src/utils/SkPatchUtils.cpp - platform/external/skia - Gitiles

 /*
  * Copyright 2014 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */

 #include "SkPatchUtils.h"

 #include "SkColorPriv.h"
 #include "SkGeometry.h"

 /**
  * Evaluator to sample the values of a cubic bezier using forward differences.
  * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only
  * adding precalculated values.
  * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h
  * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first
  * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After
  * obtaining this value (mh) we could just add this constant step to our first sampled point
  * to compute the next one.
  *
  * For the cubic case the first difference gives as a result a quadratic polynomial to which we can
  * apply again forward differences and get linear function to which we can apply again forward
  * differences to get a constant difference. This is why we keep an array of size 4, the 0th
  * position keeps the sampled value while the next ones keep the quadratic, linear and constant
  * difference values.
  */

 class FwDCubicEvaluator {

 public:
     FwDCubicEvaluator()
     : fMax(0)
     , fCurrent(0)
     , fDivisions(0) {
         memset(fPoints, 0, 4 * sizeof(SkPoint));
         memset(fPoints, 0, 4 * sizeof(SkPoint));
         memset(fPoints, 0, 4 * sizeof(SkPoint));
     }

     /**
      * Receives the 4 control points of the cubic bezier.
      */
     FwDCubicEvaluator(SkPoint a, SkPoint b, SkPoint c, SkPoint d) {
         fPoints[0] = a;
         fPoints[1] = b;
         fPoints[2] = c;
         fPoints[3] = d;

         SkCubicToCoeff(fPoints, fCoefs);

         this->restart(1);
     }

     explicit FwDCubicEvaluator(const SkPoint points[4])  {
         memcpy(fPoints, points, 4 * sizeof(SkPoint));

         SkCubicToCoeff(fPoints, fCoefs);

         this->restart(1);
     }

     /**
      * Restarts the forward differences evaluator to the first value of t = 0.
      */
     void restart(int divisions)  {
         fDivisions = divisions;
         SkScalar h  = 1.f / fDivisions;
         fCurrent    = 0;
         fMax        = fDivisions + 1;
         fFwDiff[0]  = fCoefs[3];
         SkScalar h2 = h * h;
         SkScalar h3 = h2 * h;

         fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3
         fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2
                        fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2);
         fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch
                        fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h);
     }

     /**
      * Check if the evaluator is still within the range of 0<=t<=1
      */
     bool done() const {
         return fCurrent > fMax;
     }

     /**
      * Call next to obtain the SkPoint sampled and move to the next one.
      */
     SkPoint next() {
         SkPoint point = fFwDiff[0];
         fFwDiff[0]    += fFwDiff[1];
         fFwDiff[1]    += fFwDiff[2];
         fFwDiff[2]    += fFwDiff[3];
         fCurrent++;
         return point;
     }

     const SkPoint* getCtrlPoints() const {
         return fPoints;
     }

 private:
     int fMax, fCurrent, fDivisions;
     SkPoint fFwDiff[4], fCoefs[4], fPoints[4];
 };

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

 // size in pixels of each partition per axis, adjust this knob
 static const int kPartitionSize = 10;

 /**
  * Calculate the approximate arc length given a bezier curve's control points.
  */
 static SkScalar approx_arc_length(SkPoint* points, int count) {
     if (count < 2) {
         return 0;
     }
     SkScalar arcLength = 0;
     for (int i = 0; i < count - 1; i++) {
         arcLength += SkPoint::Distance(points[i], points[i + 1]);
     }
     return arcLength;
 }

 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
                       SkScalar c11) {
     SkScalar a = c00 * (1.f - tx) + c10 * tx;
     SkScalar b = c01 * (1.f - tx) + c11 * tx;
     return a * (1.f - ty) + b * ty;
 }

 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {

     // Approximate length of each cubic.
     SkPoint pts[kNumPtsCubic];
     SkPatchUtils::getTopCubic(cubics, pts);
     matrix->mapPoints(pts, kNumPtsCubic);
     SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);

     SkPatchUtils::getBottomCubic(cubics, pts);
     matrix->mapPoints(pts, kNumPtsCubic);
     SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);

     SkPatchUtils::getLeftCubic(cubics, pts);
     matrix->mapPoints(pts, kNumPtsCubic);
     SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);

