src/effects/gradients/SkTwoPointRadialGradient.cpp

/*
 * Copyright 2012 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */

 #include "SkTwoPointRadialGradient.h"

/* Two-point radial gradients are specified by two circles, each with a center
   point and radius.  The gradient can be considered to be a series of
   concentric circles, with the color interpolated from the start circle
   (at t=0) to the end circle (at t=1).

   For each point (x, y) in the span, we want to find the
   interpolated circle that intersects that point.  The center
   of the desired circle (Cx, Cy) falls at some distance t
   along the line segment between the start point (Sx, Sy) and
   end point (Ex, Ey):

      Cx = (1 - t) * Sx + t * Ex        (0 <= t <= 1)
      Cy = (1 - t) * Sy + t * Ey

   The radius of the desired circle (r) is also a linear interpolation t
   between the start and end radii (Sr and Er):

      r = (1 - t) * Sr + t * Er

   But

      (x - Cx)^2 + (y - Cy)^2 = r^2

   so

     (x - ((1 - t) * Sx + t * Ex))^2
   + (y - ((1 - t) * Sy + t * Ey))^2
   = ((1 - t) * Sr + t * Er)^2

   Solving for t yields

     [(Sx - Ex)^2 + (Sy - Ey)^2 - (Er - Sr)^2)] * t^2
   + [2 * (Sx - Ex)(x - Sx) + 2 * (Sy - Ey)(y - Sy) - 2 * (Er - Sr) * Sr] * t
   + [(x - Sx)^2 + (y - Sy)^2 - Sr^2] = 0

   To simplify, let Dx = Sx - Ex, Dy = Sy - Ey, Dr = Er - Sr, dx = x - Sx, dy = y - Sy

     [Dx^2 + Dy^2 - Dr^2)] * t^2
   + 2 * [Dx * dx + Dy * dy - Dr * Sr] * t
   + [dx^2 + dy^2 - Sr^2] = 0

   A quadratic in t.  The two roots of the quadratic reflect the two
   possible circles on which the point may fall.  Solving for t yields
   the gradient value to use.

   If a<0, the start circle is entirely contained in the
   end circle, and one of the roots will be <0 or >1 (off the line
   segment).  If a>0, the start circle falls at least partially
   outside the end circle (or vice versa), and the gradient
   defines a "tube" where a point may be on one circle (on the
   inside of the tube) or the other (outside of the tube).  We choose
   one arbitrarily.

   In order to keep the math to within the limits of fixed point,
   we divide the entire quadratic by Dr^2, and replace
   (x - Sx)/Dr with x' and (y - Sy)/Dr with y', giving

   [Dx^2 / Dr^2 + Dy^2 / Dr^2 - 1)] * t^2
   + 2 * [x' * Dx / Dr + y' * Dy / Dr - Sr / Dr] * t
   + [x'^2 + y'^2 - Sr^2/Dr^2] = 0

   (x' and y' are computed by appending the subtract and scale to the
   fDstToIndex matrix in the constructor).

   Since the 'A' component of the quadratic is independent of x' and y', it
   is precomputed in the constructor.  Since the 'B' component is linear in
   x' and y', if x and y are linear in the span, 'B' can be computed
   incrementally with a simple delta (db below).  If it is not (e.g.,
   a perspective projection), it must be computed in the loop.

*/

namespace {

inline SkFixed two_point_radial(SkScalar b, SkScalar fx, SkScalar fy,
                                SkScalar sr2d2, SkScalar foura,
                                SkScalar oneOverTwoA, bool posRoot) {
    SkScalar c = SkScalarSquare(fx) + SkScalarSquare(fy) - sr2d2;
    if (0 == foura) {
        return SkScalarToFixed(SkScalarDiv(-c, b));
    }

