1 2 /* 3 * Copyright 2011 Google Inc. 4 * 5 * Use of this source code is governed by a BSD-style license that can be 6 * found in the LICENSE file. 7 */ 8 9 10 #include "GrPathUtils.h" 11 #include "GrPoint.h" 12 #include "SkGeometry.h" 13 14 SkScalar GrPathUtils::scaleToleranceToSrc(SkScalar devTol, 15 const SkMatrix& viewM, 16 const GrRect& pathBounds) { 17 // In order to tesselate the path we get a bound on how much the matrix can 18 // stretch when mapping to screen coordinates. 19 SkScalar stretch = viewM.getMaxStretch(); 20 SkScalar srcTol = devTol; 21 22 if (stretch < 0) { 23 // take worst case mapRadius amoung four corners. 24 // (less than perfect) 25 for (int i = 0; i < 4; ++i) { 26 SkMatrix mat; 27 mat.setTranslate((i % 2) ? pathBounds.fLeft : pathBounds.fRight, 28 (i < 2) ? pathBounds.fTop : pathBounds.fBottom); 29 mat.postConcat(viewM); 30 stretch = SkMaxScalar(stretch, mat.mapRadius(SK_Scalar1)); 31 } 32 } 33 srcTol = SkScalarDiv(srcTol, stretch); 34 return srcTol; 35 } 36 37 static const int MAX_POINTS_PER_CURVE = 1 << 10; 38 static const SkScalar gMinCurveTol = SkFloatToScalar(0.0001f); 39 40 uint32_t GrPathUtils::quadraticPointCount(const GrPoint points[], 41 SkScalar tol) { 42 if (tol < gMinCurveTol) { 43 tol = gMinCurveTol; 44 } 45 GrAssert(tol > 0); 46 47 SkScalar d = points[1].distanceToLineSegmentBetween(points[0], points[2]); 48 if (d <= tol) { 49 return 1; 50 } else { 51 // Each time we subdivide, d should be cut in 4. So we need to 52 // subdivide x = log4(d/tol) times. x subdivisions creates 2^(x) 53 // points. 54 // 2^(log4(x)) = sqrt(x); 55 int temp = SkScalarCeil(SkScalarSqrt(SkScalarDiv(d, tol))); 56 int pow2 = GrNextPow2(temp); 57 // Because of NaNs & INFs we can wind up with a degenerate temp 58 // such that pow2 comes out negative. Also, our point generator 59 // will always output at least one pt. 60 if (pow2 < 1) { 61 pow2 = 1; 62 } 63 return GrMin(pow2, MAX_POINTS_PER_CURVE); 64 } 65 } 66 67 uint32_t GrPathUtils::generateQuadraticPoints(const GrPoint& p0, 68 const GrPoint& p1, 69 const GrPoint& p2, 70 SkScalar tolSqd, 71 GrPoint** points, 72 uint32_t pointsLeft) { 73 if (pointsLeft < 2 || 74 (p1.distanceToLineSegmentBetweenSqd(p0, p2)) < tolSqd) { 75 (*points)[0] = p2; 76 *points += 1; 77 return 1; 78 } 79 80 GrPoint q[] = { 81 { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, 82 { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, 83 }; 84 GrPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }; 85 86 pointsLeft >>= 1; 87 uint32_t a = generateQuadraticPoints(p0, q[0], r, tolSqd, points, pointsLeft); 88 uint32_t b = generateQuadraticPoints(r, q[1], p2, tolSqd, points, pointsLeft); 89 return a + b; 90 } 91 92 uint32_t GrPathUtils::cubicPointCount(const GrPoint points[], 93 SkScalar tol) { 94 if (tol < gMinCurveTol) { 95 tol = gMinCurveTol; 96 } 97 GrAssert(tol > 0); 98 99 SkScalar d = GrMax( 100 points[1].distanceToLineSegmentBetweenSqd(points[0], points[3]), 