| /* |
| * Copyright 2008 The Android Open Source Project |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #include "src/core/SkStrokerPriv.h" |
| |
| #include "include/private/base/SkMacros.h" |
| #include "include/private/base/SkTo.h" |
| #include "src/core/SkGeometry.h" |
| #include "src/core/SkPathPriv.h" |
| #include "src/core/SkPointPriv.h" |
| |
| #include <utility> |
| |
| enum { |
| kTangent_RecursiveLimit, |
| kCubic_RecursiveLimit, |
| kConic_RecursiveLimit, |
| kQuad_RecursiveLimit |
| }; |
| |
| // quads with extreme widths (e.g. (0,1) (1,6) (0,3) width=5e7) recurse to point of failure |
| // largest seen for normal cubics : 5, 26 |
| // largest seen for normal quads : 11 |
| // 3x limits seen in practice, except for cubics (3x limit would be ~75). |
| // For cubics, we never get close to 75 when running through dm. The limit of 24 |
| // was chosen because it's close to the peak in a count of cubic recursion depths visited |
| // (define DEBUG_CUBIC_RECURSION_DEPTHS) and no diffs were produced on gold when using it. |
| static const int kRecursiveLimits[] = { 5*3, 24, 11*3, 11*3 }; |
| |
| static_assert(0 == kTangent_RecursiveLimit, "cubic_stroke_relies_on_tangent_equalling_zero"); |
| static_assert(1 == kCubic_RecursiveLimit, "cubic_stroke_relies_on_cubic_equalling_one"); |
| static_assert(std::size(kRecursiveLimits) == kQuad_RecursiveLimit + 1, |
| "recursive_limits_mismatch"); |
| |
| #if defined SK_DEBUG && QUAD_STROKE_APPROX_EXTENDED_DEBUGGING |
| int gMaxRecursion[std::size(kRecursiveLimits)] = { 0 }; |
| #endif |
| #ifndef DEBUG_QUAD_STROKER |
| #define DEBUG_QUAD_STROKER 0 |
| #endif |
| |
| #if DEBUG_QUAD_STROKER |
| /* Enable to show the decisions made in subdividing the curve -- helpful when the resulting |
| stroke has more than the optimal number of quadratics and lines */ |
| #define STROKER_RESULT(resultType, depth, quadPts, format, ...) \ |
| SkDebugf("[%d] %s " format "\n", depth, __FUNCTION__, __VA_ARGS__), \ |
| SkDebugf(" " #resultType " t=(%g,%g)\n", quadPts->fStartT, quadPts->fEndT), \ |
| resultType |
| #define STROKER_DEBUG_PARAMS(...) , __VA_ARGS__ |
| #else |
| #define STROKER_RESULT(resultType, depth, quadPts, format, ...) \ |
| resultType |
| #define STROKER_DEBUG_PARAMS(...) |
| #endif |
| |
| #ifndef DEBUG_CUBIC_RECURSION_DEPTHS |
| #define DEBUG_CUBIC_RECURSION_DEPTHS 0 |
| #endif |
| #if DEBUG_CUBIC_RECURSION_DEPTHS |
| /* Prints a histogram of recursion depths at process termination. */ |
| static struct DepthHistogram { |
| inline static constexpr int kMaxDepth = 75; |
| int fCubicDepths[kMaxDepth + 1]; |
| |
| DepthHistogram() { memset(fCubicDepths, 0, sizeof(fCubicDepths)); } |
| |
| ~DepthHistogram() { |
| SkDebugf("# times recursion terminated per depth:\n"); |
| for (int i = 0; i <= kMaxDepth; i++) { |
| SkDebugf(" depth %d: %d\n", i, fCubicDepths[i]); |
| } |
| } |
| |
| inline void incDepth(int depth) { |
| SkASSERT(depth >= 0 && depth <= kMaxDepth); |
| fCubicDepths[depth]++; |
| } |
| } sCubicDepthHistogram; |
| |
| #define DEBUG_CUBIC_RECURSION_TRACK_DEPTH(depth) sCubicDepthHistogram.incDepth(depth) |
| #else |
| #define DEBUG_CUBIC_RECURSION_TRACK_DEPTH(depth) (void)(depth) |
| #endif |
| |
| static inline bool degenerate_vector(const SkVector& v) { |
| return !SkPointPriv::CanNormalize(v.fX, v.fY); |
| } |
| |
| static bool set_normal_unitnormal(const SkPoint& before, const SkPoint& after, SkScalar scale, |
| SkScalar radius, |
| SkVector* normal, SkVector* unitNormal) { |
| if (!unitNormal->setNormalize((after.fX - before.fX) * scale, |
| (after.fY - before.fY) * scale)) { |
| return false; |
| } |
| SkPointPriv::RotateCCW(unitNormal); |
| unitNormal->scale(radius, normal); |
| return true; |
| } |
| |
| static bool set_normal_unitnormal(const SkVector& vec, |
| SkScalar radius, |
| SkVector* normal, SkVector* unitNormal) { |
| if (!unitNormal->setNormalize(vec.fX, vec.fY)) { |
| return false; |
| } |
| SkPointPriv::RotateCCW(unitNormal); |
| unitNormal->scale(radius, normal); |
| return true; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| struct SkQuadConstruct { // The state of the quad stroke under construction. |
| SkPoint fQuad[3]; // the stroked quad parallel to the original curve |
| SkPoint fTangentStart; // a point tangent to fQuad[0] |
| SkPoint fTangentEnd; // a point tangent to fQuad[2] |
| SkScalar fStartT; // a segment of the original curve |
| SkScalar fMidT; // " |
| SkScalar fEndT; // " |
| bool fStartSet; // state to share common points across structs |
| bool fEndSet; // " |
| bool fOppositeTangents; // set if coincident tangents have opposite directions |
| |
| // return false if start and end are too close to have a unique middle |
| bool init(SkScalar start, SkScalar end) { |
| fStartT = start; |
| fMidT = (start + end) * SK_ScalarHalf; |
| fEndT = end; |
| fStartSet = fEndSet = false; |
| return fStartT < fMidT && fMidT < fEndT; |
| } |
| |
| bool initWithStart(SkQuadConstruct* parent) { |
| if (!init(parent->fStartT, parent->fMidT)) { |
| return false; |
| } |
| fQuad[0] = parent->fQuad[0]; |
| fTangentStart = parent->fTangentStart; |
| fStartSet = true; |
| return true; |
| } |
| |
| bool initWithEnd(SkQuadConstruct* parent) { |
| if (!init(parent->fMidT, parent->fEndT)) { |
| return false; |
| } |
| fQuad[2] = parent->fQuad[2]; |
| fTangentEnd = parent->fTangentEnd; |
| fEndSet = true; |
| return true; |
| } |
| }; |
| |
| class SkPathStroker { |
| public: |
| SkPathStroker(const SkPath& src, |
| SkScalar radius, SkScalar miterLimit, SkPaint::Cap, |
| SkPaint::Join, SkScalar resScale, |
| bool canIgnoreCenter); |
| |
| bool hasOnlyMoveTo() const { return 0 == fSegmentCount; } |
| SkPoint moveToPt() const { return fFirstPt; } |
| |
| void moveTo(const SkPoint&); |
| void lineTo(const SkPoint&, const SkPath::Iter* iter = nullptr); |
| void quadTo(const SkPoint&, const SkPoint&); |
| void conicTo(const SkPoint&, const SkPoint&, SkScalar weight); |
| void cubicTo(const SkPoint&, const SkPoint&, const SkPoint&); |
| void close(bool isLine) { this->finishContour(true, isLine); } |
| |
| void done(SkPath* dst, bool isLine) { |
| this->finishContour(false, isLine); |
| dst->swap(fOuter); |
| } |
| |
| SkScalar getResScale() const { return fResScale; } |
| |
| bool isCurrentContourEmpty() const { |
| return fInner.isZeroLengthSincePoint(0) && |
| fOuter.isZeroLengthSincePoint(fFirstOuterPtIndexInContour); |
| } |
| |
| private: |
| SkScalar fRadius; |
| SkScalar fInvMiterLimit; |
| SkScalar fResScale; |
| SkScalar fInvResScale; |
| SkScalar fInvResScaleSquared; |
| |
| SkVector fFirstNormal, fPrevNormal, fFirstUnitNormal, fPrevUnitNormal; |
| SkPoint fFirstPt, fPrevPt; // on original path |
