src/core/SkPath.cpp

/* libs/graphics/sgl/SkPath.cpp
**
** Copyright 2006, The Android Open Source Project
**
** Licensed under the Apache License, Version 2.0 (the "License");
** you may not use this file except in compliance with the License.
** You may obtain a copy of the License at
**
**     http://www.apache.org/licenses/LICENSE-2.0
**
** Unless required by applicable law or agreed to in writing, software
** distributed under the License is distributed on an "AS IS" BASIS,
** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
** See the License for the specific language governing permissions and
** limitations under the License.
*/

#include "SkPath.h"
#include "SkFlattenable.h"
#include "SkMath.h"

////////////////////////////////////////////////////////////////////////////

/*  This guy's constructor/destructor bracket a path editing operation. It is
    used when we know the bounds of the amount we are going to add to the path
    (usually a new contour, but not required).

    It captures some state about the path up front (i.e. if it already has a
    cached bounds), and the if it can, it updates the cache bounds explicitly,
    avoiding the need to revisit all of the points in getBounds().

    It also notes if the path was originally empty, and if so, sets isConvex
    to true. Thus it can only be used if the contour being added is convex.
 */
class SkAutoPathBoundsUpdate {
public:
    SkAutoPathBoundsUpdate(SkPath* path, const SkRect& r) : fRect(r) {
        this->init(path);
    }

    SkAutoPathBoundsUpdate(SkPath* path, SkScalar left, SkScalar top,
                           SkScalar right, SkScalar bottom) {
        fRect.set(left, top, right, bottom);
        this->init(path);
    }

    ~SkAutoPathBoundsUpdate() {
        fPath->setIsConvex(fEmpty);
        if (fEmpty) {
            fPath->fBounds = fRect;
            fPath->fBoundsIsDirty = false;
        } else if (!fDirty) {
            fPath->fBounds.join(fRect);
            fPath->fBoundsIsDirty = false;
        }
    }

private:
    SkPath* fPath;
    SkRect  fRect;
    bool    fDirty;
    bool    fEmpty;

    // returns true if we should proceed
    void init(SkPath* path) {
        fPath = path;
        fDirty = SkToBool(path->fBoundsIsDirty);
        fEmpty = path->isEmpty();
        // Cannot use fRect for our bounds unless we know it is sorted
        fRect.sort();
    }
};

static void compute_pt_bounds(SkRect* bounds, const SkTDArray<SkPoint>& pts) {
    if (pts.count() <= 1) {  // we ignore just 1 point (moveto)
        bounds->set(0, 0, 0, 0);
    } else {
        bounds->set(pts.begin(), pts.count());
//        SkDebugf("------- compute bounds %p %d", &pts, pts.count());
    }
}

////////////////////////////////////////////////////////////////////////////

/*
    Stores the verbs and points as they are given to us, with exceptions:
    - we only record "Close" if it was immediately preceeded by Line | Quad | Cubic
    - we insert a Move(0,0) if Line | Quad | Cubic is our first command

    The iterator does more cleanup, especially if forceClose == true
    1. if we encounter Close, return a cons'd up Line() first (if the curr-pt != start-pt)
    2. if we encounter Move without a preceeding Close, and forceClose is true, goto #1
    3. if we encounter Line | Quad | Cubic after Close, cons up a Move
*/

////////////////////////////////////////////////////////////////////////////

SkPath::SkPath() : fBoundsIsDirty(true), fFillType(kWinding_FillType) {
    fIsConvex = false;
}

SkPath::SkPath(const SkPath& src) {
    SkDEBUGCODE(src.validate();)
    *this = src;
}

SkPath::~SkPath() {
    SkDEBUGCODE(this->validate();)
}

SkPath& SkPath::operator=(const SkPath& src) {
    SkDEBUGCODE(src.validate();)

    if (this != &src) {
        fBounds         = src.fBounds;
        fPts            = src.fPts;
        fVerbs          = src.fVerbs;
        fFillType       = src.fFillType;
        fBoundsIsDirty  = src.fBoundsIsDirty;
        fIsConvex       = src.fIsConvex;
    }
    SkDEBUGCODE(this->validate();)
    return *this;
}

bool operator==(const SkPath& a, const SkPath& b) {
    // note: don't need to look at isConvex or bounds, since just comparing the
    // raw data is sufficient.
    return &a == &b ||
        (a.fFillType == b.fFillType && a.fVerbs == b.fVerbs && a.fPts == b.fPts);
}

void SkPath::swap(SkPath& other) {
    SkASSERT(&other != NULL);

    if (this != &other) {
        SkTSwap<SkRect>(fBounds, other.fBounds);
        fPts.swap(other.fPts);
        fVerbs.swap(other.fVerbs);
        SkTSwap<uint8_t>(fFillType, other.fFillType);
        SkTSwap<uint8_t>(fBoundsIsDirty, other.fBoundsIsDirty);
        SkTSwap<uint8_t>(fIsConvex, other.fIsConvex);
    }
}

void SkPath::reset() {
    SkDEBUGCODE(this->validate();)

    fPts.reset();
    fVerbs.reset();
    fBoundsIsDirty = true;
}

void SkPath::rewind() {
    SkDEBUGCODE(this->validate();)

    fPts.rewind();
    fVerbs.rewind();
    fBoundsIsDirty = true;
}

bool SkPath::isEmpty() const {
    SkDEBUGCODE(this->validate();)

    int count = fVerbs.count();
    return count == 0 || (count == 1 && fVerbs[0] == kMove_Verb);
}

bool SkPath::isRect(SkRect*) const {
    SkDEBUGCODE(this->validate();)

    SkASSERT(!"unimplemented");
    return false;
}

int SkPath::getPoints(SkPoint copy[], int max) const {
    SkDEBUGCODE(this->validate();)

