Add GrAAConvexTessellator class

src/gpu/GrAAConvexTessellator.cpp

+/*
+ * 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"
+
+// Next steps:
+//  use in AAConvexPathRenderer
+//  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 = SkScalarMul(kClose, kClose);
+
+static SkScalar intersect(const SkPoint& p0, const SkPoint& n0,
+                          const SkPoint& p1, const SkPoint& n1) {
+    const SkPoint v = p1 - p0;
+
+    SkScalar perpDot = n0.fX * n1.fY - n0.fY * n1.fX;
+    return (v.fX * n1.fY - v.fY * n1.fX) / perpDot;
+}
+
+// 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 = p0.distanceToSqd(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,
+                                 bool movable) {
+    this->validate();
+
+    int index = fPts.count();
+    *fPts.push() = pt;
+    *fDepths.push() = depth;
+    *fMovable.push() = movable;
+
+    this->validate();
+    return index;
+}
+
+void GrAAConvexTessellator::popLastPt() {
+    this->validate();
+
+    fPts.pop();
+    fDepths.pop();
+    fMovable.pop();
+
+    this->validate();
+}
+
+void GrAAConvexTessellator::popFirstPtShuffle() {
+    this->validate();
+
+    fPts.removeShuffle(0);
+    fDepths.removeShuffle(0);
+    fMovable.removeShuffle(0);
+
+    this->validate();
+}
+
+void GrAAConvexTessellator::updatePt(int index,
+                                     const SkPoint& pt,
+                                     SkScalar depth) {
+    this->validate();
+    SkASSERT(fMovable[index]);
+
+    fPts[index] = pt;
+    fDepths[index] = depth;
+}
+
+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();
+    fDepths.rewind();
+    fMovable.rewind();
+    fIndices.rewind();
+    fNorms.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];
+        fBisectors[cur].normalize();
+        fBisectors[cur].negate();      // make the bisector face in
+
+        SkASSERT(SkScalarNearlyEqual(1.0f, fBisectors[cur].length()));
+    }
+}
+
+// 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 GrRing class while the GrAAConvexTessellator
+// controls the iteration. The GrCandidateVerts holds the formative points for the
+// next ring.
+bool GrAAConvexTessellator::tessellate(const SkMatrix& m, const SkPath& path) {
+    static const int kMaxNumRings = 8;
+
+    SkDEBUGCODE(fShouldCheckDepths = true;)
+
+    if (!this->extractFromPath(m, path)) {
+        return false;
+    }
+
+    this->createOuterRing();
+
+    // the bisectors are only needed for the computation of the outer ring
+    fBisectors.rewind();
+
+    GrRing* lastRing = &fInitialRing;
+    int i;
+    for (i = 0; i < kMaxNumRings; ++i) {
+        GrRing* nextRing = this->getNextRing(lastRing);
+
+        if (this->createInsetRing(*lastRing, nextRing)) {
+            break;
+        }
+
+        nextRing->init(*this);
+        lastRing = nextRing;
+    }
+
+    if (kMaxNumRings == i) {
+        // If we've exceeded the amount of time we want to throw at this, set
+        // the depth of all points in the final ring to 'fTargetDepth' and
+        // create a fan.
+        this->terminate(*lastRing);
+        SkDEBUGCODE(fShouldCheckDepths = false;)
+    }
+
+#ifdef SK_DEBUG
+    this->validate();
+    if (fShouldCheckDepths) {
+        SkDEBUGCODE(this->checkAllDepths();)
+    }
+#endif
+    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);
+    SkASSERT(depth >= 0.0f);
+    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 < fNorms.count());
+        newP = fPts[startIdx];
+    } else if (t > 0.0f) {
+        SkASSERT(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
+    t = -desiredDepth / bisector.dot(norm);
+    SkASSERT(t > 0.0f);
+    *result = bisector;
+    result->scale(t);
+    *result += newP;
+
+
+    return true;
+}
+
+bool GrAAConvexTessellator::extractFromPath(const SkMatrix& m, const SkPath& path) {
+    SkASSERT(SkPath::kLine_SegmentMask == path.getSegmentMasks());
+    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());
+
+    SkScalar minCross = SK_ScalarMax, maxCross = -SK_ScalarMax;
+
+    // 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)) != SkPath::kDone_Verb) {
+        switch (verb) {
+            case SkPath::kLine_Verb:
+                m.mapPoints(&pts[1], 1);
+                if (this->numPts() > 0 && duplicate_pt(pts[1], this->lastPoint())) {
+                    continue;
+                }
+
+                SkASSERT(fPts.count() <= 1 || fPts.count() == fNorms.count()+1);
+                if (this->numPts() >= 2 && 
+                    abs_dist_from_line(fPts.top(), fNorms.top(), pts[1]) < kClose) {
+                    // The old last point is on the line from the second to last to the new point
