work in progress

in the middle of switching to sortless version

git-svn-id: http://skia.googlecode.com/svn/trunk@3768 2bbb7eff-a529-9590-31e7-b0007b416f81

1 files changed, 1213 insertions, 0 deletions

diff --git a/experimental/Intersection/Simplify.cpp b/experimental/Intersection/Simplify.cpp
new file mode 100644
index 0000000000..5d7209a09d
--- /dev/null
+++ b/experimental/Intersection/Simplify.cpp
@@ -0,0 +1,1213 @@
+/*
+ * 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 "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"
+
+#undef SkASSERT
+#define SkASSERT(cond) while (!(cond)) { sk_throw(); }
+
+// FIXME: remove once debugging is complete
+#if 0 // set to 1 for no debugging whatsoever
+
+//const bool gxRunTestsInOneThread = false;
+
+#define DEBUG_ADD_INTERSECTING_TS 0
+#define DEBUG_BRIDGE 0
+#define DEBUG_DUMP 0
+
+#else
+
+//const bool gRunTestsInOneThread = true;
+
+#define DEBUG_ADD_INTERSECTING_TS 1
+#define DEBUG_BRIDGE 1
+#define DEBUG_DUMP 1
+
+#endif
+
+#if DEBUG_DUMP
+static const char* kLVerbStr[] = {"", "line", "quad", "cubic"};
+static const char* kUVerbStr[] = {"", "Line", "Quad", "Cubic"};
+static int gContourID;
+static int gSegmentID;
+#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}};
+    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
+    return intersect(aLine, bLine, intersections.fT[0], intersections.fT[1]);
+}
+
+static int QuadLineIntersect(const SkPoint a[3], const SkPoint b[2],
+        Intersections& intersections) {
+    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
+    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
+    intersect(aQuad, bLine, intersections);
+    return intersections.fUsed;
+}
+
+static int CubicLineIntersect(const SkPoint a[2], const SkPoint b[3],
+        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}};
+    const _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
+    return intersect(aCubic, bLine, intersections.fT[0], intersections.fT[1]);
+}
+
+static int QuadIntersect(const SkPoint a[3], const SkPoint b[3],
+        Intersections& intersections) {
+    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
+    const Quadratic bQuad = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY}};
+    intersect(aQuad, bQuad, intersections);
+    return intersections.fUsed;
+}
+
+static int CubicIntersect(const SkPoint a[4], const SkPoint b[4],
+        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}};
+    const Cubic bCubic = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}, {b[2].fX, b[2].fY},
+            {b[3].fX, b[3].fY}};
+    intersect(aCubic, bCubic, intersections);
+    return intersections.fUsed;
+}
+
+static int HLineIntersect(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 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},
+            {a[3].fX, a[3].fY}};
+    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) {
+    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);
+}
+
+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;
+    xy_at_t(line, t, x, y);
+    out->fX = SkDoubleToScalar(x);
+    out->fY = SkDoubleToScalar(y);
+}
+
+static void QuadXYAtT(const SkPoint a[3], double t, SkPoint* out) {
+    const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}, {a[2].fX, a[2].fY}};
+    double x, y;
+    xy_at_t(quad, t, x, y);
+    out->fX = SkDoubleToScalar(x);
+    out->fY = SkDoubleToScalar(y);
+}
+
+static void CubicXYAtT(const SkPoint a[4], double t, SkPoint* out) {
+    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, y;
+    xy_at_t(cubic, t, x, y);
+    out->fX = SkDoubleToScalar(x);
+    out->fY = SkDoubleToScalar(y);
+}
+
+static void (* const SegmentXYAtT[])(const SkPoint [], double , SkPoint* ) = {
+    NULL,
+    LineXYAtT,
+    QuadXYAtT,
+    CubicXYAtT
+};
+
+static SkScalar LineXAtT(const SkPoint a[2], double t) {
+    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
+    double x;
+    xy_at_t(aLine, t, x, *(double*) 0);
+    return SkDoubleToScalar(x);
+}
+
+static SkScalar QuadXAtT(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;
+    xy_at_t(quad, t, x, *(double*) 0);
+    return SkDoubleToScalar(x);
+}
+
+static SkScalar CubicXAtT(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;
+    xy_at_t(cubic, t, x, *(double*) 0);
+    return SkDoubleToScalar(x);
+}
+
+static SkScalar (* const SegmentXAtT[])(const SkPoint [], double ) = {
+    NULL,
+    LineXAtT,
+    QuadXAtT,
+    CubicXAtT
+};
+
+static SkScalar LineYAtT(const SkPoint a[2], double t) {
+    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
+    double y;
+    xy_at_t(aLine, t, *(double*) 0, y);
+    return SkDoubleToScalar(y);
+}
+