     SkPatchUtils::getRightCubic(cubics, pts);
     matrix->mapPoints(pts, kNumPtsCubic);
     SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);

     // Level of detail per axis, based on the larger side between top and bottom or left and right
     int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
     int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);

     return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
 }

 void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
     points[0] = cubics[kTopP0_CubicCtrlPts];
     points[1] = cubics[kTopP1_CubicCtrlPts];
     points[2] = cubics[kTopP2_CubicCtrlPts];
     points[3] = cubics[kTopP3_CubicCtrlPts];
 }

 void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
     points[0] = cubics[kBottomP0_CubicCtrlPts];
     points[1] = cubics[kBottomP1_CubicCtrlPts];
     points[2] = cubics[kBottomP2_CubicCtrlPts];
     points[3] = cubics[kBottomP3_CubicCtrlPts];
 }

 void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
     points[0] = cubics[kLeftP0_CubicCtrlPts];
     points[1] = cubics[kLeftP1_CubicCtrlPts];
     points[2] = cubics[kLeftP2_CubicCtrlPts];
     points[3] = cubics[kLeftP3_CubicCtrlPts];
 }

 void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
     points[0] = cubics[kRightP0_CubicCtrlPts];
     points[1] = cubics[kRightP1_CubicCtrlPts];
     points[2] = cubics[kRightP2_CubicCtrlPts];
     points[3] = cubics[kRightP3_CubicCtrlPts];
 }

 bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12],
                    const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) {
     if (lodX < 1 || lodY < 1 || NULL == cubics || NULL == data) {
         return false;
     }

     // check for overflow in multiplication
     const int64_t lodX64 = (lodX + 1),
                    lodY64 = (lodY + 1),
                    mult64 = lodX64 * lodY64;
     if (mult64 > SK_MaxS32) {
         return false;
     }
     data->fVertexCount = SkToS32(mult64);

     // it is recommended to generate draw calls of no more than 65536 indices, so we never generate
     // more than 60000 indices. To accomplish that we resize the LOD and vertex count
     if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) {
         SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY);
         SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY);

         // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of
         // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6)
         lodX = static_cast<int>(weightX * 200);
         lodY = static_cast<int>(weightY * 200);
         data->fVertexCount = (lodX + 1) * (lodY + 1);
     }
     data->fIndexCount = lodX * lodY * 6;

     data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
     data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);

     // if colors is not null then create array for colors
     SkPMColor colorsPM[kNumCorners];
     if (colors) {
         // premultiply colors to avoid color bleeding.
         for (int i = 0; i < kNumCorners; i++) {
             colorsPM[i] = SkPreMultiplyColor(colors[i]);
         }
         data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
     }

     // if texture coordinates are not null then create array for them
     if (texCoords) {
         data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
     }

     SkPoint pts[kNumPtsCubic];
     SkPatchUtils::getBottomCubic(cubics, pts);
     FwDCubicEvaluator fBottom(pts);
     SkPatchUtils::getTopCubic(cubics, pts);
     FwDCubicEvaluator fTop(pts);
     SkPatchUtils::getLeftCubic(cubics, pts);
     FwDCubicEvaluator fLeft(pts);
     SkPatchUtils::getRightCubic(cubics, pts);
     FwDCubicEvaluator fRight(pts);

     fBottom.restart(lodX);
     fTop.restart(lodX);

     SkScalar u = 0.0f;
     int stride = lodY + 1;
     for (int x = 0; x <= lodX; x++) {
         SkPoint bottom = fBottom.next(), top = fTop.next();
         fLeft.restart(lodY);
         fRight.restart(lodY);
         SkScalar v = 0.f;
         for (int y = 0; y <= lodY; y++) {
             int dataIndex = x * (lodY + 1) + y;

             SkPoint left = fLeft.next(), right = fRight.next();

             SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
                                        (1.0f - v) * top.y() + v * bottom.y());
             SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
                                        (1.0f - u) * left.y() + u * right.y());
             SkPoint s2 = SkPoint::Make(
                                        (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
                                                      + u * fTop.getCtrlPoints()[3].x())
                                        + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
                                               + u * fBottom.getCtrlPoints()[3].x()),
                                        (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
                                                      + u * fTop.getCtrlPoints()[3].y())
                                        + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
                                               + u * fBottom.getCtrlPoints()[3].y()));
             data->fPoints[dataIndex] = s0 + s1 - s2;

             if (colors) {
                 uint8_t a = uint8_t(bilerp(u, v,
                                    SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])),
                                    SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])),
                                    SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])),
                                    SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner]))));
                 uint8_t r = uint8_t(bilerp(u, v,
                                    SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])),
                                    SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])),
                                    SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])),
                                    SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner]))));
                 uint8_t g = uint8_t(bilerp(u, v,
                                    SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])),
                                    SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])),
                                    SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])),
                                    SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner]))));
                 uint8_t b = uint8_t(bilerp(u, v,
                                    SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])),
                                    SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])),
                                    SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])),
                                    SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner]))));
                 data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);
             }

             if (texCoords) {
                 data->fTexCoords[dataIndex] = SkPoint::Make(
                                             bilerp(u, v, texCoords[kTopLeft_Corner].x(),
                                                    texCoords[kTopRight_Corner].x(),
                                                    texCoords[kBottomLeft_Corner].x(),
                                                    texCoords[kBottomRight_Corner].x()),
                                             bilerp(u, v, texCoords[kTopLeft_Corner].y(),
                                                    texCoords[kTopRight_Corner].y(),
                                                    texCoords[kBottomLeft_Corner].y(),
                                                    texCoords[kBottomRight_Corner].y()));

             }

             if(x < lodX && y < lodY) {
                 int i = 6 * (x * lodY + y);
                 data->fIndices[i] = x * stride + y;
                 data->fIndices[i + 1] = x * stride + 1 + y;
                 data->fIndices[i + 2] = (x + 1) * stride + 1 + y;
                 data->fIndices[i + 3] = data->fIndices[i];
                 data->fIndices[i + 4] = data->fIndices[i + 2];
                 data->fIndices[i + 5] = (x + 1) * stride + y;
             }
             v = SkScalarClampMax(v + 1.f / lodY, 1);
         }
         u = SkScalarClampMax(u + 1.f / lodX, 1);
     }
     return true;

 }
	/*
	* Copyright 2014 Google Inc.
	*
	* Use of this source code is governed by a BSD-style license that can be
	* found in the LICENSE file.
	*/

	#include "SkPatchUtils.h"

	#include "SkColorPriv.h"
	#include "SkGeometry.h"

	/**
	* Evaluator to sample the values of a cubic bezier using forward differences.
	* Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only
	* adding precalculated values.
	* For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h
	* would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first
	* evaluation f(t) then we need to substract f(t+h) - f(t) = mt + mh + b - m*t + b = mh. After
	* obtaining this value (mh) we could just add this constant step to our first sampled point
	* to compute the next one.
	*
	* For the cubic case the first difference gives as a result a quadratic polynomial to which we can
	* apply again forward differences and get linear function to which we can apply again forward
	* differences to get a constant difference. This is why we keep an array of size 4, the 0th
	* position keeps the sampled value while the next ones keep the quadratic, linear and constant
	* difference values.
	*/

	class FwDCubicEvaluator {

	public:
	FwDCubicEvaluator()
	: fMax(0)
	, fCurrent(0)
	, fDivisions(0) {
	memset(fPoints, 0, 4 * sizeof(SkPoint));
	memset(fPoints, 0, 4 * sizeof(SkPoint));
	memset(fPoints, 0, 4 * sizeof(SkPoint));
	}

	/**
	* Receives the 4 control points of the cubic bezier.
	*/
	FwDCubicEvaluator(SkPoint a, SkPoint b, SkPoint c, SkPoint d) {
	fPoints[0] = a;
	fPoints[1] = b;
	fPoints[2] = c;
	fPoints[3] = d;

	SkCubicToCoeff(fPoints, fCoefs);

	this->restart(1);
	}

	explicit FwDCubicEvaluator(const SkPoint points[4]) {
	memcpy(fPoints, points, 4 * sizeof(SkPoint));

	SkCubicToCoeff(fPoints, fCoefs);

	this->restart(1);
	}

	/**
	* Restarts the forward differences evaluator to the first value of t = 0.
	*/
	void restart(int divisions) {
	fDivisions = divisions;
	SkScalar h = 1.f / fDivisions;
	fCurrent = 0;
	fMax = fDivisions + 1;
	fFwDiff[0] = fCoefs[3];
	SkScalar h2 = h * h;
	SkScalar h3 = h2 * h;

	fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3
	fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2
	fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2);
	fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch
	fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h);
	}