+                    this->popLastPt();
+                    fNorms.pop();
+                }
+
+                this->addPt(pts[1], 0.0f, false);
+                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()));
+                }
+
+                if (this->numPts() >= 3) {
+                    int cur = this->numPts()-1;
+                    SkScalar cross = SkPoint::CrossProduct(fNorms[cur-1], fNorms[cur-2]);
+                    maxCross = SkTMax(maxCross, cross);
+                    minCross = SkTMin(minCross, cross);
+                }
+                break;
+            case SkPath::kQuad_Verb:
+            case SkPath::kConic_Verb:
+            case SkPath::kCubic_Verb:
+                SkASSERT(false);
+                break;
+            case SkPath::kMove_Verb:
+            case SkPath::kClose_Verb:
+            case SkPath::kDone_Verb:
+                break;
+        }
+    }
+
+    if (this->numPts() < 3) {
+        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 &&
+        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();
+    }
+
+    if (this->numPts() < 3) {
+        return false;
+    }
+
+    *fNorms.push() = fPts[0] - fPts.top();
+    SkDEBUGCODE(SkScalar len =) SkPoint::Normalize(&fNorms.top());
+    SkASSERT(len > 0.0f);
+    SkASSERT(fPts.count() == fNorms.count());
+
+    if (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) {
+        return false;
+    }
+
+    // Check the cross produce of the final trio
+    SkScalar cross = SkPoint::CrossProduct(fNorms[0], fNorms.top());
+    maxCross = SkTMax(maxCross, cross);
+    minCross = SkTMin(minCross, cross);
+
+    if (maxCross > 0.0f) {
+        SkASSERT(minCross >= 0.0f);
+        fSide = SkPoint::kRight_Side;
+    } else {
+        SkASSERT(minCross <= 0.0f);
+        fSide = SkPoint::kLeft_Side;
+    }
+
+    // Make all the normals face outwards rather than along the edge
+    for (int cur = 0; cur < fNorms.count(); ++cur) {
+        fNorms[cur].setOrthog(fNorms[cur], fSide);
+        SkASSERT(SkScalarNearlyEqual(1.0f, fNorms[cur].length()));
+    }
+
+    this->computeBisectors();
+
+    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::GrRing* GrAAConvexTessellator::getNextRing(GrRing* lastRing) {
+#if GR_AA_CONVEX_TESSELLATOR_VIZ
+    GrRing* ring = *fRings.push() = SkNEW(GrRing);
+    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].setReserve1(fInitialRing.numPts());
+    fRings[nextRing].rewind1();
+    return &fRings[nextRing];
+#endif
+}
+
+void GrAAConvexTessellator::fanRing(const GrRing& ring) {
+    // fan out from point 0
+    for (int cur = 1; cur < ring.numPts()-1; ++cur) {
+        this->addTri(ring.index(0), ring.index(cur), ring.index(cur+1));
+    }
+}
+
+void GrAAConvexTessellator::createOuterRing() {
+    // For now, we're only generating one outer ring (at the start). This
+    // could be relaxed for stroking use cases.
+    SkASSERT(0 == fIndices.count());  
+    SkASSERT(fPts.count() == fNorms.count());
+
+    const int numPts = fPts.count();
+
+    // For each vertex of the original polygon we add three points to the 
+    // outset polygon - one extending perpendicular to each impinging edge
+    // and one along the bisector. Two triangles are added for each corner
+    // and two are added along each edge.
+    int prev = numPts - 1;
+    int lastPerpIdx = -1, firstPerpIdx, newIdx0, newIdx1, newIdx2;
+    for (int cur = 0; cur < numPts; ++cur) {
+        // The perpendicular point for the last edge
+        SkPoint temp = fNorms[prev];
+        temp.scale(fTargetDepth);
+        temp += fPts[cur];
+
+        // 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)
+        newIdx0 = this->addPt(temp, -fTargetDepth, false);
+
+        // The bisector outset point
+        temp = fBisectors[cur];
+        temp.scale(-fTargetDepth);  // the bisectors point in
+        temp += fPts[cur];
+
+        // For very shallow angles all the corner points could fuse
+        if (duplicate_pt(temp, this->point(newIdx0))) {
+            newIdx1 = newIdx0;
+        } else {
+            newIdx1 = this->addPt(temp, -fTargetDepth, false);
+        }
+
+        // The perpendicular point for the next edge.
+        temp = fNorms[cur];
+        temp.scale(fTargetDepth);
+        temp += fPts[cur];
+
+        // For very shallow angles all the corner points could fuse.
+        if (duplicate_pt(temp, this->point(newIdx1))) {
+            newIdx2 = newIdx1;
+        } else {
+            newIdx2 = this->addPt(temp, -fTargetDepth, false);
+        }
+
+        if (0 == cur) {
