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 computeBounds().
 */
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() {
        if (fEmpty) {
            fPath->fFastBounds = fRect;
            fPath->fFastBoundsIsDirty = false;
        } else if (!fDirty) {
            fPath->fFastBounds.join(fRect);
            fPath->fFastBoundsIsDirty = false;
        }
    }
    
private:
    const SkPath*   fPath;
    SkRect          fRect;
    bool            fDirty;
    bool            fEmpty;
    
    // returns true if we should proceed
    void init(const SkPath* path) {
        fPath = path;
        fDirty = path->fFastBoundsIsDirty;
        fEmpty = path->isEmpty();
        // can't use fRect for our bounds unless we know is upright and proper
        fRect.sort();
    }
};

static void compute_fast_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() : fFastBoundsIsDirty(true), fFillType(kWinding_FillType) {}

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) {
        fFastBounds         = src.fFastBounds;
        fPts                = src.fPts;
        fVerbs              = src.fVerbs;
        fFillType           = src.fFillType;
        fFastBoundsIsDirty  = src.fFastBoundsIsDirty;
    }
    SkDEBUGCODE(this->validate();)
    return *this;
}

bool operator==(const SkPath& a, const SkPath& b) {
    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>(fFastBounds, other.fFastBounds);
        fPts.swap(other.fPts);
        fVerbs.swap(other.fVerbs);
        SkTSwap<uint8_t>(fFillType, other.fFillType);
        SkTSwap<uint8_t>(fFastBoundsIsDirty, other.fFastBoundsIsDirty);
    }
}

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

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

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

    fPts.rewind();
    fVerbs.rewind();
    fFastBoundsIsDirty = 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;
}

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);
    }
}

#define ALWAYS_FAST_BOUNDS_FOR_NOW  true

void SkPath::computeBounds(SkRect* bounds, BoundsType bt) const {
    SkDEBUGCODE(this->validate();)

    SkASSERT(bounds);
    
    // we BoundsType for now

    if (fFastBoundsIsDirty) {
        fFastBoundsIsDirty = false;
        compute_fast_bounds(&fFastBounds, fPts);
    }
    *bounds = fFastBounds;
}

//////////////////////////////////////////////////////////////////////////////
//  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);

    fFastBoundsIsDirty = 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;

    fFastBoundsIsDirty = 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;

    fFastBoundsIsDirty = 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;

    fFastBoundsIsDirty = 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) {
    SkAutoPathBoundsUpdate apbu(this, rect);

    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;
    }
    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);
        
    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);
        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
        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
        // fFastBoundsIsDirty before we set it
        if (!fFastBoundsIsDirty && matrix.rectStaysRect() && fPts.count() > 1) {
            // if we're empty, fastbounds should not be mapped
            matrix.mapRect(&dst->fFastBounds, fFastBounds);
            dst->fFastBoundsIsDirty = false;
        } else {
            dst->fFastBoundsIsDirty = 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();)
    }
}

void SkPath::updateBoundsCache() const {
    if (fFastBoundsIsDirty) {
        SkRect  r;
        this->computeBounds(&r, kFast_BoundsType);
        SkASSERT(!fFastBoundsIsDirty);
    }
}

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

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());
    
    fFastBoundsIsDirty = true;

    SkDEBUGCODE(this->validate();)
}

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

#include "SkString.h"
#include "SkStream.h"

static void write_scalar(SkWStream* stream, SkScalar value) {
    char    buffer[SkStrAppendScalar_MaxSize];
    char*   stop = SkStrAppendScalar(buffer, value);
    stream->write(buffer, stop - buffer);
}

static void append_scalars(SkWStream* stream, char verb, const SkScalar data[],
                           int count) {
    stream->write(&verb, 1);
    write_scalar(stream, data[0]);
    for (int i = 1; i < count; i++) {
        if (data[i] >= 0) {
            // can skip the separater if data[i] is negative
            stream->write(" ", 1);
        }
        write_scalar(stream, data[i]);
    }
}

void SkPath::toString(SkString* str) const {
    SkDynamicMemoryWStream  stream;

    SkPath::Iter    iter(*this, false);
    SkPoint         pts[4];
    
    for (;;) {
        switch (iter.next(pts)) {
            case SkPath::kMove_Verb:
                append_scalars(&stream, 'M', &pts[0].fX, 2);
                break;
            case SkPath::kLine_Verb:
                append_scalars(&stream, 'L', &pts[1].fX, 2);
                break;
            case SkPath::kQuad_Verb:
                append_scalars(&stream, 'Q', &pts[1].fX, 4);
                break;
            case SkPath::kCubic_Verb:
                append_scalars(&stream, 'C', &pts[1].fX, 6);
                break;
            case SkPath::kClose_Verb:
                stream.write("Z", 1);
                break;
            case SkPath::kDone_Verb:
                str->resize(stream.getOffset());
                stream.copyTo(str->writable_str());
                return;
        }
    }
}

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

#ifdef SK_DEBUG

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

    if (!fFastBoundsIsDirty) {
        SkRect bounds;
        compute_fast_bounds(&bounds, fPts);
        // can't call contains(), since it returns false if the rect is empty
        SkASSERT(fFastBounds.fLeft <= bounds.fLeft);
        SkASSERT(fFastBounds.fTop <= bounds.fTop);
        SkASSERT(fFastBounds.fRight >= bounds.fRight);
        SkASSERT(fFastBounds.fBottom >= bounds.fBottom);
    }
}

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 : "");
}

#endif