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skia / skia / refs/heads/chrome/m57 / . / 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 "GrTessellator.h"
#include "GrDefaultGeoProcFactory.h"
#include "GrPathUtils.h"
#include "SkChunkAlloc.h"
#include "SkGeometry.h"
#include "SkPath.h"
#include <stdio.h>
/*
* There are six stages to the basic algorithm:
*
* 1) Linearize the path contours into piecewise linear segments (path_to_contours()).
* 2) Build a mesh of edges connecting the vertices (build_edges()).
* 3) Sort the vertices in Y (and secondarily in X) (merge_sort()).
* 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()).
* 5) Tessellate the simplified mesh into monotone polygons (tessellate()).
* 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()).
*
* For screenspace antialiasing, the algorithm is modified as follows:
*
* Run steps 1-5 above to produce polygons.
* 5b) Apply fill rules to extract boundary contours from the polygons (extract_boundaries()).
* 5c) Simplify boundaries to remove "pointy" vertices which cause inversions (simplify_boundary()).
* 5d) Displace edges by half a pixel inward and outward along their normals. Intersect to find
* new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a new
* antialiased mesh from those vertices (boundary_to_aa_mesh()).
* Run steps 3-6 above on the new mesh, and produce antialiased triangles.
*
* The vertex sorting in step (3) is a merge sort, since it plays well with the linked list
* of vertices (and the necessity of inserting new vertices on intersection).
*
* Stages (4) and (5) use an active edge list, which a list of all edges for which the
* sweep line has crossed the top vertex, but not the bottom vertex. It's sorted
* left-to-right based on the point where both edges are active (when both top vertices
* have been seen, so the "lower" top vertex of the two). If the top vertices are equal
* (shared), it's sorted based on the last point where both edges are active, so the
* "upper" bottom vertex.
*
* The most complex step is the simplification (4). It's based on the Bentley-Ottman
* line-sweep algorithm, but due to floating point inaccuracy, the intersection points are
* not exact and may violate the mesh topology or active edge list ordering. We
* accommodate this by adjusting the topology of the mesh and AEL to match the intersection
* points. This occurs in three ways:
*
* A) Intersections may cause a shortened edge to no longer be ordered with respect to its
* neighbouring edges at the top or bottom vertex. This is handled by merging the
* edges (merge_collinear_edges()).
* B) Intersections may cause an edge to violate the left-to-right ordering of the
* active edge list. This is handled by splitting the neighbour edge on the
* intersected vertex (cleanup_active_edges()).
* C) Shortening an edge may cause an active edge to become inactive or an inactive edge
* to become active. This is handled by removing or inserting the edge in the active
* edge list (fix_active_state()).
*
* The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and
* Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it
* currently uses a linked list for the active edge list, rather than a 2-3 tree as the
* paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also
* become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N)
* insertions and removals was greater than the cost of infrequent O(N) lookups with the
* linked list implementation. With the latter, all removals are O(1), and most insertions
* are O(1), since we know the adjacent edge in the active edge list based on the topology.
* Only type 2 vertices (see paper) require the O(N) lookups, and these are much less
* frequent. There may be other data structures worth investigating, however.
*
* Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the
* path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y
* coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall,
* we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so
* that the "left" and "right" orientation in the code remains correct (edges to the left are
* increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90
* degrees counterclockwise, rather that transposing.
*/
#define LOGGING_ENABLED 0
#if LOGGING_ENABLED
#define LOG printf
#else
#define LOG(...)
#endif
#define ALLOC_NEW(Type, args, alloc) new (alloc.allocThrow(sizeof(Type))) Type args
namespace {
struct Vertex;
struct Edge;
struct Poly;
template <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)
, fProcessed(false)
, fAlpha(alpha)
#if LOGGING_ENABLED
, fID (-1.0f)
#endif
{}
SkPoint fPoint; // Vertex position
Vertex* fPrev; // Linked list of contours, then Y-sorted vertices.
Vertex* fNext; // "
Edge* fFirstEdgeAbove; // Linked list of edges above this vertex.
Edge* fLastEdgeAbove; // "
Edge* fFirstEdgeBelow; // Linked list of edges below this vertex.
Edge* fLastEdgeBelow; // "
bool fProcessed; // Has this vertex been seen in simplify()?
uint8_t fAlpha;
#if LOGGING_ENABLED
float fID; // Identifier used for logging.
#endif
};
/***************************************************************************************/
struct AAParams {
bool fTweakAlpha;
GrColor fColor;
};
typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b);
struct Comparator {
CompareFunc sweep_lt;
CompareFunc sweep_gt;
};
bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) {
return a.fX == b.fX ? a.fY > b.fY : a.fX < b.fX;
}
bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) {
return a.fY == b.fY ? a.fX < b.fX : a.fY < b.fY;
}
bool sweep_gt_horiz(const SkPoint& a, const SkPoint& b) {
return a.fX == b.fX ? a.fY < b.fY : a.fX > b.fX;
}
bool sweep_gt_vert(const SkPoint& a, const SkPoint& b) {
return a.fY == b.fY ? a.fX > b.fX : a.fY > b.fY;
}
inline void* emit_vertex(Vertex* v, const AAParams* aaParams, void* data) {
if (!aaParams) {
SkPoint* d = static_cast<SkPoint*>(data);
*d++ = v->fPoint;
return d;
}
if (aaParams->fTweakAlpha) {
auto d = static_cast<GrDefaultGeoProcFactory::PositionColorAttr*>(data);
d->fPosition = v->fPoint;
d->fColor = SkAlphaMulQ(aaParams->fColor, SkAlpha255To256(v->fAlpha));
d++;
return d;
}
auto d = static_cast<GrDefaultGeoProcFactory::PositionColorCoverageAttr*>(data);
d->fPosition = v->fPoint;
d->fColor = aaParams->fColor;
d->fCoverage = GrNormalizeByteToFloat(v->fAlpha);
d++;
return d;
}
void* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, const AAParams* aaParams, void* data) {
#if TESSELLATOR_WIREFRAME
data = emit_vertex(v0, aaParams, data);
data = emit_vertex(v1, aaParams, data);
data = emit_vertex(v1, aaParams, data);
data = emit_vertex(v2, aaParams, data);
data = emit_vertex(v2, aaParams, data);
data = emit_vertex(v0, aaParams, data);
#else
data = emit_vertex(v0, aaParams, data);
data = emit_vertex(v1, aaParams, data);
data = emit_vertex(v2, aaParams, data);
#endif
return data;
}
struct VertexList {
VertexList() : fHead(nullptr), fTail(nullptr) {}
Vertex* fHead;
Vertex* fTail;
void insert(Vertex* v, Vertex* prev, Vertex* next) {
list_insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, prev, next, &fHead, &fTail);
}
void append(Vertex* v) {
insert(v, fTail, nullptr);
}
void prepend(Vertex* v) {
insert(v, nullptr, fHead);
}
void remove(Vertex* v) {
list_remove<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);
}
// 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<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;
}
double magSq() const {
return fA * fA + fB * fB;
}
// Compute the intersection of two (infinite) Lines.
bool intersect(const Line& other, SkPoint* point) {
double denom = fA * other.fB - fB * other.fA;
if (denom == 0.0) {
return false;
}
double scale = 1.0f / denom;
point->fX = SkDoubleToScalar((fB * other.fC - other.fB * fC) * scale);
point->fY = SkDoubleToScalar((other.fA * fC - fA * other.fC) * scale);
round(point);
return true;
}
double fA, fB, fC;
};
/**
* An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and
* "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf().
* Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating
* point). For speed, that case is only tested by the callers which require it (e.g.,
* cleanup_active_edges()). Edges also handle checking for intersection with other edges.
* Currently, this converts the edges to the parametric form, in order to avoid doing a division
* until an intersection has been confirmed. This is slightly slower in the "found" case, but
* a lot faster in the "not found" case.
*
* The coefficients of the line equation stored in double precision to avoid catastrphic
* cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is
* correct in float, since it's a polynomial of degree 2. The intersect() function, being
* degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its
* output may be incorrect, and adjusting the mesh topology to match (see comment at the top of
* this file).
*/
struct Edge {
enum class Type { kInner, kOuter, kConnector };
Edge(Vertex* top, Vertex* bottom, int winding, Type type)
: fWinding(winding)
, fTop(top)
, fBottom(bottom)
, fType(type)
, fLeft(nullptr)
, fRight(nullptr)
, fPrevEdgeAbove(nullptr)
, fNextEdgeAbove(nullptr)
, fPrevEdgeBelow(nullptr)
, fNextEdgeBelow(nullptr)
, fLeftPoly(nullptr)
, fRightPoly(nullptr)
, fLeftPolyPrev(nullptr)
, fLeftPolyNext(nullptr)
, fRightPolyPrev(nullptr)
, fRightPolyNext(nullptr)
, fUsedInLeftPoly(false)
, fUsedInRightPoly(false)
, fLine(top, bottom) {
}
int fWinding; // 1 == edge goes downward; -1 = edge goes upward.
Vertex* fTop; // The top vertex in vertex-sort-order (sweep_lt).
Vertex* fBottom; // The bottom vertex in vertex-sort-order.
Type fType;
Edge* fLeft; // The linked list of edges in the active edge list.
Edge* fRight; // "
Edge* fPrevEdgeAbove; // The linked list of edges in the bottom Vertex's "edges above".
Edge* fNextEdgeAbove; // "
Edge* fPrevEdgeBelow; // The linked list of edges in the top Vertex's "edges below".
Edge* fNextEdgeBelow; // "
Poly* fLeftPoly; // The Poly to the left of this edge, if any.
Poly* fRightPoly; // The Poly to the right of this edge, if any.
Edge* fLeftPolyPrev;
Edge* fLeftPolyNext;
Edge* fRightPolyPrev;
Edge* fRightPolyNext;
bool fUsedInLeftPoly;
bool fUsedInRightPoly;
Line fLine;
double dist(const SkPoint& p) const {
return fLine.dist(p);
}
bool isRightOf(Vertex* v) const {
return fLine.dist(v->fPoint) < 0.0;
}
bool isLeftOf(Vertex* v) const {
return fLine.dist(v->fPoint) > 0.0;
}
void recompute() {
fLine = Line(fTop, fBottom);
}
bool intersect(const Edge& other, SkPoint* p) {
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>(fTop->fPoint.fX) - other.fTop->fPoint.fX;
double dy = static_cast<double>(fTop->fPoint.fY) - other.fTop->fPoint.fY;
double sNumer = -dy * other.fLine.fB - dx * other.fLine.fA;
double tNumer = -dy * fLine.fB - dx * fLine.fA;
// If (sNumer / denom) or (tNumer / denom) is not in [0..1], exit early.
// This saves us doing the divide below unless absolutely necessary.
if (denom > 0.0 ? (sNumer < 0.0 || sNumer > denom || tNumer < 0.0 || tNumer > denom)
: (sNumer > 0.0 || sNumer < denom || tNumer > 0.0 || tNumer < denom)) {
return false;
}
double s = sNumer / denom;
SkASSERT(s >= 0.0 && s <= 1.0);
p->fX = SkDoubleToScalar(fTop->fPoint.fX - s * fLine.fB);
p->fY = SkDoubleToScalar(fTop->fPoint.fY + s * fLine.fA);
return true;
}
};
struct EdgeList {
EdgeList() : fHead(nullptr), fTail(nullptr), fNext(nullptr), fCount(0) {}
Edge* fHead;
Edge* fTail;
EdgeList* fNext;
int fCount;
void insert(Edge* edge, Edge* prev, Edge* next) {
list_insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &fHead, &fTail);
fCount++;
}
void append(Edge* e) {
insert(e, fTail, nullptr);
}
void remove(Edge* edge) {
list_remove<Edge, &Edge::fLeft, &Edge::fRight>(edge, &fHead, &fTail);
fCount--;
}
void close() {
if (fHead && fTail) {
fTail->fRight = fHead;
fHead->fLeft = fTail;
}
}
bool contains(Edge* edge) const {
return edge->fLeft || edge->fRight || fHead == edge;
}
};
/***************************************************************************************/
struct Poly {
Poly(Vertex* v, int winding)
: fFirstVertex(v)
, fWinding(winding)
, fHead(nullptr)
, fTail(nullptr)
, fNext(nullptr)
, fPartner(nullptr)
, fCount(0)
{
#if LOGGING_ENABLED
static int gID = 0;
fID = gID++;
LOG("*** created Poly %d\n", fID);
#endif
}
typedef enum { kLeft_Side, kRight_Side } Side;
struct MonotonePoly {
MonotonePoly(Edge* edge, Side side)
: fSide(side)
, fFirstEdge(nullptr)
, fLastEdge(nullptr)
, fPrev(nullptr)
, fNext(nullptr) {
this->addEdge(edge);
}
Side fSide;
Edge* fFirstEdge;
Edge* fLastEdge;
MonotonePoly* fPrev;
MonotonePoly* fNext;
void addEdge(Edge* edge) {
if (fSide == kRight_Side) {
SkASSERT(!edge->fUsedInRightPoly);
list_insert<Edge, &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(const AAParams* aaParams, void* data) {
Edge* e = fFirstEdge;
e->fTop->fPrev = e->fTop->fNext = nullptr;
VertexList vertices;
vertices.append(e->fTop);
while (e != nullptr) {
e->fBottom->fPrev = e->fBottom->fNext = nullptr;
if (kRight_Side == fSide) {
vertices.append(e->fBottom);
e = e->fRightPolyNext;
} else {
vertices.prepend(e->fBottom);
e = e->fLeftPolyNext;
}
}
Vertex* first = vertices.fHead;
Vertex* v = first->fNext;
while (v != vertices.fTail) {
SkASSERT(v && v->fPrev && v->fNext);
Vertex* prev = v->fPrev;
Vertex* curr = v;
Vertex* next = v->fNext;
double ax = static_cast<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, aaParams, data);
v->fPrev->fNext = v->fNext;
v->fNext->fPrev = v->fPrev;
if (v->fPrev == first) {
v = v->fNext;
} else {
v = v->fPrev;
}
} else {
v = v->fNext;
}
}
return data;
}
};
Poly* addEdge(Edge* e, Side side, SkChunkAlloc& alloc) {
LOG("addEdge (%g -> %g) to poly %d, %s side\n",
e->fTop->fID, e->fBottom->fID, fID, side == kLeft_Side ? "left" : "right");
Poly* partner = fPartner;
Poly* poly = this;
if (side == kRight_Side) {
if (e->fUsedInRightPoly) {
return this;
}
} else {
if (e->fUsedInLeftPoly) {
return this;
}
}
if (partner) {
fPartner = partner->fPartner = nullptr;
}
if (!fTail) {
fHead = fTail = ALLOC_NEW(MonotonePoly, (e, side), alloc);
fCount += 2;
} else if (e->fBottom == fTail->fLastEdge->fBottom) {
return poly;
} else if (side == fTail->fSide) {
fTail->addEdge(e);
fCount++;
} else {
