/* * 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 "src/gpu/GrTessellator.h" #include "src/gpu/GrDefaultGeoProcFactory.h" #include "src/gpu/GrVertexWriter.h" #include "src/gpu/geometry/GrPathUtils.h" #include "include/core/SkPath.h" #include "src/core/SkArenaAlloc.h" #include "src/core/SkGeometry.h" #include "src/core/SkPointPriv.h" #include #include #include #include #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 that 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 (stroke_boundary()). * 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 -- 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 two 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 during merging or splitting by rewind()ing the * active edge list to the vertex before potential violations occur. * * 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 namespace { const int kArenaChunkSize = 16 * 1024; const float kCosMiterAngle = 0.97f; // Corresponds to an angle of ~14 degrees. struct Vertex; struct Edge; struct Event; 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) , fLeftEnclosingEdge(nullptr), fRightEnclosingEdge(nullptr) , fPartner(nullptr) , fAlpha(alpha) , fSynthetic(false) #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; // " Edge* fLeftEnclosingEdge; // Nearest edge in the AEL left of this vertex. Edge* fRightEnclosingEdge; // Nearest edge in the AEL right of this vertex. Vertex* fPartner; // Corresponding inner or outer vertex (for AA). uint8_t fAlpha; bool fSynthetic; // Is this a synthetic vertex? #if LOGGING_ENABLED float fID; // Identifier used for logging. #endif }; /***************************************************************************************/ typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b); bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) { return a.fX < b.fX || (a.fX == b.fX && a.fY > b.fY); } bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) { return a.fY < b.fY || (a.fY == b.fY && a.fX < b.fX); } struct Comparator { enum class Direction { kVertical, kHorizontal }; Comparator(Direction direction) : fDirection(direction) {} bool sweep_lt(const SkPoint& a, const SkPoint& b) const { return fDirection == Direction::kHorizontal ? sweep_lt_horiz(a, b) : sweep_lt_vert(a, b); } Direction fDirection; }; inline void* emit_vertex(Vertex* v, bool emitCoverage, void* data) { GrVertexWriter verts{data}; verts.write(v->fPoint); if (emitCoverage) { verts.write(GrNormalizeByteToFloat(v->fAlpha)); } return verts.fPtr; } void* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, bool emitCoverage, void* data) { LOG("emit_triangle %g (%g, %g) %d\n", v0->fID, v0->fPoint.fX, v0->fPoint.fY, v0->fAlpha); LOG(" %g (%g, %g) %d\n", v1->fID, v1->fPoint.fX, v1->fPoint.fY, v1->fAlpha); LOG(" %g (%g, %g) %d\n", v2->fID, v2->fPoint.fX, v2->fPoint.fY, v2->fAlpha); #if TESSELLATOR_WIREFRAME data = emit_vertex(v0, emitCoverage, data); data = emit_vertex(v1, emitCoverage, data); data = emit_vertex(v1, emitCoverage, data); data = emit_vertex(v2, emitCoverage, data); data = emit_vertex(v2, emitCoverage, data); data = emit_vertex(v0, emitCoverage, data); #else data = emit_vertex(v0, emitCoverage, data); data = emit_vertex(v1, emitCoverage, data); data = emit_vertex(v2, emitCoverage, data); #endif return data; } struct VertexList { VertexList() : fHead(nullptr), fTail(nullptr) {} VertexList(Vertex* head, Vertex* tail) : fHead(head), fTail(tail) {} 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 append(const VertexList& list) { if (!list.fHead) { return; } if (fTail) { fTail->fNext = list.fHead; list.fHead->fPrev = fTail; } else { fHead = list.fHead; } fTail = list.fTail; } 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); } inline SkScalar double_to_clamped_scalar(double d) { return SkDoubleToScalar(std::min((double) SK_ScalarMax, std::max(d, (double) -SK_ScalarMax))); } // A line equation in implicit form. fA * x + fB * y + fC = 0, for all points (x, y) on the line. struct Line { Line(double a, double b, double c) : fA(a), fB(b), fC(c) {} 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; } Line operator*(double v) const { return Line(fA * v, fB * v, fC * v); } double magSq() const { return fA * fA + fB * fB; } void normalize() { double len = sqrt(this->magSq()); if (len == 0.0) { return; } double scale = 1.0f / len; fA *= scale; fB *= scale; fC *= scale; } bool nearParallel(const Line& o) const { return fabs(o.fA - fA) < 0.00001 && fabs(o.fB - fB) < 0.00001; } // Compute the intersection of two (infinite) Lines. bool intersect(const Line& other, SkPoint* point) const { double denom = fA * other.fB - fB * other.fA; if (denom == 0.0) { return false; } double scale = 1.0 / denom; point->fX = double_to_clamped_scalar((fB * other.fC - other.fB * fC) * scale); point->fY = double_to_clamped_scalar((other.fA * fC - fA * other.fC) * scale); round(point); return point->isFinite(); } 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 that require it. 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) const { 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(other.fTop->fPoint.fX) - fTop->fPoint.fX; double dy = static_cast(other.fTop->fPoint.fY) - 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::kConnector) { *alpha = (1.0 - s) * fTop->fAlpha + s * fBottom->fAlpha; } else if (other.fType == Type::kConnector) { double t = tNumer / denom; *alpha = (1.0 - t) * other.fTop->fAlpha + t * other.fBottom->fAlpha; } else if (fType == Type::kOuter && other.fType == Type::kOuter) { *alpha = 0; } else { *alpha = 255; } } return true; } }; struct SSEdge; struct SSVertex { SSVertex(Vertex* v) : fVertex(v), fPrev(nullptr), fNext(nullptr) {} Vertex* fVertex; SSEdge* fPrev; SSEdge* fNext; }; struct SSEdge { SSEdge(Edge* edge, SSVertex* prev, SSVertex* next) : fEdge(edge), fEvent(nullptr), fPrev(prev), fNext(next) { } Edge* fEdge; Event* fEvent; SSVertex* fPrev; SSVertex* fNext; }; typedef std::unordered_map SSVertexMap; typedef std::vector SSEdgeList; struct EdgeList { EdgeList() : fHead(nullptr), fTail(nullptr) {} Edge* fHead; Edge* fTail; void insert(Edge* edge, Edge* prev, Edge* next) { list_insert(edge, prev, next, &fHead, &fTail); } void append(Edge* e) { insert(e, fTail, nullptr); } void remove(Edge* edge) { list_remove(edge, &fHead, &fTail); } void removeAll() { while (fHead) { this->remove(fHead); } } void close() { if (fHead && fTail) { fTail->fRight = fHead; fHead->fLeft = fTail; } } bool contains(Edge* edge) const { return edge->fLeft || edge->fRight || fHead == edge; } }; struct EventList; struct Event { Event(SSEdge* edge, const SkPoint& point, uint8_t alpha) : fEdge(edge), fPoint(point), fAlpha(alpha) { } SSEdge* fEdge; SkPoint fPoint; uint8_t fAlpha; void apply(VertexList* mesh, Comparator& c, EventList* events, SkArenaAlloc& alloc); }; struct EventComparator { enum class Op { kLessThan, kGreaterThan }; EventComparator(Op op) : fOp(op) {} bool operator() (Event* const &e1, Event* const &e2) { return fOp == Op::kLessThan ? e1->fAlpha < e2->fAlpha : e1->fAlpha > e2->fAlpha; } Op fOp; }; typedef std::priority_queue, EventComparator> EventPQ; struct EventList : EventPQ { EventList(EventComparator comparison) : EventPQ(comparison) { } }; void create_event(SSEdge* e, EventList* events, SkArenaAlloc& alloc) { Vertex* prev = e->fPrev->fVertex; Vertex* next = e->fNext->fVertex; if (prev == next || !prev->fPartner || !next->fPartner) { return; } Edge bisector1(prev, prev->fPartner, 1, Edge::Type::kConnector); Edge bisector2(next, next->fPartner, 1, Edge::Type::kConnector); SkPoint p; uint8_t alpha; if (bisector1.intersect(bisector2, &p, &alpha)) { LOG("found edge event for %g, %g (original %g -> %g), will collapse to %g,%g alpha %d\n", prev->fID, next->fID, e->fEdge->fTop->fID, e->fEdge->fBottom->fID, p.fX, p.fY, alpha); e->fEvent = alloc.make(e, p, alpha); events->push(e->fEvent); } } void create_event(SSEdge* edge, Vertex* v, SSEdge* other, Vertex* dest, EventList* events, Comparator& c, SkArenaAlloc& alloc) { if (!v->fPartner) { return; } Vertex* top = edge->fEdge->fTop; Vertex* bottom = edge->fEdge->fBottom; if (!top || !bottom ) { return; } Line line = edge->fEdge->fLine; line.fC = -(dest->fPoint.fX * line.fA + dest->fPoint.fY * line.fB); Edge bisector(v, v->fPartner, 1, Edge::Type::kConnector); SkPoint p; uint8_t alpha = dest->fAlpha; if (line.intersect(bisector.fLine, &p) && !c.sweep_lt(p, top->fPoint) && c.sweep_lt(p, bottom->fPoint)) { LOG("found p edge event for %g, %g (original %g -> %g), will collapse to %g,%g alpha %d\n", dest->fID, v->fID, top->fID, bottom->fID, p.fX, p.fY, alpha); edge->fEvent = alloc.make(edge, p, alpha); events->push(edge->fEvent); } } /***************************************************************************************/ 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(bool emitCoverage, void* data) { Edge* e = fFirstEdge; VertexList vertices; vertices.append(e->fTop); int count = 1; while (e != nullptr) { if (kRight_Side == fSide) { vertices.append(e->fBottom); e = e->fRightPolyNext; } else { vertices.prepend(e->fBottom); e = e->fLeftPolyNext; } count++; } 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; if (count == 3) { return emit_triangle(prev, curr, next, emitCoverage, data); } 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, emitCoverage, data); v->fPrev->fNext = v->fNext; v->fNext->fPrev = v->fPrev; count--; if (v->fPrev == first) { v = v->fNext; } else { v = v->fPrev; } } else { v = v->fNext; } } return data; } }; Poly* addEdge(Edge* e, Side side, SkArenaAlloc& 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.make(e, side); fCount += 2; } else if (e->fBottom == fTail->fLastEdge->fBottom) { return poly; } else if (side == fTail->fSide) { fTail->addEdge(e); fCount++; } else { e = alloc.make(fTail->fLastEdge->fBottom, e->fBottom, 1, Edge::Type::kInner); fTail->addEdge(e); fCount++; if (partner) { partner->addEdge(e, side, alloc); poly = partner; } else { MonotonePoly* m = alloc.make(e, side); m->fPrev = fTail; fTail->fNext = m; fTail = m; } } return poly; } void* emit(bool emitCoverage, 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(emitCoverage, 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, SkArenaAlloc& alloc) { Poly* poly = alloc.make(v, winding); poly->fNext = *head; *head = poly; return poly; } void append_point_to_contour(const SkPoint& p, VertexList* contour, SkArenaAlloc& alloc) { Vertex* v = alloc.make(p, 255); #if LOGGING_ENABLED static float gID = 0.0f; v->fID = gID++; #endif contour->append(v); } SkScalar quad_error_at(const SkPoint pts[3], SkScalar t, SkScalar u) { SkQuadCoeff quad(pts); SkPoint p0 = to_point(quad.eval(t - 0.5f * u)); SkPoint mid = to_point(quad.eval(t)); SkPoint p1 = to_point(quad.eval(t + 0.5f * u)); if (!p0.isFinite() || !mid.isFinite() || !p1.isFinite()) { return 0; } return SkPointPriv::DistanceToLineSegmentBetweenSqd(mid, p0, p1); } void append_quadratic_to_contour(const SkPoint pts[3], SkScalar toleranceSqd, VertexList* contour, SkArenaAlloc& alloc) { SkQuadCoeff quad(pts); Sk2s aa = quad.fA * quad.fA; SkScalar denom = 2.0f * (aa[0] + aa[1]); Sk2s ab = quad.fA * quad.fB; SkScalar t = denom ? (-ab[0] - ab[1]) / denom : 0.0f; int nPoints = 1; SkScalar u = 1.0f; // Test possible subdivision values only at the point of maximum curvature. // If it passes the flatness metric there, it'll pass everywhere. while (nPoints < GrPathUtils::kMaxPointsPerCurve) { u = 1.0f / nPoints; if (quad_error_at(pts, t, u) < toleranceSqd) { break; } nPoints++; } for (int j = 1; j <= nPoints; j++) { append_point_to_contour(to_point(quad.eval(j * u)), contour, alloc); } } void generate_cubic_points(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, const SkPoint& p3, SkScalar tolSqd, VertexList* contour, int pointsLeft, SkArenaAlloc& alloc) { SkScalar d1 = SkPointPriv::DistanceToLineSegmentBetweenSqd(p1, p0, p3); SkScalar d2 = SkPointPriv::DistanceToLineSegmentBetweenSqd(p2, p0, p3); if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) || !SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) { append_point_to_contour(p3, contour, alloc); return; } 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; generate_cubic_points(p0, q[0], r[0], s, tolSqd, contour, pointsLeft, alloc); generate_cubic_points(s, r[1], q[2], p3, tolSqd, contour, pointsLeft, alloc); } // 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, VertexList* contours, SkArenaAlloc& alloc, bool *isLinear) { SkScalar toleranceSqd = tolerance * tolerance; SkPoint pts[4]; *isLinear = true; VertexList* contour = contours; SkPath::Iter iter(path, false); if (path.isInverseFillType()) { SkPoint quad[4]; clipBounds.toQuad(quad); for (int i = 3; i >= 0; i--) { append_point_to_contour(quad[i], contours, alloc); } contour++; } SkAutoConicToQuads converter; SkPath::Verb verb; while ((verb = iter.next(pts, false)) != SkPath::kDone_Verb) { 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) { append_quadratic_to_contour(quadPts, toleranceSqd, contour, alloc); quadPts += 