Remove the remainder of the skia source code from the Chromium repo. It now lives over in third_party/skia (I only removed the headers in the first CL, since it was too unwieldy with all these deletes).

BUG=none
TEST=If it builds, you're happy.
R=dglazkov

Review URL: http://codereview.chromium.org/113827

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@16893 0039d316-1c4b-4281-b951-d872f2087c98

1 files changed, 0 insertions, 1072 deletions

diff --git a/skia/sgl/SkGeometry.cpp b/skia/sgl/SkGeometry.cpp
deleted file mode 100644
index 4f22e92..0000000
--- a/skia/sgl/SkGeometry.cpp
+++ /dev/null
@@ -1,1072 +0,0 @@
-/* libs/graphics/sgl/SkGeometry.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 "SkGeometry.h"
-#include "Sk64.h"
-#include "SkMatrix.h"
-
-/** If defined, this makes eval_quad and eval_cubic do more setup (sometimes
-    involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul.
-    May also introduce overflow of fixed when we compute our setup.
-*/
-#ifdef SK_SCALAR_IS_FIXED
-    #define DIRECT_EVAL_OF_POLYNOMIALS
-#endif
-
-////////////////////////////////////////////////////////////////////////
-
-#ifdef SK_SCALAR_IS_FIXED
-    static int is_not_monotonic(int a, int b, int c, int d)
-    {
-        return (((a - b) | (b - c) | (c - d)) & ((b - a) | (c - b) | (d - c))) >> 31;
-    }
-
-    static int is_not_monotonic(int a, int b, int c)
-    {
-        return (((a - b) | (b - c)) & ((b - a) | (c - b))) >> 31;
-    }
-#else
-    static int is_not_monotonic(float a, float b, float c)
-    {
-        float ab = a - b;
-        float bc = b - c;
-        if (ab < 0)
-            bc = -bc;
-        return ab == 0 || bc < 0;
-    }
-#endif
-
-////////////////////////////////////////////////////////////////////////
-
-static bool is_unit_interval(SkScalar x)
-{
-    return x > 0 && x < SK_Scalar1;
-}
-
-static int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio)
-{
-    SkASSERT(ratio);
-
-    if (numer < 0)
-    {
-        numer = -numer;
-        denom = -denom;
-    }
-
-    if (denom == 0 || numer == 0 || numer >= denom)
-        return 0;
-
-    SkScalar r = SkScalarDiv(numer, denom);
-    SkASSERT(r >= 0 && r < SK_Scalar1);
-    if (r == 0) // catch underflow if numer <<<< denom
-        return 0;
-    *ratio = r;
-    return 1;
-}
-
-/** From Numerical Recipes in C.
-
-    Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C])
-    x1 = Q / A
-    x2 = C / Q
-*/
-int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2])
-{
-    SkASSERT(roots);
-
-    if (A == 0)
-        return valid_unit_divide(-C, B, roots);
-
-    SkScalar* r = roots;
-
-#ifdef SK_SCALAR_IS_FLOAT
-    float R = B*B - 4*A*C;
-    if (R < 0)  // complex roots
-        return 0;
-    R = sk_float_sqrt(R);
-#else
-    Sk64    RR, tmp;
-
-    RR.setMul(B,B);
-    tmp.setMul(A,C);
-    tmp.shiftLeft(2);
-    RR.sub(tmp);
-    if (RR.isNeg())
-        return 0;
-    SkFixed R = RR.getSqrt();
-#endif
-
-    SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2;
-    r += valid_unit_divide(Q, A, r);
-    r += valid_unit_divide(C, Q, r);
-    if (r - roots == 2)
-    {
-        if (roots[0] > roots[1])
-            SkTSwap<SkScalar>(roots[0], roots[1]);
-        else if (roots[0] == roots[1])  // nearly-equal?
