1 /* 2 * Copyright 2015 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 "GrTessellator.h" 9 10 #include "GrDefaultGeoProcFactory.h" 11 #include "GrPathUtils.h" 12 13 #include "SkArenaAlloc.h" 14 #include "SkGeometry.h" 15 #include "SkPath.h" 16 17 #include <stdio.h> 18 19 /* 20 * There are six stages to the basic algorithm: 21 * 22 * 1) Linearize the path contours into piecewise linear segments (path_to_contours()). 23 * 2) Build a mesh of edges connecting the vertices (build_edges()). 24 * 3) Sort the vertices in Y (and secondarily in X) (merge_sort()). 25 * 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()). 26 * 5) Tessellate the simplified mesh into monotone polygons (tessellate()). 27 * 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()). 28 * 29 * For screenspace antialiasing, the algorithm is modified as follows: 30 * 31 * Run steps 1-5 above to produce polygons. 32 * 5b) Apply fill rules to extract boundary contours from the polygons (extract_boundaries()). 33 * 5c) Simplify boundaries to remove "pointy" vertices that cause inversions (simplify_boundary()). 34 * 5d) Displace edges by half a pixel inward and outward along their normals. Intersect to find 35 * new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a new 36 * antialiased mesh from those vertices (stroke_boundary()). 37 * Run steps 3-6 above on the new mesh, and produce antialiased triangles. 38 * 39 * The vertex sorting in step (3) is a merge sort, since it plays well with the linked list 40 * of vertices (and the necessity of inserting new vertices on intersection). 41 * 42 * Stages (4) and (5) use an active edge list -- a list of all edges for which the 43 * sweep line has crossed the top vertex, but not the bottom vertex. It's sorted 44 * left-to-right based on the point where both edges are active (when both top vertices 45 * have been seen, so the "lower" top vertex of the two). If the top vertices are equal 46 * (shared), it's sorted based on the last point where both edges are active, so the 47 * "upper" bottom vertex. 48 * 49 * The most complex step is the simplification (4). It's based on the Bentley-Ottman 50 * line-sweep algorithm, but due to floating point inaccuracy, the intersection points are 51 * not exact and may violate the mesh topology or active edge list ordering. We 52 * accommodate this by adjusting the topology of the mesh and AEL to match the intersection 53 * points. This occurs in two ways: 54 * 55 * A) Intersections may cause a shortened edge to no longer be ordered with respect to its 56 * neighbouring edges at the top or bottom vertex. This is handled by merging the 57 * edges (merge_collinear_edges()). 58 * B) Intersections may cause an edge to violate the left-to-right ordering of the 59 * active edge list. This is handled by detecting potential violations and rewinding 60 * the active edge list to the vertex before they occur (rewind() during merging, 61 * rewind_if_necessary() during splitting). 62 * 63 * The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and 64 * Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it 65 * currently uses a linked list for the active edge list, rather than a 2-3 tree as the 66 * paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also 67 * become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N) 68 * insertions and removals was greater than the cost of infrequent O(N) lookups with the 69 * linked list implementation. With the latter, all removals are O(1), and most insertions 70 * are O(1), since we know the adjacent edge in the active edge list based on the topology. 71 * Only type 2 vertices (see paper) require the O(N) lookups, and these are much less 72 * frequent. There may be other data structures worth investigating, however. 73 * 74 * Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the 75 * path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y 76 * coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall, 77 * we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so 78 * that the "left" and "right" orientation in the code remains correct (edges to the left are 79 * increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90 80 * degrees counterclockwise, rather that transposing. 81 */ 82 83 #define LOGGING_ENABLED 0 84 85 #if LOGGING_ENABLED 86 #define LOG printf 87 #else 88 #define LOG(...) 89 #endif 90 91 namespace { 92 93 const int kArenaChunkSize = 16 * 1024; 94 95 struct Vertex; 96 struct Edge; 97 struct Poly; 98 99 template <class T, T* T::*Prev, T* T::*Next> 100 void list_insert(T* t, T* prev, T* next, T** head, T** tail) { 101 t->*Prev = prev; 102 t->*Next = next; 103 if (prev) { 104 prev->*Next = t; 105 } else if (head) { 106 *head = t; 107 } 108 if (next) { 109 next->*Prev = t; 110 } else if (tail) { 111 *tail = t; 112 } 113 } 114 115 template <class T, T* T::*Prev, T* T::*Next> 116 void list_remove(T* t, T** head, T** tail) { 117 if (t->*Prev) { 118 t->*Prev->*Next = t->*Next; 119 } else if (head) { 120 *head = t->*Next; 121 } 122 if (t->*Next) { 123 t->*Next->*Prev = t->*Prev; 124 } else if (tail) { 125 *tail = t->*Prev; 126 } 127 t->*Prev = t->*Next = nullptr; 128 } 129 130 /** 131 * Vertices are used in three ways: first, the path contours are converted into a 132 * circularly-linked list of Vertices for each contour. After edge construction, the same Vertices 133 * are re-ordered by the merge sort according to the sweep_lt comparator (usually, increasing 134 * in Y) using the same fPrev/fNext pointers that were used for the contours, to avoid 135 * reallocation. Finally, MonotonePolys are built containing a circularly-linked list of 136 * Vertices. (Currently, those Vertices are newly-allocated for the MonotonePolys, since 137 * an individual Vertex from the path mesh may belong to multiple 138 * MonotonePolys, so the original Vertices cannot be re-used. 139 */ 140 141 struct Vertex { 142 Vertex(const SkPoint& point, uint8_t alpha) 143 : fPoint(point), fPrev(nullptr), fNext(nullptr) 144 , fFirstEdgeAbove(nullptr), fLastEdgeAbove(nullptr) 145 , fFirstEdgeBelow(nullptr), fLastEdgeBelow(nullptr) 146 , fLeftEnclosingEdge(nullptr), fRightEnclosingEdge(nullptr) 147 , fPartner(nullptr) 148 , fAlpha(alpha) 149 #if LOGGING_ENABLED 150 , fID (-1.0f) 151 #endif 152 {} 153 SkPoint fPoint; // Vertex position 154 Vertex* fPrev; // Linked list of contours, then Y-sorted vertices. 155 Vertex* fNext; // " 156 Edge* fFirstEdgeAbove; // Linked list of edges above this vertex. 157 Edge* fLastEdgeAbove; // " 158 Edge* fFirstEdgeBelow; // Linked list of edges below this vertex. 159 Edge* fLastEdgeBelow; // " 160 Edge* fLeftEnclosingEdge; // Nearest edge in the AEL left of this vertex. 161 Edge* fRightEnclosingEdge; // Nearest edge in the AEL right of this vertex. 162 Vertex* fPartner; // Corresponding inner or outer vertex (for AA). 163 uint8_t fAlpha; 164 #if LOGGING_ENABLED 165 float fID; // Identifier used for logging. 166 #endif 167 }; 168 169 /***************************************************************************************/ 170 171 struct AAParams { 172 bool fTweakAlpha; 173 GrColor fColor; 174 }; 175 176 typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b); 177 178 bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) { 179 return a.fX < b.fX || (a.fX == b.fX && a.fY > b.fY); 180 } 181 182 bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) { 183 return a.fY < b.fY || (a.fY == b.fY && a.fX < b.fX); 184 } 185 186 struct Comparator { 187 enum class Direction { kVertical, kHorizontal }; 188 Comparator(Direction direction) : fDirection(direction) {} 189 bool sweep_lt(const SkPoint& a, const SkPoint& b) const { 190 return fDirection == Direction::kHorizontal ? sweep_lt_horiz(a, b) : sweep_lt_vert(a, b); 191 } 192 Direction fDirection; 193 }; 194 195 inline void* emit_vertex(Vertex* v, const AAParams* aaParams, void* data) { 196 if (!aaParams) { 197 SkPoint* d = static_cast<SkPoint*>(data); 198 *d++ = v->fPoint; 199 return d; 200 } 201 if (aaParams->fTweakAlpha) { 202 auto d = static_cast<GrDefaultGeoProcFactory::PositionColorAttr*>(data); 203 d->fPosition = v->fPoint; 204 d->fColor = SkAlphaMulQ(aaParams->fColor, SkAlpha255To256(v->fAlpha)); 205 d++; 206 return d; 207 } 208 auto d = static_cast<GrDefaultGeoProcFactory::PositionColorCoverageAttr*>(data); 209 d->fPosition = v->fPoint; 210 d->fColor = aaParams->fColor; 211 d->fCoverage = GrNormalizeByteToFloat(v->fAlpha); 