    SkScalar discrim = SkScalarSquare(b) - SkScalarMul(foura, c);
    if (discrim < 0) {
        discrim = -discrim;
    }
    SkScalar rootDiscrim = SkScalarSqrt(discrim);
    SkScalar result;
    if (posRoot) {
        result = SkScalarMul(-b + rootDiscrim, oneOverTwoA);
    } else {
        result = SkScalarMul(-b - rootDiscrim, oneOverTwoA);
    }
    return SkScalarToFixed(result);
}

typedef void (* TwoPointRadialShadeProc)(SkScalar fx, SkScalar dx,
        SkScalar fy, SkScalar dy,
        SkScalar b, SkScalar db,
        SkScalar fSr2D2, SkScalar foura, SkScalar fOneOverTwoA, bool posRoot,
        SkPMColor* SK_RESTRICT dstC, const SkPMColor* SK_RESTRICT cache,
        int count);

void shadeSpan_twopoint_clamp(SkScalar fx, SkScalar dx,
        SkScalar fy, SkScalar dy,
        SkScalar b, SkScalar db,
        SkScalar fSr2D2, SkScalar foura, SkScalar fOneOverTwoA, bool posRoot,
        SkPMColor* SK_RESTRICT dstC, const SkPMColor* SK_RESTRICT cache,
        int count) {
    for (; count > 0; --count) {
        SkFixed t = two_point_radial(b, fx, fy, fSr2D2, foura,
                                     fOneOverTwoA, posRoot);
        SkFixed index = SkClampMax(t, 0xFFFF);
        SkASSERT(index <= 0xFFFF);
        *dstC++ = cache[index >> SkGradientShaderBase::kCache32Shift];
        fx += dx;
        fy += dy;
        b += db;
    }
}
void shadeSpan_twopoint_mirror(SkScalar fx, SkScalar dx,
        SkScalar fy, SkScalar dy,
        SkScalar b, SkScalar db,
        SkScalar fSr2D2, SkScalar foura, SkScalar fOneOverTwoA, bool posRoot,
        SkPMColor* SK_RESTRICT dstC, const SkPMColor* SK_RESTRICT cache,
        int count) {
    for (; count > 0; --count) {
        SkFixed t = two_point_radial(b, fx, fy, fSr2D2, foura,
                                     fOneOverTwoA, posRoot);
        SkFixed index = mirror_tileproc(t);
        SkASSERT(index <= 0xFFFF);
        *dstC++ = cache[index >> SkGradientShaderBase::kCache32Shift];
        fx += dx;
        fy += dy;
        b += db;
    }
}

void shadeSpan_twopoint_repeat(SkScalar fx, SkScalar dx,
        SkScalar fy, SkScalar dy,
        SkScalar b, SkScalar db,
        SkScalar fSr2D2, SkScalar foura, SkScalar fOneOverTwoA, bool posRoot,
        SkPMColor* SK_RESTRICT dstC, const SkPMColor* SK_RESTRICT cache,
        int count) {
    for (; count > 0; --count) {
        SkFixed t = two_point_radial(b, fx, fy, fSr2D2, foura,
                                     fOneOverTwoA, posRoot);
        SkFixed index = repeat_tileproc(t);
        SkASSERT(index <= 0xFFFF);
        *dstC++ = cache[index >> SkGradientShaderBase::kCache32Shift];
        fx += dx;
        fy += dy;
        b += db;
    }
}
}

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

SkTwoPointRadialGradient::SkTwoPointRadialGradient(
    const SkPoint& start, SkScalar startRadius,
    const SkPoint& end, SkScalar endRadius,
    const SkColor colors[], const SkScalar pos[],
    int colorCount, SkShader::TileMode mode,
    SkUnitMapper* mapper)
    : SkGradientShaderBase(colors, pos, colorCount, mode, mapper),
      fCenter1(start),
      fCenter2(end),
      fRadius1(startRadius),
      fRadius2(endRadius) {
    init();
}

