1 /* 2 * Copyright 2011 Google Inc. 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 8 #ifndef GrPathUtils_DEFINED 9 #define GrPathUtils_DEFINED 10 11 #include "GrPoint.h" 12 #include "SkRect.h" 13 #include "SkPath.h" 14 #include "SkTArray.h" 15 16 class SkMatrix; 17 18 /** 19 * Utilities for evaluating paths. 20 */ 21 namespace GrPathUtils { 22 SkScalar scaleToleranceToSrc(SkScalar devTol, 23 const SkMatrix& viewM, 24 const SkRect& pathBounds); 25 26 /// Since we divide by tol if we're computing exact worst-case bounds, 27 /// very small tolerances will be increased to gMinCurveTol. 28 int worstCasePointCount(const SkPath&, 29 int* subpaths, 30 SkScalar tol); 31 32 /// Since we divide by tol if we're computing exact worst-case bounds, 33 /// very small tolerances will be increased to gMinCurveTol. 34 uint32_t quadraticPointCount(const GrPoint points[], SkScalar tol); 35 36 uint32_t generateQuadraticPoints(const GrPoint& p0, 37 const GrPoint& p1, 38 const GrPoint& p2, 39 SkScalar tolSqd, 40 GrPoint** points, 41 uint32_t pointsLeft); 42 43 /// Since we divide by tol if we're computing exact worst-case bounds, 44 /// very small tolerances will be increased to gMinCurveTol. 45 uint32_t cubicPointCount(const GrPoint points[], SkScalar tol); 46 47 uint32_t generateCubicPoints(const GrPoint& p0, 48 const GrPoint& p1, 49 const GrPoint& p2, 50 const GrPoint& p3, 51 SkScalar tolSqd, 52 GrPoint** points, 53 uint32_t pointsLeft); 54 55 // A 2x3 matrix that goes from the 2d space coordinates to UV space where 56 // u^2-v = 0 specifies the quad. The matrix is determined by the control 57 // points of the quadratic. 58 class QuadUVMatrix { 59 public: 60 QuadUVMatrix() {}; 61 // Initialize the matrix from the control pts 62 QuadUVMatrix(const GrPoint controlPts[3]) { this->set(controlPts); } 63 void set(const GrPoint controlPts[3]); 64 65 /** 66 * Applies the matrix to vertex positions to compute UV coords. This 67 * has been templated so that the compiler can easliy unroll the loop 68 * and reorder to avoid stalling for loads. The assumption is that a 69 * path renderer will have a small fixed number of vertices that it 70 * uploads for each quad. 71 * 72 * N is the number of vertices. 73 * STRIDE is the size of each vertex. 74 * UV_OFFSET is the offset of the UV values within each vertex. 75 * vertices is a pointer to the first vertex. 76 */ 77 template <int N, size_t STRIDE, size_t UV_OFFSET> 78 void apply(const void* vertices) { 79 intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices); 80 intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + UV_OFFSET; 81 float sx = fM[0]; 82 float kx = fM[1]; 83 float tx = fM[2]; 84 float ky = fM[3]; 85 float sy = fM[4]; 86 float ty = fM[5]; 87 for (int i = 0; i < N; ++i) { 88 const GrPoint* xy = reinterpret_cast<const GrPoint*>(xyPtr); 89 GrPoint* uv = reinterpret_cast<GrPoint*>(uvPtr); 90 uv->fX = sx * xy->fX + kx * xy->fY + tx; 91 uv->fY = ky * xy->fX + sy * xy->fY + ty; 92 xyPtr += STRIDE; 93 uvPtr += STRIDE; 94 } 95 } 96 private: 97 float fM[6]; 98 }; 99 100 // Input is 3 control points and a weight for a bezier conic. Calculates the 101 // three linear functionals (K,L,M) that represent the implicit equation of the 102 // conic, K^2 - LM. 103 // 104 // Output: 105 // K = (klm[0], klm[1], klm[2]) 106 // L = (klm[3], klm[4], klm[5]) 107 // M = (klm[6], klm[7], klm[8]) 108 void getConicKLM(const SkPoint p[3], const SkScalar weight, SkScalar klm[9]); 109 110 // Converts a cubic into a sequence of quads. If working in device space 111 // use tolScale = 1, otherwise set based on stretchiness of the matrix. The 112 // result