next = segment.findNext(winding,
-            startIndex, endIndex, nextStart, nextEnd);
+            startIndex, endIndex, nextStart, nextEnd, true);
     pts[1] = next->xyAtT(&next->span(nextStart));
     SkASSERT(pts[0] == pts[1]);
     return next;
diff --git a/experimental/Intersection/SimplifyFindTop_Test.cpp b/experimental/Intersection/SimplifyFindTop_Test.cpp
index 2abde363cb..9e8d2bbfe7 100644
--- a/experimental/Intersection/SimplifyFindTop_Test.cpp
+++ b/experimental/Intersection/SimplifyFindTop_Test.cpp
@@ -27,8 +27,8 @@ static const SimplifyFindTopTest::Segment* testCommon(
         addIntersectTs(contourList[1], contourList[1]);
     }
     fixOtherTIndex(contourList);
-    SimplifyFindTopTest::Segment* topStart = findTopContour(contourList,
-            contourList.count());
+    SimplifyFindTopTest::Contour* top;
+    SimplifyFindTopTest::Segment* topStart = findTopContour(contourList, top);
     const SimplifyFindTopTest::Segment* topSegment = topStart->findTop(index,
             end);
     return topSegment;
diff --git a/experimental/Intersection/SimplifyNew_Test.cpp b/experimental/Intersection/SimplifyNew_Test.cpp
index c99b8e9320..022518b8b3 100644
--- a/experimental/Intersection/SimplifyNew_Test.cpp
+++ b/experimental/Intersection/SimplifyNew_Test.cpp
@@ -5,29 +5,9 @@
  * found in the LICENSE file.
  */
 
-#include "Simplify.h"
-
-namespace SimplifyNewTest {
-
-#include "Simplify.cpp"
-
-} // end of SimplifyNewTest namespace
-
 #include "EdgeWalker_Test.h"
 #include "Intersection_Tests.h"
-
-static bool testSimplifyx(const SkPath& path) {
-    if (false) {
-        showPath(path);
-    }
-    SkPath out;
-    simplifyx(path, out);
-    if (false) {
-        return true;
-    }
-    SkBitmap bitmap;
-    return comparePaths(path, out, bitmap, 0) == 0;
-}
+#include "ShapeOps.h"
 
 static void testLine1() {
     SkPath path, simple;
@@ -146,17 +126,228 @@ static void testLine9() {
     testSimplifyx(path);
 }
 
+static void testLine10() {
+    SkPath path, simple;
+    path.moveTo(0,4);
+    path.lineTo(4,4);
+    path.lineTo(2,2);
+    path.close();
+    path.moveTo(2,1);
+    path.lineTo(3,4);
+    path.lineTo(6,1);
+    path.close();
+    testSimplifyx(path);
+}
+
+static void testLine10a() {
+    SkPath path, simple;
+    path.moveTo(0,4);
+    path.lineTo(8,4);
+    path.lineTo(4,0);
+    path.close();
+    path.moveTo(2,2);
+    path.lineTo(3,3);
+    path.lineTo(4,2);
+    path.close();
+    testSimplifyx(path);
+}
+
+static void addCWContainer(SkPath& path) {
+    path.moveTo(6,4);
+    path.lineTo(0,4);
+    path.lineTo(3,1);
+    path.close();
+}
+
+static void addCCWContainer(SkPath& path) {
+    path.moveTo(0,4);
+    path.lineTo(6,4);
+    path.lineTo(3,1);
+    path.close();
+}
+
+static void addCWContents(SkPath& path) {
+    path.moveTo(2,3);
+    path.lineTo(3,2);
+    path.lineTo(4,3);
+    path.close();
+}
+
+static void addCCWContents(SkPath& path) {
+    path.moveTo(3,2);
+    path.lineTo(2,3);
+    path.lineTo(4,3);
+    path.close();
+}
+
+static void testLine11() {
+    SkPath path, simple;
+    addCWContainer(path);
+    addCWContents(path);
+    testSimplifyx(path);
+}
+
+static void testLine12() {
+    SkPath path, simple;
+    addCCWContainer(path);
+    addCWContents(path);
+    testSimplifyx(path);
+}
+
+static void testLine13() {
+    SkPath path, simple;
+    addCWContainer(path);
+    addCCWContents(path);
+    testSimplifyx(path);
+}
+
+static void testLine14() {
+    SkPath path, simple;
+    addCCWContainer(path);
+    addCCWContents(path);
+    testSimplifyx(path);
+}
+
+static void testLine15() {
+    SkPath path, simple;
+    path.addRect(0, 0, 9, 9, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine16() {