SkShader::BitmapType SkTwoPointRadialGradient::asABitmap(
    SkBitmap* bitmap,
    SkMatrix* matrix,
    SkShader::TileMode* xy) const {
    if (bitmap) {
        this->getGradientTableBitmap(bitmap);
    }
    SkScalar diffL = 0; // just to avoid gcc warning
    if (matrix) {
        diffL = SkScalarSqrt(SkScalarSquare(fDiff.fX) +
                             SkScalarSquare(fDiff.fY));
    }
    if (matrix) {
        if (diffL) {
            SkScalar invDiffL = SkScalarInvert(diffL);
            matrix->setSinCos(-SkScalarMul(invDiffL, fDiff.fY),
                              SkScalarMul(invDiffL, fDiff.fX));
        } else {
            matrix->reset();
        }
        matrix->preConcat(fPtsToUnit);
    }
    if (xy) {
        xy[0] = fTileMode;
        xy[1] = kClamp_TileMode;
    }
    return kTwoPointRadial_BitmapType;
}

SkShader::GradientType SkTwoPointRadialGradient::asAGradient(
    SkShader::GradientInfo* info) const {
    if (info) {
        commonAsAGradient(info);
        info->fPoint[0] = fCenter1;
        info->fPoint[1] = fCenter2;
        info->fRadius[0] = fRadius1;
        info->fRadius[1] = fRadius2;
    }
    return kRadial2_GradientType;
}

void SkTwoPointRadialGradient::shadeSpan(int x, int y, SkPMColor* dstCParam,
                                         int count) {
    SkASSERT(count > 0);

    SkPMColor* SK_RESTRICT dstC = dstCParam;

    // Zero difference between radii:  fill with transparent black.
    if (fDiffRadius == 0) {
      sk_bzero(dstC, count * sizeof(*dstC));
      return;
    }
    SkMatrix::MapXYProc dstProc = fDstToIndexProc;
    TileProc            proc = fTileProc;
    const SkPMColor* SK_RESTRICT cache = this->getCache32();

    SkScalar foura = fA * 4;
    bool posRoot = fDiffRadius < 0;
    if (fDstToIndexClass != kPerspective_MatrixClass) {
        SkPoint srcPt;
        dstProc(fDstToIndex, SkIntToScalar(x) + SK_ScalarHalf,
                             SkIntToScalar(y) + SK_ScalarHalf, &srcPt);
        SkScalar dx, fx = srcPt.fX;
        SkScalar dy, fy = srcPt.fY;

        if (fDstToIndexClass == kFixedStepInX_MatrixClass) {
            SkFixed fixedX, fixedY;
            (void)fDstToIndex.fixedStepInX(SkIntToScalar(y), &fixedX, &fixedY);
            dx = SkFixedToScalar(fixedX);
            dy = SkFixedToScalar(fixedY);
        } else {
            SkASSERT(fDstToIndexClass == kLinear_MatrixClass);
            dx = fDstToIndex.getScaleX();
            dy = fDstToIndex.getSkewY();
        }
        SkScalar b = (SkScalarMul(fDiff.fX, fx) +
                     SkScalarMul(fDiff.fY, fy) - fStartRadius) * 2;
        SkScalar db = (SkScalarMul(fDiff.fX, dx) +
                      SkScalarMul(fDiff.fY, dy)) * 2;

        TwoPointRadialShadeProc shadeProc = shadeSpan_twopoint_repeat;
        if (SkShader::kClamp_TileMode == fTileMode) {
            shadeProc = shadeSpan_twopoint_clamp;
        } else if (SkShader::kMirror_TileMode == fTileMode) {
            shadeProc = shadeSpan_twopoint_mirror;
        } else {
            SkASSERT(SkShader::kRepeat_TileMode == fTileMode);
        }
        (*shadeProc)(fx, dx, fy, dy, b, db,
                     fSr2D2, foura, fOneOverTwoA, posRoot,
                     dstC, cache, count);
    } else {    // perspective case
        SkScalar dstX = SkIntToScalar(x);
        SkScalar dstY = SkIntToScalar(y);
        for (; count > 0; --count) {
            SkPoint             srcPt;
            dstProc(fDstToIndex, dstX, dstY, &srcPt);
            SkScalar fx = srcPt.fX;
            SkScalar fy = srcPt.fY;
            SkScalar b = (SkScalarMul(fDiff.fX, fx) +
                         SkScalarMul(fDiff.fY, fy) - fStartRadius) * 2;
            SkFixed t = two_point_radial(b, fx, fy, fSr2D2, foura,
                                         fOneOverTwoA, posRoot);
            SkFixed index = proc(t);
            SkASSERT(index <= 0xFFFF);
            *dstC++ = cache[index >> SkGradientShaderBase::kCache32Shift];
            dstX += SK_Scalar1;
        }
    }
}