212 d++; 213 return d; 214 } 215 216 void* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, const AAParams* aaParams, void* data) { 217 LOG("emit_triangle (%g, %g) %d\n", v0->fPoint.fX, v0->fPoint.fY, v0->fAlpha); 218 LOG(" (%g, %g) %d\n", v1->fPoint.fX, v1->fPoint.fY, v1->fAlpha); 219 LOG(" (%g, %g) %d\n", v2->fPoint.fX, v2->fPoint.fY, v2->fAlpha); 220 #if TESSELLATOR_WIREFRAME 221 data = emit_vertex(v0, aaParams, data); 222 data = emit_vertex(v1, aaParams, data); 223 data = emit_vertex(v1, aaParams, data); 224 data = emit_vertex(v2, aaParams, data); 225 data = emit_vertex(v2, aaParams, data); 226 data = emit_vertex(v0, aaParams, data); 227 #else 228 data = emit_vertex(v0, aaParams, data); 229 data = emit_vertex(v1, aaParams, data); 230 data = emit_vertex(v2, aaParams, data); 231 #endif 232 return data; 233 } 234 235 struct VertexList { 236 VertexList() : fHead(nullptr), fTail(nullptr) {} 237 VertexList(Vertex* head, Vertex* tail) : fHead(head), fTail(tail) {} 238 Vertex* fHead; 239 Vertex* fTail; 240 void insert(Vertex* v, Vertex* prev, Vertex* next) { 241 list_insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, prev, next, &fHead, &fTail); 242 } 243 void append(Vertex* v) { 244 insert(v, fTail, nullptr); 245 } 246 void append(const VertexList& list) { 247 if (!list.fHead) { 248 return; 249 } 250 if (fTail) { 251 fTail->fNext = list.fHead; 252 list.fHead->fPrev = fTail; 253 } else { 254 fHead = list.fHead; 255 } 256 fTail = list.fTail; 257 } 258 void prepend(Vertex* v) { 259 insert(v, nullptr, fHead); 260 } 261 void remove(Vertex* v) { 262 list_remove<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, &fHead, &fTail); 263 } 264 void close() { 265 if (fHead && fTail) { 266 fTail->fNext = fHead; 267 fHead->fPrev = fTail; 268 } 269 } 270 }; 271 272 // Round to nearest quarter-pixel. This is used for screenspace tessellation. 273 274 inline void round(SkPoint* p) { 275 p->fX = SkScalarRoundToScalar(p->fX * SkFloatToScalar(4.0f)) * SkFloatToScalar(0.25f); 276 p->fY = SkScalarRoundToScalar(p->fY * SkFloatToScalar(4.0f)) * SkFloatToScalar(0.25f); 277 } 278 279 // A line equation in implicit form. fA * x + fB * y + fC = 0, for all points (x, y) on the line. 280 struct Line { 281 Line(Vertex* p, Vertex* q) : Line(p->fPoint, q->fPoint) {} 282 Line(const SkPoint& p, const SkPoint& q) 283 : fA(static_cast<double>(q.fY) - p.fY) // a = dY 284 , fB(static_cast<double>(p.fX) - q.fX) // b = -dX 285 , fC(static_cast<double>(p.fY) * q.fX - // c = cross(q, p) 286 static_cast<double>(p.fX) * q.fY) {} 287 double dist(const SkPoint& p) const { 288 return fA * p.fX + fB * p.fY + fC; 289 } 290 double magSq() const { 291 return fA * fA + fB * fB; 292 } 293 294 // Compute the intersection of two (infinite) Lines. 295 bool intersect(const Line& other, SkPoint* point) { 296 double denom = fA * other.fB - fB * other.fA; 297 if (denom == 0.0) { 298 return false; 299 } 300 double scale = 1.0f / denom; 301 point->fX = SkDoubleToScalar((fB * other.fC - other.fB * fC) * scale); 302 point->fY = SkDoubleToScalar((other.fA * fC - fA * other.fC) * scale); 303 round(point); 304 return true; 305 } 306 double fA, fB, fC; 307 }; 308 309 /** 310 * An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and 311 * "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf(). 312 * Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating 313 * point). For speed, that case is only tested by the callers that require it (e.g., 314 * rewind_if_necessary()). Edges also handle checking for intersection with other edges. 315 * Currently, this converts the edges to the parametric form, in order to avoid doing a division 316 * until an intersection has been confirmed. This is slightly slower in the "found" case, but 317 * a lot faster in the "not found" case. 318 * 319 * The coefficients of the line equation stored in double precision to avoid catastrphic 320 * cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is 321 * correct in float, since it's a polynomial of degree 2. The intersect() function, being 322 * degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its 323 * output may be incorrect, and adjusting the mesh topology to match (see comment at the top of 324 * this file). 325 */ 326 327 struct Edge { 328 enum class Type { kInner, kOuter, kConnector }; 329 Edge(Vertex* top, Vertex* bottom, int winding, Type type) 330 : fWinding(winding) 331 , fTop(top) 332 , fBottom(bottom) 333 , fType(type) 334 , fLeft(nullptr) 335 , fRight(nullptr) 336 , fPrevEdgeAbove(nullptr) 337 , fNextEdgeAbove(nullptr) 338 , fPrevEdgeBelow(nullptr) 339 , fNextEdgeBelow(nullptr) 340 , fLeftPoly(nullptr) 341 , fRightPoly(nullptr) 342 , fLeftPolyPrev(nullptr) 343 , fLeftPolyNext(nullptr) 344 , fRightPolyPrev(nullptr) 345 , fRightPolyNext(nullptr) 346 , fUsedInLeftPoly(false) 347 , fUsedInRightPoly(false) 348 , fLine(top, bottom) { 349 } 350 int fWinding; // 1 == edge goes downward; -1 = edge goes upward. 351 Vertex* fTop; // The top vertex in vertex-sort-order (sweep_lt). 352 Vertex* fBottom; // The bottom vertex in vertex-sort-order. 353 Type fType; 354 Edge* fLeft; // The linked list of edges in the active edge list. 355 Edge* fRight; // " 356 Edge* fPrevEdgeAbove; // The linked list of edges in the bottom Vertex's "edges above". 357 Edge* fNextEdgeAbove; // " 358 Edge* fPrevEdgeBelow; // The linked list of edges in the top Vertex's "edges below". 359 Edge* fNextEdgeBelow; // " 360 Poly* fLeftPoly; // The Poly to the left of this edge, if any. 361 Poly* fRightPoly; // The Poly to the right of this edge, if any. 362 Edge* fLeftPolyPrev; 363 Edge* fLeftPolyNext; 364 Edge* fRightPolyPrev; 365 Edge* fRightPolyNext; 366 bool fUsedInLeftPoly; 367 bool fUsedInRightPoly; 368 Line fLine; 369 double dist(const SkPoint& p) const { 370 return fLine.dist(p); 371 } 372 bool isRightOf(Vertex* v) const { 373 return fLine.dist(v->fPoint) < 0.0; 374 } 375 bool isLeftOf(Vertex* v) const { 376 return fLine.dist(v->fPoint) > 0.0; 377 } 378 void recompute() { 379 fLine = Line(fTop, fBottom); 380 } 381 bool intersect(const Edge& other, SkPoint* p, uint8_t* alpha = nullptr) { 382 LOG("intersecting %g -> %g with %g -> %g\n", 383 fTop->fID, fBottom->fID, 384 other.fTop->fID, other.fBottom->fID); 385 if (fTop == other.fTop || fBottom == other.fBottom) { 386 return false; 387 } 388 double denom = fLine.fA * other.fLine.fB - fLine.fB * other.fLine.fA; 389 if (denom == 0.0) { 390 return false; 391 } 392 double dx = static_cast<double>(other.fTop->fPoint.fX) - fTop->fPoint.fX; 393 double dy = static_cast<double>(other.fTop->fPoint.fY) - fTop->fPoint.fY; 394 double sNumer = dy * other.fLine.fB + dx * other.fLine.fA; 395 double tNumer = dy * fLine.fB + dx * fLine.fA; 396 // If (sNumer / denom) or (tNumer / denom) is not in [0..1], exit early. 397 // This saves us doing the divide below unless absolutely necessary. 398 if (denom > 0.0 ? (sNumer < 0.0 || sNumer > denom || tNumer < 0.0 || tNumer > denom) 399 : (sNumer > 0.0 || sNumer < denom || tNumer > 0.0 || tNumer < denom)) { 400 return false; 401 } 402 double s = sNumer / denom; 403 SkASSERT(s >= 0.0 && s <= 1.0); 404 p->fX = SkDoubleToScalar(fTop->fPoint.fX - s * fLine.fB); 405 p->fY = SkDoubleToScalar(fTop->fPoint.fY + s * fLine.fA); 406 if (alpha) { 407 if (fType == Type::kConnector) { 408 *alpha = (1.0 - s) * fTop->fAlpha + s * fBottom->fAlpha; 409 } else if (other.fType == Type::kConnector) { 410 double t = tNumer / denom; 411 *alpha = (1.0 - t) * other.fTop->fAlpha + t * other.fBottom->fAlpha; 412 } else if (fType == Type::kOuter && other.fType == Type::kOuter) { 413 *alpha = 0; 414 } else { 415 *alpha = 255; 416 } 417 } 418 return true; 419 } 420 }; 421 422 struct EdgeList { 423 EdgeList() : fHead(nullptr), fTail(nullptr) {} 424 Edge* fHead; 425 Edge* fTail; 426 void insert(Edge* edge, Edge* prev, Edge* next) { 427 list_insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &fHead, &fTail); 428 } 429 void append(Edge* e) { 430 insert(e, fTail, nullptr); 431 } 432 void remove(Edge* edge) { 433 list_remove<Edge, &Edge::fLeft, &Edge::fRight>(edge, &fHead, &fTail); 434 } 435 void removeAll() { 436 while (fHead) { 437 this->remove(fHead); 438 } 439 } 440 void close() { 441 if (fHead && fTail) { 442 fTail->fRight = fHead; 443 fHead->fLeft = fTail; 444 } 445 } 446 bool contains(Edge* edge) const { 447 return edge->fLeft || edge->fRight || fHead == edge; 448 } 449 }; 450 