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 "SkColorData.h" 11 #include "SkGeometry.h" 12 #include "SkPM4f.h" 13 14 namespace { 15 enum CubicCtrlPts { 16 kTopP0_CubicCtrlPts = 0, 17 kTopP1_CubicCtrlPts = 1, 18 kTopP2_CubicCtrlPts = 2, 19 kTopP3_CubicCtrlPts = 3, 20 21 kRightP0_CubicCtrlPts = 3, 22 kRightP1_CubicCtrlPts = 4, 23 kRightP2_CubicCtrlPts = 5, 24 kRightP3_CubicCtrlPts = 6, 25 26 kBottomP0_CubicCtrlPts = 9, 27 kBottomP1_CubicCtrlPts = 8, 28 kBottomP2_CubicCtrlPts = 7, 29 kBottomP3_CubicCtrlPts = 6, 30 31 kLeftP0_CubicCtrlPts = 0, 32 kLeftP1_CubicCtrlPts = 11, 33 kLeftP2_CubicCtrlPts = 10, 34 kLeftP3_CubicCtrlPts = 9, 35 }; 36 37 // Enum for corner also clockwise. 38 enum Corner { 39 kTopLeft_Corner = 0, 40 kTopRight_Corner, 41 kBottomRight_Corner, 42 kBottomLeft_Corner 43 }; 44 } 45 46 /** 47 * Evaluator to sample the values of a cubic bezier using forward differences. 48 * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only 49 * adding precalculated values. 50 * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h 51 * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first 52 * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After 53 * obtaining this value (mh) we could just add this constant step to our first sampled point 54 * to compute the next one. 55 * 56 * For the cubic case the first difference gives as a result a quadratic polynomial to which we can 57 * apply again forward differences and get linear function to which we can apply again forward 58 * differences to get a constant difference. This is why we keep an array of size 4, the 0th 59 * position keeps the sampled value while the next ones keep the quadratic, linear and constant 60 * difference values. 61 */ 62 63 class FwDCubicEvaluator { 64 65 public: 66 67 /** 68 * Receives the 4 control points of the cubic bezier. 69 */ 70 71 explicit FwDCubicEvaluator(const SkPoint points[4]) 72 : fCoefs(points) { 73 memcpy(fPoints, points, 4 * sizeof(SkPoint)); 74 75 this->restart(1); 76 } 77 78 /** 79 * Restarts the forward differences evaluator to the first value of t = 0. 80 */ 81 void restart(int divisions) { 82 fDivisions = divisions; 83 fCurrent = 0; 84 fMax = fDivisions + 1; 85 Sk2s h = Sk2s(1.f / fDivisions); 86 Sk2s h2 = h * h; 87 Sk2s h3 = h2 * h; 88 Sk2s fwDiff3 = Sk2s(6) * fCoefs.fA * h3; 89 fFwDiff[3] = to_point(fwDiff3); 90 fFwDiff[2] = to_point(fwDiff3 + times_2(fCoefs.fB) * h2); 91 fFwDiff[1] = to_point(fCoefs.fA * h3 + fCoefs.fB * h2 + fCoefs.fC * h); 92 fFwDiff[0] = to_point(fCoefs.fD); 93 } 94 95 /** 96 * Check if the evaluator is still within the range of 0<=t<=1 97 */ 98 bool done() const { 99 return fCurrent > fMax; 100 } 101 102 /** 103 * Call next to obtain the SkPoint sampled and move to the next one. 104 */ 105 SkPoint next() { 106 SkPoint point = fFwDiff[0]; 107 fFwDiff[0] += fFwDiff[1]; 108 fFwDiff[1] += fFwDiff[2]; 109 fFwDiff[2] += fFwDiff[3]; 110 fCurrent++; 111 return point; 112 } 113 114 const SkPoint* getCtrlPoints() const { 115 return fPoints; 116 } 117 118 private: 119 SkCubicCoeff fCoefs; 120 int fMax, fCurrent, fDivisions; 121 SkPoint fFwDiff[4], fPoints[4]; 122 }; 123 124 //////////////////////////////////////////////////////////////////////////////// 125 126 // size in pixels of each partition per axis, adjust this knob 127 static const int kPartitionSize = 10; 128 129 /** 130 * Calculate the approximate arc length given a bezier curve's control points. 