+static SkScalar QuadYAtT(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 y;
+    xy_at_t(quad, t, *(double*) 0, y);
+    return SkDoubleToScalar(y);
+}
+
+static SkScalar CubicYAtT(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 y;
+    xy_at_t(cubic, t, *(double*) 0, y);
+    return SkDoubleToScalar(y);
+}
+
+static SkScalar (* const SegmentYAtT[])(const SkPoint [], double ) = {
+    NULL,
+    LineYAtT,
+    QuadYAtT,
+    CubicYAtT
+};
+
+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}};
+    _Line dst;
+    sub_divide(aLine, startT, endT, dst);
+    sub[0].fX = SkDoubleToScalar(dst[0].x);
+    sub[0].fY = SkDoubleToScalar(dst[0].y);
+    sub[1].fX = SkDoubleToScalar(dst[1].x);
+    sub[1].fY = SkDoubleToScalar(dst[1].y);
+}
+
+static void QuadSubDivide(const SkPoint a[3], double startT, double endT,
+        SkPoint sub[3]) {
+    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
+            {a[2].fX, a[2].fY}};
+    Quadratic dst;
+    sub_divide(aQuad, startT, endT, dst);
+    sub[0].fX = SkDoubleToScalar(dst[0].x);
+    sub[0].fY = SkDoubleToScalar(dst[0].y);
+    sub[1].fX = SkDoubleToScalar(dst[1].x);
+    sub[1].fY = SkDoubleToScalar(dst[1].y);
+    sub[2].fX = SkDoubleToScalar(dst[2].x);
+    sub[2].fY = SkDoubleToScalar(dst[2].y);
+}
+
+static void CubicSubDivide(const SkPoint a[4], double startT, double endT,
+        SkPoint sub[4]) {
+    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}};
+    Cubic dst;
+    sub_divide(aCubic, startT, endT, dst);
+    sub[0].fX = SkDoubleToScalar(dst[0].x);
+    sub[0].fY = SkDoubleToScalar(dst[0].y);
+    sub[1].fX = SkDoubleToScalar(dst[1].x);
+    sub[1].fY = SkDoubleToScalar(dst[1].y);
+    sub[2].fX = SkDoubleToScalar(dst[2].x);
+    sub[2].fY = SkDoubleToScalar(dst[2].y);
+    sub[3].fX = SkDoubleToScalar(dst[3].x);
+    sub[3].fY = SkDoubleToScalar(dst[3].y);
+}
+
+static void QuadSubBounds(const SkPoint a[3], double startT, double endT,
+        SkRect& bounds) {
+    SkPoint dst[3];
+    QuadSubDivide(a, startT, endT, dst);
+    bounds.fLeft = bounds.fRight = dst[0].fX;
+    bounds.fTop = bounds.fBottom = dst[0].fY;
+    for (int index = 1; index < 3; ++index) {
+        bounds.growToInclude(dst[index].fX, dst[index].fY);
+    }
+}
+
+static void CubicSubBounds(const SkPoint a[4], double startT, double endT,
+        SkRect& bounds) {
+    SkPoint dst[4];
+    CubicSubDivide(a, startT, endT, dst);
+    bounds.fLeft = bounds.fRight = dst[0].fX;
+    bounds.fTop = bounds.fBottom = dst[0].fY;
+    for (int index = 1; index < 4; ++index) {
+        bounds.growToInclude(dst[index].fX, dst[index].fY);
+    }
+}
+
+static SkPath::Verb QuadReduceOrder(const SkPoint a[4],
+        SkTDArray<SkPoint>& reducePts) {
+    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
+            {a[2].fX, a[2].fY}};
+    Quadratic dst;
+    int order = reduceOrder(aQuad, dst);
+    for (int index = 0; index < order; ++index) {
+        SkPoint* pt = reducePts.append();
+        pt->fX = SkDoubleToScalar(dst[index].x);
+        pt->fY = SkDoubleToScalar(dst[index].y);
+    }
+    return (SkPath::Verb) (order - 1);
+}
+
+static SkPath::Verb CubicReduceOrder(const SkPoint a[4],
+        SkTDArray<SkPoint>& reducePts) {
+    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}};
+    Cubic dst;
+    int order = reduceOrder(aCubic, dst, kReduceOrder_QuadraticsAllowed);
+    for (int index = 0; index < order; ++index) {
+        SkPoint* pt = reducePts.append();
+        pt->fX = SkDoubleToScalar(dst[index].x);
+        pt->fY = SkDoubleToScalar(dst[index].y);
+    }
+    return (SkPath::Verb) (order - 1);
+}
+
+static SkScalar LineLeftMost(const SkPoint a[2], double startT, double endT) {
+    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
+    double x[2];
+    xy_at_t(aLine, startT, x[0], *(double*) 0);
+    xy_at_t(aLine, endT, x[0], *(double*) 0);
+    return startT < endT ? startT : endT;
+}
+
+static SkScalar QuadLeftMost(const SkPoint a[3], double startT, double endT) {
+    const Quadratic aQuad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
+            {a[2].fX, a[2].fY}};
+    return leftMostT(aQuad, startT, endT);
+}
+
+static SkScalar CubicLeftMost(const SkPoint a[4], double startT, double endT) {
+    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 leftMostT(aCubic, startT, endT);
+}
+
+static SkScalar (* const SegmentLeftMost[])(const SkPoint [], double , double) = {
+    NULL,
+    LineLeftMost,
+    QuadLeftMost,
+    CubicLeftMost
+};
+
+static bool IsCoincident(const SkPoint a[2], const SkPoint& above,
+        const SkPoint& below) {
+    const _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
