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