src/core/SkPatch.cpp - skia - Git at Google

 /*
  * 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 "SkPatch.h"

 #include "SkGeometry.h"
 #include "SkColorPriv.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() { }

     /**
      * 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;

         SkScalar cx[4], cy[4];
         SkGetCubicCoeff(fPoints, cx, cy);
         fCoefs[0].set(cx[0], cy[0]);
         fCoefs[1].set(cx[1], cy[1]);
         fCoefs[2].set(cx[2], cy[2]);
         fCoefs[3].set(cx[3], cy[3]);

         this->restart(1);
     }

     explicit FwDCubicEvaluator(SkPoint points[4]) {
         for (int i = 0; i< 4; i++) {
             fPoints[i] = points[i];
         }

         SkScalar cx[4], cy[4];
         SkGetCubicCoeff(fPoints, cx, cy);
         fCoefs[0].set(cx[0], cy[0]);
         fCoefs[1].set(cx[1], cy[1]);
         fCoefs[2].set(cx[2], cy[2]);
         fCoefs[3].set(cx[3], cy[3]);

         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];
 };

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

 SkPatch::SkPatch(SkPoint points[12], SkColor colors[4]) {

     for (int i = 0; i < 12; i++) {
         fCtrlPoints[i] = points[i];
     }
     for (int i = 0; i < 4; i++) {
         fCornerColors[i] = colors[i];
     }

 }

 uint8_t bilinear(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 uint8_t(a * (1.f - ty) + b * ty);
 }

 bool SkPatch::getVertexData(SkPatch::VertexData* data, int lodX, int lodY) const {

     if (lodX < 1 || lodY < 1) {
         return false;
     }

     // premultiply colors to avoid color bleeding.
     SkPMColor colors[4];
     for (int i = 0; i < 4; i++) {
         colors[i] = SkPreMultiplyColor(fCornerColors[i]);
     }

     // number of indices is limited by size of uint16_t, so we clamp it to avoid overflow
     data->fVertexCount = SkMin32((lodX + 1) * (lodY + 1), 65536);
     lodX  = SkMin32(lodX, 255);
     lodY  = SkMin32(lodY, 255);
     data->fIndexCount = lodX * lodY * 6;

     data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
     data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
     data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
     data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);

     SkPoint pts[4];
     this->getBottomPoints(pts);
     FwDCubicEvaluator fBottom(pts);
     this->getTopPoints(pts);
     FwDCubicEvaluator fTop(pts);
     this->getLeftPoints(pts);
     FwDCubicEvaluator fLeft(pts);
     this->getRightPoints(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;

             uint8_t a = bilinear(u, v,
                             SkScalar(SkColorGetA(colors[kTopLeft_CornerColors])),
                             SkScalar(SkColorGetA(colors[kTopRight_CornerColors])),
                             SkScalar(SkColorGetA(colors[kBottomLeft_CornerColors])),
                             SkScalar(SkColorGetA(colors[kBottomRight_CornerColors])));
             uint8_t r = bilinear(u, v,
                             SkScalar(SkColorGetR(colors[kTopLeft_CornerColors])),
                             SkScalar(SkColorGetR(colors[kTopRight_CornerColors])),
                             SkScalar(SkColorGetR(colors[kBottomLeft_CornerColors])),
                             SkScalar(SkColorGetR(colors[kBottomRight_CornerColors])));
             uint8_t g = bilinear(u, v,
                             SkScalar(SkColorGetG(colors[kTopLeft_CornerColors])),
                             SkScalar(SkColorGetG(colors[kTopRight_CornerColors])),
                             SkScalar(SkColorGetG(colors[kBottomLeft_CornerColors])),
                             SkScalar(SkColorGetG(colors[kBottomRight_CornerColors])));
             uint8_t b = bilinear(u, v,
                             SkScalar(SkColorGetB(colors[kTopLeft_CornerColors])),
                             SkScalar(SkColorGetB(colors[kTopRight_CornerColors])),
                             SkScalar(SkColorGetB(colors[kBottomLeft_CornerColors])),
                             SkScalar(SkColorGetB(colors[kBottomRight_CornerColors])));
             data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);

             data->fTexCoords[dataIndex] = SkPoint::Make(u, v);