    SkASSERT(max >= 0);
    int count = fPts.count();
    if (copy && max > 0 && count > 0) {
        memcpy(copy, fPts.begin(), sizeof(SkPoint) * SkMin32(max, count));
    }
    return count;
}

SkPoint SkPath::getPoint(int index) const {
    if ((unsigned)index < (unsigned)fPts.count()) {
        return fPts[index];
    }
    return SkPoint::Make(0, 0);
}

void SkPath::getLastPt(SkPoint* lastPt) const {
    SkDEBUGCODE(this->validate();)

    if (lastPt) {
        int count = fPts.count();
        if (count == 0) {
            lastPt->set(0, 0);
        } else {
            *lastPt = fPts[count - 1];
        }
    }
}

void SkPath::setLastPt(SkScalar x, SkScalar y) {
    SkDEBUGCODE(this->validate();)

    int count = fPts.count();
    if (count == 0) {
        this->moveTo(x, y);
    } else {
        fPts[count - 1].set(x, y);
    }
}

void SkPath::computeBounds() const {
    SkDEBUGCODE(this->validate();)
    SkASSERT(fBoundsIsDirty);

    fBoundsIsDirty = false;
    compute_pt_bounds(&fBounds, fPts);
}

//////////////////////////////////////////////////////////////////////////////
//  Construction methods

void SkPath::incReserve(U16CPU inc) {
    SkDEBUGCODE(this->validate();)

    fVerbs.setReserve(fVerbs.count() + inc);
    fPts.setReserve(fPts.count() + inc);

    SkDEBUGCODE(this->validate();)
}

void SkPath::moveTo(SkScalar x, SkScalar y) {
    SkDEBUGCODE(this->validate();)

    int      vc = fVerbs.count();
    SkPoint* pt;

    if (vc > 0 && fVerbs[vc - 1] == kMove_Verb) {
        pt = &fPts[fPts.count() - 1];
    } else {
        pt = fPts.append();
        *fVerbs.append() = kMove_Verb;
    }
    pt->set(x, y);

    fBoundsIsDirty = true;
}

void SkPath::rMoveTo(SkScalar x, SkScalar y) {
    SkPoint pt;
    this->getLastPt(&pt);
    this->moveTo(pt.fX + x, pt.fY + y);
}

void SkPath::lineTo(SkScalar x, SkScalar y) {
    SkDEBUGCODE(this->validate();)

    if (fVerbs.count() == 0) {
        fPts.append()->set(0, 0);
        *fVerbs.append() = kMove_Verb;
    }
    fPts.append()->set(x, y);
    *fVerbs.append() = kLine_Verb;

    fBoundsIsDirty = true;
}

void SkPath::rLineTo(SkScalar x, SkScalar y) {
    SkPoint pt;
    this->getLastPt(&pt);
    this->lineTo(pt.fX + x, pt.fY + y);
}

void SkPath::quadTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2) {
    SkDEBUGCODE(this->validate();)

    if (fVerbs.count() == 0) {
        fPts.append()->set(0, 0);
        *fVerbs.append() = kMove_Verb;
    }

    SkPoint* pts = fPts.append(2);
    pts[0].set(x1, y1);
    pts[1].set(x2, y2);
    *fVerbs.append() = kQuad_Verb;

    fBoundsIsDirty = true;
}

void SkPath::rQuadTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2) {
    SkPoint pt;
    this->getLastPt(&pt);
    this->quadTo(pt.fX + x1, pt.fY + y1, pt.fX + x2, pt.fY + y2);
}

void SkPath::cubicTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2,
                     SkScalar x3, SkScalar y3) {
    SkDEBUGCODE(this->validate();)

    if (fVerbs.count() == 0) {
        fPts.append()->set(0, 0);
        *fVerbs.append() = kMove_Verb;
    }
    SkPoint* pts = fPts.append(3);
    pts[0].set(x1, y1);
    pts[1].set(x2, y2);
    pts[2].set(x3, y3);
    *fVerbs.append() = kCubic_Verb;

    fBoundsIsDirty = true;
}

void SkPath::rCubicTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2,
                      SkScalar x3, SkScalar y3) {
    SkPoint pt;
    this->getLastPt(&pt);
    this->cubicTo(pt.fX + x1, pt.fY + y1, pt.fX + x2, pt.fY + y2,
                  pt.fX + x3, pt.fY + y3);
}

void SkPath::close() {
    SkDEBUGCODE(this->validate();)

    int count = fVerbs.count();
    if (count > 0) {
        switch (fVerbs[count - 1]) {
            case kLine_Verb:
            case kQuad_Verb:
            case kCubic_Verb:
                *fVerbs.append() = kClose_Verb;
                break;
            default:
                // don't add a close if the prev wasn't a primitive
                break;
        }
    }
}

///////////////////////////////////////////////////////////////////////////////

void SkPath::addRect(const SkRect& rect, Direction dir) {
    this->addRect(rect.fLeft, rect.fTop, rect.fRight, rect.fBottom, dir);
}

void SkPath::addRect(SkScalar left, SkScalar top, SkScalar right,
                     SkScalar bottom, Direction dir) {
    SkAutoPathBoundsUpdate apbu(this, left, top, right, bottom);

    this->incReserve(5);

    this->moveTo(left, top);
    if (dir == kCCW_Direction) {
        this->lineTo(left, bottom);
        this->lineTo(right, bottom);
        this->lineTo(right, top);
    } else {
        this->lineTo(right, top);
        this->lineTo(right, bottom);
        this->lineTo(left, bottom);
    }
    this->close();
}

#define CUBIC_ARC_FACTOR    ((SK_ScalarSqrt2 - SK_Scalar1) * 4 / 3)

void SkPath::addRoundRect(const SkRect& rect, SkScalar rx, SkScalar ry,
                          Direction dir) {
    SkScalar    w = rect.width();
    SkScalar    halfW = SkScalarHalf(w);
    SkScalar    h = rect.height();
    SkScalar    halfH = SkScalarHalf(h);

    if (halfW <= 0 || halfH <= 0) {
        return;
    }

    bool skip_hori = rx >= halfW;
    bool skip_vert = ry >= halfH;

    if (skip_hori && skip_vert) {
        this->addOval(rect, dir);
        return;
    }