bool SkTwoPointRadialGradient::setContext(
    const SkBitmap& device,
    const SkPaint& paint,
    const SkMatrix& matrix){
    if (!this->INHERITED::setContext(device, paint, matrix)) {
        return false;
    }

    // For now, we might have divided by zero, so detect that
    if (0 == fDiffRadius) {
        return false;
    }

    // we don't have a span16 proc
    fFlags &= ~kHasSpan16_Flag;
    return true;
}

SkTwoPointRadialGradient::SkTwoPointRadialGradient(
    SkFlattenableReadBuffer& buffer)
    : INHERITED(buffer),
      fCenter1(buffer.readPoint()),
      fCenter2(buffer.readPoint()),
      fRadius1(buffer.readScalar()),
      fRadius2(buffer.readScalar()) {
    init();
};

void SkTwoPointRadialGradient::flatten(
    SkFlattenableWriteBuffer& buffer) const {
    this->INHERITED::flatten(buffer);
    buffer.writePoint(fCenter1);
    buffer.writePoint(fCenter2);
    buffer.writeScalar(fRadius1);
    buffer.writeScalar(fRadius2);
}

void SkTwoPointRadialGradient::init() {
    fDiff = fCenter1 - fCenter2;
    fDiffRadius = fRadius2 - fRadius1;
    // hack to avoid zero-divide for now
    SkScalar inv = fDiffRadius ? SkScalarInvert(fDiffRadius) : 0;
    fDiff.fX = SkScalarMul(fDiff.fX, inv);
    fDiff.fY = SkScalarMul(fDiff.fY, inv);
    fStartRadius = SkScalarMul(fRadius1, inv);
    fSr2D2 = SkScalarSquare(fStartRadius);
    fA = SkScalarSquare(fDiff.fX) + SkScalarSquare(fDiff.fY) - SK_Scalar1;
    fOneOverTwoA = fA ? SkScalarInvert(fA * 2) : 0;

    fPtsToUnit.setTranslate(-fCenter1.fX, -fCenter1.fY);
    fPtsToUnit.postScale(inv, inv);
}

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

#if SK_SUPPORT_GPU

#include "GrTBackendEffectFactory.h"

// For brevity
typedef GrGLUniformManager::UniformHandle UniformHandle;
static const UniformHandle kInvalidUniformHandle = GrGLUniformManager::kInvalidUniformHandle;

class GrGLRadial2Gradient : public GrGLGradientEffect {

public:

    GrGLRadial2Gradient(const GrBackendEffectFactory& factory,
                        const GrEffect&);
    virtual ~GrGLRadial2Gradient() { }

    virtual void emitCode(GrGLShaderBuilder*,
                          const GrEffectStage&,
                          EffectKey,
                          const char* vertexCoords,
                          const char* outputColor,
                          const char* inputColor,
                          const TextureSamplerArray&) SK_OVERRIDE;
    virtual void setData(const GrGLUniformManager&, const GrEffectStage&) SK_OVERRIDE;

    static EffectKey GenKey(const GrEffectStage&, const GrGLCaps& caps);

protected:

    UniformHandle   fVSParamUni;
    UniformHandle   fFSParamUni;

    const char* fVSVaryingName;
    const char* fFSVaryingName;

    bool fIsDegenerate;

    // @{
    /// Values last uploaded as uniforms

    SkScalar fCachedCenter;
    SkScalar fCachedRadius;
    bool     fCachedPosRoot;

