/* * 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 "SkArenaAlloc.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 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 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 namespace { const int kArenaChunkSize = 16 * 1024; 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) , fPartner(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; // " Vertex* fPartner; // Corresponding inner or outer vertex (for AA). 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); 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, 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) { LOG("emit_triangle (%g, %g) %d\n", v0->fPoint.fX, v0->fPoint.fY, v0->fAlpha); LOG(" (%g, %g) %d\n", v1->fPoint.fX, v1->fPoint.fY, v1->fAlpha); LOG(" (%g, %g) %d\n", v2->fPoint.fX, v2->fPoint.fY, v2->fAlpha); #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) {} 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); } // 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 that 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(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 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 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; 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, aaParams, 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, aaParams, 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(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, 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)); return mid.distanceToLineSegmentBetweenSqd(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; // Test possible subdivision values only at the point of maximum curvature. // If it passes the flatness metric there, it'll pass everywhere. for (;;) { 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 = p1.distanceToLineSegmentBetweenSqd(p0, p3); SkScalar d2 = p2.distanceToLineSegmentBetweenSqd(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)) != 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 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_lt(next->fTop->fPoint, edge->fTop->fPoint) && next->isRightOf(edge->fTop)) || (c.sweep_lt(edge->fTop->fPoint, next->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_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) { 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, SkArenaAlloc& alloc); void cleanup_active_edges(Edge* edge, EdgeList* activeEdges, Comparator& c, SkArenaAlloc& 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_lt(leftTop->fPoint, top->fPoint) && !edge->fLeft->isLeftOf(top)) { split_edge(edge->fLeft, edge->fTop, activeEdges, c, alloc); } else if (c.sweep_lt(top->fPoint, leftTop->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_lt(rightTop->fPoint, top->fPoint) && !edge->fRight->isRightOf(top)) { split_edge(edge->fRight, top, activeEdges, c, alloc); } else if (c.sweep_lt(top->fPoint, rightTop->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, SkArenaAlloc& 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_lt(edge->fBottom->fPoint, v->fPoint)) { set_bottom(edge, v, activeEdges, c); } else { Edge* newEdge = alloc.make(v, edge->fBottom, edge->fWinding, edge->fType); 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, SkArenaAlloc& alloc, int winding_scale = 1) { 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, 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; } 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, SkArenaAlloc& 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_lt(edge->fBottom->fPoint, p)) { 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_lt(other->fBottom->fPoint, p)) { 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.make(p, alpha); 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); } v->fAlpha = SkTMax(v->fAlpha, alpha); return v; } return nullptr; } 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; if (coincident(prev->fPoint, v->fPoint)) { LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY); contour->remove(v); } prev = v; v = next; } } } void merge_coincident_vertices(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) { if (!mesh->fHead) { return; } 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(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* outerVertices, Comparator& c, SkArenaAlloc& alloc) { for (Vertex* outer = outerVertices->fHead; outer; outer = outer->fNext) { if (Vertex* inner = outer->fPartner) { // 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); } } // 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); } // Stage 4: Simplify the mesh by inserting new vertices at intersecting edges. void simplify(const VertexList& vertices, Comparator& c, SkArenaAlloc& 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; Edge* rightEnclosingEdge; 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; } } // This is a stripped-down version of simplify() (the Bentley-Ottmann algorithm) that // early-returns true on the first found intersection, false if none. bool is_complex(const VertexList& vertices) { LOG("testing polygon complexity\n"); EdgeList activeEdges; for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) { if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { continue; } Edge* leftEnclosingEdge; Edge* rightEnclosingEdge; find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge); SkPoint dummy; if (v->fFirstEdgeBelow) { for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) { if (edge && leftEnclosingEdge && edge->intersect(*leftEnclosingEdge, &dummy)) { activeEdges.removeAll(); return true; } if (edge && rightEnclosingEdge && edge->intersect(*rightEnclosingEdge, &dummy)) { activeEdges.removeAll(); return true; } } } else if (leftEnclosingEdge && rightEnclosingEdge && leftEnclosingEdge->intersect(*rightEnclosingEdge, &dummy)) { activeEdges.removeAll(); return true; } 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; } } activeEdges.removeAll(); return false; } // Stage 5: Tessellate the simplified mesh into monotone polygons. Poly* tessellate(const VertexList& vertices, SkArenaAlloc& 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; 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; SkASSERT(rightEdge->isRightOf(e->fTop)); 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 (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) { 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) * 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, 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 dist = e->dist(prev->fPoint); SkVector normal; get_edge_normal(e, &normal); double denom = 0.0625f * 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; } } } void fix_inversions(Vertex* prev, Vertex* next, Edge* prevBisector, Edge* nextBisector, Edge* prevEdge, Comparator& c) { if (!prev || !next) { return; } int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1; SkPoint p; uint8_t alpha; if (winding != prevEdge->fWinding && prevBisector->intersect(*nextBisector, &p, &alpha)) { prev->fPoint = next->fPoint = p; prev->fAlpha = next->fAlpha = alpha; } } // 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) { // A boundary with fewer than 3 edges is degenerate. if (!boundary->fHead || !boundary->fHead->fRight || !boundary->fHead->fRight->fRight) { return; } Edge* prevEdge = boundary->fTail; float radius = 0.5f; double offset = radius * sqrt(prevEdge->fLine.magSq()) * prevEdge->fWinding; Line prevInner(prevEdge->fLine); prevInner.fC -= offset; Line prevOuter(prevEdge->fLine); prevOuter.fC += offset; VertexList innerVertices; VertexList outerVertices; Edge* prevBisector = nullptr; for (Edge* e = boundary->fHead; e != nullptr; e = e->fRight) { double offset = radius * sqrt(e->fLine.magSq()) * e->fWinding; Line inner(e->fLine); inner.fC -= offset; Line outer(e->fLine); outer.fC += offset; SkPoint innerPoint, outerPoint; if (prevInner.intersect(inner, &innerPoint) && prevOuter.intersect(outer, &outerPoint)) { Vertex* innerVertex = alloc.make(innerPoint, 255); Vertex* outerVertex = alloc.make(outerPoint, 0); Edge* bisector = new_edge(outerVertex, innerVertex, Edge::Type::kConnector, c, alloc); fix_inversions(innerVertices.fTail, innerVertex, prevBisector, bisector, prevEdge, c); fix_inversions(outerVertices.fTail, outerVertex, prevBisector, bisector, prevEdge, c); innerVertex->fPartner = outerVertex; outerVertex->fPartner = innerVertex; innerVertices.append(innerVertex); outerVertices.append(outerVertex); prevBisector = bisector; } prevInner = inner; prevOuter = outer; prevEdge = e; } Vertex* innerVertex = innerVertices.fHead; Vertex* outerVertex = outerVertices.fHead; if (!innerVertex || !outerVertex) { return; } Edge* bisector = new_edge(outerVertices.fHead, innerVertices.fHead, Edge::Type::kConnector, c, alloc); fix_inversions(innerVertices.fTail, innerVertices.fHead, prevBisector, bisector, prevEdge, c); fix_inversions(outerVertices.fTail, outerVertices.fHead, prevBisector, bisector, prevEdge, c); Vertex* prevInnerVertex = innerVertices.fTail; Vertex* prevOuterVertex = outerVertices.fTail; while (innerVertex && outerVertex) { // 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). connect(prevOuterVertex, outerVertex, Edge::Type::kOuter, c, alloc); connect(prevInnerVertex, innerVertex, Edge::Type::kInner, c, alloc, -2); prevInnerVertex = innerVertex; prevOuterVertex = outerVertex; innerVertex = innerVertex->fNext; outerVertex = outerVertex->fNext; } innerMesh->append(innerVertices); outerMesh->append(outerVertices); } void extract_boundary(EdgeList* boundary, Edge* e, SkPath::FillType fillType, SkArenaAlloc& alloc) { bool down = apply_fill_type(fillType, e->fWinding); 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 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); if (antialias) { VertexList innerMesh; extract_boundaries(mesh, &innerMesh, outerMesh, fillType, c, alloc); sort_mesh(&innerMesh, c, alloc); sort_mesh(outerMesh, c, alloc); if (is_complex(innerMesh) || is_complex(*outerMesh)) { LOG("found complex mesh; taking slow path\n"); VertexList aaMesh; connect_partners(outerMesh, c, alloc); sorted_merge(&innerMesh, outerMesh, &aaMesh, c); merge_coincident_vertices(&aaMesh, c, alloc); simplify(aaMesh, c, alloc); outerMesh->fHead = outerMesh->fTail = nullptr; return tessellate(aaMesh, alloc); } else { LOG("no complex polygons; taking fast path\n"); merge_coincident_vertices(&innerMesh, c, alloc); 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, 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, 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; } if (maxPts > ((int)SK_MaxU16 + 1)) { SkDebugf("Path not rendered, too many verts (%d)\n", maxPts); return 0; } return contourCnt; } 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; } int count_outer_mesh_points(const VertexList& outerMesh) { int 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, const AAParams* aaParams, 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, aaParams, data); data = emit_triangle(v0, v2, v3, aaParams, 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, const GrColor& color, bool canTweakAlphaForCoverage, 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(); int count = count_points(polys, fillType); if (0 == count) { return 0; } if (antialias) { count += count_outer_mesh_points(outerMesh); } 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); end = outer_mesh_to_triangles(outerMesh, &aaParams, 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) { 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(); 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