131 */ 132 static SkScalar approx_arc_length(SkPoint* points, int count) { 133 if (count < 2) { 134 return 0; 135 } 136 SkScalar arcLength = 0; 137 for (int i = 0; i < count - 1; i++) { 138 arcLength += SkPoint::Distance(points[i], points[i + 1]); 139 } 140 return arcLength; 141 } 142 143 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01, 144 SkScalar c11) { 145 SkScalar a = c00 * (1.f - tx) + c10 * tx; 146 SkScalar b = c01 * (1.f - tx) + c11 * tx; 147 return a * (1.f - ty) + b * ty; 148 } 149 150 static Sk4f bilerp(SkScalar tx, SkScalar ty, 151 const Sk4f& c00, const Sk4f& c10, const Sk4f& c01, const Sk4f& c11) { 152 Sk4f a = c00 * (1.f - tx) + c10 * tx; 153 Sk4f b = c01 * (1.f - tx) + c11 * tx; 154 return a * (1.f - ty) + b * ty; 155 } 156 157 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) { 158 159 // Approximate length of each cubic. 160 SkPoint pts[kNumPtsCubic]; 161 SkPatchUtils::GetTopCubic(cubics, pts); 162 matrix->mapPoints(pts, kNumPtsCubic); 163 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic); 164 165 SkPatchUtils::GetBottomCubic(cubics, pts); 166 matrix->mapPoints(pts, kNumPtsCubic); 167 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic); 168 169 SkPatchUtils::GetLeftCubic(cubics, pts); 170 matrix->mapPoints(pts, kNumPtsCubic); 171 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic); 172 173 SkPatchUtils::GetRightCubic(cubics, pts); 174 matrix->mapPoints(pts, kNumPtsCubic); 175 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic); 176 177 // Level of detail per axis, based on the larger side between top and bottom or left and right 178 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize); 179 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize); 180 181 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY)); 182 } 183 184 void SkPatchUtils::GetTopCubic(const SkPoint cubics[12], SkPoint points[4]) { 185 points[0] = cubics[kTopP0_CubicCtrlPts]; 186 points[1] = cubics[kTopP1_CubicCtrlPts]; 187 points[2] = cubics[kTopP2_CubicCtrlPts]; 188 points[3] = cubics[kTopP3_CubicCtrlPts]; 189 } 190 191 void SkPatchUtils::GetBottomCubic(const SkPoint cubics[12], SkPoint points[4]) { 192 points[0] = cubics[kBottomP0_CubicCtrlPts]; 193 points[1] = cubics[kBottomP1_CubicCtrlPts]; 194 points[2] = cubics[kBottomP2_CubicCtrlPts]; 195 points[3] = cubics[kBottomP3_CubicCtrlPts]; 196 } 197 198 void SkPatchUtils::GetLeftCubic(const SkPoint cubics[12], SkPoint points[4]) { 199 points[0] = cubics[kLeftP0_CubicCtrlPts]; 200 points[1] = cubics[kLeftP1_CubicCtrlPts]; 201 points[2] = cubics[kLeftP2_CubicCtrlPts]; 202 points[3] = cubics[kLeftP3_CubicCtrlPts]; 203 } 204 205 void SkPatchUtils::GetRightCubic(const SkPoint cubics[12], SkPoint points[4]) { 206 points[0] = cubics[kRightP0_CubicCtrlPts]; 207 points[1] = cubics[kRightP1_CubicCtrlPts]; 208 points[2] = cubics[kRightP2_CubicCtrlPts]; 209 points[3] = cubics[kRightP3_CubicCtrlPts]; 210 } 211 212 #include "SkPM4fPriv.h" 213 #include "SkColorSpaceXform.h" 214 215 struct SkRGBAf { 216 float fVec[4]; 217 218 static SkRGBAf From4f(const Sk4f& x) { 219 SkRGBAf c; 220 x.store(c.fVec); 221 return c; 222 } 223 224 static SkRGBAf FromBGRA32(SkColor c) { 225 return From4f(swizzle_rb(SkNx_cast<float>(Sk4b::Load(&c)) * (1/255.0f))); 226 } 227 228 Sk4f to4f() const { 229 return Sk4f::Load(fVec); 230 } 231 232 SkColor toBGRA32() const { 233 SkColor color; 234 SkNx_cast<uint8_t>(swizzle_rb(this->to4f()) * Sk4f(255) + Sk4f(0.5f)).store(&color); 235 return color; 236 } 237 238 SkRGBAf premul() const { 239 float a = fVec[3]; 240 return From4f(this->to4f() * Sk4f(a, a, a, 1)); 241 } 242 243 SkRGBAf unpremul() const { 244 float a = fVec[3]; 245 float inv = a ? 