+    const _Line bLine = {{above.fX, above.fY}, {below.fX, below.fY}};
+    return implicit_matches_ulps(aLine, bLine, 32);
+}
+
+// Bounds, unlike Rect, does not consider a vertical 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;
+    }
+
+    bool isEmpty() {
+        return fLeft > fRight || fTop > fBottom
+                || fLeft == fRight && fTop == fBottom
+                || isnan(fLeft) || isnan(fRight)
+                || isnan(fTop) || isnan(fBottom);
+    }
+
+    void setCubicBounds(const SkPoint a[4]) {
+        _Rect dRect;
+        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}};
+        dRect.setBounds(cubic);
+        set(dRect.left, dRect.top, dRect.right, dRect.bottom);
+    }
+
+    void setQuadBounds(const SkPoint a[3]) {
+        const Quadratic quad = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY},
+                {a[2].fX, a[2].fY}};
+        _Rect dRect;
+        dRect.setBounds(quad);
+        set(dRect.left, dRect.top, dRect.right, dRect.bottom);
+    }
+};
+
+class Segment;
+
+struct TEntry {
+    double fT;
+    const Segment* fOther;
+    double fOtherT;
+    bool fCoincident;
+};
+
+class Segment {
+public:
+    Segment() {
+#if DEBUG_DUMP
+        fID = ++gSegmentID;
+#endif
+    }
+    
+    int addT(double newT, const Segment& other) {
+        // FIXME: in the pathological case where there is a ton of intercepts,
+        //  binary search?
+        int insertedAt = -1;
+        TEntry* entry;
+        size_t tCount = fTs.count();
+        double delta;
+        for (size_t idx2 = 0; idx2 < tCount; ++idx2) {
+            if (newT <= fTs[idx2].fT) {
+                insertedAt = idx2;
+                entry = fTs.insert(idx2);
+                goto finish;
+            }
+        }
+        insertedAt = tCount;
+        entry = fTs.append();
+finish:
+        entry->fT = newT;
+        entry->fOther = &other;
+        return insertedAt;
+    }
+    
+    bool addCubic(const SkPoint pts[4]) {
+        fPts = pts;
+        fVerb = SkPath::kCubic_Verb;
+        fBounds.setCubicBounds(pts);
+    }
+
+    bool addLine(const SkPoint pts[2]) {
+        fPts = pts;
+        fVerb = SkPath::kLine_Verb;
+        fBounds.set(pts, 2);
+    }
+    
+    // add 2 to edge or out of range values to get T extremes
+    void addOtherT(int index, double other, bool coincident) {
+        fTs[index].fOtherT = other;
+        fTs[index].fCoincident = coincident;
+    }
+    
+    bool addQuad(const SkPoint pts[3]) {
+        fPts = pts;
+        fVerb = SkPath::kQuad_Verb;
+        fBounds.setQuadBounds(pts);
+    }
+    
+    const Bounds& bounds() const {
+        return fBounds;
+    }
+    
+    int findByT(double t, const Segment* match) const {
+        // OPTIMIZATION: bsearch if count is honkin huge
+        int count = fTs.count();
+        for (int index = 0; index < count; ++index) {
+            const TEntry& entry = fTs[index];
+            if (t == entry.fT && match == entry.fOther) {
+                return index;
+            }
+        }
+        SkASSERT(0); // should never get here
+        return -1;
+    }
+    
+    int findLefty(int tIndex, const SkPoint& base) const {
+        int bestTIndex;
+        SkPoint test;
+        SkScalar bestX = DBL_MAX;
+        int testTIndex = tIndex;
+        while (--testTIndex >= 0) {
+            xyAtT(testTIndex, &test);
+            if (test != base) {
+                continue;
+            }
+            bestX = test.fX;
+            bestTIndex = testTIndex;
+            break;
+        }
+        int count = fTs.count();
+        testTIndex = tIndex;
+        while (++testTIndex < count) {
+            xyAtT(testTIndex, &test);
+            if (test == base) {
+                continue;
+            }
+            return bestX > test.fX ? testTIndex : bestTIndex;
+        }
+        return -1;
+    }
+
+    const Segment* findTop(int& tIndex) const {
+        // iterate through T intersections and return topmost
+        // topmost tangent from y-min to first pt is closer to horizontal
+        int firstT = 0;
+        int lastT = 0;
+        SkScalar topY = fPts[0].fY;
+        int count = fTs.count();
+        int index;
+        for (index = 1; index < count; ++index) {
+            const TEntry& entry = fTs[index];
+            double t = entry.fT;
+            SkScalar yIntercept = (*SegmentYAtT[fVerb])(fPts, t);
+            if (topY > yIntercept) {
+                topY = yIntercept;
+                firstT = lastT = index;
+            } else if (topY == yIntercept) {
+                lastT = index;
+            }
+        }
+        // if a pair of segments go down, choose the higher endpoint
