experimental/Intersection/EdgeWalker.cpp

/*
 * 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 "LineIntersection.h"
#include "SkPath.h"
#include "SkRect.h"
#include "SkTArray.h"
#include "SkTDArray.h"
#include "TSearch.h"

static int LineIntersect(const SkPoint a[2], const SkPoint b[2],
        double aRange[2], double bRange[2]) {
    _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
    _Line bLine = {{b[0].fX, b[0].fY}, {b[1].fX, b[1].fY}};
    return intersect(aLine, bLine, aRange, bRange);
}

static int LineIntersect(const SkPoint a[2], SkScalar y, double aRange[2]) {
    _Line aLine = {{a[0].fX, a[0].fY}, {a[1].fX, a[1].fY}};
    return horizontalIntersect(aLine, y, aRange);
}

static SkScalar LineYAtT(const SkPoint a[2], double t) {
    _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 void LineSubDivide(const SkPoint a[2], double startT, double endT,
        SkPoint sub[2]) {
    _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);
}


// functions
void contourBounds(const SkPath& path, SkTDArray<SkRect>& boundsArray);
void simplify(const SkPath& path, bool asFill, SkPath& simple);
/*
list of edges
bounds for edge
sort
active T

if a contour's bounds is outside of the active area, no need to create edges 
*/

/* given one or more paths, 
 find the bounds of each contour, select the active contours
 for each active contour, compute a set of edges
 each edge corresponds to one or more lines and curves
 leave edges unbroken as long as possible
 when breaking edges, compute the t at the break but leave the control points alone

 */

void contourBounds(const SkPath& path, SkTDArray<SkRect>& boundsArray) {
    SkPath::Iter iter(path, false);
    SkPoint pts[4];
    SkPath::Verb verb;
    SkRect bounds;
    bounds.setEmpty();
    int count = 0;
    while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
        switch (verb) {
            case SkPath::kMove_Verb:
                if (!bounds.isEmpty()) {
                    *boundsArray.append() = bounds;
                }
                bounds.set(pts[0].fX, pts[0].fY, pts[0].fX, pts[0].fY);
                count = 0;
                break;
            case SkPath::kLine_Verb: 
                count = 1;
                break;
            case SkPath::kQuad_Verb:
                count = 2;
                break;
            case SkPath::kCubic_Verb:
                count = 3;
                break;
            case SkPath::kClose_Verb:
                count = 0;
                break;
            default:
                SkDEBUGFAIL("bad verb");
                return;
        }
        for (int i = 1; i <= count; ++i) {
            bounds.growToInclude(pts[i].fX, pts[i].fY);
        }
    }
}

static bool extendLine(const SkPoint line[2], const SkPoint& add) {
    // FIXME: allow this to extend lines that have slopes that are nearly equal
    SkScalar dx1 = line[1].fX - line[0].fX;
    SkScalar dy1 = line[1].fY - line[0].fY;
    SkScalar dx2 = add.fX - line[0].fX;
    SkScalar dy2 = add.fY - line[0].fY;
    return dx1 * dy2 == dx2 * dy1;
}

struct OutEdge {
    bool operator<(const OutEdge& rh) const {
        const SkPoint& first = fPts.begin()[0];
        const SkPoint& rhFirst = rh.fPts.begin()[0];
        return first.fY == rhFirst.fY
                ? first.fX < rhFirst.fX
                : first.fY < rhFirst.fY;
    }
    
    SkTDArray<SkPoint> fPts;
    SkTDArray<uint8_t> fVerbs; // FIXME: unused for now
};

// for sorting only
class OutBottomEdge : public OutEdge { 
public:    
    bool operator<(const OutBottomEdge& rh) const {
        const SkPoint& last = fPts.end()[-1];
        const SkPoint& rhLast = rh.fPts.end()[-1];
        return last.fY == rhLast.fY
                ? last.fX < rhLast.fX
                : last.fY < rhLast.fY;
    }
    