e = ALLOC_NEW(Edge, (fTail->fLastEdge->fBottom, e->fBottom, 1, Edge::Type::kInner),
alloc);
fTail->addEdge(e);
fCount++;
if (partner) {
partner->addEdge(e, side, alloc);
poly = partner;
} else {
MonotonePoly* m = ALLOC_NEW(MonotonePoly, (e, side), alloc);
m->fPrev = fTail;
fTail->fNext = m;
fTail = m;
}
}
return poly;
}
void* emit(const AAParams* aaParams, void *data) {
if (fCount < 3) {
return data;
}
LOG("emit() %d, size %d\n", fID, fCount);
for (MonotonePoly* m = fHead; m != nullptr; m = m->fNext) {
data = m->emit(aaParams, data);
}
return data;
}
Vertex* lastVertex() const { return fTail ? fTail->fLastEdge->fBottom : fFirstVertex; }
Vertex* fFirstVertex;
int fWinding;
MonotonePoly* fHead;
MonotonePoly* fTail;
Poly* fNext;
Poly* fPartner;
int fCount;
#if LOGGING_ENABLED
int fID;
#endif
};
/***************************************************************************************/
bool coincident(const SkPoint& a, const SkPoint& b) {
return a == b;
}
Poly* new_poly(Poly** head, Vertex* v, int winding, SkChunkAlloc& alloc) {
Poly* poly = ALLOC_NEW(Poly, (v, winding), alloc);
poly->fNext = *head;
*head = poly;
return poly;
}
EdgeList* new_contour(EdgeList** head, SkChunkAlloc& alloc) {
EdgeList* contour = ALLOC_NEW(EdgeList, (), alloc);
contour->fNext = *head;
*head = contour;
return contour;
}
Vertex* append_point_to_contour(const SkPoint& p, Vertex* prev, Vertex** head,
SkChunkAlloc& alloc) {
Vertex* v = ALLOC_NEW(Vertex, (p, 255), alloc);
#if LOGGING_ENABLED
static float gID = 0.0f;
v->fID = gID++;
#endif
if (prev) {
prev->fNext = v;
v->fPrev = prev;
} else {
*head = v;
}
return v;
}
Vertex* generate_quadratic_points(const SkPoint& p0,
const SkPoint& p1,
const SkPoint& p2,
SkScalar tolSqd,
Vertex* prev,
Vertex** head,
int pointsLeft,
SkChunkAlloc& alloc) {
SkScalar d = p1.distanceToLineSegmentBetweenSqd(p0, p2);
if (pointsLeft < 2 || d < tolSqd || !SkScalarIsFinite(d)) {
return append_point_to_contour(p2, prev, head, alloc);
}
const SkPoint q[] = {
{ SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
{ SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
};
const SkPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) };
pointsLeft >>= 1;
prev = generate_quadratic_points(p0, q[0], r, tolSqd, prev, head, pointsLeft, alloc);
prev = generate_quadratic_points(r, q[1], p2, tolSqd, prev, head, pointsLeft, alloc);
return prev;
}
Vertex* generate_cubic_points(const SkPoint& p0,
const SkPoint& p1,
const SkPoint& p2,
const SkPoint& p3,
SkScalar tolSqd,
Vertex* prev,
Vertex** head,
int pointsLeft,
SkChunkAlloc& alloc) {
SkScalar d1 = p1.distanceToLineSegmentBetweenSqd(p0, p3);
SkScalar d2 = p2.distanceToLineSegmentBetweenSqd(p0, p3);
if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) ||
!SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) {
return append_point_to_contour(p3, prev, head, alloc);
}
const SkPoint q[] = {
{ SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
{ SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
{ SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) }
};
const SkPoint r[] = {
{ SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) },
{ SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) }
};
const SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) };
pointsLeft >>= 1;
prev = generate_cubic_points(p0, q[0], r[0], s, tolSqd, prev, head, pointsLeft, alloc);
prev = generate_cubic_points(s, r[1], q[2], p3, tolSqd, prev, head, pointsLeft, alloc);
return prev;
}
// Stage 1: convert the input path to a set of linear contours (linked list of Vertices).
void path_to_contours(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
Vertex** contours, SkChunkAlloc& alloc, bool *isLinear) {
SkScalar toleranceSqd = tolerance * tolerance;
SkPoint pts[4];
bool done = false;
*isLinear = true;
SkPath::Iter iter(path, false);
Vertex* prev = nullptr;
Vertex* head = nullptr;
if (path.isInverseFillType()) {
SkPoint quad[4];
clipBounds.toQuad(quad);
for (int i = 3; i >= 0; i--) {
prev = append_point_to_contour(quad[i], prev, &head, alloc);
}
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
head = prev = nullptr;
}
SkAutoConicToQuads converter;
while (!done) {
SkPath::Verb verb = iter.next(pts);
switch (verb) {
case SkPath::kConic_Verb: {
SkScalar weight = iter.conicWeight();
const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd);
for (int i = 0; i < converter.countQuads(); ++i) {
int pointsLeft = GrPathUtils::quadraticPointCount(quadPts, tolerance);
prev = generate_quadratic_points(quadPts[0], quadPts[1], quadPts[2],
toleranceSqd, prev, &head, pointsLeft, alloc);
quadPts += 2;
}
*isLinear = false;
break;
}
case SkPath::kMove_Verb:
if (head) {
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
}
head = prev = nullptr;
prev = append_point_to_contour(pts[0], prev, &head, alloc);
break;
case SkPath::kLine_Verb: {
prev = append_point_to_contour(pts[1], prev, &head, alloc);
break;
}
case SkPath::kQuad_Verb: {
int pointsLeft = GrPathUtils::quadraticPointCount(pts, tolerance);
prev = generate_quadratic_points(pts[0], pts[1], pts[2], toleranceSqd, prev,
&head, pointsLeft, alloc);
*isLinear = false;
break;
}
case SkPath::kCubic_Verb: {
int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance);
prev = generate_cubic_points(pts[0], pts[1], pts[2], pts[3],
toleranceSqd, prev, &head, pointsLeft, alloc);
*isLinear = false;
break;
}
case SkPath::kClose_Verb:
if (head) {
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
}
head = prev = nullptr;
break;
case SkPath::kDone_Verb:
if (head) {
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
}
done = true;
break;
}
}
}
inline bool apply_fill_type(SkPath::FillType fillType, Poly* poly) {
if (!poly) {
return false;
}
int winding = poly->fWinding;
switch (fillType) {
case SkPath::kWinding_FillType:
return winding != 0;
case SkPath::kEvenOdd_FillType:
return (winding & 1) != 0;
case SkPath::kInverseWinding_FillType:
return winding == 1;
case SkPath::kInverseEvenOdd_FillType:
return (winding & 1) == 1;
default:
SkASSERT(false);
return false;
}
}
Edge* new_edge(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkChunkAlloc& alloc) {
int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1;