    // @}

private:

    typedef GrGLGradientEffect INHERITED;

};

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

class GrRadial2Gradient : public GrGradientEffect {
public:

    GrRadial2Gradient(GrContext* ctx,
                      const SkTwoPointRadialGradient& shader,
                      const SkMatrix& matrix,
                      SkShader::TileMode tm)
        : INHERITED(ctx, shader, matrix, tm)
        , fCenterX1(shader.getCenterX1())
        , fRadius0(shader.getStartRadius())
        , fPosRoot(shader.getDiffRadius() < 0) { }
    virtual ~GrRadial2Gradient() { }

    static const char* Name() { return "Two-Point Radial Gradient"; }
    virtual const GrBackendEffectFactory& getFactory() const SK_OVERRIDE {
        return GrTBackendEffectFactory<GrRadial2Gradient>::getInstance();
    }
    virtual bool isEqual(const GrEffect& sBase) const SK_OVERRIDE {
        const GrRadial2Gradient& s = static_cast<const GrRadial2Gradient&>(sBase);
        return (INHERITED::isEqual(sBase) &&
                this->fCenterX1 == s.fCenterX1 &&
                this->fRadius0 == s.fRadius0 &&
                this->fPosRoot == s.fPosRoot);
    }

    // The radial gradient parameters can collapse to a linear (instead of quadratic) equation.
    bool isDegenerate() const { return SK_Scalar1 == fCenterX1; }
    SkScalar center() const { return fCenterX1; }
    SkScalar radius() const { return fRadius0; }
    bool isPosRoot() const { return SkToBool(fPosRoot); }

    typedef GrGLRadial2Gradient GLEffect;

private:
    GR_DECLARE_EFFECT_TEST;

    // @{
    // Cache of values - these can change arbitrarily, EXCEPT
    // we shouldn't change between degenerate and non-degenerate?!

    SkScalar fCenterX1;
    SkScalar fRadius0;
    SkBool8  fPosRoot;

    // @}

    typedef GrGradientEffect INHERITED;
};

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

GR_DEFINE_EFFECT_TEST(GrRadial2Gradient);

GrEffect* GrRadial2Gradient::TestCreate(SkRandom* random,
                                        GrContext* context,
                                        GrTexture**) {
    SkPoint center1 = {random->nextUScalar1(), random->nextUScalar1()};
    SkScalar radius1 = random->nextUScalar1();
    SkPoint center2;
    SkScalar radius2;
    do {
        center2.set(random->nextUScalar1(), random->nextUScalar1());
        radius2 = random->nextUScalar1 ();
        // There is a bug in two point radial gradients with idenitical radii
    } while (radius1 == radius2);

    SkColor colors[kMaxRandomGradientColors];
    SkScalar stopsArray[kMaxRandomGradientColors];
    SkScalar* stops = stopsArray;
    SkShader::TileMode tm;
    int colorCount = RandomGradientParams(random, colors, &stops, &tm);
    SkAutoTUnref<SkShader> shader(SkGradientShader::CreateTwoPointRadial(center1, radius1,
                                                                         center2, radius2,
                                                                         colors, stops, colorCount,
                                                                         tm));
    GrEffectStage stage;
    shader->asNewEffect(context, &stage);
    GrAssert(NULL != stage.getEffect());
    // const_cast and ref is a hack! Will remove when asNewEffect returns GrEffect*
    stage.getEffect()->ref();
    return const_cast<GrEffect*>(stage.getEffect());
}