451 /***************************************************************************************/ 452 453 struct Poly { 454 Poly(Vertex* v, int winding) 455 : fFirstVertex(v) 456 , fWinding(winding) 457 , fHead(nullptr) 458 , fTail(nullptr) 459 , fNext(nullptr) 460 , fPartner(nullptr) 461 , fCount(0) 462 { 463 #if LOGGING_ENABLED 464 static int gID = 0; 465 fID = gID++; 466 LOG("*** created Poly %d\n", fID); 467 #endif 468 } 469 typedef enum { kLeft_Side, kRight_Side } Side; 470 struct MonotonePoly { 471 MonotonePoly(Edge* edge, Side side) 472 : fSide(side) 473 , fFirstEdge(nullptr) 474 , fLastEdge(nullptr) 475 , fPrev(nullptr) 476 , fNext(nullptr) { 477 this->addEdge(edge); 478 } 479 Side fSide; 480 Edge* fFirstEdge; 481 Edge* fLastEdge; 482 MonotonePoly* fPrev; 483 MonotonePoly* fNext; 484 void addEdge(Edge* edge) { 485 if (fSide == kRight_Side) { 486 SkASSERT(!edge->fUsedInRightPoly); 487 list_insert<Edge, &Edge::fRightPolyPrev, &Edge::fRightPolyNext>( 488 edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge); 489 edge->fUsedInRightPoly = true; 490 } else { 491 SkASSERT(!edge->fUsedInLeftPoly); 492 list_insert<Edge, &Edge::fLeftPolyPrev, &Edge::fLeftPolyNext>( 493 edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge); 494 edge->fUsedInLeftPoly = true; 495 } 496 } 497 498 void* emit(const AAParams* aaParams, void* data) { 499 Edge* e = fFirstEdge; 500 VertexList vertices; 501 vertices.append(e->fTop); 502 int count = 1; 503 while (e != nullptr) { 504 if (kRight_Side == fSide) { 505 vertices.append(e->fBottom); 506 e = e->fRightPolyNext; 507 } else { 508 vertices.prepend(e->fBottom); 509 e = e->fLeftPolyNext; 510 } 511 count++; 512 } 513 Vertex* first = vertices.fHead; 514 Vertex* v = first->fNext; 515 while (v != vertices.fTail) { 516 SkASSERT(v && v->fPrev && v->fNext); 517 Vertex* prev = v->fPrev; 518 Vertex* curr = v; 519 Vertex* next = v->fNext; 520 if (count == 3) { 521 return emit_triangle(prev, curr, next, aaParams, data); 522 } 523 double ax = static_cast<double>(curr->fPoint.fX) - prev->fPoint.fX; 524 double ay = static_cast<double>(curr->fPoint.fY) - prev->fPoint.fY; 525 double bx = static_cast<double>(next->fPoint.fX) - curr->fPoint.fX; 526 double by = static_cast<double>(next->fPoint.fY) - curr->fPoint.fY; 527 if (ax * by - ay * bx >= 0.0) { 528 data = emit_triangle(prev, curr, next, aaParams, data); 529 v->fPrev->fNext = v->fNext; 530 v->fNext->fPrev = v->fPrev; 531 count--; 532 if (v->fPrev == first) { 533 v = v->fNext; 534 } else { 535 v = v->fPrev; 536 } 537 } else { 538 v = v->fNext; 539 } 540 } 541 return data; 542 } 543 }; 544 Poly* addEdge(Edge* e, Side side, SkArenaAlloc& alloc) { 545 LOG("addEdge (%g -> %g) to poly %d, %s side\n", 546 e->fTop->fID, e->fBottom->fID, fID, side == kLeft_Side ? "left" : "right"); 547 Poly* partner = fPartner; 548 Poly* poly = this; 549 if (side == kRight_Side) { 550 if (e->fUsedInRightPoly) { 551 return this; 552 } 553 } else { 554 if (e->fUsedInLeftPoly) { 555 return this; 556 } 557 } 558 if (partner) { 559 fPartner = partner->fPartner = nullptr; 560 } 561 if (!fTail) { 562 fHead = fTail = alloc.make<MonotonePoly>(e, side); 563 fCount += 2; 564 } else if (e->fBottom == fTail->fLastEdge->fBottom) { 565 return poly; 566 } else if (side == fTail->fSide) { 567 fTail->addEdge(e); 568 fCount++; 569 } else { 570 e = alloc.make<Edge>(fTail->fLastEdge->fBottom, e->fBottom, 1, Edge::Type::kInner); 571 fTail->addEdge(e); 572 fCount++; 573 if (partner) { 574 partner->addEdge(e, side, alloc); 575 poly = partner; 576 } else { 577 MonotonePoly* m = alloc.make<MonotonePoly>(e, side); 578 m->fPrev = fTail; 579 fTail->fNext = m; 580 fTail = m; 581 } 582 } 583 return poly; 584 } 585 void* emit(const AAParams* aaParams, void *data) { 586 if (fCount < 3) { 587 return data; 588 } 589 LOG("emit() %d, size %d\n", fID, fCount); 590 for (MonotonePoly* m = fHead; m != nullptr; m = m->fNext) { 591 data = m->emit(aaParams, data); 592 } 593 return data; 594 } 595 Vertex* lastVertex() const { return fTail ? fTail->fLastEdge->fBottom : fFirstVertex; } 596 Vertex* fFirstVertex; 597 int fWinding; 598 MonotonePoly* fHead; 599 MonotonePoly* fTail; 600 Poly* fNext; 601 Poly* fPartner; 602 int fCount; 603 #if LOGGING_ENABLED 604 int fID; 605 #endif 606 }; 607 608 /***************************************************************************************/ 609 610 bool coincident(const SkPoint& a, const SkPoint& b) { 611 return a == b; 612 } 613 614 Poly* new_poly(Poly** head, Vertex* v, int winding, SkArenaAlloc& alloc) { 615 Poly* poly = alloc.make<Poly>(v, winding); 616 poly->fNext = *head; 617 *head = poly; 618 return poly; 619 } 620 621 void append_point_to_contour(const SkPoint& p, VertexList* contour, SkArenaAlloc& alloc) { 622 Vertex* v = alloc.make<Vertex>(p, 255); 623 #if LOGGING_ENABLED 624 static float gID = 0.0f; 625 v->fID = gID++; 626 #endif 627 contour->append(v); 628 } 629 630 SkScalar quad_error_at(const SkPoint pts[3], SkScalar t, SkScalar u) { 631 SkQuadCoeff quad(pts); 632 SkPoint p0 = to_point(quad.eval(t - 0.5f * u)); 633 SkPoint mid = to_point(quad.eval(t)); 634 SkPoint p1 = to_point(quad.eval(t + 0.5f * u)); 635 if (!p0.isFinite() || !mid.isFinite() || !p1.isFinite()) { 636 return 0; 637 } 638 return mid.distanceToLineSegmentBetweenSqd(p0, p1); 639 } 640 641 void append_quadratic_to_contour(const SkPoint pts[3], SkScalar toleranceSqd, VertexList* contour, 642 SkArenaAlloc& alloc) { 643 SkQuadCoeff quad(pts); 644 Sk2s aa = quad.fA * quad.fA; 645 SkScalar denom = 2.0f * (aa[0] + aa[1]); 646 Sk2s ab = quad.fA * quad.fB; 647 SkScalar t = denom ? (-ab[0] - ab[1]) / denom : 0.0f; 648 int nPoints = 1; 649 SkScalar u; 650 // Test possible subdivision values only at the point of maximum curvature. 651 // If it passes the flatness metric there, it'll pass everywhere. 652 for (;;) { 653 u = 1.0f / nPoints; 654 if (quad_error_at(pts, t, u) < toleranceSqd) { 655 break; 656 } 657 nPoints++; 658 } 659 for (int j = 1; j <= nPoints; j++) { 660 append_point_to_contour(to_point(quad.eval(j * u)), contour, alloc); 661 } 662 } 663 664 void generate_cubic_points(const SkPoint& p0, 665 const SkPoint& p1, 666 const SkPoint& p2, 667 const SkPoint& p3, 668 SkScalar tolSqd, 669 VertexList* contour, 670 int pointsLeft, 671 SkArenaAlloc& alloc) { 672 SkScalar d1 = p1.distanceToLineSegmentBetweenSqd(p0, p3); 673 SkScalar d2 = p2.distanceToLineSegmentBetweenSqd(p0, p3); 674 if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) || 675 !SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) { 676 append_point_to_contour(p3, contour, alloc); 677 return; 678 } 679 const SkPoint q[] = { 680 { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, 681 { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, 682 { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) } 683 }; 684 const SkPoint r[] = { 685 { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }, 686 { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) } 687 }; 688 const SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) }; 689 pointsLeft >>= 1; 690 generate_cubic_points(p0, q[0], r[0], s, tolSqd, contour, pointsLeft, alloc); 691 generate_cubic_points(s, r[1], q[2], p3, tolSqd, contour, pointsLeft, alloc); 692 } 693 694 // Stage 1: convert the input path to a set of linear contours (linked list of Vertices). 