/* * Copyright 2015 Google Inc. * * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ #include "GrAAConvexTessellator.h" #include "SkCanvas.h" #include "SkPath.h" #include "SkPoint.h" #include "SkString.h" #include "GrPathUtils.h" // Next steps: // add an interactive sample app slide // add debug check that all points are suitably far apart // test more degenerate cases // The tolerance for fusing vertices and eliminating colinear lines (It is in device space). static const SkScalar kClose = (SK_Scalar1 / 16); static const SkScalar kCloseSqd = kClose * kClose; // tesselation tolerance values, in device space pixels static const SkScalar kQuadTolerance = 0.2f; static const SkScalar kCubicTolerance = 0.2f; static const SkScalar kConicTolerance = 0.5f; // dot product below which we use a round cap between curve segments static const SkScalar kRoundCapThreshold = 0.8f; // dot product above which we consider two adjacent curves to be part of the "same" curve static const SkScalar kCurveConnectionThreshold = 0.8f; static bool intersect(const SkPoint& p0, const SkPoint& n0, const SkPoint& p1, const SkPoint& n1, SkScalar* t) { const SkPoint v = p1 - p0; SkScalar perpDot = n0.fX * n1.fY - n0.fY * n1.fX; if (SkScalarNearlyZero(perpDot)) { return false; } *t = (v.fX * n1.fY - v.fY * n1.fX) / perpDot; SkASSERT(SkScalarIsFinite(*t)); return true; } // This is a special case version of intersect where we have the vector // perpendicular to the second line rather than the vector parallel to it. static SkScalar perp_intersect(const SkPoint& p0, const SkPoint& n0, const SkPoint& p1, const SkPoint& perp) { const SkPoint v = p1 - p0; SkScalar perpDot = n0.dot(perp); return v.dot(perp) / perpDot; } static bool duplicate_pt(const SkPoint& p0, const SkPoint& p1) { SkScalar distSq = SkPointPriv::DistanceToSqd(p0, p1); return distSq < kCloseSqd; } static SkScalar abs_dist_from_line(const SkPoint& p0, const SkVector& v, const SkPoint& test) { SkPoint testV = test - p0; SkScalar dist = testV.fX * v.fY - testV.fY * v.fX; return SkScalarAbs(dist); } int GrAAConvexTessellator::addPt(const SkPoint& pt, SkScalar depth, SkScalar coverage, bool movable, CurveState curve) { this->validate(); int index = fPts.count(); *fPts.push() = pt; *fCoverages.push() = coverage; *fMovable.push() = movable; *fCurveState.push() = curve; this->validate(); return index; } void GrAAConvexTessellator::popLastPt() { this->validate(); fPts.pop(); fCoverages.pop(); fMovable.pop(); fCurveState.pop(); this->validate(); } void GrAAConvexTessellator::popFirstPtShuffle() { this->validate(); fPts.removeShuffle(0); fCoverages.removeShuffle(0); fMovable.removeShuffle(0); fCurveState.removeShuffle(0); this->validate(); } void GrAAConvexTessellator::updatePt(int index, const SkPoint& pt, SkScalar depth, SkScalar coverage) { this->validate(); SkASSERT(fMovable[index]); fPts[index] = pt; fCoverages[index] = coverage; } void GrAAConvexTessellator::addTri(int i0, int i1, int i2) { if (i0 == i1 || i1 == i2 || i2 == i0) { return; } *fIndices.push() = i0; *fIndices.push() = i1; *fIndices.push() = i2; } void GrAAConvexTessellator::rewind() { fPts.rewind(); fCoverages.rewind(); fMovable.rewind(); fIndices.rewind(); fNorms.rewind(); fCurveState.rewind(); fInitialRing.rewind(); fCandidateVerts.rewind(); #if GR_AA_CONVEX_TESSELLATOR_VIZ fRings.rewind(); // TODO: leak in this case! #else fRings[0].rewind(); fRings[1].rewind(); #endif } void GrAAConvexTessellator::computeBisectors() { fBisectors.setCount(fNorms.count()); int prev = fBisectors.count() - 1; for (int cur = 0; cur < fBisectors.count(); prev = cur, ++cur) { fBisectors[cur] = fNorms[cur] + fNorms[prev]; if (!fBisectors[cur].normalize()) { SkASSERT(SkPointPriv::kLeft_Side == fSide || SkPointPriv::kRight_Side == fSide); SkPointPriv::SetOrthog(&fBisectors[cur], fNorms[cur], (SkPointPriv::Side)-fSide); SkVector other; SkPointPriv::SetOrthog(&other, fNorms[prev], fSide); fBisectors[cur] += other; SkAssertResult(fBisectors[cur].normalize()); } else { fBisectors[cur].negate(); // make the bisector face in } if (fCurveState[prev] == kIndeterminate_CurveState) { if (fCurveState[cur] == kSharp_CurveState) { fCurveState[prev] = kSharp_CurveState; } else { if (SkScalarAbs(fNorms[cur].dot(fNorms[prev])) > kCurveConnectionThreshold) { fCurveState[prev] = kCurve_CurveState; fCurveState[cur] = kCurve_CurveState; } else { fCurveState[prev] = kSharp_CurveState; fCurveState[cur] = kSharp_CurveState; } } } SkASSERT(SkScalarNearlyEqual(1.0f, fBisectors[cur].length())); } } // Create as many rings as we need to (up to a predefined limit) to reach the specified target // depth. If we are in fill mode, the final ring will automatically be fanned. bool GrAAConvexTessellator::createInsetRings(Ring& previousRing, SkScalar initialDepth, SkScalar initialCoverage, SkScalar targetDepth, SkScalar targetCoverage, Ring** finalRing) { static const int kMaxNumRings = 8; if (previousRing.numPts() < 3) { return false; } Ring* currentRing = &previousRing; int i; for (i = 0; i < kMaxNumRings; ++i) { Ring* nextRing = this->getNextRing(currentRing); SkASSERT(nextRing != currentRing); bool done = this->createInsetRing(*currentRing, nextRing, initialDepth, initialCoverage, targetDepth, targetCoverage, i == 0); currentRing = nextRing; if (done) { break; } currentRing->init(*this); } if (kMaxNumRings == i) { // Bail if we've exceeded the amount of time we want to throw at this. this->terminate(*currentRing); return false; } bool done = currentRing->numPts() >= 3; if (done) { currentRing->init(*this); } *finalRing = currentRing; return done; } // The general idea here is to, conceptually, start with the original polygon and slide // the vertices along the bisectors until the first intersection. At that // point two of the edges collapse and the process repeats on the new polygon. // The polygon state is captured in the Ring class while the GrAAConvexTessellator // controls the iteration. The CandidateVerts holds the formative points for the // next ring. bool GrAAConvexTessellator::tessellate(const SkMatrix& m, const SkPath& path) { if (!this->extractFromPath(m, path)) { return false; } SkScalar coverage = 1.0f; SkScalar scaleFactor = 0.0f; if (SkStrokeRec::kStrokeAndFill_Style == fStyle) { SkASSERT(m.isSimilarity()); scaleFactor = m.getMaxScale(); // x and y scale are the same SkScalar effectiveStrokeWidth = scaleFactor * fStrokeWidth; Ring outerStrokeAndAARing; this->createOuterRing(fInitialRing, effectiveStrokeWidth / 2 + kAntialiasingRadius, 0.0, &outerStrokeAndAARing); // discard all the triangles added between the originating ring and the new outer ring fIndices.rewind(); outerStrokeAndAARing.init(*this); outerStrokeAndAARing.makeOriginalRing(); // Add the outer stroke ring's normals to the originating ring's normals // so it can also act as an originating ring fNorms.setCount(fNorms.count() + outerStrokeAndAARing.numPts()); for (int i = 0; i < outerStrokeAndAARing.numPts(); ++i) { SkASSERT(outerStrokeAndAARing.index(i) < fNorms.count()); fNorms[outerStrokeAndAARing.index(i)] = outerStrokeAndAARing.norm(i); } // the bisectors are only needed for the computation of the outer ring fBisectors.rewind(); Ring* insetAARing; this->createInsetRings(outerStrokeAndAARing, 0.0f, 0.0f, 2*kAntialiasingRadius, 1.0f, &insetAARing); SkDEBUGCODE(this->validate();) return true; } if (SkStrokeRec::kStroke_Style == fStyle) { SkASSERT(fStrokeWidth >= 0.0f); SkASSERT(m.isSimilarity()); scaleFactor = m.getMaxScale(); // x and y scale are the same SkScalar effectiveStrokeWidth = scaleFactor * fStrokeWidth; Ring outerStrokeRing; this->createOuterRing(fInitialRing, effectiveStrokeWidth / 2 - kAntialiasingRadius, coverage, &outerStrokeRing); outerStrokeRing.init(*this); Ring outerAARing; this->createOuterRing(outerStrokeRing, kAntialiasingRadius * 2, 0.0f, &outerAARing); } else { Ring outerAARing; this->createOuterRing(fInitialRing, kAntialiasingRadius, 0.0f, &outerAARing); } // the bisectors are only needed for the computation of the outer ring fBisectors.rewind(); if (SkStrokeRec::kStroke_Style == fStyle && fInitialRing.numPts() > 2) { SkASSERT(fStrokeWidth >= 0.0f); SkScalar effectiveStrokeWidth = scaleFactor * fStrokeWidth; Ring* insetStrokeRing; SkScalar strokeDepth = effectiveStrokeWidth / 2 - kAntialiasingRadius; if (this->createInsetRings(fInitialRing, 0.0f, coverage, strokeDepth, coverage, &insetStrokeRing)) { Ring* insetAARing; this->createInsetRings(*insetStrokeRing, strokeDepth, coverage, strokeDepth + kAntialiasingRadius * 2, 0.0f, &insetAARing); } } else { Ring* insetAARing; this->createInsetRings(fInitialRing, 0.0f, 0.5f, kAntialiasingRadius, 1.0f, &insetAARing); } SkDEBUGCODE(this->validate();) return true; } SkScalar GrAAConvexTessellator::computeDepthFromEdge(int edgeIdx, const SkPoint& p) const { SkASSERT(edgeIdx < fNorms.count()); SkPoint v = p - fPts[edgeIdx]; SkScalar depth = -fNorms[edgeIdx].dot(v); return depth; } // Find a point that is 'desiredDepth' away from the 'edgeIdx'-th edge and lies // along the 'bisector' from the 'startIdx'-th point. bool GrAAConvexTessellator::computePtAlongBisector(int startIdx, const SkVector& bisector, int edgeIdx, SkScalar desiredDepth, SkPoint* result) const { const SkPoint& norm = fNorms[edgeIdx]; // First find the point where the edge and the bisector intersect SkPoint newP; SkScalar t = perp_intersect(fPts[startIdx], bisector, fPts[edgeIdx], norm); if (SkScalarNearlyEqual(t, 0.0f)) { // the start point was one of the original ring points SkASSERT(startIdx < fPts.count()); newP = fPts[startIdx]; } else if (t < 0.0f) { newP = bisector; newP.scale(t); newP += fPts[startIdx]; } else { return false; } // Then offset along the bisector from that point the correct distance SkScalar dot = bisector.dot(norm); t = -desiredDepth / dot; *result = bisector; result->scale(t); *result += newP; return true; } bool GrAAConvexTessellator::extractFromPath(const SkMatrix& m, const SkPath& path) { SkASSERT(SkPath::kConvex_Convexity == path.getConvexity()); // Outer ring: 3*numPts // Middle ring: numPts // Presumptive inner ring: numPts this->reservePts(5*path.countPoints()); // Outer ring: 12*numPts // Middle ring: 0 // Presumptive inner ring: 6*numPts + 6 fIndices.setReserve(18*path.countPoints() + 6); fNorms.setReserve(path.countPoints()); // TODO: is there a faster way to extract the points from the path? Perhaps // get all the points via a new entry point, transform them all in bulk // and then walk them to find duplicates? SkPath::Iter iter(path, true); SkPoint pts[4]; SkPath::Verb verb; while ((verb = iter.next(pts, true, true)) != SkPath::kDone_Verb) { switch (verb) { case SkPath::kLine_Verb: this->lineTo(m, pts[1], kSharp_CurveState); break; case SkPath::kQuad_Verb: this->quadTo(m, pts); break; case SkPath::kCubic_Verb: this->cubicTo(m, pts); break; case SkPath::kConic_Verb: this->conicTo(m, pts, iter.conicWeight()); break; case SkPath::kMove_Verb: case SkPath::kClose_Verb: case SkPath::kDone_Verb: break; } } if (this->numPts() < 2) { return false; } // check if last point is a duplicate of the first point. If so, remove it. if (duplicate_pt(fPts[this->numPts()-1], fPts[0])) { this->popLastPt(); fNorms.pop(); } SkASSERT(fPts.count() == fNorms.count()+1); if (this->numPts() >= 3) { if (abs_dist_from_line(fPts.top(), fNorms.top(), fPts[0]) < kClose) { // The last point is on the line from the second to last to the first point. this->popLastPt(); fNorms.pop(); } *fNorms.push() = fPts[0] - fPts.top(); SkDEBUGCODE(SkScalar len =) SkPoint::Normalize(&fNorms.top()); SkASSERT(len > 0.0f); SkASSERT(fPts.count() == fNorms.count()); } if (this->numPts() >= 3 && abs_dist_from_line(fPts[0], fNorms.top(), fPts[1]) < kClose) { // The first point is on the line from the last to the second. this->popFirstPtShuffle(); fNorms.removeShuffle(0); fNorms[0] = fPts[1] - fPts[0]; SkDEBUGCODE(SkScalar len =) SkPoint::Normalize(&fNorms[0]); SkASSERT(len > 0.0f); SkASSERT(SkScalarNearlyEqual(1.0f, fNorms[0].length())); } if (this->numPts() >= 3) { // Check the cross product of the final trio SkScalar cross = SkPoint::CrossProduct(fNorms[0], fNorms.top()); if (cross > 0.0f) { fSide = SkPointPriv::kRight_Side; } else { fSide = SkPointPriv::kLeft_Side; } // Make all the normals face outwards rather than along the edge for (int cur = 0; cur < fNorms.count(); ++cur) { SkPointPriv::SetOrthog(&fNorms[cur], fNorms[cur], fSide); SkASSERT(SkScalarNearlyEqual(1.0f, fNorms[cur].length())); } this->computeBisectors(); } else if (this->numPts() == 2) { // We've got two points, so we're degenerate. if (fStyle == SkStrokeRec::kFill_Style) { // it's a fill, so we don't need to worry about degenerate paths return false; } // For stroking, we still need to process the degenerate path, so fix it up fSide = SkPointPriv::kLeft_Side; // Make all the normals face outwards rather than along the edge for (int cur = 0; cur < fNorms.count(); ++cur) { SkPointPriv::SetOrthog(&fNorms[cur], fNorms[cur], fSide); SkASSERT(SkScalarNearlyEqual(1.0f, fNorms[cur].length())); } fNorms.push(SkPoint::Make(-fNorms[0].fX, -fNorms[0].fY)); // we won't actually use the bisectors, so just push zeroes fBisectors.push(SkPoint::Make(0.0, 0.0)); fBisectors.push(SkPoint::Make(0.0, 0.0)); } else { return false; } fCandidateVerts.setReserve(this->numPts()); fInitialRing.setReserve(this->numPts()); for (int i = 0; i < this->numPts(); ++i) { fInitialRing.addIdx(i, i); } fInitialRing.init(fNorms, fBisectors); this->validate(); return true; } GrAAConvexTessellator::Ring* GrAAConvexTessellator::getNextRing(Ring* lastRing) { #if GR_AA_CONVEX_TESSELLATOR_VIZ Ring* ring = *fRings.push() = new Ring; ring->setReserve(fInitialRing.numPts()); ring->rewind(); return ring; #else // Flip flop back and forth between fRings[0] & fRings[1] int nextRing = (lastRing == &fRings[0]) ? 1 : 0; fRings[nextRing].setReserve(fInitialRing.numPts()); fRings[nextRing].rewind(); return &fRings[nextRing]; #endif } void GrAAConvexTessellator::fanRing(const Ring& ring) { // fan out from point 0 int startIdx = ring.index(0); for (int cur = ring.numPts() - 2; cur >= 0; --cur) { this->addTri(startIdx, ring.index(cur), ring.index(cur + 1)); } } void GrAAConvexTessellator::createOuterRing(const Ring& previousRing, SkScalar outset, SkScalar coverage, Ring* nextRing) { const int numPts = previousRing.numPts(); if (numPts == 0) { return; } int prev = numPts - 1; int lastPerpIdx = -1, firstPerpIdx = -1; const SkScalar outsetSq = outset * outset; SkScalar miterLimitSq = outset * fMiterLimit; miterLimitSq = miterLimitSq * miterLimitSq; for (int cur = 0; cur < numPts; ++cur) { int originalIdx = previousRing.index(cur); // For each vertex of the original polygon we add at least two points to the // outset polygon - one extending perpendicular to each impinging edge. Connecting these // two points yields a bevel join. We need one additional point for a mitered join, and // a round join requires one or more points depending upon curvature. // The perpendicular point for the last edge SkPoint normal1 = previousRing.norm(prev); SkPoint perp1 = normal1; perp1.scale(outset); perp1 += this->point(originalIdx); // The perpendicular point for the next edge. SkPoint normal2 = previousRing.norm(cur); SkPoint perp2 = normal2; perp2.scale(outset); perp2 += fPts[originalIdx]; CurveState curve = fCurveState[originalIdx]; // We know it isn't a duplicate of the prior point (since it and this // one are just perpendicular offsets from the non-merged polygon points) int perp1Idx = this->addPt(perp1, -outset, coverage, false, curve); nextRing->addIdx(perp1Idx, originalIdx); int perp2Idx; // For very shallow angles all the corner points could fuse. if (duplicate_pt(perp2, this->point(perp1Idx))) { perp2Idx = perp1Idx; } else { perp2Idx = this->addPt(perp2, -outset, coverage, false, curve); } if (perp2Idx != perp1Idx) { if (curve == kCurve_CurveState) { // bevel or round depending upon curvature SkScalar dotProd = normal1.dot(normal2); if (dotProd < kRoundCapThreshold) { // Currently we "round" by creating a single extra point, which produces // good results for common cases. For thick strokes with high curvature, we will // need to add more points; for the time being we simply fall back to software // rendering for thick strokes. SkPoint miter = previousRing.bisector(cur); miter.setLength(-outset); miter += fPts[originalIdx]; // For very shallow angles all the corner points could fuse if (!duplicate_pt(miter, this->point(perp1Idx))) { int miterIdx; miterIdx = this->addPt(miter, -outset, coverage, false, kSharp_CurveState); nextRing->addIdx(miterIdx, originalIdx); // The two triangles for the corner this->addTri(originalIdx, perp1Idx, miterIdx); this->addTri(originalIdx, miterIdx, perp2Idx); } } else { this->addTri(originalIdx, perp1Idx, perp2Idx); } } else { switch (fJoin) { case SkPaint::Join::kMiter_Join: { // The bisector outset point SkPoint miter = previousRing.bisector(cur); SkScalar dotProd = normal1.dot(normal2); SkScalar sinHalfAngleSq = SkScalarHalf(SK_Scalar1 + dotProd); SkScalar lengthSq = sk_ieee_float_divide(outsetSq, sinHalfAngleSq); if (lengthSq > miterLimitSq) { // just bevel it this->addTri(originalIdx, perp1Idx, perp2Idx); break; } miter.setLength(-SkScalarSqrt(lengthSq)); miter += fPts[originalIdx]; // For very shallow angles all the corner points could fuse if (!duplicate_pt(miter, this->point(perp1Idx))) { int miterIdx; miterIdx = this->addPt(miter, -outset, coverage, false, kSharp_CurveState); nextRing->addIdx(miterIdx, originalIdx); // The two triangles for the corner this->addTri(originalIdx, perp1Idx, miterIdx); this->addTri(originalIdx, miterIdx, perp2Idx); } break; } case SkPaint::Join::kBevel_Join: this->addTri(originalIdx, perp1Idx, perp2Idx); break; default: // kRound_Join is unsupported for now. GrAALinearizingConvexPathRenderer is // only willing to draw mitered or beveled, so we should never get here. SkASSERT(false); } } nextRing->addIdx(perp2Idx, originalIdx); } if (0 == cur) { // Store the index of the first perpendicular point to finish up firstPerpIdx = perp1Idx; SkASSERT(-1 == lastPerpIdx); } else { // The triangles for the previous edge int prevIdx = previousRing.index(prev); this->addTri(prevIdx, perp1Idx, originalIdx); this->addTri(prevIdx, lastPerpIdx, perp1Idx); } // Track the last perpendicular outset point so we can construct the // trailing edge triangles. lastPerpIdx = perp2Idx; prev = cur; } // pick up the final edge rect int lastIdx = previousRing.index(numPts - 1); this->addTri(lastIdx, firstPerpIdx, previousRing.index(0)); this->addTri(lastIdx, lastPerpIdx, firstPerpIdx); this->validate(); } // Something went wrong in the creation of the next ring. If we're filling the shape, just go ahead // and fan it. void GrAAConvexTessellator::terminate(const Ring& ring) { if (fStyle != SkStrokeRec::kStroke_Style) { this->fanRing(ring); } } static SkScalar compute_coverage(SkScalar depth, SkScalar initialDepth, SkScalar initialCoverage, SkScalar targetDepth, SkScalar targetCoverage) { if (SkScalarNearlyEqual(initialDepth, targetDepth)) { return targetCoverage; } SkScalar result = (depth - initialDepth) / (targetDepth - initialDepth) * (targetCoverage - initialCoverage) + initialCoverage; return SkScalarClampMax(result, 1.0f); } // return true when processing is complete bool GrAAConvexTessellator::createInsetRing(const Ring& lastRing, Ring* nextRing, SkScalar initialDepth, SkScalar initialCoverage, SkScalar targetDepth, SkScalar targetCoverage, bool forceNew) { bool done = false; fCandidateVerts.rewind(); // Loop through all the points in the ring and find the intersection with the smallest depth SkScalar minDist = SK_ScalarMax, minT = 0.0f; int minEdgeIdx = -1; for (int cur = 0; cur < lastRing.numPts(); ++cur) { int next = (cur + 1) % lastRing.numPts(); SkScalar t; bool result = intersect(this->point(lastRing.index(cur)), lastRing.bisector(cur), this->point(lastRing.index(next)), lastRing.bisector(next), &t); if (!result) { continue; } SkScalar dist = -t * lastRing.norm(cur).dot(lastRing.bisector(cur)); if (minDist > dist) { minDist = dist; minT = t; minEdgeIdx = cur; } } if (minEdgeIdx == -1) { return false; } SkPoint newPt = lastRing.bisector(minEdgeIdx); newPt.scale(minT); newPt += this->point(lastRing.index(minEdgeIdx)); SkScalar depth = this->computeDepthFromEdge(lastRing.origEdgeID(minEdgeIdx), newPt); if (depth >= targetDepth) { // None of the bisectors intersect before reaching the desired depth. // Just step them all to the desired depth depth = targetDepth; done = true; } // 'dst' stores where each point in the last ring maps to/transforms into // in the