+    SkPath path, simple;
+    path.addRect(0, 0, 12, 12, (SkPath::Direction) 0);
+    path.addRect(0, 4, 9, 9, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine17() {
+    SkPath path, simple;
+    path.addRect(0, 0, 12, 12, (SkPath::Direction) 0);
+    path.addRect(4, 12, 13, 13, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine18() {
+    SkPath path, simple;
+    path.addRect(0, 0, 12, 12, (SkPath::Direction) 0);
+    path.addRect(12, 4, 21, 21, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine19() {
+    SkPath path, simple;
+    path.addRect(0, 0, 12, 12, (SkPath::Direction) 0);
+    path.addRect(12, 16, 21, 21, (SkPath::Direction) 0);    
+    testSimplifyx(path);
+}
+
+static void testLine20() {
+    SkPath path, simple;
+    path.addRect(0, 12, 12, 12, (SkPath::Direction) 0);
+    path.addRect(0, 12, 9, 9, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine21() {
+    SkPath path, simple;
+    path.addRect(0, 12, 12, 12, (SkPath::Direction) 0);
+    path.addRect(0, 16, 9, 9, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine22() {
+    SkPath path, simple;
+    path.addRect(0, 12, 12, 12, (SkPath::Direction) 0);
+    path.addRect(4, 12, 13, 13, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine23() {
+    SkPath path, simple;
+    path.addRect(0, 12, 12, 12, (SkPath::Direction) 0);
+    path.addRect(12, 0, 21, 21, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+
+
+static void testLine24a() {
+    SkPath path, simple;
+    path.moveTo(2,0);
+    path.lineTo(4,4);
+    path.lineTo(0,4);
+    path.close();
+    path.moveTo(2,0);
+    path.lineTo(1,2);
+    path.lineTo(2,2);
+    path.close();
+    testSimplifyx(path);
+}
+
+static void testLine24() {
+    SkPath path, simple;
+    path.addRect(0, 18, 12, 12, (SkPath::Direction) 0);
+    path.addRect(4, 12, 13, 13, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine25() {
+    SkPath path, simple;
+    path.addRect(0, 6, 12, 12, (SkPath::Direction) 0);
+    path.addRect(12, 0, 21, 21, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine26() {
+    SkPath path, simple;
+    path.addRect(0, 18, 12, 12, (SkPath::Direction) 0);
+    path.addRect(0, 12, 9, 9, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+static void testLine27() {
+    SkPath path, simple;
+    path.addRect(0, 18, 12, 12, (SkPath::Direction) 0);
+    path.addRect(12, 8, 21, 21, (SkPath::Direction) 0);
+    testSimplifyx(path);
+}
+
+#define TEST(name) { name, #name }
 
-static void (*tests[])() = {
-    testLine1,
-    testLine2,
-    testLine3,
-    testLine4,
-    testLine5,
-    testLine6,
-    testLine7,
-    testLine8,
-    testLine9
+static struct {
+    void (*fun)();
+    const char* str;
+} tests[] = {
+    TEST(testLine1),
+    TEST(testLine2),
+    TEST(testLine3),
+    TEST(testLine4),
+    TEST(testLine5),
+    TEST(testLine6),
+    TEST(testLine7),
+    TEST(testLine8),
+    TEST(testLine9),
+    TEST(testLine10),
+    TEST(testLine10a),
+    TEST(testLine11),
+    TEST(testLine12),
+    TEST(testLine13),
+    TEST(testLine14),
+    TEST(testLine15),
+    TEST(testLine16),
+    TEST(testLine17),
+    TEST(testLine18),
+    TEST(testLine19),
+    TEST(testLine20),
+    TEST(testLine21),
+    TEST(testLine22),
+    TEST(testLine23),
+    TEST(testLine24a),
+    TEST(testLine24),
+    TEST(testLine25),
+    TEST(testLine26),
+    TEST(testLine27),
 };
 
 static const size_t testCount = sizeof(tests) / sizeof(tests[0]);
@@ -170,14 +361,14 @@ void SimplifyNew_Test() {
     }
     size_t index = 0;
     if (firstTest) {
-        while (index < testCount && tests[index] != firstTest) {
+        while (index < testCount && tests[index].fun != firstTest) {