Vertex* top = winding < 0 ? next : prev;
Vertex* bottom = winding < 0 ? prev : next;
return ALLOC_NEW(Edge, (top, bottom, winding, type), alloc);
}
void remove_edge(Edge* edge, EdgeList* edges) {
LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
SkASSERT(edges->contains(edge));
edges->remove(edge);
}
void insert_edge(Edge* edge, Edge* prev, EdgeList* edges) {
LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
SkASSERT(!edges->contains(edge));
Edge* next = prev ? prev->fRight : edges->fHead;
edges->insert(edge, prev, next);
}
void find_enclosing_edges(Vertex* v, EdgeList* edges, Edge** left, Edge** right) {
if (v->fFirstEdgeAbove) {
*left = v->fFirstEdgeAbove->fLeft;
*right = v->fLastEdgeAbove->fRight;
return;
}
Edge* next = nullptr;
Edge* prev;
for (prev = edges->fTail; prev != nullptr; prev = prev->fLeft) {
if (prev->isLeftOf(v)) {
break;
}
next = prev;
}
*left = prev;
*right = next;
}
void find_enclosing_edges(Edge* edge, EdgeList* edges, Comparator& c, Edge** left, Edge** right) {
Edge* prev = nullptr;
Edge* next;
for (next = edges->fHead; next != nullptr; next = next->fRight) {
if ((c.sweep_gt(edge->fTop->fPoint, next->fTop->fPoint) && next->isRightOf(edge->fTop)) ||
(c.sweep_gt(next->fTop->fPoint, edge->fTop->fPoint) && edge->isLeftOf(next->fTop)) ||
(c.sweep_lt(edge->fBottom->fPoint, next->fBottom->fPoint) &&
next->isRightOf(edge->fBottom)) ||
(c.sweep_lt(next->fBottom->fPoint, edge->fBottom->fPoint) &&
edge->isLeftOf(next->fBottom))) {
break;
}
prev = next;
}
*left = prev;
*right = next;
}
void fix_active_state(Edge* edge, EdgeList* activeEdges, Comparator& c) {
if (!activeEdges) {
return;
}
if (activeEdges->contains(edge)) {
if (edge->fBottom->fProcessed || !edge->fTop->fProcessed) {
remove_edge(edge, activeEdges);
}
} else if (edge->fTop->fProcessed && !edge->fBottom->fProcessed) {
Edge* left;
Edge* right;
find_enclosing_edges(edge, activeEdges, c, &left, &right);
insert_edge(edge, left, activeEdges);
}
}
void insert_edge_above(Edge* edge, Vertex* v, Comparator& c) {
if (edge->fTop->fPoint == edge->fBottom->fPoint ||
c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
return;
}
LOG("insert edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
Edge* prev = nullptr;
Edge* next;
for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) {
if (next->isRightOf(edge->fTop)) {
break;
}
prev = next;
}
list_insert<Edge, &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_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
return;
}
LOG("insert edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
Edge* prev = nullptr;
Edge* next;
for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) {
if (next->isRightOf(edge->fBottom)) {
break;
}
prev = next;
}
list_insert<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
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::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
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::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow);
}
void disconnect(Edge* edge)
{
remove_edge_above(edge);
remove_edge_below(edge);
}
void erase_edge(Edge* edge, EdgeList* edges) {
LOG("erasing edge (%g -> %g)\n", edge->fTop->fID, edge->fBottom->fID);
disconnect(edge);
if (edges && edges->contains(edge)) {
remove_edge(edge, edges);
}
}
void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c);
void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
remove_edge_below(edge);
edge->fTop = v;
edge->recompute();
insert_edge_below(edge, v, c);
fix_active_state(edge, activeEdges, c);
merge_collinear_edges(edge, activeEdges, c);
}
void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
remove_edge_above(edge);
edge->fBottom = v;
edge->recompute();
insert_edge_above(edge, v, c);
fix_active_state(edge, activeEdges, c);
merge_collinear_edges(edge, activeEdges, c);
}
void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) {
LOG("merging coincident above edges (%g, %g) -> (%g, %g)\n",
edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
other->fWinding += edge->fWinding;
erase_edge(edge, activeEdges);
} else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) {
other->fWinding += edge->fWinding;
set_bottom(edge, other->fTop, activeEdges, c);
} else {
edge->fWinding += other->fWinding;
set_bottom(other, edge->fTop, activeEdges, c);
}
}
void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) {
LOG("merging coincident below edges (%g, %g) -> (%g, %g)\n",
edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
other->fWinding += edge->fWinding;
erase_edge(edge, activeEdges);
} else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) {
edge->fWinding += other->fWinding;
set_top(other, edge->fBottom, activeEdges, c);
} else {
other->fWinding += edge->fWinding;
set_top(edge, other->fBottom, activeEdges, c);
}
}
void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c) {
if (edge->fPrevEdgeAbove && (edge->fTop == edge->fPrevEdgeAbove->fTop ||
!edge->fPrevEdgeAbove->isLeftOf(edge->fTop))) {
merge_edges_above(edge, edge->fPrevEdgeAbove, activeEdges, c);
} else if (edge->fNextEdgeAbove && (edge->fTop == edge->fNextEdgeAbove->fTop ||
!edge->isLeftOf(edge->fNextEdgeAbove->fTop))) {
merge_edges_above(edge, edge->fNextEdgeAbove, activeEdges, c);
}
if (edge->fPrevEdgeBelow && (edge->fBottom == edge->fPrevEdgeBelow->fBottom ||
!edge->fPrevEdgeBelow->isLeftOf(edge->fBottom))) {
merge_edges_below(edge, edge->fPrevEdgeBelow, activeEdges, c);
} else if (edge->fNextEdgeBelow && (edge->fBottom == edge->fNextEdgeBelow->fBottom ||
!edge->isLeftOf(edge->fNextEdgeBelow->fBottom))) {
merge_edges_below(edge, edge->fNextEdgeBelow, activeEdges, c);
}
}
void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc);
void cleanup_active_edges(Edge* edge, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
Vertex* top = edge->fTop;
Vertex* bottom = edge->fBottom;
if (edge->fLeft) {
Vertex* leftTop = edge->fLeft->fTop;
Vertex* leftBottom = edge->fLeft->fBottom;
if (c.sweep_gt(top->fPoint, leftTop->fPoint) && !edge->fLeft->isLeftOf(top)) {
split_edge(edge->fLeft, edge->fTop, activeEdges, c, alloc);
} else if (c.sweep_gt(leftTop->fPoint, top->fPoint) && !edge->isRightOf(leftTop)) {
split_edge(edge, leftTop, activeEdges, c, alloc);