| SkPoint fFirstOuterPt; |
| int fFirstOuterPtIndexInContour; |
| int fSegmentCount; |
| bool fPrevIsLine; |
| bool fCanIgnoreCenter; |
| |
| SkStrokerPriv::CapProc fCapper; |
| SkStrokerPriv::JoinProc fJoiner; |
| |
| SkPath fInner, fOuter, fCusper; // outer is our working answer, inner is temp |
| |
| enum StrokeType { |
| kOuter_StrokeType = 1, // use sign-opposite values later to flip perpendicular axis |
| kInner_StrokeType = -1 |
| } fStrokeType; |
| |
| enum ResultType { |
| kSplit_ResultType, // the caller should split the quad stroke in two |
| kDegenerate_ResultType, // the caller should add a line |
| kQuad_ResultType, // the caller should (continue to try to) add a quad stroke |
| }; |
| |
| enum ReductionType { |
| kPoint_ReductionType, // all curve points are practically identical |
| kLine_ReductionType, // the control point is on the line between the ends |
| kQuad_ReductionType, // the control point is outside the line between the ends |
| kDegenerate_ReductionType, // the control point is on the line but outside the ends |
| kDegenerate2_ReductionType, // two control points are on the line but outside ends (cubic) |
| kDegenerate3_ReductionType, // three areas of max curvature found (for cubic) |
| }; |
| |
| enum IntersectRayType { |
| kCtrlPt_RayType, |
| kResultType_RayType, |
| }; |
| |
| int fRecursionDepth; // track stack depth to abort if numerics run amok |
| bool fFoundTangents; // do less work until tangents meet (cubic) |
| bool fJoinCompleted; // previous join was not degenerate |
| |
| void addDegenerateLine(const SkQuadConstruct* ); |
| static ReductionType CheckConicLinear(const SkConic& , SkPoint* reduction); |
| static ReductionType CheckCubicLinear(const SkPoint cubic[4], SkPoint reduction[3], |
| const SkPoint** tanPtPtr); |
| static ReductionType CheckQuadLinear(const SkPoint quad[3], SkPoint* reduction); |
| ResultType compareQuadConic(const SkConic& , SkQuadConstruct* ) const; |
| ResultType compareQuadCubic(const SkPoint cubic[4], SkQuadConstruct* ); |
| ResultType compareQuadQuad(const SkPoint quad[3], SkQuadConstruct* ); |
| void conicPerpRay(const SkConic& , SkScalar t, SkPoint* tPt, SkPoint* onPt, |
| SkPoint* tangent) const; |
| void conicQuadEnds(const SkConic& , SkQuadConstruct* ) const; |
| bool conicStroke(const SkConic& , SkQuadConstruct* ); |
| bool cubicMidOnLine(const SkPoint cubic[4], const SkQuadConstruct* ) const; |
| void cubicPerpRay(const SkPoint cubic[4], SkScalar t, SkPoint* tPt, SkPoint* onPt, |
| SkPoint* tangent) const; |
| void cubicQuadEnds(const SkPoint cubic[4], SkQuadConstruct* ); |
| void cubicQuadMid(const SkPoint cubic[4], const SkQuadConstruct* , SkPoint* mid) const; |
| bool cubicStroke(const SkPoint cubic[4], SkQuadConstruct* ); |
| void init(StrokeType strokeType, SkQuadConstruct* , SkScalar tStart, SkScalar tEnd); |
| ResultType intersectRay(SkQuadConstruct* , IntersectRayType STROKER_DEBUG_PARAMS(int) ) const; |
| bool ptInQuadBounds(const SkPoint quad[3], const SkPoint& pt) const; |
| void quadPerpRay(const SkPoint quad[3], SkScalar t, SkPoint* tPt, SkPoint* onPt, |
| SkPoint* tangent) const; |
| bool quadStroke(const SkPoint quad[3], SkQuadConstruct* ); |
| void setConicEndNormal(const SkConic& , |
| const SkVector& normalAB, const SkVector& unitNormalAB, |
| SkVector* normalBC, SkVector* unitNormalBC); |
| void setCubicEndNormal(const SkPoint cubic[4], |
| const SkVector& normalAB, const SkVector& unitNormalAB, |
| SkVector* normalCD, SkVector* unitNormalCD); |
| void setQuadEndNormal(const SkPoint quad[3], |
| const SkVector& normalAB, const SkVector& unitNormalAB, |
| SkVector* normalBC, SkVector* unitNormalBC); |
| void setRayPts(const SkPoint& tPt, SkVector* dxy, SkPoint* onPt, SkPoint* tangent) const; |
| static bool SlightAngle(SkQuadConstruct* ); |
| ResultType strokeCloseEnough(const SkPoint stroke[3], const SkPoint ray[2], |
| SkQuadConstruct* STROKER_DEBUG_PARAMS(int depth) ) const; |
| ResultType tangentsMeet(const SkPoint cubic[4], SkQuadConstruct* ); |
| |
| void finishContour(bool close, bool isLine); |
| bool preJoinTo(const SkPoint&, SkVector* normal, SkVector* unitNormal, |
| bool isLine); |
| void postJoinTo(const SkPoint&, const SkVector& normal, |
| const SkVector& unitNormal); |
| |
| void line_to(const SkPoint& currPt, const SkVector& normal); |
| }; |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| bool SkPathStroker::preJoinTo(const SkPoint& currPt, SkVector* normal, |
| SkVector* unitNormal, bool currIsLine) { |
| SkASSERT(fSegmentCount >= 0); |
| |
| SkScalar prevX = fPrevPt.fX; |
| SkScalar prevY = fPrevPt.fY; |
| |
| if (!set_normal_unitnormal(fPrevPt, currPt, fResScale, fRadius, normal, unitNormal)) { |
| if (SkStrokerPriv::CapFactory(SkPaint::kButt_Cap) == fCapper) { |
| return false; |
| } |
| /* Square caps and round caps draw even if the segment length is zero. |
| Since the zero length segment has no direction, set the orientation |
| to upright as the default orientation */ |
| normal->set(fRadius, 0); |
| unitNormal->set(1, 0); |
| } |
| |
| if (fSegmentCount == 0) { |
| fFirstNormal = *normal; |
| fFirstUnitNormal = *unitNormal; |
| fFirstOuterPt.set(prevX + normal->fX, prevY + normal->fY); |
| |
| fOuter.moveTo(fFirstOuterPt.fX, fFirstOuterPt.fY); |
| fInner.moveTo(prevX - normal->fX, prevY - normal->fY); |
| } else { // we have a previous segment |
| fJoiner(&fOuter, &fInner, fPrevUnitNormal, fPrevPt, *unitNormal, |
| fRadius, fInvMiterLimit, fPrevIsLine, currIsLine); |
| } |
| fPrevIsLine = currIsLine; |
| return true; |
| } |
| |
| void SkPathStroker::postJoinTo(const SkPoint& currPt, const SkVector& normal, |
| const SkVector& unitNormal) { |
| fJoinCompleted = true; |
| fPrevPt = currPt; |
| fPrevUnitNormal = unitNormal; |
| fPrevNormal = normal; |
| fSegmentCount += 1; |
| } |
| |
| void SkPathStroker::finishContour(bool close, bool currIsLine) { |
| if (fSegmentCount > 0) { |
| SkPoint pt; |
| |
| if (close) { |
| fJoiner(&fOuter, &fInner, fPrevUnitNormal, fPrevPt, |
| fFirstUnitNormal, fRadius, fInvMiterLimit, |
| fPrevIsLine, currIsLine); |
| fOuter.close(); |
| |
| if (fCanIgnoreCenter) { |
| // If we can ignore the center just make sure the larger of the two paths |
| // is preserved and don't add the smaller one. |
| if (fInner.getBounds().contains(fOuter.getBounds())) { |
| fInner.swap(fOuter); |
| } |
| } else { |
| // now add fInner as its own contour |
| fInner.getLastPt(&pt); |
| fOuter.moveTo(pt.fX, pt.fY); |
| fOuter.reversePathTo(fInner); |
| fOuter.close(); |
| } |
| } else { // add caps to start and end |
| // cap the end |
| fInner.getLastPt(&pt); |
| fCapper(&fOuter, fPrevPt, fPrevNormal, pt, |
| currIsLine ? &fInner : nullptr); |
