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skia / skia / 7327c9ddfcd0bf7e01ed4440d0c429d49f0acdc8 / . / src / gpu / GrTessellator.cpp
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/*
* 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 <algorithm>
#include <cstdio>
#include <queue>
#include <unordered_map>
#include <utility>
/*
* 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 TESS_LOG printf
#else
#define TESS_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 <class T, T* T::*Prev, T* T::*Next>
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 <class T, T* T::*Prev, T* T::*Next>
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) {
TESS_LOG("emit_triangle %g (%g, %g) %d\n", v0->fID, v0->fPoint.fX, v0->fPoint.fY, v0->fAlpha);
TESS_LOG(" %g (%g, %g) %d\n", v1->fID, v1->fPoint.fX, v1->fPoint.fY, v1->fAlpha);
TESS_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<Vertex, &Vertex::fPrev, &Vertex::fNext>(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<Vertex, &Vertex::fPrev, &Vertex::fNext>(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<double>(q.fY) - p.fY) // a = dY
, fB(static_cast<double>(p.fX) - q.fX) // b = -dX
, fC(static_cast<double>(p.fY) * q.fX - // c = cross(q, p)
static_cast<double>(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 {
TESS_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<double>(other.fTop->fPoint.fX) - fTop->fPoint.fX;
double dy = static_cast<double>(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<Vertex*, SSVertex*> SSVertexMap;
typedef std::vector<SSEdge*> SSEdgeList;
struct EdgeList {
EdgeList() : fHead(nullptr), fTail(nullptr) {}
Edge* fHead;
Edge* fTail;
void insert(Edge* edge, Edge* prev, Edge* next) {
list_insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &fHead, &fTail);
}
void append(Edge* e) {
insert(e, fTail, nullptr);
}
void remove(Edge* edge) {
list_remove<Edge, &Edge::fLeft, &Edge::fRight>(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<Event*, std::vector<Event*>, 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)) {
TESS_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<Event>(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)) {
TESS_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<Event>(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++;
TESS_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, &Edge::fRightPolyPrev, &Edge::fRightPolyNext>(
edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge);
edge->fUsedInRightPoly = true;
} else {
SkASSERT(!edge->fUsedInLeftPoly);
list_insert<Edge, &Edge::fLeftPolyPrev, &Edge::fLeftPolyNext>(
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<double>(curr->fPoint.fX) - prev->fPoint.fX;
double ay = static_cast<double>(curr->fPoint.fY) - prev->fPoint.fY;
double bx = static_cast<double>(next->fPoint.fX) - curr->fPoint.fX;
double by = static_cast<double>(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) {
TESS_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<MonotonePoly>(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<Edge>(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<MonotonePoly>(e, side);
m->fPrev = fTail;
fTail->fNext = m;
fTail = m;
}
}
return poly;
}
void* emit(bool emitCoverage, void *data) {
if (fCount < 3) {
return data;
}
TESS_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<Poly>(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<Vertex>(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)) != 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<Edge>(top, bottom, winding, type);
}
void remove_edge(Edge* edge, EdgeList* edges) {
TESS_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) {
TESS_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;
}
TESS_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, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
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;
}
TESS_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, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
edge, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow);
}
void remove_edge_above(Edge* edge) {
SkASSERT(edge->fTop && edge->fBottom);
TESS_LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
edge->fBottom->fID);
list_remove<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove);
}
void remove_edge_below(Edge* edge) {
SkASSERT(edge->fTop && edge->fBottom);
TESS_LOG("removing edge (%g -> %g) below vertex %g\n",
edge->fTop->fID, edge->fBottom->fID, edge->fTop->fID);
list_remove<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
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;
TESS_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)) {
TESS_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)) {
TESS_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;
}
TESS_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<Edge>(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) {
TESS_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<Vertex>(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<float>::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<Vertex>(p, alpha);
TESS_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;
TESS_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)) {
TESS_LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY);
contour->remove(v);
} else if (!v->fPoint.isFinite()) {
TESS_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) {
TESS_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 <CompareFunc sweep_lt>