} else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) &&
!edge->fLeft->isLeftOf(bottom)) {
split_edge(edge->fLeft, bottom, activeEdges, c, alloc);
} else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) && !edge->isRightOf(leftBottom)) {
split_edge(edge, leftBottom, activeEdges, c, alloc);
}
}
if (edge->fRight) {
Vertex* rightTop = edge->fRight->fTop;
Vertex* rightBottom = edge->fRight->fBottom;
if (c.sweep_gt(top->fPoint, rightTop->fPoint) && !edge->fRight->isRightOf(top)) {
split_edge(edge->fRight, top, activeEdges, c, alloc);
} else if (c.sweep_gt(rightTop->fPoint, top->fPoint) && !edge->isLeftOf(rightTop)) {
split_edge(edge, rightTop, activeEdges, c, alloc);
} else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) &&
!edge->fRight->isRightOf(bottom)) {
split_edge(edge->fRight, bottom, activeEdges, c, alloc);
} else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) &&
!edge->isLeftOf(rightBottom)) {
split_edge(edge, rightBottom, activeEdges, c, alloc);
}
}
}
void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
LOG("splitting edge (%g -> %g) at vertex %g (%g, %g)\n",
edge->fTop->fID, edge->fBottom->fID,
v->fID, v->fPoint.fX, v->fPoint.fY);
if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) {
set_top(edge, v, activeEdges, c);
} else if (c.sweep_gt(v->fPoint, edge->fBottom->fPoint)) {
set_bottom(edge, v, activeEdges, c);
} else {
Edge* newEdge = ALLOC_NEW(Edge, (v, edge->fBottom, edge->fWinding, edge->fType), alloc);
insert_edge_below(newEdge, v, c);
insert_edge_above(newEdge, edge->fBottom, c);
set_bottom(edge, v, activeEdges, c);
cleanup_active_edges(edge, activeEdges, c, alloc);
fix_active_state(newEdge, activeEdges, c);
merge_collinear_edges(newEdge, activeEdges, c);
}
}
Edge* connect(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkChunkAlloc& alloc) {
Edge* edge = new_edge(prev, next, type, c, alloc);
if (edge->fWinding > 0) {
insert_edge_below(edge, prev, c);
insert_edge_above(edge, next, c);
} else {
insert_edge_below(edge, next, c);
insert_edge_above(edge, prev, c);
}
merge_collinear_edges(edge, nullptr, c);
return edge;
}
void merge_vertices(Vertex* src, Vertex* dst, VertexList* mesh, Comparator& c,
SkChunkAlloc& alloc) {
LOG("found coincident verts at %g, %g; merging %g into %g\n", src->fPoint.fX, src->fPoint.fY,
src->fID, dst->fID);
dst->fAlpha = SkTMax(src->fAlpha, dst->fAlpha);
for (Edge* edge = src->fFirstEdgeAbove; edge;) {
Edge* next = edge->fNextEdgeAbove;
set_bottom(edge, dst, nullptr, c);
edge = next;
}
for (Edge* edge = src->fFirstEdgeBelow; edge;) {
Edge* next = edge->fNextEdgeBelow;
set_top(edge, dst, nullptr, c);
edge = next;
}
mesh->remove(src);
}
uint8_t max_edge_alpha(Edge* a, Edge* b) {
if (a->fType == Edge::Type::kInner && b->fType == Edge::Type::kInner) {
return 255;
} else if (a->fType == Edge::Type::kOuter && b->fType == Edge::Type::kOuter) {
return 0;
} else {
return SkTMax(SkTMax(a->fTop->fAlpha, a->fBottom->fAlpha),
SkTMax(b->fTop->fAlpha, b->fBottom->fAlpha));
}
}
Vertex* check_for_intersection(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c,
SkChunkAlloc& alloc) {
SkPoint p;
if (!edge || !other) {
return nullptr;
}
if (edge->intersect(*other, &p)) {
Vertex* v;
LOG("found intersection, pt is %g, %g\n", p.fX, p.fY);
if (p == edge->fTop->fPoint || c.sweep_lt(p, edge->fTop->fPoint)) {
split_edge(other, edge->fTop, activeEdges, c, alloc);
v = edge->fTop;
} else if (p == edge->fBottom->fPoint || c.sweep_gt(p, edge->fBottom->fPoint)) {
split_edge(other, edge->fBottom, activeEdges, c, alloc);
v = edge->fBottom;
} else if (p == other->fTop->fPoint || c.sweep_lt(p, other->fTop->fPoint)) {
split_edge(edge, other->fTop, activeEdges, c, alloc);
v = other->fTop;
} else if (p == other->fBottom->fPoint || c.sweep_gt(p, other->fBottom->fPoint)) {
split_edge(edge, other->fBottom, activeEdges, c, alloc);
v = other->fBottom;
} else {
Vertex* nextV = edge->fTop;
while (c.sweep_lt(p, nextV->fPoint)) {
nextV = nextV->fPrev;
}
while (c.sweep_lt(nextV->fPoint, p)) {
nextV = nextV->fNext;
}
Vertex* prevV = nextV->fPrev;
if (coincident(prevV->fPoint, p)) {
v = prevV;
} else if (coincident(nextV->fPoint, p)) {
v = nextV;
} else {
uint8_t alpha = max_edge_alpha(edge, other);
v = ALLOC_NEW(Vertex, (p, alpha), alloc);
LOG("inserting between %g (%g, %g) and %g (%g, %g)\n",
prevV->fID, prevV->fPoint.fX, prevV->fPoint.fY,
nextV->fID, nextV->fPoint.fX, nextV->fPoint.fY);
#if LOGGING_ENABLED
v->fID = (nextV->fID + prevV->fID) * 0.5f;
#endif
v->fPrev = prevV;
v->fNext = nextV;
prevV->fNext = v;
nextV->fPrev = v;
}
split_edge(edge, v, activeEdges, c, alloc);
split_edge(other, v, activeEdges, c, alloc);
}
return v;
}
return nullptr;
}
void sanitize_contours(Vertex** contours, int contourCnt, bool approximate) {
for (int i = 0; i < contourCnt; ++i) {
SkASSERT(contours[i]);
for (Vertex* v = contours[i];;) {
if (approximate) {
round(&v->fPoint);
}
if (coincident(v->fPrev->fPoint, v->fPoint)) {
LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY);
if (v->fPrev == v) {
contours[i] = nullptr;
break;
}
v->fPrev->fNext = v->fNext;
v->fNext->fPrev = v->fPrev;
if (contours[i] == v) {
contours[i] = v->fNext;
}
v = v->fPrev;
} else {
v = v->fNext;
if (v == contours[i]) break;
}
}
}
}
void merge_coincident_vertices(VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) {
for (Vertex* v = mesh->fHead->fNext; v != nullptr; v = v->fNext) {
if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) {
v->fPoint = v->fPrev->fPoint;
}
if (coincident(v->fPrev->fPoint, v->fPoint)) {
merge_vertices(v->fPrev, v, mesh, c, alloc);
}
}
}
// Stage 2: convert the contours to a mesh of edges connecting the vertices.
void build_edges(Vertex** contours, int contourCnt, VertexList* mesh, Comparator& c,
SkChunkAlloc& alloc) {
Vertex* prev = nullptr;
for (int i = 0; i < contourCnt; ++i) {
for (Vertex* v = contours[i]; v != nullptr;) {
Vertex* vNext = v->fNext;
connect(v->fPrev, v, Edge::Type::kInner, c, alloc);
if (prev) {
prev->fNext = v;
v->fPrev = prev;
} else {
mesh->fHead = v;
}
prev = v;
v = vNext;
if (v == contours[i]) break;
}
}
if (prev) {
prev->fNext = mesh->fHead->fPrev = nullptr;
}
mesh->fTail = prev;
}
// Stage 3: sort the vertices by increasing sweep direction.