-            r -= 1; // skip the double root
-    }
-    return (int)(r - roots);
-}
-
-#ifdef SK_SCALAR_IS_FIXED
-/** Trim A/B/C down so that they are all <= 32bits
-    and then call SkFindUnitQuadRoots()
-*/
-static int Sk64FindFixedQuadRoots(const Sk64& A, const Sk64& B, const Sk64& C, SkFixed roots[2])
-{
-    int na = A.shiftToMake32();
-    int nb = B.shiftToMake32();
-    int nc = C.shiftToMake32();
-
-    int shift = SkMax32(na, SkMax32(nb, nc));
-    SkASSERT(shift >= 0);
-
-    return SkFindUnitQuadRoots(A.getShiftRight(shift), B.getShiftRight(shift), C.getShiftRight(shift), roots);
-}
-#endif
-
-/////////////////////////////////////////////////////////////////////////////////////
-/////////////////////////////////////////////////////////////////////////////////////
-
-static SkScalar eval_quad(const SkScalar src[], SkScalar t)
-{
-    SkASSERT(src);
-    SkASSERT(t >= 0 && t <= SK_Scalar1);
-
-#ifdef DIRECT_EVAL_OF_POLYNOMIALS
-    SkScalar    C = src[0];
-    SkScalar    A = src[4] - 2 * src[2] + C;
-    SkScalar    B = 2 * (src[2] - C);
-    return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
-#else
-    SkScalar    ab = SkScalarInterp(src[0], src[2], t);
-    SkScalar    bc = SkScalarInterp(src[2], src[4], t); 
-    return SkScalarInterp(ab, bc, t);
-#endif
-}
-
-static SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t)
-{
-    SkScalar A = src[4] - 2 * src[2] + src[0];
-    SkScalar B = src[2] - src[0];
-
-    return 2 * SkScalarMulAdd(A, t, B);
-}
-
-static SkScalar eval_quad_derivative_at_half(const SkScalar src[])
-{
-    SkScalar A = src[4] - 2 * src[2] + src[0];
-    SkScalar B = src[2] - src[0];
-    return A + 2 * B;
-}
-
-void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent)
-{
-    SkASSERT(src);
-    SkASSERT(t >= 0 && t <= SK_Scalar1);
-
-    if (pt)
-        pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t));
-    if (tangent)
-        tangent->set(eval_quad_derivative(&src[0].fX, t),
-                     eval_quad_derivative(&src[0].fY, t));
-}
-
-void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent)
-{
-    SkASSERT(src);
-
-    if (pt)
-    {
-        SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
-        SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
-        SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
-        SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
-        pt->set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));
-    }
-    if (tangent)
-        tangent->set(eval_quad_derivative_at_half(&src[0].fX),
-                     eval_quad_derivative_at_half(&src[0].fY));
-}
-
-static void interp_quad_coords(const SkScalar* src, SkScalar* dst, SkScalar t)
-{
-    SkScalar    ab = SkScalarInterp(src[0], src[2], t);
-    SkScalar    bc = SkScalarInterp(src[2], src[4], t);
-
-    dst[0] = src[0];
-    dst[2] = ab;
-    dst[4] = SkScalarInterp(ab, bc, t);
-    dst[6] = bc;
-    dst[8] = src[4];
-}
-
-void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t)
-{
-    SkASSERT(t > 0 && t < SK_Scalar1);
-
-    interp_quad_coords(&src[0].fX, &dst[0].fX, t);
-    interp_quad_coords(&src[0].fY, &dst[0].fY, t);
-}
-
-void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5])
-{
-    SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
-    SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
-    SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
-    SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
-
-    dst[0] = src[0];
-    dst[1].set(x01, y01);
-    dst[2].set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));
-    dst[3].set(x12, y12);
-    dst[4] = src[2];
-}
-
-/** Quad'(t) = At + B, where
-    A = 2(a - 2b + c)
-    B = 2(b - a)
-    Solve for t, only if it fits between 0 < t < 1
-*/
-int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1])
-{
-    /*  At + B == 0
-        t = -B / A
-    */
-#ifdef SK_SCALAR_IS_FIXED
-    return is_not_monotonic(a, b, c) && valid_unit_divide(a - b, a - b - b + c, tValue);
-#else
-    return valid_unit_divide(a - b, a - b - b + c, tValue);
-#endif
-}
-
-static void flatten_double_quad_extrema(SkScalar coords[14])
-{
-    coords[2] = coords[6] = coords[4];
-}
-
-static void force_quad_monotonic_in_y(SkPoint pts[3])
-{
-    // zap pts[1].fY to the nearest value
-    SkScalar ab = SkScalarAbs(pts[0].fY - pts[1].fY);
-    SkScalar bc = SkScalarAbs(pts[1].fY - pts[2].fY);
-    pts[1].fY = ab < bc ? pts[0].fY : pts[2].fY;
-}
-
-/*  Returns 0 for 1 quad, and 1 for two quads, either way the answer is
-    stored in dst[]. Guarantees that the 1/2 quads will be monotonic.