};

class OutEdgeBuilder {
public:
    OutEdgeBuilder(bool fill)
        : fFill(fill) {
        }

    void addLine(const SkPoint line[2]) {
        size_t count = fEdges.count();
        for (size_t index = 0; index < count; ++index) {
            SkTDArray<SkPoint>& pts = fEdges[index].fPts;
            SkPoint* last = pts.end() - 1;
            if (last[0] == line[0]) {
                if (extendLine(&last[-1], line[1])) {
                    last[0] = line[1];
                } else {
                    *pts.append() = line[1];
                }
                return;
            }
        }
        OutEdge& edge = fEdges.push_back();
        *edge.fPts.append() = line[0];
        *edge.fPts.append() = line[1];
    }

    void assemble(SkPath& simple) {
        size_t listCount = fEdges.count();
        if (listCount == 0) {
            return;
        }
        do {
            size_t listIndex = 0;
            int advance = 1;
            while (listIndex < listCount && fTops[listIndex] == 0) {
                ++listIndex;
            }
            if (listIndex >= listCount) {
                break;
            }
            SkPoint firstPt;
            bool doMove = true;
            int edgeIndex;
            do {
                SkTDArray<SkPoint>& ptArray = fEdges[listIndex].fPts;
                SkASSERT(ptArray.count() > 0);
                SkPoint* pts, * end;
                if (advance < 0) {
                    pts = ptArray.end() - 1;
                    end = ptArray.begin();
                } else {
                    pts = ptArray.begin();
                    end = ptArray.end() - 1;
                }
                if (doMove) {
                    firstPt = pts[0];
                    simple.moveTo(pts[0].fX, pts[0].fY);
                    SkDebugf("%s moveTo (%g,%g)\n", __FUNCTION__, pts[0].fX, pts[0].fY);
                    doMove = false;
                } else {
                    simple.lineTo(pts[0].fX, pts[0].fY);
                    SkDebugf("%s 1 lineTo (%g,%g)\n", __FUNCTION__, pts[0].fX, pts[0].fY);
                    if (firstPt == pts[0]) {
                        simple.close();
                        SkDebugf("%s close\n", __FUNCTION__);
                        break;
                    }
                }
                while (pts != end) {
                    pts += advance;
                    simple.lineTo(pts->fX, pts->fY);
                    SkDebugf("%s 2 lineTo (%g,%g)\n", __FUNCTION__, pts[0].fX, pts[0].fY);
                }
                if (advance < 0) {
                    edgeIndex = fTops[listIndex];
                    fTops[listIndex] = 0;
                 } else {
                    edgeIndex = fBottoms[listIndex];
                    fBottoms[listIndex] = 0;
                }
                listIndex = abs(edgeIndex) - 1;
                if (edgeIndex < 0) {
                    fTops[listIndex] = 0;
                } else {
                    fBottoms[listIndex] = 0;
                }
                // if this and next edge go different directions 
                if (advance > 0 ^ edgeIndex < 0) {
                    advance = -advance;
                }
            } while (edgeIndex);
        } while (true);
    }
    
    static bool lessThan(SkTArray<OutEdge>& edges, const int* onePtr,
            const int* twoPtr) {
        int one = *onePtr;
        const OutEdge& oneEdge = edges[(one < 0 ? -one : one) - 1];
        const SkPoint* onePt = one < 0 ? oneEdge.fPts.begin()
                : oneEdge.fPts.end() - 1;
        int two = *twoPtr;
        const OutEdge& twoEdge = edges[(two < 0 ? -two : two) - 1];
        const SkPoint* twoPt = two < 0 ? twoEdge.fPts.begin()
                : twoEdge.fPts.end() - 1;
        return onePt->fY == twoPt->fY ? onePt->fX < twoPt->fX : onePt->fY < twoPt->fY;
    }

    // Sort the indices of paired points and then create more indices so
    // assemble() can find the next edge and connect the top or bottom
    void bridge() {
        size_t index;
        size_t count = fEdges.count();
        if (!count) {
            return;
        }
        SkASSERT(!fFill || (count & 1) == 0);
        fTops.setCount(count);
        sk_bzero(fTops.begin(), sizeof(fTops[0]) * count);
        fBottoms.setCount(count);
        sk_bzero(fBottoms.begin(), sizeof(fBottoms[0]) * count);
        SkTDArray<int> order;
        for (index = 1; index <= count; ++index) {
            *order.append() = index;
            *order.append() = -index;
        }
        QSort<SkTArray<OutEdge>, int>(fEdges, order.begin(), count * 2, lessThan);
        int* lastPtr = order.end() - 1;
        int* leftPtr = order.begin();
        while (leftPtr < lastPtr) {
            int leftIndex = *leftPtr;
            int leftOutIndex = abs(leftIndex) - 1;
            const OutEdge& left = fEdges[leftOutIndex];
            int* rightPtr = leftPtr + 1;
            int rightIndex = *rightPtr;
            int rightOutIndex = abs(rightIndex) - 1;
            const OutEdge& right = fEdges[rightOutIndex];
        // OPTIMIZATION: if fFill is true, we don't need leftMatch, rightMatch
            SkPoint& leftMatch = left.fPts[leftIndex < 0 ? 0
                    : left.fPts.count() - 1];
            SkPoint& rightMatch = right.fPts[rightIndex < 0 ? 0
                    : right.fPts.count() - 1];
            SkASSERT(!fFill || leftMatch.fY == rightMatch.fY);
            if (fFill || leftMatch == rightMatch) {
                if (leftIndex < 0) {
                    fTops[leftOutIndex] = rightIndex;
                } else {
                    fBottoms[leftOutIndex] = rightIndex;
                }
                if (rightIndex < 0) {
                    fTops[rightOutIndex] = leftIndex;
                } else {
                    fBottoms[rightOutIndex] = leftIndex;
                }
                ++rightPtr;
            }
            leftPtr = rightPtr;
        }
    }