	/**
	* Check if the evaluator is still within the range of 0<=t<=1
	*/
	bool done() const {
	return fCurrent > fMax;
	}

	/**
	* Call next to obtain the SkPoint sampled and move to the next one.
	*/
	SkPoint next() {
	SkPoint point = fFwDiff[0];
	fFwDiff[0] += fFwDiff[1];
	fFwDiff[1] += fFwDiff[2];
	fFwDiff[2] += fFwDiff[3];
	fCurrent++;
	return point;
	}

	const SkPoint* getCtrlPoints() const {
	return fPoints;
	}

	private:
	int fMax, fCurrent, fDivisions;
	SkPoint fFwDiff[4], fCoefs[4], fPoints[4];
	};

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

	// size in pixels of each partition per axis, adjust this knob
	static const int kPartitionSize = 10;

	/**
	* Calculate the approximate arc length given a bezier curve's control points.
	*/
	static SkScalar approx_arc_length(SkPoint* points, int count) {
	if (count < 2) {
	return 0;
	}
	SkScalar arcLength = 0;
	for (int i = 0; i < count - 1; i++) {
	arcLength += SkPoint::Distance(points[i], points[i + 1]);
	}
	return arcLength;
	}

	static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
	SkScalar c11) {
	SkScalar a = c00 * (1.f - tx) + c10 * tx;
	SkScalar b = c01 * (1.f - tx) + c11 * tx;
	return a * (1.f - ty) + b * ty;
	}

	SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {

	// Approximate length of each cubic.
	SkPoint pts[kNumPtsCubic];
	SkPatchUtils::getTopCubic(cubics, pts);
	matrix->mapPoints(pts, kNumPtsCubic);
	SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);

	SkPatchUtils::getBottomCubic(cubics, pts);
	matrix->mapPoints(pts, kNumPtsCubic);
	SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);

	SkPatchUtils::getLeftCubic(cubics, pts);
	matrix->mapPoints(pts, kNumPtsCubic);
	SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);

	SkPatchUtils::getRightCubic(cubics, pts);
	matrix->mapPoints(pts, kNumPtsCubic);
	SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);

	// Level of detail per axis, based on the larger side between top and bottom or left and right
	int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
	int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);

	return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
	}

	void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
	points[0] = cubics[kTopP0_CubicCtrlPts];
	points[1] = cubics[kTopP1_CubicCtrlPts];
	points[2] = cubics[kTopP2_CubicCtrlPts];
	points[3] = cubics[kTopP3_CubicCtrlPts];
	}

	void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
	points[0] = cubics[kBottomP0_CubicCtrlPts];
	points[1] = cubics[kBottomP1_CubicCtrlPts];
	points[2] = cubics[kBottomP2_CubicCtrlPts];
	points[3] = cubics[kBottomP3_CubicCtrlPts];
	}

	void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
	points[0] = cubics[kLeftP0_CubicCtrlPts];
	points[1] = cubics[kLeftP1_CubicCtrlPts];
	points[2] = cubics[kLeftP2_CubicCtrlPts];
	points[3] = cubics[kLeftP3_CubicCtrlPts];
	}

	void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
	points[0] = cubics[kRightP0_CubicCtrlPts];
	points[1] = cubics[kRightP1_CubicCtrlPts];
	points[2] = cubics[kRightP2_CubicCtrlPts];
	points[3] = cubics[kRightP3_CubicCtrlPts];
	}

	bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12],
	const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) {
	if (lodX < 1 \|\| lodY < 1 \|\| NULL == cubics \|\| NULL == data) {
	return false;
	}

	// check for overflow in multiplication
	const int64_t lodX64 = (lodX + 1),
	lodY64 = (lodY + 1),
	mult64 = lodX64 * lodY64;
	if (mult64 > SK_MaxS32) {
	return false;
	}
	data->fVertexCount = SkToS32(mult64);

	// it is recommended to generate draw calls of no more than 65536 indices, so we never generate
	// more than 60000 indices. To accomplish that we resize the LOD and vertex count
	if (data->fVertexCount > 10000 \|\| lodX > 200 \|\| lodY > 200) {
	SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY);
	SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY);

