src/gpu/GrPathUtils.h - platform/external/skqp - Gitiles

 /*
  * Copyright 2011 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */

 #ifndef GrPathUtils_DEFINED
 #define GrPathUtils_DEFINED

 #include "SkRect.h"
 #include "SkPathPriv.h"
 #include "SkTArray.h"

 class SkMatrix;

 /**
  *  Utilities for evaluating paths.
  */
 namespace GrPathUtils {
     SkScalar scaleToleranceToSrc(SkScalar devTol,
                                  const SkMatrix& viewM,
                                  const SkRect& pathBounds);

     /// Since we divide by tol if we're computing exact worst-case bounds,
     /// very small tolerances will be increased to gMinCurveTol.
     int worstCasePointCount(const SkPath&,
                             int* subpaths,
                             SkScalar tol);

     /// Since we divide by tol if we're computing exact worst-case bounds,
     /// very small tolerances will be increased to gMinCurveTol.
     uint32_t quadraticPointCount(const SkPoint points[], SkScalar tol);

     uint32_t generateQuadraticPoints(const SkPoint& p0,
                                      const SkPoint& p1,
                                      const SkPoint& p2,
                                      SkScalar tolSqd,
                                      SkPoint** points,
                                      uint32_t pointsLeft);

     /// Since we divide by tol if we're computing exact worst-case bounds,
     /// very small tolerances will be increased to gMinCurveTol.
     uint32_t cubicPointCount(const SkPoint points[], SkScalar tol);

     uint32_t generateCubicPoints(const SkPoint& p0,
                                  const SkPoint& p1,
                                  const SkPoint& p2,
                                  const SkPoint& p3,
                                  SkScalar tolSqd,
                                  SkPoint** points,
                                  uint32_t pointsLeft);

     // A 2x3 matrix that goes from the 2d space coordinates to UV space where
     // u^2-v = 0 specifies the quad. The matrix is determined by the control
     // points of the quadratic.
     class QuadUVMatrix {
     public:
         QuadUVMatrix() {};
         // Initialize the matrix from the control pts
         QuadUVMatrix(const SkPoint controlPts[3]) { this->set(controlPts); }
         void set(const SkPoint controlPts[3]);

         /**
          * Applies the matrix to vertex positions to compute UV coords. This
          * has been templated so that the compiler can easliy unroll the loop
          * and reorder to avoid stalling for loads. The assumption is that a
          * path renderer will have a small fixed number of vertices that it
          * uploads for each quad.
          *
          * N is the number of vertices.
          * STRIDE is the size of each vertex.
          * UV_OFFSET is the offset of the UV values within each vertex.
          * vertices is a pointer to the first vertex.
          */
         template <int N, size_t STRIDE, size_t UV_OFFSET>
         void apply(const void* vertices) {
             intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices);
             intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + UV_OFFSET;
             float sx = fM[0];
             float kx = fM[1];
             float tx = fM[2];
             float ky = fM[3];
             float sy = fM[4];
             float ty = fM[5];
             for (int i = 0; i < N; ++i) {
                 const SkPoint* xy = reinterpret_cast<const SkPoint*>(xyPtr);
                 SkPoint* uv = reinterpret_cast<SkPoint*>(uvPtr);
                 uv->fX = sx * xy->fX + kx * xy->fY + tx;
                 uv->fY = ky * xy->fX + sy * xy->fY + ty;
                 xyPtr += STRIDE;
                 uvPtr += STRIDE;
             }
         }
     private:
         float fM[6];
     };

     // Input is 3 control points and a weight for a bezier conic. Calculates the
     // three linear functionals (K,L,M) that represent the implicit equation of the
     // conic, K^2 - LM.
     //
     // Output:
     //  K = (klm[0], klm[1], klm[2])
     //  L = (klm[3], klm[4], klm[5])
     //  M = (klm[6], klm[7], klm[8])
     void getConicKLM(const SkPoint p[3], const SkScalar weight, SkScalar klm[9]);

