| /* |
| * 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 "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 = 1; curr < polygonSize - 1; ++curr) { |
| int next = (curr + 1) % polygonSize; |
| SkVector v1 = polygonVerts[next] - polygonVerts[0]; |
| quadArea += v0.cross(v1); |
| v0 = v1; |
| } |
| if (SkScalarNearlyZero(quadArea, kCrossTolerance)) { |
| return 0; |
| } |
| // 1 == ccw, -1 == cw |
| return (quadArea > 0) ? 1 : -1; |
| } |
| |
| // Helper function to compute the individual vector for non-equal offsets |
| inline void compute_offset(SkScalar d, const SkPoint& polyPoint, int side, |
| const SkPoint& outerTangentIntersect, SkVector* v) { |
| SkScalar dsq = d * d; |
| SkVector dP = outerTangentIntersect - polyPoint; |
| SkScalar dPlenSq = SkPointPriv::LengthSqd(dP); |
| if (SkScalarNearlyZero(dPlenSq, SK_ScalarNearlyZero*SK_ScalarNearlyZero)) { |
| v->set(0, 0); |
| } else { |
| SkScalar discrim = SkScalarSqrt(dPlenSq - dsq); |
| v->fX = (dsq*dP.fX - side * d*dP.fY*discrim) / dPlenSq; |
| v->fY = (dsq*dP.fY + side * d*dP.fX*discrim) / dPlenSq; |
| } |
| } |
| |
| // Compute difference vector to offset p0-p1 'd0' and 'd1' units in direction specified by 'side' |
| bool compute_offset_vectors(const SkPoint& p0, const SkPoint& p1, SkScalar d0, SkScalar d1, |
| int side, SkPoint* vector0, SkPoint* vector1) { |
| SkASSERT(side == -1 || side == 1); |
| if (SkScalarNearlyEqual(d0, d1)) { |
| // if distances are equal, can just outset by the perpendicular |
| SkVector perp = SkVector::Make(p0.fY - p1.fY, p1.fX - p0.fX); |
| perp.setLength(d0*side); |
| *vector0 = perp; |
| *vector1 = perp; |
| } else { |
| SkScalar d0abs = SkTAbs(d0); |
| SkScalar d1abs = SkTAbs(d1); |
| // Otherwise we need to compute the outer tangent. |
| // See: http://www.ambrsoft.com/TrigoCalc/Circles2/Circles2Tangent_.htm |
| if (d0abs < d1abs) { |
| side = -side; |
| } |
| SkScalar dD = d0abs - d1abs; |
| // if one circle is inside another, we can't compute an offset |
| if (dD*dD >= SkPointPriv::DistanceToSqd(p0, p1)) { |
| return false; |
| } |
| SkPoint outerTangentIntersect = SkPoint::Make((p1.fX*d0abs - p0.fX*d1abs) / dD, |
| (p1.fY*d0abs - p0.fY*d1abs) / dD); |
| |
| compute_offset(d0, p0, side, outerTangentIntersect, vector0); |
| compute_offset(d1, p1, side, outerTangentIntersect, vector1); |
| } |
| |
| return true; |
| } |
| |
| // Offset line segment p0-p1 'd0' and 'd1' units in the direction specified by 'side' |
| bool SkOffsetSegment(const SkPoint& p0, const SkPoint& p1, SkScalar d0, SkScalar d1, |
| int side, SkPoint* offset0, SkPoint* offset1) { |
| SkVector v0, v1; |
| if (!compute_offset_vectors(p0, p1, d0, d1, side, &v0, &v1)) { |
| return false; |
| } |
| *offset0 = p0 + v0; |
| *offset1 = p1 + v1; |
| |
| 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 fInset; |
| SkPoint fIntersection; |
| SkScalar fTValue; |
| uint16_t fIndex; |
| uint16_t fEnd; |
| |
| void init(uint16_t start = 0, uint16_t end = 0) { |
| fIntersection = fInset.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->fInset.fP0 + this->fInset.fV; |
| if (SkPointPriv::EqualsWithinTolerance(p1, that->fInset.fP0)) { |
| *p = p1; |
| *s = SK_Scalar1; |
| *t = 0; |
| return true; |
| } |
| } |
| |
| return compute_intersection(this->fInset, that->fInset, 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->fInset |
| SkScalar computeCrossingDistance(const OffsetEdge* that) { |
| const OffsetSegment& s0 = this->fInset; |
| const OffsetSegment& s1 = that->fInset; |
| 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, |
| std::function<SkScalar(const SkPoint&)> insetDistanceFunc, |
| 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 >= (1 << 16)) { |
| return false; |
| } |
| |
| // 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; |
| } |
| SkPoint p0, p1; |