-*/
-int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5])
-{
-    SkASSERT(src);
-    SkASSERT(dst);
-
-#if 0
-    static bool once = true;
-    if (once)
-    {
-        once = false;
-        SkPoint s[3] = { 0, 26398, 0, 26331, 0, 20621428 };
-        SkPoint d[6];
-        
-        int n = SkChopQuadAtYExtrema(s, d);
-        SkDebugf("chop=%d, Y=[%x %x %x %x %x %x]\n", n, d[0].fY, d[1].fY, d[2].fY, d[3].fY, d[4].fY, d[5].fY);
-    }
-#endif
-
-    SkScalar a = src[0].fY;
-    SkScalar b = src[1].fY;
-    SkScalar c = src[2].fY;
-
-    if (is_not_monotonic(a, b, c))
-    {
-        SkScalar    tValue;
-        if (valid_unit_divide(a - b, a - b - b + c, &tValue))
-        {
-            SkChopQuadAt(src, dst, tValue);
-            flatten_double_quad_extrema(&dst[0].fY);
-            return 1;
-        }
-        // if we get here, we need to force dst to be monotonic, even though
-        // we couldn't compute a unit_divide value (probably underflow).
-        b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c;
-    }
-    dst[0].set(src[0].fX, a);
-    dst[1].set(src[1].fX, b);
-    dst[2].set(src[2].fX, c);
-    return 0;
-}
-
-//  F(t)    = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2
-//  F'(t)   = 2 (b - a) + 2 (a - 2b + c) t
-//  F''(t)  = 2 (a - 2b + c)
-//
-//  A = 2 (b - a)
-//  B = 2 (a - 2b + c)
-//
-//  Maximum curvature for a quadratic means solving
-//  Fx' Fx'' + Fy' Fy'' = 0
-//
-//  t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2)
-//
-int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5])
-{
-    SkScalar    Ax = src[1].fX - src[0].fX;
-    SkScalar    Ay = src[1].fY - src[0].fY;
-    SkScalar    Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX;
-    SkScalar    By = src[0].fY - src[1].fY - src[1].fY + src[2].fY;
-    SkScalar    t = 0;  // 0 means don't chop
-
-#ifdef SK_SCALAR_IS_FLOAT
-    (void)valid_unit_divide(-(Ax * Bx + Ay * By), Bx * Bx + By * By, &t);
-#else
-    // !!! should I use SkFloat here? seems like it
-    Sk64    numer, denom, tmp;
-
-    numer.setMul(Ax, -Bx);
-    tmp.setMul(Ay, -By);
-    numer.add(tmp);
-
-    if (numer.isPos())  // do nothing if numer <= 0
-    {
-        denom.setMul(Bx, Bx);
-        tmp.setMul(By, By);
-        denom.add(tmp);
-        SkASSERT(!denom.isNeg());
-        if (numer < denom)
-        {
-            t = numer.getFixedDiv(denom);
-            SkASSERT(t >= 0 && t <= SK_Fixed1);     // assert that we're numerically stable (ha!)
-            if ((unsigned)t >= SK_Fixed1)           // runtime check for numerical stability
-                t = 0;  // ignore the chop
-        }
-    }
-#endif
-
-    if (t == 0)
-    {
-        memcpy(dst, src, 3 * sizeof(SkPoint));
-        return 1;
-    }
-    else
-    {
-        SkChopQuadAt(src, dst, t);
-        return 2;
-    }
-}
-
-////////////////////////////////////////////////////////////////////////////////////////
-///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS /////
-////////////////////////////////////////////////////////////////////////////////////////
-
-static void get_cubic_coeff(const SkScalar pt[], SkScalar coeff[4])
-{
-    coeff[0] = pt[6] + 3*(pt[2] - pt[4]) - pt[0];
-    coeff[1] = 3*(pt[4] - pt[2] - pt[2] + pt[0]);
-    coeff[2] = 3*(pt[2] - pt[0]);
-    coeff[3] = pt[0];
-}
-
-void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4])
-{
-    SkASSERT(pts);
-
-    if (cx)
-        get_cubic_coeff(&pts[0].fX, cx);
-    if (cy)
-        get_cubic_coeff(&pts[0].fY, cy);
-}
-
-static SkScalar eval_cubic(const SkScalar src[], SkScalar t)
-{
-    SkASSERT(src);
-    SkASSERT(t >= 0 && t <= SK_Scalar1);
-
-    if (t == 0)
-        return src[0];
-
-#ifdef DIRECT_EVAL_OF_POLYNOMIALS
-    SkScalar D = src[0];
-    SkScalar A = src[6] + 3*(src[2] - src[4]) - D;
-    SkScalar B = 3*(src[4] - src[2] - src[2] + D);
-    SkScalar C = 3*(src[2] - D);
-
-    return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D);
-#else
-    SkScalar    ab = SkScalarInterp(src[0], src[2], t);
-    SkScalar    bc = SkScalarInterp(src[2], src[4], t);
-    SkScalar    cd = SkScalarInterp(src[4], src[6], t);
-    SkScalar    abc = SkScalarInterp(ab, bc, t);
-    SkScalar    bcd = SkScalarInterp(bc, cd, t);
-    return SkScalarInterp(abc, bcd, t);
-#endif
-}
-
-/** return At^2 + Bt + C
-*/
-static SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t)
-{
-    SkASSERT(t >= 0 && t <= SK_Scalar1);
-
-    return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