    SkAutoPathBoundsUpdate apbu(this, rect);

    if (skip_hori) {
        rx = halfW;
    } else if (skip_vert) {
        ry = halfH;
    }

    SkScalar    sx = SkScalarMul(rx, CUBIC_ARC_FACTOR);
    SkScalar    sy = SkScalarMul(ry, CUBIC_ARC_FACTOR);

    this->incReserve(17);
    this->moveTo(rect.fRight - rx, rect.fTop);
    if (dir == kCCW_Direction) {
        if (!skip_hori) {
            this->lineTo(rect.fLeft + rx, rect.fTop);       // top
        }
        this->cubicTo(rect.fLeft + rx - sx, rect.fTop,
                      rect.fLeft, rect.fTop + ry - sy,
                      rect.fLeft, rect.fTop + ry);          // top-left
        if (!skip_vert) {
            this->lineTo(rect.fLeft, rect.fBottom - ry);        // left
        }
        this->cubicTo(rect.fLeft, rect.fBottom - ry + sy,
                      rect.fLeft + rx - sx, rect.fBottom,
                      rect.fLeft + rx, rect.fBottom);       // bot-left
        if (!skip_hori) {
            this->lineTo(rect.fRight - rx, rect.fBottom);   // bottom
        }
        this->cubicTo(rect.fRight - rx + sx, rect.fBottom,
                      rect.fRight, rect.fBottom - ry + sy,
                      rect.fRight, rect.fBottom - ry);      // bot-right
        if (!skip_vert) {
            this->lineTo(rect.fRight, rect.fTop + ry);
        }
        this->cubicTo(rect.fRight, rect.fTop + ry - sy,
                      rect.fRight - rx + sx, rect.fTop,
                      rect.fRight - rx, rect.fTop);         // top-right
    } else {
        this->cubicTo(rect.fRight - rx + sx, rect.fTop,
                      rect.fRight, rect.fTop + ry - sy,
                      rect.fRight, rect.fTop + ry);         // top-right
        if (!skip_vert) {
            this->lineTo(rect.fRight, rect.fBottom - ry);
        }
        this->cubicTo(rect.fRight, rect.fBottom - ry + sy,
                      rect.fRight - rx + sx, rect.fBottom,
                      rect.fRight - rx, rect.fBottom);      // bot-right
        if (!skip_hori) {
            this->lineTo(rect.fLeft + rx, rect.fBottom);    // bottom
        }
        this->cubicTo(rect.fLeft + rx - sx, rect.fBottom,
                      rect.fLeft, rect.fBottom - ry + sy,
                      rect.fLeft, rect.fBottom - ry);       // bot-left
        if (!skip_vert) {
            this->lineTo(rect.fLeft, rect.fTop + ry);       // left
        }
        this->cubicTo(rect.fLeft, rect.fTop + ry - sy,
                      rect.fLeft + rx - sx, rect.fTop,
                      rect.fLeft + rx, rect.fTop);          // top-left
        if (!skip_hori) {
            this->lineTo(rect.fRight - rx, rect.fTop);      // top
        }
    }
    this->close();
}

static void add_corner_arc(SkPath* path, const SkRect& rect,
                           SkScalar rx, SkScalar ry, int startAngle,
                           SkPath::Direction dir, bool forceMoveTo) {
    rx = SkMinScalar(SkScalarHalf(rect.width()), rx);
    ry = SkMinScalar(SkScalarHalf(rect.height()), ry);

    SkRect   r;
    r.set(-rx, -ry, rx, ry);

    switch (startAngle) {
        case   0:
            r.offset(rect.fRight - r.fRight, rect.fBottom - r.fBottom);
            break;
        case  90:
            r.offset(rect.fLeft - r.fLeft,   rect.fBottom - r.fBottom);
            break;
        case 180: r.offset(rect.fLeft - r.fLeft,   rect.fTop - r.fTop); break;
        case 270: r.offset(rect.fRight - r.fRight, rect.fTop - r.fTop); break;
        default: SkASSERT(!"unexpected startAngle in add_corner_arc");
    }

    SkScalar start = SkIntToScalar(startAngle);
    SkScalar sweep = SkIntToScalar(90);
    if (SkPath::kCCW_Direction == dir) {
        start += sweep;
        sweep = -sweep;
    }

    path->arcTo(r, start, sweep, forceMoveTo);
}

void SkPath::addRoundRect(const SkRect& rect, const SkScalar rad[],
                          Direction dir) {
    SkAutoPathBoundsUpdate apbu(this, rect);

    if (kCW_Direction == dir) {
        add_corner_arc(this, rect, rad[0], rad[1], 180, dir, true);
        add_corner_arc(this, rect, rad[2], rad[3], 270, dir, false);
        add_corner_arc(this, rect, rad[4], rad[5],   0, dir, false);
        add_corner_arc(this, rect, rad[6], rad[7],  90, dir, false);
    } else {
        add_corner_arc(this, rect, rad[0], rad[1], 180, dir, true);
        add_corner_arc(this, rect, rad[6], rad[7],  90, dir, false);
        add_corner_arc(this, rect, rad[4], rad[5],   0, dir, false);
        add_corner_arc(this, rect, rad[2], rad[3], 270, dir, false);
    }
    this->close();
}

void SkPath::addOval(const SkRect& oval, Direction dir) {
    SkAutoPathBoundsUpdate apbu(this, oval);