1/a : 0; 246 return From4f(this->to4f() * Sk4f(inv, inv, inv, 1)); 247 } 248 }; 249 250 static void skcolor_to_linear(SkRGBAf dst[], const SkColor src[], int count, SkColorSpace* cs, 251 bool doPremul) { 252 if (cs) { 253 auto srcCS = SkColorSpace::MakeSRGB(); 254 auto dstCS = cs->makeLinearGamma(); 255 auto op = doPremul ? SkColorSpaceXform::kPremul_AlphaOp 256 : SkColorSpaceXform::kPreserve_AlphaOp; 257 SkColorSpaceXform::Apply(dstCS.get(), SkColorSpaceXform::kRGBA_F32_ColorFormat, dst, 258 srcCS.get(), SkColorSpaceXform::kBGRA_8888_ColorFormat, src, 259 count, op); 260 } else { 261 for (int i = 0; i < count; ++i) { 262 dst[i] = SkRGBAf::FromBGRA32(src[i]); 263 if (doPremul) { 264 dst[i] = dst[i].premul(); 265 } 266 } 267 } 268 } 269 270 static void linear_to_skcolor(SkColor dst[], const SkRGBAf src[], int count, SkColorSpace* cs) { 271 if (cs) { 272 auto srcCS = cs->makeLinearGamma(); 273 auto dstCS = SkColorSpace::MakeSRGB(); 274 SkColorSpaceXform::Apply(dstCS.get(), SkColorSpaceXform::kBGRA_8888_ColorFormat, dst, 275 srcCS.get(), SkColorSpaceXform::kRGBA_F32_ColorFormat, src, 276 count, SkColorSpaceXform::kPreserve_AlphaOp); 277 } else { 278 for (int i = 0; i < count; ++i) { 279 dst[i] = src[i].toBGRA32(); 280 } 281 } 282 } 283 284 static void unpremul(SkRGBAf array[], int count) { 285 for (int i = 0; i < count; ++i) { 286 array[i] = array[i].unpremul(); 287 } 288 } 289 290 sk_sp<SkVertices> SkPatchUtils::MakeVertices(const SkPoint cubics[12], const SkColor srcColors[4], 291 const SkPoint srcTexCoords[4], int lodX, int lodY, 292 bool interpColorsLinearly) { 293 if (lodX < 1 || lodY < 1 || nullptr == cubics) { 294 return nullptr; 295 } 296 297 // check for overflow in multiplication 298 const int64_t lodX64 = (lodX + 1), 299 lodY64 = (lodY + 1), 300 mult64 = lodX64 * lodY64; 301 if (mult64 > SK_MaxS32) { 302 return nullptr; 303 } 304 305 int vertexCount = SkToS32(mult64); 306 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate 307 // more than 60000 indices. To accomplish that we resize the LOD and vertex count 308 if (vertexCount > 10000 || lodX > 200 || lodY > 200) { 309 float weightX = static_cast<float>(lodX) / (lodX + lodY); 310 float weightY = static_cast<float>(lodY) / (lodX + lodY); 311 312 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of 313 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6) 314 lodX = static_cast<int>(weightX * 200); 315 lodY = static_cast<int>(weightY * 200); 316 vertexCount = (lodX + 1) * (lodY + 1); 317 } 318 const int indexCount = lodX * lodY * 6; 319 uint32_t flags = 0; 320 if (srcTexCoords) { 321 flags |= SkVertices::kHasTexCoords_BuilderFlag; 322 } 323 if (srcColors) { 324 flags |= SkVertices::kHasColors_BuilderFlag; 325 } 326 327 SkSTArenaAlloc<2048> alloc; 328 SkRGBAf* cornerColors = srcColors ? alloc.makeArray<SkRGBAf>(4) : nullptr; 329 SkRGBAf* tmpColors = srcColors ? alloc.makeArray<SkRGBAf>(vertexCount) : nullptr; 330 auto convertCS = interpColorsLinearly ? SkColorSpace::MakeSRGB() : nullptr; 331 332 SkVertices::Builder builder(SkVertices::kTriangles_VertexMode, vertexCount, indexCount, flags); 333 SkPoint* pos = builder.positions(); 334 SkPoint* texs = builder.texCoords(); 335 uint16_t* indices = builder.indices(); 336 bool is_opaque = false; 337 338 /* 339 * 1. Should we offer this as a runtime choice, as we do in gradients? 