695 696 void path_to_contours(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, 697 VertexList* contours, SkArenaAlloc& alloc, bool *isLinear) { 698 SkScalar toleranceSqd = tolerance * tolerance; 699 700 SkPoint pts[4]; 701 *isLinear = true; 702 VertexList* contour = contours; 703 SkPath::Iter iter(path, false); 704 if (path.isInverseFillType()) { 705 SkPoint quad[4]; 706 clipBounds.toQuad(quad); 707 for (int i = 3; i >= 0; i--) { 708 append_point_to_contour(quad[i], contours, alloc); 709 } 710 contour++; 711 } 712 SkAutoConicToQuads converter; 713 SkPath::Verb verb; 714 while ((verb = iter.next(pts)) != SkPath::kDone_Verb) { 715 switch (verb) { 716 case SkPath::kConic_Verb: { 717 SkScalar weight = iter.conicWeight(); 718 const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd); 719 for (int i = 0; i < converter.countQuads(); ++i) { 720 append_quadratic_to_contour(quadPts, toleranceSqd, contour, alloc); 721 quadPts += 2; 722 } 723 *isLinear = false; 724 break; 725 } 726 case SkPath::kMove_Verb: 727 if (contour->fHead) { 728 contour++; 729 } 730 append_point_to_contour(pts[0], contour, alloc); 731 break; 732 case SkPath::kLine_Verb: { 733 append_point_to_contour(pts[1], contour, alloc); 734 break; 735 } 736 case SkPath::kQuad_Verb: { 737 append_quadratic_to_contour(pts, toleranceSqd, contour, alloc); 738 *isLinear = false; 739 break; 740 } 741 case SkPath::kCubic_Verb: { 742 int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance); 743 generate_cubic_points(pts[0], pts[1], pts[2], pts[3], toleranceSqd, contour, 744 pointsLeft, alloc); 745 *isLinear = false; 746 break; 747 } 748 case SkPath::kClose_Verb: 749 case SkPath::kDone_Verb: 750 break; 751 } 752 } 753 } 754 755 inline bool apply_fill_type(SkPath::FillType fillType, int winding) { 756 switch (fillType) { 757 case SkPath::kWinding_FillType: 758 return winding != 0; 759 case SkPath::kEvenOdd_FillType: 760 return (winding & 1) != 0; 761 case SkPath::kInverseWinding_FillType: 762 return winding == 1; 763 case SkPath::kInverseEvenOdd_FillType: 764 return (winding & 1) == 1; 765 default: 766 SkASSERT(false); 767 return false; 768 } 769 } 770 771 inline bool apply_fill_type(SkPath::FillType fillType, Poly* poly) { 772 return poly && apply_fill_type(fillType, poly->fWinding); 773 } 774 775 Edge* new_edge(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkArenaAlloc& alloc) { 776 int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1; 777 Vertex* top = winding < 0 ? next : prev; 778 Vertex* bottom = winding < 0 ? prev : next; 779 return alloc.make<Edge>(top, bottom, winding, type); 780 } 781 782 void remove_edge(Edge* edge, EdgeList* edges) { 783 LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID); 784 SkASSERT(edges->contains(edge)); 785 edges->remove(edge); 786 } 787 788 void insert_edge(Edge* edge, Edge* prev, EdgeList* edges) { 789 LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID); 790 SkASSERT(!edges->contains(edge)); 791 Edge* next = prev ? prev->fRight : edges->fHead; 792 edges->insert(edge, prev, next); 793 } 794 795 void find_enclosing_edges(Vertex* v, EdgeList* edges, Edge** left, Edge** right) { 796 if (v->fFirstEdgeAbove && v->fLastEdgeAbove) { 797 *left = v->fFirstEdgeAbove->fLeft; 798 *right = v->fLastEdgeAbove->fRight; 799 return; 800 } 801 Edge* next = nullptr; 802 Edge* prev; 803 for (prev = edges->fTail; prev != nullptr; prev = prev->fLeft) { 804 if (prev->isLeftOf(v)) { 805 break; 806 } 807 next = prev; 808 } 809 *left = prev; 810 *right = next; 811 } 812 813 void insert_edge_above(Edge* edge, Vertex* v, Comparator& c) { 814 if (edge->fTop->fPoint == edge->fBottom->fPoint || 815 c.sweep_lt(edge->fBottom->fPoint, edge->fTop->fPoint)) { 816 return; 817 } 818 LOG("insert edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID); 819 Edge* prev = nullptr; 820 Edge* next; 821 for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) { 822 if (next->isRightOf(edge->fTop)) { 823 break; 824 } 825 prev = next; 826 } 827 list_insert<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>( 828 edge, prev, next, &v->fFirstEdgeAbove, &v->fLastEdgeAbove); 829 } 830 831 void insert_edge_below(Edge* edge, Vertex* v, Comparator& c) { 832 if (edge->fTop->fPoint == edge->fBottom->fPoint || 833 c.sweep_lt(edge->fBottom->fPoint, edge->fTop->fPoint)) { 834 return; 835 } 836 LOG("insert edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID); 837 Edge* prev = nullptr; 838 Edge* next; 839 for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) { 840 if (next->isRightOf(edge->fBottom)) { 841 break; 842 } 843 prev = next; 844 } 845 list_insert<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>( 846 edge, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow); 847 } 848 849 void remove_edge_above(Edge* edge) { 850 LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, 851 edge->fBottom->fID); 852 list_remove<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>( 853 edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove); 854 } 855 856 void remove_edge_below(Edge* edge) { 857 LOG("removing edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, 858 edge->fTop->fID); 859 list_remove<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>( 860 edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow); 861 } 862 863 void disconnect(Edge* edge) 864 { 865 remove_edge_above(edge); 866 remove_edge_below(edge); 867 } 868 869 void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c); 870 871 void rewind(EdgeList* activeEdges, Vertex** current, Vertex* dst, Comparator& c) { 872 if (!current || *current == dst || c.sweep_lt((*current)->fPoint, dst->fPoint)) { 873 return; 874 } 875 Vertex* v = *current; 876 LOG("rewinding active edges from vertex %g to vertex %g\n", v->fID, dst->fID); 877 while (v != dst) { 878 v = v->fPrev; 879 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { 880 remove_edge(e, activeEdges); 881 } 882 Edge* leftEdge = v->fLeftEnclosingEdge; 883 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { 884 insert_edge(e, leftEdge, activeEdges); 885 leftEdge = e; 886 } 887 } 888 *current = v; 889 } 890 891 void rewind_if_necessary(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c) { 892 if (!activeEdges || !current) { 893 return; 894 } 895 Vertex* top = edge->fTop; 896 Vertex* bottom = edge->fBottom; 897 if (edge->fLeft) { 898 Vertex* leftTop = edge->fLeft->fTop; 899 Vertex* leftBottom = edge->fLeft->fBottom; 900 if (c.sweep_lt(leftTop->fPoint, top->fPoint) && !edge->fLeft->isLeftOf(top)) { 901 rewind(activeEdges, current, leftTop, c); 902 } else if (c.sweep_lt(top->fPoint, leftTop->fPoint) && !edge->isRightOf(leftTop)) { 903 rewind(activeEdges, current, top, c); 904 } else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) && 905 !edge->fLeft->isLeftOf(bottom)) { 906 rewind(activeEdges, current, leftTop, c); 907 } else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) && !edge->isRightOf(leftBottom)) { 908 rewind(activeEdges, current, top, c); 909 } 910 } 911 if (edge->fRight) { 912 Vertex* rightTop = edge->fRight->fTop; 913 Vertex* rightBottom = edge->fRight->fBottom; 914 if (c.sweep_lt(rightTop->fPoint, top->fPoint) && !edge->fRight->isRightOf(top)) { 915 rewind(activeEdges, current, rightTop, c); 916 } else if (c.sweep_lt(top->fPoint, rightTop->fPoint) && !edge->isLeftOf(rightTop)) { 917 rewind(activeEdges, current, top, c); 918 } else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) && 919 !edge->fRight->isRightOf(bottom)) { 920 rewind(activeEdges, current, rightTop, c); 921 } else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) && 922 !edge->isLeftOf(rightBottom)) { 923 rewind(activeEdges, current, top, c); 924 } 925 } 926 } 927 928 void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c) { 929 remove_edge_below(edge); 930 edge->fTop = v; 931 edge->recompute(); 932 insert_edge_below(edge, v, c); 933 rewind_if_necessary(edge, activeEdges, current, c); 934 merge_collinear_edges(edge, activeEdges, current, c); 935 } 936 937 void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c) { 938 remove_edge_above(edge); 939 edge->fBottom = v; 940 edge->recompute(); 941 insert_edge_above(edge, v, c); 942 rewind_if_necessary(edge, activeEdges, current, c); 943 merge_collinear_edges(edge, activeEdges, current, c); 944 } 945 946 void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Vertex** current, 947 Comparator& c) { 948 if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) { 949 LOG("merging coincident above edges (%g, %g) -> (%g, %g)\n", 950 edge->fTop->fPoint.fX, edge->fTop->fPoint.fY, 951 edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY); 952 rewind(activeEdges, current, edge->fTop, c); 953 other->fWinding += edge->fWinding; 954 disconnect(edge); 955 } else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) { 956 rewind(activeEdges, current, edge->fTop, c); 957 other->fWinding += edge->fWinding; 958 set_bottom(edge, other->fTop, activeEdges, current, c); 959 } else { 960 rewind(activeEdges, current, other->fTop, c); 961 edge->fWinding += other->fWinding; 962 set_bottom(other, edge->fTop, activeEdges, current, c); 963 } 964 } 965 966 void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Vertex** current, 967 Comparator& c) { 968 if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) { 969 LOG("merging coincident below edges (%g, %g) -> (%g, %g)\n", 970 edge->fTop->fPoint.fX, edge->fTop->fPoint.fY, 971 edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY); 972 