/*
* Copyright 2017 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "SkPolyUtils.h"
#include <limits>
#include "SkNx.h"
#include "SkPointPriv.h"
#include "SkTArray.h"
#include "SkTemplates.h"
#include "SkTDPQueue.h"
#include "SkTInternalLList.h"
//////////////////////////////////////////////////////////////////////////////////
// Helper data structures and functions
struct OffsetSegment {
SkPoint fP0;
SkVector fV;
};
constexpr SkScalar kCrossTolerance = SK_ScalarNearlyZero * SK_ScalarNearlyZero;
// Computes perpDot for point p compared to segment defined by origin p0 and vector v.
// A positive value means the point is to the left of the segment,
// negative is to the right, 0 is collinear.
static int compute_side(const SkPoint& p0, const SkVector& v, const SkPoint& p) {
SkVector w = p - p0;
SkScalar perpDot = v.cross(w);
if (!SkScalarNearlyZero(perpDot, kCrossTolerance)) {
return ((perpDot > 0) ? 1 : -1);
}
return 0;
}
// Returns 1 for cw, -1 for ccw and 0 if zero signed area (either degenerate or self-intersecting)
int SkGetPolygonWinding(const SkPoint* polygonVerts, int polygonSize) {
if (polygonSize < 3) {
return 0;
}
// compute area and use sign to determine winding
SkScalar quadArea = 0;
SkVector v0 = polygonVerts[1] - polygonVerts[0];
for (int curr = 2; curr < polygonSize; ++curr) {
SkVector v1 = polygonVerts[curr] - polygonVerts[0];
quadArea += v0.cross(v1);
v0 = v1;
}
if (SkScalarNearlyZero(quadArea, kCrossTolerance)) {
return 0;
}
// 1 == ccw, -1 == cw
return (quadArea > 0) ? 1 : -1;
}
// Compute difference vector to offset p0-p1 'offset' units in direction specified by 'side'
bool compute_offset_vector(const SkPoint& p0, const SkPoint& p1, SkScalar offset, int side,
SkPoint* vector) {
SkASSERT(side == -1 || side == 1);
// if distances are equal, can just outset by the perpendicular
SkVector perp = SkVector::Make(p0.fY - p1.fY, p1.fX - p0.fX);
if (!perp.setLength(offset*side)) {
return false;
}
*vector = perp;
return true;
}
// check interval to see if intersection is in segment
static inline bool outside_interval(SkScalar numer, SkScalar denom, bool denomPositive) {
return (denomPositive && (numer < 0 || numer > denom)) ||
(!denomPositive && (numer > 0 || numer < denom));
}
// Compute the intersection 'p' between segments s0 and s1, if any.
// 's' is the parametric value for the intersection along 's0' & 't' is the same for 's1'.
// Returns false if there is no intersection.
static bool compute_intersection(const OffsetSegment& s0, const OffsetSegment& s1,
SkPoint* p, SkScalar* s, SkScalar* t) {
const SkVector& v0 = s0.fV;
const SkVector& v1 = s1.fV;
SkVector w = s1.fP0 - s0.fP0;
SkScalar denom = v0.cross(v1);
bool denomPositive = (denom > 0);
SkScalar sNumer, tNumer;
if (SkScalarNearlyZero(denom, kCrossTolerance)) {
// segments are parallel, but not collinear
if (!SkScalarNearlyZero(w.cross(v0), kCrossTolerance) ||
!SkScalarNearlyZero(w.cross(v1), kCrossTolerance)) {
return false;
}
// Check for zero-length segments
if (!SkPointPriv::CanNormalize(v0.fX, v0.fY)) {
// Both are zero-length
if (!SkPointPriv::CanNormalize(v1.fX, v1.fY)) {
// Check if they're the same point
if (!SkPointPriv::CanNormalize(w.fX, w.fY)) {
*p = s0.fP0;
*s = 0;
*t = 0;
return true;
} else {
return false;
}
}
// Otherwise project segment0's origin onto segment1
tNumer = v1.dot(-w);
denom = v1.dot(v1);
if (outside_interval(tNumer, denom, true)) {
return false;
}
sNumer = 0;
} else {
// Project segment1's endpoints onto segment0
sNumer = v0.dot(w);
denom = v0.dot(v0);
tNumer = 0;
if (outside_interval(sNumer, denom, true)) {
// The first endpoint doesn't lie on segment0
// If segment1 is degenerate, then there's no collision
if (!SkPointPriv::CanNormalize(v1.fX, v1.fY)) {
return false;
}
// Otherwise try the other one
SkScalar oldSNumer = sNumer;
sNumer = v0.dot(w + v1);
tNumer = denom;
if (outside_interval(sNumer, denom, true)) {
// it's possible that segment1's interval surrounds segment0
// this is false if params have the same signs, and in that case no collision
if (sNumer*oldSNumer > 0) {
return false;
}
// otherwise project segment0's endpoint onto segment1 instead
sNumer = 0;
tNumer = v1.dot(-w);
denom = v1.dot(v1);
}
}
}
} else {
sNumer = w.cross(v1);
if (outside_interval(sNumer, denom, denomPositive)) {
return false;
}
tNumer = w.cross(v0);
if (outside_interval(tNumer, denom, denomPositive)) {
return false;
}
}
SkScalar localS = sNumer/denom;
SkScalar localT = tNumer/denom;
*p = s0.fP0 + v0*localS;
*s = localS;
*t = localT;
return true;
}
bool SkIsConvexPolygon(const SkPoint* polygonVerts, int polygonSize) {
if (polygonSize < 3) {
return false;
}
SkScalar lastArea = 0;
SkScalar lastPerpDot = 0;
int prevIndex = polygonSize - 1;
int currIndex = 0;
int nextIndex = 1;
SkPoint origin = polygonVerts[0];
SkVector v0 = polygonVerts[currIndex] - polygonVerts[prevIndex];
SkVector v1 = polygonVerts[nextIndex] - polygonVerts[currIndex];
SkVector w0 = polygonVerts[currIndex] - origin;
SkVector w1 = polygonVerts[nextIndex] - origin;
for (int i = 0; i < polygonSize; ++i) {
if (!polygonVerts[i].isFinite()) {
return false;
}
// Check that winding direction is always the same (otherwise we have a reflex vertex)
SkScalar perpDot = v0.cross(v1);
if (lastPerpDot*perpDot < 0) {
return false;
}
if (0 != perpDot) {
lastPerpDot = perpDot;
}
// If the signed area ever flips it's concave
// TODO: see if we can verify convexity only with signed area
SkScalar quadArea = w0.cross(w1);
if (quadArea*lastArea < 0) {
return false;
}
if (0 != quadArea) {
lastArea = quadArea;
}
prevIndex = currIndex;
currIndex = nextIndex;
nextIndex = (currIndex + 1) % polygonSize;
v0 = v1;
v1 = polygonVerts[nextIndex] - polygonVerts[currIndex];
w0 = w1;
w1 = polygonVerts[nextIndex] - origin;
}
return true;
}
struct OffsetEdge {
OffsetEdge* fPrev;
OffsetEdge* fNext;
OffsetSegment fOffset;
SkPoint fIntersection;
SkScalar fTValue;
uint16_t fIndex;
uint16_t fEnd;
void init(uint16_t start = 0, uint16_t end = 0) {
fIntersection = fOffset.fP0;
fTValue = SK_ScalarMin;
fIndex = start;
fEnd = end;
}
// special intersection check that looks for endpoint intersection
bool checkIntersection(const OffsetEdge* that,
SkPoint* p, SkScalar* s, SkScalar* t) {
if (this->fEnd == that->fIndex) {
SkPoint p1 = this->fOffset.fP0 + this->fOffset.fV;
if (SkPointPriv::EqualsWithinTolerance(p1, that->fOffset.fP0)) {
*p = p1;
*s = SK_Scalar1;
*t = 0;
return true;
}
}
return compute_intersection(this->fOffset, that->fOffset, p, s, t);
}
// computes the line intersection and then the "distance" from that to this
// this is really a signed squared distance, where negative means that
// the intersection lies inside this->fOffset
SkScalar computeCrossingDistance(const OffsetEdge* that) {
const OffsetSegment& s0 = this->fOffset;
const OffsetSegment& s1 = that->fOffset;
const SkVector& v0 = s0.fV;
const SkVector& v1 = s1.fV;
SkScalar denom = v0.cross(v1);
if (SkScalarNearlyZero(denom, kCrossTolerance)) {
// segments are parallel
return SK_ScalarMax;
}
SkVector w = s1.fP0 - s0.fP0;
SkScalar localS = w.cross(v1) / denom;
if (localS < 0) {
localS = -localS;
} else {
localS -= SK_Scalar1;
}
localS *= SkScalarAbs(localS);
localS *= v0.dot(v0);
return localS;
}
};
static void remove_node(const OffsetEdge* node, OffsetEdge** head) {
// remove from linked list
node->fPrev->fNext = node->fNext;
node->fNext->fPrev = node->fPrev;
if (node == *head) {
*head = (node->fNext == node) ? nullptr : node->fNext;
}
}
//////////////////////////////////////////////////////////////////////////////////
// The objective here is to inset all of the edges by the given distance, and then
// remove any invalid inset edges by detecting right-hand turns. In a ccw polygon,
// we should only be making left-hand turns (for cw polygons, we use the winding
// parameter to reverse this). We detect this by checking whether the second intersection
// on an edge is closer to its tail than the first one.