protected:
    SkTArray<OutEdge> fEdges;
    SkTDArray<int> fTops;
    SkTDArray<int> fBottoms;
    bool fFill;
};

// 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);
    }
};

struct Intercepts {
    SkTDArray<double> fTs;
};

struct InEdge {
    bool operator<(const InEdge& rh) const {
        return fBounds.fTop == rh.fBounds.fTop
                ? fBounds.fLeft < rh.fBounds.fLeft
                : fBounds.fTop < rh.fBounds.fTop;
    }

    bool add(double* ts, size_t count, ptrdiff_t verbIndex) {
        // FIXME: in the pathological case where there is a ton of intercepts, binary search?
        bool foundIntercept = false;
        Intercepts& intercepts = fIntercepts[verbIndex];
        for (size_t index = 0; index < count; ++index) {
            double t = ts[index];
            if (t <= 0 || t >= 1) {
                continue;
            }
            foundIntercept = true;
            size_t tCount = intercepts.fTs.count();
            for (size_t idx2 = 0; idx2 < tCount; ++idx2) {
                if (t <= intercepts.fTs[idx2]) {
                    if (t < intercepts.fTs[idx2]) {
                        *intercepts.fTs.insert(idx2) = t;
                        break;
                    }
                }
            }
            if (tCount == 0 || t > intercepts.fTs[tCount - 1]) {
                *intercepts.fTs.append() = t;
            }
        }
        return foundIntercept;
    }

    bool cached(const InEdge* edge) {
        // FIXME: in the pathological case where there is a ton of edges, binary search?
        size_t count = fCached.count();
        for (size_t index = 0; index < count; ++index) {
            if (edge == fCached[index]) {
                return true;
            }
            if (edge < fCached[index]) {
                *fCached.insert(index) = edge;
                return false;
            }
        }
        *fCached.append() = edge;
        return false;
    }

    void complete(signed char winding) {
        SkPoint* ptPtr = fPts.begin();
        SkPoint* ptLast = fPts.end();
        if (ptPtr == ptLast) {
            SkDebugf("empty edge\n");
            SkASSERT(0);
            // FIXME: delete empty edge?
            return;
        }
        fBounds.set(ptPtr->fX, ptPtr->fY, ptPtr->fX, ptPtr->fY);
        ++ptPtr;
        while (ptPtr != ptLast) {
            fBounds.growToInclude(ptPtr->fX, ptPtr->fY);
            ++ptPtr;
        }
        fIntercepts.push_back_n(fVerbs.count());
        if ((fWinding = winding) < 0) { // reverse verbs, pts, if bottom to top
            size_t index;
            size_t last = fPts.count() - 1;
            for (index = 0; index < last; ++index, --last) {
                SkTSwap<SkPoint>(fPts[index], fPts[last]);
            }
            last = fVerbs.count() - 1;
            for (index = 0; index < last; ++index, --last) {
                SkTSwap<uint8_t>(fVerbs[index], fVerbs[last]);
            }
        }
        fContainsIntercepts = false;
    }

    // temporary data : move this to a separate struct?
    SkTDArray<const InEdge*> fCached; // list of edges already intercepted
    SkTArray<Intercepts> fIntercepts; // one per verb
    
    // persistent data
    SkTDArray<SkPoint> fPts;
    SkTDArray<uint8_t> fVerbs;
    Bounds fBounds;
    signed char fWinding;
    bool fContainsIntercepts;
};

class InEdgeBuilder {
public:

