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 /* * 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 "src/utils/SkPolyUtils.h" #include "include/core/SkRect.h" #include "include/core/SkTypes.h" #include "include/private/base/SkFloatingPoint.h" #include "include/private/base/SkTArray.h" #include "include/private/base/SkTDArray.h" #include "include/private/base/SkTemplates.h" #include "include/private/base/SkVx.h" #include "include/private/base/SkMalloc.h" #include "src/core/SkPointPriv.h" #include "src/core/SkRectPriv.h" #include "src/core/SkTDPQueue.h" #include "src/core/SkTInternalLList.h" #include #include #include #include using namespace skia_private; #if !defined(SK_ENABLE_OPTIMIZE_SIZE) ////////////////////////////////////////////////////////////////////////////////// // 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)); } // special zero-length test when we're using vdotv as a denominator static inline bool zero_length(const SkPoint& v, SkScalar vdotv) { return !(SkScalarsAreFinite(v.fX, v.fY) && vdotv); } // 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. // If the length squared of a segment is 0, then we treat the segment as degenerate // and use only the first endpoint for tests. 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 SkScalar v0dotv0 = v0.dot(v0); if (zero_length(v0, v0dotv0)) { // Both are zero-length SkScalar v1dotv1 = v1.dot(v1); if (zero_length(v1, v1dotv1)) { // Check if they're the same point if (!SkPointPriv::CanNormalize(w.fX, w.fY)) { *p = s0.fP0; *s = 0; *t = 0; return true; } else { // Intersection is indeterminate return false; } } // Otherwise project segment0's origin onto segment1 tNumer = v1.dot(-w); denom = v1dotv1; if (outside_interval(tNumer, denom, true)) { return false; } sNumer = 0; } else { // Project segment1's endpoints onto segment0 sNumer = v0.dot(w); denom = v0dotv0; 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 SkScalar v1dotv1 = v1.dot(v1); if (zero_length(v1, v1dotv1)) { 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 = v1dotv1; } } } } 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 lastPerpDot = 0; int xSignChangeCount = 0; int ySignChangeCount = 0; int prevIndex = polygonSize - 1; int currIndex = 0; int nextIndex = 1; SkVector v0 = polygonVerts[currIndex] - polygonVerts[prevIndex]; SkScalar lastVx = v0.fX; SkScalar lastVy = v0.fY; SkVector v1 = polygonVerts[nextIndex] - polygonVerts[currIndex]; 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; } // Check that the signs of the edge vectors don't change more than twice per coordinate if (lastVx*v1.fX < 0) { xSignChangeCount++; } if (lastVy*v1.fY < 0) { ySignChangeCount++; } if (xSignChangeCount > 2 || ySignChangeCount > 2) { return false; } prevIndex = currIndex; currIndex = nextIndex; nextIndex = (currIndex + 1) % polygonSize; if (v1.fX != 0) { lastVx = v1.fX; } if (v1.fY != 0) { lastVy = v1.fY; } v0 = v1; v1 = polygonVerts[nextIndex] - polygonVerts[currIndex]; } 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* 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::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->append() = inputPolygonVerts[i]; } return true; } // get winding direction int winding = SkGetPolygonWinding(inputPolygonVerts, inputPolygonSize); if (0 == winding) { return false; } // set up AutoSTMalloc<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->reserve(insetVertexCount); } int currIndex = 0; *insetPolygon->append() = head->fIntersection; currEdge = head->fNext; while (currEdge != head) { if (!SkPointPriv::EqualsWithinTolerance(currEdge->fIntersection, (*insetPolygon)[currIndex], kCleanupTolerance)) { *insetPolygon->append() = 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_back(); } return SkIsConvexPolygon(insetPolygon->begin(), insetPolygon->size()); } /////////////////////////////////////////////////////////////////////////////////////////// // 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::max()) { return false; } int steps = SkScalarRoundToInt(floatSteps); SkScalar dTheta = steps > 0 ? theta / steps : 0; *rotSin = SkScalarSin(dTheta); *rotCos = SkScalarCos(dTheta); // Our offset may be so large that we end up with a tiny dTheta, in which case we // lose precision when computing rotSin and rotCos. if (steps > 0 && (*rotSin == 0 || *rotCos == 1)) { return false; } *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) { if (pred->fSegment.fP0 == curr->fSegment.fP0 && pred->fSegment.fV == curr->fSegment.fV) { return