//
// We might also have the case that there is no intersection between two neighboring inset edges.
// In this case, one edge will lie to the right of the other and should be discarded along with
// its previous intersection (if any).
//
// Note: the assumption is that inputPolygon is convex and has no coincident points.
//
bool SkInsetConvexPolygon(const SkPoint* inputPolygonVerts, int inputPolygonSize,
SkScalar inset, SkTDArray<SkPoint>* insetPolygon) {
if (inputPolygonSize < 3) {
return false;
}
// restrict this to match other routines
// practically we don't want anything bigger than this anyway
if (inputPolygonSize > std::numeric_limits<uint16_t>::max()) {
return false;
}
// can't inset by a negative or non-finite amount
if (inset < -SK_ScalarNearlyZero || !SkScalarIsFinite(inset)) {
return false;
}
// insetting close to zero just returns the original poly
if (inset <= SK_ScalarNearlyZero) {
for (int i = 0; i < inputPolygonSize; ++i) {
*insetPolygon->push() = inputPolygonVerts[i];
}
return true;
}
// get winding direction
int winding = SkGetPolygonWinding(inputPolygonVerts, inputPolygonSize);
if (0 == winding) {
return false;
}
// set up
SkAutoSTMalloc<64, OffsetEdge> edgeData(inputPolygonSize);
int prev = inputPolygonSize - 1;
for (int curr = 0; curr < inputPolygonSize; prev = curr, ++curr) {
int next = (curr + 1) % inputPolygonSize;
if (!inputPolygonVerts[curr].isFinite()) {
return false;
}
// check for convexity just to be sure
if (compute_side(inputPolygonVerts[prev], inputPolygonVerts[curr] - inputPolygonVerts[prev],
inputPolygonVerts[next])*winding < 0) {
return false;
}
SkVector v = inputPolygonVerts[next] - inputPolygonVerts[curr];
SkVector perp = SkVector::Make(-v.fY, v.fX);
perp.setLength(inset*winding);
edgeData[curr].fPrev = &edgeData[prev];
edgeData[curr].fNext = &edgeData[next];
edgeData[curr].fOffset.fP0 = inputPolygonVerts[curr] + perp;
edgeData[curr].fOffset.fV = v;
edgeData[curr].init();
}
OffsetEdge* head = &edgeData[0];
OffsetEdge* currEdge = head;
OffsetEdge* prevEdge = currEdge->fPrev;
int insetVertexCount = inputPolygonSize;
unsigned int iterations = 0;
unsigned int maxIterations = inputPolygonSize * inputPolygonSize;
while (head && prevEdge != currEdge) {
++iterations;
// we should check each edge against each other edge at most once
if (iterations > maxIterations) {
return false;
}
SkScalar s, t;
SkPoint intersection;
if (compute_intersection(prevEdge->fOffset, currEdge->fOffset,
&intersection, &s, &t)) {
// if new intersection is further back on previous inset from the prior intersection
if (s < prevEdge->fTValue) {
// no point in considering this one again
remove_node(prevEdge, &head);
--insetVertexCount;
// go back one segment
prevEdge = prevEdge->fPrev;
// we've already considered this intersection, we're done
} else if (currEdge->fTValue > SK_ScalarMin &&
SkPointPriv::EqualsWithinTolerance(intersection,
currEdge->fIntersection,
1.0e-6f)) {
break;
} else {
// add intersection
currEdge->fIntersection = intersection;
currEdge->fTValue = t;
// go to next segment
prevEdge = currEdge;
currEdge = currEdge->fNext;
}
} else {
// if prev to right side of curr
int side = winding*compute_side(currEdge->fOffset.fP0,
currEdge->fOffset.fV,
prevEdge->fOffset.fP0);
if (side < 0 &&
side == winding*compute_side(currEdge->fOffset.fP0,
currEdge->fOffset.fV,
prevEdge->fOffset.fP0 + prevEdge->fOffset.fV)) {
// no point in considering this one again
remove_node(prevEdge, &head);
--insetVertexCount;
// go back one segment
prevEdge = prevEdge->fPrev;
} else {
// move to next segment
remove_node(currEdge, &head);
--insetVertexCount;
currEdge = currEdge->fNext;
}
}
}
// store all the valid intersections that aren't nearly coincident
// TODO: look at the main algorithm and see if we can detect these better
insetPolygon->reset();
if (!head) {
return false;
}
static constexpr SkScalar kCleanupTolerance = 0.01f;
if (insetVertexCount >= 0) {
insetPolygon->setReserve(insetVertexCount);
}
int currIndex = 0;
*insetPolygon->push() = head->fIntersection;
currEdge = head->fNext;
while (currEdge != head) {
if (!SkPointPriv::EqualsWithinTolerance(currEdge->fIntersection,
(*insetPolygon)[currIndex],
kCleanupTolerance)) {
*insetPolygon->push() = currEdge->fIntersection;
currIndex++;
}
currEdge = currEdge->fNext;
}
// make sure the first and last points aren't coincident
if (currIndex >= 1 &&
SkPointPriv::EqualsWithinTolerance((*insetPolygon)[0], (*insetPolygon)[currIndex],
kCleanupTolerance)) {
insetPolygon->pop();
}
return SkIsConvexPolygon(insetPolygon->begin(), insetPolygon->count());
}
///////////////////////////////////////////////////////////////////////////////////////////
// compute the number of points needed for a circular join when offsetting a reflex vertex
bool SkComputeRadialSteps(const SkVector& v1, const SkVector& v2, SkScalar offset,
SkScalar* rotSin, SkScalar* rotCos, int* n) {
const SkScalar kRecipPixelsPerArcSegment = 0.25f;
SkScalar rCos = v1.dot(v2);
if (!SkScalarIsFinite(rCos)) {
return false;
}
SkScalar rSin = v1.cross(v2);
if (!SkScalarIsFinite(rSin)) {
return false;
}
SkScalar theta = SkScalarATan2(rSin, rCos);
SkScalar floatSteps = SkScalarAbs(offset*theta*kRecipPixelsPerArcSegment);
// limit the number of steps to at most max uint16_t (that's all we can index)
// knock one value off the top to account for rounding
if (floatSteps >= std::numeric_limits<uint16_t>::max()) {
return false;
}
int steps = SkScalarRoundToInt(floatSteps);
SkScalar dTheta = steps > 0 ? theta / steps : 0;
*rotSin = SkScalarSinCos(dTheta, rotCos);
*n = steps;
return true;
}
///////////////////////////////////////////////////////////////////////////////////////////
// a point is "left" to another if its x-coord is less, or if equal, its y-coord is greater
static bool left(const SkPoint& p0, const SkPoint& p1) {
return p0.fX < p1.fX || (!(p0.fX > p1.fX) && p0.fY > p1.fY);
}