+        if (firstT == lastT && (firstT == 0 || firstT == count - 1)) {
+            tIndex = firstT;
+            return this;
+        }
+        // if the topmost T is not on end, or is three-way or more, find left
+        SkPoint leftBase;
+        xyAtT(firstT, &leftBase);
+        int tLeft = findLefty(firstT, leftBase);
+        SkASSERT(tLeft > 0);
+        const Segment* leftSegment = this;
+        SkScalar left = leftMost(firstT, tLeft);
+        for (index = firstT; index <= lastT; ++index) {
+            const Segment* other = fTs[index].fOther;
+            double otherT = fTs[index].fOtherT;
+            int otherTIndex = other->findByT(otherT, this);
+            // pick companionT closest (but not too close) on either side
+            int otherTLeft = other->findLefty(otherTIndex, leftBase);
+            if (otherTLeft < 0) {
+                continue;
+            }
+            SkScalar otherMost = other->leftMost(otherTIndex, otherTLeft);
+            if (otherMost < left) {
+                leftSegment = other;
+            }
+        }
+        return leftSegment;
+    }
+
+    bool intersected() const {
+        return fTs.count() > 0;
+    }
+
+    bool isHorizontal() const {
+        return fBounds.fTop == fBounds.fBottom;
+    }
+    
+    bool isVertical() const {
+        return fBounds.fLeft == fBounds.fRight;
+    }
+    
+    SkScalar leftMost(int start, int end) const {
+        return (*SegmentLeftMost[fVerb])(fPts, fTs[start].fT, fTs[end].fT);
+    }
+
+    const SkPoint* pts() const {
+        return fPts;
+    }
+    
+    void reset() {
+        fPts = NULL;
+        fVerb = (SkPath::Verb) -1;
+        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
+        fTs.reset();
+    }
+
+    // OPTIMIZATION: remove this function if it's never called
+    double t(int tIndex) const {
+        return fTs[tIndex].fT;
+    }
+    
+    SkPath::Verb verb() const {
+        return fVerb;
+    }
+    
+    SkScalar xAtT(double t) const {
+        return (*SegmentXAtT[fVerb])(fPts, t);
+    }
+
+    void xyAtT(double t, SkPoint* pt) const {
+        (*SegmentXYAtT[fVerb])(fPts, t, pt);
+    }
+
+#if DEBUG_DUMP
+    void dump() const {
+        const char className[] = "Segment";
+        const int tab = 4;
+        for (int i = 0; i < fTs.count(); ++i) {
+            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 coincident=%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].fCoincident);
+        }
+        SkDebugf("%*s [%d] fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)\n",
+                tab + sizeof(className), className, fID,
+                fBounds.fLeft, fBounds.fTop, fBounds.fRight, fBounds.fBottom);
+    }
+#endif
+
+private:
+    const SkPoint* fPts;
+    SkPath::Verb fVerb;
+    Bounds fBounds;
+    SkTDArray<TEntry> fTs;
+#if DEBUG_DUMP
+    int fID;
+#endif
+};
+
+class Contour {
+public:
+    Contour() {
+        reset();
+#if DEBUG_DUMP
+        fID = ++gContourID;
+#endif
+    }
+
+    bool operator<(const Contour& rh) const {
+        return fBounds.fTop == rh.fBounds.fTop
+                ? fBounds.fLeft < rh.fBounds.fLeft
+                : fBounds.fTop < rh.fBounds.fTop;
+    }
+
+    void addCubic(const SkPoint pts[4]) {
+        fSegments.push_back().addCubic(pts);
+        fContainsCurves = true;
+    }
+    void addLine(const SkPoint pts[2]) {
+        fSegments.push_back().addLine(pts);
+    }
+    
+    void addQuad(const SkPoint pts[3]) {
+        fSegments.push_back().addQuad(pts);
+        fContainsCurves = true;
+    }
+    
+    const Bounds& bounds() const { 
+        return fBounds;
+    }
+
+    void complete() {
+        setBounds();
+        fContainsIntercepts = false;
+    }
+    
+    void containsIntercepts() {
+        fContainsIntercepts = true;
+    }
+    
+    void reset() {
+        fSegments.reset();
+        fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
+        fContainsCurves = fContainsIntercepts = false;
+    }
+    
+    Segment& topSegment() {
+        return fSegments[fTopSegment];
+    }
+
+#if DEBUG_DUMP
+    void dump() {
+        int i;
+        const char className[] = "Contour";
+        const int tab = 4;
+        SkDebugf("%s %p (contour=%d)\n", className, this, fID);
+        for (i = 0; i < fSegments.count(); ++i) {
+            SkDebugf("%*s.fSegments[%d]:\n", tab + sizeof(className),
+                    className, i);
+            fSegments[i].dump();
+        }
+        SkDebugf("%*s.fBounds=(l:%1.9g, t:%1.9g r:%1.9g, b:%1.9g)\n",
+                tab + sizeof(className), className,
+                fBounds.fLeft, fBounds.fTop,
