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 SkScalar cx[4], cy[4]; 52 SkGetCubicCoeff(fPoints, cx, cy); 53 fCoefs[0].set(cx[0], cy[0]); 54 fCoefs[1].set(cx[1], cy[1]); 55 fCoefs[2].set(cx[2], cy[2]); 56 fCoefs[3].set(cx[3], cy[3]); 57 58 this->restart(1); 59 } 60 61 explicit FwDCubicEvaluator(const SkPoint points[4]) { 62 memcpy(fPoints, points, 4 * sizeof(SkPoint)); 63 64 SkScalar cx[4], cy[4]; 65 SkGetCubicCoeff(fPoints, cx, cy); 66 fCoefs[0].set(cx[0], cy[0]); 67 fCoefs[1].set(cx[1], cy[1]); 68 fCoefs[2].set(cx[2], cy[2]); 69 fCoefs[3].set(cx[3], cy[3]); 70 71 this->restart(1); 72 } 73 74 /** 75 * Restarts the forward differences evaluator to the first value of t = 0. 76 */ 77 void restart(int divisions) { 78 fDivisions = divisions; 79 SkScalar h = 1.f / fDivisions; 80 fCurrent = 0; 81 fMax = fDivisions + 1; 82 fFwDiff[0] = fCoefs[3]; 83 SkScalar h2 = h * h; 84 SkScalar h3 = h2 * h; 85 86 fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3 87 fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2 88 fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2); 89 fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch 90 fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h); 91 } 92 93 /** 94 * Check if the evaluator is still within the range of 0<=t<=1 95 */ 96 bool done() const { 97 return fCurrent > fMax; 98 } 99 100 /** 101 * Call next to obtain the SkPoint sampled and move to the next one. 102 */ 103 SkPoint next() { 104 SkPoint point = fFwDiff[0]; 105 fFwDiff[0] += fFwDiff[1]; 106 fFwDiff[1] += fFwDiff[2]; 107 fFwDiff[2] += fFwDiff[3]; 108 fCurrent++; 109 return point; 110 } 111 112 const SkPoint* getCtrlPoints() const { 113 return fPoints; 114 } 115 116 private: 117 int fMax, fCurrent, fDivisions; 118 SkPoint fFwDiff[4], fCoefs[4], fPoints[4]; 119 }; 120 121 //////////////////////////////////////////////////////////////////////////////// 122 123 // size in pixels of each partition per axis, adjust this knob 124 static const int kPartitionSize = 10; 125 126 /** 127 * Calculate the approximate arc length given a bezier curve's control points. 128 */ 129 static SkScalar approx_arc_length(SkPoint* points, int count) { 130 if (count < 2) { 131 return 0; 132 } 133 SkScalar arcLength = 0; 134 for (int i = 0; i < count - 1; i++) { 135 arcLength += SkPoint::Distance(points[i], points[i + 1]); 136 } 137 return arcLength; 138 } 139 140 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01, 141 SkScalar c11) { 142 SkScalar a = c00 * (1.f - tx) + c10 * tx; 143 SkScalar b = c01 * (1.f - tx) + c11 * tx; 144 return a * (1.f - ty) + b * ty; 145 } 146 147 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) { 148 149 // Approximate length of each cubic. 150 SkPoint pts[kNumPtsCubic]; 151 SkPatchUtils::getTopCubic(cubics, pts); 152 matrix->mapPoints(pts, kNumPtsCubic); 153 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic); 154 155 SkPatchUtils::getBottomCubic(cubics, pts); 156 matrix->mapPoints(pts, kNumPtsCubic); 157 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic); 158 159 SkPatchUtils::getLeftCubic(cubics, pts); 160 matrix->mapPoints(pts, kNumPtsCubic); 161 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic); 162 163 SkPatchUtils::getRightCubic(cubics, pts); 164 matrix->mapPoints(pts, kNumPtsCubic); 165 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic); 166 167 // Level of detail per axis, based on the larger side between top and bottom or left and right 168 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize); 169 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize); 170 171 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY)); 172 } 173 174 void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) { 175 points[0] = cubics[kTopP0_CubicCtrlPts]; 176 points[1] = cubics[kTopP1_CubicCtrlPts]; 177 points[2] = cubics[kTopP2_CubicCtrlPts]; 178 points[3] = cubics[kTopP3_CubicCtrlPts]; 179 } 180 181 void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) { 182 points[0] = cubics[kBottomP0_CubicCtrlPts]; 183 points[1] = cubics[kBottomP1_CubicCtrlPts]; 184 points[2] = cubics[kBottomP2_CubicCtrlPts]; 185 points[3] = cubics[kBottomP3_CubicCtrlPts]; 186 } 187 188 void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) { 189 points[0] = cubics[kLeftP0_CubicCtrlPts]; 190 points[1] = cubics[kLeftP1_CubicCtrlPts]; 191 points[2] = cubics[kLeftP2_CubicCtrlPts]; 192 points[3] = cubics[kLeftP3_CubicCtrlPts]; 193 } 194 195 void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) { 196 points[0] = cubics[kRightP0_CubicCtrlPts]; 197 points[1] = cubics[kRightP1_CubicCtrlPts]; 198 points[2] = cubics[kRightP2_CubicCtrlPts]; 199 points[3] = cubics[kRightP3_CubicCtrlPts]; 200 } 201 202 bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12], 203 const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) { 204 if (lodX < 1 || lodY < 1 || NULL == cubics || NULL == data) { 205 return false; 206 } 207 208 // check for overflow in multiplication 209 const int64_t lodX64 = (lodX + 1), 210 lodY64 = (lodY + 1), 211 mult64 = lodX64 * lodY64; 212 if (mult64 > SK_MaxS32) { 213 return false; 214 } 215 data->fVertexCount = SkToS32(mult64); 216 217 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate 218 // more than 60000 indices. To accomplish that we resize the LOD and vertex count 219 if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) { 220 SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY); 221 SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY); 222 223 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of 224 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6) 225 lodX = static_cast<int>(weightX * 200); 226 lodY = static_cast<int>(weightY * 200); 227 data->fVertexCount = (lodX + 1) * (lodY + 1); 228 } 229 data->fIndexCount = lodX * lodY * 6; 230 231 data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount); 232 data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount); 233 234 // if colors is not null then create array for colors 235 SkPMColor colorsPM[kNumCorners]; 236 if (colors) { 237 // premultiply colors to avoid color bleeding. 238 for (int i = 0; i < kNumCorners; i++) { 239 colorsPM[i] = SkPreMultiplyColor(colors[i]); 240 } 241 data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount); 242 } 243 244 // if texture coordinates are not null then create array for them 245 if (texCoords) { 246 data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount); 247 } 248 249 SkPoint pts[kNumPtsCubic]; 250 SkPatchUtils::getBottomCubic(cubics, pts); 251 FwDCubicEvaluator fBottom(pts); 252 SkPatchUtils::getTopCubic(cubics, pts); 253 FwDCubicEvaluator fTop(pts); 254 SkPatchUtils::getLeftCubic(cubics, pts); 255 FwDCubicEvaluator fLeft(pts); 256 SkPatchUtils::getRightCubic(cubics, pts); 257 FwDCubicEvaluator fRight(pts); 258 259 fBottom.restart(lodX); 260 fTop.restart(lodX); 261 262 SkScalar u = 0.0f; 263 int stride = lodY + 1; 264 for (int x = 0; x <= lodX; x++) { 265 SkPoint bottom = fBottom.next(), top = fTop.next(); 266 fLeft.restart(lodY); 267 fRight.restart(lodY); 268 SkScalar v = 0.f; 269 for (int y = 0; y <= lodY; y++) { 270 int dataIndex = x * (lodY + 1) + y; 271 272 SkPoint left = fLeft.next(), right = fRight.next(); 273 274 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(), 275 (1.0f - v) * top.y() + v * bottom.y()); 276 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(), 277 (1.0f - u) * left.y() + u * right.y()); 278 SkPoint s2 = SkPoint::Make( 279 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x() 280 + u * fTop.getCtrlPoints()[3].x()) 281 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x() 282 + u * fBottom.getCtrlPoints()[3].x()), 283 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y() 284 + u * fTop.getCtrlPoints()[3].y()) 285 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y() 286 + u * fBottom.getCtrlPoints()[3].y())); 287 data->fPoints[dataIndex] = s0 + s1 - s2; 288 289 if (colors) { 290 uint8_t a = uint8_t(bilerp(u, v, 291 SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])), 292 SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])), 293 SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])), 294 SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner])))); 295 uint8_t r = uint8_t(bilerp(u, v, 296 SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])), 297 SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])), 298 SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])), 299 SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner])))); 300 uint8_t g = uint8_t(bilerp(u, v, 301 SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])), 302 SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])), 303 SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])), 304 SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner])))); 305 uint8_t b = uint8_t(bilerp(u, v, 306 SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])), 307 SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])), 308 SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])), 309 SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner])))); 310 data->fColors[dataIndex] = SkPackARGB32(a,r,g,b); 311 } 312 313 if (texCoords) { 314 data->fTexCoords[dataIndex] = SkPoint::Make( 315 bilerp(u, v, texCoords[kTopLeft_Corner].x(), 316 texCoords[kTopRight_Corner].x(), 317 texCoords[kBottomLeft_Corner].x(), 318 texCoords[kBottomRight_Corner].x()), 319 bilerp(u, v, texCoords[kTopLeft_Corner].y(), 320 texCoords[kTopRight_Corner].y(), 321 texCoords[kBottomLeft_Corner].y(), 322 texCoords[kBottomRight_Corner].y())); 323 324 } 325 326 if(x < lodX && y < lodY) { 327 int i = 6 * (x * lodY + y); 328 data->fIndices[i] = x * stride + y; 329 data->fIndices[i + 1] = x * stride + 1 + y; 330 data->fIndices[i + 2] = (x + 1) * stride + 1 + y; 331 data->fIndices[i + 3] = data->fIndices[i]; 332 data->fIndices[i + 4] = data->fIndices[i + 2]; 333 data->fIndices[i + 5] = (x + 1) * stride + y; 334 } 335 v = SkScalarClampMax(v + 1.f / lodY, 1); 336 } 337 u = SkScalarClampMax(u + 1.f / lodX, 1); 338 } 339 return true; 340 341 } 342