| fOuter.reversePathTo(fInner); |
| // cap the start |
| fCapper(&fOuter, fFirstPt, -fFirstNormal, fFirstOuterPt, |
| fPrevIsLine ? &fInner : nullptr); |
| fOuter.close(); |
| } |
| if (!fCusper.isEmpty()) { |
| fOuter.addPath(fCusper); |
| fCusper.rewind(); |
| } |
| } |
| // since we may re-use fInner, we rewind instead of reset, to save on |
| // reallocating its internal storage. |
| fInner.rewind(); |
| fSegmentCount = -1; |
| fFirstOuterPtIndexInContour = fOuter.countPoints(); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| SkPathStroker::SkPathStroker(const SkPath& src, |
| SkScalar radius, SkScalar miterLimit, |
| SkPaint::Cap cap, SkPaint::Join join, SkScalar resScale, |
| bool canIgnoreCenter) |
| : fRadius(radius) |
| , fResScale(resScale) |
| , fCanIgnoreCenter(canIgnoreCenter) { |
| |
| /* This is only used when join is miter_join, but we initialize it here |
| so that it is always defined, to fis valgrind warnings. |
| */ |
| fInvMiterLimit = 0; |
| |
| if (join == SkPaint::kMiter_Join) { |
| if (miterLimit <= SK_Scalar1) { |
| join = SkPaint::kBevel_Join; |
| } else { |
| fInvMiterLimit = SkScalarInvert(miterLimit); |
| } |
| } |
| fCapper = SkStrokerPriv::CapFactory(cap); |
| fJoiner = SkStrokerPriv::JoinFactory(join); |
| fSegmentCount = -1; |
| fFirstOuterPtIndexInContour = 0; |
| fPrevIsLine = false; |
| |
| // Need some estimate of how large our final result (fOuter) |
| // and our per-contour temp (fInner) will be, so we don't spend |
| // extra time repeatedly growing these arrays. |
| // |
| // 3x for result == inner + outer + join (swag) |
| // 1x for inner == 'wag' (worst contour length would be better guess) |
| fOuter.incReserve(src.countPoints() * 3); |
| fOuter.setIsVolatile(true); |
| fInner.incReserve(src.countPoints()); |
| fInner.setIsVolatile(true); |
| // TODO : write a common error function used by stroking and filling |
| // The '4' below matches the fill scan converter's error term |
| fInvResScale = SkScalarInvert(resScale * 4); |
| fInvResScaleSquared = fInvResScale * fInvResScale; |
| fRecursionDepth = 0; |
| } |
| |
| void SkPathStroker::moveTo(const SkPoint& pt) { |
| if (fSegmentCount > 0) { |
| this->finishContour(false, false); |
| } |
| fSegmentCount = 0; |
| fFirstPt = fPrevPt = pt; |
| fJoinCompleted = false; |
| } |
| |
| void SkPathStroker::line_to(const SkPoint& currPt, const SkVector& normal) { |
| fOuter.lineTo(currPt.fX + normal.fX, currPt.fY + normal.fY); |
| fInner.lineTo(currPt.fX - normal.fX, currPt.fY - normal.fY); |
| } |
| |
| static bool has_valid_tangent(const SkPath::Iter* iter) { |
| SkPath::Iter copy = *iter; |
| SkPath::Verb verb; |
| SkPoint pts[4]; |
| while ((verb = copy.next(pts))) { |
| switch (verb) { |
| case SkPath::kMove_Verb: |
| return false; |
| case SkPath::kLine_Verb: |
| if (pts[0] == pts[1]) { |
| continue; |
| } |
| return true; |
| case SkPath::kQuad_Verb: |
| case SkPath::kConic_Verb: |
| if (pts[0] == pts[1] && pts[0] == pts[2]) { |
| continue; |
| } |
| return true; |
| case SkPath::kCubic_Verb: |
| if (pts[0] == pts[1] && pts[0] == pts[2] && pts[0] == pts[3]) { |
| continue; |
| } |
| return true; |
| case SkPath::kClose_Verb: |
| case SkPath::kDone_Verb: |
| return false; |
| } |
| } |
| return false; |
| } |
| |
| void SkPathStroker::lineTo(const SkPoint& currPt, const SkPath::Iter* iter) { |
| bool teenyLine = SkPointPriv::EqualsWithinTolerance(fPrevPt, currPt, SK_ScalarNearlyZero * fInvResScale); |
| if (SkStrokerPriv::CapFactory(SkPaint::kButt_Cap) == fCapper && teenyLine) { |
| return; |
| } |
| if (teenyLine && (fJoinCompleted || (iter && has_valid_tangent(iter)))) { |
| return; |
| } |
| SkVector normal, unitNormal; |
| |
| if (!this->preJoinTo(currPt, &normal, &unitNormal, true)) { |
| return; |
| } |
| this->line_to(currPt, normal); |
| this->postJoinTo(currPt, normal, unitNormal); |
| } |
| |
| void SkPathStroker::setQuadEndNormal(const SkPoint quad[3], const SkVector& normalAB, |
| const SkVector& unitNormalAB, SkVector* normalBC, SkVector* unitNormalBC) { |
| if (!set_normal_unitnormal(quad[1], quad[2], fResScale, fRadius, normalBC, unitNormalBC)) { |
| *normalBC = normalAB; |
| *unitNormalBC = unitNormalAB; |
| } |
| } |
| |
| void SkPathStroker::setConicEndNormal(const SkConic& conic, const SkVector& normalAB, |
| const SkVector& unitNormalAB, SkVector* normalBC, SkVector* unitNormalBC) { |
| setQuadEndNormal(conic.fPts, normalAB, unitNormalAB, normalBC, unitNormalBC); |
| } |
| |
| void SkPathStroker::setCubicEndNormal(const SkPoint cubic[4], const SkVector& normalAB, |
| const SkVector& unitNormalAB, SkVector* normalCD, SkVector* unitNormalCD) { |
| SkVector ab = cubic[1] - cubic[0]; |
| SkVector cd = cubic[3] - cubic[2]; |
| |
| bool degenerateAB = degenerate_vector(ab); |
| bool degenerateCD = degenerate_vector(cd); |
| |
| if (degenerateAB && degenerateCD) { |
| goto DEGENERATE_NORMAL; |
| } |
| |
| if (degenerateAB) { |
| ab = cubic[2] - cubic[0]; |
| degenerateAB = degenerate_vector(ab); |
| } |
| if (degenerateCD) { |
| cd = cubic[3] - cubic[1]; |
| degenerateCD = degenerate_vector(cd); |
| } |
| if (degenerateAB || degenerateCD) { |
| DEGENERATE_NORMAL: |
| *normalCD = normalAB; |
| *unitNormalCD = unitNormalAB; |
| return; |
| } |
| SkAssertResult(set_normal_unitnormal(cd, fRadius, normalCD, unitNormalCD)); |
| } |
| |
| void SkPathStroker::init(StrokeType strokeType, SkQuadConstruct* quadPts, SkScalar tStart, |
| SkScalar tEnd) { |
| fStrokeType = strokeType; |
| fFoundTangents = false; |
| quadPts->init(tStart, tEnd); |
| } |
| |
| // returns the distance squared from the point to the line |
| static SkScalar pt_to_line(const SkPoint& pt, const SkPoint& lineStart, const SkPoint& lineEnd) { |
| SkVector dxy = lineEnd - lineStart; |
| SkVector ab0 = pt - lineStart; |
| SkScalar numer = dxy.dot(ab0); |
| SkScalar denom = dxy.dot(dxy); |
| SkScalar t = sk_ieee_float_divide(numer, denom); |
| if (t >= 0 && t <= 1) { |
| SkPoint hit; |
| hit.fX = lineStart.fX * (1 - t) + lineEnd.fX * t; |
| hit.fY = lineStart.fY * (1 - t) + lineEnd.fY * t; |
| return SkPointPriv::DistanceToSqd(hit, pt); |
| } else { |
| return SkPointPriv::DistanceToSqd(pt, lineStart); |
| } |
| } |
| |
| /* Given a cubic, determine if all four points are in a line. |
| Return true if the inner points is close to a line connecting the outermost points. |
| |
| Find the outermost point by looking for the largest difference in X or Y. |
| Given the indices of the outermost points, and that outer_1 is greater than outer_2, |
| this table shows the index of the smaller of the remaining points: |
| |
| outer_2 |
| 0 1 2 3 |
| outer_1 ---------------- |
| 0 | - 2 1 1 |