InEdgeBuilder(const SkPath& path, bool ignoreHorizontal, SkTArray<InEdge>& edges) 
    : fPath(path)
    , fCurrentEdge(NULL)
    , fEdges(edges)
    , fIgnoreHorizontal(ignoreHorizontal)
{
    walk();
}

protected:

void addEdge() {
    SkASSERT(fCurrentEdge);
    fCurrentEdge->fPts.append(fPtCount - fPtOffset, &fPts[fPtOffset]);
    fPtOffset = 1;
    *fCurrentEdge->fVerbs.append() = fVerb;
}

bool complete() {
    if (fCurrentEdge && fCurrentEdge->fVerbs.count()) {
        fCurrentEdge->complete(fWinding);
        fCurrentEdge = NULL;
        return true;
    }
    return false;
}

int direction(int count) {
    fPtCount = count;
    fIgnorableHorizontal = fIgnoreHorizontal && isHorizontal();
    if (fIgnorableHorizontal) {
        return 0;
    }
    int last = count - 1;
    return fPts[0].fY == fPts[last].fY
            ? fPts[0].fX == fPts[last].fX ? 0 : fPts[0].fX < fPts[last].fX
            ? 1 : -1 : fPts[0].fY < fPts[last].fY ? 1 : -1;
}

bool isHorizontal() {
    SkScalar y = fPts[0].fY;
    for (int i = 1; i < fPtCount; ++i) {
        if (fPts[i].fY != y) {
            return false;
        }
    }
    return true;
}

void startEdge() {
    if (!fCurrentEdge) {
        fCurrentEdge = fEdges.push_back_n(1);
    }
    fWinding = 0;
    fPtOffset = 0;
}

void walk() {
    SkPath::Iter iter(fPath, true);
    int winding;
    while ((fVerb = iter.next(fPts)) != SkPath::kDone_Verb) {
        switch (fVerb) {
            case SkPath::kMove_Verb:
                startEdge();
                continue;
            case SkPath::kLine_Verb:
                winding = direction(2);
                break;
            case SkPath::kQuad_Verb:
                winding = direction(3);
                break;
            case SkPath::kCubic_Verb:
                winding = direction(4);
                break;
            case SkPath::kClose_Verb:
                SkASSERT(fCurrentEdge);
                complete();
                continue;
            default:
                SkDEBUGFAIL("bad verb");
                return;
        }
        if (fIgnorableHorizontal) {
            if (complete()) {
                startEdge();
            }
            continue;
        }
        if (fWinding + winding == 0) {
            // FIXME: if prior verb or this verb is a horizontal line, reverse
            // it instead of starting a new edge
            SkASSERT(fCurrentEdge);
            fCurrentEdge->complete(fWinding);
            startEdge();
        }
        fWinding = winding;
        addEdge();
    }
    if (!complete()) {
        if (fCurrentEdge) {
            fEdges.pop_back();
        }
    }
}

private:
    const SkPath& fPath;
    InEdge* fCurrentEdge;
    SkTArray<InEdge>& fEdges;
    SkPoint fPts[4];
    SkPath::Verb fVerb;
    int fPtCount;
    int fPtOffset;
    int8_t fWinding;
    bool fIgnorableHorizontal;
    bool fIgnoreHorizontal;
};

struct WorkEdge {
    SkScalar bottom() const {
        return fPts[verb()].fY;
    }

    void init(const InEdge* edge) {
        fEdge = edge;
        fPts = edge->fPts.begin();
        fVerb = edge->fVerbs.begin();
    }

    bool next() {
        SkASSERT(fVerb < fEdge->fVerbs.end());
        fPts += *fVerb++;
        return fVerb != fEdge->fVerbs.end();
    }

    SkPath::Verb verb() const {
        return (SkPath::Verb) *fVerb;
    }

    ptrdiff_t verbIndex() const {
        return fVerb - fEdge->fVerbs.begin();
    }
    
    int winding() const {
        return fEdge->fWinding;
    }

    const InEdge* fEdge;
    const SkPoint* fPts;
    const uint8_t* fVerb;
};

// always constructed with SkTDArray because new edges are inserted
// this may be a inappropriate optimization, suggesting that a separate array of
// ActiveEdge* may be faster to insert and search
struct ActiveEdge {
    bool operator<(const ActiveEdge& rh) const {
        return fX < rh.fX;
    }

    void calcLeft() {
        fX = fWorkEdge.fPts[fWorkEdge.verb()].fX;
    }

    void init(const InEdge* edge) {
        fWorkEdge.init(edge);
        initT();
    }
    
    void initT() {
        const Intercepts& intercepts = fWorkEdge.fEdge->fIntercepts.front();
        SkASSERT(fWorkEdge.verbIndex() <= fWorkEdge.fEdge->fIntercepts.count());
        const Intercepts* interceptPtr = &intercepts + fWorkEdge.verbIndex();
        fTs = &interceptPtr->fTs; 
  //  the above is conceptually the same as
  //    fTs = &fWorkEdge.fEdge->fIntercepts[fWorkEdge.verbIndex()].fTs;
  //  but templated arrays don't allow returning a pointer to the end() element
        fTIndex = 0;
    }