// a point is "right" to another if its x-coord is greater, or if equal, its y-coord is less
static bool right(const SkPoint& p0, const SkPoint& p1) {
return p0.fX > p1.fX || (!(p0.fX < p1.fX) && p0.fY < p1.fY);
}
struct Vertex {
static bool Left(const Vertex& qv0, const Vertex& qv1) {
return left(qv0.fPosition, qv1.fPosition);
}
// packed to fit into 16 bytes (one cache line)
SkPoint fPosition;
uint16_t fIndex; // index in unsorted polygon
uint16_t fPrevIndex; // indices for previous and next vertex in unsorted polygon
uint16_t fNextIndex;
uint16_t fFlags;
};
enum VertexFlags {
kPrevLeft_VertexFlag = 0x1,
kNextLeft_VertexFlag = 0x2,
};
struct ActiveEdge {
ActiveEdge() : fChild{ nullptr, nullptr }, fAbove(nullptr), fBelow(nullptr), fRed(false) {}
ActiveEdge(const SkPoint& p0, const SkVector& v, uint16_t index0, uint16_t index1)
: fSegment({ p0, v })
, fIndex0(index0)
, fIndex1(index1)
, fAbove(nullptr)
, fBelow(nullptr)
, fRed(true) {
fChild[0] = nullptr;
fChild[1] = nullptr;
}
// Returns true if "this" is above "that", assuming this->p0 is to the left of that->p0
// This is only used to verify the edgelist -- the actual test for insertion/deletion is much
// simpler because we can make certain assumptions then.
bool aboveIfLeft(const ActiveEdge* that) const {
const SkPoint& p0 = this->fSegment.fP0;
const SkPoint& q0 = that->fSegment.fP0;
SkASSERT(p0.fX <= q0.fX);
SkVector d = q0 - p0;
const SkVector& v = this->fSegment.fV;
const SkVector& w = that->fSegment.fV;
// The idea here is that if the vector between the origins of the two segments (d)
// rotates counterclockwise up to the vector representing the "this" segment (v),
// then we know that "this" is above "that". If the result is clockwise we say it's below.
if (this->fIndex0 != that->fIndex0) {
SkScalar cross = d.cross(v);
if (cross > kCrossTolerance) {
return true;
} else if (cross < -kCrossTolerance) {
return false;
}
} else if (this->fIndex1 == that->fIndex1) {
return false;
}
// At this point either the two origins are nearly equal or the origin of "that"
// lies on dv. So then we try the same for the vector from the tail of "this"
// to the head of "that". Again, ccw means "this" is above "that".
// d = that.P1 - this.P0
// = that.fP0 + that.fV - this.fP0
// = that.fP0 - this.fP0 + that.fV
// = old_d + that.fV
d += w;
SkScalar cross = d.cross(v);
if (cross > kCrossTolerance) {
return true;
} else if (cross < -kCrossTolerance) {
return false;
}
// If the previous check fails, the two segments are nearly collinear
// First check y-coord of first endpoints
if (p0.fX < q0.fX) {
return (p0.fY >= q0.fY);
} else if (p0.fY > q0.fY) {
return true;
} else if (p0.fY < q0.fY) {
return false;
}
// The first endpoints are the same, so check the other endpoint
SkPoint p1 = p0 + v;
SkPoint q1 = q0 + w;
if (p1.fX < q1.fX) {
return (p1.fY >= q1.fY);
} else {
return (p1.fY > q1.fY);
}
}
// same as leftAndAbove(), but generalized
bool above(const ActiveEdge* that) const {
const SkPoint& p0 = this->fSegment.fP0;
const SkPoint& q0 = that->fSegment.fP0;
if (right(p0, q0)) {
return !that->aboveIfLeft(this);
} else {
return this->aboveIfLeft(that);
}
}
bool intersect(const SkPoint& q0, const SkVector& w, uint16_t index0, uint16_t index1) const {
// check first to see if these edges are neighbors in the polygon
if (this->fIndex0 == index0 || this->fIndex1 == index0 ||
this->fIndex0 == index1 || this->fIndex1 == index1) {
return false;
}
// We don't need the exact intersection point so we can do a simpler test here.
const SkPoint& p0 = this->fSegment.fP0;
const SkVector& v = this->fSegment.fV;
SkPoint p1 = p0 + v;
SkPoint q1 = q0 + w;
// We assume some x-overlap due to how the edgelist works
// This allows us to simplify our test
// We need some slop here because storing the vector and recomputing the second endpoint
// doesn't necessary give us the original result in floating point.
// TODO: Store vector as double? Store endpoint as well?
SkASSERT(q0.fX <= p1.fX + SK_ScalarNearlyZero);
// if each segment straddles the other (i.e., the endpoints have different sides)
// then they intersect
bool result;
if (p0.fX < q0.fX) {
if (q1.fX < p1.fX) {
result = (compute_side(p0, v, q0)*compute_side(p0, v, q1) < 0);
} else {
result = (compute_side(p0, v, q0)*compute_side(q0, w, p1) > 0);
}
} else {
if (p1.fX < q1.fX) {
result = (compute_side(q0, w, p0)*compute_side(q0, w, p1) < 0);
} else {
result = (compute_side(q0, w, p0)*compute_side(p0, v, q1) > 0);
}
}
return result;
}
bool intersect(const ActiveEdge* edge) {
return this->intersect(edge->fSegment.fP0, edge->fSegment.fV, edge->fIndex0, edge->fIndex1);
}
bool lessThan(const ActiveEdge* that) const {
SkASSERT(!this->above(this));
SkASSERT(!that->above(that));
SkASSERT(!(this->above(that) && that->above(this)));
return this->above(that);
}
bool equals(uint16_t index0, uint16_t index1) const {
return (this->fIndex0 == index0 && this->fIndex1 == index1);
}
OffsetSegment fSegment;
uint16_t fIndex0; // indices for previous and next vertex in polygon
uint16_t fIndex1;
ActiveEdge* fChild[2];
ActiveEdge* fAbove;
ActiveEdge* fBelow;
int32_t fRed;
};
class ActiveEdgeList {
public:
ActiveEdgeList(int maxEdges) {
fAllocation = (char*) sk_malloc_throw(sizeof(ActiveEdge)*maxEdges);
fCurrFree = 0;
fMaxFree = maxEdges;
}
~ActiveEdgeList() {
fTreeHead.fChild[1] = nullptr;
sk_free(fAllocation);
}
bool insert(const SkPoint& p0, const SkPoint& p1, uint16_t index0, uint16_t index1) {
SkVector v = p1 - p0;
if (!v.isFinite()) {
return false;
}
// empty tree case -- easy
if (!fTreeHead.fChild[1]) {
ActiveEdge* root = fTreeHead.fChild[1] = this->allocate(p0, v, index0, index1);
SkASSERT(root);
if (!root) {
return false;
}
root->fRed = false;
return true;
}
// set up helpers
ActiveEdge* top = &fTreeHead;
ActiveEdge *grandparent = nullptr;
ActiveEdge *parent = nullptr;
ActiveEdge *curr = top->fChild[1];
int dir = 0;
int last = 0; // ?