2; } *isLinear = false; break; } case SkPath::kMove_Verb: if (contour->fHead) { contour++; } append_point_to_contour(pts[0], contour, alloc); break; case SkPath::kLine_Verb: { append_point_to_contour(pts[1], contour, alloc); break; } case SkPath::kQuad_Verb: { append_quadratic_to_contour(pts, toleranceSqd, contour, alloc); *isLinear = false; break; } case SkPath::kCubic_Verb: { int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance); generate_cubic_points(pts[0], pts[1], pts[2], pts[3], toleranceSqd, contour, pointsLeft, alloc); *isLinear = false; break; } case SkPath::kClose_Verb: case SkPath::kDone_Verb: break; } } } inline bool apply_fill_type(SkPath::FillType fillType, int winding) { 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; } } inline bool apply_fill_type(SkPath::FillType fillType, Poly* poly) { return poly && apply_fill_type(fillType, poly->fWinding); } Edge* new_edge(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkArenaAlloc& 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.make(top, bottom, winding, type); } 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 && v->fLastEdgeAbove) { *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 insert_edge_above(Edge* edge, Vertex* v, Comparator& c) { if (edge->fTop->fPoint == edge->fBottom->fPoint || c.sweep_lt(edge->fBottom->fPoint, edge->fTop->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_lt(edge->fBottom->fPoint, edge->fTop->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) { SkASSERT(edge->fTop && edge->fBottom); 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) { SkASSERT(edge->fTop && edge->fBottom); 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 merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c); void rewind(EdgeList* activeEdges, Vertex** current, Vertex* dst, Comparator& c) { if (!current || *current == dst || c.sweep_lt((*current)->fPoint, dst->fPoint)) { return; } Vertex* v = *current; LOG("rewinding active edges from vertex %g to vertex %g\n", v->fID, dst->fID); while (v != dst) { v = v->fPrev; for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { remove_edge(e, activeEdges); } Edge* leftEdge = v->fLeftEnclosingEdge; for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { insert_edge(e, leftEdge, activeEdges); leftEdge = e; } } *current = v; } void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c) { remove_edge_below(edge); edge->fTop = v; edge->recompute(); insert_edge_below(edge, v, c); rewind(activeEdges, current, edge->fTop, c); merge_collinear_edges(edge, activeEdges, current, c); } void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c) { remove_edge_above(edge); edge->fBottom = v; edge->recompute(); insert_edge_above(edge, v, c); rewind(activeEdges, current, edge->fTop, c); merge_collinear_edges(edge, activeEdges, current, c); } void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Vertex** current, 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); rewind(activeEdges, current, edge->fTop, c); other->fWinding += edge->fWinding; disconnect(edge); edge->fTop = edge->fBottom = nullptr; } else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) { rewind(activeEdges, current, edge->fTop, c); other->fWinding += edge->fWinding; set_bottom(edge, other->fTop, activeEdges, current, c); } else { rewind(activeEdges, current, other->fTop, c); edge->fWinding += other->fWinding; set_bottom(other, edge->fTop, activeEdges, current, c); } } void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Vertex** current, 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); rewind(activeEdges, current, edge->fTop, c); other->fWinding += edge->fWinding; disconnect(edge); edge->fTop = edge->fBottom = nullptr; } else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) { rewind(activeEdges, current, other->fTop, c); edge->fWinding += other->fWinding; set_top(other, edge->fBottom, activeEdges, current, c); } else { rewind(activeEdges, current, edge->fTop, c); other->fWinding += edge->fWinding; set_top(edge, other->fBottom, activeEdges, current, c); } } bool top_collinear(Edge* left, Edge* right) { if (!left || !right) { return false; } return left->fTop->fPoint == right->fTop->fPoint || !left->isLeftOf(right->fTop) || !right->isRightOf(left->fTop); } bool bottom_collinear(Edge* left, Edge* right) { if (!left || !right) { return false; } return left->fBottom->fPoint == right->fBottom->fPoint || !left->isLeftOf(right->fBottom) || !right->isRightOf(left->fBottom); } void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c) { for (;;) { if (top_collinear(edge->fPrevEdgeAbove, edge)) { merge_edges_above(edge->fPrevEdgeAbove, edge, activeEdges, current, c); } else if (top_collinear(edge, edge->fNextEdgeAbove)) { merge_edges_above(edge->fNextEdgeAbove, edge, activeEdges, current, c); } else if (bottom_collinear(edge->fPrevEdgeBelow, edge)) { merge_edges_below(edge->fPrevEdgeBelow, edge, activeEdges, current, c); } else if (bottom_collinear(edge, edge->fNextEdgeBelow)) { merge_edges_below(edge->fNextEdgeBelow, edge, activeEdges, current, c); } else { break; } } SkASSERT(!top_collinear(edge->fPrevEdgeAbove, edge)); SkASSERT(!top_collinear(edge, edge->fNextEdgeAbove)); SkASSERT(!bottom_collinear(edge->fPrevEdgeBelow, edge)); SkASSERT(!bottom_collinear(edge, edge->fNextEdgeBelow)); } bool split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c, SkArenaAlloc& alloc) { if (!edge->fTop || !edge->fBottom || v == edge->fTop || v == edge->fBottom) { return false; } 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); Vertex* top; Vertex* bottom; int winding = edge->fWinding; if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) { top = v; bottom = edge->fTop; set_top(edge, v, activeEdges, current, c); } else if (c.sweep_lt(edge->fBottom->fPoint, v->fPoint)) { top = edge->fBottom; bottom = v; set_bottom(edge, v, activeEdges, current, c); } else { top = v; bottom = edge->fBottom; set_bottom(edge, v, activeEdges, current, c); } Edge* newEdge = alloc.make(top, bottom, winding, edge->fType); insert_edge_below(newEdge, top, c); insert_edge_above(newEdge, bottom, c); merge_collinear_edges(newEdge, activeEdges, current, c); return true; } bool intersect_edge_pair(Edge* left, Edge* right, EdgeList* activeEdges, Vertex** current, Comparator& c, SkArenaAlloc& alloc) { if (!left->fTop || !left->fBottom || !right->fTop || !right->fBottom) { return false; } if (left->fTop == right->fTop || left->fBottom == right->fBottom) { return false; } if (c.sweep_lt(left->fTop->fPoint, right->fTop->fPoint)) { if (!left->isLeftOf(right->fTop)) { rewind(activeEdges, current, right->fTop, c); return split_edge(left, right->fTop, activeEdges, current, c, alloc); } } else { if (!right->isRightOf(left->fTop)) { rewind(activeEdges, current, left->fTop, c); return split_edge(right, left->fTop, activeEdges, current, c, alloc); } } if (c.sweep_lt(right->fBottom->fPoint, left->fBottom->fPoint)) { if (!left->isLeftOf(right->fBottom)) { rewind(activeEdges, current, right->fBottom, c); return split_edge(left, right->fBottom, activeEdges, current, c, alloc); } } else { if (!right->isRightOf(left->fBottom)) { rewind(activeEdges, current, left->fBottom, c); return split_edge(right, left->fBottom, activeEdges, current, c, alloc); } } return false; } Edge* connect(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkArenaAlloc& alloc, int winding_scale = 1) { if (!prev || !next || prev->fPoint == next->fPoint) { return nullptr; } Edge* edge = new_edge(prev, next, type, c, alloc); insert_edge_below(edge, edge->fTop, c); insert_edge_above(edge, edge->fBottom, c); edge->fWinding *= winding_scale; merge_collinear_edges(edge, nullptr, nullptr, c); return edge; } void merge_vertices(Vertex* src, Vertex* dst, VertexList* mesh, Comparator& c, SkArenaAlloc& 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); if (src->fPartner) { src->fPartner->fPartner = dst; } while (Edge* edge = src->fFirstEdgeAbove) { set_bottom(edge, dst, nullptr, nullptr, c); } while (Edge* edge = src->fFirstEdgeBelow) { set_top(edge, dst, nullptr, nullptr, c); } mesh->remove(src); dst->fSynthetic = true; } Vertex* create_sorted_vertex(const SkPoint& p, uint8_t alpha, VertexList* mesh, Vertex* reference, Comparator& c, SkArenaAlloc& alloc) { Vertex* prevV = reference; while (prevV && c.sweep_lt(p, prevV->fPoint)) { prevV = prevV->fPrev; } Vertex* nextV = prevV ? prevV->fNext : mesh->fHead; while (nextV && c.sweep_lt(nextV->fPoint, p)) { prevV = nextV; nextV = nextV->fNext; } Vertex* v; if (prevV && coincident(prevV->fPoint, p)) { v = prevV; } else if (nextV && coincident(nextV->fPoint, p)) { v = nextV; } else { v = alloc.make(p, alpha); #if LOGGING_ENABLED if (!prevV) { v->fID = mesh->fHead->fID - 1.0f; } else if (!nextV) { v->fID = mesh->fTail->fID + 1.0f; } else { v->fID = (prevV->fID + nextV->fID) * 0.5f; } #endif mesh->insert(v, prevV, nextV); } return v; } // If an edge's top and bottom points differ only by 1/2 machine epsilon in the primary // sort criterion, it may not be possible to split correctly, since there is no point which is // below the top and above the bottom. This function detects that case. bool nearly_flat(Comparator& c, Edge* edge) { SkPoint diff = edge->fBottom->fPoint - edge->fTop->fPoint; float primaryDiff = c.fDirection == Comparator::Direction::kHorizontal ? diff.fX : diff.fY; return fabs(primaryDiff) < std::numeric_limits::epsilon() && primaryDiff != 0.0f; } SkPoint clamp(SkPoint p, SkPoint min, SkPoint max, Comparator& c) { if (c.sweep_lt(p, min)) { return min; } else if (c.sweep_lt(max, p)) { return max; } else { return p; } } void compute_bisector(Edge* edge1, Edge* edge2, Vertex* v, SkArenaAlloc& alloc) { Line line1 = edge1->fLine; Line line2 = edge2->fLine; line1.normalize(); line2.normalize(); double cosAngle = line1.fA * line2.fA + line1.fB * line2.fB; if (cosAngle > 0.999) { return; } line1.fC += edge1->fWinding > 0 ? -1 : 1; line2.fC += edge2->fWinding > 0 ? -1 : 1; SkPoint p; if (line1.intersect(line2, &p)) { uint8_t alpha = edge1->fType == Edge::Type::kOuter ? 255 : 0; v->fPartner = alloc.make(p, alpha); LOG("computed bisector (%g,%g) alpha %d for vertex %g\n", p.fX, p.fY, alpha, v->fID); } } bool check_for_intersection(Edge* left, Edge* right, EdgeList* activeEdges, Vertex** current, VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { if (!left || !right) { return false; } SkPoint p; uint8_t alpha; if (left->intersect(*right, &p, &alpha) && p.isFinite()) { Vertex* v; LOG("found intersection, pt is %g, %g\n", p.fX, p.fY); Vertex* top = *current; // If the intersection point is above the current vertex, rewind to the vertex above the // intersection. while (top && c.sweep_lt(p, top->fPoint)) { top = top->fPrev; } if (!nearly_flat(c, left)) { p = clamp(p, left->fTop->fPoint, left->fBottom->fPoint, c); } if (!nearly_flat(c, right)) { p = clamp(p, right->fTop->fPoint, right->fBottom->fPoint, c); } if (p == left->fTop->fPoint) { v = left->fTop; } else if (p == left->fBottom->fPoint) { v = left->fBottom; } else if (p == right->fTop->fPoint) { v = right->fTop; } else if (p == right->fBottom->fPoint) { v = right->fBottom; } else { v = create_sorted_vertex(p, alpha, mesh, top, c, alloc); if (left->fTop->fPartner) { v->fSynthetic = true; compute_bisector(left, right, v, alloc); } } rewind(activeEdges, current, top ? top : v, c); split_edge(left, v, activeEdges, current, c, alloc); split_edge(right, v, activeEdges, current, c, alloc); v->fAlpha = SkTMax(v->fAlpha, alpha); return true; } return intersect_edge_pair(left, right, activeEdges, current, c, alloc); } void sanitize_contours(VertexList* contours, int contourCnt, bool approximate) { for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) { SkASSERT(contour->fHead); Vertex* prev = contour->fTail; if (approximate) { round(&prev->fPoint); } for (Vertex* v = contour->fHead; v;) { if (approximate) { round(&v->fPoint); } Vertex* next = v->fNext; Vertex* nextWrap = next ? next : contour->fHead; if (coincident(prev->fPoint, v->fPoint)) { LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY); contour->remove(v); } else if (!v->fPoint.isFinite()) { LOG("vertex %g,%g non-finite; removing\n", v->fPoint.fX, v->fPoint.fY); contour->remove(v); } else if (Line(prev->fPoint, nextWrap->fPoint).dist(v->fPoint) == 0.0) { LOG("vertex %g,%g collinear; removing\n", v->fPoint.fX, v->fPoint.fY); contour->remove(v); } else { prev = v; } v = next; } } } bool merge_coincident_vertices(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { if (!mesh->fHead) { return false; } bool merged = false; for (Vertex* v = mesh->fHead->fNext; v;) { Vertex* next = 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, v->fPrev, mesh, c, alloc); merged = true; } v = next; } return merged; } // Stage 2: convert the contours to a mesh of edges connecting the vertices. void build_edges(VertexList* contours, int contourCnt, VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) { Vertex* prev = contour->fTail; for (Vertex* v = contour->fHead; v;) { Vertex* next = v->fNext; connect(prev, v, Edge::Type::kInner, c, alloc); mesh->append(v); prev = v; v = next; } } } void connect_partners(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { for (Vertex* outer = mesh->fHead; outer; outer = outer->fNext) { if (Vertex* inner = outer->fPartner) { if ((inner->fPrev || inner->fNext) && (outer->fPrev || outer->fNext)) { // 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(outer, inner, Edge::Type::kConnector, c, alloc, 0); inner->fPartner = outer->fPartner = nullptr; } } } } template void sorted_merge(VertexList* front, VertexList* back, VertexList* result) { Vertex* a = front->fHead; Vertex* b = back->fHead; while (a && b) { if (sweep_lt(a->fPoint, b->fPoint)) { front->remove(a); result->append(a); a = front->fHead; } else { back->remove(b); result->append(b); b = back->fHead; } } result->append(*front); result->append(*back); } void sorted_merge(VertexList* front, VertexList* back, VertexList* result, Comparator& c) { if (c.fDirection == Comparator::Direction::kHorizontal) { sorted_merge(front, back, result); } else { sorted_merge(front, back, result); } #if LOGGING_ENABLED float id = 0.0f; for (Vertex* v = result->fHead; v; v = v->fNext) { v->fID = id++; } #endif } // Stage 3: sort the vertices by increasing sweep direction. template void merge_sort(VertexList* vertices) { Vertex* slow = vertices->fHead; if (!slow) { return; } Vertex* fast = slow->fNext; if (!fast) { return; } do { fast = fast->fNext; if (fast) { fast = fast->fNext; slow = slow->fNext; } } while (fast); VertexList front(vertices->fHead, slow); VertexList back(slow->fNext, vertices->fTail); front.fTail->fNext = back.fHead->fPrev = nullptr; merge_sort(&front); merge_sort(&back); vertices->fHead = vertices->fTail = nullptr; sorted_merge(&front, &back, vertices); } void dump_mesh(const VertexList& mesh) { #if LOGGING_ENABLED for (Vertex* v = mesh.fHead; v; v = v->fNext) { LOG("vertex %g (%g, %g) alpha %d", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha); if (Vertex* p = v->fPartner) { LOG(", partner %g (%g, %g) alpha %d\n", p->fID, p->fPoint.fX, p->fPoint.fY, p->fAlpha); } else { LOG(", null partner\n"); } for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) { LOG(" edge %g -> %g, winding %d\n", e->fTop->fID, e->fBottom->fID, e->fWinding); } for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { LOG(" edge %g -> %g, winding %d\n", e->fTop->fID, e->fBottom->fID, e->fWinding); } } #endif } void dump_skel(const SSEdgeList& ssEdges) { #if LOGGING_ENABLED for (SSEdge* edge : ssEdges) { if (edge->fEdge) { LOG("skel edge %g -> %g", edge->fPrev->fVertex->fID, edge->fNext->fVertex->fID); if (edge->fEdge->fTop && edge->fEdge->fBottom) { LOG(" (original %g -> %g)\n", edge->fEdge->fTop->fID, edge->fEdge->fBottom->fID); } else { LOG("\n"); } } } #endif } #ifdef SK_DEBUG void validate_edge_pair(Edge* left, Edge* right, Comparator& c) { if (!left || !right) { return; } if (left->fTop == right->fTop) { SkASSERT(left->isLeftOf(right->fBottom)); SkASSERT(right->isRightOf(left->fBottom)); } else if (c.sweep_lt(left->fTop->fPoint, right->fTop->fPoint)) { SkASSERT(left->isLeftOf(right->fTop)); } else { SkASSERT(right->isRightOf(left->fTop)); } if (left->fBottom == right->fBottom) { SkASSERT(left->isLeftOf(right->fTop)); SkASSERT(right->isRightOf(left->fTop)); } else if (c.sweep_lt(right->fBottom->fPoint, left->fBottom->fPoint)) { SkASSERT(left->isLeftOf(right->fBottom)); } else { SkASSERT(right->isRightOf(left->fBottom)); } } void validate_edge_list(EdgeList* edges, Comparator& c) { Edge* left = edges->fHead; if (!left) { return; } for (Edge* right = left->fRight; right; right = right->fRight) { validate_edge_pair(left, right, c); left = right; } } #endif // Stage 4: Simplify the mesh by inserting new vertices at intersecting edges. bool connected(Vertex* v) { return v->fFirstEdgeAbove || v->fFirstEdgeBelow; } bool simplify(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { LOG("simplifying complex polygons\n"); EdgeList activeEdges; bool found = false; for (Vertex* v = mesh->fHead; v != nullptr; v = v->fNext) { if (!connected(v)) { continue; } Edge* leftEnclosingEdge; Edge* rightEnclosingEdge; bool restartChecks; do { LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha); restartChecks = false; find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); v->fLeftEnclosingEdge = leftEnclosingEdge; v->fRightEnclosingEdge = rightEnclosingEdge; if (v->fFirstEdgeBelow) { for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) { if (check_for_intersection(leftEnclosingEdge, edge, &activeEdges, &v, mesh, c, alloc)) { restartChecks = true; break; } if (check_for_intersection(edge, rightEnclosingEdge, &activeEdges, &v, mesh, c, alloc)) { restartChecks = true; break; } } } else { if (check_for_intersection(leftEnclosingEdge, rightEnclosingEdge, &activeEdges, &v, mesh, c, alloc)) { restartChecks = true; } } found = found || restartChecks; } while (restartChecks); #ifdef SK_DEBUG validate_edge_list(&activeEdges, c); #endif 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; } } SkASSERT(!activeEdges.fHead && !activeEdges.fTail); return found; } // Stage 5: Tessellate the simplified mesh into monotone polygons. Poly* tessellate(const VertexList& vertices, SkArenaAlloc& alloc) { LOG("\ntessellating simple polygons\n"); EdgeList activeEdges; Poly* polys = nullptr; for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) { if (!connected(v)) { 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; Edge* rightEnclosingEdge; find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); Poly* leftPoly; Poly* rightPoly; 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* rightEdge = e->fNextEdgeAbove; remove_edge(e, &activeEdges); if (e->fRightPoly) { e->fRightPoly->addEdge(e, Poly::kLeft_Side, alloc); } if (rightEdge->fLeftPoly && rightEdge->fLeftPoly != e->fRightPoly) { 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.make(leftPoly->lastVertex(), v, 1, Edge::Type::kInner); 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; } void remove_non_boundary_edges(const VertexList& mesh, SkPath::FillType fillType, SkArenaAlloc& alloc) { LOG("removing non-boundary edges\n"); EdgeList activeEdges; for (Vertex* v = mesh.fHead; v != nullptr; v = v->fNext) { if (!connected(v)) { continue; } Edge* leftEnclosingEdge; Edge* rightEnclosingEdge; find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); bool prevFilled = leftEnclosingEdge && apply_fill_type(fillType, leftEnclosingEdge->fWinding); for (Edge* e = v->fFirstEdgeAbove; e;) { Edge* next = e->fNextEdgeAbove; remove_edge(e, &activeEdges); bool filled = apply_fill_type(fillType, e->fWinding); if (filled == prevFilled) { disconnect(e); } prevFilled = filled; e = next; } Edge* prev = leftEnclosingEdge; for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { if (prev) { e->fWinding += prev->fWinding; } insert_edge(e, prev, &activeEdges); prev = e; } } } // Note: this is the normal to the edge, but not necessarily unit length. void get_edge_normal(const Edge* e, SkVector* normal) { normal->set(SkDoubleToScalar(e->fLine.fA), SkDoubleToScalar(e->fLine.fB)); } // 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, SkArenaAlloc& 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 distPrev = e->dist(prev->fPoint); double distNext = prevEdge->dist(next->fPoint); SkVector normal; get_edge_normal(e, &normal); constexpr double kQuarterPixelSq = 0.25f * 0.25f; if (prev == next) { remove_edge(prevEdge, boundary); remove_edge(e, boundary); prevEdge = boundary->fTail; e = boundary->fHead; if (prevEdge) { get_edge_normal(prevEdge, &prevNormal); } } else if (prevNormal.dot(normal) < 0.0 && (distPrev * distPrev <= kQuarterPixelSq || distNext * distNext <= kQuarterPixelSq)) { Edge* join = new_edge(prev, next, Edge::Type::kInner, c, alloc); if (prev->fPoint != next->fPoint) { join->fLine.normalize(); join->fLine = join->fLine * join->fWinding; } 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; } } } void ss_connect(Vertex* v, Vertex* dest, Comparator& c, SkArenaAlloc& alloc) { if (v == dest) { return; } LOG("ss_connecting vertex %g to vertex %g\n", v->fID, dest->fID); if (v->fSynthetic) { connect(v, dest, Edge::Type::kConnector, c, alloc, 0); } else if (v->fPartner) { LOG("setting %g's partner to %g ", v->fPartner->fID, dest->fID); LOG("and %g's partner to null\n", v->fID); v->fPartner->fPartner = dest; v->fPartner = nullptr; } } void Event::apply(VertexList* mesh, Comparator& c, EventList* events, SkArenaAlloc& alloc) { if (!fEdge) { return; } Vertex* prev = fEdge->fPrev->fVertex; Vertex* next = fEdge->fNext->fVertex; SSEdge* prevEdge = fEdge->fPrev->fPrev; SSEdge* nextEdge = fEdge->fNext->fNext; if (!prevEdge || !nextEdge || !prevEdge->fEdge || !nextEdge->fEdge) { return; } Vertex* dest = create_sorted_vertex(fPoint, fAlpha, mesh, prev, c, alloc); dest->fSynthetic = true; SSVertex* ssv = alloc.make(dest); LOG("collapsing %g, %g (original edge %g -> %g) to %g (%g, %g) alpha %d\n", prev->fID, next->fID, fEdge->fEdge->fTop->fID, fEdge->fEdge->fBottom->fID, dest->fID, fPoint.fX, fPoint.fY, fAlpha); fEdge->fEdge = nullptr; ss_connect(prev, dest, c, alloc); ss_connect(next, dest, c, alloc); prevEdge->fNext = nextEdge->fPrev = ssv; ssv->fPrev = prevEdge; ssv->fNext = nextEdge; if (!prevEdge->fEdge || !nextEdge->fEdge) { return; } if (prevEdge->fEvent) { prevEdge->fEvent->fEdge = nullptr; } if (nextEdge->fEvent) { nextEdge->fEvent->fEdge = nullptr; } if (prevEdge->fPrev == nextEdge->fNext) { ss_connect(prevEdge->fPrev->fVertex, dest, c, alloc); prevEdge->fEdge = nextEdge->fEdge = nullptr; } else { compute_bisector(prevEdge->fEdge, nextEdge->fEdge, dest, alloc); SkASSERT(prevEdge != fEdge && nextEdge != fEdge); if (dest->fPartner) { create_event(prevEdge, events, alloc); create_event(nextEdge, events, alloc); } else { create_event(prevEdge, prevEdge->fPrev->fVertex, nextEdge, dest, events, c, alloc); create_event(nextEdge, nextEdge->fNext->fVertex, prevEdge, dest, events, c, alloc); } } } bool is_overlap_edge(Edge* e) { if (e->fType == Edge::Type::kOuter) { return e->fWinding != 0 && e->fWinding != 1; } else if (e->fType == Edge::Type::kInner) { return e->fWinding != 0 && e->fWinding != -2; } else { return false; } } // This is a stripped-down version of tessellate() which computes edges which // join two filled regions, which represent overlap regions, and collapses them. bool collapse_overlap_regions(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc, EventComparator comp) { LOG("\nfinding overlap regions\n"); EdgeList activeEdges; EventList events(comp); SSVertexMap ssVertices; SSEdgeList ssEdges; for (Vertex* v = mesh->fHead; v != nullptr; v = v->fNext) { if (!connected(v)) { continue; } Edge* leftEnclosingEdge; Edge* rightEnclosingEdge; find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); for (Edge* e = v->fLastEdgeAbove; e && e != leftEnclosingEdge;) { Edge* prev = e->fPrevEdgeAbove ? e->fPrevEdgeAbove : leftEnclosingEdge; remove_edge(e, &activeEdges); bool leftOverlap = prev && is_overlap_edge(prev); bool rightOverlap = is_overlap_edge(e); bool isOuterBoundary = e->fType == Edge::Type::kOuter && (!prev || prev->fWinding == 0 || e->fWinding == 0); if (prev) { e->fWinding -= prev->fWinding; } if (leftOverlap && rightOverlap) { LOG("found interior overlap edge %g -> %g, disconnecting\n", e->fTop->fID, e->fBottom->fID); disconnect(e); } else if (leftOverlap || rightOverlap) { LOG("found overlap edge %g -> %g%s\n", e->fTop->fID, e->fBottom->fID, isOuterBoundary ? ", is outer boundary" : ""); Vertex* prevVertex = e->fWinding < 0 ? e->fBottom : e->fTop; Vertex* nextVertex = e->fWinding < 0 ? e->fTop : e->fBottom; SSVertex* ssPrev = ssVertices[prevVertex]; if (!ssPrev) { ssPrev = ssVertices[prevVertex] = alloc.make(prevVertex); } SSVertex* ssNext = ssVertices[nextVertex]; if (!ssNext) { ssNext = ssVertices[nextVertex] = alloc.make(nextVertex); } SSEdge* ssEdge = alloc.make(e, ssPrev, ssNext); ssEdges.push_back(ssEdge); // SkASSERT(!ssPrev->fNext && !ssNext->fPrev); ssPrev->fNext = ssNext->fPrev = ssEdge; create_event(ssEdge, &events, alloc); if (!isOuterBoundary) { disconnect(e); } } e = prev; } Edge* prev = leftEnclosingEdge; for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { if (prev) { e->fWinding += prev->fWinding; } insert_edge(e, prev, &activeEdges); prev = e; } } bool complex = events.size() > 0; LOG("\ncollapsing overlap regions\n"); LOG("skeleton before:\n"); dump_skel(ssEdges); while (events.size() > 0) { Event* event = events.top(); events.pop(); event->apply(mesh, c, &events, alloc); } LOG("skeleton after:\n"); dump_skel(ssEdges); for (SSEdge* edge : ssEdges) { if (Edge* e = edge->fEdge) { connect(edge->fPrev->fVertex, edge->fNext->fVertex, e->fType, c, alloc, 0); } } return complex; } bool inversion(Vertex* prev, Vertex* next, Edge* origEdge, Comparator& c) { if (!prev || !next) { return true; } int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1; return winding != origEdge->fWinding; } // 