+                fBounds.fRight, fBounds.fBottom);
+        SkDebugf("%*s.fTopSegment=%d\n", tab + sizeof(className), className,
+                fTopSegment);
+        SkDebugf("%*s.fContainsIntercepts=%d\n", tab + sizeof(className),
+                className, fContainsIntercepts);
+        SkDebugf("%*s.fContainsCurves=%d\n", tab + sizeof(className),
+                className, fContainsCurves);
+    }
+#endif
+
+protected:
+    void setBounds() {
+        int count = fSegments.count();
+        if (count == 0) {
+            SkDebugf("%s empty contour\n", __FUNCTION__);
+            SkASSERT(0);
+            // FIXME: delete empty contour?
+            return;
+        }
+        fTopSegment = 0;
+        fBounds = fSegments.front().bounds();
+        SkScalar top = fBounds.fTop;
+        for (int index = 1; index < count; ++index) {
+            fBounds.growToInclude(fSegments[index].bounds());
+            if (top > fBounds.fTop) {
+                fTopSegment = index;
+                top = fBounds.fTop;
+            }
+        }
+    }
+    
+public:
+    SkTArray<Segment> fSegments; // not worth accessor functions?
+    
+private:
+    Bounds fBounds;
+    int fTopSegment;
+    bool fContainsIntercepts;
+    bool fContainsCurves;
+#if DEBUG_DUMP
+    int fID;
+#endif
+};
+
+class EdgeBuilder {
+public:
+
+EdgeBuilder(const SkPath& path, SkTArray<Contour>& contours) 
+    : fPath(path)
+    , fCurrentContour(NULL)
+    , fContours(contours)
+{
+#if DEBUG_DUMP
+    gContourID = 0;
+    gSegmentID = 0;
+#endif
+    walk();
+}
+
+protected:
+
+void complete() {
+    if (fCurrentContour && fCurrentContour->fSegments.count()) {
+        fCurrentContour->complete();
+        fCurrentContour = NULL;
+    }
+}
+
+void startContour() {
+    if (!fCurrentContour) {
+        fCurrentContour = fContours.push_back_n(1);
+    }
+}
+
+void walk() {
+    // FIXME:remove once we can access path pts directly
+    SkPath::RawIter iter(fPath); // FIXME: access path directly when allowed
+    SkPoint pts[4];
+    SkPath::Verb verb;
+    do {
+        verb = iter.next(pts);
+        *fPathVerbs.append() = verb;
+        if (verb == SkPath::kMove_Verb) {
+            *fPathPts.append() = pts[0];
+        } else if (verb >= SkPath::kLine_Verb && verb <= SkPath::kCubic_Verb) {
+            fPathPts.append(verb, &pts[1]);
+        }
+    } while (verb != SkPath::kDone_Verb);
+    // FIXME: end of section to remove once path pts are accessed directly
+    
+    SkPath::Verb reducedVerb;
+    uint8_t* verbPtr = fPathVerbs.begin();
+    const SkPoint* pointsPtr = fPathPts.begin();
+    while ((verb = (SkPath::Verb) *verbPtr++) != SkPath::kDone_Verb) {
+        switch (verb) {
+            case SkPath::kMove_Verb:
+                complete();
+                startContour();
+                pointsPtr += 1;
+                continue;
+            case SkPath::kLine_Verb:
+                // skip degenerate points
+                if (pointsPtr[-1].fX != pointsPtr[0].fX
+                        || pointsPtr[-1].fY != pointsPtr[0].fY) {
+                    fCurrentContour->addLine(&pointsPtr[-1]);
+                }
+                break;
+            case SkPath::kQuad_Verb:
+                reducedVerb = QuadReduceOrder(&pointsPtr[-1], fReducePts);
+                if (reducedVerb == 0) {
+                    break; // skip degenerate points
+                }
+                if (reducedVerb == 1) {
+                    fCurrentContour->addLine(fReducePts.end() - 2);
+                    break;
+                }
+                fCurrentContour->addQuad(&pointsPtr[-1]);
+                break;
+            case SkPath::kCubic_Verb:
+                reducedVerb = CubicReduceOrder(&pointsPtr[-1], fReducePts);
+                if (reducedVerb == 0) {
+                    break; // skip degenerate points
+                }
+                if (reducedVerb == 1) {
+                    fCurrentContour->addLine(fReducePts.end() - 2);
+                    break;
+                }
+                if (reducedVerb == 2) {
+                    fCurrentContour->addQuad(fReducePts.end() - 3);
+                    break;
+                }
+                fCurrentContour->addCubic(&pointsPtr[-1]);
+                break;
+            case SkPath::kClose_Verb:
+                SkASSERT(fCurrentContour);
+                complete();
+                continue;
+            default:
+                SkDEBUGFAIL("bad verb");
+                return;
+        }
+        pointsPtr += verb;
+        SkASSERT(fCurrentContour);
+    }
+    complete();
+    if (fCurrentContour && !fCurrentContour->fSegments.count()) {
+        fContours.pop_back();
+    }