             ++index;
         }
     }
     bool firstTestComplete = false;
     for ( ; index < testCount; ++index) {
-        SkDebugf("%s [%d]\n", __FUNCTION__, index + 1);
-        (*tests[index])();
+        SkDebugf("%s [%s]\n", __FUNCTION__, tests[index].str);
+        (*tests[index].fun)();
         firstTestComplete = true;
     }
 }
diff --git a/experimental/Intersection/SimplifyRect4x4_Test.cpp b/experimental/Intersection/SimplifyRect4x4_Test.cpp
new file mode 100644
index 0000000000..b83c1cd032
--- /dev/null
+++ b/experimental/Intersection/SimplifyRect4x4_Test.cpp
@@ -0,0 +1,209 @@
+/*
+ * Copyright 2012 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+#include "EdgeWalker_Test.h"
+#include "Intersection_Tests.h"
+#include "ShapeOps.h"
+#include "SkBitmap.h"
+#include "SkCanvas.h"
+#include <assert.h>
+#include <pthread.h>
+
+// four rects, of four sizes
+// for 3 smaller sizes, tall, wide
+    // top upper mid lower bottom aligned (3 bits, 5 values)
+    // same with x (3 bits, 5 values)
+// not included, square, tall, wide (2 bits)
+// cw or ccw (1 bit)
+
+static void* testSimplify4x4RectsMain(void* data)
+{
+    char pathStr[1024]; // gdb: set print elements 400
+    bzero(pathStr, sizeof(pathStr));
+    SkASSERT(data);
+    State4& state = *(State4*) data;
+    int aShape = state.a & 0x03;
+    int aCW = state.a >> 1;
+    int bShape = state.b & 0x03;
+    int bCW = state.b >> 1;
+    int cShape = state.c & 0x03;
+    int cCW = state.c >> 1;
+    int dShape = state.d & 0x03;
+    int dCW = state.d >> 1;
+    for (int aXAlign = 0 ; aXAlign < 5; ++aXAlign) {
+    for (int aYAlign = 0 ; aYAlign < 5; ++aYAlign) {
+    for (int bXAlign = 0 ; bXAlign < 5; ++bXAlign) {
+    for (int bYAlign = 0 ; bYAlign < 5; ++bYAlign) {
+    for (int cXAlign = 0 ; cXAlign < 5; ++cXAlign) {
+    for (int cYAlign = 0 ; cYAlign < 5; ++cYAlign) {
+    for (int dXAlign = 0 ; dXAlign < 5; ++dXAlign) {
+    for (int dYAlign = 0 ; dYAlign < 5; ++dYAlign) {
+        SkPath path, out;
+        char* str = pathStr;
+        path.setFillType(SkPath::kWinding_FillType);
+        int l, t, r, b;
+        if (aShape) {
+            switch (aShape) {
+                case 1: // square
+                    l =  0; r = 60;
+                    t =  0; b = 60;
+                    aXAlign = 5;
+                    aYAlign = 5;
+                    break;
+                case 2:
+                    l =  aXAlign * 12;
+                    r =  l + 30; 
+                    t =  0; b = 60;
+                    aYAlign = 5;
+                    break;
+                case 3:
+                    l =  0; r = 60;
+                    t =  aYAlign * 12;
+                    b =  l + 30; 
+                    aXAlign = 5;
+                    break;
+            }
+            path.addRect(l, t, r, b, (SkPath::Direction) aCW);
+            str += sprintf(str, "    path.addRect(%d, %d, %d, %d,"
+                    " (SkPath::Direction) %d);\n", l, t, r, b, aCW);
+        } else {
+            aXAlign = 5;
+            aYAlign = 5;
+        }
+        if (bShape) {
+            switch (bShape) {
+                case 1: // square
+                    l =  bXAlign * 10;
+                    r =  l + 20; 
+                    t =  bYAlign * 10;
+                    b =  l + 20; 
+                    break;
+                case 2:
+                    l =  bXAlign * 10;
+                    r =  l + 20; 
+                    t =  10; b = 40;
+                    bYAlign = 5;
+                    break;
+                case 3:
+                    l =  10; r = 40;
+                    t =  bYAlign * 10;
+                    b =  l + 20; 