is sets of 3 points in quads (TODO: share endpoints in returned 113 // array) 114 // When we approximate a cubic {a,b,c,d} with a quadratic we may have to 115 // ensure that the new control point lies between the lines ab and cd. The 116 // convex path renderer requires this. It starts with a path where all the 117 // control points taken together form a convex polygon. It relies on this 118 // property and the quadratic approximation of cubics step cannot alter it. 119 // Setting constrainWithinTangents to true enforces this property. When this 120 // is true the cubic must be simple and dir must specify the orientation of 121 // the cubic. Otherwise, dir is ignored. 122 void convertCubicToQuads(const GrPoint p[4], 123 SkScalar tolScale, 124 bool constrainWithinTangents, 125 SkPath::Direction dir, 126 SkTArray<SkPoint, true>* quads); 127 128 // Chops the cubic bezier passed in by src, at the double point (intersection point) 129 // if the curve is a cubic loop. If it is a loop, there will be two parametric values for 130 // the double point: ls and ms. We chop the cubic at these values if they are between 0 and 1. 131 // Return value: 132 // Value of 3: ls and ms are both between (0,1), and dst will contain the three cubics, 133 // dst[0..3], dst[3..6], and dst[6..9] if dst is not NULL 134 // Value of 2: Only one of ls and ms are between (0,1), and dst will contain the two cubics, 135 // dst[0..3] and dst[3..6] if dst is not NULL 136 // Value of 1: Neither ls or ms are between (0,1), and dst will contain the one original cubic, 137 // dst[0..3] if dst is not NULL 138 // 139 // Optional KLM Calculation: 140 // The function can also return the KLM linear functionals for the chopped cubic implicit form 141 // of K^3 - LM. 142 // It will calculate a single set of KLM values that can be shared by all sub cubics, except 143 // for the subsection that is "the loop" the K and L values need to be negated. 144 // Output: 145 // klm: Holds the values for the linear functionals as: 146 // K = (klm[0], klm[1], klm[2]) 147 // L = (klm[3], klm[4], klm[5]) 148 // M = (klm[6], klm[7], klm[8]) 149 // klm_rev: These values are flags for the corresponding sub cubic saying whether or not 150 // the K and L values need to be flipped. A value of -1.f means flip K and L and 151 // a value of 1.f means do nothing. 152 // *****DO NOT FLIP M, JUST K AND L***** 153 // 154 // Notice that the klm lines are calculated in the same space as the input control points. 155 // If you transform the points the lines will also need to be transformed. This can be done 156 // by mapping the lines with the inverse-transpose of the matrix used to map the points. 157 int chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10] = NULL, 158 SkScalar klm[9] = NULL, SkScalar klm_rev[3] = NULL); 159 160 // Input is p which holds the 4 control points of a non-rational cubic Bezier curve. 161 // Output is the coefficients of the three linear functionals K, L, & M which 162 // represent the implicit form of the cubic as f(x,y,w) = K^3 - LM. The w term 163 // will always be 1. The output is stored in the array klm, where the values are: 164 // K = (klm[0], klm[1], klm[2]) 165 // L = (klm[3], klm[4], klm[5]) 166 // M = (klm[6], klm[7], klm[8]) 167 // 168 // Notice that the klm lines are calculated in the same space as the input control points. 169 // If you transform the points the lines will also need to be transformed. This can be done 170 // by mapping the lines with the inverse-transpose of the matrix used to map the points. 171 void getCubicKLM(const SkPoint p[4], SkScalar klm[9]); 172 }; 173 #endif 174