void sorted_merge(Vertex* a, Vertex* b, VertexList* result, Comparator& c);
void front_back_split(VertexList* v, VertexList* front, VertexList* back) {
Vertex* fast;
Vertex* slow;
if (!v->fHead || !v->fHead->fNext) {
*front = *v;
} else {
slow = v->fHead;
fast = v->fHead->fNext;
while (fast != nullptr) {
fast = fast->fNext;
if (fast != nullptr) {
slow = slow->fNext;
fast = fast->fNext;
}
}
front->fHead = v->fHead;
front->fTail = slow;
back->fHead = slow->fNext;
back->fTail = v->fTail;
slow->fNext->fPrev = nullptr;
slow->fNext = nullptr;
}
v->fHead = v->fTail = nullptr;
}
void merge_sort(VertexList* mesh, Comparator& c) {
if (!mesh->fHead || !mesh->fHead->fNext) {
return;
}
VertexList a;
VertexList b;
front_back_split(mesh, &a, &b);
merge_sort(&a, c);
merge_sort(&b, c);
sorted_merge(a.fHead, b.fHead, mesh, c);
}
void sorted_merge(Vertex* a, Vertex* b, VertexList* result, Comparator& c) {
VertexList vertices;
while (a && b) {
if (c.sweep_lt(a->fPoint, b->fPoint)) {
Vertex* next = a->fNext;
vertices.append(a);
a = next;
} else {
Vertex* next = b->fNext;
vertices.append(b);
b = next;
}
}
if (a) {
vertices.insert(a, vertices.fTail, a->fNext);
}
if (b) {
vertices.insert(b, vertices.fTail, b->fNext);
}
*result = vertices;
}
// Stage 4: Simplify the mesh by inserting new vertices at intersecting edges.
void simplify(const VertexList& vertices, Comparator& c, SkChunkAlloc& alloc) {
LOG("simplifying complex polygons\n");
EdgeList activeEdges;
for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) {
if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
continue;
}
#if LOGGING_ENABLED
LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
#endif
Edge* leftEnclosingEdge = nullptr;
Edge* rightEnclosingEdge = nullptr;
bool restartChecks;
do {
restartChecks = false;
find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
if (v->fFirstEdgeBelow) {
for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) {
if (check_for_intersection(edge, leftEnclosingEdge, &activeEdges, c, alloc)) {
restartChecks = true;
break;
}
if (check_for_intersection(edge, rightEnclosingEdge, &activeEdges, c, alloc)) {
restartChecks = true;
break;
}
}
} else {
if (Vertex* pv = check_for_intersection(leftEnclosingEdge, rightEnclosingEdge,
&activeEdges, c, alloc)) {
if (c.sweep_lt(pv->fPoint, v->fPoint)) {
v = pv;
}
restartChecks = true;
}
}
} while (restartChecks);
if (v->fAlpha == 0) {
if ((leftEnclosingEdge && leftEnclosingEdge->fWinding > 0) &&
(rightEnclosingEdge && rightEnclosingEdge->fWinding < 0)) {
v->fAlpha = max_edge_alpha(leftEnclosingEdge, rightEnclosingEdge);
}
}
for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
remove_edge(e, &activeEdges);
}
Edge* leftEdge = leftEnclosingEdge;
for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
insert_edge(e, leftEdge, &activeEdges);
leftEdge = e;
}
v->fProcessed = true;
}
}
// Stage 5: Tessellate the simplified mesh into monotone polygons.
Poly* tessellate(const VertexList& vertices, SkChunkAlloc& alloc) {
LOG("tessellating simple polygons\n");
EdgeList activeEdges;
Poly* polys = nullptr;
for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) {
if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
continue;
}
#if LOGGING_ENABLED
LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
#endif
Edge* leftEnclosingEdge = nullptr;
Edge* rightEnclosingEdge = nullptr;
find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
Poly* leftPoly = nullptr;
Poly* rightPoly = nullptr;
if (v->fFirstEdgeAbove) {
leftPoly = v->fFirstEdgeAbove->fLeftPoly;
rightPoly = v->fLastEdgeAbove->fRightPoly;
} else {
leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : nullptr;
rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : nullptr;
}
#if LOGGING_ENABLED
LOG("edges above:\n");
for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
}
LOG("edges below:\n");
for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
}
#endif
if (v->fFirstEdgeAbove) {
if (leftPoly) {
leftPoly = leftPoly->addEdge(v->fFirstEdgeAbove, Poly::kRight_Side, alloc);
}
if (rightPoly) {
rightPoly = rightPoly->addEdge(v->fLastEdgeAbove, Poly::kLeft_Side, alloc);
}
for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) {
Edge* leftEdge = e;
Edge* rightEdge = e->fNextEdgeAbove;
SkASSERT(rightEdge->isRightOf(leftEdge->fTop));
remove_edge(leftEdge, &activeEdges);
if (leftEdge->fRightPoly) {
leftEdge->fRightPoly->addEdge(e, Poly::kLeft_Side, alloc);
}
if (rightEdge->fLeftPoly) {
rightEdge->fLeftPoly->addEdge(e, Poly::kRight_Side, alloc);
}
}
remove_edge(v->fLastEdgeAbove, &activeEdges);
if (!v->fFirstEdgeBelow) {
if (leftPoly && rightPoly && leftPoly != rightPoly) {
SkASSERT(leftPoly->fPartner == nullptr && rightPoly->fPartner == nullptr);
rightPoly->fPartner = leftPoly;
leftPoly->fPartner = rightPoly;
}
}
}
if (v->fFirstEdgeBelow) {
if (!v->fFirstEdgeAbove) {
if (leftPoly && rightPoly) {
if (leftPoly == rightPoly) {
if (leftPoly->fTail && leftPoly->fTail->fSide == Poly::kLeft_Side) {
leftPoly = new_poly(&polys, leftPoly->lastVertex(),
leftPoly->fWinding, alloc);
leftEnclosingEdge->fRightPoly = leftPoly;
} else {
rightPoly = new_poly(&polys, rightPoly->lastVertex(),
rightPoly->fWinding, alloc);
rightEnclosingEdge->fLeftPoly = rightPoly;
}
}
Edge* join = ALLOC_NEW(Edge,
(leftPoly->lastVertex(), v, 1, Edge::Type::kInner), alloc);
leftPoly = leftPoly->addEdge(join, Poly::kRight_Side, alloc);
rightPoly = rightPoly->addEdge(join, Poly::kLeft_Side, alloc);
}
}
Edge* leftEdge = v->fFirstEdgeBelow;
leftEdge->fLeftPoly = leftPoly;
insert_edge(leftEdge, leftEnclosingEdge, &activeEdges);
for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge;
rightEdge = rightEdge->fNextEdgeBelow) {
insert_edge(rightEdge, leftEdge, &activeEdges);
int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0;
winding += leftEdge->fWinding;
if (winding != 0) {
Poly* poly = new_poly(&polys, v, winding, alloc);
leftEdge->fRightPoly = rightEdge->fLeftPoly = poly;
}
leftEdge = rightEdge;
}
v->fLastEdgeBelow->fRightPoly = rightPoly;
}
#if LOGGING_ENABLED
LOG("\nactive edges:\n");
for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) {
LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
}
#endif
}
return polys;
}
bool is_boundary_edge(Edge* edge, SkPath::FillType fillType) {
return apply_fill_type(fillType, edge->fLeftPoly) !=
apply_fill_type(fillType, edge->fRightPoly);
}
bool is_boundary_start(Edge* edge, SkPath::FillType fillType) {
return !apply_fill_type(fillType, edge->fLeftPoly) &&
apply_fill_type(fillType, edge->fRightPoly);
}
void remove_non_boundary_edges(const VertexList& mesh, SkPath::FillType fillType,
SkChunkAlloc& alloc) {
for (Vertex* v = mesh.fHead; v != nullptr; v = v->fNext) {
for (Edge* e = v->fFirstEdgeBelow; e != nullptr;) {
Edge* next = e->fNextEdgeBelow;
if (!is_boundary_edge(e, fillType)) {
disconnect(e);
}
e = next;
}
}
}
void get_edge_normal(const Edge* e, SkVector* normal) {
normal->setNormalize(SkDoubleToScalar(e->fLine.fA) * e->fWinding,
SkDoubleToScalar(e->fLine.fB) * e->fWinding);
}
// Stage 5c: detect and remove "pointy" vertices whose edge normals point in opposite directions
// and whose adjacent vertices are less than a quarter pixel from an edge. These are guaranteed to
// invert on stroking.