// predecessor and successor, for intersection check
ActiveEdge* pred = nullptr;
ActiveEdge* succ = nullptr;
// search down the tree
while (true) {
if (!curr) {
// check for intersection with predecessor and successor
if ((pred && pred->intersect(p0, v, index0, index1)) ||
(succ && succ->intersect(p0, v, index0, index1))) {
return false;
}
// insert new node at bottom
parent->fChild[dir] = curr = this->allocate(p0, v, index0, index1);
SkASSERT(curr);
if (!curr) {
return false;
}
curr->fAbove = pred;
curr->fBelow = succ;
if (pred) {
pred->fBelow = curr;
}
if (succ) {
succ->fAbove = curr;
}
if (IsRed(parent)) {
int dir2 = (top->fChild[1] == grandparent);
if (curr == parent->fChild[last]) {
top->fChild[dir2] = SingleRotation(grandparent, !last);
} else {
top->fChild[dir2] = DoubleRotation(grandparent, !last);
}
}
break;
} else if (IsRed(curr->fChild[0]) && IsRed(curr->fChild[1])) {
// color flip
curr->fRed = true;
curr->fChild[0]->fRed = false;
curr->fChild[1]->fRed = false;
if (IsRed(parent)) {
int dir2 = (top->fChild[1] == grandparent);
if (curr == parent->fChild[last]) {
top->fChild[dir2] = SingleRotation(grandparent, !last);
} else {
top->fChild[dir2] = DoubleRotation(grandparent, !last);
}
}
}
last = dir;
int side;
// check to see if segment is above or below
if (curr->fIndex0 == index0) {
side = compute_side(curr->fSegment.fP0, curr->fSegment.fV, p1);
} else {
side = compute_side(curr->fSegment.fP0, curr->fSegment.fV, p0);
}
if (0 == side) {
return false;
}
dir = (side < 0);
if (0 == dir) {
succ = curr;
} else {
pred = curr;
}
// update helpers
if (grandparent) {
top = grandparent;
}
grandparent = parent;
parent = curr;
curr = curr->fChild[dir];
}
// update root and make it black
fTreeHead.fChild[1]->fRed = false;
SkDEBUGCODE(VerifyTree(fTreeHead.fChild[1]));
return true;
}
// replaces edge p0p1 with p1p2
bool replace(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2,
uint16_t index0, uint16_t index1, uint16_t index2) {
if (!fTreeHead.fChild[1]) {
return false;
}
SkVector v = p2 - p1;
ActiveEdge* curr = &fTreeHead;
ActiveEdge* found = nullptr;
int dir = 1;
// search
while (curr->fChild[dir] != nullptr) {
// update helpers
curr = curr->fChild[dir];
// save found node
if (curr->equals(index0, index1)) {
found = curr;
break;
} else {
// check to see if segment is above or below
int side;
if (curr->fIndex1 == index1) {
side = compute_side(curr->fSegment.fP0, curr->fSegment.fV, p0);
} else {
side = compute_side(curr->fSegment.fP0, curr->fSegment.fV, p1);
}
if (0 == side) {
return false;
}
dir = (side < 0);
}
}
if (!found) {
return false;
}
// replace if found
ActiveEdge* pred = found->fAbove;
ActiveEdge* succ = found->fBelow;
// check deletion and insert intersection cases
if (pred && (pred->intersect(found) || pred->intersect(p1, v, index1, index2))) {
return false;
}
if (succ && (succ->intersect(found) || succ->intersect(p1, v, index1, index2))) {
return false;
}
found->fSegment.fP0 = p1;
found->fSegment.fV = v;
found->fIndex0 = index1;
found->fIndex1 = index2;
// above and below should stay the same
SkDEBUGCODE(VerifyTree(fTreeHead.fChild[1]));
return true;
}
bool remove(const SkPoint& p0, const SkPoint& p1, uint16_t index0, uint16_t index1) {
if (!fTreeHead.fChild[1]) {
return false;
}
ActiveEdge* curr = &fTreeHead;
ActiveEdge* parent = nullptr;
ActiveEdge* grandparent = nullptr;
ActiveEdge* found = nullptr;
int dir = 1;
// search and push a red node down
while (curr->fChild[dir] != nullptr) {
int last = dir;
// update helpers
grandparent = parent;
parent = curr;
curr = curr->fChild[dir];
// save found node
if (curr->equals(index0, index1)) {
found = curr;
dir = 0;
} else {
// check to see if segment is above or below
int side;
if (curr->fIndex1 == index1) {
side = compute_side(curr->fSegment.fP0, curr->fSegment.fV, p0);
} else {
side = compute_side(curr->fSegment.fP0, curr->fSegment.fV, p1);
}
if (0 == side) {
return false;
}
dir = (side < 0);
}
// push the red node down
if (!IsRed(curr) && !IsRed(curr->fChild[dir])) {
if (IsRed(curr->fChild[!dir])) {
parent = parent->fChild[last] = SingleRotation(curr, dir);
} else {
ActiveEdge *s = parent->fChild[!last];
if (s != NULL) {
if (!IsRed(s->fChild[!last]) && !IsRed(s->fChild[last])) {
// color flip
parent->fRed = false;
s->fRed = true;
curr->fRed = true;
} else {
int dir2 = (grandparent->fChild[1] == parent);
if (IsRed(s->fChild[last])) {
grandparent->fChild[dir2] = DoubleRotation(parent, last);
} else if (IsRed(s->fChild[!last])) {
grandparent->fChild[dir2] = SingleRotation(parent, last);
}
// ensure correct coloring
curr->fRed = grandparent->fChild[dir2]->fRed = true;
grandparent->fChild[dir2]->fChild[0]->fRed = false;
grandparent->fChild[dir2]->fChild[1]->fRed = false;
}
}
}
}
}
// replace and remove if found
if (found) {
ActiveEdge* pred = found->fAbove;
ActiveEdge* succ = found->fBelow;
if ((pred && pred->intersect(found)) || (succ && succ->intersect(found))) {
return false;
}
if (found != curr) {
found->fSegment = curr->fSegment;
found->fIndex0 = curr->fIndex0;
found->fIndex1 = curr->fIndex1;
found->fAbove = curr->fAbove;
pred = found->fAbove;
// we don't need to set found->fBelow here
} else {
if (succ) {
succ->fAbove = pred;
}
}
if (pred) {
pred->fBelow = curr->fBelow;
}
parent->fChild[parent->fChild[1] == curr] = curr->fChild[!curr->fChild[0]];
// no need to delete
curr->fAbove = reinterpret_cast<ActiveEdge*>(0xdeadbeefll);
curr->fBelow = reinterpret_cast<ActiveEdge*>(0xdeadbeefll);
if (fTreeHead.fChild[1]) {
fTreeHead.fChild[1]->fRed = false;
}
}
// update root and make it black
if (fTreeHead.fChild[1]) {
fTreeHead.fChild[1]->fRed = false;
}
SkDEBUGCODE(VerifyTree(fTreeHead.fChild[1]));
return true;
}
private:
// allocator
ActiveEdge * allocate(const SkPoint& p0, const SkPoint& p1, uint16_t index0, uint16_t index1) {
if (fCurrFree >= fMaxFree) {
return nullptr;
}
char* bytes = fAllocation + sizeof(ActiveEdge)*fCurrFree;
++fCurrFree;
return new(bytes) ActiveEdge(p0, p1, index0, index1);
}
///////////////////////////////////////////////////////////////////////////////////
// Red-black tree methods
///////////////////////////////////////////////////////////////////////////////////
static bool IsRed(const ActiveEdge* node) {
return node && node->fRed;
}
static ActiveEdge* SingleRotation(ActiveEdge* node, int dir) {
ActiveEdge* tmp = node->fChild[!dir];
node->fChild[!dir] = tmp->fChild[dir];
tmp->fChild[dir] = node;
node->fRed = true;
tmp->fRed = false;
return tmp;
}
static ActiveEdge* DoubleRotation(ActiveEdge* node, int dir) {
node->fChild[!dir] = SingleRotation(node->fChild[!dir], !dir);