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<sweep_lt_horiz>(front, back, result);
} else {
sorted_merge<sweep_lt_vert>(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 <CompareFunc sweep_lt>
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<sweep_lt>(&front);
merge_sort<sweep_lt>(&back);
vertices->fHead = vertices->fTail = nullptr;
sorted_merge<sweep_lt>(&front, &back, vertices);
}
void dump_mesh(const VertexList& mesh) {
#if LOGGING_ENABLED
for (Vertex* v = mesh.fHead; v; v = v->fNext) {
TESS_LOG("vertex %g (%g, %g) alpha %d", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
if (Vertex* p = v->fPartner) {
TESS_LOG(", partner %g (%g, %g) alpha %d\n",
p->fID, p->fPoint.fX, p->fPoint.fY, p->fAlpha);
} else {
TESS_LOG(", null partner\n");
}
for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
TESS_LOG(" edge %g -> %g, winding %d\n", e->fTop->fID, e->fBottom->fID, e->fWinding);
}
for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
TESS_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) {
TESS_LOG("skel edge %g -> %g",
edge->fPrev->fVertex->fID,
edge->fNext->fVertex->fID);
if (edge->fEdge->fTop && edge->fEdge->fBottom) {
TESS_LOG(" (original %g -> %g)\n",
edge->fEdge->fTop->fID,
edge->fEdge->fBottom->fID);
} else {
TESS_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) {
TESS_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 {
TESS_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) {
TESS_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
TESS_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
TESS_LOG("edges above:\n");
for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
TESS_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);
}
TESS_LOG("edges below:\n");
for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
TESS_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<Edge>(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
TESS_LOG("\nactive edges:\n");
for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) {
TESS_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) {
TESS_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;
}
TESS_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) {
TESS_LOG("setting %g's partner to %g ", v->fPartner->fID, dest->fID);
TESS_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<SSVertex>(dest);
TESS_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) {
TESS_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) {
TESS_LOG("found interior overlap edge %g -> %g, disconnecting\n",
e->fTop->fID, e->fBottom->fID);
disconnect(e);
} else if (leftOverlap || rightOverlap) {
TESS_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<SSVertex>(prevVertex);
}
SSVertex* ssNext = ssVertices[nextVertex];
if (!ssNext) {
ssNext = ssVertices[nextVertex] = alloc.make<SSVertex>(nextVertex);
}
SSEdge* ssEdge = alloc.make<SSEdge>(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;
TESS_LOG("\ncollapsing overlap regions\n");
TESS_LOG("skeleton before:\n");
dump_skel(ssEdges);
while (events.size() > 0) {
Event* event = events.top();
events.pop();
event->apply(mesh, c, &events, alloc);
}
TESS_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) {
TESS_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;
TESS_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;
}
TESS_LOG("inner (%g, %g), (%g, %g), ",
innerPoint1.fX, innerPoint1.fY, innerPoint2.fX, innerPoint2.fY);
TESS_LOG("outer (%g, %g), (%g, %g)\n",
outerPoint1.fX, outerPoint1.fY, outerPoint2.fX, outerPoint2.fY);
Vertex* innerVertex1 = alloc.make<Vertex>(innerPoint1, 255);
Vertex* innerVertex2 = alloc.make<Vertex>(innerPoint2, 255);
Vertex* outerVertex1 = alloc.make<Vertex>(outerPoint1, 0);
Vertex* outerVertex2 = alloc.make<Vertex>(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 {
TESS_LOG("inner (%g, %g), ", innerPoint.fX, innerPoint.fY);
TESS_LOG("outer (%g, %g)\n", outerPoint.fX, outerPoint.fY);
Vertex* innerVertex = alloc.make<Vertex>(innerPoint, 255);
Vertex* outerVertex = alloc.make<Vertex>(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) {
TESS_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);
TESS_LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
for (v = v->fNext; v; v = v->fNext) {
TESS_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<sweep_lt_horiz>(vertices);
} else {
merge_sort<sweep_lt_vert>(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);
TESS_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;
TESS_LOG("\ninner mesh before:\n");
dump_mesh(innerMesh);
TESS_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) {
TESS_LOG("found complex mesh; taking slow path\n");
VertexList aaMesh;
TESS_LOG("\ninner mesh after:\n");
dump_mesh(innerMesh);
TESS_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);
TESS_LOG("combined and simplified mesh:\n");
dump_mesh(aaMesh);
outerMesh->fHead = outerMesh->fTail = nullptr;
return tessellate(aaMesh, alloc);
} else {
TESS_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<VertexList[]> 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;
}
TESS_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<int>((static_cast<uint8_t*>(end) - static_cast<uint8_t*>(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<SkPoint*>(poly->emit(false, pointsEnd));
while (start != pointsEnd) {
vertsEnd->fPos = *start;
vertsEnd->fWinding = poly->fWinding;
++start;
++vertsEnd;
}
}
}
int actualCount = static_cast<int>(vertsEnd - *verts);
SkASSERT(actualCount <= count);
SkASSERT(pointsEnd - points == actualCount);
delete[] points;
return actualCount;
}
} // namespace