    SkScalar    cx = oval.centerX();
    SkScalar    cy = oval.centerY();
    SkScalar    rx = SkScalarHalf(oval.width());
    SkScalar    ry = SkScalarHalf(oval.height());
#if 0   // these seem faster than using quads (1/2 the number of edges)
    SkScalar    sx = SkScalarMul(rx, CUBIC_ARC_FACTOR);
    SkScalar    sy = SkScalarMul(ry, CUBIC_ARC_FACTOR);

    this->incReserve(13);
    this->moveTo(cx + rx, cy);
    if (dir == kCCW_Direction) {
        this->cubicTo(cx + rx, cy - sy, cx + sx, cy - ry, cx, cy - ry);
        this->cubicTo(cx - sx, cy - ry, cx - rx, cy - sy, cx - rx, cy);
        this->cubicTo(cx - rx, cy + sy, cx - sx, cy + ry, cx, cy + ry);
        this->cubicTo(cx + sx, cy + ry, cx + rx, cy + sy, cx + rx, cy);
    } else {
        this->cubicTo(cx + rx, cy + sy, cx + sx, cy + ry, cx, cy + ry);
        this->cubicTo(cx - sx, cy + ry, cx - rx, cy + sy, cx - rx, cy);
        this->cubicTo(cx - rx, cy - sy, cx - sx, cy - ry, cx, cy - ry);
        this->cubicTo(cx + sx, cy - ry, cx + rx, cy - sy, cx + rx, cy);
    }
#else
    SkScalar    sx = SkScalarMul(rx, SK_ScalarTanPIOver8);
    SkScalar    sy = SkScalarMul(ry, SK_ScalarTanPIOver8);
    SkScalar    mx = SkScalarMul(rx, SK_ScalarRoot2Over2);
    SkScalar    my = SkScalarMul(ry, SK_ScalarRoot2Over2);

    /*
        To handle imprecision in computing the center and radii, we revert to
        the provided bounds when we can (i.e. use oval.fLeft instead of cx-rx)
        to ensure that we don't exceed the oval's bounds *ever*, since we want
        to use oval for our fast-bounds, rather than have to recompute it.
    */
    const SkScalar L = oval.fLeft;      // cx - rx
    const SkScalar T = oval.fTop;       // cy - ry
    const SkScalar R = oval.fRight;     // cx + rx
    const SkScalar B = oval.fBottom;    // cy + ry

    this->incReserve(17);   // 8 quads + close
    this->moveTo(R, cy);
    if (dir == kCCW_Direction) {
        this->quadTo(      R, cy - sy, cx + mx, cy - my);
        this->quadTo(cx + sx,       T, cx     ,       T);
        this->quadTo(cx - sx,       T, cx - mx, cy - my);
        this->quadTo(      L, cy - sy,       L, cy     );
        this->quadTo(      L, cy + sy, cx - mx, cy + my);
        this->quadTo(cx - sx,       B, cx     ,       B);
        this->quadTo(cx + sx,       B, cx + mx, cy + my);
        this->quadTo(      R, cy + sy,       R, cy     );
    } else {
        this->quadTo(      R, cy + sy, cx + mx, cy + my);
        this->quadTo(cx + sx,       B, cx     ,       B);
        this->quadTo(cx - sx,       B, cx - mx, cy + my);
        this->quadTo(      L, cy + sy,       L, cy     );
        this->quadTo(      L, cy - sy, cx - mx, cy - my);
        this->quadTo(cx - sx,       T, cx     ,       T);
        this->quadTo(cx + sx,       T, cx + mx, cy - my);
        this->quadTo(      R, cy - sy,       R, cy     );
    }
#endif
    this->close();
}

void SkPath::addCircle(SkScalar x, SkScalar y, SkScalar r, Direction dir) {
    if (r > 0) {
        SkRect  rect;
        rect.set(x - r, y - r, x + r, y + r);
        this->addOval(rect, dir);
    }
}

#include "SkGeometry.h"

static int build_arc_points(const SkRect& oval, SkScalar startAngle,
                            SkScalar sweepAngle,
                            SkPoint pts[kSkBuildQuadArcStorage]) {
    SkVector start, stop;

    start.fY = SkScalarSinCos(SkDegreesToRadians(startAngle), &start.fX);
    stop.fY = SkScalarSinCos(SkDegreesToRadians(startAngle + sweepAngle),
                             &stop.fX);

    /*  If the sweep angle is nearly (but less than) 360, then due to precision
        loss in radians-conversion and/or sin/cos, we may end up with coincident
        vectors, which will fool SkBuildQuadArc into doing nothing (bad) instead
        of drawing a nearly complete circle (good).
             e.g. canvas.drawArc(0, 359.99, ...)
             -vs- canvas.drawArc(0, 359.9, ...)
        We try to detect this edge case, and tweak the stop vector
     */
    if (start == stop) {
        SkScalar sw = SkScalarAbs(sweepAngle);
        if (sw < SkIntToScalar(360) && sw > SkIntToScalar(359)) {
            SkScalar stopRad = SkDegreesToRadians(startAngle + sweepAngle);
            // make a guess at a tiny angle (in radians) to tweak by
            SkScalar deltaRad = SkScalarCopySign(SK_Scalar1/512, sweepAngle);
            // not sure how much will be enough, so we use a loop
            do {
                stopRad -= deltaRad;
                stop.fY = SkScalarSinCos(stopRad, &stop.fX);
            } while (start == stop);
        }
    }

    SkMatrix    matrix;

    matrix.setScale(SkScalarHalf(oval.width()), SkScalarHalf(oval.height()));
    matrix.postTranslate(oval.centerX(), oval.centerY());

    return SkBuildQuadArc(start, stop,
          sweepAngle > 0 ? kCW_SkRotationDirection : kCCW_SkRotationDirection,
                          &matrix, pts);
}

void SkPath::arcTo(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle,
                   bool forceMoveTo) {
    if (oval.width() < 0 || oval.height() < 0) {
        return;
    }

