/* * Copyright 2015 Google Inc. * * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ #include "GrTessellator.h" #include "GrDefaultGeoProcFactory.h" #include "GrPathUtils.h" #include "SkChunkAlloc.h" #include "SkGeometry.h" #include "SkPath.h" #include /* * There are six stages to the basic algorithm: * * 1) Linearize the path contours into piecewise linear segments (path_to_contours()). * 2) Build a mesh of edges connecting the vertices (build_edges()). * 3) Sort the vertices in Y (and secondarily in X) (merge_sort()). * 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()). * 5) Tessellate the simplified mesh into monotone polygons (tessellate()). * 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()). * * For screenspace antialiasing, the algorithm is modified as follows: * * Run steps 1-5 above to produce polygons. * 5b) Apply fill rules to extract boundary contours from the polygons (extract_boundaries()). * 5c) Simplify boundaries to remove "pointy" vertices which cause inversions (simplify_boundary()). * 5d) Displace edges by half a pixel inward and outward along their normals. Intersect to find * new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a new * antialiased mesh from those vertices (boundary_to_aa_mesh()). * Run steps 3-6 above on the new mesh, and produce antialiased triangles. * * The vertex sorting in step (3) is a merge sort, since it plays well with the linked list * of vertices (and the necessity of inserting new vertices on intersection). * * Stages (4) and (5) use an active edge list, which a list of all edges for which the * sweep line has crossed the top vertex, but not the bottom vertex. It's sorted * left-to-right based on the point where both edges are active (when both top vertices * have been seen, so the "lower" top vertex of the two). If the top vertices are equal * (shared), it's sorted based on the last point where both edges are active, so the * "upper" bottom vertex. * * The most complex step is the simplification (4). It's based on the Bentley-Ottman * line-sweep algorithm, but due to floating point inaccuracy, the intersection points are * not exact and may violate the mesh topology or active edge list ordering. We * accommodate this by adjusting the topology of the mesh and AEL to match the intersection * points. This occurs in three ways: * * A) Intersections may cause a shortened edge to no longer be ordered with respect to its * neighbouring edges at the top or bottom vertex. This is handled by merging the * edges (merge_collinear_edges()). * B) Intersections may cause an edge to violate the left-to-right ordering of the * active edge list. This is handled by splitting the neighbour edge on the * intersected vertex (cleanup_active_edges()). * C) Shortening an edge may cause an active edge to become inactive or an inactive edge * to become active. This is handled by removing or inserting the edge in the active * edge list (fix_active_state()). * * The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and * Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it * currently uses a linked list for the active edge list, rather than a 2-3 tree as the * paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also * become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N) * insertions and removals was greater than the cost of infrequent O(N) lookups with the * linked list implementation. With the latter, all removals are O(1), and most insertions * are O(1), since we know the adjacent edge in the active edge list based on the topology. * Only type 2 vertices (see paper) require the O(N) lookups, and these are much less * frequent. There may be other data structures worth investigating, however. * * Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the * path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y * coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall, * we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so * that the "left" and "right" orientation in the code remains correct (edges to the left are * increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90 * degrees counterclockwise, rather that transposing. */ #define LOGGING_ENABLED 0 #if LOGGING_ENABLED #define LOG printf #else #define LOG(...) #endif #define ALLOC_NEW(Type, args, alloc) new (alloc.allocThrow(sizeof(Type))) Type args namespace { struct Vertex; struct Edge; struct Poly; template void list_insert(T* t, T* prev, T* next, T** head, T** tail) { t->*Prev = prev; t->*Next = next; if (prev) { prev->*Next = t; } else if (head) { *head = t; } if (next) { next->*Prev = t; } else if (tail) { *tail = t; } } template void list_remove(T* t, T** head, T** tail) { if (t->*Prev) { t->*Prev->*Next = t->*Next; } else if (head) { *head = t->*Next; } if (t->*Next) { t->*Next->*Prev = t->*Prev; } else if (tail) { *tail = t->*Prev; } t->*Prev = t->*Next = nullptr; } /** * Vertices are used in three ways: first, the path contours are converted into a * circularly-linked list of Vertices for each contour. After edge construction, the same Vertices * are re-ordered by the merge sort according to the sweep_lt comparator (usually, increasing * in Y) using the same fPrev/fNext pointers that were used for the contours, to avoid * reallocation. Finally, MonotonePolys are built containing a circularly-linked list of * Vertices. (Currently, those Vertices are newly-allocated for the MonotonePolys, since * an individual Vertex from the path mesh may belong to multiple * MonotonePolys, so the original Vertices cannot be re-used. */ struct Vertex { Vertex(const SkPoint& point, uint8_t alpha) : fPoint(point), fPrev(nullptr), fNext(nullptr) , fFirstEdgeAbove(nullptr), fLastEdgeAbove(nullptr) , fFirstEdgeBelow(nullptr), fLastEdgeBelow(nullptr) , fProcessed(false) , fAlpha(alpha) #if LOGGING_ENABLED , fID (-1.0f) #endif {} SkPoint fPoint; // Vertex position Vertex* fPrev; // Linked list of contours, then Y-sorted vertices. Vertex* fNext; // " Edge* fFirstEdgeAbove; // Linked list of edges above this vertex. Edge* fLastEdgeAbove; // " Edge* fFirstEdgeBelow; // Linked list of edges below this vertex. Edge* fLastEdgeBelow; // " bool fProcessed; // Has this vertex been seen in simplify()? uint8_t fAlpha; #if LOGGING_ENABLED float fID; // Identifier used for logging. #endif }; /***************************************************************************************/ struct AAParams { bool fTweakAlpha; GrColor fColor; }; typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b); struct Comparator { CompareFunc sweep_lt; CompareFunc sweep_gt; }; bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) { return a.fX == b.fX ? a.fY > b.fY : a.fX < b.fX; } bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) { return a.fY == b.fY ? a.fX < b.fX : a.fY < b.fY; } bool sweep_gt_horiz(const