return SingleRotation(node, dir);
}
// returns black link count
static int VerifyTree(const ActiveEdge* tree) {
if (!tree) {
return 1;
}
const ActiveEdge* left = tree->fChild[0];
const ActiveEdge* right = tree->fChild[1];
// no consecutive red links
if (IsRed(tree) && (IsRed(left) || IsRed(right))) {
SkASSERT(false);
return 0;
}
// check secondary links
if (tree->fAbove) {
SkASSERT(tree->fAbove->fBelow == tree);
SkASSERT(tree->fAbove->lessThan(tree));
}
if (tree->fBelow) {
SkASSERT(tree->fBelow->fAbove == tree);
SkASSERT(tree->lessThan(tree->fBelow));
}
// violates binary tree order
if ((left && tree->lessThan(left)) || (right && right->lessThan(tree))) {
SkASSERT(false);
return 0;
}
int leftCount = VerifyTree(left);
int rightCount = VerifyTree(right);
// return black link count
if (leftCount != 0 && rightCount != 0) {
// black height mismatch
if (leftCount != rightCount) {
SkASSERT(false);
return 0;
}
return IsRed(tree) ? leftCount : leftCount + 1;
} else {
return 0;
}
}
ActiveEdge fTreeHead;
char* fAllocation;
int fCurrFree;
int fMaxFree;
};
// Here we implement a sweep line algorithm to determine whether the provided points
// represent a simple polygon, i.e., the polygon is non-self-intersecting.
// We first insert the vertices into a priority queue sorting horizontally from left to right.
// Then as we pop the vertices from the queue we generate events which indicate that an edge
// should be added or removed from an edge list. If any intersections are detected in the edge
// list, then we know the polygon is self-intersecting and hence not simple.
bool SkIsSimplePolygon(const SkPoint* polygon, int polygonSize) {
if (polygonSize < 3) {
return false;
}
// need to be able to represent all the vertices in the 16-bit indices
if (polygonSize > std::numeric_limits<uint16_t>::max()) {
return false;
}
// If it's convex, it's simple
if (SkIsConvexPolygon(polygon, polygonSize)) {
return true;
}
SkTDPQueue <Vertex, Vertex::Left> vertexQueue(polygonSize);
for (int i = 0; i < polygonSize; ++i) {
Vertex newVertex;
if (!polygon[i].isFinite()) {
return false;
}
newVertex.fPosition = polygon[i];
newVertex.fIndex = i;
newVertex.fPrevIndex = (i - 1 + polygonSize) % polygonSize;
newVertex.fNextIndex = (i + 1) % polygonSize;
newVertex.fFlags = 0;
if (left(polygon[newVertex.fPrevIndex], polygon[i])) {
newVertex.fFlags |= kPrevLeft_VertexFlag;
}
if (left(polygon[newVertex.fNextIndex], polygon[i])) {
newVertex.fFlags |= kNextLeft_VertexFlag;
}
vertexQueue.insert(newVertex);
}
// pop each vertex from the queue and generate events depending on
// where it lies relative to its neighboring edges
ActiveEdgeList sweepLine(polygonSize);
while (vertexQueue.count() > 0) {
const Vertex& v = vertexQueue.peek();
// both to the right -- insert both
if (v.fFlags == 0) {
if (!sweepLine.insert(v.fPosition, polygon[v.fPrevIndex], v.fIndex, v.fPrevIndex)) {
break;
}
if (!sweepLine.insert(v.fPosition, polygon[v.fNextIndex], v.fIndex, v.fNextIndex)) {
break;
}
// both to the left -- remove both
} else if (v.fFlags == (kPrevLeft_VertexFlag | kNextLeft_VertexFlag)) {
if (!sweepLine.remove(polygon[v.fPrevIndex], v.fPosition, v.fPrevIndex, v.fIndex)) {
break;
}
if (!sweepLine.remove(polygon[v.fNextIndex], v.fPosition, v.fNextIndex, v.fIndex)) {
break;
}
// one to left and right -- replace one with another
} else {
if (v.fFlags & kPrevLeft_VertexFlag) {
if (!sweepLine.replace(polygon[v.fPrevIndex], v.fPosition, polygon[v.fNextIndex],
v.fPrevIndex, v.fIndex, v.fNextIndex)) {
break;
}
} else {
SkASSERT(v.fFlags & kNextLeft_VertexFlag);
if (!sweepLine.replace(polygon[v.fNextIndex], v.fPosition, polygon[v.fPrevIndex],
v.fNextIndex, v.fIndex, v.fPrevIndex)) {
break;
}
}
}
vertexQueue.pop();
}
return (vertexQueue.count() == 0);
}
///////////////////////////////////////////////////////////////////////////////////////////
// helper function for SkOffsetSimplePolygon
static void setup_offset_edge(OffsetEdge* currEdge,
const SkPoint& endpoint0, const SkPoint& endpoint1,
uint16_t startIndex, uint16_t endIndex) {
currEdge->fOffset.fP0 = endpoint0;
currEdge->fOffset.fV = endpoint1 - endpoint0;
currEdge->init(startIndex, endIndex);
}
static bool is_reflex_vertex(const SkPoint* inputPolygonVerts, int winding, SkScalar offset,
uint16_t prevIndex, uint16_t currIndex, uint16_t nextIndex) {
int side = compute_side(inputPolygonVerts[prevIndex],
inputPolygonVerts[currIndex] - inputPolygonVerts[prevIndex],
inputPolygonVerts[nextIndex]);
// if reflex point, we need to add extra edges
return (side*winding*offset < 0);
}
bool SkOffsetSimplePolygon(const SkPoint* inputPolygonVerts, int inputPolygonSize, SkScalar offset,
SkTDArray<SkPoint>* offsetPolygon, SkTDArray<int>* polygonIndices) {
if (inputPolygonSize < 3) {
return false;
}
// need to be able to represent all the vertices in the 16-bit indices
if (inputPolygonSize >= std::numeric_limits<uint16_t>::max()) {
return false;
}
if (!SkScalarIsFinite(offset)) {
return false;
}
// offsetting close to zero just returns the original poly
if (SkScalarNearlyZero(offset)) {
for (int i = 0; i < inputPolygonSize; ++i) {
*offsetPolygon->push() = inputPolygonVerts[i];
*polygonIndices->push() = i;
}
return true;
}
// get winding direction
int winding = SkGetPolygonWinding(inputPolygonVerts, inputPolygonSize);
if (0 == winding) {
return false;
}
// build normals
SkAutoSTMalloc<64, SkVector> normals(inputPolygonSize);
unsigned int numEdges = 0;
for (int currIndex = 0, prevIndex = inputPolygonSize - 1;
currIndex < inputPolygonSize;
prevIndex = currIndex, ++currIndex) {
if (!inputPolygonVerts[currIndex].isFinite()) {
return false;
}
int nextIndex = (currIndex + 1) % inputPolygonSize;
if (!compute_offset_vector(inputPolygonVerts[currIndex], inputPolygonVerts[nextIndex],
offset, winding, &normals[currIndex])) {
return false;
}
if (currIndex > 0) {
// if reflex point, we need to add extra edges
if (is_reflex_vertex(inputPolygonVerts, winding, offset,
prevIndex, currIndex, nextIndex)) {
SkScalar rotSin, rotCos;
int numSteps;
if (!SkComputeRadialSteps(normals[prevIndex], normals[currIndex], offset,
&rotSin, &rotCos, &numSteps)) {
return false;
}
numEdges += SkTMax(numSteps, 1);
}
}
numEdges++;
}
// finish up the edge counting
if (is_reflex_vertex(inputPolygonVerts, winding, offset, inputPolygonSize-1, 0, 1)) {
SkScalar rotSin, rotCos;
int numSteps;
if (!SkComputeRadialSteps(normals[inputPolygonSize-1], normals[0], offset,
&rotSin, &rotCos, &numSteps)) {
return false;
}
numEdges += SkTMax(numSteps, 1);
}
// Make sure we don't overflow the max array count.