+                    bXAlign = 5;
+                    break;
+            }
+            path.addRect(l, t, r, b, (SkPath::Direction) bCW);
+            str += sprintf(str, "    path.addRect(%d, %d, %d, %d,"
+                    " (SkPath::Direction) %d);\n", l, t, r, b, bCW);
+        } else {
+            bXAlign = 5;
+            bYAlign = 5;
+        }
+        if (cShape) {
+            switch (cShape) {
+                case 1: // square
+                    l =  cXAlign * 6;
+                    r =  l + 12; 
+                    t =  cYAlign * 6;
+                    b =  l + 12; 
+                    break;
+                case 2:
+                    l =  cXAlign * 6;
+                    r =  l + 12; 
+                    t =  20; b = 30;
+                    cYAlign = 5;
+                    break;
+                case 3:
+                    l =  20; r = 30;
+                    t =  cYAlign * 6;
+                    b =  l + 20; 
+                    cXAlign = 5;
+                    break;
+            }
+            path.addRect(l, t, r, b, (SkPath::Direction) cCW);
+            str += sprintf(str, "    path.addRect(%d, %d, %d, %d,"
+                    " (SkPath::Direction) %d);\n", l, t, r, b, cCW);
+        } else {
+            cXAlign = 5;
+            cYAlign = 5;
+        }
+        if (dShape) {
+            switch (dShape) {
+                case 1: // square
+                    l =  dXAlign * 4;
+                    r =  l + 9; 
+                    t =  dYAlign * 4;
+                    b =  l + 9; 
+                    break;
+                case 2:
+                    l =  dXAlign * 6;
+                    r =  l + 9; 
+                    t =  32; b = 36;
+                    dYAlign = 5;
+                    break;
+                case 3:
+                    l =  32; r = 36;
+                    t =  dYAlign * 6;
+                    b =  l + 9; 
+                    dXAlign = 5;
+                    break;
+            }
+            path.addRect(l, t, r, b, (SkPath::Direction) dCW);
+            str += sprintf(str, "    path.addRect(%d, %d, %d, %d,"
+                    " (SkPath::Direction) %d);\n", l, t, r, b, dCW);
+        } else {
+            dXAlign = 5;
+            dYAlign = 5;
+        }
+        path.close();
+        SkDebugf("%s", pathStr);
+        if (!testSimplifyx(path, out, state.bitmap, state.canvas)) {
+            SkDebugf("*/\n{ %s %d, %d, %d, %d, %d, %d, %d, %d,"
+                    " %d, %d, %d, %d },\n/*\n", 
+                    __FUNCTION__, state.a, state.b, state.c, state.d,
+                    aXAlign, aYAlign, bXAlign, bYAlign,
+                    cXAlign, cYAlign, dXAlign, dYAlign);
+        }               
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+    return NULL;
+}
+
+const int maxThreads = 1; // gRunTestsInOneThread ? 1 : 24;
+
+void Simplify4x4RectsThreaded_Test()
+{
+    State4 threadState[maxThreads];
+    int threadIndex = 0;
+    for (int a = 0; a < 8; ++a) { // outermost
+        for (int b = a ; b < 8; ++b) {
+            for (int c = b ; c < 8; ++c) {
+                for (int d = c; d < 8; ++d) {                 
+                    State4* statePtr = &threadState[threadIndex];
+                    statePtr->a = a;
+                    statePtr->b = b;
+                    statePtr->c = c;
+                    statePtr->d = d;
+                    if (maxThreads > 1) {
+                        createThread(statePtr, testSimplify4x4RectsMain);
+                        if (++threadIndex >= maxThreads) {
+                            waitForCompletion(threadState, threadIndex);
+                        }
+                    } else {