| if (!SkOffsetSegment(inputPolygonVerts[curr], inputPolygonVerts[next], |
| insetDistanceFunc(inputPolygonVerts[curr]), |
| insetDistanceFunc(inputPolygonVerts[next]), |
| winding, |
| &p0, &p1)) { |
| return false; |
| } |
| edgeData[curr].fPrev = &edgeData[prev]; |
| edgeData[curr].fNext = &edgeData[next]; |
| edgeData[curr].fInset.fP0 = p0; |
| edgeData[curr].fInset.fV = p1 - p0; |
| edgeData[curr].init(); |
| } |
| |
| OffsetEdge* head = &edgeData[0]; |
| OffsetEdge* currEdge = head; |
| OffsetEdge* prevEdge = currEdge->fPrev; |
| int insetVertexCount = inputPolygonSize; |
| int iterations = 0; |
| while (head && prevEdge != currEdge) { |
| ++iterations; |
| // we should check each edge against each other edge at most once |
| if (iterations > inputPolygonSize*inputPolygonSize) { |
| return false; |
| } |
| |
| SkScalar s, t; |
| SkPoint intersection; |
| if (compute_intersection(prevEdge->fInset, currEdge->fInset, |
| &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->fInset.fP0, |
| currEdge->fInset.fV, |
| prevEdge->fInset.fP0); |
| if (side < 0 && |
| side == winding*compute_side(currEdge->fInset.fP0, |
| currEdge->fInset.fV, |
| prevEdge->fInset.fP0 + prevEdge->fInset.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) { |
| static constexpr SkScalar kCleanupTolerance = 0.01f; |
| if (insetVertexCount >= 0) { |
| insetPolygon->setReserve(insetVertexCount); |
| } |
| int currIndex = 0; |
| OffsetEdge* currEdge = head; |
| *insetPolygon->push() = currEdge->fIntersection; |
| currEdge = currEdge->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 >= (1 << 16)-1) { |
| 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; |
| // 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 >= (1 << 16)) { |
| 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->fInset.fP0 = endpoint0; |
| currEdge->fInset.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, |
| std::function<SkScalar(const SkPoint&)> offsetDistanceFunc, |
| 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 >= (1 << 16)) { |
| return false; |
| } |
| |
| // get winding direction |
| int winding = SkGetPolygonWinding(inputPolygonVerts, inputPolygonSize); |
| if (0 == winding) { |
| return false; |
| } |
| |
| // build normals |
| SkAutoSTMalloc<64, SkVector> normal0(inputPolygonSize); |
| SkAutoSTMalloc<64, SkVector> normal1(inputPolygonSize); |
| SkAutoSTMalloc<64, SkScalar> offset(inputPolygonSize); |
| SkScalar currOffset = offsetDistanceFunc(inputPolygonVerts[0]); |
| if (!SkScalarIsFinite(currOffset)) { |
| return false; |
| } |
| offset[0] = currOffset; |
| 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; |
| SkScalar nextOffset = offsetDistanceFunc(inputPolygonVerts[nextIndex]); |
| if (!SkScalarIsFinite(nextOffset)) { |
| return false; |
| } |
| offset[nextIndex] = nextOffset; |
| if (!compute_offset_vectors(inputPolygonVerts[currIndex], inputPolygonVerts[nextIndex], |
| currOffset, nextOffset, winding, |
| &normal0[currIndex], &normal1[nextIndex])) { |
| return false; |
| } |
| if (currIndex > 0) { |
| // if reflex point, we need to add extra edges |
| if (is_reflex_vertex(inputPolygonVerts, winding, currOffset, |
| prevIndex, currIndex, nextIndex)) { |
| SkScalar rotSin, rotCos; |
| int numSteps; |
| if (!SkComputeRadialSteps(normal1[currIndex], normal0[currIndex], currOffset, |
| &rotSin, &rotCos, &numSteps)) { |
| return false; |
| } |
| numEdges += SkTMax(numSteps, 1); |
| } |
| } |
| numEdges++; |
| currOffset = nextOffset; |
| } |
| // finish up the edge counting |
| if (is_reflex_vertex(inputPolygonVerts, winding, currOffset, inputPolygonSize-1, 0, 1)) { |
| SkScalar rotSin, rotCos; |
| int numSteps; |
| if (!SkComputeRadialSteps(normal1[0], normal0[0], currOffset, |
| &rotSin, &rotCos, &numSteps)) { |
| return false; |
| } |
| numEdges += SkTMax(numSteps, 1); |
| } |
| |