| 1 | - - 0 0 |
| 2 | - - - 0 |
| 3 | - - - - |
| |
| If outer_1 == 0 and outer_2 == 1, the smaller of the remaining indices (2 and 3) is 2. |
| |
| This table can be collapsed to: (1 + (2 >> outer_2)) >> outer_1 |
| |
| Given three indices (outer_1 outer_2 mid_1) from 0..3, the remaining index is: |
| |
| mid_2 == (outer_1 ^ outer_2 ^ mid_1) |
| */ |
| static bool cubic_in_line(const SkPoint cubic[4]) { |
| SkScalar ptMax = -1; |
| int outer1 SK_INIT_TO_AVOID_WARNING; |
| int outer2 SK_INIT_TO_AVOID_WARNING; |
| for (int index = 0; index < 3; ++index) { |
| for (int inner = index + 1; inner < 4; ++inner) { |
| SkVector testDiff = cubic[inner] - cubic[index]; |
| SkScalar testMax = std::max(SkScalarAbs(testDiff.fX), SkScalarAbs(testDiff.fY)); |
| if (ptMax < testMax) { |
| outer1 = index; |
| outer2 = inner; |
| ptMax = testMax; |
| } |
| } |
| } |
| SkASSERT(outer1 >= 0 && outer1 <= 2); |
| SkASSERT(outer2 >= 1 && outer2 <= 3); |
| SkASSERT(outer1 < outer2); |
| int mid1 = (1 + (2 >> outer2)) >> outer1; |
| SkASSERT(mid1 >= 0 && mid1 <= 2); |
| SkASSERT(outer1 != mid1 && outer2 != mid1); |
| int mid2 = outer1 ^ outer2 ^ mid1; |
| SkASSERT(mid2 >= 1 && mid2 <= 3); |
| SkASSERT(mid2 != outer1 && mid2 != outer2 && mid2 != mid1); |
| SkASSERT(((1 << outer1) | (1 << outer2) | (1 << mid1) | (1 << mid2)) == 0x0f); |
| SkScalar lineSlop = ptMax * ptMax * 0.00001f; // this multiplier is pulled out of the air |
| return pt_to_line(cubic[mid1], cubic[outer1], cubic[outer2]) <= lineSlop |
| && pt_to_line(cubic[mid2], cubic[outer1], cubic[outer2]) <= lineSlop; |
| } |
| |
| /* Given quad, see if all there points are in a line. |
| Return true if the inside point is close to a line connecting the outermost points. |
| |
| Find the outermost point by looking for the largest difference in X or Y. |
| Since the XOR of the indices is 3 (0 ^ 1 ^ 2) |
| the missing index equals: outer_1 ^ outer_2 ^ 3 |
| */ |
| static bool quad_in_line(const SkPoint quad[3]) { |
| SkScalar ptMax = -1; |
| int outer1 SK_INIT_TO_AVOID_WARNING; |
| int outer2 SK_INIT_TO_AVOID_WARNING; |
| for (int index = 0; index < 2; ++index) { |
| for (int inner = index + 1; inner < 3; ++inner) { |
| SkVector testDiff = quad[inner] - quad[index]; |
| SkScalar testMax = std::max(SkScalarAbs(testDiff.fX), SkScalarAbs(testDiff.fY)); |
| if (ptMax < testMax) { |
| outer1 = index; |
| outer2 = inner; |
| ptMax = testMax; |
| } |
| } |
| } |
| SkASSERT(outer1 >= 0 && outer1 <= 1); |
| SkASSERT(outer2 >= 1 && outer2 <= 2); |
| SkASSERT(outer1 < outer2); |
| int mid = outer1 ^ outer2 ^ 3; |
| const float kCurvatureSlop = 0.000005f; // this multiplier is pulled out of the air |
| SkScalar lineSlop = ptMax * ptMax * kCurvatureSlop; |
| return pt_to_line(quad[mid], quad[outer1], quad[outer2]) <= lineSlop; |
| } |
| |
| static bool conic_in_line(const SkConic& conic) { |
| return quad_in_line(conic.fPts); |
| } |
| |
| SkPathStroker::ReductionType SkPathStroker::CheckCubicLinear(const SkPoint cubic[4], |
| SkPoint reduction[3], const SkPoint** tangentPtPtr) { |
| bool degenerateAB = degenerate_vector(cubic[1] - cubic[0]); |
| bool degenerateBC = degenerate_vector(cubic[2] - cubic[1]); |
| bool degenerateCD = degenerate_vector(cubic[3] - cubic[2]); |
| if (degenerateAB & degenerateBC & degenerateCD) { |
| return kPoint_ReductionType; |
| } |
| if (degenerateAB + degenerateBC + degenerateCD == 2) { |
| return kLine_ReductionType; |
| } |
| if (!cubic_in_line(cubic)) { |
| *tangentPtPtr = degenerateAB ? &cubic[2] : &cubic[1]; |
| return kQuad_ReductionType; |
| } |
| SkScalar tValues[3]; |
| int count = SkFindCubicMaxCurvature(cubic, tValues); |
| int rCount = 0; |
| // Now loop over the t-values, and reject any that evaluate to either end-point |
| for (int index = 0; index < count; ++index) { |
| SkScalar t = tValues[index]; |
| if (0 >= t || t >= 1) { |
| continue; |
| } |
| SkEvalCubicAt(cubic, t, &reduction[rCount], nullptr, nullptr); |
| if (reduction[rCount] != cubic[0] && reduction[rCount] != cubic[3]) { |
| ++rCount; |
| } |
| } |
| if (rCount == 0) { |
| return kLine_ReductionType; |
| } |
| static_assert(kQuad_ReductionType + 1 == kDegenerate_ReductionType, "enum_out_of_whack"); |
| static_assert(kQuad_ReductionType + 2 == kDegenerate2_ReductionType, "enum_out_of_whack"); |
| static_assert(kQuad_ReductionType + 3 == kDegenerate3_ReductionType, "enum_out_of_whack"); |
| |
| return (ReductionType) (kQuad_ReductionType + rCount); |
| } |
| |
| SkPathStroker::ReductionType SkPathStroker::CheckConicLinear(const SkConic& conic, |
| SkPoint* reduction) { |
| bool degenerateAB = degenerate_vector(conic.fPts[1] - conic.fPts[0]); |
| bool degenerateBC = degenerate_vector(conic.fPts[2] - conic.fPts[1]); |
| if (degenerateAB & degenerateBC) { |
| return kPoint_ReductionType; |
| } |
| if (degenerateAB | degenerateBC) { |
| return kLine_ReductionType; |
| } |
| if (!conic_in_line(conic)) { |
| return kQuad_ReductionType; |
| } |
| // SkFindConicMaxCurvature would be a better solution, once we know how to |
| // implement it. Quad curvature is a reasonable substitute |
| SkScalar t = SkFindQuadMaxCurvature(conic.fPts); |
| if (0 == t) { |
| return kLine_ReductionType; |
| } |
| conic.evalAt(t, reduction, nullptr); |
| return kDegenerate_ReductionType; |
| } |
| |
| SkPathStroker::ReductionType SkPathStroker::CheckQuadLinear(const SkPoint quad[3], |
| SkPoint* reduction) { |
| bool degenerateAB = degenerate_vector(quad[1] - quad[0]); |
| bool degenerateBC = degenerate_vector(quad[2] - quad[1]); |
| if (degenerateAB & degenerateBC) { |
| return kPoint_ReductionType; |
| } |
| if (degenerateAB | degenerateBC) { |
| return kLine_ReductionType; |
| } |
| if (!quad_in_line(quad)) { |
| return kQuad_ReductionType; |
| } |
| SkScalar t = SkFindQuadMaxCurvature(quad); |
| if (0 == t || 1 == t) { |
| return kLine_ReductionType; |
| } |
| *reduction = SkEvalQuadAt(quad, t); |
| return kDegenerate_ReductionType; |
| } |
| |
| void SkPathStroker::conicTo(const SkPoint& pt1, const SkPoint& pt2, SkScalar weight) { |
| const SkConic conic(fPrevPt, pt1, pt2, weight); |
| SkPoint reduction; |
| ReductionType reductionType = CheckConicLinear(conic, &reduction); |
| if (kPoint_ReductionType == reductionType) { |
| /* If the stroke consists of a moveTo followed by a degenerate curve, treat it |
| as if it were followed by a zero-length line. Lines without length |
| can have square and round end caps. */ |
| this->lineTo(pt2); |
| return; |
| } |
| if (kLine_ReductionType == reductionType) { |
| this->lineTo(pt2); |
| return; |
| } |
| if (kDegenerate_ReductionType == reductionType) { |
| this->lineTo(reduction); |
| SkStrokerPriv::JoinProc saveJoiner = fJoiner; |