    SkPoint pts[kSkBuildQuadArcStorage];
    int count = build_arc_points(oval, startAngle, sweepAngle, pts);
    SkASSERT((count & 1) == 1);

    if (fVerbs.count() == 0) {
        forceMoveTo = true;
    }
    this->incReserve(count);
    forceMoveTo ? this->moveTo(pts[0]) : this->lineTo(pts[0]);
    for (int i = 1; i < count; i += 2) {
        this->quadTo(pts[i], pts[i+1]);
    }
}

void SkPath::addArc(const SkRect& oval, SkScalar startAngle,
                    SkScalar sweepAngle) {
    if (oval.isEmpty() || 0 == sweepAngle) {
        return;
    }

    const SkScalar kFullCircleAngle = SkIntToScalar(360);

    if (sweepAngle >= kFullCircleAngle || sweepAngle <= -kFullCircleAngle) {
        this->addOval(oval, sweepAngle > 0 ? kCW_Direction : kCCW_Direction);
        return;
    }

    SkPoint pts[kSkBuildQuadArcStorage];
    int count = build_arc_points(oval, startAngle, sweepAngle, pts);

    this->incReserve(count);
    this->moveTo(pts[0]);
    for (int i = 1; i < count; i += 2) {
        this->quadTo(pts[i], pts[i+1]);
    }
}

/*
    Need to handle the case when the angle is sharp, and our computed end-points
    for the arc go behind pt1 and/or p2...
*/
void SkPath::arcTo(SkScalar x1, SkScalar y1, SkScalar x2, SkScalar y2,
                   SkScalar radius) {
    SkVector    before, after;

    // need to know our prev pt so we can construct tangent vectors
    {
        SkPoint start;
        this->getLastPt(&start);
        // Handle degenerate cases by adding a line to the first point and
        // bailing out.
        if ((x1 == start.fX && y1 == start.fY) ||
            (x1 == x2 && y1 == y2) ||
            radius == 0) {
            this->lineTo(x1, y1);
            return;
        }
        before.setNormalize(x1 - start.fX, y1 - start.fY);
        after.setNormalize(x2 - x1, y2 - y1);
    }

    SkScalar cosh = SkPoint::DotProduct(before, after);
    SkScalar sinh = SkPoint::CrossProduct(before, after);

    if (SkScalarNearlyZero(sinh)) {   // angle is too tight
        this->lineTo(x1, y1);
        return;
    }

    SkScalar dist = SkScalarMulDiv(radius, SK_Scalar1 - cosh, sinh);
    if (dist < 0) {
        dist = -dist;
    }

    SkScalar xx = x1 - SkScalarMul(dist, before.fX);
    SkScalar yy = y1 - SkScalarMul(dist, before.fY);
    SkRotationDirection arcDir;

    // now turn before/after into normals
    if (sinh > 0) {
        before.rotateCCW();
        after.rotateCCW();
        arcDir = kCW_SkRotationDirection;
    } else {
        before.rotateCW();
        after.rotateCW();
        arcDir = kCCW_SkRotationDirection;
    }

    SkMatrix    matrix;
    SkPoint     pts[kSkBuildQuadArcStorage];

    matrix.setScale(radius, radius);
    matrix.postTranslate(xx - SkScalarMul(radius, before.fX),
                         yy - SkScalarMul(radius, before.fY));

    int count = SkBuildQuadArc(before, after, arcDir, &matrix, pts);

    this->incReserve(count);
    // [xx,yy] == pts[0]
    this->lineTo(xx, yy);
    for (int i = 1; i < count; i += 2) {
        this->quadTo(pts[i], pts[i+1]);
    }
}

///////////////////////////////////////////////////////////////////////////////

void SkPath::addPath(const SkPath& path, SkScalar dx, SkScalar dy) {
    SkMatrix matrix;

    matrix.setTranslate(dx, dy);
    this->addPath(path, matrix);
}

void SkPath::addPath(const SkPath& path, const SkMatrix& matrix) {
    this->incReserve(path.fPts.count());

    Iter    iter(path, false);
    SkPoint pts[4];
    Verb    verb;

    SkMatrix::MapPtsProc proc = matrix.getMapPtsProc();

    while ((verb = iter.next(pts)) != kDone_Verb) {
        switch (verb) {
            case kMove_Verb:
                proc(matrix, &pts[0], &pts[0], 1);
                this->moveTo(pts[0]);
                break;
            case kLine_Verb:
                proc(matrix, &pts[1], &pts[1], 1);
                this->lineTo(pts[1]);
                break;
            case kQuad_Verb:
                proc(matrix, &pts[1], &pts[1], 2);
                this->quadTo(pts[1], pts[2]);
                break;
            case kCubic_Verb:
                proc(matrix, &pts[1], &pts[1], 3);
                this->cubicTo(pts[1], pts[2], pts[3]);
                break;
            case kClose_Verb:
                this->close();
                break;
            default:
                SkASSERT(!"unknown verb");
        }
    }
}

///////////////////////////////////////////////////////////////////////////////

static const uint8_t gPtsInVerb[] = {
    1,  // kMove
    1,  // kLine
    2,  // kQuad
    3,  // kCubic
    0,  // kClose
    0   // kDone
};

// ignore the initial moveto, and stop when the 1st contour ends
void SkPath::pathTo(const SkPath& path) {
    int i, vcount = path.fVerbs.count();
    if (vcount == 0) {
        return;
    }

    this->incReserve(vcount);

    const uint8_t*  verbs = path.fVerbs.begin();
    const SkPoint*  pts = path.fPts.begin() + 1;    // 1 for the initial moveTo