| // 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[currIndex], |
| prevIndex, currIndex, nextIndex)) { |
| SkScalar rotSin, rotCos; |
| int numSteps; |
| SkVector prevNormal = normal1[currIndex]; |
| if (!SkComputeRadialSteps(prevNormal, normal0[currIndex], offset[currIndex], |
| &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] + normal0[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] + normal0[currIndex], |
| inputPolygonVerts[nextIndex] + normal1[nextIndex], |
| 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() == numEdges); |
| auto head = &edgeData[0]; |
| auto currEdge = head; |
| int offsetVertexCount = numEdges; |
| int iterations = 0; |
| while (head && prevEdge != currEdge) { |
| ++iterations; |
| // we should check each edge against each other edge at most once |
| if (iterations > numEdges*numEdges) { |
| 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->fInset.fP0 + prevPrevEdge->fInset.fV; |
| bool prevSameContour = SkPointPriv::EqualsWithinTolerance(p1, |
| prevEdge->fInset.fP0); |
| p1 = currEdge->fInset.fP0 + currEdge->fInset.fV; |
| bool currSameContour = SkPointPriv::EqualsWithinTolerance(p1, |
| currNextEdge->fInset.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) { |
| static constexpr SkScalar kCleanupTolerance = 0.01f; |
| if (offsetVertexCount >= 0) { |
| offsetPolygon->setReserve(offsetVertexCount); |
| } |
| int currIndex = 0; |
| OffsetEdge* currEdge = head; |
| *offsetPolygon->push() = currEdge->fIntersection; |
| if (polygonIndices) { |
| *polygonIndices->push() = currEdge->fIndex; |
| } |
| currEdge = currEdge->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; |
| }; |
| |
| // 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: |
| void add(TriangulationVertex* v) { |
| fReflexList.addToTail(v); |
| } |
| |
| void remove(TriangulationVertex* v) { |
| fReflexList.remove(v); |
| } |
| |
| bool checkTriangle(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, |
| uint16_t ignoreIndex0, uint16_t ignoreIndex1) { |
| for (SkTInternalLList<TriangulationVertex>::Iter reflexIter = fReflexList.begin(); |
| reflexIter != fReflexList.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: |
| // TODO: switch to an actual spatial hash |
| SkTInternalLList<TriangulationVertex> fReflexList; |
| }; |
| |
| // 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 >= (1 << 16)) { |
| 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; |
| } |
| |
| // 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; |
| SkAutoSTMalloc<64, TriangulationVertex> triangulationVertices(polygonSize); |
| int prevIndex = polygonSize - 1; |
| int currIndex = 0; |
| int nextIndex = 1; |
| SkVector v0 = polygonVerts[currIndex] - polygonVerts[prevIndex]; |
| SkVector v1 = polygonVerts[nextIndex] - polygonVerts[currIndex]; |
| for (int i = 0; i < polygonSize; ++i) { |
| SkDEBUGCODE(memset(&triangulationVertices[currIndex], 0, sizeof(TriangulationVertex))); |
| triangulationVertices[currIndex].fPosition = polygonVerts[currIndex]; |
| triangulationVertices[currIndex].fIndex = currIndex; |
| triangulationVertices[currIndex].fPrevIndex = prevIndex; |
| triangulationVertices[currIndex].fNextIndex = nextIndex; |
| if (winding*v0.cross(v1) > SK_ScalarNearlyZero*SK_ScalarNearlyZero) { |
| triangulationVertices[currIndex].fVertexType = TriangulationVertex::VertexType::kConvex; |
| convexList.addToTail(&triangulationVertices[currIndex]); |
| } else { |
| // We treat near collinear vertices as reflex |
| triangulationVertices[currIndex].fVertexType = TriangulationVertex::VertexType::kReflex; |
| reflexHash.add(&triangulationVertices[currIndex]); |
| } |
| |
| prevIndex = currIndex; |
| currIndex = nextIndex; |
| nextIndex = (currIndex + 1) % polygonSize; |
| v0 = v1; |
| v1 = polygonVerts[nextIndex] - polygonVerts[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; |
| } |