| fJoiner = SkStrokerPriv::JoinFactory(SkPaint::kRound_Join); |
| this->lineTo(pt2); |
| fJoiner = saveJoiner; |
| return; |
| } |
| SkASSERT(kQuad_ReductionType == reductionType); |
| SkVector normalAB, unitAB, normalBC, unitBC; |
| if (!this->preJoinTo(pt1, &normalAB, &unitAB, false)) { |
| this->lineTo(pt2); |
| return; |
| } |
| SkQuadConstruct quadPts; |
| this->init(kOuter_StrokeType, &quadPts, 0, 1); |
| (void) this->conicStroke(conic, &quadPts); |
| this->init(kInner_StrokeType, &quadPts, 0, 1); |
| (void) this->conicStroke(conic, &quadPts); |
| this->setConicEndNormal(conic, normalAB, unitAB, &normalBC, &unitBC); |
| this->postJoinTo(pt2, normalBC, unitBC); |
| } |
| |
| void SkPathStroker::quadTo(const SkPoint& pt1, const SkPoint& pt2) { |
| const SkPoint quad[3] = { fPrevPt, pt1, pt2 }; |
| SkPoint reduction; |
| ReductionType reductionType = CheckQuadLinear(quad, &reduction); |
| if (kPoint_ReductionType == reductionType) { |
| /* If the stroke consists of a moveTo followed by a degenerate curve, treat it |
| as if it were followed by a zero-length line. Lines without length |
| can have square and round end caps. */ |
| this->lineTo(pt2); |
| return; |
| } |
| if (kLine_ReductionType == reductionType) { |
| this->lineTo(pt2); |
| return; |
| } |
| if (kDegenerate_ReductionType == reductionType) { |
| this->lineTo(reduction); |
| SkStrokerPriv::JoinProc saveJoiner = fJoiner; |
| fJoiner = SkStrokerPriv::JoinFactory(SkPaint::kRound_Join); |
| this->lineTo(pt2); |
| fJoiner = saveJoiner; |
| return; |
| } |
| SkASSERT(kQuad_ReductionType == reductionType); |
| SkVector normalAB, unitAB, normalBC, unitBC; |
| if (!this->preJoinTo(pt1, &normalAB, &unitAB, false)) { |
| this->lineTo(pt2); |
| return; |
| } |
| SkQuadConstruct quadPts; |
| this->init(kOuter_StrokeType, &quadPts, 0, 1); |
| (void) this->quadStroke(quad, &quadPts); |
| this->init(kInner_StrokeType, &quadPts, 0, 1); |
| (void) this->quadStroke(quad, &quadPts); |
| this->setQuadEndNormal(quad, normalAB, unitAB, &normalBC, &unitBC); |
| |
| this->postJoinTo(pt2, normalBC, unitBC); |
| } |
| |
| // Given a point on the curve and its derivative, scale the derivative by the radius, and |
| // compute the perpendicular point and its tangent. |
| void SkPathStroker::setRayPts(const SkPoint& tPt, SkVector* dxy, SkPoint* onPt, |
| SkPoint* tangent) const { |
| if (!dxy->setLength(fRadius)) { |
| dxy->set(fRadius, 0); |
| } |
| SkScalar axisFlip = SkIntToScalar(fStrokeType); // go opposite ways for outer, inner |
| onPt->fX = tPt.fX + axisFlip * dxy->fY; |
| onPt->fY = tPt.fY - axisFlip * dxy->fX; |
| if (tangent) { |
| tangent->fX = onPt->fX + dxy->fX; |
| tangent->fY = onPt->fY + dxy->fY; |
| } |
| } |
| |
| // Given a conic and t, return the point on curve, its perpendicular, and the perpendicular tangent. |
| // Returns false if the perpendicular could not be computed (because the derivative collapsed to 0) |
| void SkPathStroker::conicPerpRay(const SkConic& conic, SkScalar t, SkPoint* tPt, SkPoint* onPt, |
| SkPoint* tangent) const { |
| SkVector dxy; |
| conic.evalAt(t, tPt, &dxy); |
| if (dxy.fX == 0 && dxy.fY == 0) { |
| dxy = conic.fPts[2] - conic.fPts[0]; |
| } |
| this->setRayPts(*tPt, &dxy, onPt, tangent); |
| } |
| |
| // Given a conic and a t range, find the start and end if they haven't been found already. |
| void SkPathStroker::conicQuadEnds(const SkConic& conic, SkQuadConstruct* quadPts) const { |
| if (!quadPts->fStartSet) { |
| SkPoint conicStartPt; |
| this->conicPerpRay(conic, quadPts->fStartT, &conicStartPt, &quadPts->fQuad[0], |
| &quadPts->fTangentStart); |
| quadPts->fStartSet = true; |
| } |
| if (!quadPts->fEndSet) { |
| SkPoint conicEndPt; |
| this->conicPerpRay(conic, quadPts->fEndT, &conicEndPt, &quadPts->fQuad[2], |
| &quadPts->fTangentEnd); |
| quadPts->fEndSet = true; |
| } |
| } |
| |
| |
| // Given a cubic and t, return the point on curve, its perpendicular, and the perpendicular tangent. |
| void SkPathStroker::cubicPerpRay(const SkPoint cubic[4], SkScalar t, SkPoint* tPt, SkPoint* onPt, |
| SkPoint* tangent) const { |
| SkVector dxy; |
| SkPoint chopped[7]; |
| SkEvalCubicAt(cubic, t, tPt, &dxy, nullptr); |
| if (dxy.fX == 0 && dxy.fY == 0) { |
| const SkPoint* cPts = cubic; |
| if (SkScalarNearlyZero(t)) { |
| dxy = cubic[2] - cubic[0]; |
| } else if (SkScalarNearlyZero(1 - t)) { |
| dxy = cubic[3] - cubic[1]; |
| } else { |
| // If the cubic inflection falls on the cusp, subdivide the cubic |
| // to find the tangent at that point. |
| SkChopCubicAt(cubic, chopped, t); |
| dxy = chopped[3] - chopped[2]; |
| if (dxy.fX == 0 && dxy.fY == 0) { |
| dxy = chopped[3] - chopped[1]; |
| cPts = chopped; |
| } |
| } |
| if (dxy.fX == 0 && dxy.fY == 0) { |
| dxy = cPts[3] - cPts[0]; |
| } |
| } |
| setRayPts(*tPt, &dxy, onPt, tangent); |
| } |
| |
| // Given a cubic and a t range, find the start and end if they haven't been found already. |
| void SkPathStroker::cubicQuadEnds(const SkPoint cubic[4], SkQuadConstruct* quadPts) { |
| if (!quadPts->fStartSet) { |
| SkPoint cubicStartPt; |
| this->cubicPerpRay(cubic, quadPts->fStartT, &cubicStartPt, &quadPts->fQuad[0], |
| &quadPts->fTangentStart); |
| quadPts->fStartSet = true; |
| } |
| if (!quadPts->fEndSet) { |
| SkPoint cubicEndPt; |
| this->cubicPerpRay(cubic, quadPts->fEndT, &cubicEndPt, &quadPts->fQuad[2], |
| &quadPts->fTangentEnd); |
| quadPts->fEndSet = true; |
| } |
| } |
| |
| void SkPathStroker::cubicQuadMid(const SkPoint cubic[4], const SkQuadConstruct* quadPts, |
| SkPoint* mid) const { |
| SkPoint cubicMidPt; |
| this->cubicPerpRay(cubic, quadPts->fMidT, &cubicMidPt, mid, nullptr); |
| } |
| |
| // Given a quad and t, return the point on curve, its perpendicular, and the perpendicular tangent. |
| void SkPathStroker::quadPerpRay(const SkPoint quad[3], SkScalar t, SkPoint* tPt, SkPoint* onPt, |
| SkPoint* tangent) const { |
| SkVector dxy; |
| SkEvalQuadAt(quad, t, tPt, &dxy); |
| if (dxy.fX == 0 && dxy.fY == 0) { |
| dxy = quad[2] - quad[0]; |
| } |
| setRayPts(*tPt, &dxy, onPt, tangent); |
| } |
| |
| // Find the intersection of the stroke tangents to construct a stroke quad. |
| // Return whether the stroke is a degenerate (a line), a quad, or must be split. |
| // Optionally compute the quad's control point. |
| SkPathStroker::ResultType SkPathStroker::intersectRay(SkQuadConstruct* quadPts, |
| IntersectRayType intersectRayType STROKER_DEBUG_PARAMS(int depth)) const { |
| const SkPoint& start = quadPts->fQuad[0]; |
| const SkPoint& end = quadPts->fQuad[2]; |
| SkVector aLen = quadPts->fTangentStart - start; |
| SkVector bLen = quadPts->fTangentEnd - end; |
| /* Slopes match when denom goes to zero: |
| axLen / ayLen == bxLen / byLen |