+            // Store the index of the first perpendicular point to finish up
+            firstPerpIdx = newIdx0;
+            SkASSERT(-1 == lastPerpIdx);
+        } else {
+            // The triangles for the previous edge
+            this->addTri(prev, newIdx0, cur);
+            this->addTri(prev, lastPerpIdx, newIdx0);
+        }
+
+        // The two triangles for the corner
+        this->addTri(cur, newIdx0, newIdx1);
+        this->addTri(cur, newIdx1, newIdx2);
+
+        prev = cur;
+        // Track the last perpendicular outset point so we can construct the
+        // trailing edge triangles.
+        lastPerpIdx = newIdx2;
+    }
+
+    // pick up the final edge rect
+    this->addTri(numPts-1, firstPerpIdx, 0);
+    this->addTri(numPts-1, lastPerpIdx, firstPerpIdx);
+
+    this->validate();
+}
+
+// Something went wrong in the creation of the next ring. Mark the last good
+// ring as being at the desired depth and fan it.
+void GrAAConvexTessellator::terminate(const GrRing& ring) {
+    for (int i = 0; i < ring.numPts(); ++i) {
+        fDepths[ring.index(i)] = fTargetDepth;
+    }
+
+    this->fanRing(ring);
+}
+
+// return true when processing is complete
+bool GrAAConvexTessellator::createInsetRing(const GrRing& lastRing, GrRing* nextRing) {
+    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;
+    int minEdgeIdx;
+
+    for (int cur = 0; cur < lastRing.numPts(); ++cur) {
+        int next = (cur + 1) % lastRing.numPts();
+
+        SkScalar t = intersect(this->point(lastRing.index(cur)),  lastRing.bisector(cur),
+                               this->point(lastRing.index(next)), lastRing.bisector(next));
+        SkScalar dist = -t * lastRing.norm(cur).dot(lastRing.bisector(cur));
+
+        if (minDist > dist) {
+            minDist = dist;
+            minT = t;
+            minEdgeIdx = cur;
+        }
+    }
+
+    SkPoint newPt = lastRing.bisector(minEdgeIdx);
+    newPt.scale(minT);
+    newPt += this->point(lastRing.index(minEdgeIdx));
+
+    SkScalar depth = this->computeDepthFromEdge(lastRing.origEdgeID(minEdgeIdx), newPt);
+    if (depth >= fTargetDepth) {
+        // None of the bisectors intersect before reaching the desired depth.
+        // Just step them all to the desired depth
+        depth = fTargetDepth;
+        done = true;
+    }
+
+    // 'dst' stores where each point in the last ring maps to/transforms into
+    // in the next ring.
+    SkTDArray<int> 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);
+        SkDEBUGCODE(fShouldCheckDepths = false;)
+        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);
+            SkDEBUGCODE(fShouldCheckDepths = false;)
+            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);
+        SkDEBUGCODE(fShouldCheckDepths = false;)
+        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 {
+            dst[cur] = dst[cur-1] = fCandidateVerts.fuseWithBoth();
+        }
+    }
+
+    // Fold the new ring's points into the global pool
+    for (int i = 0; i < fCandidateVerts.numPts(); ++i) {
+        int newIdx;
+        if (fCandidateVerts.needsToBeNew(i)) {
+            // if the originating index is still valid then this point wasn't 
+            // fused (and is thus movable)
+            newIdx = this->addPt(fCandidateVerts.point(i), depth,
+                                 fCandidateVerts.originatingIdx(i) != -1);
+        } else {
+            SkASSERT(fCandidateVerts.originatingIdx(i) != -1);
+            this->updatePt(fCandidateVerts.originatingIdx(i), fCandidateVerts.point(i), depth);
+            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 cur = 0; cur < lastRing.numPts(); ++cur) {
+        int next = (cur + 1) % lastRing.numPts();
+
+        this->addTri(lastRing.index(cur), lastRing.index(next), dst[next]);
+        this->addTri(lastRing.index(cur), dst[next], dst[cur]);
+    }
+
+    if (done) {
+        this->fanRing(*nextRing);
+    }
+
+    if (nextRing->numPts() < 3) {
+        done = true;
+    }
+
+    return done;
+}
+
+void GrAAConvexTessellator::validate() const {
+    SkASSERT(fPts.count() == fDepths.count());
+    SkASSERT(fPts.count() == fMovable.count());
+    SkASSERT(0 == (fIndices.count() % 3));
+}
+
+//////////////////////////////////////////////////////////////////////////////
+void GrAAConvexTessellator::GrRing::init(const GrAAConvexTessellator& tess) {
+    this->computeNormals(tess);
+    this->computeBisectors();
+    SkASSERT(this->isConvex(tess));
+}
+
+void GrAAConvexTessellator::GrRing::init(const SkTDArray<SkVector>& norms,
+                  const SkTDArray<SkVector>& bisectors) {