rewind(activeEdges, current, edge->fTop, c); 973 other->fWinding += edge->fWinding; 974 disconnect(edge); 975 } else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) { 976 rewind(activeEdges, current, other->fTop, c); 977 edge->fWinding += other->fWinding; 978 set_top(other, edge->fBottom, activeEdges, current, c); 979 } else { 980 rewind(activeEdges, current, edge->fTop, c); 981 other->fWinding += edge->fWinding; 982 set_top(edge, other->fBottom, activeEdges, current, c); 983 } 984 } 985 986 void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c) { 987 for (;;) { 988 if (edge->fPrevEdgeAbove && (edge->fTop == edge->fPrevEdgeAbove->fTop || 989 !edge->fPrevEdgeAbove->isLeftOf(edge->fTop))) { 990 merge_edges_above(edge, edge->fPrevEdgeAbove, activeEdges, current, c); 991 } else if (edge->fNextEdgeAbove && (edge->fTop == edge->fNextEdgeAbove->fTop || 992 !edge->isLeftOf(edge->fNextEdgeAbove->fTop))) { 993 merge_edges_above(edge, edge->fNextEdgeAbove, activeEdges, current, c); 994 } else if (edge->fPrevEdgeBelow && (edge->fBottom == edge->fPrevEdgeBelow->fBottom || 995 !edge->fPrevEdgeBelow->isLeftOf(edge->fBottom))) { 996 merge_edges_below(edge, edge->fPrevEdgeBelow, activeEdges, current, c); 997 } else if (edge->fNextEdgeBelow && (edge->fBottom == edge->fNextEdgeBelow->fBottom || 998 !edge->isLeftOf(edge->fNextEdgeBelow->fBottom))) { 999 merge_edges_below(edge, edge->fNextEdgeBelow, activeEdges, current, c); 1000 } else { 1001 break; 1002 } 1003 } 1004 SkASSERT(!edge->fPrevEdgeAbove || edge->fPrevEdgeAbove->isLeftOf(edge->fTop)); 1005 SkASSERT(!edge->fPrevEdgeBelow || edge->fPrevEdgeBelow->isLeftOf(edge->fBottom)); 1006 SkASSERT(!edge->fNextEdgeAbove || edge->fNextEdgeAbove->isRightOf(edge->fTop)); 1007 SkASSERT(!edge->fNextEdgeBelow || edge->fNextEdgeBelow->isRightOf(edge->fBottom)); 1008 } 1009 1010 void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c, 1011 SkArenaAlloc& alloc) { 1012 if (v == edge->fTop || v == edge->fBottom) { 1013 return; 1014 } 1015 LOG("splitting edge (%g -> %g) at vertex %g (%g, %g)\n", 1016 edge->fTop->fID, edge->fBottom->fID, 1017 v->fID, v->fPoint.fX, v->fPoint.fY); 1018 Vertex* top; 1019 Vertex* bottom; 1020 if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) { 1021 top = v; 1022 bottom = edge->fTop; 1023 set_top(edge, v, activeEdges, current, c); 1024 } else if (c.sweep_lt(edge->fBottom->fPoint, v->fPoint)) { 1025 top = edge->fBottom; 1026 bottom = v; 1027 set_bottom(edge, v, activeEdges, current, c); 1028 } else { 1029 top = v; 1030 bottom = edge->fBottom; 1031 set_bottom(edge, v, activeEdges, current, c); 1032 } 1033 Edge* newEdge = alloc.make<Edge>(top, bottom, edge->fWinding, edge->fType); 1034 insert_edge_below(newEdge, top, c); 1035 insert_edge_above(newEdge, bottom, c); 1036 merge_collinear_edges(newEdge, activeEdges, current, c); 1037 } 1038 1039 Edge* connect(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkArenaAlloc& alloc, 1040 int winding_scale = 1) { 1041 Edge* edge = new_edge(prev, next, type, c, alloc); 1042 insert_edge_below(edge, edge->fTop, c); 1043 insert_edge_above(edge, edge->fBottom, c); 1044 edge->fWinding *= winding_scale; 1045 merge_collinear_edges(edge, nullptr, nullptr, c); 1046 return edge; 1047 } 1048 1049 void merge_vertices(Vertex* src, Vertex* dst, VertexList* mesh, Comparator& c, 1050 SkArenaAlloc& alloc) { 1051 LOG("found coincident verts at %g, %g; merging %g into %g\n", src->fPoint.fX, src->fPoint.fY, 1052 src->fID, dst->fID); 1053 dst->fAlpha = SkTMax(src->fAlpha, dst->fAlpha); 1054 if (src->fPartner) { 1055 src->fPartner->fPartner = dst; 1056 } 1057 for (Edge* edge = src->fFirstEdgeAbove; edge;) { 1058 Edge* next = edge->fNextEdgeAbove; 1059 set_bottom(edge, dst, nullptr, nullptr, c); 1060 edge = next; 1061 } 1062 for (Edge* edge = src->fFirstEdgeBelow; edge;) { 1063 Edge* next = edge->fNextEdgeBelow; 1064 set_top(edge, dst, nullptr, nullptr, c); 1065 edge = next; 1066 } 1067 mesh->remove(src); 1068 } 1069 1070 uint8_t max_edge_alpha(Edge* a, Edge* b) { 1071 if (a->fType == Edge::Type::kInner || b->fType == Edge::Type::kInner) { 1072 return 255; 1073 } else if (a->fType == Edge::Type::kOuter && b->fType == Edge::Type::kOuter) { 1074 return 0; 1075 } else { 1076 return SkTMax(SkTMax(a->fTop->fAlpha, a->fBottom->fAlpha), 1077 SkTMax(b->fTop->fAlpha, b->fBottom->fAlpha)); 1078 } 1079 } 1080 1081 bool check_for_intersection(Edge* edge, Edge* other, EdgeList* activeEdges, Vertex** current, 1082 VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { 1083 if (!edge || !other) { 1084 return false; 1085 } 1086 SkPoint p; 1087 uint8_t alpha; 1088 if (edge->intersect(*other, &p, &alpha) && p.isFinite()) { 1089 Vertex* v; 1090 LOG("found intersection, pt is %g, %g\n", p.fX, p.fY); 1091 Vertex* top = *current; 1092 // If the intersection point is above the current vertex, rewind to the vertex above the 1093 // intersection. 1094 while (top && c.sweep_lt(p, top->fPoint)) { 1095 top = top->fPrev; 1096 } 1097 if (p == edge->fTop->fPoint) { 1098 v = edge->fTop; 1099 } else if (p == edge->fBottom->fPoint) { 1100 v = edge->fBottom; 1101 } else if (p == other->fTop->fPoint) { 1102 v = other->fTop; 1103 } else if (p == other->fBottom->fPoint) { 1104 v = other->fBottom; 1105 } else { 1106 Vertex* prevV = top; 1107 Vertex* nextV = top ? top->fNext : mesh->fHead; 1108 while (nextV && c.sweep_lt(nextV->fPoint, p)) { 1109 prevV = nextV; 1110 nextV = nextV->fNext; 1111 } 1112 if (prevV && coincident(prevV->fPoint, p)) { 1113 v = prevV; 1114 } else if (nextV && coincident(nextV->fPoint, p)) { 1115 v = nextV; 1116 } else { 1117 v = alloc.make<Vertex>(p, alpha); 1118 #if LOGGING_ENABLED 1119 if (!prevV) { 1120 v->fID = mesh->fHead->fID - 1.0f; 1121 } else if (!nextV) { 1122 v->fID = mesh->fTail->fID + 1.0f; 1123 } else { 1124 v->fID = (prevV->fID + nextV->fID) * 0.5f; 1125 } 1126 #endif 1127 mesh->insert(v, prevV, nextV); 1128 } 1129 } 1130 rewind(activeEdges, current, top ? top : v, c); 1131 split_edge(edge, v, activeEdges, current, c, alloc); 1132 split_edge(other, v, activeEdges, current, c, alloc); 1133 v->fAlpha = SkTMax(v->fAlpha, alpha); 1134 return true; 1135 } 1136 return false; 1137 } 1138 1139 void sanitize_contours(VertexList* contours, int contourCnt, bool approximate) { 1140 for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) { 1141 SkASSERT(contour->fHead); 1142 Vertex* prev = contour->fTail; 1143 if (approximate) { 1144 round(&prev->fPoint); 1145 } 1146 for (Vertex* v = contour->fHead; v;) { 1147 if (approximate) { 1148 round(&v->fPoint); 1149 } 1150 Vertex* next = v->fNext; 1151 if (coincident(prev->fPoint, v->fPoint)) { 1152 LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY); 1153 contour->remove(v); 1154 } 1155 prev = v; 1156 v = next; 1157 } 1158 } 1159 } 1160 1161 void merge_coincident_vertices(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { 1162 if (!mesh->fHead) { 1163 return; 1164 } 1165 for (Vertex* v = mesh->fHead->fNext; v != nullptr; v = v->fNext) { 1166 if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) { 1167 v->fPoint = v->fPrev->fPoint; 1168 } 1169 if (coincident(v->fPrev->fPoint, v->fPoint)) { 1170 merge_vertices(v->fPrev, v, mesh, c, alloc); 1171 } 1172 } 1173 } 1174 1175 // Stage 2: convert the contours to a mesh of edges connecting the vertices. 1176 1177 void build_edges(VertexList* contours, int contourCnt, VertexList* mesh, Comparator& c, 1178 SkArenaAlloc& alloc) { 1179 for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) { 1180 Vertex* prev = contour->fTail; 1181 for (Vertex* v = contour->fHead; v;) { 1182 Vertex* next = v->fNext; 1183 connect(prev, v, Edge::Type::kInner, c, alloc); 1184 mesh->append(v); 1185 prev = v; 1186 v = next; 1187 } 1188 } 1189 } 1190 1191 void connect_partners(VertexList* outerVertices, Comparator& c, SkArenaAlloc& alloc) { 1192 for (Vertex* outer = outerVertices->fHead; outer; outer = outer->fNext) { 1193 if (Vertex* inner = outer->fPartner) { 1194 // Connector edges get zero winding, since they're only structural (i.e., to ensure 1195 // no 0-0-0 alpha triangles are produced), and shouldn't affect the poly winding number. 