-}
-
-static SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t)
-{
-    SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];
-    SkScalar B = 2*(src[4] - 2 * src[2] + src[0]);
-    SkScalar C = src[2] - src[0];
-
-    return eval_quadratic(A, B, C, t);
-}
-
-static SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t)
-{
-    SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];
-    SkScalar B = src[4] - 2 * src[2] + src[0];
-
-    return SkScalarMulAdd(A, t, B);
-}
-
-void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, SkVector* tangent, SkVector* curvature)
-{
-    SkASSERT(src);
-    SkASSERT(t >= 0 && t <= SK_Scalar1);
-
-    if (loc)
-        loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t));
-    if (tangent)
-        tangent->set(eval_cubic_derivative(&src[0].fX, t),
-                     eval_cubic_derivative(&src[0].fY, t));
-    if (curvature)
-        curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t),
-                       eval_cubic_2ndDerivative(&src[0].fY, t));
-}
-
-/** Cubic'(t) = At^2 + Bt + C, where
-    A = 3(-a + 3(b - c) + d)
-    B = 6(a - 2b + c)
-    C = 3(b - a)
-    Solve for t, keeping only those that fit betwee 0 < t < 1
-*/
-int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d, SkScalar tValues[2])
-{
-#ifdef SK_SCALAR_IS_FIXED
-    if (!is_not_monotonic(a, b, c, d))
-        return 0;
-#endif
-
-    // we divide A,B,C by 3 to simplify
-    SkScalar A = d - a + 3*(b - c);
-    SkScalar B = 2*(a - b - b + c);
-    SkScalar C = b - a;
-
-    return SkFindUnitQuadRoots(A, B, C, tValues);
-}
-
-static void interp_cubic_coords(const SkScalar* src, SkScalar* dst, SkScalar t)
-{
-    SkScalar    ab = SkScalarInterp(src[0], src[2], t);
-    SkScalar    bc = SkScalarInterp(src[2], src[4], t);
-    SkScalar    cd = SkScalarInterp(src[4], src[6], t);
-    SkScalar    abc = SkScalarInterp(ab, bc, t);
-    SkScalar    bcd = SkScalarInterp(bc, cd, t);
-    SkScalar    abcd = SkScalarInterp(abc, bcd, t);
-
-    dst[0] = src[0];
-    dst[2] = ab;
-    dst[4] = abc;
-    dst[6] = abcd;
-    dst[8] = bcd;
-    dst[10] = cd;
-    dst[12] = src[6];
-}
-
-void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t)
-{
-    SkASSERT(t > 0 && t < SK_Scalar1);
-
-    interp_cubic_coords(&src[0].fX, &dst[0].fX, t);
-    interp_cubic_coords(&src[0].fY, &dst[0].fY, t);
-}
-
-void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar tValues[], int roots)
-{
-#ifdef SK_DEBUG
-    {
-        for (int i = 0; i < roots - 1; i++)
-        {
-            SkASSERT(is_unit_interval(tValues[i]));
-            SkASSERT(is_unit_interval(tValues[i+1]));
-            SkASSERT(tValues[i] < tValues[i+1]);
-        }
-    }
-#endif
-
-    if (dst)
-    {
-        if (roots == 0) // nothing to chop
-            memcpy(dst, src, 4*sizeof(SkPoint));
-        else
-        {
-            SkScalar    t = tValues[0];
-            SkPoint     tmp[4];
-
-            for (int i = 0; i < roots; i++)
-            {
-                SkChopCubicAt(src, dst, t);
-                if (i == roots - 1)
-                    break;
-
-                SkDEBUGCODE(int valid =) valid_unit_divide(tValues[i+1] - tValues[i], SK_Scalar1 - tValues[i], &t);
-                SkASSERT(valid);
-
-                dst += 3;
-                memcpy(tmp, dst, 4 * sizeof(SkPoint));
-                src = tmp;
-            }
-        }
-    }
-}
-
-void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7])
-{
-    SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
-    SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
-    SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
-    SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
-    SkScalar x23 = SkScalarAve(src[2].fX, src[3].fX);
-    SkScalar y23 = SkScalarAve(src[2].fY, src[3].fY);
-
-    SkScalar x012 = SkScalarAve(x01, x12);
-    SkScalar y012 = SkScalarAve(y01, y12);
-    SkScalar x123 = SkScalarAve(x12, x23);
-    SkScalar y123 = SkScalarAve(y12, y23);
-
-    dst[0] = src[0];
-    dst[1].set(x01, y01);
-    dst[2].set(x012, y012);
-    dst[3].set(SkScalarAve(x012, x123), SkScalarAve(y012, y123));
-    dst[4].set(x123, y123);
-    dst[5].set(x23, y23);
-    dst[6] = src[3];
-}
-
-static void flatten_double_cubic_extrema(SkScalar coords[14])
-{
-    coords[4] = coords[8] = coords[6];
-}
-
-/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
-    the resulting beziers are monotonic in Y. This is called by the scan converter.