    bool nextT() {
        SkASSERT(fTIndex <= fTs->count());
        return ++fTIndex == fTs->count() + 1;
    }
    
    bool next() {
        bool result = fWorkEdge.next();
        initT();
        return result;
    }

    double t() {
        if (fTIndex == 0) {
            return 0;
        }
        if (fTIndex > fTs->count()) {
            return 1;
        }
        return (*fTs)[fTIndex - 1];
    }

    WorkEdge fWorkEdge;
    const SkTDArray<double>* fTs;
    SkScalar fX;
    int fTIndex;
    bool fSkip;
};

static void addToActive(SkTDArray<ActiveEdge>& activeEdges, const InEdge* edge) {
    size_t count = activeEdges.count();
    for (size_t index = 0; index < count; ++index) {
        if (edge == activeEdges[index].fWorkEdge.fEdge) {
            return;
        }
    }
    ActiveEdge* active = activeEdges.append();
    active->init(edge);
}

    // find any intersections in the range of active edges
static void addBottomT(InEdge** currentPtr, InEdge** lastPtr, SkScalar bottom) {
    InEdge** testPtr = currentPtr;
    InEdge* test = *testPtr;
    while (testPtr != lastPtr) {
        if (test->fBounds.fBottom > bottom) {
            WorkEdge wt;
            wt.init(test);
            do {
                // FIXME: add all curve types
                // OPTIMIZATION: if bottom intersection does not change
                // the winding on either side of the split, don't intersect
                if (wt.verb() == SkPath::kLine_Verb) {
                    double wtTs[2];
                    int pts = LineIntersect(wt.fPts, bottom, wtTs);
                    if (pts) {
                        test->fContainsIntercepts |= test->add(wtTs, pts,
                                wt.verbIndex());
                    }
                }
            } while (wt.next());
        }
        test = *++testPtr;
    }
}

static void addIntersectingTs(InEdge** currentPtr, InEdge** lastPtr) {
    InEdge** testPtr = currentPtr;
    InEdge* test = *testPtr;
    while (testPtr != lastPtr - 1) {
        InEdge* next = *++testPtr;
        if (!test->cached(next)
                && Bounds::Intersects(test->fBounds, next->fBounds)) {
            WorkEdge wt, wn;
            wt.init(test);
            wn.init(next);
            do {
                // FIXME: add all combinations of curve types
                if (wt.verb() == SkPath::kLine_Verb
                        && wn.verb() == SkPath::kLine_Verb) {
                    double wtTs[2], wnTs[2];
                    int pts = LineIntersect(wt.fPts, wn.fPts, wtTs, wnTs);
                    if (pts) {
                        test->fContainsIntercepts |= test->add(wtTs, pts,
                                wt.verbIndex());
                        next->fContainsIntercepts |= next->add(wnTs, pts,
                                wn.verbIndex());
                    }
                }
            } while (wt.bottom() <= wn.bottom() ? wt.next() : wn.next());
        }
        test = next;
    }
}

static InEdge** advanceEdges(SkTDArray<ActiveEdge>& activeEdges,
        InEdge** currentPtr, InEdge** lastPtr,  SkScalar y) {
    InEdge** testPtr = currentPtr - 1;
    while (++testPtr != lastPtr) {
        if ((*testPtr)->fBounds.fBottom > y) {
            continue;
        }
        InEdge* test = *testPtr;
        ActiveEdge* activePtr = activeEdges.begin() - 1;
        ActiveEdge* lastActive = activeEdges.end();
        while (++activePtr != lastActive) {
            if (activePtr->fWorkEdge.fEdge == test) {
                activeEdges.remove(activePtr - activeEdges.begin());
                break;
            }
        }
        if (testPtr == currentPtr) {
            ++currentPtr;
        }
    }
    return currentPtr;
}