1196 connect(outer, inner, Edge::Type::kConnector, c, alloc, 0); 1197 inner->fPartner = outer->fPartner = nullptr; 1198 } 1199 } 1200 } 1201 1202 template <CompareFunc sweep_lt> 1203 void sorted_merge(VertexList* front, VertexList* back, VertexList* result) { 1204 Vertex* a = front->fHead; 1205 Vertex* b = back->fHead; 1206 while (a && b) { 1207 if (sweep_lt(a->fPoint, b->fPoint)) { 1208 front->remove(a); 1209 result->append(a); 1210 a = front->fHead; 1211 } else { 1212 back->remove(b); 1213 result->append(b); 1214 b = back->fHead; 1215 } 1216 } 1217 result->append(*front); 1218 result->append(*back); 1219 } 1220 1221 void sorted_merge(VertexList* front, VertexList* back, VertexList* result, Comparator& c) { 1222 if (c.fDirection == Comparator::Direction::kHorizontal) { 1223 sorted_merge<sweep_lt_horiz>(front, back, result); 1224 } else { 1225 sorted_merge<sweep_lt_vert>(front, back, result); 1226 } 1227 #if LOGGING_ENABLED 1228 float id = 0.0f; 1229 for (Vertex* v = result->fHead; v; v = v->fNext) { 1230 v->fID = id++; 1231 } 1232 #endif 1233 } 1234 1235 // Stage 3: sort the vertices by increasing sweep direction. 1236 1237 template <CompareFunc sweep_lt> 1238 void merge_sort(VertexList* vertices) { 1239 Vertex* slow = vertices->fHead; 1240 if (!slow) { 1241 return; 1242 } 1243 Vertex* fast = slow->fNext; 1244 if (!fast) { 1245 return; 1246 } 1247 do { 1248 fast = fast->fNext; 1249 if (fast) { 1250 fast = fast->fNext; 1251 slow = slow->fNext; 1252 } 1253 } while (fast); 1254 VertexList front(vertices->fHead, slow); 1255 VertexList back(slow->fNext, vertices->fTail); 1256 front.fTail->fNext = back.fHead->fPrev = nullptr; 1257 1258 merge_sort<sweep_lt>(&front); 1259 merge_sort<sweep_lt>(&back); 1260 1261 vertices->fHead = vertices->fTail = nullptr; 1262 sorted_merge<sweep_lt>(&front, &back, vertices); 1263 } 1264 1265 // Stage 4: Simplify the mesh by inserting new vertices at intersecting edges. 1266 1267 void simplify(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { 1268 LOG("simplifying complex polygons\n"); 1269 EdgeList activeEdges; 1270 for (Vertex* v = mesh->fHead; v != nullptr; v = v->fNext) { 1271 if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { 1272 continue; 1273 } 1274 Edge* leftEnclosingEdge; 1275 Edge* rightEnclosingEdge; 1276 bool restartChecks; 1277 do { 1278 LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha); 1279 restartChecks = false; 1280 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); 1281 if (rightEnclosingEdge && !rightEnclosingEdge->isRightOf(v)) { 1282 split_edge(rightEnclosingEdge, v, &activeEdges, &v, c, alloc); 1283 restartChecks = true; 1284 continue; 1285 } 1286 SkASSERT(!rightEnclosingEdge || rightEnclosingEdge->isRightOf(v)); 1287 v->fLeftEnclosingEdge = leftEnclosingEdge; 1288 v->fRightEnclosingEdge = rightEnclosingEdge; 1289 if (v->fFirstEdgeBelow) { 1290 for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) { 1291 if (check_for_intersection(edge, leftEnclosingEdge, &activeEdges, &v, mesh, c, 1292 alloc)) { 1293 restartChecks = true; 1294 break; 1295 } 1296 if (check_for_intersection(edge, rightEnclosingEdge, &activeEdges, &v, mesh, c, 1297 alloc)) { 1298 restartChecks = true; 1299 break; 1300 } 1301 } 1302 } else { 1303 if (check_for_intersection(leftEnclosingEdge, rightEnclosingEdge, 1304 &activeEdges, &v, mesh, c, alloc)) { 1305 restartChecks = true; 1306 } 1307 1308 } 1309 } while (restartChecks); 1310 if (v->fAlpha == 0) { 1311 if ((leftEnclosingEdge && leftEnclosingEdge->fWinding < 0) && 1312 (rightEnclosingEdge && rightEnclosingEdge->fWinding > 0)) { 1313 v->fAlpha = max_edge_alpha(leftEnclosingEdge, rightEnclosingEdge); 1314 } 1315 } 1316 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { 1317 remove_edge(e, &activeEdges); 1318 } 1319 Edge* leftEdge = leftEnclosingEdge; 1320 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { 1321 insert_edge(e, leftEdge, &activeEdges); 1322 leftEdge = e; 1323 } 1324 } 1325 } 1326 1327 // This is a stripped-down version of simplify() (the Bentley-Ottmann algorithm) that 1328 // early-returns true on the first found intersection, false if none. 1329 bool is_complex(const VertexList& vertices) { 1330 LOG("testing polygon complexity\n"); 1331 EdgeList activeEdges; 1332 for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) { 1333 if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { 1334 continue; 1335 } 1336 Edge* leftEnclosingEdge; 1337 Edge* rightEnclosingEdge; 1338 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); 1339 SkPoint dummy; 1340 if (v->fFirstEdgeBelow) { 1341 for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) { 1342 if (edge && leftEnclosingEdge && edge->intersect(*leftEnclosingEdge, &dummy)) { 1343 activeEdges.removeAll(); 1344 return true; 1345 } 1346 if (edge && rightEnclosingEdge && edge->intersect(*rightEnclosingEdge, &dummy)) { 1347 activeEdges.removeAll(); 1348 return true; 1349 } 1350 } 1351 } else if (leftEnclosingEdge && rightEnclosingEdge && 1352 leftEnclosingEdge->intersect(*rightEnclosingEdge, &dummy)) { 1353 activeEdges.removeAll(); 1354 return true; 1355 } 1356 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { 1357 remove_edge(e, &activeEdges); 1358 } 1359 Edge* leftEdge = leftEnclosingEdge; 1360 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { 1361 insert_edge(e, leftEdge, &activeEdges); 1362 leftEdge = e; 1363 } 1364 } 1365 activeEdges.removeAll(); 1366 return false; 1367 } 1368 1369 // Stage 5: Tessellate the simplified mesh into monotone polygons. 1370 1371 Poly* tessellate(const VertexList& vertices, SkArenaAlloc& alloc) { 1372 LOG("tessellating simple polygons\n"); 1373 EdgeList activeEdges; 1374 Poly* polys = nullptr; 1375 for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) { 1376 if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { 1377 continue; 1378 } 1379 #if LOGGING_ENABLED 1380 LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha); 1381 #endif 1382 Edge* leftEnclosingEdge; 1383 Edge* rightEnclosingEdge; 1384 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); 1385 Poly* leftPoly; 1386 Poly* rightPoly; 1387 if (v->fFirstEdgeAbove) { 1388 leftPoly = v->fFirstEdgeAbove->fLeftPoly; 1389 rightPoly = v->fLastEdgeAbove->fRightPoly; 1390 } else { 1391 leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : nullptr; 1392 rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : nullptr; 1393 } 1394 #if LOGGING_ENABLED 1395 LOG("edges above:\n"); 1396 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { 1397 LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID, 1398 e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1); 1399 } 1400 LOG("edges below:\n"); 1401 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { 1402 LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID, 1403 e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1); 1404 } 1405 #endif 1406 if (v->fFirstEdgeAbove) { 1407 if (leftPoly) { 1408 leftPoly = leftPoly->addEdge(v->fFirstEdgeAbove, Poly::kRight_Side, alloc); 1409 } 1410 if (rightPoly) { 1411 rightPoly = rightPoly->addEdge(v->fLastEdgeAbove, Poly::kLeft_Side, alloc); 1412 } 1413 for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) { 1414 Edge* rightEdge = e->fNextEdgeAbove; 1415 remove_edge(e, &activeEdges); 1416 if (e->fRightPoly) { 1417 e->fRightPoly->addEdge(e, Poly::kLeft_Side, alloc); 1418 } 1419 if (rightEdge->fLeftPoly && rightEdge->fLeftPoly != e->fRightPoly) { 1420 rightEdge->fLeftPoly->addEdge(e, Poly::kRight_Side, alloc); 1421 } 1422 } 1423 remove_edge(v->fLastEdgeAbove, &activeEdges); 1424 if (!v->fFirstEdgeBelow) { 1425 if (leftPoly && rightPoly && leftPoly != rightPoly) { 1426 SkASSERT(leftPoly->fPartner == nullptr && rightPoly->fPartner == nullptr); 1427 rightPoly->fPartner = leftPoly; 1428 leftPoly->fPartner = rightPoly; 1429 } 1430 } 1431 } 1432 if (v->fFirstEdgeBelow) { 1433 if (!v->fFirstEdgeAbove) { 1434 if (leftPoly && rightPoly) { 1435 if (leftPoly == rightPoly) { 1436 if (leftPoly->fTail && leftPoly->fTail->fSide == Poly::kLeft_Side) { 1437 leftPoly = new_poly(&polys, leftPoly->lastVertex(), 1438 leftPoly->fWinding, alloc); 1439 leftEnclosingEdge->fRightPoly = leftPoly; 1440 } else { 1441 rightPoly = new_poly(&polys, rightPoly->lastVertex(), 1442 rightPoly->fWinding, alloc); 1443 rightEnclosingEdge->fLeftPoly = rightPoly; 1444 } 1445 } 1446 Edge* join = alloc.make<Edge>(leftPoly->lastVertex(), v, 1, Edge::Type::kInner); 1447 leftPoly = leftPoly->addEdge(join, Poly::kRight_Side, alloc); 1448 rightPoly = rightPoly->addEdge(join, Poly::kLeft_Side, alloc); 1449 } 1450 } 1451 Edge* leftEdge = v->fFirstEdgeBelow; 1452 leftEdge->fLeftPoly = leftPoly; 1453 insert_edge(leftEdge, leftEnclosingEdge, &activeEdges); 