             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 "SkPatch.h"

	#include "SkGeometry.h"
	#include "SkColorPriv.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() { }

	/**
	* 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;

	SkScalar cx[4], cy[4];
	SkGetCubicCoeff(fPoints, cx, cy);
	fCoefs[0].set(cx[0], cy[0]);
	fCoefs[1].set(cx[1], cy[1]);
	fCoefs[2].set(cx[2], cy[2]);
	fCoefs[3].set(cx[3], cy[3]);

	this->restart(1);
	}

	explicit FwDCubicEvaluator(SkPoint points[4]) {
	for (int i = 0; i< 4; i++) {
	fPoints[i] = points[i];
	}

	SkScalar cx[4], cy[4];
	SkGetCubicCoeff(fPoints, cx, cy);
	fCoefs[0].set(cx[0], cy[0]);
	fCoefs[1].set(cx[1], cy[1]);
	fCoefs[2].set(cx[2], cy[2]);
	fCoefs[3].set(cx[3], cy[3]);

	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];
	};

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

	SkPatch::SkPatch(SkPoint points[12], SkColor colors[4]) {

	for (int i = 0; i < 12; i++) {
	fCtrlPoints[i] = points[i];
	}
	for (int i = 0; i < 4; i++) {
	fCornerColors[i] = colors[i];
	}

	}

	uint8_t bilinear(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 uint8_t(a * (1.f - ty) + b * ty);
	}

	bool SkPatch::getVertexData(SkPatch::VertexData* data, int lodX, int lodY) const {

	if (lodX < 1 \|\| lodY < 1) {
	return false;
	}

	// premultiply colors to avoid color bleeding.
	SkPMColor colors[4];
	for (int i = 0; i < 4; i++) {
	colors[i] = SkPreMultiplyColor(fCornerColors[i]);
	}

	// number of indices is limited by size of uint16_t, so we clamp it to avoid overflow
	data->fVertexCount = SkMin32((lodX + 1) * (lodY + 1), 65536);
	lodX = SkMin32(lodX, 255);
	lodY = SkMin32(lodY, 255);
	data->fIndexCount = lodX * lodY * 6;

	data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
	data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
	data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
	data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);

	SkPoint pts[4];
	this->getBottomPoints(pts);
	FwDCubicEvaluator fBottom(pts);
	this->getTopPoints(pts);
	FwDCubicEvaluator fTop(pts);
	this->getLeftPoints(pts);
	FwDCubicEvaluator fLeft(pts);
	this->getRightPoints(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;

	uint8_t a = bilinear(u, v,
	SkScalar(SkColorGetA(colors[kTopLeft_CornerColors])),
	SkScalar(SkColorGetA(colors[kTopRight_CornerColors])),
	SkScalar(SkColorGetA(colors[kBottomLeft_CornerColors])),
	SkScalar(SkColorGetA(colors[kBottomRight_CornerColors])));
	uint8_t r = bilinear(u, v,
	SkScalar(SkColorGetR(colors[kTopLeft_CornerColors])),
	SkScalar(SkColorGetR(colors[kTopRight_CornerColors])),
	SkScalar(SkColorGetR(colors[kBottomLeft_CornerColors])),
	SkScalar(SkColorGetR(colors[kBottomRight_CornerColors])));
	uint8_t g = bilinear(u, v,
	SkScalar(SkColorGetG(colors[kTopLeft_CornerColors])),
	SkScalar(SkColorGetG(colors[kTopRight_CornerColors])),
	SkScalar(SkColorGetG(colors[kBottomLeft_CornerColors])),
	SkScalar(SkColorGetG(colors[kBottomRight_CornerColors])));
	uint8_t b = bilinear(u, v,
	SkScalar(SkColorGetB(colors[kTopLeft_CornerColors])),
	SkScalar(SkColorGetB(colors[kTopRight_CornerColors])),
	SkScalar(SkColorGetB(colors[kBottomLeft_CornerColors])),
	SkScalar(SkColorGetB(colors[kBottomRight_CornerColors])));
	data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);

	data->fTexCoords[dataIndex] = SkPoint::Make(u, v);

	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;
	}