// compute bottom taking into account any intersected edges
static void computeInterceptBottom(SkTDArray<ActiveEdge>& activeEdges,
        SkScalar y, SkScalar& bottom) {
    ActiveEdge* activePtr = activeEdges.begin() - 1;
    ActiveEdge* lastActive = activeEdges.end();
    while (++activePtr != lastActive) {
        const InEdge* test = activePtr->fWorkEdge.fEdge;
        if (!test->fContainsIntercepts) {
            continue;
        }
        WorkEdge wt;
        wt.init(test);
        do {
            // FIXME: add all curve types
            const Intercepts& intercepts = test->fIntercepts[wt.verbIndex()];
            const SkTDArray<double>& fTs = intercepts.fTs;
            size_t count = fTs.count();
            for (size_t index = 0; index < count; ++index) {
                if (wt.verb() == SkPath::kLine_Verb) {
                    SkScalar yIntercept = LineYAtT(wt.fPts, fTs[index]);
                    if (yIntercept > y && bottom > yIntercept) {
                        bottom = yIntercept;
                    }
                }
            }
        } while (wt.next());
    }
}

static SkScalar findBottom(InEdge** currentPtr, 
        InEdge** edgeListEnd, SkTDArray<ActiveEdge>& activeEdges, SkScalar y,
        bool asFill, InEdge**& testPtr) {
    InEdge* current = *currentPtr;
    SkScalar bottom = current->fBounds.fBottom;
    
    // find the list of edges that cross y
    InEdge* test = *testPtr;
    while (testPtr != edgeListEnd) {
        SkScalar testTop = test->fBounds.fTop;
        if (bottom <= testTop) {
            break;
        }
        SkScalar testBottom = test->fBounds.fBottom;
        // OPTIMIZATION: Shortening the bottom is only interesting when filling
        // and when the edge is to the left of a longer edge. If it's a framing
        // edge, or part of the right, it won't effect the longer edges.
        if (testTop > y) {
            bottom = testTop;
            break;
        } 
        if (y < testBottom) {
            if (bottom > testBottom) {
                bottom = testBottom;
            }
            addToActive(activeEdges, test);
        }
        test = *++testPtr;
    }
    if (asFill && testPtr - currentPtr <= 1) {
        SkDebugf("expect 2 or more edges\n");
        SkASSERT(0);
    }
    return bottom;
}

static void makeEdgeList(SkTArray<InEdge>& edges, InEdge& edgeSentinel,
        SkTDArray<InEdge*>& edgeList) {
    size_t edgeCount = edges.count();
    if (edgeCount == 0) {
        return;
    }
    for (size_t index = 0; index < edgeCount; ++index) {
        *edgeList.append() = &edges[index];
    }
    edgeSentinel.fBounds.set(SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, SK_ScalarMax);
    *edgeList.append() = &edgeSentinel;
    ++edgeCount;
    QSort<InEdge>(edgeList.begin(), edgeCount);
}


static void skipCoincidence(int lastWinding, int winding, int windingMask,
            ActiveEdge* activePtr, ActiveEdge* firstCoincident) {
    if (((lastWinding & windingMask) == 0) ^ (winding & windingMask) != 0) {
        return;
    } 
    if (lastWinding) {
        activePtr->fSkip = false;
    } else {
        firstCoincident->fSkip = false;
    }
}

static void sortHorizontal(SkTDArray<ActiveEdge>& activeEdges,
        SkTDArray<ActiveEdge*>& edgeList, int windingMask) {
    size_t edgeCount = activeEdges.count();
    if (edgeCount == 0) {
        return;
    }
    size_t index;
    for (index = 0; index < edgeCount; ++index) {
        ActiveEdge& activeEdge = activeEdges[index];
        activeEdge.calcLeft();
        activeEdge.fSkip = false;
        *edgeList.append() = &activeEdge;
    }
    QSort<ActiveEdge>(edgeList.begin(), edgeCount);
    // remove coincident edges
    // OPTIMIZE: remove edges? This is tricky because the current logic expects
    // the winding count to be maintained while skipping coincident edges. In
    // addition to removing the coincident edges, the remaining edges would need
    // to have a different winding value, possibly different per intercept span.
    int lastWinding = 0;
    bool lastSkipped = false;
    ActiveEdge* activePtr = edgeList[0];
    ActiveEdge* firstCoincident = NULL;
    int winding = 0;
    for (index = 1; index < edgeCount; ++index) {
        winding += activePtr->fWorkEdge.winding();
        ActiveEdge* nextPtr = edgeList[index];
        if (activePtr->fX == nextPtr->fX) {
            SkDebugf("%s coincident\n", __FUNCTION__);
            if (!firstCoincident) {
                firstCoincident = activePtr;
            }
            activePtr->fSkip = nextPtr->fSkip = lastSkipped = true;
        } else if (lastSkipped) {
            skipCoincidence(lastWinding, winding, windingMask, activePtr,
                    firstCoincident);
            lastSkipped = false;
            firstCoincident = NULL;
        }
        if (!lastSkipped) {
            lastWinding = winding;
        }
        activePtr = nextPtr;
    }
    if (lastSkipped) {
        winding += activePtr->fWorkEdge.winding();
        skipCoincidence(lastWinding, winding, windingMask, activePtr,
                firstCoincident);
    }
}