1454 for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge; 1455 rightEdge = rightEdge->fNextEdgeBelow) { 1456 insert_edge(rightEdge, leftEdge, &activeEdges); 1457 int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0; 1458 winding += leftEdge->fWinding; 1459 if (winding != 0) { 1460 Poly* poly = new_poly(&polys, v, winding, alloc); 1461 leftEdge->fRightPoly = rightEdge->fLeftPoly = poly; 1462 } 1463 leftEdge = rightEdge; 1464 } 1465 v->fLastEdgeBelow->fRightPoly = rightPoly; 1466 } 1467 #if LOGGING_ENABLED 1468 LOG("\nactive edges:\n"); 1469 for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) { 1470 LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID, 1471 e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1); 1472 } 1473 #endif 1474 } 1475 return polys; 1476 } 1477 1478 void remove_non_boundary_edges(const VertexList& mesh, SkPath::FillType fillType, 1479 SkArenaAlloc& alloc) { 1480 LOG("removing non-boundary edges\n"); 1481 EdgeList activeEdges; 1482 for (Vertex* v = mesh.fHead; v != nullptr; v = v->fNext) { 1483 if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { 1484 continue; 1485 } 1486 Edge* leftEnclosingEdge; 1487 Edge* rightEnclosingEdge; 1488 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); 1489 bool prevFilled = leftEnclosingEdge && 1490 apply_fill_type(fillType, leftEnclosingEdge->fWinding); 1491 for (Edge* e = v->fFirstEdgeAbove; e;) { 1492 Edge* next = e->fNextEdgeAbove; 1493 remove_edge(e, &activeEdges); 1494 bool filled = apply_fill_type(fillType, e->fWinding); 1495 if (filled == prevFilled) { 1496 disconnect(e); 1497 } 1498 prevFilled = filled; 1499 e = next; 1500 } 1501 Edge* prev = leftEnclosingEdge; 1502 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { 1503 if (prev) { 1504 e->fWinding += prev->fWinding; 1505 } 1506 insert_edge(e, prev, &activeEdges); 1507 prev = e; 1508 } 1509 } 1510 } 1511 1512 // Note: this is the normal to the edge, but not necessarily unit length. 1513 void get_edge_normal(const Edge* e, SkVector* normal) { 1514 normal->set(SkDoubleToScalar(e->fLine.fA) * e->fWinding, 1515 SkDoubleToScalar(e->fLine.fB) * e->fWinding); 1516 } 1517 1518 // Stage 5c: detect and remove "pointy" vertices whose edge normals point in opposite directions 1519 // and whose adjacent vertices are less than a quarter pixel from an edge. These are guaranteed to 1520 // invert on stroking. 1521 1522 void simplify_boundary(EdgeList* boundary, Comparator& c, SkArenaAlloc& alloc) { 1523 Edge* prevEdge = boundary->fTail; 1524 SkVector prevNormal; 1525 get_edge_normal(prevEdge, &prevNormal); 1526 for (Edge* e = boundary->fHead; e != nullptr;) { 1527 Vertex* prev = prevEdge->fWinding == 1 ? prevEdge->fTop : prevEdge->fBottom; 1528 Vertex* next = e->fWinding == 1 ? e->fBottom : e->fTop; 1529 double dist = e->dist(prev->fPoint); 1530 SkVector normal; 1531 get_edge_normal(e, &normal); 1532 double denom = 0.0625f * e->fLine.magSq(); 1533 if (prevNormal.dot(normal) < 0.0 && (dist * dist) <= denom) { 1534 Edge* join = new_edge(prev, next, Edge::Type::kInner, c, alloc); 1535 insert_edge(join, e, boundary); 1536 remove_edge(prevEdge, boundary); 1537 remove_edge(e, boundary); 1538 if (join->fLeft && join->fRight) { 1539 prevEdge = join->fLeft; 1540 e = join; 1541 } else { 1542 prevEdge = boundary->fTail; 1543 e = boundary->fHead; // join->fLeft ? join->fLeft : join; 1544 } 1545 get_edge_normal(prevEdge, &prevNormal); 1546 } else { 1547 prevEdge = e; 1548 prevNormal = normal; 1549 e = e->fRight; 1550 } 1551 } 1552 } 1553 1554 void fix_inversions(Vertex* prev, Vertex* next, Edge* prevBisector, Edge* nextBisector, 1555 Edge* prevEdge, Comparator& c) { 1556 if (!prev || !next) { 1557 return; 1558 } 1559 int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1; 1560 SkPoint p; 1561 uint8_t alpha; 1562 if (winding != prevEdge->fWinding && prevBisector->intersect(*nextBisector, &p, &alpha)) { 1563 prev->fPoint = next->fPoint = p; 1564 prev->fAlpha = next->fAlpha = alpha; 1565 } 1566 } 1567 1568 // Stage 5d: Displace edges by half a pixel inward and outward along their normals. Intersect to 1569 // find new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a 1570 // new antialiased mesh from those vertices. 1571 1572 void stroke_boundary(EdgeList* boundary, VertexList* innerMesh, VertexList* outerMesh, 1573 Comparator& c, SkArenaAlloc& alloc) { 1574 // A boundary with fewer than 3 edges is degenerate. 1575 if (!boundary->fHead || !boundary->fHead->fRight || !boundary->fHead->fRight->fRight) { 1576 return; 1577 } 1578 Edge* prevEdge = boundary->fTail; 1579 float radius = 0.5f; 1580 double offset = radius * sqrt(prevEdge->fLine.magSq()) * prevEdge->fWinding; 1581 Line prevInner(prevEdge->fLine); 1582 prevInner.fC -= offset; 1583 Line prevOuter(prevEdge->fLine); 1584 prevOuter.fC += offset; 1585 VertexList innerVertices; 1586 VertexList outerVertices; 1587 Edge* prevBisector = nullptr; 1588 for (Edge* e = boundary->fHead; e != nullptr; e = e->fRight) { 1589 double offset = radius * sqrt(e->fLine.magSq()) * e->fWinding; 1590 Line inner(e->fLine); 1591 inner.fC -= offset; 1592 Line outer(e->fLine); 1593 outer.fC += offset; 1594 SkPoint innerPoint, outerPoint; 1595 if (prevInner.intersect(inner, &innerPoint) && 1596 prevOuter.intersect(outer, &outerPoint)) { 1597 Vertex* innerVertex = alloc.make<Vertex>(innerPoint, 255); 1598 Vertex* outerVertex = alloc.make<Vertex>(outerPoint, 0); 1599 Edge* bisector = new_edge(outerVertex, innerVertex, Edge::Type::kConnector, c, alloc); 1600 fix_inversions(innerVertices.fTail, innerVertex, prevBisector, bisector, prevEdge, c); 1601 fix_inversions(outerVertices.fTail, outerVertex, prevBisector, bisector, prevEdge, c); 1602 innerVertex->fPartner = outerVertex; 1603 outerVertex->fPartner = innerVertex; 1604 innerVertices.append(innerVertex); 1605 outerVertices.append(outerVertex); 1606 prevBisector = bisector; 1607 } 1608 prevInner = inner; 1609 prevOuter = outer; 1610 prevEdge = e; 1611 } 1612 1613 Vertex* innerVertex = innerVertices.fHead; 1614 Vertex* outerVertex = outerVertices.fHead; 1615 if (!innerVertex || !outerVertex) { 1616 return; 1617 } 1618 Edge* bisector = new_edge(outerVertices.fHead, innerVertices.fHead, Edge::Type::kConnector, c, 1619 alloc); 1620 fix_inversions(innerVertices.fTail, innerVertices.fHead, prevBisector, bisector, prevEdge, c); 1621 fix_inversions(outerVertices.fTail, outerVertices.fHead, prevBisector, bisector, prevEdge, c); 1622 Vertex* prevInnerVertex = innerVertices.fTail; 1623 Vertex* prevOuterVertex = outerVertices.fTail; 1624 while (innerVertex && outerVertex) { 1625 // Connect vertices into a quad mesh. Outer edges get default (1) winding. 1626 // Inner edges get -2 winding. This ensures that the interior is always filled 1627 // (-1 winding number for normal cases, 3 for thin features where the interior inverts). 1628 connect(prevOuterVertex, outerVertex, Edge::Type::kOuter, c, alloc); 1629 connect(prevInnerVertex, innerVertex, Edge::Type::kInner, c, alloc, -2); 1630 prevInnerVertex = innerVertex; 1631 prevOuterVertex = outerVertex; 1632 innerVertex = innerVertex->fNext; 1633 outerVertex = outerVertex->fNext; 1634 } 1635 innerMesh->append(innerVertices); 1636 outerMesh->append(outerVertices); 1637 } 1638 1639 void extract_boundary(EdgeList* boundary, Edge* e, SkPath::FillType fillType, SkArenaAlloc& alloc) { 1640 bool down = apply_fill_type(fillType, e->fWinding); 1641 while (e) { 1642 e->fWinding = down ? 1 : -1; 1643 Edge* next; 1644 boundary->append(e); 1645 if (down) { 1646 // Find outgoing edge, in clockwise order. 1647 if ((next = e->fNextEdgeAbove)) { 1648 down = false; 1649 } else if ((next = e->fBottom->fLastEdgeBelow)) { 1650 down = true; 1651 } else if ((next = e->fPrevEdgeAbove)) { 1652 down = false; 1653 } 1654 } else { 1655 // Find outgoing edge, in counter-clockwise order. 