-    Depending on what is returned, dst[] is treated as follows
-    0   dst[0..3] is the original cubic
-    1   dst[0..3] and dst[3..6] are the two new cubics
-    2   dst[0..3], dst[3..6], dst[6..9] are the three new cubics
-    If dst == null, it is ignored and only the count is returned.
-*/
-int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10])
-{
-    SkScalar    tValues[2];
-    int         roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY, src[3].fY, tValues);
-
-    SkChopCubicAt(src, dst, tValues, roots);
-    if (dst && roots > 0)
-    {
-        // we do some cleanup to ensure our Y extrema are flat
-        flatten_double_cubic_extrema(&dst[0].fY);
-        if (roots == 2)
-            flatten_double_cubic_extrema(&dst[3].fY);
-    }
-    return roots;
-}
-
-/** http://www.faculty.idc.ac.il/arik/quality/appendixA.html
-
-    Inflection means that curvature is zero.
-    Curvature is [F' x F''] / [F'^3]
-    So we solve F'x X F''y - F'y X F''y == 0
-    After some canceling of the cubic term, we get
-    A = b - a
-    B = c - 2b + a
-    C = d - 3c + 3b - a
-    (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0
-*/
-int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[])
-{
-    SkScalar    Ax = src[1].fX - src[0].fX;
-    SkScalar    Ay = src[1].fY - src[0].fY;
-    SkScalar    Bx = src[2].fX - 2 * src[1].fX + src[0].fX;
-    SkScalar    By = src[2].fY - 2 * src[1].fY + src[0].fY;
-    SkScalar    Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX;
-    SkScalar    Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY;
-    int         count;
-
-#ifdef SK_SCALAR_IS_FLOAT
-    count = SkFindUnitQuadRoots(Bx*Cy - By*Cx, Ax*Cy - Ay*Cx, Ax*By - Ay*Bx, tValues);
-#else
-    Sk64    A, B, C, tmp;
-
-    A.setMul(Bx, Cy);
-    tmp.setMul(By, Cx);
-    A.sub(tmp);
-
-    B.setMul(Ax, Cy);
-    tmp.setMul(Ay, Cx);
-    B.sub(tmp);
-
-    C.setMul(Ax, By);
-    tmp.setMul(Ay, Bx);
-    C.sub(tmp);
-
-    count = Sk64FindFixedQuadRoots(A, B, C, tValues);
-#endif
-
-    return count;
-}
-
-int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10])
-{
-    SkScalar    tValues[2];
-    int         count = SkFindCubicInflections(src, tValues);
-
-    if (dst)
-    {
-        if (count == 0)
-            memcpy(dst, src, 4 * sizeof(SkPoint));
-        else
-            SkChopCubicAt(src, dst, tValues, count);
-    }
-    return count + 1;
-}
-
-template <typename T> void bubble_sort(T array[], int count)
-{
-    for (int i = count - 1; i > 0; --i)
-        for (int j = i; j > 0; --j)
-            if (array[j] < array[j-1])
-            {
-                T   tmp(array[j]);
-                array[j] = array[j-1];
-                array[j-1] = tmp;
-            }
-}
-
-#include "SkFP.h"
-
-// newton refinement
-#if 0
-static SkScalar refine_cubic_root(const SkFP coeff[4], SkScalar root)
-{
-    //  x1 = x0 - f(t) / f'(t)
-
-    SkFP    T = SkScalarToFloat(root);
-    SkFP    N, D;
-
-    // f' = 3*coeff[0]*T^2 + 2*coeff[1]*T + coeff[2]
-    D = SkFPMul(SkFPMul(coeff[0], SkFPMul(T,T)), 3);
-    D = SkFPAdd(D, SkFPMulInt(SkFPMul(coeff[1], T), 2));
-    D = SkFPAdd(D, coeff[2]);
-
-    if (D == 0)
-        return root;
-
-    // f = coeff[0]*T^3 + coeff[1]*T^2 + coeff[2]*T + coeff[3]
-    N = SkFPMul(SkFPMul(SkFPMul(T, T), T), coeff[0]);
-    N = SkFPAdd(N, SkFPMul(SkFPMul(T, T), coeff[1]));
-    N = SkFPAdd(N, SkFPMul(T, coeff[2]));
-    N = SkFPAdd(N, coeff[3]);
-
-    if (N)
-    {
-        SkScalar delta = SkFPToScalar(SkFPDiv(N, D));
-
-        if (delta)
-            root -= delta;
-    }
-    return root;
-}
-#endif
-
-#if defined _WIN32 && _MSC_VER >= 1300  && defined SK_SCALAR_IS_FIXED // disable warning : unreachable code if building fixed point for windows desktop
-#pragma warning ( disable : 4702 )
-#endif
-
-/*  Solve coeff(t) == 0, returning the number of roots that
-    lie withing 0 < t < 1.