101 points[2].distanceToLineSegmentBetweenSqd(points[0], points[3])); 102 d = SkScalarSqrt(d); 103 if (d <= tol) { 104 return 1; 105 } else { 106 int temp = SkScalarCeil(SkScalarSqrt(SkScalarDiv(d, tol))); 107 int pow2 = GrNextPow2(temp); 108 // Because of NaNs & INFs we can wind up with a degenerate temp 109 // such that pow2 comes out negative. Also, our point generator 110 // will always output at least one pt. 111 if (pow2 < 1) { 112 pow2 = 1; 113 } 114 return GrMin(pow2, MAX_POINTS_PER_CURVE); 115 } 116 } 117 118 uint32_t GrPathUtils::generateCubicPoints(const GrPoint& p0, 119 const GrPoint& p1, 120 const GrPoint& p2, 121 const GrPoint& p3, 122 SkScalar tolSqd, 123 GrPoint** points, 124 uint32_t pointsLeft) { 125 if (pointsLeft < 2 || 126 (p1.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd && 127 p2.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd)) { 128 (*points)[0] = p3; 129 *points += 1; 130 return 1; 131 } 132 GrPoint q[] = { 133 { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, 134 { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, 135 { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) } 136 }; 137 GrPoint r[] = { 138 { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }, 139 { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) } 140 }; 141 GrPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) }; 142 pointsLeft >>= 1; 143 uint32_t a = generateCubicPoints(p0, q[0], r[0], s, tolSqd, points, pointsLeft); 144 uint32_t b = generateCubicPoints(s, r[1], q[2], p3, tolSqd, points, pointsLeft); 145 return a + b; 146 } 147 148 int GrPathUtils::worstCasePointCount(const SkPath& path, int* subpaths, 149 SkScalar tol) { 150 if (tol < gMinCurveTol) { 151 tol = gMinCurveTol; 152 } 153 GrAssert(tol > 0); 154 155 int pointCount = 0; 156 *subpaths = 1; 157 158 bool first = true; 159 160 SkPath::Iter iter(path, false); 161 GrPathCmd cmd; 162 163 GrPoint pts[4]; 164 while ((cmd = (GrPathCmd)iter.next(pts)) != kEnd_PathCmd) { 165 166 switch (cmd) { 167 case kLine_PathCmd: 168 pointCount += 1; 169 break; 170 case kQuadratic_PathCmd: 171 pointCount += quadraticPointCount(pts, tol); 172 break; 173 case kCubic_PathCmd: 174 pointCount += cubicPointCount(pts, tol); 175 break; 176 case kMove_PathCmd: 177 pointCount += 1; 178 if (!first) { 179 ++(*subpaths); 180 } 181 break; 182 default: 183 break; 184 } 185 first = false; 186 } 187 return pointCount; 188 } 189 190 void GrPathUtils::QuadUVMatrix::set(const GrPoint qPts[3]) { 191 // can't make this static, no cons :( 192 SkMatrix UVpts; 193 #ifndef SK_SCALAR_IS_FLOAT 194 GrCrash("Expected scalar is float."); 195 #endif 196 SkMatrix m; 197 // We want M such that M * xy_pt = uv_pt 198 // We know M * control_pts = [0 1/2 1] 199 // [0 0 1] 200 // [1 1 1] 201 // We invert the control pt matrix and post concat to both sides to get M. 202 UVpts.setAll(0, SK_ScalarHalf, SK_Scalar1, 203 0, 0, SK_Scalar1, 