    SkASSERT(verbs[0] == kMove_Verb);
    for (i = 1; i < vcount; i++) {
        switch (verbs[i]) {
            case kLine_Verb:
                this->lineTo(pts[0].fX, pts[0].fY);
                break;
            case kQuad_Verb:
                this->quadTo(pts[0].fX, pts[0].fY, pts[1].fX, pts[1].fY);
                break;
            case kCubic_Verb:
                this->cubicTo(pts[0].fX, pts[0].fY, pts[1].fX, pts[1].fY,
                              pts[2].fX, pts[2].fY);
                break;
            case kClose_Verb:
                return;
        }
        pts += gPtsInVerb[verbs[i]];
    }
}

// ignore the last point of the 1st contour
void SkPath::reversePathTo(const SkPath& path) {
    int i, vcount = path.fVerbs.count();
    if (vcount == 0) {
        return;
    }

    this->incReserve(vcount);

    const uint8_t*  verbs = path.fVerbs.begin();
    const SkPoint*  pts = path.fPts.begin();

    SkASSERT(verbs[0] == kMove_Verb);
    for (i = 1; i < vcount; i++) {
        int n = gPtsInVerb[verbs[i]];
        if (n == 0) {
            break;
        }
        pts += n;
    }

    while (--i > 0) {
        switch (verbs[i]) {
            case kLine_Verb:
                this->lineTo(pts[-1].fX, pts[-1].fY);
                break;
            case kQuad_Verb:
                this->quadTo(pts[-1].fX, pts[-1].fY, pts[-2].fX, pts[-2].fY);
                break;
            case kCubic_Verb:
                this->cubicTo(pts[-1].fX, pts[-1].fY, pts[-2].fX, pts[-2].fY,
                              pts[-3].fX, pts[-3].fY);
                break;
            default:
                SkASSERT(!"bad verb");
                break;
        }
        pts -= gPtsInVerb[verbs[i]];
    }
}

///////////////////////////////////////////////////////////////////////////////

void SkPath::offset(SkScalar dx, SkScalar dy, SkPath* dst) const {
    SkMatrix    matrix;

    matrix.setTranslate(dx, dy);
    this->transform(matrix, dst);
}

#include "SkGeometry.h"

static void subdivide_quad_to(SkPath* path, const SkPoint pts[3],
                              int level = 2) {
    if (--level >= 0) {
        SkPoint tmp[5];

        SkChopQuadAtHalf(pts, tmp);
        subdivide_quad_to(path, &tmp[0], level);
        subdivide_quad_to(path, &tmp[2], level);
    } else {
        path->quadTo(pts[1], pts[2]);
    }
}

static void subdivide_cubic_to(SkPath* path, const SkPoint pts[4],
                               int level = 2) {
    if (--level >= 0) {
        SkPoint tmp[7];

        SkChopCubicAtHalf(pts, tmp);
        subdivide_cubic_to(path, &tmp[0], level);
        subdivide_cubic_to(path, &tmp[3], level);
    } else {
        path->cubicTo(pts[1], pts[2], pts[3]);
    }
}

void SkPath::transform(const SkMatrix& matrix, SkPath* dst) const {
    SkDEBUGCODE(this->validate();)
    if (dst == NULL) {
        dst = (SkPath*)this;
    }

    if (matrix.getType() & SkMatrix::kPerspective_Mask) {
        SkPath  tmp;
        tmp.fFillType = fFillType;

        SkPath::Iter    iter(*this, false);
        SkPoint         pts[4];
        SkPath::Verb    verb;

        while ((verb = iter.next(pts)) != kDone_Verb) {
            switch (verb) {
                case kMove_Verb:
                    tmp.moveTo(pts[0]);
                    break;
                case kLine_Verb:
                    tmp.lineTo(pts[1]);
                    break;
                case kQuad_Verb:
                    subdivide_quad_to(&tmp, pts);
                    break;
                case kCubic_Verb:
                    subdivide_cubic_to(&tmp, pts);
                    break;
                case kClose_Verb:
                    tmp.close();
                    break;
                default:
                    SkASSERT(!"unknown verb");
                    break;
            }
        }

        dst->swap(tmp);
        matrix.mapPoints(dst->fPts.begin(), dst->fPts.count());
    } else {
        // remember that dst might == this, so be sure to check
        // fBoundsIsDirty before we set it
        if (!fBoundsIsDirty && matrix.rectStaysRect() && fPts.count() > 1) {
            // if we're empty, fastbounds should not be mapped
            matrix.mapRect(&dst->fBounds, fBounds);
            dst->fBoundsIsDirty = false;
        } else {
            dst->fBoundsIsDirty = true;
        }

        if (this != dst) {
            dst->fVerbs = fVerbs;
            dst->fPts.setCount(fPts.count());
            dst->fFillType = fFillType;
        }
        matrix.mapPoints(dst->fPts.begin(), fPts.begin(), fPts.count());
        SkDEBUGCODE(dst->validate();)
    }
}

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////

enum NeedMoveToState {
    kAfterClose_NeedMoveToState,
    kAfterCons_NeedMoveToState,
    kAfterPrefix_NeedMoveToState
};

SkPath::Iter::Iter() {
#ifdef SK_DEBUG
    fPts = NULL;
    fMoveTo.fX = fMoveTo.fY = fLastPt.fX = fLastPt.fY = 0;
    fForceClose = fNeedMoveTo = fCloseLine = false;
#endif
    // need to init enough to make next() harmlessly return kDone_Verb
    fVerbs = NULL;
    fVerbStop = NULL;
    fNeedClose = false;
}