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

GrGLRadial2Gradient::GrGLRadial2Gradient(
        const GrBackendEffectFactory& factory,
        const GrEffect& baseData)
    : INHERITED(factory)
    , fVSParamUni(kInvalidUniformHandle)
    , fFSParamUni(kInvalidUniformHandle)
    , fVSVaryingName(NULL)
    , fFSVaryingName(NULL)
    , fCachedCenter(SK_ScalarMax)
    , fCachedRadius(-SK_ScalarMax)
    , fCachedPosRoot(0) {

    const GrRadial2Gradient& data =
        static_cast<const GrRadial2Gradient&>(baseData);
    fIsDegenerate = data.isDegenerate();
}

void GrGLRadial2Gradient::emitCode(GrGLShaderBuilder* builder,
                                   const GrEffectStage& stage,
                                   EffectKey key,
                                   const char* vertexCoords,
                                   const char* outputColor,
                                   const char* inputColor,
                                   const TextureSamplerArray& samplers) {

    this->emitYCoordUniform(builder);
    const char* fsCoords;
    const char* vsCoordsVarying;
    GrSLType coordsVaryingType;
    this->setupMatrix(builder, key, vertexCoords, &fsCoords, &vsCoordsVarying, &coordsVaryingType);

    // 2 copies of uniform array, 1 for each of vertex & fragment shader,
    // to work around Xoom bug. Doesn't seem to cause performance decrease
    // in test apps, but need to keep an eye on it.
    fVSParamUni = builder->addUniformArray(GrGLShaderBuilder::kVertex_ShaderType,
                                           kFloat_GrSLType, "Radial2VSParams", 6);
    fFSParamUni = builder->addUniformArray(GrGLShaderBuilder::kFragment_ShaderType,
                                           kFloat_GrSLType, "Radial2FSParams", 6);

    // For radial gradients without perspective we can pass the linear
    // part of the quadratic as a varying.
    if (kVec2f_GrSLType == coordsVaryingType) {
        builder->addVarying(kFloat_GrSLType, "Radial2BCoeff", &fVSVaryingName, &fFSVaryingName);
    }

    // VS
    {
        SkString* code = &builder->fVSCode;
        SkString p2;
        SkString p3;
        builder->getUniformVariable(fVSParamUni).appendArrayAccess(2, &p2);
        builder->getUniformVariable(fVSParamUni).appendArrayAccess(3, &p3);

        // For radial gradients without perspective we can pass the linear
        // part of the quadratic as a varying.
        if (kVec2f_GrSLType == coordsVaryingType) {
            // r2Var = 2 * (r2Parm[2] * varCoord.x - r2Param[3])
            code->appendf("\t%s = 2.0 *(%s * %s.x - %s);\n",
                          fVSVaryingName, p2.c_str(),
                          vsCoordsVarying, p3.c_str());
        }
    }

    // FS
    {
        SkString* code = &builder->fFSCode;
        SkString cName("c");
        SkString ac4Name("ac4");
        SkString rootName("root");
        SkString t;
        SkString p0;
        SkString p1;
        SkString p2;
        SkString p3;
        SkString p4;
        SkString p5;
        builder->getUniformVariable(fFSParamUni).appendArrayAccess(0, &p0);
        builder->getUniformVariable(fFSParamUni).appendArrayAccess(1, &p1);
        builder->getUniformVariable(fFSParamUni).appendArrayAccess(2, &p2);
        builder->getUniformVariable(fFSParamUni).appendArrayAccess(3, &p3);
        builder->getUniformVariable(fFSParamUni).appendArrayAccess(4, &p4);
        builder->getUniformVariable(fFSParamUni).appendArrayAccess(5, &p5);

        // If we we're able to interpolate the linear component,
        // bVar is the varying; otherwise compute it
        SkString bVar;
        if (kVec2f_GrSLType == coordsVaryingType) {
            bVar = fFSVaryingName;
        } else {
            bVar = "b";
            code->appendf("\tfloat %s = 2.0 * (%s * %s.x - %s);\n",
                          bVar.c_str(), p2.c_str(), fsCoords, p3.c_str());
        }

        // c = (x^2)+(y^2) - params[4]
        code->appendf("\tfloat %s = dot(%s, %s) - %s;\n",
                      cName.c_str(),
                      fsCoords,
                      fsCoords,
                      p4.c_str());

        // If we aren't degenerate, emit some extra code, and accept a slightly
        // more complex coord.
        if (!fIsDegenerate) {