next ring. SkTDArray dst; dst.setCount(lastRing.numPts()); // Create the first point (who compares with no one) if (!this->computePtAlongBisector(lastRing.index(0), lastRing.bisector(0), lastRing.origEdgeID(0), depth, &newPt)) { this->terminate(lastRing); return true; } dst[0] = fCandidateVerts.addNewPt(newPt, lastRing.index(0), lastRing.origEdgeID(0), !this->movable(lastRing.index(0))); // Handle the middle points (who only compare with the prior point) for (int cur = 1; cur < lastRing.numPts()-1; ++cur) { if (!this->computePtAlongBisector(lastRing.index(cur), lastRing.bisector(cur), lastRing.origEdgeID(cur), depth, &newPt)) { this->terminate(lastRing); return true; } if (!duplicate_pt(newPt, fCandidateVerts.lastPoint())) { dst[cur] = fCandidateVerts.addNewPt(newPt, lastRing.index(cur), lastRing.origEdgeID(cur), !this->movable(lastRing.index(cur))); } else { dst[cur] = fCandidateVerts.fuseWithPrior(lastRing.origEdgeID(cur)); } } // Check on the last point (handling the wrap around) int cur = lastRing.numPts()-1; if (!this->computePtAlongBisector(lastRing.index(cur), lastRing.bisector(cur), lastRing.origEdgeID(cur), depth, &newPt)) { this->terminate(lastRing); return true; } bool dupPrev = duplicate_pt(newPt, fCandidateVerts.lastPoint()); bool dupNext = duplicate_pt(newPt, fCandidateVerts.firstPoint()); if (!dupPrev && !dupNext) { dst[cur] = fCandidateVerts.addNewPt(newPt, lastRing.index(cur), lastRing.origEdgeID(cur), !this->movable(lastRing.index(cur))); } else if (dupPrev && !dupNext) { dst[cur] = fCandidateVerts.fuseWithPrior(lastRing.origEdgeID(cur)); } else if (!dupPrev && dupNext) { dst[cur] = fCandidateVerts.fuseWithNext(); } else { bool dupPrevVsNext = duplicate_pt(fCandidateVerts.firstPoint(), fCandidateVerts.lastPoint()); if (!dupPrevVsNext) { dst[cur] = fCandidateVerts.fuseWithPrior(lastRing.origEdgeID(cur)); } else { const int fused = fCandidateVerts.fuseWithBoth(); dst[cur] = fused; const int targetIdx = dst[cur - 1]; for (int i = cur - 1; i >= 0 && dst[i] == targetIdx; i--) { dst[i] = fused; } } } // Fold the new ring's points into the global pool for (int i = 0; i < fCandidateVerts.numPts(); ++i) { int newIdx; if (fCandidateVerts.needsToBeNew(i) || forceNew) { // if the originating index is still valid then this point wasn't // fused (and is thus movable) SkScalar coverage = compute_coverage(depth, initialDepth, initialCoverage, targetDepth, targetCoverage); newIdx = this->addPt(fCandidateVerts.point(i), depth, coverage, fCandidateVerts.originatingIdx(i) != -1, kSharp_CurveState); } else { SkASSERT(fCandidateVerts.originatingIdx(i) != -1); this->updatePt(fCandidateVerts.originatingIdx(i), fCandidateVerts.point(i), depth, targetCoverage); newIdx = fCandidateVerts.originatingIdx(i); } nextRing->addIdx(newIdx, fCandidateVerts.origEdge(i)); } // 'dst' currently has indices into the ring. Remap these to be indices // into the global pool since the triangulation operates in that space. for (int i = 0; i < dst.count(); ++i) { dst[i] = nextRing->index(dst[i]); } for (int i = 0; i < lastRing.numPts(); ++i) { int next = (i + 1) % lastRing.numPts(); this->addTri(lastRing.index(i), lastRing.index(next), dst[next]); this->addTri(lastRing.index(i), dst[next], dst[i]); } if (done && fStyle != SkStrokeRec::kStroke_Style) { // fill or stroke-and-fill this->fanRing(*nextRing); } if (nextRing->numPts() < 3) { done = true; } return done; } void GrAAConvexTessellator::validate() const { SkASSERT(fPts.count() == fMovable.count()); SkASSERT(fPts.count() == fCoverages.count()); SkASSERT(fPts.count() == fCurveState.count()); SkASSERT(0 == (fIndices.count() % 3)); SkASSERT(!fBisectors.count() || fBisectors.count() == fNorms.count()); } ////////////////////////////////////////////////////////////////////////////// void GrAAConvexTessellator::Ring::init(const GrAAConvexTessellator& tess) { this->computeNormals(tess); this->computeBisectors(tess); } void GrAAConvexTessellator::Ring::init(const SkTDArray& norms, const SkTDArray& bisectors) { for (int i = 0; i < fPts.count(); ++i) { fPts[i].fNorm = norms[i]; fPts[i].fBisector = bisectors[i]; } } // Compute the outward