[bsalomon, 2015/05/05 17:13:42]

align?

[robertphillips, 2015/05/06 12:16:32]

Done.

+    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::GrRing::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);
+        SkDEBUGCODE(SkScalar len =) SkPoint::Normalize(&fPts[cur].fNorm);
+        SkASSERT(len > 0.0f);
+        fPts[cur].fNorm.setOrthog(fPts[cur].fNorm, tess.side());
+
+        SkASSERT(SkScalarNearlyEqual(1.0f, fPts[cur].fNorm.length()));
+    }
+}
+
+void GrAAConvexTessellator::GrRing::computeBisectors() {
+    int prev = fPts.count() - 1;
+    for (int cur = 0; cur < fPts.count(); prev = cur, ++cur) {
+        fPts[cur].fBisector = fPts[cur].fNorm + fPts[prev].fNorm;
+        fPts[cur].fBisector.normalize();
+        fPts[cur].fBisector.negate();      // make the bisector face in
+
+        SkASSERT(SkScalarNearlyEqual(1.0f, fPts[cur].fBisector.length()));
+    }    
+}
+
+//////////////////////////////////////////////////////////////////////////////
+#ifdef SK_DEBUG
+// Is this ring convex?
+bool GrAAConvexTessellator::GrRing::isConvex(const GrAAConvexTessellator& tess) const {
+    if (fPts.count() < 3) {
+        return false;
+    }
+
+    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;
+    }
+
+    return (maxDot > 0.0f) == (minDot >= 0.0f);
+}
+
+static SkScalar capsule_depth(const SkPoint& p0, const SkPoint& p1,
+                              const SkPoint& test, SkPoint::Side side,
+                              int* sign) {
+    *sign = -1;
+    SkPoint edge = p1 - p0;
+    SkScalar len = SkPoint::Normalize(&edge);
+
+    SkPoint testVec = test - p0;
+
+    SkScalar d0 = edge.dot(testVec);
+    if (d0 < 0.0f) {
+        return SkPoint::Distance(p0, test);
+    }
+    if (d0 > len) {
+        return SkPoint::Distance(p1, test);
+    }
+
+    SkScalar perpDist = testVec.fY * edge.fX - testVec.fX * edge.fY;
+    if (SkPoint::kRight_Side == side) {
+        perpDist = -perpDist;
+    }
+
+    if (perpDist < 0.0f) {
+        perpDist = -perpDist;
+    } else {
+        *sign = 1;
+    }
+    return perpDist;
+}
+
+SkScalar GrAAConvexTessellator::computeRealDepth(const SkPoint& p) const {
+    SkScalar minDist = SK_ScalarMax;
+    int closestEdge, closestSign, sign;
+
+    for (int edge = 0; edge < fNorms.count(); ++edge) {
+        SkScalar dist = capsule_depth(this->point(edge),
+                                      this->point((edge+1) % fNorms.count()),
+                                      p, fSide, &sign);
+        SkASSERT(dist >= 0.0f);
+
+        if (minDist > dist) {
+            minDist = dist;
+            closestEdge = edge;
+            closestSign = sign;
+        }
+    }
+
+    return closestSign * minDist;
+}
+
+// Verify that the incrementally computed depths are close to the actual depths.
+void GrAAConvexTessellator::checkAllDepths() const {
+    for (int cur = 0; cur < this->numPts(); ++cur) {
+        SkScalar realDepth = this->computeRealDepth(this->point(cur));
+        SkScalar computedDepth = this->depth(cur);
+        SkASSERT(SkScalarNearlyEqual(realDepth, computedDepth, 0.01f));
+    }
+}
+#endif
+
+//////////////////////////////////////////////////////////////////////////////
+#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::GrRing::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->drawText(num.c_str(), num.size(), 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*fTargetDepth)), 
+                   !this->movable(i));
+
+        SkPaint paint;
+        paint.setTextSize(kPointTextSize);
+        paint.setTextAlign(SkPaint::kCenter_Align);
+        if (this->depth(i) <= -fTargetDepth) {
+            paint.setColor(SK_ColorWHITE);
+        }
+
+        SkString num;
+        num.printf("%d", i);
+        canvas->drawText(num.c_str(), num.size(), 
+                         this->point(i).fX, this->point(i).fY+(kPointRadius/2.0f), 
+                         paint);
+    }
+}
+
+#endif
+