            // ac4 = 4.0 * params[0] * c
            code->appendf("\tfloat %s = %s * 4.0 * %s;\n",
                          ac4Name.c_str(), p0.c_str(),
                          cName.c_str());

            // root = sqrt(b^2-4ac)
            // (abs to avoid exception due to fp precision)
            code->appendf("\tfloat %s = sqrt(abs(%s*%s - %s));\n",
                          rootName.c_str(), bVar.c_str(), bVar.c_str(),
                          ac4Name.c_str());

            // t is: (-b + params[5] * sqrt(b^2-4ac)) * params[1]
            t.printf("(-%s + %s * %s) * %s", bVar.c_str(), p5.c_str(),
                     rootName.c_str(), p1.c_str());
        } else {
            // t is: -c/b
            t.printf("-%s / %s", cName.c_str(), bVar.c_str());
        }

        this->emitColorLookup(builder, t.c_str(), outputColor, inputColor, samplers[0]);
    }
}

void GrGLRadial2Gradient::setData(const GrGLUniformManager& uman, const GrEffectStage& stage) {
    INHERITED::setData(uman, stage);
    const GrRadial2Gradient& data = static_cast<const GrRadial2Gradient&>(*stage.getEffect());
    GrAssert(data.isDegenerate() == fIsDegenerate);
    SkScalar centerX1 = data.center();
    SkScalar radius0 = data.radius();
    if (fCachedCenter != centerX1 ||
        fCachedRadius != radius0 ||
        fCachedPosRoot != data.isPosRoot()) {

        SkScalar a = SkScalarMul(centerX1, centerX1) - SK_Scalar1;

        // When we're in the degenerate (linear) case, the second
        // value will be INF but the program doesn't read it. (We
        // use the same 6 uniforms even though we don't need them
        // all in the linear case just to keep the code complexity
        // down).
        float values[6] = {
            SkScalarToFloat(a),
            1 / (2.f * SkScalarToFloat(a)),
            SkScalarToFloat(centerX1),
            SkScalarToFloat(radius0),
            SkScalarToFloat(SkScalarMul(radius0, radius0)),
            data.isPosRoot() ? 1.f : -1.f
        };

        uman.set1fv(fVSParamUni, 0, 6, values);
        uman.set1fv(fFSParamUni, 0, 6, values);
        fCachedCenter = centerX1;
        fCachedRadius = radius0;
        fCachedPosRoot = data.isPosRoot();
    }
}

GrGLEffect::EffectKey GrGLRadial2Gradient::GenKey(const GrEffectStage& s, const GrGLCaps&) {
    enum {
        kIsDegenerate = 1 << kMatrixKeyBitCnt,
    };

    EffectKey key = GenMatrixKey(s);
    if (static_cast<const GrRadial2Gradient&>(*s.getEffect()).isDegenerate()) {
        key |= kIsDegenerate;
    }
    return key;
}

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

bool SkTwoPointRadialGradient::asNewEffect(GrContext* context,
                                           GrEffectStage* stage) const {
    SkASSERT(NULL != context && NULL != stage);
    // invert the localM, translate to center1 (fPtsToUni), rotate so center2 is on x axis.
    SkMatrix matrix;
    if (!this->getLocalMatrix().invert(&matrix)) {
        return false;
    }
    matrix.postConcat(fPtsToUnit);

    SkScalar diffLen = fDiff.length();
    if (0 != diffLen) {
        SkScalar invDiffLen = SkScalarInvert(diffLen);
        SkMatrix rot;
        rot.setSinCos(-SkScalarMul(invDiffLen, fDiff.fY),
                       SkScalarMul(invDiffLen, fDiff.fX));
        matrix.postConcat(rot);
    }

    stage->setEffect(SkNEW_ARGS(GrRadial2Gradient, (context, *this, matrix, fTileMode)))->unref();
    return true;
}

#else

bool SkTwoPointRadialGradient::asNewEffect(GrContext*, GrEffectStage*) const {
    SkDEBUGFAIL("Should not call in GPU-less build");
    return false;
}

#endif