// stitch edge and t range that satisfies operation
static void stitchEdge(SkTDArray<ActiveEdge*>& edgeList, SkScalar y,
        SkScalar bottom, int windingMask, OutEdgeBuilder& outBuilder) {
    int winding = 0;
    ActiveEdge** activeHandle = edgeList.begin() - 1;
    ActiveEdge** lastActive = edgeList.end();
    SkDebugf("%s y=%g bottom=%g\n", __FUNCTION__, y, bottom);
    while (++activeHandle != lastActive) {
        ActiveEdge* activePtr = *activeHandle;
        const WorkEdge& wt = activePtr->fWorkEdge;
        int lastWinding = winding;
        winding += wt.winding();
        bool inWinding = (lastWinding & windingMask) == 0
                || (winding & windingMask) == 0;
        do {
            double currentT = activePtr->t();
            SkASSERT(currentT < 1);
            const SkPoint* points = wt.fPts;
            bool last;
            do {
                last = activePtr->nextT();
                double nextT = activePtr->t();
                // FIXME: add all combinations of curve types
                if (wt.verb() == SkPath::kLine_Verb) {
                    SkPoint clippedPts[2];
                    const SkPoint* clipped;
                    if (currentT * nextT != 0 || currentT + nextT != 1) {
                        // OPTIMIZATION: if !inWinding, we only need 
                        // clipped[1].fY
                        LineSubDivide(points, currentT, nextT, clippedPts);
                        clipped = clippedPts;
                    } else {
                        clipped = points;
                    }
                    if (inWinding && !activePtr->fSkip) {
                        SkDebugf("%s line %g,%g %g,%g\n", __FUNCTION__,
                                clipped[0].fX, clipped[0].fY,
                                clipped[1].fX, clipped[1].fY);
                        outBuilder.addLine(clipped);
                    }
                    if (clipped[1].fY >= bottom) {
                        if (last) {
                            activePtr->next();
                        }
                        goto nextEdge;
                    }
                }
                currentT = nextT;
            } while (!last);
        } while (activePtr->next());
nextEdge:
        ;
    }
}

void simplify(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 edges increasing in y
    // if an edge is a quad or a cubic with a y extrema, note it, but leave it unbroken
    // once we have a list, sort it, then walk the list (walk edges twice that have y extrema's on top)
    //  and detect crossings -- look for raw bounds that cross over, then tight bounds that cross
    SkTArray<InEdge> edges;
    InEdgeBuilder builder(path, asFill, edges);
    SkTDArray<InEdge*> edgeList;
    InEdge edgeSentinel;
    makeEdgeList(edges, edgeSentinel, edgeList);
    InEdge** currentPtr = edgeList.begin();
    // walk the sorted edges from top to bottom, computing accumulated winding
    SkTDArray<ActiveEdge> activeEdges;
    OutEdgeBuilder outBuilder(asFill);
    SkScalar y = (*currentPtr)->fBounds.fTop;
    do {
        InEdge** lastPtr = currentPtr; // find the edge below the bottom of the first set
        SkScalar bottom = findBottom(currentPtr, edgeList.end(),
            activeEdges, y, asFill, lastPtr);
        addBottomT(currentPtr, lastPtr, bottom);
        addIntersectingTs(currentPtr, lastPtr);
        computeInterceptBottom(activeEdges, y, bottom);
        SkTDArray<ActiveEdge*> activeEdgeList;
        sortHorizontal(activeEdges, activeEdgeList, windingMask);
        stitchEdge(activeEdgeList, y, bottom, windingMask, outBuilder);
        y = bottom;
        currentPtr = advanceEdges(activeEdges, currentPtr, lastPtr, y);
    } while (*currentPtr != &edgeSentinel);
    // assemble output path from string of pts, verbs
    outBuilder.bridge();
    outBuilder.assemble(simple);
}

static void testSimplifyCoincidentVertical() {
    SkPath path, out;
    path.setFillType(SkPath::kWinding_FillType);
    path.addRect(10, 10, 30, 30);
    path.addRect(10, 30, 30, 40);
    simplify(path, true, out);
    SkRect rect;
    if (!out.isRect(&rect)) {
        SkDebugf("%s expected rect\n", __FUNCTION__);
    }
    if (rect != SkRect::MakeLTRB(10, 10, 30, 40)) {
        SkDebugf("%s expected union\n", __FUNCTION__);
    }
}