	// 200 comes from the 100 * 2 which is the max value of vertices because of the limit of
	// 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6)
	lodX = static_cast<int>(weightX * 200);
	lodY = static_cast<int>(weightY * 200);
	data->fVertexCount = (lodX + 1) * (lodY + 1);
	}
	data->fIndexCount = lodX * lodY * 6;

	data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
	data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);

	// if colors is not null then create array for colors
	SkPMColor colorsPM[kNumCorners];
	if (colors) {
	// premultiply colors to avoid color bleeding.
	for (int i = 0; i < kNumCorners; i++) {
	colorsPM[i] = SkPreMultiplyColor(colors[i]);
	}
	data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
	}

	// if texture coordinates are not null then create array for them
	if (texCoords) {
	data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
	}

	SkPoint pts[kNumPtsCubic];
	SkPatchUtils::getBottomCubic(cubics, pts);
	FwDCubicEvaluator fBottom(pts);
	SkPatchUtils::getTopCubic(cubics, pts);
	FwDCubicEvaluator fTop(pts);
	SkPatchUtils::getLeftCubic(cubics, pts);
	FwDCubicEvaluator fLeft(pts);
	SkPatchUtils::getRightCubic(cubics, pts);
	FwDCubicEvaluator fRight(pts);

	fBottom.restart(lodX);
	fTop.restart(lodX);

	SkScalar u = 0.0f;
	int stride = lodY + 1;
	for (int x = 0; x <= lodX; x++) {
	SkPoint bottom = fBottom.next(), top = fTop.next();
	fLeft.restart(lodY);
	fRight.restart(lodY);
	SkScalar v = 0.f;
	for (int y = 0; y <= lodY; y++) {
	int dataIndex = x * (lodY + 1) + y;

	SkPoint left = fLeft.next(), right = fRight.next();

	SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
	(1.0f - v) * top.y() + v * bottom.y());
	SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
	(1.0f - u) * left.y() + u * right.y());
	SkPoint s2 = SkPoint::Make(
	(1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
	+ u * fTop.getCtrlPoints()[3].x())
	+ v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
	+ u * fBottom.getCtrlPoints()[3].x()),
	(1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
	+ u * fTop.getCtrlPoints()[3].y())
	+ v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
	+ u * fBottom.getCtrlPoints()[3].y()));
	data->fPoints[dataIndex] = s0 + s1 - s2;

	if (colors) {
	uint8_t a = uint8_t(bilerp(u, v,
	SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])),
	SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])),
	SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])),
	SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner]))));
	uint8_t r = uint8_t(bilerp(u, v,
	SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])),
	SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])),
	SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])),
	SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner]))));
	uint8_t g = uint8_t(bilerp(u, v,
	SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])),
	SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])),
	SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])),
	SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner]))));
	uint8_t b = uint8_t(bilerp(u, v,
	SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])),
	SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])),
	SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])),
	SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner]))));
	data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);
	}

	if (texCoords) {
	data->fTexCoords[dataIndex] = SkPoint::Make(
	bilerp(u, v, texCoords[kTopLeft_Corner].x(),
	texCoords[kTopRight_Corner].x(),
	texCoords[kBottomLeft_Corner].x(),
	texCoords[kBottomRight_Corner].x()),
	bilerp(u, v, texCoords[kTopLeft_Corner].y(),
	texCoords[kTopRight_Corner].y(),
	texCoords[kBottomLeft_Corner].y(),
	texCoords[kBottomRight_Corner].y()));

	}

	if(x < lodX && y < lodY) {
	int i = 6 * (x * lodY + y);
	data->fIndices[i] = x * stride + y;
	data->fIndices[i + 1] = x * stride + 1 + y;
	data->fIndices[i + 2] = (x + 1) * stride + 1 + y;
	data->fIndices[i + 3] = data->fIndices[i];
	data->fIndices[i + 4] = data->fIndices[i + 2];
	data->fIndices[i + 5] = (x + 1) * stride + y;
	}
	v = SkScalarClampMax(v + 1.f / lodY, 1);
	}
	u = SkScalarClampMax(u + 1.f / lodX, 1);
	}
	return true;

	}