-    coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3]
-*/
-static int solve_cubic_polynomial(const SkFP coeff[4], SkScalar tValues[3])
-{
-#ifndef SK_SCALAR_IS_FLOAT
-    return 0;   // this is not yet implemented for software float
-#endif
-
-    if (SkScalarNearlyZero(coeff[0]))   // we're just a quadratic
-    {
-        return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues);
-    }
-
-    SkFP    a, b, c, Q, R;
-
-    {
-        SkASSERT(coeff[0] != 0);
-
-        SkFP inva = SkFPInvert(coeff[0]);
-        a = SkFPMul(coeff[1], inva);
-        b = SkFPMul(coeff[2], inva);
-        c = SkFPMul(coeff[3], inva);
-    }
-    Q = SkFPDivInt(SkFPSub(SkFPMul(a,a), SkFPMulInt(b, 3)), 9);
-//  R = (2*a*a*a - 9*a*b + 27*c) / 54;
-    R = SkFPMulInt(SkFPMul(SkFPMul(a, a), a), 2);
-    R = SkFPSub(R, SkFPMulInt(SkFPMul(a, b), 9));
-    R = SkFPAdd(R, SkFPMulInt(c, 27));
-    R = SkFPDivInt(R, 54);
-
-    SkFP Q3 = SkFPMul(SkFPMul(Q, Q), Q);
-    SkFP R2MinusQ3 = SkFPSub(SkFPMul(R,R), Q3);
-    SkFP adiv3 = SkFPDivInt(a, 3);
-
-    SkScalar*   roots = tValues;
-    SkScalar    r;
-
-    if (SkFPLT(R2MinusQ3, 0))   // we have 3 real roots
-    {
-#ifdef SK_SCALAR_IS_FLOAT
-        float theta = sk_float_acos(R / sk_float_sqrt(Q3));
-        float neg2RootQ = -2 * sk_float_sqrt(Q);
-
-        r = neg2RootQ * sk_float_cos(theta/3) - adiv3;
-        if (is_unit_interval(r))
-            *roots++ = r;
-
-        r = neg2RootQ * sk_float_cos((theta + 2*SK_ScalarPI)/3) - adiv3;
-        if (is_unit_interval(r))
-            *roots++ = r;
-
-        r = neg2RootQ * sk_float_cos((theta - 2*SK_ScalarPI)/3) - adiv3;
-        if (is_unit_interval(r))
-            *roots++ = r;
-
-        // now sort the roots
-        bubble_sort(tValues, (int)(roots - tValues));
-#endif
-    }
-    else                // we have 1 real root
-    {
-        SkFP A = SkFPAdd(SkFPAbs(R), SkFPSqrt(R2MinusQ3));
-        A = SkFPCubeRoot(A);
-        if (SkFPGT(R, 0))
-            A = SkFPNeg(A);
-
-        if (A != 0)
-            A = SkFPAdd(A, SkFPDiv(Q, A));
-        r = SkFPToScalar(SkFPSub(A, adiv3));
-        if (is_unit_interval(r))
-            *roots++ = r;
-    }
-
-    return (int)(roots - tValues);
-}
-
-/*  Looking for F' dot F'' == 0
-    
-    A = b - a
-    B = c - 2b + a
-    C = d - 3c + 3b - a
-
-    F' = 3Ct^2 + 6Bt + 3A
-    F'' = 6Ct + 6B
-
-    F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
-*/
-static void formulate_F1DotF2(const SkScalar src[], SkFP coeff[4])
-{
-    SkScalar    a = src[2] - src[0];
-    SkScalar    b = src[4] - 2 * src[2] + src[0];
-    SkScalar    c = src[6] + 3 * (src[2] - src[4]) - src[0];
-
-    SkFP    A = SkScalarToFP(a);
-    SkFP    B = SkScalarToFP(b);
-    SkFP    C = SkScalarToFP(c);
-
-    coeff[0] = SkFPMul(C, C);
-    coeff[1] = SkFPMulInt(SkFPMul(B, C), 3);
-    coeff[2] = SkFPMulInt(SkFPMul(B, B), 2);
-    coeff[2] = SkFPAdd(coeff[2], SkFPMul(C, A));
-    coeff[3] = SkFPMul(A, B);
-}
-
-// EXPERIMENTAL: can set this to zero to accept all t-values 0 < t < 1
-//#define kMinTValueForChopping (SK_Scalar1 / 256)
-#define kMinTValueForChopping   0
-
-/*  Looking for F' dot F'' == 0
-    
-    A = b - a
-    B = c - 2b + a
-    C = d - 3c + 3b - a
-
-    F' = 3Ct^2 + 6Bt + 3A
-    F'' = 6Ct + 6B
-