1656 if ((next = e->fPrevEdgeBelow)) { 1657 down = true; 1658 } else if ((next = e->fTop->fFirstEdgeAbove)) { 1659 down = false; 1660 } else if ((next = e->fNextEdgeBelow)) { 1661 down = true; 1662 } 1663 } 1664 disconnect(e); 1665 e = next; 1666 } 1667 } 1668 1669 // Stage 5b: Extract boundaries from mesh, simplify and stroke them into a new mesh. 1670 1671 void extract_boundaries(const VertexList& inMesh, VertexList* innerVertices, 1672 VertexList* outerVertices, SkPath::FillType fillType, 1673 Comparator& c, SkArenaAlloc& alloc) { 1674 remove_non_boundary_edges(inMesh, fillType, alloc); 1675 for (Vertex* v = inMesh.fHead; v; v = v->fNext) { 1676 while (v->fFirstEdgeBelow) { 1677 EdgeList boundary; 1678 extract_boundary(&boundary, v->fFirstEdgeBelow, fillType, alloc); 1679 simplify_boundary(&boundary, c, alloc); 1680 stroke_boundary(&boundary, innerVertices, outerVertices, c, alloc); 1681 } 1682 } 1683 } 1684 1685 // This is a driver function that calls stages 2-5 in turn. 1686 1687 void contours_to_mesh(VertexList* contours, int contourCnt, bool antialias, 1688 VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { 1689 #if LOGGING_ENABLED 1690 for (int i = 0; i < contourCnt; ++i) { 1691 Vertex* v = contours[i].fHead; 1692 SkASSERT(v); 1693 LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY); 1694 for (v = v->fNext; v; v = v->fNext) { 1695 LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY); 1696 } 1697 } 1698 #endif 1699 sanitize_contours(contours, contourCnt, antialias); 1700 build_edges(contours, contourCnt, mesh, c, alloc); 1701 } 1702 1703 void sort_mesh(VertexList* vertices, Comparator& c, SkArenaAlloc& alloc) { 1704 if (!vertices || !vertices->fHead) { 1705 return; 1706 } 1707 1708 // Sort vertices in Y (secondarily in X). 1709 if (c.fDirection == Comparator::Direction::kHorizontal) { 1710 merge_sort<sweep_lt_horiz>(vertices); 1711 } else { 1712 merge_sort<sweep_lt_vert>(vertices); 1713 } 1714 #if LOGGING_ENABLED 1715 for (Vertex* v = vertices->fHead; v != nullptr; v = v->fNext) { 1716 static float gID = 0.0f; 1717 v->fID = gID++; 1718 } 1719 #endif 1720 } 1721 1722 Poly* contours_to_polys(VertexList* contours, int contourCnt, SkPath::FillType fillType, 1723 const SkRect& pathBounds, bool antialias, VertexList* outerMesh, 1724 SkArenaAlloc& alloc) { 1725 Comparator c(pathBounds.width() > pathBounds.height() ? Comparator::Direction::kHorizontal 1726 : Comparator::Direction::kVertical); 1727 VertexList mesh; 1728 contours_to_mesh(contours, contourCnt, antialias, &mesh, c, alloc); 1729 sort_mesh(&mesh, c, alloc); 1730 merge_coincident_vertices(&mesh, c, alloc); 1731 simplify(&mesh, c, alloc); 1732 if (antialias) { 1733 VertexList innerMesh; 1734 extract_boundaries(mesh, &innerMesh, outerMesh, fillType, c, alloc); 1735 sort_mesh(&innerMesh, c, alloc); 1736 sort_mesh(outerMesh, c, alloc); 1737 if (is_complex(innerMesh) || is_complex(*outerMesh)) { 1738 LOG("found complex mesh; taking slow path\n"); 1739 VertexList aaMesh; 1740 connect_partners(outerMesh, c, alloc); 1741 sorted_merge(&innerMesh, outerMesh, &aaMesh, c); 1742 merge_coincident_vertices(&aaMesh, c, alloc); 1743 simplify(&aaMesh, c, alloc); 1744 outerMesh->fHead = outerMesh->fTail = nullptr; 1745 return tessellate(aaMesh, alloc); 1746 } else { 1747 LOG("no complex polygons; taking fast path\n"); 1748 merge_coincident_vertices(&innerMesh, c, alloc); 1749 return tessellate(innerMesh, alloc); 1750 } 1751 } else { 1752 return tessellate(mesh, alloc); 1753 } 1754 } 1755 1756 // Stage 6: Triangulate the monotone polygons into a vertex buffer. 1757 void* polys_to_triangles(Poly* polys, SkPath::FillType fillType, const AAParams* aaParams, 1758 void* data) { 1759 for (Poly* poly = polys; poly; poly = poly->fNext) { 1760 if (apply_fill_type(fillType, poly)) { 1761 data = poly->emit(aaParams, data); 1762 } 1763 } 1764 return data; 1765 } 1766 1767 Poly* path_to_polys(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, 1768 int contourCnt, SkArenaAlloc& alloc, bool antialias, bool* isLinear, 1769 VertexList* outerMesh) { 1770 SkPath::FillType fillType = path.getFillType(); 1771 if (SkPath::IsInverseFillType(fillType)) { 1772 contourCnt++; 1773 } 1774 std::unique_ptr<VertexList[]> contours(new VertexList[contourCnt]); 1775 1776 path_to_contours(path, tolerance, clipBounds, contours.get(), alloc, isLinear); 1777 return contours_to_polys(contours.get(), contourCnt, path.getFillType(), path.getBounds(), 1778 antialias, outerMesh, alloc); 1779 } 1780 1781 int get_contour_count(const SkPath& path, SkScalar tolerance) { 1782 int contourCnt; 1783 int maxPts = GrPathUtils::worstCasePointCount(path, &contourCnt, tolerance); 1784 if (maxPts <= 0) { 1785 return 0; 1786 } 1787 if (maxPts > ((int)SK_MaxU16 + 1)) { 1788 SkDebugf("Path not rendered, too many verts (%d)\n", maxPts); 1789 return 0; 1790 } 1791 return contourCnt; 1792 } 1793 1794 int count_points(Poly* polys, SkPath::FillType fillType) { 1795 int count = 0; 1796 for (Poly* poly = polys; poly; poly = poly->fNext) { 1797 if (apply_fill_type(fillType, poly) && poly->fCount >= 3) { 1798 count += (poly->fCount - 2) * (TESSELLATOR_WIREFRAME ? 6 : 3); 1799 } 1800 } 1801 return count; 1802 } 1803 1804 int count_outer_mesh_points(const VertexList& outerMesh) { 1805 int count = 0; 1806 for (Vertex* v = outerMesh.fHead; v; v = v->fNext) { 1807 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { 1808 count += TESSELLATOR_WIREFRAME ? 12 : 6; 1809 } 1810 } 1811 return count; 1812 } 1813 1814 void* outer_mesh_to_triangles(const VertexList& outerMesh, const AAParams* aaParams, void* data) { 1815 for (Vertex* v = outerMesh.fHead; v; v = v->fNext) { 1816 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { 1817 Vertex* v0 = e->fTop; 1818 Vertex* v1 = e->fBottom; 1819 Vertex* v2 = e->fBottom->fPartner; 1820 Vertex* v3 = e->fTop->fPartner; 1821 data = emit_triangle(v0, v1, v2, aaParams, data); 1822 data = emit_triangle(v0, v2, v3, aaParams, data); 1823 } 1824 } 1825 return data; 1826 } 1827 1828 } // namespace 1829 1830 namespace GrTessellator { 1831 1832 // Stage 6: Triangulate the monotone polygons into a vertex buffer. 1833 1834 int PathToTriangles(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, 1835 VertexAllocator* vertexAllocator, bool antialias, const GrColor& color, 1836 bool canTweakAlphaForCoverage, bool* isLinear) { 1837 int contourCnt = get_contour_count(path, tolerance); 1838 if (contourCnt <= 0) { 1839 *isLinear = true; 1840 return 0; 1841 } 1842 SkArenaAlloc alloc(kArenaChunkSize); 1843 VertexList outerMesh; 1844 Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, antialias, 1845 isLinear, &outerMesh); 1846 SkPath::FillType fillType = antialias ? SkPath::kWinding_FillType : path.getFillType(); 1847 int count = count_points(polys, fillType); 1848 if (antialias) { 1849 count += count_outer_mesh_points(outerMesh); 1850 } 1851 if (0 == count) { 1852 return 0; 1853 } 1854 1855 void* verts = vertexAllocator->lock(count); 1856 if (!verts) { 1857 SkDebugf("Could not allocate vertices\n"); 1858 return 0; 1859 } 1860 1861 LOG("emitting %d verts\n", count); 1862 AAParams aaParams; 1863 aaParams.fTweakAlpha = canTweakAlphaForCoverage; 1864 aaParams.fColor = color; 1865 1866 void* end = polys_to_triangles(polys, fillType, antialias ? &aaParams : nullptr, verts); 1867 end = outer_mesh_to_triangles(outerMesh, &aaParams, end); 1868 int actualCount = static_cast<int>((static_cast<uint8_t*>(end) - static_cast<uint8_t*>(verts)) 1869 / vertexAllocator->stride()); 1870 SkASSERT(actualCount <= count); 1871 vertexAllocator->unlock(actualCount); 1872 return actualCount; 1873 } 1874 1875 int PathToVertices(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, 1876 GrTessellator::WindingVertex** verts) { 1877 int contourCnt = get_contour_count(path, tolerance); 1878 if (contourCnt <= 0) { 1879 return 0; 1880 } 1881 SkArenaAlloc alloc(kArenaChunkSize); 1882 bool isLinear; 1883 Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, false, &isLinear, 1884 nullptr); 1885 SkPath::FillType fillType = path.getFillType(); 1886 int count = count_points(polys, fillType); 1887 if (0 == count) { 1888 *verts = nullptr; 1889 return 0; 1890 } 1891 1892 *verts = new GrTessellator::WindingVertex[count]; 1893 GrTessellator::WindingVertex* vertsEnd = *verts; 1894 SkPoint* points = new SkPoint[count]; 1895 SkPoint* pointsEnd = points; 1896 for (Poly* poly = polys; poly; poly = poly->fNext) { 1897 if (apply_fill_type(fillType, poly)) { 1898 SkPoint* start = pointsEnd; 1899 pointsEnd = static_cast<SkPoint*>(poly->emit(nullptr, pointsEnd)); 1900 while (start != pointsEnd) { 1901 vertsEnd->fPos = *start; 1902 vertsEnd->fWinding = poly->fWinding; 1903 ++start; 1904 ++vertsEnd; 1905 } 1906 } 1907 } 1908 int actualCount = static_cast<int>(vertsEnd - *verts); 1909 SkASSERT(actualCount <= count); 1910 SkASSERT(pointsEnd - points == actualCount); 1911 delete[] points; 1912 return actualCount; 1913 } 1914 1915 } // namespace 1916