1 /* 2 * Copyright 2014 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 #include "SkPatchUtils.h" 9 10 #include "SkColorPriv.h" 11 #include "SkGeometry.h" 12 13 /** 14 * Evaluator to sample the values of a cubic bezier using forward differences. 15 * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only 16 * adding precalculated values. 17 * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h 18 * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first 19 * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After 20 * obtaining this value (mh) we could just add this constant step to our first sampled point 21 * to compute the next one. 22 * 23 * For the cubic case the first difference gives as a result a quadratic polynomial to which we can 24 * apply again forward differences and get linear function to which we can apply again forward 25 * differences to get a constant difference. This is why we keep an array of size 4, the 0th 26 * position keeps the sampled value while the next ones keep the quadratic, linear and constant 27 * difference values. 28 */ 29 30 class FwDCubicEvaluator { 31 32 public: 33 34 /** 35 * Receives the 4 control points of the cubic bezier. 36 */ 37 38 explicit FwDCubicEvaluator(const SkPoint points[4]) 39 : fCoefs(points) { 40 memcpy(fPoints, points, 4 * sizeof(SkPoint)); 41 42 this->restart(1); 43 } 44 45 /** 46 * Restarts the forward differences evaluator to the first value of t = 0. 47 */ 48 void restart(int divisions) { 49 fDivisions = divisions; 50 fCurrent = 0; 51 fMax = fDivisions + 1; 52 Sk2s h = Sk2s(1.f / fDivisions); 53 Sk2s h2 = h * h; 54 Sk2s h3 = h2 * h; 55 Sk2s fwDiff3 = Sk2s(6) * fCoefs.fA * h3; 56 fFwDiff[3] = to_point(fwDiff3); 57 fFwDiff[2] = to_point(fwDiff3 + times_2(fCoefs.fB) * h2); 58 fFwDiff[1] = to_point(fCoefs.fA * h3 + fCoefs.fB * h2 + fCoefs.fC * h); 59 fFwDiff[0] = to_point(fCoefs.fD); 60 } 61 62 /** 63 * Check if the evaluator is still within the range of 0<=t<=1 64 */ 65 bool done() const { 66 return fCurrent > fMax; 67 } 68 69 /** 70 * Call next to obtain the SkPoint sampled and move to the next one. 71 */ 72 SkPoint next() { 73 SkPoint point = fFwDiff[0]; 74 fFwDiff[0] += fFwDiff[1]; 75 fFwDiff[1] += fFwDiff[2]; 76 fFwDiff[2] += fFwDiff[3]; 77 fCurrent++; 78 return point; 79 } 80 81 const SkPoint* getCtrlPoints() const { 82 return fPoints; 83 } 84 85 private: 86 SkCubicCoeff fCoefs; 87 int fMax, fCurrent, fDivisions; 88 SkPoint fFwDiff[4], fPoints[4]; 89 }; 90 91 //////////////////////////////////////////////////////////////////////////////// 92 93 // size in pixels of each partition per axis, adjust this knob 94 static const int kPartitionSize = 10; 95 96 /** 97 * Calculate the approximate arc length given a bezier curve's control points. 98 */ 99 static SkScalar approx_arc_length(SkPoint* points, int count) { 100 if (count < 2) { 101 return 0; 102 } 103 SkScalar arcLength = 0; 104 for (int i = 0; i < count - 1; i++) { 105 arcLength += SkPoint::Distance(points[i], points[i + 1]); 106 } 107 return arcLength; 108 } 109 110 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01, 111 SkScalar c11) { 112 SkScalar a = c00 * (1.f - tx) + c10 * tx; 113 SkScalar b = c01 * (1.f - tx) + c11 * tx; 114 return a * (1.f - ty) + b * ty; 115 } 116 117 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) { 118 119 // Approximate length of each cubic. 120 SkPoint pts[kNumPtsCubic]; 121 SkPatchUtils::getTopCubic(cubics, pts); 122 matrix->mapPoints(pts, kNumPtsCubic); 123 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic); 124 125 SkPatchUtils::getBottomCubic(cubics, pts); 126 matrix->mapPoints(pts, kNumPtsCubic); 127 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic); 128 129 SkPatchUtils::getLeftCubic(cubics, pts); 130 matrix->mapPoints(pts, kNumPtsCubic); 131 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic); 132 133 SkPatchUtils::getRightCubic(cubics, pts); 134 matrix->mapPoints(pts, kNumPtsCubic); 135 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic); 136 137 // Level of detail per axis, based on the larger side between top and bottom or left and right 138 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize); 139 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize); 140 141 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY)); 142 } 143 144 void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) { 145 points[0] = cubics[kTopP0_CubicCtrlPts]; 146 points[1] = cubics[kTopP1_CubicCtrlPts]; 147 points[2] = cubics[kTopP2_CubicCtrlPts]; 148 points[3] = cubics[kTopP3_CubicCtrlPts]; 149 } 150 151 void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) { 152 points[0] = cubics[kBottomP0_CubicCtrlPts]; 153 points[1] = cubics[kBottomP1_CubicCtrlPts]; 154 points[2] = cubics[kBottomP2_CubicCtrlPts]; 155 points[3] = cubics[kBottomP3_CubicCtrlPts]; 156 } 157 158 void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) { 159 points[0] = cubics[kLeftP0_CubicCtrlPts]; 160 points[1] = cubics[kLeftP1_CubicCtrlPts]; 161 points[2] = cubics[kLeftP2_CubicCtrlPts]; 162 points[3] = cubics[kLeftP3_CubicCtrlPts]; 163 } 164 165 void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) { 166 points[0] = cubics[kRightP0_CubicCtrlPts]; 167 points[1] = cubics[kRightP1_CubicCtrlPts]; 168 points[2] = cubics[kRightP2_CubicCtrlPts]; 169 points[3] = cubics[kRightP3_CubicCtrlPts]; 170 } 171 172 bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12], 173 const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) { 174 if (lodX < 1 || lodY < 1 || nullptr == cubics || nullptr == data) { 175 return false; 176 } 177 178 // check for overflow in multiplication 179 const int64_t lodX64 = (lodX + 1), 180 lodY64 = (lodY + 1), 181 mult64 = lodX64 * lodY64; 182 if (mult64 > SK_MaxS32) { 183 return false; 184 } 185 data->fVertexCount = SkToS32(mult64); 186 187 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate 188 // more than 60000 indices. To accomplish that we resize the LOD and vertex count 189 if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) { 190 SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY); 191 SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY); 192 193 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of 194 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6) 195 lodX = static_cast<int>(weightX * 200); 196 lodY = static_cast<int>(weightY * 200); 197 data->fVertexCount = (lodX + 1) * (lodY + 1); 198 } 199 data->fIndexCount = lodX * lodY * 6; 200 201 data->fPoints = new SkPoint[data->fVertexCount]; 202 data->fIndices = new uint16_t[data->fIndexCount]; 203 204 // if colors is not null then create array for colors 205 SkPMColor colorsPM[kNumCorners]; 206 if (colors) { 207 // premultiply colors to avoid color bleeding. 208 for (int i = 0; i < kNumCorners; i++) { 209 colorsPM[i] = SkPreMultiplyColor(colors[i]); 210 } 211 data->fColors = new uint32_t[data->fVertexCount]; 212 } 213 214 // if texture coordinates are not null then create array for them 215 if (texCoords) { 216 data->fTexCoords = new SkPoint[data->fVertexCount]; 217 } 218 219 SkPoint pts[kNumPtsCubic]; 220 SkPatchUtils::getBottomCubic(cubics, pts); 221 FwDCubicEvaluator fBottom(pts); 222 SkPatchUtils::getTopCubic(cubics, pts); 223 FwDCubicEvaluator fTop(pts); 224 SkPatchUtils::getLeftCubic(cubics, pts); 225 FwDCubicEvaluator fLeft(pts); 226 SkPatchUtils::getRightCubic(cubics, pts); 227 FwDCubicEvaluator fRight(pts); 228 229 fBottom.restart(lodX); 230 fTop.restart(lodX); 231 232 SkScalar u = 0.0f; 233 int stride = lodY + 1; 234 for (int x = 0; x <= lodX; x++) { 235 SkPoint bottom = fBottom.next(), top = fTop.next(); 236 fLeft.restart(lodY); 237 fRight.restart(lodY); 238 SkScalar v = 0.f; 239 for (int y = 0; y <= lodY; y++) { 240 int dataIndex = x * (lodY + 1) + y; 241 242 SkPoint left = fLeft.next(), right = fRight.next(); 243 244 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(), 245 (1.0f - v) * top.y() + v * bottom.y()); 246 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(), 247 (1.0f - u) * left.y() + u * right.y()); 248 SkPoint s2 = SkPoint::Make( 249 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x() 250 + u * fTop.getCtrlPoints()[3].x()) 251 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x() 252 + u * fBottom.getCtrlPoints()[3].x()), 253 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y() 254 + u * fTop.getCtrlPoints()[3].y()) 255 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y() 256 + u * fBottom.getCtrlPoints()[3].y())); 257 data->fPoints[dataIndex] = s0 + s1 - s2; 258 259 if (colors) { 260 uint8_t a = uint8_t(bilerp(u, v, 261 SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])), 262 SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])), 263 SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])), 264 SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner])))); 265 uint8_t r = uint8_t(bilerp(u, v, 266 SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])), 267 SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])), 268 SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])), 269 SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner])))); 270 uint8_t g = uint8_t(bilerp(u, v, 271 SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])), 272 SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])), 273 SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])), 274 SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner])))); 275 uint8_t b = uint8_t(bilerp(u, v, 276 SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])), 277 SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])), 278 SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])), 279 SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner])))); 280 data->fColors[dataIndex] = SkPackARGB32(a,r,g,b); 281 } 282 283 if (texCoords) { 284 data->fTexCoords[dataIndex] = SkPoint::Make( 285 bilerp(u, v, texCoords[kTopLeft_Corner].x(), 286 texCoords[kTopRight_Corner].x(), 287 texCoords[kBottomLeft_Corner].x(), 288 texCoords[kBottomRight_Corner].x()), 289 bilerp(u, v, texCoords[kTopLeft_Corner].y(), 290 texCoords[kTopRight_Corner].y(), 291 texCoords[kBottomLeft_Corner].y(), 292 texCoords[kBottomRight_Corner].y())); 293 294 } 295 296 if(x < lodX && y < lodY) { 297 int i = 6 * (x * lodY + y); 298 data->fIndices[i] = x * stride + y; 299 data->fIndices[i + 1] = x * stride + 1 + y; 300 data->fIndices[i + 2] = (x + 1) * stride + 1 + y; 301 data->fIndices[i + 3] = data->fIndices[i]; 302 data->fIndices[i + 4] = data->fIndices[i + 2]; 303 data->fIndices[i + 5] = (x + 1) * stride + y; 304 } 305 v = SkScalarClampMax(v + 1.f / lodY, 1); 306 } 307 u = SkScalarClampMax(u + 1.f / lodX, 1); 308 } 309 return true; 310 311 } 312