| (ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen |
| byLen * axLen == ayLen * bxLen |
| byLen * axLen - ayLen * bxLen ( == denom ) |
| */ |
| SkScalar denom = aLen.cross(bLen); |
| if (denom == 0 || !SkScalarIsFinite(denom)) { |
| quadPts->fOppositeTangents = aLen.dot(bLen) < 0; |
| return STROKER_RESULT(kDegenerate_ResultType, depth, quadPts, "denom == 0"); |
| } |
| quadPts->fOppositeTangents = false; |
| SkVector ab0 = start - end; |
| SkScalar numerA = bLen.cross(ab0); |
| SkScalar numerB = aLen.cross(ab0); |
| if ((numerA >= 0) == (numerB >= 0)) { // if the control point is outside the quad ends |
| // if the perpendicular distances from the quad points to the opposite tangent line |
| // are small, a straight line is good enough |
| SkScalar dist1 = pt_to_line(start, end, quadPts->fTangentEnd); |
| SkScalar dist2 = pt_to_line(end, start, quadPts->fTangentStart); |
| if (std::max(dist1, dist2) <= fInvResScaleSquared) { |
| return STROKER_RESULT(kDegenerate_ResultType, depth, quadPts, |
| "std::max(dist1=%g, dist2=%g) <= fInvResScaleSquared", dist1, dist2); |
| } |
| return STROKER_RESULT(kSplit_ResultType, depth, quadPts, |
| "(numerA=%g >= 0) == (numerB=%g >= 0)", numerA, numerB); |
| } |
| // check to see if the denominator is teeny relative to the numerator |
| // if the offset by one will be lost, the ratio is too large |
| numerA /= denom; |
| bool validDivide = numerA > numerA - 1; |
| if (validDivide) { |
| if (kCtrlPt_RayType == intersectRayType) { |
| SkPoint* ctrlPt = &quadPts->fQuad[1]; |
| // the intersection of the tangents need not be on the tangent segment |
| // so 0 <= numerA <= 1 is not necessarily true |
| ctrlPt->fX = start.fX * (1 - numerA) + quadPts->fTangentStart.fX * numerA; |
| ctrlPt->fY = start.fY * (1 - numerA) + quadPts->fTangentStart.fY * numerA; |
| } |
| return STROKER_RESULT(kQuad_ResultType, depth, quadPts, |
| "(numerA=%g >= 0) != (numerB=%g >= 0)", numerA, numerB); |
| } |
| quadPts->fOppositeTangents = aLen.dot(bLen) < 0; |
| // if the lines are parallel, straight line is good enough |
| return STROKER_RESULT(kDegenerate_ResultType, depth, quadPts, |
| "SkScalarNearlyZero(denom=%g)", denom); |
| } |
| |
| // Given a cubic and a t-range, determine if the stroke can be described by a quadratic. |
| SkPathStroker::ResultType SkPathStroker::tangentsMeet(const SkPoint cubic[4], |
| SkQuadConstruct* quadPts) { |
| this->cubicQuadEnds(cubic, quadPts); |
| return this->intersectRay(quadPts, kResultType_RayType STROKER_DEBUG_PARAMS(fRecursionDepth)); |
| } |
| |
| // Intersect the line with the quad and return the t values on the quad where the line crosses. |
| static int intersect_quad_ray(const SkPoint line[2], const SkPoint quad[3], SkScalar roots[2]) { |
| SkVector vec = line[1] - line[0]; |
| SkScalar r[3]; |
| for (int n = 0; n < 3; ++n) { |
| r[n] = (quad[n].fY - line[0].fY) * vec.fX - (quad[n].fX - line[0].fX) * vec.fY; |
| } |
| SkScalar A = r[2]; |
| SkScalar B = r[1]; |
| SkScalar C = r[0]; |
| A += C - 2 * B; // A = a - 2*b + c |
| B -= C; // B = -(b - c) |
| return SkFindUnitQuadRoots(A, 2 * B, C, roots); |
| } |
| |
| // Return true if the point is close to the bounds of the quad. This is used as a quick reject. |
| bool SkPathStroker::ptInQuadBounds(const SkPoint quad[3], const SkPoint& pt) const { |
| SkScalar xMin = std::min(std::min(quad[0].fX, quad[1].fX), quad[2].fX); |
| if (pt.fX + fInvResScale < xMin) { |
| return false; |
| } |
| SkScalar xMax = std::max(std::max(quad[0].fX, quad[1].fX), quad[2].fX); |
| if (pt.fX - fInvResScale > xMax) { |
| return false; |
| } |
| SkScalar yMin = std::min(std::min(quad[0].fY, quad[1].fY), quad[2].fY); |
| if (pt.fY + fInvResScale < yMin) { |
| return false; |
| } |
| SkScalar yMax = std::max(std::max(quad[0].fY, quad[1].fY), quad[2].fY); |
| if (pt.fY - fInvResScale > yMax) { |
| return false; |
| } |
| return true; |
| } |
| |
| static bool points_within_dist(const SkPoint& nearPt, const SkPoint& farPt, SkScalar limit) { |
| return SkPointPriv::DistanceToSqd(nearPt, farPt) <= limit * limit; |
| } |
| |
| static bool sharp_angle(const SkPoint quad[3]) { |
| SkVector smaller = quad[1] - quad[0]; |
| SkVector larger = quad[1] - quad[2]; |
| SkScalar smallerLen = SkPointPriv::LengthSqd(smaller); |
| SkScalar largerLen = SkPointPriv::LengthSqd(larger); |
| if (smallerLen > largerLen) { |
| using std::swap; |
| swap(smaller, larger); |
| largerLen = smallerLen; |
| } |
| if (!smaller.setLength(largerLen)) { |
| return false; |
| } |
| SkScalar dot = smaller.dot(larger); |
| return dot > 0; |
| } |
| |
| SkPathStroker::ResultType SkPathStroker::strokeCloseEnough(const SkPoint stroke[3], |
| const SkPoint ray[2], SkQuadConstruct* quadPts STROKER_DEBUG_PARAMS(int depth)) const { |
| SkPoint strokeMid = SkEvalQuadAt(stroke, SK_ScalarHalf); |
| // measure the distance from the curve to the quad-stroke midpoint, compare to radius |
| if (points_within_dist(ray[0], strokeMid, fInvResScale)) { // if the difference is small |
| if (sharp_angle(quadPts->fQuad)) { |
| return STROKER_RESULT(kSplit_ResultType, depth, quadPts, |
| "sharp_angle (1) =%g,%g, %g,%g, %g,%g", |
| quadPts->fQuad[0].fX, quadPts->fQuad[0].fY, |
| quadPts->fQuad[1].fX, quadPts->fQuad[1].fY, |
| quadPts->fQuad[2].fX, quadPts->fQuad[2].fY); |
| } |
| return STROKER_RESULT(kQuad_ResultType, depth, quadPts, |
| "points_within_dist(ray[0]=%g,%g, strokeMid=%g,%g, fInvResScale=%g)", |
| ray[0].fX, ray[0].fY, strokeMid.fX, strokeMid.fY, fInvResScale); |
| } |
| // measure the distance to quad's bounds (quick reject) |
| // an alternative : look for point in triangle |
| if (!ptInQuadBounds(stroke, ray[0])) { // if far, subdivide |
| return STROKER_RESULT(kSplit_ResultType, depth, quadPts, |
| "!pt_in_quad_bounds(stroke=(%g,%g %g,%g %g,%g), ray[0]=%g,%g)", |
| stroke[0].fX, stroke[0].fY, stroke[1].fX, stroke[1].fY, stroke[2].fX, stroke[2].fY, |
| ray[0].fX, ray[0].fY); |
| } |
| // measure the curve ray distance to the quad-stroke |
| SkScalar roots[2]; |
| int rootCount = intersect_quad_ray(ray, stroke, roots); |
| if (rootCount != 1) { |
| return STROKER_RESULT(kSplit_ResultType, depth, quadPts, |
| "rootCount=%d != 1", rootCount); |
| } |
| SkPoint quadPt = SkEvalQuadAt(stroke, roots[0]); |
| SkScalar error = fInvResScale * (SK_Scalar1 - SkScalarAbs(roots[0] - 0.5f) * 2); |
| if (points_within_dist(ray[0], quadPt, error)) { // if the difference is small, we're done |
| if (sharp_angle(quadPts->fQuad)) { |
| return STROKER_RESULT(kSplit_ResultType, depth, quadPts, |
| "sharp_angle (2) =%g,%g, %g,%g, %g,%g", |
| quadPts->fQuad[0].fX, quadPts->fQuad[0].fY, |
| quadPts->fQuad[1].fX, quadPts->fQuad[1].fY, |