facing normal at each vertex. void GrAAConvexTessellator::Ring::computeNormals(const GrAAConvexTessellator& tess) { for (int cur = 0; cur < fPts.count(); ++cur) { int next = (cur + 1) % fPts.count(); fPts[cur].fNorm = tess.point(fPts[next].fIndex) - tess.point(fPts[cur].fIndex); SkPoint::Normalize(&fPts[cur].fNorm); SkPointPriv::SetOrthog(&fPts[cur].fNorm, fPts[cur].fNorm, tess.side()); } } void GrAAConvexTessellator::Ring::computeBisectors(const GrAAConvexTessellator& tess) { int prev = fPts.count() - 1; for (int cur = 0; cur < fPts.count(); prev = cur, ++cur) { fPts[cur].fBisector = fPts[cur].fNorm + fPts[prev].fNorm; if (!fPts[cur].fBisector.normalize()) { SkASSERT(SkPointPriv::kLeft_Side == tess.side() || SkPointPriv::kRight_Side == tess.side()); SkPointPriv::SetOrthog(&fPts[cur].fBisector, fPts[cur].fNorm, (SkPointPriv::Side)-tess.side()); SkVector other; SkPointPriv::SetOrthog(&other, fPts[prev].fNorm, tess.side()); fPts[cur].fBisector += other; SkAssertResult(fPts[cur].fBisector.normalize()); } else { fPts[cur].fBisector.negate(); // make the bisector face in } } } ////////////////////////////////////////////////////////////////////////////// #ifdef SK_DEBUG // Is this ring convex? bool GrAAConvexTessellator::Ring::isConvex(const GrAAConvexTessellator& tess) const { if (fPts.count() < 3) { return true; } SkPoint prev = tess.point(fPts[0].fIndex) - tess.point(fPts.top().fIndex); SkPoint cur = tess.point(fPts[1].fIndex) - tess.point(fPts[0].fIndex); SkScalar minDot = prev.fX * cur.fY - prev.fY * cur.fX; SkScalar maxDot = minDot; prev = cur; for (int i = 1; i < fPts.count(); ++i) { int next = (i + 1) % fPts.count(); cur = tess.point(fPts[next].fIndex) - tess.point(fPts[i].fIndex); SkScalar dot = prev.fX * cur.fY - prev.fY * cur.fX; minDot = SkMinScalar(minDot, dot); maxDot = SkMaxScalar(maxDot, dot); prev = cur; } if (SkScalarNearlyEqual(maxDot, 0.0f, 0.005f)) { maxDot = 0; } if (SkScalarNearlyEqual(minDot, 0.0f, 0.005f)) { minDot = 0; } return (maxDot >= 0.0f) == (minDot >= 0.0f); } #endif void GrAAConvexTessellator::lineTo(const SkPoint& p, CurveState curve) { if (this->numPts() > 0 && duplicate_pt(p, this->lastPoint())) { return; } SkASSERT(fPts.count() <= 1 || fPts.count() == fNorms.count()+1); if (this->numPts() >= 2 && abs_dist_from_line(fPts.top(), fNorms.top(), p) < kClose) { // The old last point is on the line from the second to last to the new point this->popLastPt(); fNorms.pop(); // double-check that the new last point is not a duplicate of the new point. In an ideal // world this wouldn't be necessary (since it's only possible for non-convex paths), but // floating point precision issues mean it can actually happen on paths that were // determined to be convex. if (duplicate_pt(p, this->lastPoint())) { return; } } SkScalar initialRingCoverage = (SkStrokeRec::kFill_Style == fStyle) ? 0.5f : 1.0f; this->addPt(p, 0.0f, initialRingCoverage, false, curve); if (this->numPts() > 1) { *fNorms.push() = fPts.top() - fPts[fPts.count()-2]; SkDEBUGCODE(SkScalar len =) SkPoint::Normalize(&fNorms.top()); SkASSERT(len > 0.0f); SkASSERT(SkScalarNearlyEqual(1.0f, fNorms.top().length())); } } void GrAAConvexTessellator::lineTo(const SkMatrix& m, SkPoint p, CurveState curve) { m.mapPoints(&p, 1); this->lineTo(p, curve); } void GrAAConvexTessellator::quadTo(const SkPoint pts[3]) { int maxCount = GrPathUtils::quadraticPointCount(pts, kQuadTolerance); fPointBuffer.setReserve(maxCount); SkPoint* target = fPointBuffer.begin(); int count = GrPathUtils::generateQuadraticPoints(pts[0], pts[1], pts[2], kQuadTolerance, &target, maxCount); fPointBuffer.setCount(count); for (int i = 0; i < count - 1; i++) { this->lineTo(fPointBuffer[i], kCurve_CurveState); } this->lineTo(fPointBuffer[count - 1], kIndeterminate_CurveState); } void GrAAConvexTessellator::quadTo(const SkMatrix& m, SkPoint pts[3]) { m.mapPoints(pts, 3); this->quadTo(pts); } void GrAAConvexTessellator::cubicTo(const SkMatrix& m, SkPoint pts[4]) { m.mapPoints(pts, 4); int maxCount = GrPathUtils::cubicPointCount(pts, kCubicTolerance); fPointBuffer.setReserve(maxCount); SkPoint* target = fPointBuffer.begin(); int