SkPoint& a, const SkPoint& b) { return a.fX == b.fX ? a.fY < b.fY : a.fX > b.fX; } bool sweep_gt_vert(const SkPoint& a, const SkPoint& b) { return a.fY == b.fY ? a.fX > b.fX : a.fY > b.fY; } inline void* emit_vertex(Vertex* v, const AAParams* aaParams, void* data) { if (!aaParams) { SkPoint* d = static_cast(data); *d++ = v->fPoint; return d; } if (aaParams->fTweakAlpha) { auto d = static_cast(data); d->fPosition = v->fPoint; d->fColor = SkAlphaMulQ(aaParams->fColor, SkAlpha255To256(v->fAlpha)); d++; return d; } auto d = static_cast(data); d->fPosition = v->fPoint; d->fColor = aaParams->fColor; d->fCoverage = GrNormalizeByteToFloat(v->fAlpha); d++; return d; } void* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, const AAParams* aaParams, void* data) { #if TESSELLATOR_WIREFRAME data = emit_vertex(v0, aaParams, data); data = emit_vertex(v1, aaParams, data); data = emit_vertex(v1, aaParams, data); data = emit_vertex(v2, aaParams, data); data = emit_vertex(v2, aaParams, data); data = emit_vertex(v0, aaParams, data); #else data = emit_vertex(v0, aaParams, data); data = emit_vertex(v1, aaParams, data); data = emit_vertex(v2, aaParams, data); #endif return data; } struct VertexList { VertexList() : fHead(nullptr), fTail(nullptr) {} Vertex* fHead; Vertex* fTail; void insert(Vertex* v, Vertex* prev, Vertex* next) { list_insert(v, prev, next, &fHead, &fTail); } void append(Vertex* v) { insert(v, fTail, nullptr); } void prepend(Vertex* v) { insert(v, nullptr, fHead); } void remove(Vertex* v) { list_remove(v, &fHead, &fTail); } void close() { if (fHead && fTail) { fTail->fNext = fHead; fHead->fPrev = fTail; } } }; // Round to nearest quarter-pixel. This is used for screenspace tessellation. inline void round(SkPoint* p) { p->fX = SkScalarRoundToScalar(p->fX * SkFloatToScalar(4.0f)) * SkFloatToScalar(0.25f); p->fY = SkScalarRoundToScalar(p->fY * SkFloatToScalar(4.0f)) * SkFloatToScalar(0.25f); } // A line equation in implicit form. fA * x + fB * y + fC = 0, for all points (x, y) on the line. struct Line { Line(Vertex* p, Vertex* q) : Line(p->fPoint, q->fPoint) {} Line(const SkPoint& p, const SkPoint& q) : fA(static_cast(q.fY) - p.fY) // a = dY , fB(static_cast(p.fX) - q.fX) // b = -dX , fC(static_cast(p.fY) * q.fX - // c = cross(q, p) static_cast(p.fX) * q.fY) {} double dist(const SkPoint& p) const { return fA * p.fX + fB * p.fY + fC; } double magSq() const { return fA * fA + fB * fB; } // Compute the intersection of two (infinite) Lines. bool intersect(const Line& other, SkPoint* point) { double denom = fA * other.fB - fB * other.fA; if (denom == 0.0) { return false; } double scale = 1.0f / denom; point->fX = SkDoubleToScalar((fB * other.fC - other.fB * fC) * scale); point->fY = SkDoubleToScalar((other.fA * fC - fA * other.fC) * scale); round(point); return true; } double fA, fB, fC; }; /** * An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and * "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf(). * Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating * point). For speed, that case is only tested by the callers which require it (e.g., * cleanup_active_edges()). Edges also handle checking for intersection with other edges. * Currently, this converts the edges to the parametric form, in order to avoid doing a division * until an intersection has been confirmed. This is slightly slower in the "found" case, but * a lot faster in the "not found" case. * * The coefficients of the line equation stored in double precision to avoid catastrphic * cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is * correct in float, since it's a polynomial of degree 2. The intersect() function, being * degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its * output may be incorrect, and adjusting the mesh topology to match (see comment at the top of * this file). */ struct Edge { enum class Type { kInner, kOuter, kConnector }; Edge(Vertex* top, Vertex* bottom, int winding, Type type) : fWinding(winding) , fTop(top) , fBottom(bottom) , fType(type) , fLeft(nullptr) , fRight(nullptr) , fPrevEdgeAbove(nullptr) , fNextEdgeAbove(nullptr) , fPrevEdgeBelow(nullptr) , fNextEdgeBelow(nullptr) , fLeftPoly(nullptr) , fRightPoly(nullptr) , fLeftPolyPrev(nullptr) , fLeftPolyNext(nullptr) , fRightPolyPrev(nullptr) , fRightPolyNext(nullptr) , fUsedInLeftPoly(false) , fUsedInRightPoly(false) , fLine(top, bottom) { } int fWinding; // 1 == edge goes downward; -1 = edge goes upward. Vertex* fTop; // The top vertex in vertex-sort-order (sweep_lt). Vertex* fBottom; // The bottom vertex in vertex-sort-order. Type fType; Edge* fLeft; // The linked list of edges in the active edge list. Edge* fRight; // " Edge* fPrevEdgeAbove; // The linked list of edges in the bottom Vertex's "edges above". Edge* fNextEdgeAbove; // " Edge* fPrevEdgeBelow; // The linked list of edges in the top Vertex's "edges below". Edge* fNextEdgeBelow; // " Poly* fLeftPoly; // The Poly to the left of this edge, if any. Poly* fRightPoly; // The Poly to the right of this edge, if any. Edge* fLeftPolyPrev; Edge* fLeftPolyNext; Edge* fRightPolyPrev; Edge* fRightPolyNext; bool fUsedInLeftPoly; bool fUsedInRightPoly; Line fLine; double dist(const SkPoint& p) const { return fLine.dist(p); } bool isRightOf(Vertex* v) const { return fLine.dist(v->fPoint) < 0.0; } bool isLeftOf(Vertex* v) const { return fLine.dist(v->fPoint) > 0.0; } void recompute() { fLine = Line(fTop, fBottom); } bool intersect(const Edge& other, SkPoint* p, uint8_t* alpha = nullptr) { LOG("intersecting %g -> %g with %g -> %g\n", fTop->fID, fBottom->fID, other.fTop->fID, other.fBottom->fID); if (fTop == other.fTop || fBottom == other.fBottom) { return false; } double denom = fLine.fA * other.fLine.fB - fLine.fB * other.fLine.fA; if (denom == 0.0) { return false; } double dx = static_cast(fTop->fPoint.fX) - other.fTop->fPoint.fX; double dy = static_cast(fTop->fPoint.fY) - other.fTop->fPoint.fY; double sNumer = -dy * other.fLine.fB - dx * other.fLine.fA; double tNumer = -dy * fLine.fB - dx * fLine.fA; // If (sNumer / denom) or (tNumer / denom) is not in [0..1], exit early. // This saves us doing the divide below unless absolutely necessary. if (denom > 0.0 ? (sNumer < 0.0 || sNumer > denom || tNumer < 0.0 || tNumer > denom) : (sNumer > 0.0 || sNumer < denom || tNumer > 0.0 || tNumer < denom)) { return false; } double s = sNumer / denom; SkASSERT(s >= 0.0 && s <= 1.0); p->fX = SkDoubleToScalar(fTop->fPoint.fX - s * fLine.fB); p->fY = SkDoubleToScalar(fTop->fPoint.fY + s * fLine.fA); if (alpha) { if (fType == Type::kInner || other.fType == Type::kInner) { *alpha = 255; } else if (fType == Type::kOuter && other.fType == Type::kOuter) { *alpha = 0; } else { *alpha = (1.0 - s) * fTop->fAlpha + s * fBottom->fAlpha; } } return true; } }; struct EdgeList { EdgeList() : fHead(nullptr), fTail(nullptr), fNext(nullptr), fCount(0) {} Edge* fHead; Edge* fTail; EdgeList* fNext; int