| quadPts->fQuad[2].fX, quadPts->fQuad[2].fY); |
| } |
| return STROKER_RESULT(kQuad_ResultType, depth, quadPts, |
| "points_within_dist(ray[0]=%g,%g, quadPt=%g,%g, error=%g)", |
| ray[0].fX, ray[0].fY, quadPt.fX, quadPt.fY, error); |
| } |
| // otherwise, subdivide |
| return STROKER_RESULT(kSplit_ResultType, depth, quadPts, "%s", "fall through"); |
| } |
| |
| SkPathStroker::ResultType SkPathStroker::compareQuadCubic(const SkPoint cubic[4], |
| SkQuadConstruct* quadPts) { |
| // get the quadratic approximation of the stroke |
| this->cubicQuadEnds(cubic, quadPts); |
| ResultType resultType = this->intersectRay(quadPts, kCtrlPt_RayType |
| STROKER_DEBUG_PARAMS(fRecursionDepth) ); |
| if (resultType != kQuad_ResultType) { |
| return resultType; |
| } |
| // project a ray from the curve to the stroke |
| SkPoint ray[2]; // points near midpoint on quad, midpoint on cubic |
| this->cubicPerpRay(cubic, quadPts->fMidT, &ray[1], &ray[0], nullptr); |
| return this->strokeCloseEnough(quadPts->fQuad, ray, quadPts |
| STROKER_DEBUG_PARAMS(fRecursionDepth)); |
| } |
| |
| SkPathStroker::ResultType SkPathStroker::compareQuadConic(const SkConic& conic, |
| SkQuadConstruct* quadPts) const { |
| // get the quadratic approximation of the stroke |
| this->conicQuadEnds(conic, quadPts); |
| ResultType resultType = this->intersectRay(quadPts, kCtrlPt_RayType |
| STROKER_DEBUG_PARAMS(fRecursionDepth) ); |
| if (resultType != kQuad_ResultType) { |
| return resultType; |
| } |
| // project a ray from the curve to the stroke |
| SkPoint ray[2]; // points near midpoint on quad, midpoint on conic |
| this->conicPerpRay(conic, quadPts->fMidT, &ray[1], &ray[0], nullptr); |
| return this->strokeCloseEnough(quadPts->fQuad, ray, quadPts |
| STROKER_DEBUG_PARAMS(fRecursionDepth)); |
| } |
| |
| SkPathStroker::ResultType SkPathStroker::compareQuadQuad(const SkPoint quad[3], |
| SkQuadConstruct* quadPts) { |
| // get the quadratic approximation of the stroke |
| if (!quadPts->fStartSet) { |
| SkPoint quadStartPt; |
| this->quadPerpRay(quad, quadPts->fStartT, &quadStartPt, &quadPts->fQuad[0], |
| &quadPts->fTangentStart); |
| quadPts->fStartSet = true; |
| } |
| if (!quadPts->fEndSet) { |
| SkPoint quadEndPt; |
| this->quadPerpRay(quad, quadPts->fEndT, &quadEndPt, &quadPts->fQuad[2], |
| &quadPts->fTangentEnd); |
| quadPts->fEndSet = true; |
| } |
| ResultType resultType = this->intersectRay(quadPts, kCtrlPt_RayType |
| STROKER_DEBUG_PARAMS(fRecursionDepth)); |
| if (resultType != kQuad_ResultType) { |
| return resultType; |
| } |
| // project a ray from the curve to the stroke |
| SkPoint ray[2]; |
| this->quadPerpRay(quad, quadPts->fMidT, &ray[1], &ray[0], nullptr); |
| return this->strokeCloseEnough(quadPts->fQuad, ray, quadPts |
| STROKER_DEBUG_PARAMS(fRecursionDepth)); |
| } |
| |
| void SkPathStroker::addDegenerateLine(const SkQuadConstruct* quadPts) { |
| const SkPoint* quad = quadPts->fQuad; |
| SkPath* path = fStrokeType == kOuter_StrokeType ? &fOuter : &fInner; |
| path->lineTo(quad[2].fX, quad[2].fY); |
| } |
| |
| bool SkPathStroker::cubicMidOnLine(const SkPoint cubic[4], const SkQuadConstruct* quadPts) const { |
| SkPoint strokeMid; |
| this->cubicQuadMid(cubic, quadPts, &strokeMid); |
| SkScalar dist = pt_to_line(strokeMid, quadPts->fQuad[0], quadPts->fQuad[2]); |
| return dist < fInvResScaleSquared; |
| } |
| |
| bool SkPathStroker::cubicStroke(const SkPoint cubic[4], SkQuadConstruct* quadPts) { |
| if (!fFoundTangents) { |
| ResultType resultType = this->tangentsMeet(cubic, quadPts); |
| if (kQuad_ResultType != resultType) { |
| if ((kDegenerate_ResultType == resultType |
| || points_within_dist(quadPts->fQuad[0], quadPts->fQuad[2], |
| fInvResScale)) && cubicMidOnLine(cubic, quadPts)) { |
| addDegenerateLine(quadPts); |
| DEBUG_CUBIC_RECURSION_TRACK_DEPTH(fRecursionDepth); |
| return true; |
| } |
| } else { |
| fFoundTangents = true; |
| } |
| } |
| if (fFoundTangents) { |
| ResultType resultType = this->compareQuadCubic(cubic, quadPts); |
| if (kQuad_ResultType == resultType) { |
| SkPath* path = fStrokeType == kOuter_StrokeType ? &fOuter : &fInner; |
| const SkPoint* stroke = quadPts->fQuad; |
| path->quadTo(stroke[1].fX, stroke[1].fY, stroke[2].fX, stroke[2].fY); |
| DEBUG_CUBIC_RECURSION_TRACK_DEPTH(fRecursionDepth); |
| return true; |
| } |
| if (kDegenerate_ResultType == resultType) { |
| if (!quadPts->fOppositeTangents) { |
| addDegenerateLine(quadPts); |
| DEBUG_CUBIC_RECURSION_TRACK_DEPTH(fRecursionDepth); |
| return true; |
| } |
| } |
| } |
| if (!SkScalarIsFinite(quadPts->fQuad[2].fX) || !SkScalarIsFinite(quadPts->fQuad[2].fY)) { |
| DEBUG_CUBIC_RECURSION_TRACK_DEPTH(fRecursionDepth); |
| return false; // just abort if projected quad isn't representable |
| } |
| #if QUAD_STROKE_APPROX_EXTENDED_DEBUGGING |
| SkDEBUGCODE(gMaxRecursion[fFoundTangents] = std::max(gMaxRecursion[fFoundTangents], |
| fRecursionDepth + 1)); |
| #endif |
| if (++fRecursionDepth > kRecursiveLimits[fFoundTangents]) { |
| DEBUG_CUBIC_RECURSION_TRACK_DEPTH(fRecursionDepth); |
| return false; // just abort if projected quad isn't representable |
| } |
| SkQuadConstruct half; |
| if (!half.initWithStart(quadPts)) { |
| addDegenerateLine(quadPts); |
| DEBUG_CUBIC_RECURSION_TRACK_DEPTH(fRecursionDepth); |
| --fRecursionDepth; |
| return true; |
| } |
| if (!this->cubicStroke(cubic, &half)) { |
| return false; |
| } |
| if (!half.initWithEnd(quadPts)) { |
| addDegenerateLine(quadPts); |
| DEBUG_CUBIC_RECURSION_TRACK_DEPTH(fRecursionDepth); |
| --fRecursionDepth; |
| return true; |
| } |
| if (!this->cubicStroke(cubic, &half)) { |
| return false; |
| } |
| --fRecursionDepth; |
| return true; |
| } |
| |
| bool SkPathStroker::conicStroke(const SkConic& conic, SkQuadConstruct* quadPts) { |
| ResultType resultType = this->compareQuadConic(conic, quadPts); |
| if (kQuad_ResultType == resultType) { |
| const SkPoint* stroke = quadPts->fQuad; |
| SkPath* path = fStrokeType == kOuter_StrokeType ? &fOuter : &fInner; |
| path->quadTo(stroke[1].fX, stroke[1].fY, stroke[2].fX, stroke[2].fY); |
| return true; |
| } |
| if (kDegenerate_ResultType == resultType) { |
| addDegenerateLine(quadPts); |
| return true; |
| } |
| #if QUAD_STROKE_APPROX_EXTENDED_DEBUGGING |
| SkDEBUGCODE(gMaxRecursion[kConic_RecursiveLimit] = std::max(gMaxRecursion[kConic_RecursiveLimit], |
| fRecursionDepth + 1)); |
| #endif |
| if (++fRecursionDepth > kRecursiveLimits[kConic_RecursiveLimit]) { |
| return false; // just abort if projected quad isn't representable |
| } |
| SkQuadConstruct half; |
| (void) half.initWithStart(quadPts); |
| if (!this->conicStroke(conic, &half)) { |
| return false; |
| } |
| (void) half.initWithEnd(quadPts); |