340 * 2. Since drawing the vertices wants premul, shoudl we extend SkVertices to store 341 * premul colors (as floats, w/ a colorspace)? 342 */ 343 bool doPremul = true; 344 if (cornerColors) { 345 SkColor c = ~0; 346 for (int i = 0; i < kNumCorners; i++) { 347 c &= srcColors[i]; 348 } 349 is_opaque = (SkColorGetA(c) == 0xFF); 350 if (is_opaque) { 351 doPremul = false; // no need 352 } 353 354 skcolor_to_linear(cornerColors, srcColors, kNumCorners, convertCS.get(), doPremul); 355 } 356 357 SkPoint pts[kNumPtsCubic]; 358 SkPatchUtils::GetBottomCubic(cubics, pts); 359 FwDCubicEvaluator fBottom(pts); 360 SkPatchUtils::GetTopCubic(cubics, pts); 361 FwDCubicEvaluator fTop(pts); 362 SkPatchUtils::GetLeftCubic(cubics, pts); 363 FwDCubicEvaluator fLeft(pts); 364 SkPatchUtils::GetRightCubic(cubics, pts); 365 FwDCubicEvaluator fRight(pts); 366 367 fBottom.restart(lodX); 368 fTop.restart(lodX); 369 370 SkScalar u = 0.0f; 371 int stride = lodY + 1; 372 for (int x = 0; x <= lodX; x++) { 373 SkPoint bottom = fBottom.next(), top = fTop.next(); 374 fLeft.restart(lodY); 375 fRight.restart(lodY); 376 SkScalar v = 0.f; 377 for (int y = 0; y <= lodY; y++) { 378 int dataIndex = x * (lodY + 1) + y; 379 380 SkPoint left = fLeft.next(), right = fRight.next(); 381 382 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(), 383 (1.0f - v) * top.y() + v * bottom.y()); 384 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(), 385 (1.0f - u) * left.y() + u * right.y()); 386 SkPoint s2 = SkPoint::Make( 387 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x() 388 + u * fTop.getCtrlPoints()[3].x()) 389 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x() 390 + u * fBottom.getCtrlPoints()[3].x()), 391 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y() 392 + u * fTop.getCtrlPoints()[3].y()) 393 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y() 394 + u * fBottom.getCtrlPoints()[3].y())); 395 pos[dataIndex] = s0 + s1 - s2; 396 397 if (cornerColors) { 398 bilerp(u, v, cornerColors[kTopLeft_Corner].to4f(), 399 cornerColors[kTopRight_Corner].to4f(), 400 cornerColors[kBottomLeft_Corner].to4f(), 401 cornerColors[kBottomRight_Corner].to4f()).store(tmpColors[dataIndex].fVec); 402 if (is_opaque) { 403 tmpColors[dataIndex].fVec[3] = 1; 404 } 405 } 406 407 if (texs) { 408 texs[dataIndex] = SkPoint::Make(bilerp(u, v, srcTexCoords[kTopLeft_Corner].x(), 409 srcTexCoords[kTopRight_Corner].x(), 410 srcTexCoords[kBottomLeft_Corner].x(), 411 srcTexCoords[kBottomRight_Corner].x()), 412 bilerp(u, v, srcTexCoords[kTopLeft_Corner].y(), 413 srcTexCoords[kTopRight_Corner].y(), 414 srcTexCoords[kBottomLeft_Corner].y(), 415 srcTexCoords[kBottomRight_Corner].y())); 416 417 } 418 419 if(x < lodX && y < lodY) { 420 int i = 6 * (x * lodY + y); 421 indices[i] = x * stride + y; 422 indices[i + 1] = x * stride + 1 + y; 423 indices[i + 2] = (x + 1) * stride + 1 + y; 424 indices[i + 3] = indices[i]; 425 indices[i + 4] = indices[i + 2]; 426 indices[i + 5] = (x + 1) * stride + y; 427 } 428 v = SkScalarClampMax(v + 1.f / lodY, 1); 429 } 430 u = SkScalarClampMax(u + 1.f / lodX, 1); 431 } 432 433 if (tmpColors) { 434 if (doPremul) { 435 unpremul(tmpColors, vertexCount); 436 } 437 linear_to_skcolor(builder.colors(), tmpColors, vertexCount, convertCS.get()); 438 } 439 return builder.detach(); 440 } 441