fCount; void insert(Edge* edge, Edge* prev, Edge* next) { list_insert(edge, prev, next, &fHead, &fTail); fCount++; } void append(Edge* e) { insert(e, fTail, nullptr); } void remove(Edge* edge) { list_remove(edge, &fHead, &fTail); fCount--; } void close() { if (fHead && fTail) { fTail->fRight = fHead; fHead->fLeft = fTail; } } bool contains(Edge* edge) const { return edge->fLeft || edge->fRight || fHead == edge; } }; /***************************************************************************************/ struct Poly { Poly(Vertex* v, int winding) : fFirstVertex(v) , fWinding(winding) , fHead(nullptr) , fTail(nullptr) , fNext(nullptr) , fPartner(nullptr) , fCount(0) { #if LOGGING_ENABLED static int gID = 0; fID = gID++; LOG("*** created Poly %d\n", fID); #endif } typedef enum { kLeft_Side, kRight_Side } Side; struct MonotonePoly { MonotonePoly(Edge* edge, Side side) : fSide(side) , fFirstEdge(nullptr) , fLastEdge(nullptr) , fPrev(nullptr) , fNext(nullptr) { this->addEdge(edge); } Side fSide; Edge* fFirstEdge; Edge* fLastEdge; MonotonePoly* fPrev; MonotonePoly* fNext; void addEdge(Edge* edge) { if (fSide == kRight_Side) { SkASSERT(!edge->fUsedInRightPoly); list_insert( edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge); edge->fUsedInRightPoly = true; } else { SkASSERT(!edge->fUsedInLeftPoly); list_insert( edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge); edge->fUsedInLeftPoly = true; } } void* emit(const AAParams* aaParams, void* data) { Edge* e = fFirstEdge; e->fTop->fPrev = e->fTop->fNext = nullptr; VertexList vertices; vertices.append(e->fTop); while (e != nullptr) { e->fBottom->fPrev = e->fBottom->fNext = nullptr; if (kRight_Side == fSide) { vertices.append(e->fBottom); e = e->fRightPolyNext; } else { vertices.prepend(e->fBottom); e = e->fLeftPolyNext; } } Vertex* first = vertices.fHead; Vertex* v = first->fNext; while (v != vertices.fTail) { SkASSERT(v && v->fPrev && v->fNext); Vertex* prev = v->fPrev; Vertex* curr = v; Vertex* next = v->fNext; double ax = static_cast(curr->fPoint.fX) - prev->fPoint.fX; double ay = static_cast(curr->fPoint.fY) - prev->fPoint.fY; double bx = static_cast(next->fPoint.fX) - curr->fPoint.fX; double by = static_cast(next->fPoint.fY) - curr->fPoint.fY; if (ax * by - ay * bx >= 0.0) { data = emit_triangle(prev, curr, next, aaParams, data); v->fPrev->fNext = v->fNext; v->fNext->fPrev = v->fPrev; if (v->fPrev == first) { v = v->fNext; } else { v = v->fPrev; } } else { v = v->fNext; } } return data; } }; Poly* addEdge(Edge* e, Side side, SkChunkAlloc& alloc) { LOG("addEdge (%g -> %g) to poly %d, %s side\n", e->fTop->fID, e->fBottom->fID, fID, side == kLeft_Side ? "left" : "right"); Poly* partner = fPartner; Poly* poly = this; if (side == kRight_Side) { if (e->fUsedInRightPoly) { return this; } } else { if (e->fUsedInLeftPoly) { return this; } } if (partner) { fPartner = partner->fPartner = nullptr; } if (!fTail) { fHead = fTail = ALLOC_NEW(MonotonePoly, (e, side), alloc); fCount += 2; } else if (e->fBottom == fTail->fLastEdge->fBottom) { return poly; } else if (side == fTail->fSide) { fTail->addEdge(e); fCount++; } else { e = ALLOC_NEW(Edge, (fTail->fLastEdge->fBottom, e->fBottom, 1, Edge::Type::kInner), alloc); fTail->addEdge(e); fCount++; if (partner) { partner->addEdge(e, side, alloc); poly = partner; } else { MonotonePoly* m = ALLOC_NEW(MonotonePoly, (e, side), alloc); m->fPrev = fTail; fTail->fNext = m; fTail = m; } } return poly; } void* emit(const AAParams* aaParams, void *data) { if (fCount < 3) { return data; } LOG("emit() %d, size %d\n", fID, fCount); for (MonotonePoly* m = fHead; m != nullptr; m = m->fNext) { data = m->emit(aaParams, data); } return data; } Vertex* lastVertex() const { return fTail ? fTail->fLastEdge->fBottom : fFirstVertex; } Vertex* fFirstVertex; int fWinding; MonotonePoly* fHead; MonotonePoly* fTail; Poly* fNext; Poly* fPartner; int fCount; #if LOGGING_ENABLED int fID; #endif }; /***************************************************************************************/ bool coincident(const SkPoint& a, const SkPoint& b) { return a == b; } Poly* new_poly(Poly** head, Vertex* v, int winding, SkChunkAlloc& alloc) { Poly* poly = ALLOC_NEW(Poly, (v, winding), alloc); poly->fNext = *head; *head = poly; return poly; } EdgeList* new_contour(EdgeList** head, SkChunkAlloc& alloc) { EdgeList* contour = ALLOC_NEW(EdgeList, (), alloc); contour->fNext = *head; *head = contour; return contour; } Vertex* append_point_to_contour(const SkPoint& p, Vertex* prev, Vertex** head, SkChunkAlloc& alloc) { Vertex* v = ALLOC_NEW(Vertex, (p, 255), alloc); #if LOGGING_ENABLED static float gID = 0.0f; v->fID = gID++; #endif if (prev) { prev->fNext = v; v->fPrev = prev; } else { *head = v; } return v; } Vertex* generate_quadratic_points(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, SkScalar tolSqd, Vertex* prev, Vertex** head, int pointsLeft, SkChunkAlloc& alloc) { SkScalar d = p1.distanceToLineSegmentBetweenSqd(p0, p2); if (pointsLeft < 2 || d < tolSqd || !SkScalarIsFinite(d)) { return append_point_to_contour(p2, prev, head, alloc); } const SkPoint q[] = { { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, }; const SkPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }; pointsLeft >>= 1; prev = generate_quadratic_points(p0, q[0], r, tolSqd, prev, head, pointsLeft, alloc); prev = generate_quadratic_points(r, q[1], p2, tolSqd, prev, head, pointsLeft, alloc); return prev; } Vertex* generate_cubic_points(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, const SkPoint& p3, SkScalar tolSqd, Vertex* prev, Vertex** head, int pointsLeft, SkChunkAlloc& alloc) { SkScalar d1 = p1.distanceToLineSegmentBetweenSqd(p0, p3); SkScalar d2 = p2.distanceToLineSegmentBetweenSqd(p0, p3); if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) || !SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) { return append_point_to_contour(p3, prev, head, alloc); } const SkPoint q[] = { { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) } }; const SkPoint r[] = { { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }, { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) } }; const SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) }; pointsLeft >>= 1; prev = generate_cubic_points(p0, q[0], r[0], s, tolSqd, prev, head, pointsLeft, alloc); prev = generate_cubic_points(s, r[1], q[2], p3, tolSqd, prev, head, pointsLeft, alloc); return prev; } // Stage 1: convert the input path to a set of linear contours (linked list of Vertices). void path_to_contours(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, Vertex** contours, SkChunkAlloc& alloc, bool *isLinear) { SkScalar toleranceSqd = tolerance * tolerance; SkPoint pts[4]; bool done = false; *isLinear = true; SkPath::Iter iter(path, false); Vertex* prev = nullptr; Vertex* head = nullptr; if (path.isInverseFillType()) { SkPoint quad[4]; clipBounds.toQuad(quad); for (int i = 3; i >= 0; i--) { prev = append_point_to_contour(quad[i], prev, &head, alloc); } head->fPrev = prev; prev->fNext = head; *contours++ = head; head = prev = nullptr; } SkAutoConicToQuads converter; while (!done) { SkPath::Verb verb = iter.next(pts); switch (verb) { case SkPath::kConic_Verb: { SkScalar weight = iter.conicWeight(); const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd); for (int i = 0; i < converter.countQuads(); ++i) { int pointsLeft = GrPathUtils::quadraticPointCount(quadPts, tolerance); prev = generate_quadratic_points(quadPts[0], quadPts[1], quadPts[2], toleranceSqd, prev, &head, pointsLeft, alloc); quadPts += 2; } *isLinear = false; break; } case SkPath::kMove_Verb: if (head) { head->fPrev = prev; prev->fNext = head; *contours++ = head; } head = prev = nullptr; prev = append_point_to_contour(pts[0], prev, &head, alloc); break; case SkPath::kLine_Verb: { prev = append_point_to_contour(pts[1], prev, &head, alloc); break; } case SkPath::kQuad_Verb: { int pointsLeft = GrPathUtils::quadraticPointCount(pts, tolerance); prev = generate_quadratic_points(pts[0], pts[1], pts[2], toleranceSqd, prev, &head, pointsLeft, alloc); *isLinear = false; break; } case SkPath::kCubic_Verb: { int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance); prev = generate_cubic_points(pts[0], pts[1], pts[2], pts[3], toleranceSqd, prev, &head, pointsLeft, alloc); *isLinear = false; break; } case SkPath::kClose_Verb: if (head) { head->fPrev = prev; prev->fNext = head; *contours++ = head; } head = prev = nullptr; break; case SkPath::kDone_Verb: if (head) { head->fPrev = prev; prev->fNext = head; *contours++ = head; } done = true; break; } } } inline bool apply_fill_type(SkPath::FillType fillType, Poly* poly) { if (!poly) { return false; } int winding = poly->fWinding; switch (fillType) { case SkPath::kWinding_FillType: return winding != 0; case SkPath::kEvenOdd_FillType: return (winding & 1) != 0; case SkPath::kInverseWinding_FillType: return winding == 1; case SkPath::kInverseEvenOdd_FillType: return (winding & 1) == 1; default: SkASSERT(false); return false; } } Edge* new_edge(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkChunkAlloc& alloc) { int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1; Vertex* top = winding < 0 ? next : prev; Vertex* bottom = winding < 0 ? prev : next; return ALLOC_NEW(Edge, (top, bottom, winding, type), alloc); } void remove_edge(Edge* edge, EdgeList* edges) { LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID); SkASSERT(edges->contains(edge)); edges->remove(edge); } void insert_edge(Edge* edge, Edge* prev, EdgeList* edges) { LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID); SkASSERT(!edges->contains(edge)); Edge* next = prev ? prev->fRight : edges->fHead; edges->insert(edge, prev, next); } void find_enclosing_edges(Vertex* v, EdgeList* edges, Edge** left, Edge** right) { if (v->fFirstEdgeAbove) { *left = v->fFirstEdgeAbove->fLeft; *right = v->fLastEdgeAbove->fRight; return; } Edge* next = nullptr; Edge* prev; for (prev = edges->fTail; prev != nullptr; prev = prev->fLeft) { if (prev->isLeftOf(v)) { break; } next = prev; } *left = prev; *right = next; } void find_enclosing_edges(Edge* edge, EdgeList* edges, Comparator& c, Edge** left, Edge** right) { Edge* prev = nullptr; Edge* next; for (next = edges->fHead; next != nullptr; next = next->fRight) { if ((c.sweep_gt(edge->fTop->fPoint, next->fTop->fPoint) && next->isRightOf(edge->fTop)) || (c.sweep_gt(next->fTop->fPoint, edge->fTop->fPoint) && edge->isLeftOf(next->fTop)) || (c.sweep_lt(edge->fBottom->fPoint, next->fBottom->fPoint) && next->isRightOf(edge->fBottom)) || (c.sweep_lt(next->fBottom->fPoint, edge->fBottom->fPoint) && edge->isLeftOf(next->fBottom))) { break; } prev = next; } *left = prev; *right = next; } void fix_active_state(Edge* edge, EdgeList* activeEdges, Comparator& c) { if (!activeEdges) { return; } if (activeEdges->contains(edge)) { if (edge->fBottom->fProcessed || !edge->fTop->fProcessed) { remove_edge(edge, activeEdges); } } else if (edge->fTop->fProcessed && !edge->fBottom->fProcessed) { Edge* left; Edge* right; find_enclosing_edges(edge, activeEdges, c, &left, &right); insert_edge(edge, left, activeEdges); } } void insert_edge_above(Edge* edge, Vertex* v, Comparator& c) { if (edge->fTop->fPoint == edge->fBottom->fPoint || c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) { return; } LOG("insert edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID); Edge* prev = nullptr; Edge* next; for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) { if (next->isRightOf(edge->fTop)) { break; } prev = next; } list_insert( edge, prev, next, &v->fFirstEdgeAbove, &v->fLastEdgeAbove); } void insert_edge_below(Edge* edge, Vertex* v, Comparator& c) { if (edge->fTop->fPoint == edge->fBottom->fPoint || c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) { return; } LOG("insert edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID); Edge* prev = nullptr; Edge* next; for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) { if (next->isRightOf(edge->fBottom)) { break; } prev = next; } list_insert( edge, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow); } void remove_edge_above(Edge* edge) { LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, edge->fBottom->fID); list_remove( edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove); } void remove_edge_below(Edge* edge) { LOG("removing edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, edge->fTop->fID); list_remove( edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow); } void disconnect(Edge* edge) { remove_edge_above(edge); remove_edge_below(edge); } void erase_edge(Edge* edge, EdgeList* edges) { LOG("erasing edge (%g -> %g)\n", edge->fTop->fID, edge->fBottom->fID); disconnect(edge); if (edges && edges->contains(edge)) { remove_edge(edge, edges); } } void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c); void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) { remove_edge_below(edge); edge->fTop = v; edge->recompute(); insert_edge_below(edge, v, c); fix_active_state(edge, activeEdges, c); merge_collinear_edges(edge, activeEdges, c); } void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) { remove_edge_above(edge); edge->fBottom = v; edge->recompute(); insert_edge_above(edge, v, c); fix_active_state(edge, activeEdges, c); merge_collinear_edges(edge, activeEdges, c); } void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) { if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) { LOG("merging coincident above edges (%g, %g) -> (%g, %g)\n", edge->fTop->fPoint.fX, edge->fTop->fPoint.fY, edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY); other->fWinding += edge->fWinding; erase_edge(edge, activeEdges); } else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) { other->fWinding += edge->fWinding; set_bottom(edge, other->fTop, activeEdges, c); } else { edge->fWinding += other->fWinding; set_bottom(other, edge->fTop, activeEdges, c); } } void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) { if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) { LOG("merging coincident below edges (%g, %g) -> (%g, %g)\n", edge->fTop->fPoint.fX, edge->fTop->fPoint.fY, edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY); other->fWinding += edge->fWinding; erase_edge(edge, activeEdges); } else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) { edge->fWinding += other->fWinding; set_top(other, edge->fBottom, activeEdges, c); } else { other->fWinding += edge->fWinding; set_top(edge, other->fBottom, activeEdges, c); } } void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c) { if (edge->fPrevEdgeAbove && (edge->fTop == edge->fPrevEdgeAbove->fTop || !edge->fPrevEdgeAbove->isLeftOf(edge->fTop))) { merge_edges_above(edge, edge->fPrevEdgeAbove, activeEdges, c); } else if (edge->fNextEdgeAbove && (edge->fTop == edge->fNextEdgeAbove->fTop || !edge->isLeftOf(edge->fNextEdgeAbove->fTop))) { merge_edges_above(edge, edge->fNextEdgeAbove, activeEdges, c); } if (edge->fPrevEdgeBelow && (edge->fBottom == edge->fPrevEdgeBelow->fBottom || !edge->fPrevEdgeBelow->isLeftOf(edge->fBottom))) { merge_edges_below(edge, edge->fPrevEdgeBelow, activeEdges, c); } else if (edge->fNextEdgeBelow && (edge->fBottom == edge->fNextEdgeBelow->fBottom || !edge->isLeftOf(edge->fNextEdgeBelow->fBottom))) { merge_edges_below(edge, edge->fNextEdgeBelow, activeEdges, c); } } void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc); void cleanup_active_edges(Edge* edge, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) { Vertex* top = edge->fTop; Vertex* bottom = edge->fBottom; if (edge->fLeft) { Vertex* leftTop = edge->fLeft->fTop; Vertex* leftBottom = edge->fLeft->fBottom; if (c.sweep_gt(top->fPoint, leftTop->fPoint) && !edge->fLeft->isLeftOf(top)) { split_edge(edge->fLeft, edge->fTop, activeEdges, c, alloc); } else if (c.sweep_gt(leftTop->fPoint, top->fPoint) && !edge->isRightOf(leftTop)) { split_edge(edge, leftTop, activeEdges, c, alloc); } else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) && !edge->fLeft->isLeftOf(bottom)) { split_edge(edge->fLeft, bottom, activeEdges, c, alloc); } else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) && !edge->isRightOf(leftBottom)) { split_edge(edge, leftBottom, activeEdges, c, alloc); } } if (edge->fRight) { Vertex* rightTop = edge->fRight->fTop; Vertex* rightBottom = edge->fRight->fBottom; if (c.sweep_gt(top->fPoint, rightTop->fPoint) && !edge->fRight->isRightOf(top)) { split_edge(edge->fRight, top, activeEdges, c, alloc); } else if (c.sweep_gt(rightTop->fPoint, top->fPoint) && !edge->isLeftOf(rightTop)) { split_edge(edge, rightTop, activeEdges, c, alloc); } else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) && !edge->fRight->isRightOf(bottom)) { split_edge(edge->fRight, bottom, activeEdges, c, alloc); } else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) && !edge->isLeftOf(rightBottom)) { split_edge(edge, rightBottom, activeEdges, c, alloc); } } } void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) { LOG("splitting edge (%g -> %g) at vertex %g (%g, %g)\n", edge->fTop->fID, edge->fBottom->fID, v->fID, v->fPoint.fX, v->fPoint.fY); if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) { set_top(edge, v, activeEdges, c); } else if (c.sweep_gt(v->fPoint, edge->fBottom->fPoint)) { set_bottom(edge, v, activeEdges, c); } else { Edge* newEdge = ALLOC_NEW(Edge, (v, edge->fBottom, edge->fWinding, edge->fType), alloc); insert_edge_below(newEdge, v, c); insert_edge_above(newEdge, edge->fBottom, c); set_bottom(edge, v, activeEdges, c); cleanup_active_edges(edge, activeEdges, c, alloc); fix_active_state(newEdge, activeEdges, c); merge_collinear_edges(newEdge, activeEdges, c); } } Edge* connect(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkChunkAlloc& alloc, int winding_scale = 1) { Edge* edge = new_edge(prev, next, type, c, alloc); if (edge->fWinding > 0) { insert_edge_below(edge, prev, c); insert_edge_above(edge, next, c); } else { insert_edge_below(edge, next, c); insert_edge_above(edge, prev, c); } edge->fWinding *= winding_scale; merge_collinear_edges(edge, nullptr, c); return edge; } void merge_vertices(Vertex* src, Vertex* dst, VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) { LOG("found coincident verts at %g, %g; merging %g into %g\n", src->fPoint.fX, src->fPoint.fY, src->fID, dst->fID); dst->fAlpha = SkTMax(src->fAlpha, dst->fAlpha); for (Edge* edge = src->fFirstEdgeAbove; edge;) { Edge* next = edge->fNextEdgeAbove; set_bottom(edge, dst, nullptr, c); edge = next; } for (Edge* edge = src->fFirstEdgeBelow; edge;) { Edge* next = edge->fNextEdgeBelow; set_top(edge, dst, nullptr, c); edge = next; } mesh->remove(src); } uint8_t max_edge_alpha(Edge* a, Edge* b) { if (a->fType == Edge::Type::kInner || b->fType == Edge::Type::kInner) { return 255; } else if (a->fType == Edge::Type::kOuter && b->fType == Edge::Type::kOuter) { return 0; } else { return SkTMax(SkTMax(a->fTop->fAlpha, a->fBottom->fAlpha), SkTMax(b->fTop->fAlpha, b->fBottom->fAlpha)); } } Vertex* check_for_intersection(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) { if (!edge || !other) { return nullptr; } SkPoint p; uint8_t alpha; if (edge->intersect(*other, &p, &alpha)) { Vertex* v; LOG("found intersection, pt is %g, %g\n", p.fX, p.fY); if (p == edge->fTop->fPoint || c.sweep_lt(p, edge->fTop->fPoint)) { split_edge(other, edge->fTop, activeEdges, c, alloc); v = edge->fTop; } else if (p == edge->fBottom->fPoint || c.sweep_gt(p, edge->fBottom->fPoint)) { split_edge(other, edge->fBottom, activeEdges, c, alloc); v = edge->fBottom; } else if (p == other->fTop->fPoint || c.sweep_lt(p, other->fTop->fPoint)) { split_edge(edge, other->fTop, activeEdges, c, alloc); v = other->fTop; } else if (p == other->fBottom->fPoint || c.sweep_gt(p, other->fBottom->fPoint)) { split_edge(edge, other->fBottom, activeEdges, c, alloc); v = other->fBottom; } else { Vertex* nextV = edge->fTop; while (c.sweep_lt(p, nextV->fPoint)) { nextV = nextV->fPrev; } while (c.sweep_lt(nextV->fPoint, p)) { nextV = nextV->fNext; } Vertex* prevV = nextV->fPrev; if (coincident(prevV->fPoint, p)) { v = prevV; } else if (coincident(nextV->fPoint, p)) { v = nextV; } else { v = ALLOC_NEW(Vertex, (p, alpha), alloc); LOG("inserting between %g (%g, %g) and %g (%g, %g)\n", prevV->fID, prevV->fPoint.fX, prevV->fPoint.fY, nextV->fID, nextV->fPoint.fX, nextV->fPoint.fY); #if LOGGING_ENABLED v->fID = (nextV->fID + prevV->fID) * 0.5f; #endif v->fPrev = prevV; v->fNext = nextV; prevV->fNext = v; nextV->fPrev = v; } split_edge(edge, v, activeEdges, c, alloc); split_edge(other, v, activeEdges, c, alloc); } return v; } return nullptr; } void sanitize_contours(Vertex** contours, int contourCnt, bool approximate) { for (int i = 0; i < contourCnt; ++i) { SkASSERT(contours[i]); for (Vertex* v = contours[i];;) { if (approximate) { round(&v->fPoint); } if (coincident(v->fPrev->fPoint, v->fPoint)) { LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY); if (v->fPrev == v) { contours[i] = nullptr; break; } v->fPrev->fNext = v->fNext; v->fNext->fPrev = v->fPrev; if (contours[i] == v) { contours[i] = v->fNext; } v = v->fPrev; } else { v = v->fNext; if (v == contours[i]) break; } } } } void merge_coincident_vertices(VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) { for (Vertex* v = mesh->fHead->fNext; v != nullptr; v = v->fNext) { if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) { v->fPoint = v->fPrev->fPoint; } if (coincident(v->fPrev->fPoint, v->fPoint)) { merge_vertices(v->fPrev, v, mesh, c, alloc); } } } // Stage 2: convert the contours to a mesh of edges connecting the vertices. void build_edges(Vertex** contours, int contourCnt, VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) { Vertex* prev = nullptr; for (int i = 0; i < contourCnt; ++i) { for (Vertex* v = contours[i]; v != nullptr;) { Vertex* vNext = v->fNext; connect(v->fPrev, v, Edge::Type::kInner, c, alloc); if (prev) { prev->fNext = v; v->fPrev = prev; } else { mesh->fHead = v; } prev = v; v = vNext; if (v == contours[i]) break; } } if (prev) { prev->fNext = mesh->fHead->fPrev = nullptr; } mesh->fTail = prev; } // Stage 3: sort the vertices by increasing sweep direction. void sorted_merge(Vertex* a, Vertex* b, VertexList* result, Comparator& c); void front_back_split(VertexList* v, VertexList* front, VertexList* back) { Vertex* fast; Vertex* slow; if (!v->fHead || !v->fHead->fNext) { *front = *v; } else { slow = v->fHead; fast = v->fHead->fNext; while (fast != nullptr) { fast = fast->fNext; if (fast != nullptr) { slow = slow->fNext; fast = fast->fNext; } } front->fHead = v->fHead; front->fTail = slow; back->fHead = slow->fNext; back->fTail = v->fTail; slow->fNext->fPrev = nullptr; slow->fNext = nullptr; } v->fHead = v->fTail = nullptr; } void merge_sort(VertexList* mesh, Comparator& c) { if (!mesh->fHead || !mesh->fHead->fNext) { return; } VertexList a; VertexList b; front_back_split(mesh, &a, &b); merge_sort(&a, c); merge_sort(&b, c); sorted_merge(a.fHead, b.fHead, mesh, c); } void sorted_merge(Vertex* a, Vertex* b, VertexList* result, Comparator& c) { VertexList vertices; while (a && b) { if (c.sweep_lt(a->fPoint, b->fPoint)) { Vertex* next = a->fNext; vertices.append(a); a = next; } else { Vertex* next = b->fNext; vertices.append(b); b = next; } } if (a) { vertices.insert(a, vertices.fTail, a->fNext); } if (b) { vertices.insert(b, vertices.fTail, b->fNext); } *result = vertices; } // Stage 4: Simplify the mesh by inserting new vertices at intersecting edges. void simplify(const VertexList& vertices, Comparator& c, SkChunkAlloc& alloc) { LOG("simplifying complex polygons\n"); EdgeList activeEdges; for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) { if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { continue; } #if LOGGING_ENABLED LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha); #endif Edge* leftEnclosingEdge = nullptr; Edge* rightEnclosingEdge = nullptr; bool restartChecks; do { restartChecks = false; find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); if (v->fFirstEdgeBelow) { for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) { if (check_for_intersection(edge, leftEnclosingEdge, &activeEdges, c, alloc)) { restartChecks = true; break; } if (check_for_intersection(edge, rightEnclosingEdge, &activeEdges, c, alloc)) { restartChecks = true; break; } } } else { if (Vertex* pv = check_for_intersection(leftEnclosingEdge, rightEnclosingEdge, &activeEdges, c, alloc)) { if (c.sweep_lt(pv->fPoint, v->fPoint)) { v = pv; } restartChecks = true; } } } while (restartChecks); if (v->fAlpha == 0) { if ((leftEnclosingEdge && leftEnclosingEdge->fWinding < 0) && (rightEnclosingEdge && rightEnclosingEdge->fWinding > 0)) { v->fAlpha = max_edge_alpha(leftEnclosingEdge, rightEnclosingEdge); } } for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { remove_edge(e, &activeEdges); } Edge* leftEdge = leftEnclosingEdge; for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { insert_edge(e, leftEdge, &activeEdges); leftEdge = e; } v->fProcessed = true; } } // Stage 5: Tessellate the simplified mesh into monotone polygons. Poly* tessellate(const VertexList& vertices, SkChunkAlloc& alloc) { LOG("tessellating simple polygons\n"); EdgeList activeEdges; Poly* polys = nullptr; for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) { if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { continue; } #if LOGGING_ENABLED LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha); #endif Edge* leftEnclosingEdge = nullptr; Edge* rightEnclosingEdge = nullptr; find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); Poly* leftPoly = nullptr; Poly* rightPoly = nullptr; if (v->fFirstEdgeAbove) { leftPoly = v->fFirstEdgeAbove->fLeftPoly; rightPoly = v->fLastEdgeAbove->fRightPoly; } else { leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : nullptr; rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : nullptr; } #if LOGGING_ENABLED LOG("edges above:\n"); for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID, e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1); } LOG("edges below:\n"); for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID, e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1); } #endif if (v->fFirstEdgeAbove) { if (leftPoly) { leftPoly = leftPoly->addEdge(v->fFirstEdgeAbove, Poly::kRight_Side, alloc); } if (rightPoly) { rightPoly = rightPoly->addEdge(v->fLastEdgeAbove, Poly::kLeft_Side, alloc); } for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) { Edge* leftEdge = e; Edge* rightEdge = e->fNextEdgeAbove; SkASSERT(rightEdge->isRightOf(leftEdge->fTop)); remove_edge(leftEdge, &activeEdges); if (leftEdge->fRightPoly) { leftEdge->fRightPoly->addEdge(e, Poly::kLeft_Side, alloc); } if (rightEdge->fLeftPoly) { rightEdge->fLeftPoly->addEdge(e, Poly::kRight_Side, alloc); } } remove_edge(v->fLastEdgeAbove, &activeEdges); if (!v->fFirstEdgeBelow) { if (leftPoly && rightPoly && leftPoly != rightPoly) { SkASSERT(leftPoly->fPartner == nullptr && rightPoly->fPartner == nullptr); rightPoly->fPartner = leftPoly; leftPoly->fPartner = rightPoly; } } } if (v->fFirstEdgeBelow) { if (!v->fFirstEdgeAbove) { if (leftPoly && rightPoly) { if (leftPoly == rightPoly) { if (leftPoly->fTail && leftPoly->fTail->fSide == Poly::kLeft_Side) { leftPoly = new_poly(&polys, leftPoly->lastVertex(), leftPoly->fWinding, alloc); leftEnclosingEdge->fRightPoly = leftPoly; } else { rightPoly = new_poly(&polys, rightPoly->lastVertex(), rightPoly->fWinding, alloc); rightEnclosingEdge->fLeftPoly = rightPoly; } } Edge* join = ALLOC_NEW(Edge, (leftPoly->lastVertex(), v, 1, Edge::Type::kInner), alloc); leftPoly = leftPoly->addEdge(join, Poly::kRight_Side, alloc); rightPoly = rightPoly->addEdge(join, Poly::kLeft_Side, alloc); } } Edge* leftEdge = v->fFirstEdgeBelow; leftEdge->fLeftPoly = leftPoly; insert_edge(leftEdge, leftEnclosingEdge, &activeEdges); for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge; rightEdge = rightEdge->fNextEdgeBelow) { insert_edge(rightEdge, leftEdge, &activeEdges); int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0; winding += leftEdge->fWinding; if (winding != 0) { Poly* poly = new_poly(&polys, v, winding, alloc); leftEdge->fRightPoly = rightEdge->fLeftPoly = poly; } leftEdge = rightEdge; } v->fLastEdgeBelow->fRightPoly = rightPoly; } #if LOGGING_ENABLED LOG("\nactive edges:\n"); for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) { LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID, e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1); } #endif } return polys; } bool is_boundary_edge(Edge* edge, SkPath::FillType fillType) { return apply_fill_type(fillType, edge->fLeftPoly) != apply_fill_type(fillType, edge->fRightPoly); } bool is_boundary_start(Edge* edge, SkPath::FillType fillType) { return !apply_fill_type(fillType, edge->fLeftPoly) && apply_fill_type(fillType, edge->fRightPoly); } void remove_non_boundary_edges(const VertexList& mesh, SkPath::FillType fillType, SkChunkAlloc& alloc) { for (Vertex* v = mesh.fHead; v != nullptr; v = v->fNext) { for (Edge* e = v->fFirstEdgeBelow; e != nullptr;) { Edge* next = e->fNextEdgeBelow; if (!is_boundary_edge(e, fillType)) { disconnect(e); } e = next; } } } void get_edge_normal(const Edge* e, SkVector* normal) { normal->setNormalize(SkDoubleToScalar(e->fLine.fA) * e->fWinding, SkDoubleToScalar(e->fLine.fB) * e->fWinding); } // Stage 5c: detect and remove "pointy" vertices whose edge normals point in opposite directions // and whose adjacent vertices are less than a quarter pixel from an edge. These are guaranteed to // invert on stroking. void simplify_boundary(EdgeList* boundary, Comparator& c, SkChunkAlloc& alloc) { Edge* prevEdge = boundary->fTail; SkVector prevNormal; get_edge_normal(prevEdge, &prevNormal); for (Edge* e = boundary->fHead; e != nullptr;) { Vertex* prev = prevEdge->fWinding == 1 ? prevEdge->fTop : prevEdge->fBottom; Vertex* next = e->fWinding == 1 ? e->fBottom : e->fTop; double dist = e->dist(prev->fPoint); SkVector normal; get_edge_normal(e, &normal); float denom = 0.0625f * static_cast(e->fLine.magSq()); if (prevNormal.dot(normal) < 0.0 && (dist * dist) <= denom) { Edge* join = new_edge(prev, next, Edge::Type::kInner, c, alloc); insert_edge(join, e, boundary); remove_edge(prevEdge, boundary); remove_edge(e, boundary); if (join->fLeft && join->fRight) { prevEdge = join->fLeft; e = join; } else { prevEdge = boundary->fTail; e = boundary->fHead; // join->fLeft ? join->fLeft : join; } get_edge_normal(prevEdge, &prevNormal); } else { prevEdge = e; prevNormal = normal; e = e->fRight; } } } // Stage 5d: Displace edges by half a pixel inward and outward along their normals. Intersect to // find new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a // new antialiased mesh from those vertices. void boundary_to_aa_mesh(EdgeList* boundary, VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) { Edge* prevEdge = boundary->fTail; float radius = 0.5f; double offset = radius * sqrt(prevEdge->fLine.magSq()) * prevEdge->fWinding; Line prevInner(prevEdge->fTop, prevEdge->fBottom); prevInner.fC -= offset; Line prevOuter(prevEdge->fTop, prevEdge->fBottom); prevOuter.fC += offset; VertexList innerVertices; VertexList outerVertices; SkVector prevNormal; get_edge_normal(prevEdge, &prevNormal); for (Edge* e = boundary->fHead; e != nullptr; e = e->fRight) { double offset = radius * sqrt(e->fLine.magSq()) * e->fWinding; Line inner(e->fTop, e->fBottom); inner.fC -= offset; Line outer(e->fTop, e->fBottom); outer.fC += offset; SkPoint innerPoint, outerPoint; SkVector normal; get_edge_normal(e, &normal); if (prevInner.intersect(inner, &innerPoint) && prevOuter.intersect(outer, &outerPoint)) { // cos(theta) < -0.999 implies a miter angle of ~2.5 degrees, // below which we'll bevel the outer edges. if (prevNormal.dot(normal) < -0.999) { SkPoint p = e->fWinding > 0 ? e->fTop->fPoint : e->fBottom->fPoint; SkPoint outerPoint1 = p - prevNormal * radius; SkPoint outerPoint2 = p - normal * radius; innerVertices.append(ALLOC_NEW(Vertex, (innerPoint, 255), alloc)); innerVertices.append(ALLOC_NEW(Vertex, (innerPoint, 255), alloc)); outerVertices.append(ALLOC_NEW(Vertex, (outerPoint1, 0), alloc)); outerVertices.append(ALLOC_NEW(Vertex, (outerPoint2, 0), alloc)); } else { innerVertices.append(ALLOC_NEW(Vertex, (innerPoint, 255), alloc)); outerVertices.append(ALLOC_NEW(Vertex, (outerPoint, 0), alloc)); } } prevInner = inner; prevOuter = outer; prevEdge = e; prevNormal = normal; } innerVertices.close(); outerVertices.close(); Vertex* innerVertex = innerVertices.fHead; Vertex* outerVertex = outerVertices.fHead; if (!innerVertex || !outerVertex) { return; } do { // Connect vertices into a quad mesh. Outer edges get default (1) winding. // Inner edges get -2 winding. This ensures that the interior is always filled // (-1 winding number for normal cases, 3 for thin features where the interior inverts). // Connector edges get zero winding, since they're only structural (i.e., to ensure // no 0-0-0 alpha triangles are produced), and shouldn't affect the poly winding number. connect(outerVertex->fPrev, outerVertex, Edge::Type::kOuter, c, alloc); connect(innerVertex->fPrev, innerVertex, Edge::Type::kInner, c, alloc, -2); connect(outerVertex, innerVertex, Edge::Type::kConnector, c, alloc, 0); Vertex* innerNext = innerVertex->fNext; Vertex* outerNext = outerVertex->fNext; mesh->append(innerVertex); mesh->append(outerVertex); innerVertex = innerNext; outerVertex = outerNext; } while (innerVertex != innerVertices.fHead && outerVertex != outerVertices.fHead); } void extract_boundary(EdgeList* boundary, Edge* e, SkPath::FillType fillType, SkChunkAlloc& alloc) { bool down = is_boundary_start(e, fillType); while (e) { e->fWinding = down ? 