     // Converts a cubic into a sequence of quads. If working in device space
     // use tolScale = 1, otherwise set based on stretchiness of the matrix. The
     // result is sets of 3 points in quads (TODO: share endpoints in returned
     // array)
     // When we approximate a cubic {a,b,c,d} with a quadratic we may have to
     // ensure that the new control point lies between the lines ab and cd. The
     // convex path renderer requires this. It starts with a path where all the
     // control points taken together form a convex polygon. It relies on this
     // property and the quadratic approximation of cubics step cannot alter it.
     // Setting constrainWithinTangents to true enforces this property. When this
     // is true the cubic must be simple and dir must specify the orientation of
     // the cubic. Otherwise, dir is ignored.
     void convertCubicToQuads(const SkPoint p[4],
                              SkScalar tolScale,
                              bool constrainWithinTangents,
                              SkPathPriv::FirstDirection dir,
                              SkTArray<SkPoint, true>* quads);

     // Chops the cubic bezier passed in by src, at the double point (intersection point)
     // if the curve is a cubic loop. If it is a loop, there will be two parametric values for
     // the double point: ls and ms. We chop the cubic at these values if they are between 0 and 1.
     // Return value:
     // Value of 3: ls and ms are both between (0,1), and dst will contain the three cubics,
     //             dst[0..3], dst[3..6], and dst[6..9] if dst is not nullptr
     // Value of 2: Only one of ls and ms are between (0,1), and dst will contain the two cubics,
     //             dst[0..3] and dst[3..6] if dst is not nullptr
     // Value of 1: Neither ls or ms are between (0,1), and dst will contain the one original cubic,
     //             dst[0..3] if dst is not nullptr
     //
     // Optional KLM Calculation:
     // The function can also return the KLM linear functionals for the chopped cubic implicit form
     // of K^3 - LM.
     // It will calculate a single set of KLM values that can be shared by all sub cubics, except
     // for the subsection that is "the loop" the K and L values need to be negated.
     // Output:
     // klm:     Holds the values for the linear functionals as:
     //          K = (klm[0], klm[1], klm[2])
     //          L = (klm[3], klm[4], klm[5])
     //          M = (klm[6], klm[7], klm[8])
     // klm_rev: These values are flags for the corresponding sub cubic saying whether or not
     //          the K and L values need to be flipped. A value of -1.f means flip K and L and
     //          a value of 1.f means do nothing.
     //          *****DO NOT FLIP M, JUST K AND L*****
     //
     // Notice that the klm lines are calculated in the same space as the input control points.
     // If you transform the points the lines will also need to be transformed. This can be done
     // by mapping the lines with the inverse-transpose of the matrix used to map the points.
     int chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10] = nullptr,
                                     SkScalar klm[9] = nullptr, SkScalar klm_rev[3] = nullptr);

     // Input is p which holds the 4 control points of a non-rational cubic Bezier curve.
     // Output is the coefficients of the three linear functionals K, L, & M which
     // represent the implicit form of the cubic as f(x,y,w) = K^3 - LM. The w term
     // will always be 1. The output is stored in the array klm, where the values are:
     // K = (klm[0], klm[1], klm[2])
     // L = (klm[3], klm[4], klm[5])
     // M = (klm[6], klm[7], klm[8])
     //
     // Notice that the klm lines are calculated in the same space as the input control points.
     // If you transform the points the lines will also need to be transformed. This can be done
     // by mapping the lines with the inverse-transpose of the matrix used to map the points.
     void getCubicKLM(const SkPoint p[4], SkScalar klm[9]);

     // When tessellating curved paths into linear segments, this defines the maximum distance
     // in screen space which a segment may deviate from the mathmatically correct value.
     // Above this value, the segment will be subdivided.
     // This value was chosen to approximate the supersampling accuracy of the raster path (16
     // samples, or one quarter pixel).
     static const SkScalar kDefaultTolerance = SkDoubleToScalar(0.25);
 };
 #endif
	/*
	* Copyright 2011 Google Inc.
	*
	* Use of this source code is governed by a BSD-style license that can be
	* found in the LICENSE file.
	*/