204 SkScalarToPersp(SK_Scalar1), 205 SkScalarToPersp(SK_Scalar1), 206 SkScalarToPersp(SK_Scalar1)); 207 m.setAll(qPts[0].fX, qPts[1].fX, qPts[2].fX, 208 qPts[0].fY, qPts[1].fY, qPts[2].fY, 209 SkScalarToPersp(SK_Scalar1), 210 SkScalarToPersp(SK_Scalar1), 211 SkScalarToPersp(SK_Scalar1)); 212 if (!m.invert(&m)) { 213 // The quad is degenerate. Hopefully this is rare. Find the pts that are 214 // farthest apart to compute a line (unless it is really a pt). 215 SkScalar maxD = qPts[0].distanceToSqd(qPts[1]); 216 int maxEdge = 0; 217 SkScalar d = qPts[1].distanceToSqd(qPts[2]); 218 if (d > maxD) { 219 maxD = d; 220 maxEdge = 1; 221 } 222 d = qPts[2].distanceToSqd(qPts[0]); 223 if (d > maxD) { 224 maxD = d; 225 maxEdge = 2; 226 } 227 // We could have a tolerance here, not sure if it would improve anything 228 if (maxD > 0) { 229 // Set the matrix to give (u = 0, v = distance_to_line) 230 GrVec lineVec = qPts[(maxEdge + 1)%3] - qPts[maxEdge]; 231 // when looking from the point 0 down the line we want positive 232 // distances to be to the left. This matches the non-degenerate 233 // case. 234 lineVec.setOrthog(lineVec, GrPoint::kLeft_Side); 235 lineVec.dot(qPts[0]); 236 // first row 237 fM[0] = 0; 238 fM[1] = 0; 239 fM[2] = 0; 240 // second row 241 fM[3] = lineVec.fX; 242 fM[4] = lineVec.fY; 243 fM[5] = -lineVec.dot(qPts[maxEdge]); 244 } else { 245 // It's a point. It should cover zero area. Just set the matrix such 246 // that (u, v) will always be far away from the quad. 247 fM[0] = 0; fM[1] = 0; fM[2] = 100.f; 248 fM[3] = 0; fM[4] = 0; fM[5] = 100.f; 249 } 250 } else { 251 m.postConcat(UVpts); 252 253 // The matrix should not have perspective. 254 SkDEBUGCODE(static const SkScalar gTOL = SkFloatToScalar(1.f / 100.f)); 255 GrAssert(SkScalarAbs(m.get(SkMatrix::kMPersp0)) < gTOL); 256 GrAssert(SkScalarAbs(m.get(SkMatrix::kMPersp1)) < gTOL); 257 258 // It may not be normalized to have 1.0 in the bottom right 259 float m33 = m.get(SkMatrix::kMPersp2); 260 if (1.f != m33) { 261 m33 = 1.f / m33; 262 fM[0] = m33 * m.get(SkMatrix::kMScaleX); 263 fM[1] = m33 * m.get(SkMatrix::kMSkewX); 264 fM[2] = m33 * m.get(SkMatrix::kMTransX); 265 fM[3] = m33 * m.get(SkMatrix::kMSkewY); 266 fM[4] = m33 * m.get(SkMatrix::kMScaleY); 267 fM[5] = m33 * m.get(SkMatrix::kMTransY); 268 } else { 269 fM[0] = m.get(SkMatrix::kMScaleX); 270 fM[1] = m.get(SkMatrix::kMSkewX); 271 fM[2] = m.get(SkMatrix::kMTransX); 272 fM[3] = m.get(SkMatrix::kMSkewY); 273 fM[4] = m.get(SkMatrix::kMScaleY); 274 fM[5] = m.get(SkMatrix::kMTransY); 275 } 276 } 277 } 278 279 namespace { 280 281 // a is the first control point of the cubic. 282 // ab is the vector from a to the second control point. 283 // dc is the vector from the fourth to the third control point. 284 // d is the fourth control point. 285 // p is the candidate quadratic control point. 