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 stroke_boundary(EdgeList* boundary, VertexList* innerMesh, VertexList* outerMesh, Comparator& c, SkArenaAlloc& alloc) { LOG("\nstroking boundary\n"); // A boundary with fewer than 3 edges is degenerate. if (!boundary->fHead || !boundary->fHead->fRight || !boundary->fHead->fRight->fRight) { return; } Edge* prevEdge = boundary->fTail; Vertex* prevV = prevEdge->fWinding > 0 ? prevEdge->fTop : prevEdge->fBottom; SkVector prevNormal; get_edge_normal(prevEdge, &prevNormal); double radius = 0.5; Line prevInner(prevEdge->fLine); prevInner.fC -= radius; Line prevOuter(prevEdge->fLine); prevOuter.fC += radius; VertexList innerVertices; VertexList outerVertices; bool innerInversion = true; bool outerInversion = true; for (Edge* e = boundary->fHead; e != nullptr; e = e->fRight) { Vertex* v = e->fWinding > 0 ? e->fTop : e->fBottom; SkVector normal; get_edge_normal(e, &normal); Line inner(e->fLine); inner.fC -= radius; Line outer(e->fLine); outer.fC += radius; SkPoint innerPoint, outerPoint; LOG("stroking vertex %g (%g, %g)\n", v->fID, v->fPoint.fX, v->fPoint.fY); if (!prevEdge->fLine.nearParallel(e->fLine) && prevInner.intersect(inner, &innerPoint) && prevOuter.intersect(outer, &outerPoint)) { float cosAngle = normal.dot(prevNormal); if (cosAngle < -kCosMiterAngle) { Vertex* nextV = e->fWinding > 0 ? e->fBottom : e->fTop; // This is a pointy vertex whose angle is smaller than the threshold; miter it. Line bisector(innerPoint, outerPoint); Line tangent(v->fPoint, v->fPoint + SkPoint::Make(bisector.fA, bisector.fB)); if (tangent.fA == 0 && tangent.fB == 0) { continue; } tangent.normalize(); Line innerTangent(tangent); Line outerTangent(tangent); innerTangent.fC -= 0.5; outerTangent.fC += 0.5; SkPoint innerPoint1, innerPoint2, outerPoint1, outerPoint2; if (prevNormal.cross(normal) > 0) { // Miter inner points if (!innerTangent.intersect(prevInner, &innerPoint1) || !innerTangent.intersect(inner, &innerPoint2) || !outerTangent.intersect(bisector, &outerPoint)) { continue; } Line prevTangent(prevV->fPoint, prevV->fPoint + SkVector::Make(prevOuter.fA, prevOuter.fB)); Line nextTangent(nextV->fPoint, nextV->fPoint + SkVector::Make(outer.fA, outer.fB)); if (prevTangent.dist(outerPoint) > 0) { bisector.intersect(prevTangent, &outerPoint); } if (nextTangent.dist(outerPoint) < 0) { bisector.intersect(nextTangent, &outerPoint); } outerPoint1 = outerPoint2 = outerPoint; } else { // Miter outer points if (!outerTangent.intersect(prevOuter, &outerPoint1) || !outerTangent.intersect(outer, &outerPoint2)) { continue; } Line prevTangent(prevV->fPoint, prevV->fPoint + SkVector::Make(prevInner.fA, prevInner.fB)); Line nextTangent(nextV->fPoint, nextV->fPoint + SkVector::Make(inner.fA, inner.fB)); if (prevTangent.dist(innerPoint) > 0) { bisector.intersect(prevTangent, &innerPoint); } if (nextTangent.dist(innerPoint) < 0) { bisector.intersect(nextTangent, &innerPoint); } innerPoint1 = innerPoint2 = innerPoint; } if (!innerPoint1.isFinite() || !innerPoint2.isFinite() || !outerPoint1.isFinite() || !outerPoint2.isFinite()) { continue; } LOG("inner (%g, %g), (%g, %g), ", innerPoint1.fX, innerPoint1.fY, innerPoint2.fX, innerPoint2.fY); LOG("outer (%g, %g), (%g, %g)\n", outerPoint1.fX, outerPoint1.fY, outerPoint2.fX, outerPoint2.fY); Vertex* innerVertex1 = alloc.make(innerPoint1, 255); Vertex* innerVertex2 = alloc.make(innerPoint2, 255); Vertex* outerVertex1 = alloc.make(outerPoint1, 0); Vertex* outerVertex2 = alloc.make(outerPoint2, 0); innerVertex1->fPartner = outerVertex1; innerVertex2->fPartner = outerVertex2; outerVertex1->fPartner = innerVertex1; outerVertex2->fPartner = innerVertex2; if (!inversion(innerVertices.fTail, innerVertex1, prevEdge, c)) { innerInversion = false; } if (!inversion(outerVertices.fTail, outerVertex1, prevEdge, c)) { outerInversion = false; } innerVertices.append(innerVertex1); innerVertices.append(innerVertex2); outerVertices.append(outerVertex1); outerVertices.append(outerVertex2); } else { LOG("inner (%g, %g), ", innerPoint.fX, innerPoint.fY); LOG("outer (%g, %g)\n", outerPoint.fX, outerPoint.fY); Vertex* innerVertex = alloc.make(innerPoint, 255); Vertex* outerVertex = alloc.make(outerPoint, 0); innerVertex->fPartner = outerVertex; outerVertex->fPartner = innerVertex; if (!inversion(innerVertices.fTail, innerVertex, prevEdge, c)) { innerInversion = false; } if (!inversion(outerVertices.fTail, outerVertex, prevEdge, c)) { outerInversion = false; } innerVertices.append(innerVertex); outerVertices.append(outerVertex); } } prevInner = inner; prevOuter = outer; prevV = v; prevEdge = e; prevNormal = normal; } if (!inversion(innerVertices.fTail, innerVertices.fHead, prevEdge, c)) { innerInversion = false; } if (!inversion(outerVertices.fTail, outerVertices.fHead, prevEdge, c)) { outerInversion = false; } // Outer edges get 1 winding, and inner edges get -2 winding. This ensures that the interior // is always filled (1 + -2 = -1 for normal cases, 1 + 2 = 3 for thin features where the // interior inverts). // For total inversion cases, the shape has now reversed handedness, so invert the winding // so it will be detected during collapse_overlap_regions(). int innerWinding = innerInversion ? 2 : -2; int outerWinding = outerInversion ? -1 : 1; for (Vertex* v = innerVertices.fHead; v && v->fNext; v = v->fNext) { connect(v, v->fNext, Edge::Type::kInner, c, alloc, innerWinding); } connect(innerVertices.fTail, innerVertices.fHead, Edge::Type::kInner, c, alloc, innerWinding); for (Vertex* v = outerVertices.fHead; v && v->fNext; v = v->fNext) { connect(v, v->fNext, Edge::Type::kOuter, c, alloc, outerWinding); } connect(outerVertices.fTail, outerVertices.fHead, Edge::Type::kOuter, c, alloc, outerWinding); innerMesh->append(innerVertices); outerMesh->append(outerVertices); } void extract_boundary(EdgeList* boundary, Edge* e, SkPath::FillType fillType, SkArenaAlloc& alloc) { LOG("\nextracting boundary\n"); bool down = apply_fill_type(fillType, e->fWinding); Vertex* start = down ? e->fTop : e->fBottom; do { e->fWinding = down ? 