	#ifndef GrPathUtils_DEFINED
	#define GrPathUtils_DEFINED

	#include "SkRect.h"
	#include "SkPathPriv.h"
	#include "SkTArray.h"

	class SkMatrix;

	/**
	* Utilities for evaluating paths.
	*/
	namespace GrPathUtils {
	SkScalar scaleToleranceToSrc(SkScalar devTol,
	const SkMatrix& viewM,
	const SkRect& pathBounds);

	/// Since we divide by tol if we're computing exact worst-case bounds,
	/// very small tolerances will be increased to gMinCurveTol.
	int worstCasePointCount(const SkPath&,
	int* subpaths,
	SkScalar tol);

	/// Since we divide by tol if we're computing exact worst-case bounds,
	/// very small tolerances will be increased to gMinCurveTol.
	uint32_t quadraticPointCount(const SkPoint points[], SkScalar tol);

	uint32_t generateQuadraticPoints(const SkPoint& p0,
	const SkPoint& p1,
	const SkPoint& p2,
	SkScalar tolSqd,
	SkPoint** points,
	uint32_t pointsLeft);

	/// Since we divide by tol if we're computing exact worst-case bounds,
	/// very small tolerances will be increased to gMinCurveTol.
	uint32_t cubicPointCount(const SkPoint points[], SkScalar tol);

	uint32_t generateCubicPoints(const SkPoint& p0,
	const SkPoint& p1,
	const SkPoint& p2,
	const SkPoint& p3,
	SkScalar tolSqd,
	SkPoint** points,
	uint32_t pointsLeft);

	// A 2x3 matrix that goes from the 2d space coordinates to UV space where
	// u^2-v = 0 specifies the quad. The matrix is determined by the control
	// points of the quadratic.
	class QuadUVMatrix {
	public:
	QuadUVMatrix() {};
	// Initialize the matrix from the control pts
	QuadUVMatrix(const SkPoint controlPts[3]) { this->set(controlPts); }
	void set(const SkPoint controlPts[3]);

	/**
	* Applies the matrix to vertex positions to compute UV coords. This
	* has been templated so that the compiler can easliy unroll the loop
	* and reorder to avoid stalling for loads. The assumption is that a
	* path renderer will have a small fixed number of vertices that it
	* uploads for each quad.
	*
	* N is the number of vertices.
	* STRIDE is the size of each vertex.
	* UV_OFFSET is the offset of the UV values within each vertex.
	* vertices is a pointer to the first vertex.
	*/
	template <int N, size_t STRIDE, size_t UV_OFFSET>
	void apply(const void* vertices) {
	intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices);
	intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + UV_OFFSET;
	float sx = fM[0];
	float kx = fM[1];
	float tx = fM[2];
	float ky = fM[3];
	float sy = fM[4];
	float ty = fM[5];
	for (int i = 0; i < N; ++i) {
	const SkPoint* xy = reinterpret_cast<const SkPoint*>(xyPtr);
	SkPoint* uv = reinterpret_cast<SkPoint*>(uvPtr);
	uv->fX = sx * xy->fX + kx * xy->fY + tx;
	uv->fY = ky * xy->fX + sy * xy->fY + ty;
	xyPtr += STRIDE;
	uvPtr += STRIDE;
	}
	}
	private:
	float fM[6];
	};

	// Input is 3 control points and a weight for a bezier conic. Calculates the
	// three linear functionals (K,L,M) that represent the implicit equation of the
	// conic, K^2 - LM.
	//
	// Output:
	// K = (klm[0], klm[1], klm[2])
	// L = (klm[3], klm[4], klm[5])
	// M = (klm[6], klm[7], klm[8])
	void getConicKLM(const SkPoint p[3], const SkScalar weight, SkScalar klm[9]);