286 // this assumes that the cubic doesn't inflect and is simple 287 bool is_point_within_cubic_tangents(const SkPoint& a, 288 const SkVector& ab, 289 const SkVector& dc, 290 const SkPoint& d, 291 SkPath::Direction dir, 292 const SkPoint p) { 293 SkVector ap = p - a; 294 SkScalar apXab = ap.cross(ab); 295 if (SkPath::kCW_Direction == dir) { 296 if (apXab > 0) { 297 return false; 298 } 299 } else { 300 GrAssert(SkPath::kCCW_Direction == dir); 301 if (apXab < 0) { 302 return false; 303 } 304 } 305 306 SkVector dp = p - d; 307 SkScalar dpXdc = dp.cross(dc); 308 if (SkPath::kCW_Direction == dir) { 309 if (dpXdc < 0) { 310 return false; 311 } 312 } else { 313 GrAssert(SkPath::kCCW_Direction == dir); 314 if (dpXdc > 0) { 315 return false; 316 } 317 } 318 return true; 319 } 320 321 void convert_noninflect_cubic_to_quads(const SkPoint p[4], 322 SkScalar toleranceSqd, 323 bool constrainWithinTangents, 324 SkPath::Direction dir, 325 SkTArray<SkPoint, true>* quads, 326 int sublevel = 0) { 327 328 // Notation: Point a is always p[0]. Point b is p[1] unless p[1] == p[0], in which case it is 329 // p[2]. Point d is always p[3]. Point c is p[2] unless p[2] == p[3], in which case it is p[1]. 330 331 SkVector ab = p[1] - p[0]; 332 SkVector dc = p[2] - p[3]; 333 334 if (ab.isZero()) { 335 if (dc.isZero()) { 336 SkPoint* degQuad = quads->push_back_n(3); 337 degQuad[0] = p[0]; 338 degQuad[1] = p[0]; 339 degQuad[2] = p[3]; 340 return; 341 } 342 ab = p[2] - p[0]; 343 } 344 if (dc.isZero()) { 345 dc = p[1] - p[3]; 346 } 347 348 // When the ab and cd tangents are nearly parallel with vector from d to a the constraint that 349 // the quad point falls between the tangents becomes hard to enforce and we are likely to hit 350 // the max subdivision count. However, in this case the cubic is approaching a line and the 351 // accuracy of the quad point isn't so important. We check if the two middle cubic control 352 // points are very close to the baseline vector. If so then we just pick quadratic points on the 353 // control polygon. 354 355 if (constrainWithinTangents) { 356 SkVector da = p[0] - p[3]; 357 SkScalar invDALengthSqd = da.lengthSqd(); 358 if (invDALengthSqd > SK_ScalarNearlyZero) { 359 invDALengthSqd = SkScalarInvert(invDALengthSqd); 360 // cross(ab, da)^2/length(da)^2 == sqd distance from b to line from d to a. 361 // same goed for point c using vector cd. 362 SkScalar detABSqd = ab.cross(da); 363 detABSqd = SkScalarSquare(detABSqd); 364 SkScalar detDCSqd = dc.cross(da); 365 detDCSqd = SkScalarSquare(detDCSqd); 366 if (SkScalarMul(detABSqd, invDALengthSqd) < toleranceSqd && 367 SkScalarMul(detDCSqd, invDALengthSqd) < toleranceSqd) { 368 SkPoint b = p[0] + ab; 369 SkPoint c = p[3] + dc; 370 SkPoint mid = b + c; 371 mid.scale(SK_ScalarHalf); 372 // Insert two quadratics to cover the case when ab points away from d and/or dc 373 // points away from a. 374 if (SkVector::DotProduct(da, dc) < 0 || SkVector::DotProduct(ab,da) > 0) { 375 SkPoint* qpts = quads->push_back_n(6); 376 