1 : -1; Edge* next; boundary->append(e); if (down) { // Find outgoing edge, in clockwise order. if ((next = e->fNextEdgeAbove)) { down = false; } else if ((next = e->fBottom->fLastEdgeBelow)) { down = true; } else if ((next = e->fPrevEdgeAbove)) { down = false; } } else { // Find outgoing edge, in counter-clockwise order. if ((next = e->fPrevEdgeBelow)) { down = true; } else if ((next = e->fTop->fFirstEdgeAbove)) { down = false; } else if ((next = e->fNextEdgeBelow)) { down = true; } } disconnect(e); e = next; } } // Stage 5b: Extract boundary edges. EdgeList* extract_boundaries(const VertexList& mesh, SkPath::FillType fillType, SkChunkAlloc& alloc) { LOG("extracting boundaries\n"); remove_non_boundary_edges(mesh, fillType, alloc); EdgeList* boundaries = nullptr; for (Vertex* v = mesh.fHead; v != nullptr; v = v->fNext) { while (v->fFirstEdgeBelow) { EdgeList* boundary = new_contour(&boundaries, alloc); extract_boundary(boundary, v->fFirstEdgeBelow, fillType, alloc); } } return boundaries; } // This is a driver function which calls stages 2-5 in turn. void contours_to_mesh(Vertex** contours, int contourCnt, bool antialias, VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) { #if LOGGING_ENABLED for (int i = 0; i < contourCnt; ++i) { Vertex* v = contours[i]; SkASSERT(v); LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY); for (v = v->fNext; v != contours[i]; v = v->fNext) { LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY); } } #endif sanitize_contours(contours, contourCnt, antialias); build_edges(contours, contourCnt, mesh, c, alloc); } void sort_and_simplify(VertexList* vertices, Comparator& c, SkChunkAlloc& alloc) { if (!vertices || !vertices->fHead) { return; } // Sort vertices in Y (secondarily in X). merge_sort(vertices, c); merge_coincident_vertices(vertices, c, alloc); #if LOGGING_ENABLED for (Vertex* v = vertices->fHead; v != nullptr; v = v->fNext) { static float gID = 0.0f; v->fID = gID++; } #endif simplify(*vertices, c, alloc); } Poly* mesh_to_polys(VertexList* vertices, Comparator& c, SkChunkAlloc& alloc) { sort_and_simplify(vertices, c, alloc); return tessellate(*vertices, alloc); } Poly* contours_to_polys(Vertex** contours, int contourCnt, SkPath::FillType fillType, const SkRect& pathBounds, bool antialias, SkChunkAlloc& alloc) { Comparator c; if (pathBounds.width() > pathBounds.height()) { c.sweep_lt = sweep_lt_horiz; c.sweep_gt = sweep_gt_horiz; } else { c.sweep_lt = sweep_lt_vert; c.sweep_gt = sweep_gt_vert; } VertexList mesh; contours_to_mesh(contours, contourCnt, antialias, &mesh, c, alloc); Poly* polys = mesh_to_polys(&mesh, c, alloc); if (antialias) { EdgeList* boundaries = extract_boundaries(mesh, fillType, alloc); VertexList aaMesh; for (EdgeList* boundary = boundaries; boundary != nullptr; boundary = boundary->fNext) { simplify_boundary(boundary, c, alloc); if (boundary->fCount > 2) { boundary_to_aa_mesh(boundary, &aaMesh, c, alloc); } } sort_and_simplify(&aaMesh, c, alloc); return tessellate(aaMesh, alloc); } return polys; } // Stage 6: Triangulate the monotone polygons into a vertex buffer. void* polys_to_triangles(Poly* polys, SkPath::FillType fillType, const AAParams* aaParams, void* data) { for (Poly* poly = polys; poly; poly = poly->fNext) { if (apply_fill_type(fillType, poly)) { data = poly->emit(aaParams, data); } } return data; } Poly* path_to_polys(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, int contourCnt, SkChunkAlloc& alloc, bool antialias, bool* isLinear) { SkPath::FillType fillType = path.getFillType(); if (SkPath::IsInverseFillType(fillType)) { contourCnt++; } std::unique_ptr contours(new Vertex* [contourCnt]); path_to_contours(path, tolerance, clipBounds, contours.get(), alloc, isLinear); return contours_to_polys(contours.get(), contourCnt, path.getFillType(), path.getBounds(), antialias, alloc); } void get_contour_count_and_size_estimate(const SkPath& path, SkScalar tolerance, int* contourCnt, int* sizeEstimate) { int maxPts = GrPathUtils::worstCasePointCount(path, contourCnt, tolerance); if (maxPts <= 0) { *contourCnt = 0; return; } if (maxPts > ((int)SK_MaxU16 + 1)) { SkDebugf("Path not rendered, too many verts (%d)\n", maxPts); *contourCnt = 0; return; } // For the initial size of the chunk allocator, estimate based on the point count: // one vertex per point for the initial passes, plus two for the vertices in the // resulting Polys, since the same point may end up in two Polys. Assume minimal // connectivity of one Edge per Vertex (will grow for intersections). *sizeEstimate = maxPts * (3 * sizeof(Vertex) + sizeof(Edge)); } int count_points(Poly* polys, SkPath::FillType fillType) { int count = 0; for (Poly* poly = polys; poly; poly = poly->fNext) { if (apply_fill_type(fillType, poly) && poly->fCount >= 3) { count += (poly->fCount - 2) * (TESSELLATOR_WIREFRAME ? 6 : 3); } } return count; } } // namespace namespace GrTessellator { // Stage 6: Triangulate the monotone polygons into a vertex buffer. int PathToTriangles(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, VertexAllocator* vertexAllocator, bool antialias, const GrColor& color, bool canTweakAlphaForCoverage, bool* isLinear) { int contourCnt; int sizeEstimate; get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate); if (contourCnt <= 0) { *isLinear = true; return 0; } SkChunkAlloc alloc(sizeEstimate); Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, antialias, isLinear); SkPath::FillType fillType = antialias ? SkPath::kWinding_FillType : path.getFillType(); int count = count_points(polys, fillType); if (0 == count) { return 0; } void* verts = vertexAllocator->lock(count); if (!verts) { SkDebugf("Could not allocate vertices\n"); return 0; } LOG("emitting %d verts\n", count); AAParams aaParams; aaParams.fTweakAlpha = canTweakAlphaForCoverage; aaParams.fColor = color; void* end = polys_to_triangles(polys, fillType, antialias ? &aaParams : nullptr, verts); int actualCount = static_cast((static_cast(end) - static_cast(verts)) / vertexAllocator->stride()); SkASSERT(actualCount <= count); vertexAllocator->unlock(actualCount); return actualCount; } int PathToVertices(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, GrTessellator::WindingVertex** verts) { int contourCnt; int sizeEstimate; get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate); if (contourCnt <= 0) { return 0; } SkChunkAlloc alloc(sizeEstimate); bool isLinear; Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, false, &isLinear); SkPath::FillType fillType = path.getFillType(); int count = count_points(polys, fillType); if (0 == count) { *verts = nullptr; return 0; } *verts = new GrTessellator::WindingVertex[count]; GrTessellator::WindingVertex* vertsEnd = *verts; SkPoint* points = new SkPoint[count]; SkPoint* pointsEnd = points; for (Poly* poly = polys; poly; poly = poly->fNext) { if (apply_fill_type(fillType, poly)) { SkPoint* start = pointsEnd; pointsEnd = static_cast(poly->emit(nullptr, pointsEnd)); while (start != pointsEnd) { vertsEnd->fPos = *start; vertsEnd->fWinding = poly->fWinding; ++start; ++vertsEnd; } } } int actualCount = static_cast(vertsEnd - *verts); SkASSERT(actualCount <= count); SkASSERT(pointsEnd - points == actualCount); delete[] points; return actualCount; } } // namespace