-    F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
-*/
-int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3])
-{
-    SkFP    coeffX[4], coeffY[4];
-    int     i;
-
-    formulate_F1DotF2(&src[0].fX, coeffX);
-    formulate_F1DotF2(&src[0].fY, coeffY);
-
-    for (i = 0; i < 4; i++)
-        coeffX[i] = SkFPAdd(coeffX[i],coeffY[i]);
-
-    SkScalar    t[3];
-    int         count = solve_cubic_polynomial(coeffX, t);
-    int         maxCount = 0;
-
-    // now remove extrema where the curvature is zero (mins)
-    // !!!! need a test for this !!!!
-    for (i = 0; i < count; i++)
-    {
-        // if (not_min_curvature())
-        if (t[i] > kMinTValueForChopping && t[i] < SK_Scalar1 - kMinTValueForChopping)
-            tValues[maxCount++] = t[i];
-    }
-    return maxCount;
-}
-
-int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13], SkScalar tValues[3])
-{
-    SkScalar    t_storage[3];
-
-    if (tValues == NULL)
-        tValues = t_storage;
-
-    int count = SkFindCubicMaxCurvature(src, tValues);
-
-    if (dst)
-    {
-        if (count == 0)
-            memcpy(dst, src, 4 * sizeof(SkPoint));
-        else
-            SkChopCubicAt(src, dst, tValues, count);
-    }
-    return count + 1;
-}
-
-////////////////////////////////////////////////////////////////////////////////
-
-/*  Find t value for quadratic [a, b, c] = d.
-    Return 0 if there is no solution within [0, 1)
-*/
-static SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d)
-{
-    // At^2 + Bt + C = d
-    SkScalar A = a - 2 * b + c;
-    SkScalar B = 2 * (b - a);
-    SkScalar C = a - d;
-
-    SkScalar    roots[2];
-    int         count = SkFindUnitQuadRoots(A, B, C, roots);
-
-    SkASSERT(count <= 1);
-    return count == 1 ? roots[0] : 0;
-}
-
-/*  given a quad-curve and a point (x,y), chop the quad at that point and return
-    the new quad's offCurve point. Should only return false if the computed pos
-    is the start of the curve (i.e. root == 0)
-*/
-static bool quad_pt2OffCurve(const SkPoint quad[3], SkScalar x, SkScalar y, SkPoint* offCurve)
-{
-    const SkScalar* base;
-    SkScalar        value;
-
-    if (SkScalarAbs(x) < SkScalarAbs(y)) {
-        base = &quad[0].fX;
-        value = x;
-    } else {
-        base = &quad[0].fY;
-        value = y;
-    }
-
-    // note: this returns 0 if it thinks value is out of range, meaning the
-    // root might return something outside of [0, 1)
-    SkScalar t = quad_solve(base[0], base[2], base[4], value);
-
-    if (t > 0)
-    {
-        SkPoint tmp[5];
-        SkChopQuadAt(quad, tmp, t);
-        *offCurve = tmp[1];
-        return true;
-    } else {
-        /*  t == 0 means either the value triggered a root outside of [0, 1)
-            For our purposes, we can ignore the <= 0 roots, but we want to
-            catch the >= 1 roots (which given our caller, will basically mean
-            a root of 1, give-or-take numerical instability). If we are in the
-            >= 1 case, return the existing offCurve point.
-        
-            The test below checks to see if we are close to the "end" of the
-            curve (near base[4]). Rather than specifying a tolerance, I just
-            check to see if value is on to the right/left of the middle point
-            (depending on the direction/sign of the end points).