void simplify_boundary(EdgeList* boundary, Comparator& c, SkChunkAlloc& alloc) {
Edge* prevEdge = boundary->fTail;
SkVector prevNormal;
get_edge_normal(prevEdge, &prevNormal);
for (Edge* e = boundary->fHead; e != nullptr;) {
Vertex* prev = prevEdge->fWinding == 1 ? prevEdge->fTop : prevEdge->fBottom;
Vertex* next = e->fWinding == 1 ? e->fBottom : e->fTop;
double dist = e->dist(prev->fPoint);
SkVector normal;
get_edge_normal(e, &normal);
float denom = 0.0625f * static_cast<float>(e->fLine.magSq());
if (prevNormal.dot(normal) < 0.0 && (dist * dist) <= denom) {
Edge* join = new_edge(prev, next, Edge::Type::kInner, c, alloc);
insert_edge(join, e, boundary);
remove_edge(prevEdge, boundary);
remove_edge(e, boundary);
if (join->fLeft && join->fRight) {
prevEdge = join->fLeft;
e = join;
} else {
prevEdge = boundary->fTail;
e = boundary->fHead; // join->fLeft ? join->fLeft : join;
}
get_edge_normal(prevEdge, &prevNormal);
} else {
prevEdge = e;
prevNormal = normal;
e = e->fRight;
}
}
}
// Stage 5d: Displace edges by half a pixel inward and outward along their normals. Intersect to
// find new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a
// new antialiased mesh from those vertices.
void boundary_to_aa_mesh(EdgeList* boundary, VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) {
EdgeList outerContour;
Edge* prevEdge = boundary->fTail;
float radius = 0.5f;
double offset = radius * sqrt(prevEdge->fLine.magSq()) * prevEdge->fWinding;
Line prevInner(prevEdge->fTop, prevEdge->fBottom);
prevInner.fC -= offset;
Line prevOuter(prevEdge->fTop, prevEdge->fBottom);
prevOuter.fC += offset;
VertexList innerVertices;
VertexList outerVertices;
SkScalar innerCount = SK_Scalar1, outerCount = SK_Scalar1;
for (Edge* e = boundary->fHead; e != nullptr; e = e->fRight) {
double offset = radius * sqrt(e->fLine.magSq()) * e->fWinding;
Line inner(e->fTop, e->fBottom);
inner.fC -= offset;
Line outer(e->fTop, e->fBottom);
outer.fC += offset;
SkPoint innerPoint, outerPoint;
if (prevInner.intersect(inner, &innerPoint) &&
prevOuter.intersect(outer, &outerPoint)) {
Vertex* innerVertex = ALLOC_NEW(Vertex, (innerPoint, 255), alloc);
Vertex* outerVertex = ALLOC_NEW(Vertex, (outerPoint, 0), alloc);
if (innerVertices.fTail && outerVertices.fTail) {
Edge innerEdge(innerVertices.fTail, innerVertex, 1, Edge::Type::kInner);
Edge outerEdge(outerVertices.fTail, outerVertex, 1, Edge::Type::kInner);
SkVector innerNormal;
get_edge_normal(&innerEdge, &innerNormal);
SkVector outerNormal;
get_edge_normal(&outerEdge, &outerNormal);
SkVector normal;
get_edge_normal(prevEdge, &normal);
if (normal.dot(innerNormal) < 0) {
innerPoint += innerVertices.fTail->fPoint * innerCount;
innerCount++;
innerPoint *= SkScalarInvert(innerCount);
innerVertices.fTail->fPoint = innerVertex->fPoint = innerPoint;
} else {
innerCount = SK_Scalar1;
}
if (normal.dot(outerNormal) < 0) {
outerPoint += outerVertices.fTail->fPoint * outerCount;
outerCount++;
outerPoint *= SkScalarInvert(outerCount);
outerVertices.fTail->fPoint = outerVertex->fPoint = outerPoint;
} else {
outerCount = SK_Scalar1;
}
}
innerVertices.append(innerVertex);
outerVertices.append(outerVertex);
prevEdge = e;
}
prevInner = inner;
prevOuter = outer;
}
innerVertices.close();
outerVertices.close();
Vertex* innerVertex = innerVertices.fHead;
Vertex* outerVertex = outerVertices.fHead;
// Alternate clockwise and counterclockwise polys, so the tesselator
// doesn't cancel out the interior edges.
if (!innerVertex || !outerVertex) {
return;
}
do {
connect(outerVertex->fPrev, outerVertex, Edge::Type::kOuter, c, alloc);
connect(innerVertex->fPrev, innerVertex, Edge::Type::kInner, c, alloc);
connect(outerVertex, innerVertex, Edge::Type::kConnector, c, alloc)->fWinding = 0;
Vertex* innerNext = innerVertex->fNext;
Vertex* outerNext = outerVertex->fNext;
mesh->append(innerVertex);
mesh->append(outerVertex);
innerVertex = innerNext;
outerVertex = outerNext;
} while (innerVertex != innerVertices.fHead && outerVertex != outerVertices.fHead);
}
void extract_boundary(EdgeList* boundary, Edge* e, SkPath::FillType fillType, SkChunkAlloc& alloc) {
bool down = is_boundary_start(e, fillType);
while (e) {
e->fWinding = down ? 1 : -1;
Edge* next;
boundary->append(e);
if (down) {
// Find outgoing edge, in clockwise order.
if ((next = e->fNextEdgeAbove)) {
down = false;
} else if ((next = e->fBottom->fLastEdgeBelow)) {
down = true;
} else if ((next = e->fPrevEdgeAbove)) {
down = false;
}
} else {
// Find outgoing edge, in counter-clockwise order.
if ((next = e->fPrevEdgeBelow)) {
down = true;
} else if ((next = e->fTop->fFirstEdgeAbove)) {
down = false;
} else if ((next = e->fNextEdgeBelow)) {
down = true;
}
}
disconnect(e);
e = next;
}
}
// Stage 5b: Extract boundary edges.