// We shouldn't overflow numEdges, as SkComputeRadialSteps returns a max of 2^16-1,
// and we have a max of 2^16-1 original vertices.
if (numEdges > (unsigned int)std::numeric_limits<int32_t>::max()) {
return false;
}
// build initial offset edge list
SkSTArray<64, OffsetEdge> edgeData(numEdges);
OffsetEdge* prevEdge = nullptr;
for (int currIndex = 0, prevIndex = inputPolygonSize - 1;
currIndex < inputPolygonSize;
prevIndex = currIndex, ++currIndex) {
int nextIndex = (currIndex + 1) % inputPolygonSize;
// if reflex point, fill in curve
if (is_reflex_vertex(inputPolygonVerts, winding, offset,
prevIndex, currIndex, nextIndex)) {
SkScalar rotSin, rotCos;
int numSteps;
SkVector prevNormal = normals[prevIndex];
if (!SkComputeRadialSteps(prevNormal, normals[currIndex], offset,
&rotSin, &rotCos, &numSteps)) {
return false;
}
auto currEdge = edgeData.push_back_n(SkTMax(numSteps, 1));
for (int i = 0; i < numSteps - 1; ++i) {
SkVector currNormal = SkVector::Make(prevNormal.fX*rotCos - prevNormal.fY*rotSin,
prevNormal.fY*rotCos + prevNormal.fX*rotSin);
setup_offset_edge(currEdge,
inputPolygonVerts[currIndex] + prevNormal,
inputPolygonVerts[currIndex] + currNormal,
currIndex, currIndex);
prevNormal = currNormal;
currEdge->fPrev = prevEdge;
if (prevEdge) {
prevEdge->fNext = currEdge;
}
prevEdge = currEdge;
++currEdge;
}
setup_offset_edge(currEdge,
inputPolygonVerts[currIndex] + prevNormal,
inputPolygonVerts[currIndex] + normals[currIndex],
currIndex, currIndex);
currEdge->fPrev = prevEdge;
if (prevEdge) {
prevEdge->fNext = currEdge;
}
prevEdge = currEdge;
}
// Add the edge
auto currEdge = edgeData.push_back_n(1);
setup_offset_edge(currEdge,
inputPolygonVerts[currIndex] + normals[currIndex],
inputPolygonVerts[nextIndex] + normals[currIndex],
currIndex, nextIndex);
currEdge->fPrev = prevEdge;
if (prevEdge) {
prevEdge->fNext = currEdge;
}
prevEdge = currEdge;
}
// close up the linked list
SkASSERT(prevEdge);
prevEdge->fNext = &edgeData[0];
edgeData[0].fPrev = prevEdge;
// now clip edges
SkASSERT(edgeData.count() == (int)numEdges);
auto head = &edgeData[0];
auto currEdge = head;
unsigned int offsetVertexCount = numEdges;
unsigned long long iterations = 0;
unsigned long long maxIterations = (unsigned long long)(numEdges) * numEdges;
while (head && prevEdge != currEdge && offsetVertexCount > 0) {
++iterations;
// we should check each edge against each other edge at most once
if (iterations > maxIterations) {
return false;
}
SkScalar s, t;
SkPoint intersection;
if (prevEdge->checkIntersection(currEdge, &intersection, &s, &t)) {
// if new intersection is further back on previous inset from the prior intersection
if (s < prevEdge->fTValue) {
// no point in considering this one again
remove_node(prevEdge, &head);
--offsetVertexCount;
// go back one segment
prevEdge = prevEdge->fPrev;
// we've already considered this intersection, we're done
} else if (currEdge->fTValue > SK_ScalarMin &&
SkPointPriv::EqualsWithinTolerance(intersection,
currEdge->fIntersection,
1.0e-6f)) {
break;
} else {
// add intersection
currEdge->fIntersection = intersection;
currEdge->fTValue = t;
currEdge->fIndex = prevEdge->fEnd;
// go to next segment
prevEdge = currEdge;
currEdge = currEdge->fNext;
}
} else {
// If there is no intersection, we want to minimize the distance between
// the point where the segment lines cross and the segments themselves.