+}
+
+private:
+    const SkPath& fPath;
+    SkTDArray<SkPoint> fPathPts; // FIXME: point directly to path pts instead
+    SkTDArray<uint8_t> fPathVerbs; // FIXME: remove 
+    Contour* fCurrentContour;
+    SkTArray<Contour>& fContours;
+    SkTDArray<SkPoint> fReducePts; // segments created on the fly
+};
+
+class Work {
+public:
+    enum SegmentType {
+        kHorizontalLine_Segment = -1,
+        kVerticalLine_Segment = 0,
+        kLine_Segment = SkPath::kLine_Verb,
+        kQuad_Segment = SkPath::kQuad_Verb,
+        kCubic_Segment = SkPath::kCubic_Verb,
+    };
+    
+    void addOtherT(int index, double other, bool coincident) {
+        fContour->fSegments[fIndex].addOtherT(index, other, coincident);
+    }
+    
+    // Avoid collapsing t values that are close to the same since
+    // we walk ts to describe consecutive intersections. Since a pair of ts can
+    // 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) {
+        fContour->containsIntercepts();
+        return fContour->fSegments[fIndex].addT(newT,
+                other.fContour->fSegments[other.fIndex]);
+    }
+    
+    bool advance() {
+        return ++fIndex < fLast;
+    }
+    
+    SkScalar bottom() const {
+        return bounds().fBottom;
+    }
+    
+    const Bounds& bounds() const {
+        return fContour->fSegments[fIndex].bounds();
+    }
+    
+    const SkPoint* cubic() const {
+        return fCubic;
+    }
+
+    void init(Contour* contour) {
+        fContour = contour;
+        fIndex = 0;
+        fLast = contour->fSegments.count();
+    }
+
+    SkScalar left() const {
+        return bounds().fLeft;
+    }
+    
+    void promoteToCubic() {
+        fCubic[0] = pts()[0];
+        fCubic[2] = pts()[1];
+        fCubic[3] = pts()[2];
+        fCubic[1].fX = (fCubic[0].fX + fCubic[2].fX * 2) / 3;
+        fCubic[1].fY = (fCubic[0].fY + fCubic[2].fY * 2) / 3;
+        fCubic[2].fX = (fCubic[3].fX + fCubic[2].fX * 2) / 3;
+        fCubic[2].fY = (fCubic[3].fY + fCubic[2].fY * 2) / 3;
+    }
+    
+    const SkPoint* pts() const {
+        return fContour->fSegments[fIndex].pts();
+    }
+
+    SkScalar right() const {
+        return bounds().fRight;
+    }
+    
+    ptrdiff_t segmentIndex() const {
+        return fIndex;
+    }
+    
+    SegmentType segmentType() const {
+        const Segment& segment = fContour->fSegments[fIndex];
+        SegmentType type = (SegmentType) segment.verb();
+        if (type != kLine_Segment) {
+            return type;
+        }
+        if (segment.isHorizontal()) {
+            return kHorizontalLine_Segment;
+        }
+        if (segment.isVertical()) {
+            return kVerticalLine_Segment;
+        }
+        return kLine_Segment;
+    }
+    
+    bool startAfter(const Work& after) {
+        fIndex = after.fIndex;
+        return advance();
+    }
+
+    SkScalar top() const {
+        return bounds().fTop;
+    }
+    
+    SkPath::Verb verb() const {
+        return fContour->fSegments[fIndex].verb();
+    }
+    
+    SkScalar x() const {
+        return bounds().fLeft;
+    }
+
+    bool xFlipped() const {
+        return x() != pts()[0].fX;
+    }
+
+    SkScalar y() const {
+        return bounds().fTop;
+    }
+
+    bool yFlipped() const {
+        return y() != pts()[0].fX;
+    }
+
+protected:
+    Contour* fContour;
+    SkPoint fCubic[4];
+    int fIndex;
+    int fLast;
+};
+
+static void debugShowLineIntersection(int pts, const Work& wt,
+        const Work& wn, const double wtTs[2], const double wnTs[2]) {
+#if DEBUG_ADD_INTERSECTING_TS
+    if (!pts) {
+        return;
+    }
+    SkPoint wtOutPt, wnOutPt;
+    LineXYAtT(wt.pts(), wtTs[0], &wtOutPt);
+    LineXYAtT(wn.pts(), wnTs[0], &wnOutPt);
+    SkDebugf("%s wtTs[0]=%g (%g,%g, %g,%g) (%g,%g)\n",
+            __FUNCTION__,
+            wtTs[0], wt.pts()[0].fX, wt.pts()[0].fY,
+            wt.pts()[1].fX, wt.pts()[1].fY, wtOutPt.fX, wtOutPt.fY);
+    if (pts == 2) {
+        SkDebugf("%s wtTs[1]=%g\n", __FUNCTION__, wtTs[1]);
+    }
+    SkDebugf("%s wnTs[0]=%g (%g,%g, %g,%g) (%g,%g)\n",
+            __FUNCTION__,
+            wnTs[0], wn.pts()[0].fX, wn.pts()[0].fY,
+            wn.pts()[1].fX, wn.pts()[1].fY, wnOutPt.fX, wnOutPt.fY);
+    if (pts == 2) {
+        SkDebugf("%s wnTs[1]=%g\n", __FUNCTION__, wnTs[1]);
+    }
+#endif
+}
+
+static bool addIntersectingTs(Contour* test, Contour* next) {
+    if (test != next) {
+        if (test->bounds().fBottom < next->bounds().fTop) {
+            return false;
+        }
+        if (!Bounds::Intersects(test->bounds(), next->bounds())) {
+            return true;
+        }
+    }
+    Work wt, wn;
+    wt.init(test);