count = GrPathUtils::generateCubicPoints(pts[0], pts[1], pts[2], pts[3], kCubicTolerance, &target, maxCount); fPointBuffer.setCount(count); for (int i = 0; i < count - 1; i++) { this->lineTo(fPointBuffer[i], kCurve_CurveState); } this->lineTo(fPointBuffer[count - 1], kIndeterminate_CurveState); } // include down here to avoid compilation errors caused by "-" overload in SkGeometry.h #include "SkGeometry.h" void GrAAConvexTessellator::conicTo(const SkMatrix& m, SkPoint pts[3], SkScalar w) { m.mapPoints(pts, 3); SkAutoConicToQuads quadder; const SkPoint* quads = quadder.computeQuads(pts, w, kConicTolerance); SkPoint lastPoint = *(quads++); int count = quadder.countQuads(); for (int i = 0; i < count; ++i) { SkPoint quadPts[3]; quadPts[0] = lastPoint; quadPts[1] = quads[0]; quadPts[2] = i == count - 1 ? pts[2] : quads[1]; this->quadTo(quadPts); lastPoint = quadPts[2]; quads += 2; } } ////////////////////////////////////////////////////////////////////////////// #if GR_AA_CONVEX_TESSELLATOR_VIZ static const SkScalar kPointRadius = 0.02f; static const SkScalar kArrowStrokeWidth = 0.0f; static const SkScalar kArrowLength = 0.2f; static const SkScalar kEdgeTextSize = 0.1f; static const SkScalar kPointTextSize = 0.02f; static void draw_point(SkCanvas* canvas, const SkPoint& p, SkScalar paramValue, bool stroke) { SkPaint paint; SkASSERT(paramValue <= 1.0f); int gs = int(255*paramValue); paint.setARGB(255, gs, gs, gs); canvas->drawCircle(p.fX, p.fY, kPointRadius, paint); if (stroke) { SkPaint stroke; stroke.setColor(SK_ColorYELLOW); stroke.setStyle(SkPaint::kStroke_Style); stroke.setStrokeWidth(kPointRadius/3.0f); canvas->drawCircle(p.fX, p.fY, kPointRadius, stroke); } } static void draw_line(SkCanvas* canvas, const SkPoint& p0, const SkPoint& p1, SkColor color) { SkPaint p; p.setColor(color); canvas->drawLine(p0.fX, p0.fY, p1.fX, p1.fY, p); } static void draw_arrow(SkCanvas*canvas, const SkPoint& p, const SkPoint &n, SkScalar len, SkColor color) { SkPaint paint; paint.setColor(color); paint.setStrokeWidth(kArrowStrokeWidth); paint.setStyle(SkPaint::kStroke_Style); canvas->drawLine(p.fX, p.fY, p.fX + len * n.fX, p.fY + len * n.fY, paint); } void GrAAConvexTessellator::Ring::draw(SkCanvas* canvas, const GrAAConvexTessellator& tess) const { SkPaint paint; paint.setTextSize(kEdgeTextSize); for (int cur = 0; cur < fPts.count(); ++cur) { int next = (cur + 1) % fPts.count(); draw_line(canvas, tess.point(fPts[cur].fIndex), tess.point(fPts[next].fIndex), SK_ColorGREEN); SkPoint mid = tess.point(fPts[cur].fIndex) + tess.point(fPts[next].fIndex); mid.scale(0.5f); if (fPts.count()) { draw_arrow(canvas, mid, fPts[cur].fNorm, kArrowLength, SK_ColorRED); mid.fX += (kArrowLength/2) * fPts[cur].fNorm.fX; mid.fY += (kArrowLength/2) * fPts[cur].fNorm.fY; } SkString num; num.printf("%d", this->origEdgeID(cur)); canvas->drawString(num, mid.fX, mid.fY, paint); if (fPts.count()) { draw_arrow(canvas, tess.point(fPts[cur].fIndex), fPts[cur].fBisector, kArrowLength, SK_ColorBLUE); } } } void GrAAConvexTessellator::draw(SkCanvas* canvas) const { for (int i = 0; i < fIndices.count(); i += 3) { SkASSERT(fIndices[i] < this->numPts()) ; SkASSERT(fIndices[i+1] < this->numPts()) ; SkASSERT(fIndices[i+2] < this->numPts()) ; draw_line(canvas, this->point(this->fIndices[i]), this->point(this->fIndices[i+1]), SK_ColorBLACK); draw_line(canvas, this->point(this->fIndices[i+1]), this->point(this->fIndices[i+2]), SK_ColorBLACK); draw_line(canvas, this->point(this->fIndices[i+2]), this->point(this->fIndices[i]), SK_ColorBLACK); } fInitialRing.draw(canvas, *this); for (int i = 0; i < fRings.count(); ++i) { fRings[i]->draw(canvas, *this); } for (int i = 0; i < this->numPts(); ++i) { draw_point(canvas, this->point(i), 0.5f + (this->depth(i)/(2 * kAntialiasingRadius)), !this->movable(i)); SkPaint paint; paint.setTextSize(kPointTextSize); paint.setTextAlign(SkPaint::kCenter_Align); if (this->depth(i) <= -kAntialiasingRadius) { paint.setColor(SK_ColorWHITE); } SkString num; num.printf("%d", i); canvas->drawString(num, this->point(i).fX, this->point(i).fY+(kPointRadius/2.0f), paint); } } #endif