+                        testSimplify4x4RectsMain(statePtr);
+                    }
+                }
+            }
+        }
+    }
+    waitForCompletion(threadState, threadIndex);
+}
+
diff --git a/experimental/Intersection/edge.xcodeproj/project.pbxproj b/experimental/Intersection/edge.xcodeproj/project.pbxproj
deleted file mode 100644
index 6a6ea320b0..0000000000
--- a/experimental/Intersection/edge.xcodeproj/project.pbxproj
+++ /dev/null
@@ -1,1134 +0,0 @@
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diff --git a/experimental/Intersection/op.htm b/experimental/Intersection/op.htm
index 5173eaba27..f496f7c16a 100644
--- a/experimental/Intersection/op.htm
+++ b/experimental/Intersection/op.htm
@@ -259,11 +259,76 @@ path.close();
     testSimplify(path, true, out, bitmap);
     drawAsciiPaths(path, out, true);
 </div>
+
+<div id="testSimplifyQuadratic19">
+    SkPath path, simple;
+    path.moveTo(0,4);
+    path.lineTo(6,4);
+    path.lineTo(3,1);
+    path.close();
+    path.moveTo(2,3);
+    path.lineTo(3,2);
+    path.lineTo(4,3);
+    path.close();
+    testSimplifyx(path);
+</div>
+
+<div id="testSimplifyQuadratic20">
+    SkPath path, simple;
+    path.moveTo(0,4);
+    path.lineTo(6,4);
+    path.lineTo(3,1);
+    path.close();
+    path.moveTo(2,3);
+    path.lineTo(4,3);
+    path.lineTo(3,2);
+    path.close();
+    testSimplifyx(path);
+</div>
+
+<div id="testSimplifyQuadratic21">
+    SkPath path, simple;
+    path.moveTo(0,4);
+    path.lineTo(8,4);
+    path.lineTo(4,0);
+    path.close();
+    path.moveTo(2,2);
+    path.lineTo(3,3);
+    path.lineTo(4,2);
+    path.close();
+    testSimplifyx(path);
+</div>
+
+<div id="testLine6">
+    SkPath path, simple;
+    path.moveTo(0,0);
+    path.lineTo(4,0);
+    path.lineTo(2,2);
+    path.close();
+    path.moveTo(2,0);
+    path.lineTo(6,0);
+    path.lineTo(4,2);
+    path.close();
+    testSimplifyx(path);
+</div>
+
+<!-- don't support addRect yet -->
+<div id="testLine17">
+    SkPath path, simple;
+    path.addRect(0, 0, 12, 12, (SkPath::Direction) 0);
+    path.addRect(4, 12, 13, 13, (SkPath::Direction) 0);
+    testSimplifyx(path);
+</div>
+
 </div>
 
 <script type="text/javascript">
 
 var testDivs = [
+    testLine6,
+    testSimplifyQuadratic21,
+    testSimplifyQuadratic20,
+    testSimplifyQuadratic19,
     testSimplifyQuadratic18,
     testSimplifyQuadratic17,
     testSimplifyQuadratic16,
@@ -412,10 +477,10 @@ function draw(test, _at_x, _at_y, scale) {
     }
     ctx.strokeStyle = "red";
     var contours, verbs, pts;
+    ctx.beginPath();
     for (contours in test) {
         var contour = test[contours];
         if (contours == 2) ctx.strokeStyle = "blue";
-        ctx.beginPath();
         var first = true;
         for (verbs in contour) {
             var verb = contour[verbs];
@@ -438,8 +503,11 @@ function draw(test, _at_x, _at_y, scale) {
                     break;
             }
         }
-        ctx.stroke();
+        ctx.closePath();
     }
+    ctx.stroke();
+    ctx.fillStyle="rgba(192,192,255, 0.3)";
+    ctx.fill();
     
     ctx.fillStyle="blue";
     for (contours in test) {
diff --git a/experimental/Intersection/thingsToDo.txt b/experimental/Intersection/thingsToDo.txt
index e3aec3e9cd..ab1be7fbf3 100644
--- a/experimental/Intersection/thingsToDo.txt
+++ b/experimental/Intersection/thingsToDo.txt
@@ -164,3 +164,356 @@ According to Mike/Rob, the flatness for quadratics increases by 4 for each
 subdivision, and a crude guess of the curvature can be had by comparing P1 to
 (P0+P2)/2. By looking at the ULPS of the numbers, I can guess what value of
 T may be far enough that the curves diverge but don't cross.
