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 FwDCubicEvaluator() 34 : fMax(0) 35 , fCurrent(0) 36 , fDivisions(0) { 37 memset(fPoints, 0, 4 * sizeof(SkPoint)); 38 memset(fPoints, 0, 4 * sizeof(SkPoint)); 39 memset(fPoints, 0, 4 * sizeof(SkPoint)); 40 } 41 42 /** 43 * Receives the 4 control points of the cubic bezier. 44 */ 45 FwDCubicEvaluator(SkPoint a, SkPoint b, SkPoint c, SkPoint d) { 46 fPoints[0] = a; 47 fPoints[1] = b; 48 fPoints[2] = c; 49 fPoints[3] = d; 50 51 SkCubicToCoeff(fPoints, fCoefs); 52 53 this->restart(1); 54 } 55 56 explicit FwDCubicEvaluator(const SkPoint points[4]) { 57 memcpy(fPoints, points, 4 * sizeof(SkPoint)); 58 59 SkCubicToCoeff(fPoints, fCoefs); 60 61 this->restart(1); 62 } 63 64 /** 65 * Restarts the forward differences evaluator to the first value of t = 0. 66 */ 67 void restart(int divisions) { 68 fDivisions = divisions; 69 SkScalar h = 1.f / fDivisions; 70 fCurrent = 0; 71 fMax = fDivisions + 1; 72 fFwDiff[0] = fCoefs[3]; 73 SkScalar h2 = h * h; 74 SkScalar h3 = h2 * h; 75 76 fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3 77 fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2 78 fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2); 79 fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch 80 fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h); 81 } 82 83 /** 84 * Check if the evaluator is still within the range of 0<=t<=1 85 */ 86 bool done() const { 87 return fCurrent > fMax; 88 } 89 90 /** 91 * Call next to obtain the SkPoint sampled and move to the next one. 92 */ 93 SkPoint next() { 94 SkPoint point = fFwDiff[0]; 95 fFwDiff[0] += fFwDiff[1]; 96 fFwDiff[1] += fFwDiff[2]; 97 fFwDiff[2] += fFwDiff[3]; 98 fCurrent++; 99 return point; 100 } 101 102 const SkPoint* getCtrlPoints() const { 103 return fPoints; 104 } 105 106 private: 107 int fMax, fCurrent, fDivisions; 108 SkPoint fFwDiff[4], fCoefs[4], fPoints[4]; 109 }; 110 111 //////////////////////////////////////////////////////////////////////////////// 112 113 // size in pixels of each partition per axis, adjust this knob 114 static const int kPartitionSize = 10; 115 116 /** 117 * Calculate the approximate arc length given a bezier curve's control points. 118 */ 119 static SkScalar approx_arc_length(SkPoint* points, int count) { 120 if (count < 2) { 121 return 0; 122 } 123 SkScalar arcLength = 0; 124 for (int i = 0; i < count - 1; i++) { 125 arcLength += SkPoint::Distance(points[i], points[i + 1]); 126 } 127 return arcLength; 128 } 129 130 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01, 131 SkScalar c11) { 132 SkScalar a = c00 * (1.f - tx) + c10 * tx; 133 SkScalar b = c01 * (1.f - tx) + c11 * tx; 134 return a * (1.f - ty) + b * ty; 135 } 136 137 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) { 138 139 // Approximate length of each cubic. 140 SkPoint pts[kNumPtsCubic]; 141 SkPatchUtils::getTopCubic(cubics, pts); 142 matrix->mapPoints(pts, kNumPtsCubic); 143 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic); 144 145 SkPatchUtils::getBottomCubic(cubics, pts); 146 matrix->mapPoints(pts, kNumPtsCubic); 147 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic); 148 149 SkPatchUtils::getLeftCubic(cubics, pts); 150 matrix->mapPoints(pts, kNumPtsCubic); 151 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic); 152 153 SkPatchUtils::getRightCubic(cubics, pts); 154 matrix->mapPoints(pts, kNumPtsCubic); 155 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic); 156 157 // Level of detail per axis, based on the larger side between top and bottom or left and right 158 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize); 159 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize); 160 161 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY)); 162 } 163 164 void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) { 165 points[0] = cubics[kTopP0_CubicCtrlPts]; 166 points[1] = cubics[kTopP1_CubicCtrlPts]; 167 points[2] = cubics[kTopP2_CubicCtrlPts]; 168 points[3] = cubics[kTopP3_CubicCtrlPts]; 169 } 170 171 void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) { 172 points[0] = cubics[kBottomP0_CubicCtrlPts]; 173 points[1] = cubics[kBottomP1_CubicCtrlPts]; 174 points[2] = cubics[kBottomP2_CubicCtrlPts]; 175 points[3] = cubics[kBottomP3_CubicCtrlPts]; 176 } 177 178 void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) { 179 points[0] = cubics[kLeftP0_CubicCtrlPts]; 180 points[1] = cubics[kLeftP1_CubicCtrlPts]; 181 points[2] = cubics[kLeftP2_CubicCtrlPts]; 182 points[3] = cubics[kLeftP3_CubicCtrlPts]; 183 } 184 185 void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) { 186 points[0] = cubics[kRightP0_CubicCtrlPts]; 187 points[1] = cubics[kRightP1_CubicCtrlPts]; 188 points[2] = cubics[kRightP2_CubicCtrlPts]; 189 points[3] = cubics[kRightP3_CubicCtrlPts]; 190 } 191 192 bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12], 193 const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) { 194 if (lodX < 1 || lodY < 1 || NULL == cubics || NULL == data) { 195 return false; 196 } 197 198 // check for overflow in multiplication 199 const int64_t lodX64 = (lodX + 1), 200 lodY64 = (lodY + 1), 201 mult64 = lodX64 * lodY64; 202 if (mult64 > SK_MaxS32) { 203 return false; 204 } 205 data->fVertexCount = SkToS32(mult64); 206 207 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate 208 // more than 60000 indices. To accomplish that we resize the LOD and vertex count 209 if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) { 210 SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY); 211 SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY); 212 213 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of 214 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6) 215 lodX = static_cast<int>(weightX * 200); 216 lodY = static_cast<int>(weightY * 200); 217 data->fVertexCount = (lodX + 1) * (lodY + 1); 218 } 219 data->fIndexCount = lodX * lodY * 6; 220 221 data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount); 222 data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount); 223 224 // if colors is not null then create array for colors 225 SkPMColor colorsPM[kNumCorners]; 226 if (colors) { 227 // premultiply colors to avoid color bleeding. 228 for (int i = 0; i < kNumCorners; i++) { 229 colorsPM[i] = SkPreMultiplyColor(colors[i]); 230 } 231 data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount); 232 } 233 234 // if texture coordinates are not null then create array for them 235 if (texCoords) { 236 data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount); 237 } 238 239 SkPoint pts[kNumPtsCubic]; 240 SkPatchUtils::getBottomCubic(cubics, pts); 241 FwDCubicEvaluator fBottom(pts); 242 SkPatchUtils::getTopCubic(cubics, pts); 243 FwDCubicEvaluator fTop(pts); 244 SkPatchUtils::getLeftCubic(cubics, pts); 245 FwDCubicEvaluator fLeft(pts); 246 SkPatchUtils::getRightCubic(cubics, pts); 247 FwDCubicEvaluator fRight(pts); 248 249 fBottom.restart(lodX); 250 fTop.restart(lodX); 251 252 SkScalar u = 0.0f; 253 int stride = lodY + 1; 254 for (int x = 0; x <= lodX; x++) { 255 SkPoint bottom = fBottom.next(), top = fTop.next(); 256 fLeft.restart(lodY); 257 fRight.restart(lodY); 258 SkScalar v = 0.f; 259 for (int y = 0; y <= lodY; y++) { 260 int dataIndex = x * (lodY + 1) + y; 261 262 SkPoint left = fLeft.next(), right = fRight.next(); 263 264 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(), 265 (1.0f - v) * top.y() + v * bottom.y()); 266 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(), 267 (1.0f - u) * left.y() + u * right.y()); 268 SkPoint s2 = SkPoint::Make( 269 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x() 270 + u * fTop.getCtrlPoints()[3].x()) 271 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x() 272 + u * fBottom.getCtrlPoints()[3].x()), 273 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y() 274 + u * fTop.getCtrlPoints()[3].y()) 275 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y() 276 + u * fBottom.getCtrlPoints()[3].y())); 277 data->fPoints[dataIndex] = s0 + s1 - s2; 278 279 if (colors) { 280 uint8_t a = uint8_t(bilerp(u, v, 281 SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])), 282 SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])), 283 SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])), 284 SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner])))); 285 uint8_t r = uint8_t(bilerp(u, v, 286 SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])), 287 SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])), 288 SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])), 289 SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner])))); 290 uint8_t g = uint8_t(bilerp(u, v, 291 SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])), 292 SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])), 293 SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])), 294 SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner])))); 295 uint8_t b = uint8_t(bilerp(u, v, 296 SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])), 297 SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])), 298 SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])), 299 SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner])))); 300 data->fColors[dataIndex] = SkPackARGB32(a,r,g,b); 301 } 302 303 if (texCoords) { 304 data->fTexCoords[dataIndex] = SkPoint::Make( 305 bilerp(u, v, texCoords[kTopLeft_Corner].x(), 306 texCoords[kTopRight_Corner].x(), 307 texCoords[kBottomLeft_Corner].x(), 308 texCoords[kBottomRight_Corner].x()), 309 bilerp(u, v, texCoords[kTopLeft_Corner].y(), 310 texCoords[kTopRight_Corner].y(), 311 texCoords[kBottomLeft_Corner].y(), 312 texCoords[kBottomRight_Corner].y())); 313 314 } 315 316 if(x < lodX && y < lodY) { 317 int i = 6 * (x * lodY + y); 318 data->fIndices[i] = x * stride + y; 319 data->fIndices[i + 1] = x * stride + 1 + y; 320 data->fIndices[i + 2] = (x + 1) * stride + 1 + y; 321 data->fIndices[i + 3] = data->fIndices[i]; 322 data->fIndices[i + 4] = data->fIndices[i + 2]; 323 data->fIndices[i + 5] = (x + 1) * stride + y; 324 } 325 v = SkScalarClampMax(v + 1.f / lodY, 1); 326 } 327 u = SkScalarClampMax(u + 1.f / lodX, 1); 328 } 329 return true; 330 331 } 332