+    wn.init(next);
+    do {
+        if (test == next && !wn.startAfter(wt)) {
+            continue;
+        }
+        do {
+            if (!Bounds::Intersects(wt.bounds(), wn.bounds())) {
+                continue;
+            }
+            int pts;
+            Intersections ts;
+            bool swap = false;
+            switch (wt.segmentType()) {
+                case Work::kHorizontalLine_Segment:
+                    swap = true;
+                    switch (wn.segmentType()) {
+                        case Work::kHorizontalLine_Segment:
+                        case Work::kVerticalLine_Segment:
+                        case Work::kLine_Segment: {
+                            pts = HLineIntersect(wn.pts(), wt.left(),
+                                    wt.right(), wt.y(), wt.xFlipped(), ts);
+                            break;
+                        }
+                        case Work::kQuad_Segment: {
+                            pts = HQuadIntersect(wn.pts(), wt.left(),
+                                    wt.right(), wt.y(), wt.xFlipped(), ts);
+                            break;
+                        }
+                        case Work::kCubic_Segment: {
+                            pts = HCubicIntersect(wn.pts(), wt.left(),
+                                    wt.right(), wt.y(), wt.xFlipped(), ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case Work::kVerticalLine_Segment:
+                    swap = true;
+                    switch (wn.segmentType()) {
+                        case Work::kHorizontalLine_Segment:
+                        case Work::kVerticalLine_Segment:
+                        case Work::kLine_Segment: {
+                            pts = VLineIntersect(wn.pts(), wt.top(),
+                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
+                            break;
+                        }
+                        case Work::kQuad_Segment: {
+                            pts = VQuadIntersect(wn.pts(), wt.top(),
+                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
+                            break;
+                        }
+                        case Work::kCubic_Segment: {
+                            pts = VCubicIntersect(wn.pts(), wt.top(),
+                                    wt.bottom(), wt.x(), wt.yFlipped(), ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case Work::kLine_Segment:
+                    switch (wn.segmentType()) {
+                        case Work::kHorizontalLine_Segment:
+                            pts = HLineIntersect(wt.pts(), wn.left(),
+                                    wn.right(), wn.y(), wn.xFlipped(), ts);
+                            break;
+                        case Work::kVerticalLine_Segment:
+                            pts = VLineIntersect(wt.pts(), wn.top(),
+                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
+                            break;
+                        case Work::kLine_Segment: {
+                            pts = LineIntersect(wt.pts(), wn.pts(), ts);
+                            debugShowLineIntersection(pts, wt, wn,
+                                    ts.fT[1], ts.fT[0]);
+                            break;
+                        }
+                        case Work::kQuad_Segment: {
+                            swap = true;
+                            pts = QuadLineIntersect(wn.pts(), wt.pts(), ts);
+                            break;
+                        }
+                        case Work::kCubic_Segment: {
+                            swap = true;
+                            pts = CubicLineIntersect(wn.pts(), wt.pts(), ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case Work::kQuad_Segment:
+                    switch (wn.segmentType()) {
+                        case Work::kHorizontalLine_Segment:
+                            pts = HQuadIntersect(wt.pts(), wn.left(),
+                                    wn.right(), wn.y(), wn.xFlipped(), ts);
+                            break;
+                        case Work::kVerticalLine_Segment:
+                            pts = VQuadIntersect(wt.pts(), wn.top(),
+                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
+                            break;
+                        case Work::kLine_Segment: {
+                            pts = QuadLineIntersect(wt.pts(), wn.pts(), ts);
+                            break;
+                        }
+                        case Work::kQuad_Segment: {
+                            pts = QuadIntersect(wt.pts(), wn.pts(), ts);
+                            break;
+                        }