+
+====
+
+Code I May Not Need Any More
+
+    static bool CoincidentCandidate(const Angle* current) {
+        const Segment* segment = current->segment();
+        int min = SkMin32(current->start(), current->end());
+        do {
+            const Span& span = segment->fTs[min];
+            if (span.fCoincident == Span::kStart_Coincidence) {
+                return true;
+            }
+        } while (--min >= 0);
+        return false;
+    }
+
+    static bool CoincidentHalf(const Angle* current, const Angle* next) {
+        const Segment* other = next->segment();
+        const Segment* segment = current->segment();
+        int min = SkMin32(current->start(), current->end());
+        const Span& minSpan = segment->fTs[min];
+        if (minSpan.fOther == other) {
+            return minSpan.fCoincident == Span::kStart_Coincidence;
+        }
+        int index = min;
+        int spanCount = segment->fTs.count();
+        while (++index < spanCount) {
+            const Span& span = segment->fTs[index];
+            if (minSpan.fT != span.fT) {
+                break;
+            }
+            if (span.fOther != other) {
+                continue;
+            }
+            return span.fCoincident == Span::kStart_Coincidence;
+        }
+        index = min;
+        while (--index >= 0) {
+            const Span& span = segment->fTs[index];
+            if (span.fOther != other) {
+                continue;
+            }
+            return span.fCoincident == Span::kStart_Coincidence;
+        }
+        return false;
+    }
+    
+    static bool Coincident(const Angle* current, const Angle* next) {
+        return CoincidentHalf(current, next) &&
+                CoincidentHalf(next, current);
+    }
+
+    // If three lines cancel in a - b - c order, a - b may or may not
+    // eliminate the edge that describes the b - c cancellation. Check done to
+    // determine this.
+    static bool CoincidentCancels(const Angle* current, const Angle* next) {
+        int curMin = SkMin32(current->start(), current->end());
+        if (current->segment()->fTs[curMin].fDone) {
+            return false;
+        }
+        int nextMin = SkMin32(next->start(), next->end());
+        if (next->segment()->fTs[nextMin].fDone) {
+            return false;
+        }
+        return SkSign32(current->start() - current->end())
+                != SkSign32(next->start() - next->end());
+    }
+
+    // FIXME: at this point, just have two functions for the different steps
+    int coincidentEnd(int from, int step) const {
+        double fromT = fTs[from].fT;
+        int count = fTs.count();
+        int to = from;
+        while (step > 0 ? ++to < count : --to >= 0) {
+            const Span& span = fTs[to];
+            if ((step > 0 ? span.fT - fromT : fromT - span.fT) >= FLT_EPSILON ) {
+                // FIXME: we assume that if the T changes, we don't care about 
+                // coincident -- but in nextSpan, we require that both the T
+                // and actual loc change to represent a span. This asymettry may
+                // be OK or may be trouble -- if trouble, probably will need to
+                // detect coincidence earlier or sort differently 
+                break;
+            }
+#if 01
+            if (span.fCoincident == (step < 0 ? Span::kStart_Coincidence :
+                    Span::kEnd_Coincidence)) {
+                from = to;
+            }
+#else
+            from = to;
+#endif
+        }
+        return from;
+    }
+
+    // once past current span, if step>0, look for coicident==1
+    // if step<0, look for coincident==-1
+    int nextSpanEnd(int from, int step) const {
+        int result = nextSpan(from, step);
+        if (result < 0) {
+            return result;
+        }
+        return coincidentEnd(result, step);
+    }
+
+    
+    void adjustFirst(const SkTDArray<Angle*>& sorted, int& first, int& winding,
+            bool outside) {
+        int firstIndex = first;
+        int angleCount = sorted.count();
+        if (true || outside) {
+            const Angle* angle = sorted[firstIndex];
+            int prior = firstIndex;
+            do {
+                if (--prior < 0) {
+                    prior = angleCount - 1;
+                }
+                if (prior == firstIndex) { // all are coincident with each other
+                    return;
+                }
+                if (!Coincident(sorted[prior], sorted[first])) {