false; } pred->fBelow = curr; } if (succ) { if (succ->fSegment.fP0 == curr->fSegment.fP0 && succ->fSegment.fV == curr->fSegment.fV) { return false; } 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 != nullptr) { 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(0xdeadbeefll); curr->fBelow = reinterpret_cast(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; } // If it's convex, it's simple if (SkIsConvexPolygon(polygon, polygonSize)) { return true; } // practically speaking, it takes too long to process large polygons if (polygonSize > 2048) { return false; } SkTDPQueue 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; // The two edges adjacent to this vertex are the same, so polygon is not simple if (polygon[newVertex.fPrevIndex] == polygon[newVertex.fNextIndex]) { return false; } 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, const SkRect& bounds, SkScalar offset, SkTDArray* offsetPolygon, SkTDArray* 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::max()) { return false; } if (!SkScalarIsFinite(offset)) { return false; } // can't inset more than the half bounds of the polygon if (offset > std::min(SkTAbs(SkRectPriv::HalfWidth(bounds)), SkTAbs(SkRectPriv::HalfHeight(bounds)))) { return false; } // offsetting close to zero just returns the original poly if (SkScalarNearlyZero(offset)) { for (int i = 0; i < inputPolygonSize; ++i) { *offsetPolygon->append() = inputPolygonVerts[i]; if (polygonIndices) { *polygonIndices->append() = i; } } return true; } // get winding direction int winding = SkGetPolygonWinding(inputPolygonVerts, inputPolygonSize); if (0 == winding) { return false; } // build normals AutoSTMalloc<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 += std::max(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 += std::max(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::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(std::max(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.size() == (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::max()) { return false; } static constexpr SkScalar kCleanupTolerance = 0.01f; offsetPolygon->reserve(offsetVertexCount); int currIndex = 0; *offsetPolygon->append() = head->fIntersection; if (polygonIndices) { *polygonIndices->append() = head->fIndex; } currEdge = head->fNext; while (currEdge != head) { if (!SkPointPriv::EqualsWithinTolerance(currEdge->fIntersection, (*offsetPolygon)[currIndex], kCleanupTolerance)) { *offsetPolygon->append() = currEdge->fIntersection; if (polygonIndices) { *polygonIndices->append() = 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_back(); if (polygonIndices) { polygonIndices->pop_back(); } } // check winding of offset polygon (it should be same as the original polygon) SkScalar offsetWinding = SkGetPolygonWinding(offsetPolygon->begin(), offsetPolygon->size()); return (winding*offsetWinding > 0 && SkIsSimplePolygon(offsetPolygon->begin(), offsetPolygon->size())); } ////////////////////////////////////////////////////////////////////////////////////////// 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) { skvx::float4 min, max; min = max = skvx::float4(p0.fX, p0.fY, p0.fX, p0.fY); skvx::float4 xy(p1.fX, p1.fY, p2.fX, p2.fY); min = skvx::min(min, xy); max = skvx::max(max, xy); bounds->setLTRB(std::min(min[0], min[2]), std::min(min[1], min[3]), std::max(max[0], max[2]), std::max(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 = std::max(std::min(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.resize(fHCount*fVCount); for (int i = 0; i < fGrid.size(); ++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::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> 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* 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* 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::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 AutoSTArray<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; triangulationVertices[currIndex] = 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 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->reserve(triangleIndices->size() + 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::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::Iter vertexIter = convexList.begin(); vertexIter != convexList.end(); ++vertexIter) { TriangulationVertex* vertex = *vertexIter; *triangleIndices->append() = indexMap[vertex->fIndex]; } return true; } #endif // !defined(SK_ENABLE_OPTIMIZE_SIZE)