+                        case Work::kCubic_Segment: {
+                            wt.promoteToCubic();
+                            pts = CubicIntersect(wt.cubic(), wn.pts(), ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                case Work::kCubic_Segment:
+                    switch (wn.segmentType()) {
+                        case Work::kHorizontalLine_Segment:
+                            pts = HCubicIntersect(wt.pts(), wn.left(),
+                                    wn.right(), wn.y(), wn.xFlipped(), ts);
+                            break;
+                        case Work::kVerticalLine_Segment:
+                            pts = VCubicIntersect(wt.pts(), wn.top(),
+                                    wn.bottom(), wn.x(), wn.yFlipped(), ts);
+                            break;
+                        case Work::kLine_Segment: {
+                            pts = CubicLineIntersect(wt.pts(), wn.pts(), ts);
+                            break;
+                        }
+                        case Work::kQuad_Segment: {
+                            wn.promoteToCubic();
+                            pts = CubicIntersect(wt.pts(), wn.cubic(), ts);
+                            break;
+                        }
+                        case Work::kCubic_Segment: {
+                            pts = CubicIntersect(wt.pts(), wn.pts(), ts);
+                            break;
+                        }
+                        default:
+                            SkASSERT(0);
+                    }
+                    break;
+                default:
+                    SkASSERT(0);
+            }
+            // in addition to recording T values, record matching segment
+            bool coincident = pts == 2 && wn.segmentType() <= Work::kLine_Segment
+                    && wt.segmentType() <= Work::kLine_Segment;
+            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);
+                int nextTAt = wn.addT(ts.fT[!swap][pt], wt);
+                wt.addOtherT(testTAt, ts.fT[!swap][pt], coincident);
+                wn.addOtherT(nextTAt, ts.fT[swap][pt], coincident);
+            }
+        } while (wn.advance());
+    } while (wt.advance());
+    return true;
+}
+
+// Each segment may have an inside or an outside. Segments contained within
+// winding may have insides on either side, and form a contour that should be
+// ignored. Segments that are coincident with opposing direction segments may
+// have outsides on either side, and should also disappear.
+// 'Normal' segments will have one inside and one outside. Subsequent connections
+// when winding should follow the intersection direction. If more than one edge
+// is an option, choose first edge that continues the inside.
+ 
+static void bridge(SkTDArray<Contour*>& contourList) {
+    // Start at the top. Above the top is outside, below is inside.
+    Contour* topContour = contourList[0];
+    Segment& topStart = topContour->topSegment();
+    int index;
+    const Segment* topSegment = topStart.findTop(index);
+    start here ;
+    // find span
+    // handle coincident
+    // mark neighbors winding coverage
+    // output span
+    // mark span as processed
+    
+}
+
+static void makeContourList(SkTArray<Contour>& contours, Contour& sentinel,
+        SkTDArray<Contour*>& list) {
+    size_t count = contours.count();
+    if (count == 0) {
+        return;
+    }
+    for (size_t index = 0; index < count; ++index) {
+        *list.append() = &contours[index];
+    }
+    *list.append() = &sentinel;
+    QSort<Contour>(list.begin(), list.end() - 1);
+}
+
+void simplifyx(const SkPath& path, bool asFill, SkPath& simple) {
+    // returns 1 for evenodd, -1 for winding, regardless of inverse-ness
+    int windingMask = (path.getFillType() & 1) ? 1 : -1;
+    simple.reset();
+    simple.setFillType(SkPath::kEvenOdd_FillType);
+
+    // turn path into list of segments
+    SkTArray<Contour> contours;
+    // FIXME: add self-intersecting cubics' T values to segment
+    EdgeBuilder builder(path, contours);
+    SkTDArray<Contour*> contourList;
+    Contour sentinel;
+    sentinel.reset();
+    makeContourList(contours, sentinel, contourList);
+    Contour** currentPtr = contourList.begin();
+    if (!currentPtr) {
+        return;
+    }
+    // find all intersections between segments
+    do {
+        Contour** nextPtr = currentPtr;
+        Contour* current = *currentPtr++;
+        Contour* next;
+        do {
+            next = *nextPtr++;
+        } while (next != &sentinel && addIntersectingTs(current, next));
+    } while (*currentPtr != &sentinel);
+    // construct closed contours
+    bridge(contourList);
+}
+