+                    return;
+                }
+                winding += angle->sign();
+                first = prior;
+                angle = sorted[prior];
+                winding -= angle->sign();
+            } while (true);
+        }
+        do {
+            int next = first + 1;
+            if (next == angleCount) {
+                next = 0;
+            }
+            if (next == firstIndex) { // all are coincident with each other
+                return;
+            }
+            if (!Coincident(sorted[first], sorted[next])) {
+                return;
+            }
+            first = next;
+        } while (true);
+    }
+
+            bool nextIsCoincident = CoincidentCandidate(nextAngle);
+            bool finalOrNoCoincident = true;
+            bool pairCoincides = false;
+            bool pairCancels = false;
+            if (nextIsCoincident) {
+                int followIndex = nextIndex + 1;
+                if (followIndex == angleCount) {
+                    followIndex = 0;
+                }
+                const Angle* followAngle = sorted[followIndex];
+                finalOrNoCoincident = !Coincident(nextAngle, followAngle);
+                if ((pairCoincides = Coincident(angle, nextAngle))) {
+                    pairCancels = CoincidentCancels(angle, nextAngle);
+                }
+            }
+            if (pairCancels && !foundAngle && !nextSegment->done()) {
+                Segment* aSeg = angle->segment();
+      //          alreadyMarked |= aSeg == sorted[firstIndex]->segment();
+                aSeg->markAndChaseCoincident(angle->start(), angle->end(),
+                        nextSegment);
+                if (firstEdge) {
+                    return NULL;
+                }
+            }
+            if (pairCoincides) {
+                if (pairCancels) {
+                    goto doNext;
+                }
+                int minT = SkMin32(nextAngle->start(), nextAngle->end());
+                bool markNext = abs(maxWinding) < abs(winding);
+                if (markNext) {
+                    nextSegment->markDone(minT, winding);
+                } 
+                int oldMinT = SkMin32(angle->start(), angle->end());
+                if (true || !foundAngle) {
+                 //   SkASSERT(0); // do we ever get here?
+                    Segment* aSeg = angle->segment();
+        //            alreadyMarked |= aSeg == sorted[firstIndex]->segment();
+                    aSeg->markDone(oldMinT, maxWinding);
+                }
+            }
+
+    // OPTIMIZATION: uses tail recursion. Unwise?
+    void innerCoincidentChase(int step, Segment* other) {
+        // find other at index
+   //     SkASSERT(!done());
+        const Span* start = NULL;
+        const Span* end = NULL;
+        int index, startIndex, endIndex;
+        int count = fTs.count();
+        for (index = 0; index < count; ++index) {
+            const Span& span = fTs[index];
+            if (!span.fCoincident || span.fOther != other) {
+                continue;
+            }
+            if (!start) {
+                startIndex = index;
+                start = &span;
+            } else {
+                SkASSERT(!end);
+                endIndex = index;
+                end = &span;
+            }
+        }
+        if (!end) {
+            return;
+        }
+        bool thisDone = fTs[SkMin32(startIndex, endIndex)].fDone;
+        bool otherDone = other->fTs[SkMin32(start->fOtherIndex,
+                end->fOtherIndex)].fDone;
+        if (thisDone && otherDone) {
+            return;
+        }
+        Segment* next;
+        Segment* nextOther;
+        if (step < 0) {
+            next = start->fT == 0 ? NULL : this;
+            nextOther = other->fTs[start->fOtherIndex].fT > 1 - FLT_EPSILON ? NULL : other;
+        } else {
+            next = end->fT == 1 ? NULL : this;
+            nextOther = other->fTs[end->fOtherIndex].fT < FLT_EPSILON ? NULL : other;
+        }
+        SkASSERT(!next || !nextOther);
+        for (index = 0; index < count; ++index) {
+            const Span& span = fTs[index];
+            if (span.fCoincident || span.fOther == other) {
+                continue;
+            }
+            bool checkNext = !next && (step < 0 ? span.fT < FLT_EPSILON
+                && span.fOtherT > 1 - FLT_EPSILON : span.fT > 1 - FLT_EPSILON
+                && span.fOtherT < FLT_EPSILON);