	// Converts a cubic into a sequence of quads. If working in device space
	// use tolScale = 1, otherwise set based on stretchiness of the matrix. The
	// result is sets of 3 points in quads (TODO: share endpoints in returned
	// array)
	// When we approximate a cubic {a,b,c,d} with a quadratic we may have to
	// ensure that the new control point lies between the lines ab and cd. The
	// convex path renderer requires this. It starts with a path where all the
	// control points taken together form a convex polygon. It relies on this
	// property and the quadratic approximation of cubics step cannot alter it.
	// Setting constrainWithinTangents to true enforces this property. When this
	// is true the cubic must be simple and dir must specify the orientation of
	// the cubic. Otherwise, dir is ignored.
	void convertCubicToQuads(const SkPoint p[4],
	SkScalar tolScale,
	bool constrainWithinTangents,
	SkPathPriv::FirstDirection dir,
	SkTArray<SkPoint, true>* quads);

	// Chops the cubic bezier passed in by src, at the double point (intersection point)
	// if the curve is a cubic loop. If it is a loop, there will be two parametric values for
	// the double point: ls and ms. We chop the cubic at these values if they are between 0 and 1.
	// Return value:
	// Value of 3: ls and ms are both between (0,1), and dst will contain the three cubics,
	// dst[0..3], dst[3..6], and dst[6..9] if dst is not nullptr
	// Value of 2: Only one of ls and ms are between (0,1), and dst will contain the two cubics,
	// dst[0..3] and dst[3..6] if dst is not nullptr
	// Value of 1: Neither ls or ms are between (0,1), and dst will contain the one original cubic,
	// dst[0..3] if dst is not nullptr
	//
	// Optional KLM Calculation:
	// The function can also return the KLM linear functionals for the chopped cubic implicit form
	// of K^3 - LM.
	// It will calculate a single set of KLM values that can be shared by all sub cubics, except
	// for the subsection that is "the loop" the K and L values need to be negated.
	// Output:
	// klm: Holds the values for the linear functionals as:
	// K = (klm[0], klm[1], klm[2])
	// L = (klm[3], klm[4], klm[5])
	// M = (klm[6], klm[7], klm[8])
	// klm_rev: These values are flags for the corresponding sub cubic saying whether or not
	// the K and L values need to be flipped. A value of -1.f means flip K and L and
	// a value of 1.f means do nothing.
	// ***DO NOT FLIP M, JUST K AND L***
	//
	// Notice that the klm lines are calculated in the same space as the input control points.
	// If you transform the points the lines will also need to be transformed. This can be done
	// by mapping the lines with the inverse-transpose of the matrix used to map the points.
	int chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10] = nullptr,
	SkScalar klm[9] = nullptr, SkScalar klm_rev[3] = nullptr);

	// Input is p which holds the 4 control points of a non-rational cubic Bezier curve.
	// Output is the coefficients of the three linear functionals K, L, & M which
	// represent the implicit form of the cubic as f(x,y,w) = K^3 - LM. The w term
	// will always be 1. The output is stored in the array klm, where the values are:
	// K = (klm[0], klm[1], klm[2])
	// L = (klm[3], klm[4], klm[5])
	// M = (klm[6], klm[7], klm[8])
	//
	// Notice that the klm lines are calculated in the same space as the input control points.
	// If you transform the points the lines will also need to be transformed. This can be done
	// by mapping the lines with the inverse-transpose of the matrix used to map the points.
	void getCubicKLM(const SkPoint p[4], SkScalar klm[9]);

	// When tessellating curved paths into linear segments, this defines the maximum distance
	// in screen space which a segment may deviate from the mathmatically correct value.
	// Above this value, the segment will be subdivided.
	// This value was chosen to approximate the supersampling accuracy of the raster path (16
	// samples, or one quarter pixel).
	static const SkScalar kDefaultTolerance = SkDoubleToScalar(0.25);
	};
	#endif