OffsetEdge* prevPrevEdge = prevEdge->fPrev;
OffsetEdge* currNextEdge = currEdge->fNext;
SkScalar dist0 = currEdge->computeCrossingDistance(prevPrevEdge);
SkScalar dist1 = prevEdge->computeCrossingDistance(currNextEdge);
// if both lead to direct collision
if (dist0 < 0 && dist1 < 0) {
// check first to see if either represent parts of one contour
SkPoint p1 = prevPrevEdge->fOffset.fP0 + prevPrevEdge->fOffset.fV;
bool prevSameContour = SkPointPriv::EqualsWithinTolerance(p1,
prevEdge->fOffset.fP0);
p1 = currEdge->fOffset.fP0 + currEdge->fOffset.fV;
bool currSameContour = SkPointPriv::EqualsWithinTolerance(p1,
currNextEdge->fOffset.fP0);
// want to step along contour to find intersections rather than jump to new one
if (currSameContour && !prevSameContour) {
remove_node(currEdge, &head);
currEdge = currNextEdge;
--offsetVertexCount;
continue;
} else if (prevSameContour && !currSameContour) {
remove_node(prevEdge, &head);
prevEdge = prevPrevEdge;
--offsetVertexCount;
continue;
}
}
// otherwise minimize collision distance along segment
if (dist0 < dist1) {
remove_node(prevEdge, &head);
prevEdge = prevPrevEdge;
} else {
remove_node(currEdge, &head);
currEdge = currNextEdge;
}
--offsetVertexCount;
}
}
// store all the valid intersections that aren't nearly coincident
// TODO: look at the main algorithm and see if we can detect these better
offsetPolygon->reset();
if (!head || offsetVertexCount == 0 ||
offsetVertexCount >= std::numeric_limits<uint16_t>::max()) {
return false;
}
static constexpr SkScalar kCleanupTolerance = 0.01f;
offsetPolygon->setReserve(offsetVertexCount);
int currIndex = 0;
*offsetPolygon->push() = head->fIntersection;
if (polygonIndices) {
*polygonIndices->push() = head->fIndex;
}
currEdge = head->fNext;
while (currEdge != head) {
if (!SkPointPriv::EqualsWithinTolerance(currEdge->fIntersection,
(*offsetPolygon)[currIndex],
kCleanupTolerance)) {
*offsetPolygon->push() = currEdge->fIntersection;
if (polygonIndices) {
*polygonIndices->push() = currEdge->fIndex;
}
currIndex++;
}
currEdge = currEdge->fNext;
}
// make sure the first and last points aren't coincident
if (currIndex >= 1 &&
SkPointPriv::EqualsWithinTolerance((*offsetPolygon)[0], (*offsetPolygon)[currIndex],
kCleanupTolerance)) {
offsetPolygon->pop();
if (polygonIndices) {
polygonIndices->pop();
}
}
// check winding of offset polygon (it should be same as the original polygon)
SkScalar offsetWinding = SkGetPolygonWinding(offsetPolygon->begin(), offsetPolygon->count());
return (winding*offsetWinding > 0 &&
SkIsSimplePolygon(offsetPolygon->begin(), offsetPolygon->count()));
}
//////////////////////////////////////////////////////////////////////////////////////////
struct TriangulationVertex {
SK_DECLARE_INTERNAL_LLIST_INTERFACE(TriangulationVertex);
enum class VertexType { kConvex, kReflex };
SkPoint fPosition;
VertexType fVertexType;
uint16_t fIndex;
uint16_t fPrevIndex;
uint16_t fNextIndex;
};
static void compute_triangle_bounds(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2,
SkRect* bounds) {
Sk4s min, max;
min = max = Sk4s(p0.fX, p0.fY, p0.fX, p0.fY);
Sk4s xy(p1.fX, p1.fY, p2.fX, p2.fY);
min = Sk4s::Min(min, xy);
max = Sk4s::Max(max, xy);
bounds->set(SkTMin(min[0], min[2]), SkTMin(min[1], min[3]),
SkTMax(max[0], max[2]), SkTMax(max[1], max[3]));
}
// test to see if point p is in triangle p0p1p2.
// for now assuming strictly inside -- if on the edge it's outside
static bool point_in_triangle(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2,
const SkPoint& p) {
SkVector v0 = p1 - p0;
SkVector v1 = p2 - p1;
SkScalar n = v0.cross(v1);
SkVector w0 = p - p0;
if (n*v0.cross(w0) < SK_ScalarNearlyZero) {
return false;
}
SkVector w1 = p - p1;
if (n*v1.cross(w1) < SK_ScalarNearlyZero) {
return false;
}
SkVector v2 = p0 - p2;
SkVector w2 = p - p2;
if (n*v2.cross(w2) < SK_ScalarNearlyZero) {
return false;
}
return true;
}
// Data structure to track reflex vertices and check whether any are inside a given triangle
class ReflexHash {
public:
bool init(const SkRect& bounds, int vertexCount) {
fBounds = bounds;
fNumVerts = 0;
SkScalar width = bounds.width();
SkScalar height = bounds.height();
if (!SkScalarIsFinite(width) || !SkScalarIsFinite(height)) {
return false;
}
// We want vertexCount grid cells, roughly distributed to match the bounds ratio
SkScalar hCount = SkScalarSqrt(sk_ieee_float_divide(vertexCount*width, height));
if (!SkScalarIsFinite(hCount)) {
return false;
}
fHCount = SkTMax(SkTMin(SkScalarRoundToInt(hCount), vertexCount), 1);
fVCount = vertexCount/fHCount;
fGridConversion.set(sk_ieee_float_divide(fHCount - 0.001f, width),
sk_ieee_float_divide(fVCount - 0.001f, height));
if (!fGridConversion.isFinite()) {
return false;
}
fGrid.setCount(fHCount*fVCount);
for (int i = 0; i < fGrid.count(); ++i) {
fGrid[i].reset();
}
return true;
}
void add(TriangulationVertex* v) {
int index = hash(v);
fGrid[index].addToTail(v);
++fNumVerts;
}
void remove(TriangulationVertex* v) {
int index = hash(v);
fGrid[index].remove(v);
--fNumVerts;
}
bool checkTriangle(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2,
uint16_t ignoreIndex0, uint16_t ignoreIndex1) const {
if (!fNumVerts) {
return false;
}
SkRect triBounds;
compute_triangle_bounds(p0, p1, p2, &triBounds);
int h0 = (triBounds.fLeft - fBounds.fLeft)*fGridConversion.fX;
int h1 = (triBounds.fRight - fBounds.fLeft)*fGridConversion.fX;
int v0 = (triBounds.fTop - fBounds.fTop)*fGridConversion.fY;
int v1 = (triBounds.fBottom - fBounds.fTop)*fGridConversion.fY;
for (int v = v0; v <= v1; ++v) {
for (int h = h0; h <= h1; ++h) {
int i = v * fHCount + h;
for (SkTInternalLList<TriangulationVertex>::Iter reflexIter = fGrid[i].begin();
reflexIter != fGrid[i].end(); ++reflexIter) {
TriangulationVertex* reflexVertex = *reflexIter;
if (reflexVertex->fIndex != ignoreIndex0 &&
reflexVertex->fIndex != ignoreIndex1 &&
point_in_triangle(p0, p1, p2, reflexVertex->fPosition)) {
return true;
}
}
}
}
return false;
}
private:
int hash(TriangulationVertex* vert) const {
int h = (vert->fPosition.fX - fBounds.fLeft)*fGridConversion.fX;
int v = (vert->fPosition.fY - fBounds.fTop)*fGridConversion.fY;
SkASSERT(v*fHCount + h >= 0);
return v*fHCount + h;
}
SkRect fBounds;
int fHCount;
int fVCount;
int fNumVerts;
// converts distance from the origin to a grid location (when cast to int)
SkVector fGridConversion;
SkTDArray<SkTInternalLList<TriangulationVertex>> fGrid;
};
// Check to see if a reflex vertex has become a convex vertex after clipping an ear
static void reclassify_vertex(TriangulationVertex* p, const SkPoint* polygonVerts,
int winding, ReflexHash* reflexHash,
SkTInternalLList<TriangulationVertex>* convexList) {
if (TriangulationVertex::VertexType::kReflex == p->fVertexType) {
SkVector v0 = p->fPosition - polygonVerts[p->fPrevIndex];
SkVector v1 = polygonVerts[p->fNextIndex] - p->fPosition;
if (winding*v0.cross(v1) > SK_ScalarNearlyZero*SK_ScalarNearlyZero) {