SkPath::Iter::Iter(const SkPath& path, bool forceClose) {
    this->setPath(path, forceClose);
}

void SkPath::Iter::setPath(const SkPath& path, bool forceClose) {
    fPts = path.fPts.begin();
    fVerbs = path.fVerbs.begin();
    fVerbStop = path.fVerbs.end();
    fForceClose = SkToU8(forceClose);
    fNeedClose = false;
    fNeedMoveTo = kAfterPrefix_NeedMoveToState;
}

bool SkPath::Iter::isClosedContour() const {
    if (fVerbs == NULL || fVerbs == fVerbStop) {
        return false;
    }
    if (fForceClose) {
        return true;
    }

    const uint8_t* verbs = fVerbs;
    const uint8_t* stop = fVerbStop;

    if (kMove_Verb == *verbs) {
        verbs += 1; // skip the initial moveto
    }

    while (verbs < stop) {
        unsigned v = *verbs++;
        if (kMove_Verb == v) {
            break;
        }
        if (kClose_Verb == v) {
            return true;
        }
    }
    return false;
}

SkPath::Verb SkPath::Iter::autoClose(SkPoint pts[2]) {
    if (fLastPt != fMoveTo) {
        // A special case: if both points are NaN, SkPoint::operation== returns
        // false, but the iterator expects that they are treated as the same.
        // (consider SkPoint is a 2-dimension float point).
        if (SkScalarIsNaN(fLastPt.fX) || SkScalarIsNaN(fLastPt.fY) ||
            SkScalarIsNaN(fMoveTo.fX) || SkScalarIsNaN(fMoveTo.fY)) {
            return kClose_Verb;
        }

        if (pts) {
            pts[0] = fLastPt;
            pts[1] = fMoveTo;
        }
        fLastPt = fMoveTo;
        fCloseLine = true;
        return kLine_Verb;
    }
    return kClose_Verb;
}

bool SkPath::Iter::cons_moveTo(SkPoint pts[1]) {
    if (fNeedMoveTo == kAfterClose_NeedMoveToState) {
        if (pts) {
            *pts = fMoveTo;
        }
        fNeedClose = fForceClose;
        fNeedMoveTo = kAfterCons_NeedMoveToState;
        fVerbs -= 1;
        return true;
    }

    if (fNeedMoveTo == kAfterCons_NeedMoveToState) {
        if (pts) {
            *pts = fMoveTo;
        }
        fNeedMoveTo = kAfterPrefix_NeedMoveToState;
    } else {
        SkASSERT(fNeedMoveTo == kAfterPrefix_NeedMoveToState);
        if (pts) {
            *pts = fPts[-1];
        }
    }
    return false;
}

SkPath::Verb SkPath::Iter::next(SkPoint pts[4]) {
    if (fVerbs == fVerbStop) {
        if (fNeedClose) {
            if (kLine_Verb == this->autoClose(pts)) {
                return kLine_Verb;
            }
            fNeedClose = false;
            return kClose_Verb;
        }
        return kDone_Verb;
    }

    unsigned        verb = *fVerbs++;
    const SkPoint*  srcPts = fPts;

    switch (verb) {
        case kMove_Verb:
            if (fNeedClose) {
                fVerbs -= 1;
                verb = this->autoClose(pts);
                if (verb == kClose_Verb) {
                    fNeedClose = false;
                }
                return (Verb)verb;
            }
            if (fVerbs == fVerbStop) {    // might be a trailing moveto
                return kDone_Verb;
            }
            fMoveTo = *srcPts;
            if (pts) {
                pts[0] = *srcPts;
            }
            srcPts += 1;
            fNeedMoveTo = kAfterCons_NeedMoveToState;
            fNeedClose = fForceClose;
            break;
        case kLine_Verb:
            if (this->cons_moveTo(pts)) {
                return kMove_Verb;
            }
            if (pts) {
                pts[1] = srcPts[0];
            }
            fLastPt = srcPts[0];
            fCloseLine = false;
            srcPts += 1;
            break;
        case kQuad_Verb:
            if (this->cons_moveTo(pts)) {
                return kMove_Verb;
            }
            if (pts) {
                memcpy(&pts[1], srcPts, 2 * sizeof(SkPoint));
            }
            fLastPt = srcPts[1];
            srcPts += 2;
            break;
        case kCubic_Verb:
            if (this->cons_moveTo(pts)) {
                return kMove_Verb;
            }
            if (pts) {
                memcpy(&pts[1], srcPts, 3 * sizeof(SkPoint));
            }
            fLastPt = srcPts[2];
            srcPts += 3;
            break;
        case kClose_Verb:
            verb = this->autoClose(pts);
            if (verb == kLine_Verb) {
                fVerbs -= 1;
            } else {
                fNeedClose = false;
            }
            fNeedMoveTo = kAfterClose_NeedMoveToState;
            break;
    }
    fPts = srcPts;
    return (Verb)verb;
}

///////////////////////////////////////////////////////////////////////////////

static bool exceeds_dist(const SkScalar p[], const SkScalar q[], SkScalar dist,
                         int count) {
    SkASSERT(dist > 0);

    count *= 2;
    for (int i = 0; i < count; i++) {
        if (SkScalarAbs(p[i] - q[i]) > dist) {
            return true;
        }
    }
    return false;
}

static void subdivide_quad(SkPath* dst, const SkPoint pts[3], SkScalar dist,
                           int subLevel = 4) {
    if (--subLevel >= 0 && exceeds_dist(&pts[0].fX, &pts[1].fX, dist, 4)) {
        SkPoint tmp[5];
        SkChopQuadAtHalf(pts, tmp);

        subdivide_quad(dst, &tmp[0], dist, subLevel);
        subdivide_quad(dst, &tmp[2], dist, subLevel);
    } else {
        dst->quadTo(pts[1], pts[2]);
    }
}

static void subdivide_cubic(SkPath* dst, const SkPoint pts[4], SkScalar dist,
                            int subLevel = 4) {
    if (--subLevel >= 0 && exceeds_dist(&pts[0].fX, &pts[1].fX, dist, 6)) {
        SkPoint tmp[7];
        SkChopCubicAtHalf(pts, tmp);

        subdivide_cubic(dst, &tmp[0], dist, subLevel);
        subdivide_cubic(dst, &tmp[3], dist, subLevel);
    } else {
        dst->cubicTo(pts[1], pts[2], pts[3]);
    }
}

void SkPath::subdivide(SkScalar dist, bool bendLines, SkPath* dst) const {
    SkPath  tmpPath;
    if (NULL == dst || this == dst) {
        dst = &tmpPath;
    }