qpts[0] = p[0]; 377 qpts[1] = b; 378 qpts[2] = mid; 379 qpts[3] = mid; 380 qpts[4] = c; 381 qpts[5] = p[3]; 382 } else { 383 SkPoint* qpts = quads->push_back_n(3); 384 qpts[0] = p[0]; 385 qpts[1] = mid; 386 qpts[2] = p[3]; 387 } 388 return; 389 } 390 } 391 } 392 393 static const SkScalar kLengthScale = 3 * SK_Scalar1 / 2; 394 static const int kMaxSubdivs = 10; 395 396 ab.scale(kLengthScale); 397 dc.scale(kLengthScale); 398 399 // e0 and e1 are extrapolations along vectors ab and dc. 400 SkVector c0 = p[0]; 401 c0 += ab; 402 SkVector c1 = p[3]; 403 c1 += dc; 404 405 SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : c0.distanceToSqd(c1); 406 if (dSqd < toleranceSqd) { 407 SkPoint cAvg = c0; 408 cAvg += c1; 409 cAvg.scale(SK_ScalarHalf); 410 411 bool subdivide = false; 412 413 if (constrainWithinTangents && 414 !is_point_within_cubic_tangents(p[0], ab, dc, p[3], dir, cAvg)) { 415 // choose a new cAvg that is the intersection of the two tangent lines. 416 ab.setOrthog(ab); 417 SkScalar z0 = -ab.dot(p[0]); 418 dc.setOrthog(dc); 419 SkScalar z1 = -dc.dot(p[3]); 420 cAvg.fX = SkScalarMul(ab.fY, z1) - SkScalarMul(z0, dc.fY); 421 cAvg.fY = SkScalarMul(z0, dc.fX) - SkScalarMul(ab.fX, z1); 422 SkScalar z = SkScalarMul(ab.fX, dc.fY) - SkScalarMul(ab.fY, dc.fX); 423 z = SkScalarInvert(z); 424 cAvg.fX *= z; 425 cAvg.fY *= z; 426 if (sublevel <= kMaxSubdivs) { 427 SkScalar d0Sqd = c0.distanceToSqd(cAvg); 428 SkScalar d1Sqd = c1.distanceToSqd(cAvg); 429 // We need to subdivide if d0 + d1 > tolerance but we have the sqd values. We know 430 // the distances and tolerance can't be negative. 431 // (d0 + d1)^2 > toleranceSqd 432 // d0Sqd + 2*d0*d1 + d1Sqd > toleranceSqd 433 SkScalar d0d1 = SkScalarSqrt(SkScalarMul(d0Sqd, d1Sqd)); 434 subdivide = 2 * d0d1 + d0Sqd + d1Sqd > toleranceSqd; 435 } 436 } 437 if (!subdivide) { 438 SkPoint* pts = quads->push_back_n(3); 439 pts[0] = p[0]; 440 pts[1] = cAvg; 441 pts[2] = p[3]; 442 return; 443 } 444 } 445 SkPoint choppedPts[7]; 446 SkChopCubicAtHalf(p, choppedPts); 447 convert_noninflect_cubic_to_quads(choppedPts + 0, 448 toleranceSqd, 449 constrainWithinTangents, 450 dir, 451 quads, 452 sublevel + 1); 453 convert_noninflect_cubic_to_quads(choppedPts + 3, 454 toleranceSqd, 455 constrainWithinTangents, 456 dir, 457 quads, 458 sublevel + 1); 459 } 460 } 461 462 void GrPathUtils::convertCubicToQuads(const GrPoint p[4], 463 SkScalar tolScale, 464 bool constrainWithinTangents, 465 SkPath::Direction dir, 466 SkTArray<SkPoint, true>* quads) { 467 SkPoint chopped[10]; 468 int count = SkChopCubicAtInflections(p, chopped); 469 470 // base tolerance is 1 pixel. 471 static const SkScalar kTolerance = SK_Scalar1; 472 const SkScalar tolSqd = SkScalarSquare(SkScalarMul(tolScale, kTolerance)); 473 474 for (int i = 0; i < count; ++i) { 475 SkPoint* cubic = chopped + 3*i; 476 convert_noninflect_cubic_to_quads(cubic, tolSqd, constrainWithinTangents, dir, quads); 477 } 478 479 } 480