p->fVertexType = TriangulationVertex::VertexType::kConvex;
reflexHash->remove(p);
p->fPrev = p->fNext = nullptr;
convexList->addToTail(p);
}
}
}
bool SkTriangulateSimplePolygon(const SkPoint* polygonVerts, uint16_t* indexMap, int polygonSize,
SkTDArray<uint16_t>* triangleIndices) {
if (polygonSize < 3) {
return false;
}
// need to be able to represent all the vertices in the 16-bit indices
if (polygonSize >= std::numeric_limits<uint16_t>::max()) {
return false;
}
// get bounds
SkRect bounds;
if (!bounds.setBoundsCheck(polygonVerts, polygonSize)) {
return false;
}
// get winding direction
// TODO: we do this for all the polygon routines -- might be better to have the client
// compute it and pass it in
int winding = SkGetPolygonWinding(polygonVerts, polygonSize);
if (0 == winding) {
return false;
}
// Set up vertices
SkAutoSTMalloc<64, TriangulationVertex> triangulationVertices(polygonSize);
int prevIndex = polygonSize - 1;
SkVector v0 = polygonVerts[0] - polygonVerts[prevIndex];
for (int currIndex = 0; currIndex < polygonSize; ++currIndex) {
int nextIndex = (currIndex + 1) % polygonSize;
SkDEBUGCODE(memset(&triangulationVertices[currIndex], 0, sizeof(TriangulationVertex)));
triangulationVertices[currIndex].fPosition = polygonVerts[currIndex];
triangulationVertices[currIndex].fIndex = currIndex;
triangulationVertices[currIndex].fPrevIndex = prevIndex;
triangulationVertices[currIndex].fNextIndex = nextIndex;
SkVector v1 = polygonVerts[nextIndex] - polygonVerts[currIndex];
if (winding*v0.cross(v1) > SK_ScalarNearlyZero*SK_ScalarNearlyZero) {
triangulationVertices[currIndex].fVertexType = TriangulationVertex::VertexType::kConvex;
} else {
triangulationVertices[currIndex].fVertexType = TriangulationVertex::VertexType::kReflex;
}
prevIndex = currIndex;
v0 = v1;
}
// Classify initial vertices into a list of convex vertices and a hash of reflex vertices
// TODO: possibly sort the convexList in some way to get better triangles
SkTInternalLList<TriangulationVertex> convexList;
ReflexHash reflexHash;
if (!reflexHash.init(bounds, polygonSize)) {
return false;
}
prevIndex = polygonSize - 1;
for (int currIndex = 0; currIndex < polygonSize; prevIndex = currIndex, ++currIndex) {
TriangulationVertex::VertexType currType = triangulationVertices[currIndex].fVertexType;
if (TriangulationVertex::VertexType::kConvex == currType) {
int nextIndex = (currIndex + 1) % polygonSize;
TriangulationVertex::VertexType prevType = triangulationVertices[prevIndex].fVertexType;
TriangulationVertex::VertexType nextType = triangulationVertices[nextIndex].fVertexType;
// We prioritize clipping vertices with neighboring reflex vertices.
// The intent here is that it will cull reflex vertices more quickly.
if (TriangulationVertex::VertexType::kReflex == prevType ||
TriangulationVertex::VertexType::kReflex == nextType) {
convexList.addToHead(&triangulationVertices[currIndex]);
} else {
convexList.addToTail(&triangulationVertices[currIndex]);
}
} else {
// We treat near collinear vertices as reflex
reflexHash.add(&triangulationVertices[currIndex]);
}
}
// The general concept: We are trying to find three neighboring vertices where
// no other vertex lies inside the triangle (an "ear"). If we find one, we clip
// that ear off, and then repeat on the new polygon. Once we get down to three vertices
// we have triangulated the entire polygon.
// In the worst case this is an n^2 algorithm. We can cut down the search space somewhat by
// noting that only convex vertices can be potential ears, and we only need to check whether
// any reflex vertices lie inside the ear.
triangleIndices->setReserve(triangleIndices->count() + 3 * (polygonSize - 2));
int vertexCount = polygonSize;
while (vertexCount > 3) {
bool success = false;
TriangulationVertex* earVertex = nullptr;
TriangulationVertex* p0 = nullptr;
TriangulationVertex* p2 = nullptr;
// find a convex vertex to clip
for (SkTInternalLList<TriangulationVertex>::Iter convexIter = convexList.begin();
convexIter != convexList.end(); ++convexIter) {
earVertex = *convexIter;
SkASSERT(TriangulationVertex::VertexType::kReflex != earVertex->fVertexType);
p0 = &triangulationVertices[earVertex->fPrevIndex];
p2 = &triangulationVertices[earVertex->fNextIndex];
// see if any reflex vertices are inside the ear
bool failed = reflexHash.checkTriangle(p0->fPosition, earVertex->fPosition,
p2->fPosition, p0->fIndex, p2->fIndex);
if (failed) {
continue;
}
// found one we can clip
success = true;
break;
}
// If we can't find any ears to clip, this probably isn't a simple polygon
if (!success) {
return false;
}
// add indices
auto indices = triangleIndices->append(3);
indices[0] = indexMap[p0->fIndex];
indices[1] = indexMap[earVertex->fIndex];
indices[2] = indexMap[p2->fIndex];
// clip the ear
convexList.remove(earVertex);
--vertexCount;
// reclassify reflex verts
p0->fNextIndex = earVertex->fNextIndex;
reclassify_vertex(p0, polygonVerts, winding, &reflexHash, &convexList);
p2->fPrevIndex = earVertex->fPrevIndex;
reclassify_vertex(p2, polygonVerts, winding, &reflexHash, &convexList);
}
// output indices
for (SkTInternalLList<TriangulationVertex>::Iter vertexIter = convexList.begin();
vertexIter != convexList.end(); ++vertexIter) {
TriangulationVertex* vertex = *vertexIter;
*triangleIndices->push() = indexMap[vertex->fIndex];
}
return true;
}
///////////
static double crs(SkVector a, SkVector b) {
return a.fX * b.fY - a.fY * b.fX;
}
static int sign(SkScalar v) {
return v < 0 ? -1 : (v > 0);
}
struct SignTracker {
int fSign;
int fSignChanges;
void reset() {
fSign = 0;
fSignChanges = 0;
}
void init(int s) {
SkASSERT(fSignChanges == 0);
SkASSERT(s == 1 || s == -1 || s == 0);
fSign = s;
fSignChanges = 1;
}
void update(int s) {
if (s) {
if (fSign != s) {
fSignChanges += 1;
fSign = s;
}
}
}
};
struct ConvexTracker {
SkVector fFirst, fPrev;
SignTracker fDSign, fCSign;
int fVecCounter;
bool fIsConcave;
ConvexTracker() { this->reset(); }
void reset() {
fPrev = {0, 0};
fDSign.reset();
fCSign.reset();
fVecCounter = 0;
fIsConcave = false;
}
void addVec(SkPoint p1, SkPoint p0) {
this->addVec(p1 - p0);
}
void addVec(SkVector v) {
if (v.fX == 0 && v.fY == 0) {
return;
}
fVecCounter += 1;
if (fVecCounter == 1) {
fFirst = fPrev = v;
fDSign.update(sign(v.fX));
return;
}
SkScalar d = v.fX;
SkScalar c = crs(fPrev, v);
int sign_c;
if (c) {
sign_c = sign(c);
} else {
if (d >= 0) {
sign_c = fCSign.fSign;
} else {
sign_c = -fCSign.fSign;
}
}
fDSign.update(sign(d));
fCSign.update(sign_c);
fPrev = v;
if (fDSign.fSignChanges > 3 || fCSign.fSignChanges > 1) {
fIsConcave = true;
}
}
void finalCross() {
this->addVec(fFirst);
}
};
bool SkIsPolyConvex_experimental(const SkPoint pts[], int count) {
if (count <= 3) {
return true;
}
ConvexTracker tracker;
for (int i = 0; i < count - 1; ++i) {
tracker.addVec(pts[i + 1], pts[i]);
if (tracker.fIsConcave) {
return false;
}
}
tracker.addVec(pts[0], pts[count - 1]);
tracker.finalCross();
return !tracker.fIsConcave;
}