-        */
-        if ((base[0] < base[4] && value > base[2]) ||
-            (base[0] > base[4] && value < base[2]))   // should root have been 1
-        {
-            *offCurve = quad[1];
-            return true;
-        }
-    }
-    return false;
-}
-
-static const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = {
-    { SK_Scalar1,           0               },
-    { SK_Scalar1,           SK_ScalarTanPIOver8 },
-    { SK_ScalarRoot2Over2,  SK_ScalarRoot2Over2 },
-    { SK_ScalarTanPIOver8,  SK_Scalar1          },
-
-    { 0,                    SK_Scalar1      },
-    { -SK_ScalarTanPIOver8, SK_Scalar1  },
-    { -SK_ScalarRoot2Over2, SK_ScalarRoot2Over2 },
-    { -SK_Scalar1,          SK_ScalarTanPIOver8 },
-
-    { -SK_Scalar1,          0               },
-    { -SK_Scalar1,          -SK_ScalarTanPIOver8    },
-    { -SK_ScalarRoot2Over2, -SK_ScalarRoot2Over2    },
-    { -SK_ScalarTanPIOver8, -SK_Scalar1     },
-
-    { 0,                    -SK_Scalar1     },
-    { SK_ScalarTanPIOver8,  -SK_Scalar1     },
-    { SK_ScalarRoot2Over2,  -SK_ScalarRoot2Over2    },
-    { SK_Scalar1,           -SK_ScalarTanPIOver8    },
-
-    { SK_Scalar1,           0   }
-};
-
-int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop,
-                   SkRotationDirection dir, const SkMatrix* userMatrix,
-                   SkPoint quadPoints[])
-{
-    // rotate by x,y so that uStart is (1.0)
-    SkScalar x = SkPoint::DotProduct(uStart, uStop);
-    SkScalar y = SkPoint::CrossProduct(uStart, uStop);
-
-    SkScalar absX = SkScalarAbs(x);
-    SkScalar absY = SkScalarAbs(y);
-
-    int pointCount;
-
-    // check for (effectively) coincident vectors
-    // this can happen if our angle is nearly 0 or nearly 180 (y == 0)
-    // ... we use the dot-prod to distinguish between 0 and 180 (x > 0)
-    if (absY <= SK_ScalarNearlyZero && x > 0 &&
-        ((y >= 0 && kCW_SkRotationDirection == dir) ||
-         (y <= 0 && kCCW_SkRotationDirection == dir))) {
-            
-        // just return the start-point
-        quadPoints[0].set(SK_Scalar1, 0);
-        pointCount = 1;
-    } else {
-        if (dir == kCCW_SkRotationDirection)
-            y = -y;
-
-        // what octant (quadratic curve) is [xy] in?
-        int oct = 0;
-        bool sameSign = true;
-
-        if (0 == y)
-        {
-            oct = 4;        // 180
-            SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero);
-        }
-        else if (0 == x)
-        {
-            SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero);
-            if (y > 0)
-                oct = 2;    // 90
-            else
-                oct = 6;    // 270
-        }
-        else
-        {
-            if (y < 0)
-                oct += 4;
-            if ((x < 0) != (y < 0))
-            {
-                oct += 2;
-                sameSign = false;
-            }
-            if ((absX < absY) == sameSign)
-                oct += 1;
-        }
-
-        int wholeCount = oct << 1;
-        memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint));
-
-        const SkPoint* arc = &gQuadCirclePts[wholeCount];
-        if (quad_pt2OffCurve(arc, x, y, &quadPoints[wholeCount + 1]))
-        {
-            quadPoints[wholeCount + 2].set(x, y);
-            wholeCount += 2;
-        }
-        pointCount = wholeCount + 1;
-    }
-
-    // now handle counter-clockwise and the initial unitStart rotation
-    SkMatrix    matrix;
-    matrix.setSinCos(uStart.fY, uStart.fX);
-    if (dir == kCCW_SkRotationDirection) {
-        matrix.preScale(SK_Scalar1, -SK_Scalar1);
-    }
-    if (userMatrix) {
-        matrix.postConcat(*userMatrix);
-    }
-    matrix.mapPoints(quadPoints, pointCount);
-    return pointCount;
-}
-
-
-/////////////////////////////////////////////////////////////////////////////////////////
-/////////////////////////////////////////////////////////////////////////////////////////
-
-#ifdef SK_DEBUG
-
-void SkGeometry::UnitTest()
-{
-#ifdef SK_SUPPORT_UNITTEST
-    SkPoint pts[3], dst[5];
-
-    pts[0].set(0, 0);
-    pts[1].set(100, 50);
-    pts[2].set(0, 100);
-
-    int count = SkChopQuadAtMaxCurvature(pts, dst);
-    SkASSERT(count == 1 || count == 2);
-#endif
-}
-
-#endif
-
-