static void testSimplifyCoincidentHorizontal() {
    SkPath path, out;
    path.setFillType(SkPath::kWinding_FillType);
    path.addRect(10, 10, 30, 30);
    path.addRect(30, 10, 40, 30);
    simplify(path, true, out);
    SkRect rect;
    if (!out.isRect(&rect)) {
        SkDebugf("%s expected rect\n", __FUNCTION__);
    }
    if (rect != SkRect::MakeLTRB(10, 10, 40, 30)) {
        SkDebugf("%s expected union\n", __FUNCTION__);
    }
}

static void testSimplifyMulti() {
    SkPath path, out;
    path.setFillType(SkPath::kWinding_FillType);
    path.addRect(10, 10, 30, 30);
    path.addRect(20, 20, 40, 40);
    simplify(path, true, out);
    SkPath expected;
    expected.setFillType(SkPath::kEvenOdd_FillType);
    expected.moveTo(10,10); // two cutout corners
    expected.lineTo(10,30);
    expected.lineTo(20,30);
    expected.lineTo(20,40);
    expected.lineTo(40,40);
    expected.lineTo(40,20);
    expected.lineTo(30,20);
    expected.lineTo(30,10);
    expected.lineTo(10,10);
    expected.close();
    if (out != expected) {
        SkDebugf("%s expected equal\n", __FUNCTION__);
    }
    
    path = out;
    path.addRect(30, 10, 40, 20);
    path.addRect(10, 30, 20, 40);
    simplify(path, true, out);
    SkRect rect;
    if (!out.isRect(&rect)) {
        SkDebugf("%s expected rect\n", __FUNCTION__);
    }
    if (rect != SkRect::MakeLTRB(10, 10, 40, 40)) {
        SkDebugf("%s expected union\n", __FUNCTION__);
    }
    
    path = out;
    path.addRect(10, 10, 40, 40, SkPath::kCCW_Direction);
    simplify(path, true, out);
    if (!out.isEmpty()) {
        SkDebugf("%s expected empty\n", __FUNCTION__);
    }
}

static void testSimplifyAddL() {
    SkPath path, out;
    path.moveTo(10,10); // 'L' shape
    path.lineTo(10,40);
    path.lineTo(40,40);
    path.lineTo(40,20);
    path.lineTo(30,20);
    path.lineTo(30,10);
    path.lineTo(10,10);
    path.close();
    path.addRect(30, 10, 40, 20); // missing notch of 'L'
    simplify(path, true, out);
    SkRect rect;
    if (!out.isRect(&rect)) {
        SkDebugf("%s expected rect\n", __FUNCTION__);
    }
    if (rect != SkRect::MakeLTRB(10, 10, 40, 40)) {
        SkDebugf("%s expected union\n", __FUNCTION__);
    }
}

static void testSimplifyCoincidentCCW() {
    SkPath path, out;
    path.addRect(10, 10, 40, 40, SkPath::kCCW_Direction);
    path.addRect(10, 10, 40, 40, SkPath::kCCW_Direction);
    simplify(path, true, out);
    SkRect rect;
    if (!out.isRect(&rect)) {
        SkDebugf("%s expected rect\n", __FUNCTION__);
    }
    if (rect != SkRect::MakeLTRB(10, 10, 40, 40)) {
        SkDebugf("%s expected union\n", __FUNCTION__);
    }
}

static void testSimplifyCoincidentCW() {
    SkPath path, out;
    path.addRect(10, 10, 40, 40, SkPath::kCCW_Direction);
    path.addRect(10, 10, 40, 40, SkPath::kCW_Direction);
    simplify(path, true, out);
    if (!out.isEmpty()) {
        SkDebugf("%s expected empty\n", __FUNCTION__);
    }
}

void testSimplify();

void (*simplifyTests[])() = {
    testSimplifyCoincidentCW,
    testSimplifyCoincidentCCW,
    testSimplifyCoincidentVertical, 
    testSimplifyCoincidentHorizontal,
    testSimplifyAddL,                
    testSimplifyMulti,               
};

size_t simplifyTestsCount = sizeof(simplifyTests) / sizeof(simplifyTests[0]);

static void (*firstTest)()  = 0;

void testSimplify() {
    size_t index = 0;
    if (firstTest) {
        while (index < simplifyTestsCount && simplifyTests[index] != firstTest) {
            ++index;
        }
    }
    for ( ; index < simplifyTestsCount; ++index) {
        (*simplifyTests[index])();
    }
}