    SkPath::Iter    iter(*this, false);
    SkPoint         pts[4];

    for (;;) {
        switch (iter.next(pts)) {
            case SkPath::kMove_Verb:
                dst->moveTo(pts[0]);
                break;
            case SkPath::kLine_Verb:
                if (!bendLines) {
                    dst->lineTo(pts[1]);
                    break;
                }
                // construct a quad from the line
                pts[2] = pts[1];
                pts[1].set(SkScalarAve(pts[0].fX, pts[2].fX),
                           SkScalarAve(pts[0].fY, pts[2].fY));
                // fall through to the quad case
            case SkPath::kQuad_Verb:
                subdivide_quad(dst, pts, dist);
                break;
            case SkPath::kCubic_Verb:
                subdivide_cubic(dst, pts, dist);
                break;
            case SkPath::kClose_Verb:
                dst->close();
                break;
            case SkPath::kDone_Verb:
                goto DONE;
        }
    }
DONE:
    if (&tmpPath == dst) {   // i.e. the dst should be us
        dst->swap(*(SkPath*)this);
    }
}

///////////////////////////////////////////////////////////////////////
/*
    Format in flattened buffer: [ptCount, verbCount, pts[], verbs[]]
*/

void SkPath::flatten(SkFlattenableWriteBuffer& buffer) const {
    SkDEBUGCODE(this->validate();)

    buffer.write32(fPts.count());
    buffer.write32(fVerbs.count());
    buffer.write32(fFillType);
    buffer.writeMul4(fPts.begin(), sizeof(SkPoint) * fPts.count());
    buffer.writePad(fVerbs.begin(), fVerbs.count());
}

void SkPath::unflatten(SkFlattenableReadBuffer& buffer) {
    fPts.setCount(buffer.readS32());
    fVerbs.setCount(buffer.readS32());
    fFillType = buffer.readS32();
    buffer.read(fPts.begin(), sizeof(SkPoint) * fPts.count());
    buffer.read(fVerbs.begin(), fVerbs.count());

    fBoundsIsDirty = true;

    SkDEBUGCODE(this->validate();)
}

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////

void SkPath::dump(bool forceClose, const char title[]) const {
    Iter    iter(*this, forceClose);
    SkPoint pts[4];
    Verb    verb;

    SkDebugf("path: forceClose=%s %s\n", forceClose ? "true" : "false",
             title ? title : "");

    while ((verb = iter.next(pts)) != kDone_Verb) {
        switch (verb) {
            case kMove_Verb:
#ifdef SK_CAN_USE_FLOAT
                SkDebugf("  path: moveTo [%g %g]\n",
                        SkScalarToFloat(pts[0].fX), SkScalarToFloat(pts[0].fY));
#else
                SkDebugf("  path: moveTo [%x %x]\n", pts[0].fX, pts[0].fY);
#endif
                break;
            case kLine_Verb:
#ifdef SK_CAN_USE_FLOAT
                SkDebugf("  path: lineTo [%g %g]\n",
                        SkScalarToFloat(pts[1].fX), SkScalarToFloat(pts[1].fY));
#else
                SkDebugf("  path: lineTo [%x %x]\n", pts[1].fX, pts[1].fY);
#endif
                break;
            case kQuad_Verb:
#ifdef SK_CAN_USE_FLOAT
                SkDebugf("  path: quadTo [%g %g] [%g %g]\n",
                        SkScalarToFloat(pts[1].fX), SkScalarToFloat(pts[1].fY),
                        SkScalarToFloat(pts[2].fX), SkScalarToFloat(pts[2].fY));
#else
                SkDebugf("  path: quadTo [%x %x] [%x %x]\n",
                         pts[1].fX, pts[1].fY, pts[2].fX, pts[2].fY);
#endif
                break;
            case kCubic_Verb:
#ifdef SK_CAN_USE_FLOAT
                SkDebugf("  path: cubeTo [%g %g] [%g %g] [%g %g]\n",
                        SkScalarToFloat(pts[1].fX), SkScalarToFloat(pts[1].fY),
                        SkScalarToFloat(pts[2].fX), SkScalarToFloat(pts[2].fY),
                        SkScalarToFloat(pts[3].fX), SkScalarToFloat(pts[3].fY));
#else
                SkDebugf("  path: cubeTo [%x %x] [%x %x] [%x %x]\n",
                         pts[1].fX, pts[1].fY, pts[2].fX, pts[2].fY,
                         pts[3].fX, pts[3].fY);
#endif
                break;
            case kClose_Verb:
                SkDebugf("  path: close\n");
                break;
            default:
                SkDebugf("  path: UNKNOWN VERB %d, aborting dump...\n", verb);
                verb = kDone_Verb;  // stop the loop
                break;
        }
    }
    SkDebugf("path: done %s\n", title ? title : "");
}

void SkPath::dump() const {
    this->dump(false);
}

#ifdef SK_DEBUG
void SkPath::validate() const {
    SkASSERT(this != NULL);
    SkASSERT((fFillType & ~3) == 0);
    fPts.validate();
    fVerbs.validate();

    if (!fBoundsIsDirty) {
        SkRect bounds;
        compute_pt_bounds(&bounds, fPts);
        if (fPts.count() <= 1) {
            // if we're empty, fBounds may be empty but translated, so we can't
            // necessarily compare to bounds directly
            // try path.addOval(2, 2, 2, 2) which is empty, but the bounds will
            // be [2, 2, 2, 2]
            SkASSERT(bounds.isEmpty());
            SkASSERT(fBounds.isEmpty());
        } else {
            fBounds.contains(bounds);
        }
    }
}
#endif