1 : -1; Edge* next; e->fLine.normalize(); e->fLine = e->fLine * e->fWinding; 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; } while (e && (down ? e->fTop : e->fBottom) != start); } // Stage 5b: Extract boundaries from mesh, simplify and stroke them into a new mesh. void extract_boundaries(const VertexList& inMesh, VertexList* innerVertices, VertexList* outerVertices, SkPath::FillType fillType, Comparator& c, SkArenaAlloc& alloc) { remove_non_boundary_edges(inMesh, fillType, alloc); for (Vertex* v = inMesh.fHead; v; v = v->fNext) { while (v->fFirstEdgeBelow) { EdgeList boundary; extract_boundary(&boundary, v->fFirstEdgeBelow, fillType, alloc); simplify_boundary(&boundary, c, alloc); stroke_boundary(&boundary, innerVertices, outerVertices, c, alloc); } } } // This is a driver function that calls stages 2-5 in turn. void contours_to_mesh(VertexList* contours, int contourCnt, bool antialias, VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { #if LOGGING_ENABLED for (int i = 0; i < contourCnt; ++i) { Vertex* v = contours[i].fHead; SkASSERT(v); LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY); for (v = v->fNext; v; 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_mesh(VertexList* vertices, Comparator& c, SkArenaAlloc& alloc) { if (!vertices || !vertices->fHead) { return; } // Sort vertices in Y (secondarily in X). if (c.fDirection == Comparator::Direction::kHorizontal) { merge_sort(vertices); } else { merge_sort(vertices); } #if LOGGING_ENABLED for (Vertex* v = vertices->fHead; v != nullptr; v = v->fNext) { static float gID = 0.0f; v->fID = gID++; } #endif } Poly* contours_to_polys(VertexList* contours, int contourCnt, SkPath::FillType fillType, const SkRect& pathBounds, bool antialias, VertexList* outerMesh, SkArenaAlloc& alloc) { Comparator c(pathBounds.width() > pathBounds.height() ? Comparator::Direction::kHorizontal : Comparator::Direction::kVertical); VertexList mesh; contours_to_mesh(contours, contourCnt, antialias, &mesh, c, alloc); sort_mesh(&mesh, c, alloc); merge_coincident_vertices(&mesh, c, alloc); simplify(&mesh, c, alloc); LOG("\nsimplified mesh:\n"); dump_mesh(mesh); if (antialias) { VertexList innerMesh; extract_boundaries(mesh, &innerMesh, outerMesh, fillType, c, alloc); sort_mesh(&innerMesh, c, alloc); sort_mesh(outerMesh, c, alloc); merge_coincident_vertices(&innerMesh, c, alloc); bool was_complex = merge_coincident_vertices(outerMesh, c, alloc); was_complex = simplify(&innerMesh, c, alloc) || was_complex; was_complex = simplify(outerMesh, c, alloc) || was_complex; LOG("\ninner mesh before:\n"); dump_mesh(innerMesh); LOG("\nouter mesh before:\n"); dump_mesh(*outerMesh); EventComparator eventLT(EventComparator::Op::kLessThan); EventComparator eventGT(EventComparator::Op::kGreaterThan); was_complex = collapse_overlap_regions(&innerMesh, c, alloc, eventLT) || was_complex; was_complex = collapse_overlap_regions(outerMesh, c, alloc, eventGT) || was_complex; if (was_complex) { LOG("found complex mesh; taking slow path\n"); VertexList aaMesh; LOG("\ninner mesh after:\n"); dump_mesh(innerMesh); LOG("\nouter mesh after:\n"); dump_mesh(*outerMesh); connect_partners(outerMesh, c, alloc); connect_partners(&innerMesh, c, alloc); sorted_merge(&innerMesh, outerMesh, &aaMesh, c); merge_coincident_vertices(&aaMesh, c, alloc); simplify(&aaMesh, c, alloc); LOG("combined and simplified mesh:\n"); dump_mesh(aaMesh); outerMesh->fHead = outerMesh->fTail = nullptr; return tessellate(aaMesh, alloc); } else { LOG("no complex polygons; taking fast path\n"); return tessellate(innerMesh, alloc); } } else { return tessellate(mesh, alloc); } } // Stage 6: Triangulate the monotone polygons into a vertex buffer. void* polys_to_triangles(Poly* polys, SkPath::FillType fillType, bool emitCoverage, void* data) { for (Poly* poly = polys; poly; poly = poly->fNext) { if (apply_fill_type(fillType, poly)) { data = poly->emit(emitCoverage, data); } } return data; } Poly* path_to_polys(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, int contourCnt, SkArenaAlloc& alloc, bool antialias, bool* isLinear, VertexList* outerMesh) { SkPath::FillType fillType = path.getFillType(); if (SkPath::IsInverseFillType(fillType)) { contourCnt++; } std::unique_ptr contours(new VertexList[contourCnt]); path_to_contours(path, tolerance, clipBounds, contours.get(), alloc, isLinear); return contours_to_polys(contours.get(), contourCnt, path.getFillType(), path.getBounds(), antialias, outerMesh, alloc); } int get_contour_count(const SkPath& path, SkScalar tolerance) { int contourCnt; int maxPts = GrPathUtils::worstCasePointCount(path, &contourCnt, tolerance); if (maxPts <= 0) { return 0; } return contourCnt; } int64_t count_points(Poly* polys, SkPath::FillType fillType) { int64_t 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; } int64_t count_outer_mesh_points(const VertexList& outerMesh) { int64_t count = 0; for (Vertex* v = outerMesh.fHead; v; v = v->fNext) { for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { count += TESSELLATOR_WIREFRAME ? 12 : 6; } } return count; } void* outer_mesh_to_triangles(const VertexList& outerMesh, bool emitCoverage, void* data) { for (Vertex* v = outerMesh.fHead; v; v = v->fNext) { for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) { Vertex* v0 = e->fTop; Vertex* v1 = e->fBottom; Vertex* v2 = e->fBottom->fPartner; Vertex* v3 = e->fTop->fPartner; data = emit_triangle(v0, v1, v2, emitCoverage, data); data = emit_triangle(v0, v2, v3, emitCoverage, data); } } return data; } } // 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, bool* isLinear) { int contourCnt = get_contour_count(path, tolerance); if (contourCnt <= 0) { *isLinear = true; return 0; } SkArenaAlloc alloc(kArenaChunkSize); VertexList outerMesh; Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, antialias, isLinear, &outerMesh); SkPath::FillType fillType = antialias ? SkPath::kWinding_FillType : path.getFillType(); int64_t count64 = count_points(polys, fillType); if (antialias) { count64 += count_outer_mesh_points(outerMesh); } if (0 == count64 || count64 > SK_MaxS32) { return 0; } int count = count64; void* verts = vertexAllocator->lock(count); if (!verts) { SkDebugf("Could not allocate vertices\n"); return 0; } LOG("emitting %d verts\n", count); void* end = polys_to_triangles(polys, fillType, antialias, verts); end = outer_mesh_to_triangles(outerMesh, true, end); 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 = get_contour_count(path, tolerance); if (contourCnt <= 0) { *verts = nullptr; return 0; } SkArenaAlloc alloc(kArenaChunkSize); bool isLinear; Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, false, &isLinear, nullptr); SkPath::FillType fillType = path.getFillType(); int64_t count64 = count_points(polys, fillType); if (0 == count64 || count64 > SK_MaxS32) { *verts = nullptr; return 0; } int count = count64; *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(false, 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