+            bool checkOther = !nextOther && (step < 0 ? fabs(span.fT - start->fT) < FLT_EPSILON
+                && span.fOtherT < FLT_EPSILON : fabs(span.fT - end->fT) < FLT_EPSILON
+                && span.fOtherT > 1 - FLT_EPSILON);
+            if (!checkNext && !checkOther) {
+                continue;
+            }
+            Segment* oSegment = span.fOther;
+            if (oSegment->done()) {
+                continue;
+            }
+            int oCount = oSegment->fTs.count();
+            for (int oIndex = 0; oIndex < oCount; ++oIndex) {
+                const Span& oSpan = oSegment->fTs[oIndex];
+                if (oSpan.fT >= FLT_EPSILON && oSpan.fT <= 1 - FLT_EPSILON) {
+                    continue;
+                }
+                if (!oSpan.fCoincident) {
+                    continue;
+                }
+                if (checkNext && (oSpan.fT < FLT_EPSILON ^ step < 0)) { 
+                    next = oSegment;
+                    checkNext = false;
+                }
+                if (checkOther && (oSpan.fT > 1 - FLT_EPSILON ^ step < 0)) {
+                    nextOther = oSegment;
+                    checkOther = false;
+                }
+            }
+        }
+        // this needs to walk both spans in lock step, skipping edges that
+        // are already marked done on one or the other
+        markCanceled(startIndex, endIndex);
+        if (next && nextOther) {
+            next->innerCoincidentChase(step, nextOther);
+        }
+    }
+
+    // cancel coincident edges in lock step
+    void markCanceled(int start, int end) {
+        if (done()) {
+            return;
+        }
+        Segment* other = fTs[start].fOther;
+        if (other->done()) {
+            return;
+        }
+        if (start > end) {
+            SkTSwap<int>(start, end);
+        }
+        double maxT = fTs[end].fT - FLT_EPSILON;
+        int spanCount = fTs.count();
+        // since these cancel, this walks up and other walks down
+        int oStart = fTs[start].fOtherIndex;
+        double oStartT = other->fTs[oStart].fT;
+        while (oStartT - other->fTs[--oStart].fT < FLT_EPSILON)
+            ;
+        double startT = fTs[start].fT;
+        while (start > 0 && startT - fTs[start - 1].fT < FLT_EPSILON) {
+            --start;
+        }
+        do {
+            Span* span = &fTs[start];
+            Span* oSpan = &other->fTs[oStart];
+            // find start of each, and see if both are not done
+            bool markDone = !span->fDone && !oSpan->fDone;
+            double spanT = span->fT;
+            do {
+                if (markDone) {
+                    span->fCanceled = true;
+                #if DEBUG_MARK_DONE
+                    const SkPoint& pt = xyAtT(span);
+                    SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g)\n",
+                            __FUNCTION__, fID, start, span->fT, pt.fX, pt.fY);
+                #endif
+                    SkASSERT(!span->fDone);
+                    span->fDone = true;
+                    span->fWinding = 0;
+                    fDoneSpans++;
+                }
+                if (++start == spanCount) {
+                    break;
+                }
+                span = &fTs[start];
+            } while (span->fT - spanT < FLT_EPSILON);
+            double oSpanT = oSpan->fT;
+            do {
+                if (markDone) {
+                    oSpan->fCanceled = true;
+                #if DEBUG_MARK_DONE
+                    const SkPoint& oPt = xyAtT(oSpan);
+                    SkDebugf("%s segment=%d index=%d t=%1.9g pt=(%1.9g,%1.9g)\n",
+                            __FUNCTION__, other->fID, oStart, oSpan->fT,
+                            oPt.fX, oPt.fY);
+                #endif
+                    SkASSERT(!oSpan->fDone);
+                    oSpan->fDone = true;
+                    oSpan->fWinding = 0;
+                    other->fDoneSpans++;
+                }
+                if (--oStart < 0) {
+                    break;
+                }
+                oSpan = &other->fTs[oStart];
+            } while (oSpanT - oSpan->fT < FLT_EPSILON);
+        } while (fTs[start].fT <= maxT);
+    }
+
+    bool canceled(int start, int end) const {
+        int min = SkMin32(start, end);
+        return fTs[min].fCanceled;
+    }
+
+    void markAndChaseCoincident(int index, int endIndex, Segment* other) {
+        int step = SkSign32(endIndex - index);
+        innerCoincidentChase(step, other);
+    }
+