EdgeList* extract_boundaries(const VertexList& mesh, SkPath::FillType fillType,
SkChunkAlloc& alloc) {
LOG("extracting boundaries\n");
remove_non_boundary_edges(mesh, fillType, alloc);
EdgeList* boundaries = nullptr;
for (Vertex* v = mesh.fHead; v != nullptr; v = v->fNext) {
while (v->fFirstEdgeBelow) {
EdgeList* boundary = new_contour(&boundaries, alloc);
extract_boundary(boundary, v->fFirstEdgeBelow, fillType, alloc);
}
}
return boundaries;
}
// This is a driver function which calls stages 2-5 in turn.
void contours_to_mesh(Vertex** contours, int contourCnt, bool antialias,
VertexList* mesh, Comparator& c, SkChunkAlloc& alloc) {
#if LOGGING_ENABLED
for (int i = 0; i < contourCnt; ++i) {
Vertex* v = contours[i];
SkASSERT(v);
LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
for (v = v->fNext; v != contours[i]; v = v->fNext) {
LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
}
}
#endif
sanitize_contours(contours, contourCnt, antialias);
build_edges(contours, contourCnt, mesh, c, alloc);
}
void sort_and_simplify(VertexList* vertices, Comparator& c, SkChunkAlloc& alloc) {
if (!vertices || !vertices->fHead) {
return;
}
// Sort vertices in Y (secondarily in X).
merge_sort(vertices, c);
merge_coincident_vertices(vertices, c, alloc);
#if LOGGING_ENABLED
for (Vertex* v = vertices->fHead; v != nullptr; v = v->fNext) {
static float gID = 0.0f;
v->fID = gID++;
}
#endif
simplify(*vertices, c, alloc);
}
Poly* mesh_to_polys(VertexList* vertices, Comparator& c, SkChunkAlloc& alloc) {
sort_and_simplify(vertices, c, alloc);
return tessellate(*vertices, alloc);
}
Poly* contours_to_polys(Vertex** contours, int contourCnt, SkPath::FillType fillType,
const SkRect& pathBounds, bool antialias,
SkChunkAlloc& alloc) {
Comparator c;
if (pathBounds.width() > pathBounds.height()) {
c.sweep_lt = sweep_lt_horiz;
c.sweep_gt = sweep_gt_horiz;
} else {
c.sweep_lt = sweep_lt_vert;
c.sweep_gt = sweep_gt_vert;
}
VertexList mesh;
contours_to_mesh(contours, contourCnt, antialias, &mesh, c, alloc);
Poly* polys = mesh_to_polys(&mesh, c, alloc);
if (antialias) {
EdgeList* boundaries = extract_boundaries(mesh, fillType, alloc);
VertexList aaMesh;
for (EdgeList* boundary = boundaries; boundary != nullptr; boundary = boundary->fNext) {
simplify_boundary(boundary, c, alloc);
if (boundary->fCount > 2) {
boundary_to_aa_mesh(boundary, &aaMesh, c, alloc);
}
}
sort_and_simplify(&aaMesh, c, alloc);
return tessellate(aaMesh, alloc);
}
return polys;
}
// Stage 6: Triangulate the monotone polygons into a vertex buffer.
void* polys_to_triangles(Poly* polys, SkPath::FillType fillType, const AAParams* aaParams,
void* data) {
for (Poly* poly = polys; poly; poly = poly->fNext) {
if (apply_fill_type(fillType, poly)) {
data = poly->emit(aaParams, data);
}
}
return data;
}
Poly* path_to_polys(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
int contourCnt, SkChunkAlloc& alloc, bool antialias, bool* isLinear) {
SkPath::FillType fillType = path.getFillType();
if (SkPath::IsInverseFillType(fillType)) {
contourCnt++;
}
std::unique_ptr<Vertex*[]> contours(new Vertex* [contourCnt]);
path_to_contours(path, tolerance, clipBounds, contours.get(), alloc, isLinear);
return contours_to_polys(contours.get(), contourCnt, path.getFillType(), path.getBounds(),
antialias, alloc);
}
void get_contour_count_and_size_estimate(const SkPath& path, SkScalar tolerance, int* contourCnt,
int* sizeEstimate) {
int maxPts = GrPathUtils::worstCasePointCount(path, contourCnt, tolerance);
if (maxPts <= 0) {
*contourCnt = 0;
return;
}
if (maxPts > ((int)SK_MaxU16 + 1)) {
SkDebugf("Path not rendered, too many verts (%d)\n", maxPts);
*contourCnt = 0;
return;
}
// For the initial size of the chunk allocator, estimate based on the point count:
// one vertex per point for the initial passes, plus two for the vertices in the
// resulting Polys, since the same point may end up in two Polys. Assume minimal
// connectivity of one Edge per Vertex (will grow for intersections).
*sizeEstimate = maxPts * (3 * sizeof(Vertex) + sizeof(Edge));
}
int count_points(Poly* polys, SkPath::FillType fillType) {
int count = 0;
for (Poly* poly = polys; poly; poly = poly->fNext) {
if (apply_fill_type(fillType, poly) && poly->fCount >= 3) {
count += (poly->fCount - 2) * (TESSELLATOR_WIREFRAME ? 6 : 3);
}
}
return count;
}
} // namespace
namespace GrTessellator {
// Stage 6: Triangulate the monotone polygons into a vertex buffer.
int PathToTriangles(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
VertexAllocator* vertexAllocator, bool antialias, const GrColor& color,
bool canTweakAlphaForCoverage, bool* isLinear) {
int contourCnt;
int sizeEstimate;
get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate);
if (contourCnt <= 0) {
*isLinear = true;
return 0;
}
SkChunkAlloc alloc(sizeEstimate);
Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, antialias,
isLinear);
SkPath::FillType fillType = antialias ? SkPath::kWinding_FillType : path.getFillType();
int count = count_points(polys, fillType);
if (0 == count) {
return 0;
}
void* verts = vertexAllocator->lock(count);
if (!verts) {
SkDebugf("Could not allocate vertices\n");
return 0;
}
LOG("emitting %d verts\n", count);
AAParams aaParams;
aaParams.fTweakAlpha = canTweakAlphaForCoverage;
aaParams.fColor = color;
void* end = polys_to_triangles(polys, fillType, antialias ? &aaParams : nullptr, verts);
int actualCount = static_cast<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;
int sizeEstimate;
get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate);
if (contourCnt <= 0) {
return 0;
}
SkChunkAlloc alloc(sizeEstimate);
bool isLinear;
Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, false, &isLinear);
SkPath::FillType fillType = path.getFillType();
int count = count_points(polys, fillType);
if (0 == count) {
*verts = nullptr;
return 0;
}
*verts = new GrTessellator::WindingVertex[count];
GrTessellator::WindingVertex* vertsEnd = *verts;
SkPoint* points = new SkPoint[count];
SkPoint* pointsEnd = points;
for (Poly* poly = polys; poly; poly = poly->fNext) {
if (apply_fill_type(fillType, poly)) {
SkPoint* start = pointsEnd;
pointsEnd = static_cast<SkPoint*>(poly->emit(nullptr, 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