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 "SkRect.h" 12 #include "SkPathPriv.h" 13 #include "SkTArray.h" 14 15 class SkMatrix; 16 17 /** 18 * Utilities for evaluating paths. 19 */ 20 namespace GrPathUtils { 21 SkScalar scaleToleranceToSrc(SkScalar devTol, 22 const SkMatrix& viewM, 23 const SkRect& pathBounds); 24 25 /// Since we divide by tol if we're computing exact worst-case bounds, 26 /// very small tolerances will be increased to gMinCurveTol. 27 int worstCasePointCount(const SkPath&, 28 int* subpaths, 29 SkScalar tol); 30 31 /// Since we divide by tol if we're computing exact worst-case bounds, 32 /// very small tolerances will be increased to gMinCurveTol. 33 uint32_t quadraticPointCount(const SkPoint points[], SkScalar tol); 34 35 uint32_t generateQuadraticPoints(const SkPoint& p0, 36 const SkPoint& p1, 37 const SkPoint& p2, 38 SkScalar tolSqd, 39 SkPoint** points, 40 uint32_t pointsLeft); 41 42 /// Since we divide by tol if we're computing exact worst-case bounds, 43 /// very small tolerances will be increased to gMinCurveTol. 44 uint32_t cubicPointCount(const SkPoint points[], SkScalar tol); 45 46 uint32_t generateCubicPoints(const SkPoint& p0, 47 const SkPoint& p1, 48 const SkPoint& p2, 49 const SkPoint& p3, 50 SkScalar tolSqd, 51 SkPoint** points, 52 uint32_t pointsLeft); 53 54 // A 2x3 matrix that goes from the 2d space coordinates to UV space where 55 // u^2-v = 0 specifies the quad. The matrix is determined by the control 56 // points of the quadratic. 57 class QuadUVMatrix { 58 public: QuadUVMatrix()59 QuadUVMatrix() {} 60 // Initialize the matrix from the control pts QuadUVMatrix(const SkPoint controlPts[3])61 QuadUVMatrix(const SkPoint controlPts[3]) { this->set(controlPts); } 62 void set(const SkPoint controlPts[3]); 63 64 /** 65 * Applies the matrix to vertex positions to compute UV coords. This 66 * has been templated so that the compiler can easliy unroll the loop 67 * and reorder to avoid stalling for loads. The assumption is that a 68 * path renderer will have a small fixed number of vertices that it 69 * uploads for each quad. 70 * 71 * N is the number of vertices. 72 * STRIDE is the size of each vertex. 73 * UV_OFFSET is the offset of the UV values within each vertex. 74 * vertices is a pointer to the first vertex. 75 */ 76 template <int N, size_t STRIDE, size_t UV_OFFSET> apply(const void * vertices)77 void apply(const void* vertices) const { 78 intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices); 79 intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + UV_OFFSET; 80 float sx = fM[0]; 81 float kx = fM[1]; 82 float tx = fM[2]; 83 float ky = fM[3]; 84 float sy = fM[4]; 85 float ty = fM[5]; 86 for (int i = 0; i < N; ++i) { 87 const SkPoint* xy = reinterpret_cast<const SkPoint*>(xyPtr); 88 SkPoint* uv = reinterpret_cast<SkPoint*>(uvPtr); 89 uv->fX = sx * xy->fX + kx * xy->fY + tx; 90 uv->fY = ky * xy->fX + sy * xy->fY + ty; 91 xyPtr += STRIDE; 92 uvPtr += STRIDE; 93 } 94 } 95 private: 96 float fM[6]; 97 }; 98 99 // Input is 3 control points and a weight for a bezier conic. Calculates the 100 // three linear functionals (K,L,M) that represent the implicit equation of the 101 // conic, K^2 - LM. 102 // 103 // Output: 104 // K = (klm[0], klm[1], klm[2]) 105 // L = (klm[3], klm[4], klm[5]) 106 // M = (klm[6], klm[7], klm[8]) 107 void getConicKLM(const SkPoint p[3], const SkScalar weight, SkScalar klm[9]); 108 109 // Converts a cubic into a sequence of quads. If working in device space 110 // use tolScale = 1, otherwise set based on stretchiness of the matrix. The 111 // result is sets of 3 points in quads. 112 void convertCubicToQuads(const SkPoint p[4], 113 SkScalar tolScale, 114 SkTArray<SkPoint, true>* quads); 115 116 // When we approximate a cubic {a,b,c,d} with a quadratic we may have to 117 // ensure that the new control point lies between the lines ab and cd. The 118 // convex path renderer requires this. It starts with a path where all the 119 // control points taken together form a convex polygon. It relies on this 120 // property and the quadratic approximation of cubics step cannot alter it. 121 // This variation enforces this constraint. The cubic must be simple and dir 122 // must specify the orientation of the contour containing the cubic. 123 void convertCubicToQuadsConstrainToTangents(const SkPoint p[4], 124 SkScalar tolScale, 125 SkPathPriv::FirstDirection 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 nullptr 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 nullptr 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 nullptr 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] = nullptr, 158 SkScalar klm[9] = nullptr, SkScalar klm_rev[3] = nullptr); 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 // When tessellating curved paths into linear segments, this defines the maximum distance 174 // in screen space which a segment may deviate from the mathmatically correct value. 175 // Above this value, the segment will be subdivided. 176 // This value was chosen to approximate the supersampling accuracy of the raster path (16 177 // samples, or one quarter pixel). 178 static const SkScalar kDefaultTolerance = SkDoubleToScalar(0.25); 179 }; 180 #endif 181