| if (!this->conicStroke(conic, &half)) { |
| return false; |
| } |
| --fRecursionDepth; |
| return true; |
| } |
| |
| bool SkPathStroker::quadStroke(const SkPoint quad[3], SkQuadConstruct* quadPts) { |
| ResultType resultType = this->compareQuadQuad(quad, quadPts); |
| if (kQuad_ResultType == resultType) { |
| const SkPoint* stroke = quadPts->fQuad; |
| SkPath* path = fStrokeType == kOuter_StrokeType ? &fOuter : &fInner; |
| path->quadTo(stroke[1].fX, stroke[1].fY, stroke[2].fX, stroke[2].fY); |
| return true; |
| } |
| if (kDegenerate_ResultType == resultType) { |
| addDegenerateLine(quadPts); |
| return true; |
| } |
| #if QUAD_STROKE_APPROX_EXTENDED_DEBUGGING |
| SkDEBUGCODE(gMaxRecursion[kQuad_RecursiveLimit] = std::max(gMaxRecursion[kQuad_RecursiveLimit], |
| fRecursionDepth + 1)); |
| #endif |
| if (++fRecursionDepth > kRecursiveLimits[kQuad_RecursiveLimit]) { |
| return false; // just abort if projected quad isn't representable |
| } |
| SkQuadConstruct half; |
| (void) half.initWithStart(quadPts); |
| if (!this->quadStroke(quad, &half)) { |
| return false; |
| } |
| (void) half.initWithEnd(quadPts); |
| if (!this->quadStroke(quad, &half)) { |
| return false; |
| } |
| --fRecursionDepth; |
| return true; |
| } |
| |
| void SkPathStroker::cubicTo(const SkPoint& pt1, const SkPoint& pt2, |
| const SkPoint& pt3) { |
| const SkPoint cubic[4] = { fPrevPt, pt1, pt2, pt3 }; |
| SkPoint reduction[3]; |
| const SkPoint* tangentPt; |
| ReductionType reductionType = CheckCubicLinear(cubic, reduction, &tangentPt); |
| if (kPoint_ReductionType == reductionType) { |
| /* If the stroke consists of a moveTo followed by a degenerate curve, treat it |
| as if it were followed by a zero-length line. Lines without length |
| can have square and round end caps. */ |
| this->lineTo(pt3); |
| return; |
| } |
| if (kLine_ReductionType == reductionType) { |
| this->lineTo(pt3); |
| return; |
| } |
| if (kDegenerate_ReductionType <= reductionType && kDegenerate3_ReductionType >= reductionType) { |
| this->lineTo(reduction[0]); |
| SkStrokerPriv::JoinProc saveJoiner = fJoiner; |
| fJoiner = SkStrokerPriv::JoinFactory(SkPaint::kRound_Join); |
| if (kDegenerate2_ReductionType <= reductionType) { |
| this->lineTo(reduction[1]); |
| } |
| if (kDegenerate3_ReductionType == reductionType) { |
| this->lineTo(reduction[2]); |
| } |
| this->lineTo(pt3); |
| fJoiner = saveJoiner; |
| return; |
| } |
| SkASSERT(kQuad_ReductionType == reductionType); |
| SkVector normalAB, unitAB, normalCD, unitCD; |
| if (!this->preJoinTo(*tangentPt, &normalAB, &unitAB, false)) { |
| this->lineTo(pt3); |
| return; |
| } |
| SkScalar tValues[2]; |
| int count = SkFindCubicInflections(cubic, tValues); |
| SkScalar lastT = 0; |
| for (int index = 0; index <= count; ++index) { |
| SkScalar nextT = index < count ? tValues[index] : 1; |
| SkQuadConstruct quadPts; |
| this->init(kOuter_StrokeType, &quadPts, lastT, nextT); |
| (void) this->cubicStroke(cubic, &quadPts); |
| this->init(kInner_StrokeType, &quadPts, lastT, nextT); |
| (void) this->cubicStroke(cubic, &quadPts); |
| lastT = nextT; |
| } |
| SkScalar cusp = SkFindCubicCusp(cubic); |
| if (cusp > 0) { |
| SkPoint cuspLoc; |
| SkEvalCubicAt(cubic, cusp, &cuspLoc, nullptr, nullptr); |
| fCusper.addCircle(cuspLoc.fX, cuspLoc.fY, fRadius); |
| } |
| // emit the join even if one stroke succeeded but the last one failed |
| // this avoids reversing an inner stroke with a partial path followed by another moveto |
| this->setCubicEndNormal(cubic, normalAB, unitAB, &normalCD, &unitCD); |
| |
| this->postJoinTo(pt3, normalCD, unitCD); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| #include "src/core/SkPaintDefaults.h" |
| |
| SkStroke::SkStroke() { |
| fWidth = SK_Scalar1; |
| fMiterLimit = SkPaintDefaults_MiterLimit; |
| fResScale = 1; |
| fCap = SkPaint::kDefault_Cap; |
| fJoin = SkPaint::kDefault_Join; |
| fDoFill = false; |
| } |
| |
| SkStroke::SkStroke(const SkPaint& p) { |
| fWidth = p.getStrokeWidth(); |
| fMiterLimit = p.getStrokeMiter(); |
| fResScale = 1; |
| fCap = (uint8_t)p.getStrokeCap(); |
| fJoin = (uint8_t)p.getStrokeJoin(); |
| fDoFill = SkToU8(p.getStyle() == SkPaint::kStrokeAndFill_Style); |
| } |
| |
| SkStroke::SkStroke(const SkPaint& p, SkScalar width) { |
| fWidth = width; |
| fMiterLimit = p.getStrokeMiter(); |
| fResScale = 1; |
| fCap = (uint8_t)p.getStrokeCap(); |
| fJoin = (uint8_t)p.getStrokeJoin(); |
| fDoFill = SkToU8(p.getStyle() == SkPaint::kStrokeAndFill_Style); |
| } |
| |
| void SkStroke::setWidth(SkScalar width) { |
| SkASSERT(width >= 0); |
| fWidth = width; |
| } |
| |
| void SkStroke::setMiterLimit(SkScalar miterLimit) { |
| SkASSERT(miterLimit >= 0); |
| fMiterLimit = miterLimit; |
| } |
| |
| void SkStroke::setCap(SkPaint::Cap cap) { |
| SkASSERT((unsigned)cap < SkPaint::kCapCount); |
| fCap = SkToU8(cap); |
| } |
| |
| void SkStroke::setJoin(SkPaint::Join join) { |
| SkASSERT((unsigned)join < SkPaint::kJoinCount); |
| fJoin = SkToU8(join); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| // If src==dst, then we use a tmp path to record the stroke, and then swap |
| // its contents with src when we're done. |
| class AutoTmpPath { |
| public: |
| AutoTmpPath(const SkPath& src, SkPath** dst) : fSrc(src) { |
| if (&src == *dst) { |
| *dst = &fTmpDst; |
| fSwapWithSrc = true; |
| } else { |
| (*dst)->reset(); |
| fSwapWithSrc = false; |
| } |
| } |
| |
| ~AutoTmpPath() { |
| if (fSwapWithSrc) { |
| fTmpDst.swap(*const_cast<SkPath*>(&fSrc)); |
| } |
| } |
| |
| private: |
| SkPath fTmpDst; |
| const SkPath& fSrc; |
| bool fSwapWithSrc; |
| }; |
| |
| void SkStroke::strokePath(const SkPath& src, SkPath* dst) const { |
| SkASSERT(dst); |
| |
| SkScalar radius = SkScalarHalf(fWidth); |
| |
| AutoTmpPath tmp(src, &dst); |
| |
| if (radius <= 0) { |
| return; |
| } |
| |
| // If src is really a rect, call our specialty strokeRect() method |
| { |
| SkRect rect; |
| bool isClosed = false; |
| SkPathDirection dir; |
| if (src.isRect(&rect, &isClosed, &dir) && isClosed) { |
| this->strokeRect(rect, dst, dir); |
| // our answer should preserve the inverseness of the src |
| if (src.isInverseFillType()) { |
| SkASSERT(!dst->isInverseFillType()); |
| dst->toggleInverseFillType(); |
| } |
| return; |
| } |
| } |
| |
| // We can always ignore centers for stroke and fill convex line-only paths |
| // TODO: remove the line-only restriction |
| bool ignoreCenter = fDoFill && (src.getSegmentMasks() == SkPath::kLine_SegmentMask) && |
| src.isLastContourClosed() && src.isConvex(); |
| |
| SkPathStroker stroker(src, radius, fMiterLimit, this->getCap(), this->getJoin(), |
| fResScale, ignoreCenter); |
| SkPath::Iter iter(src, false); |
| SkPath::Verb lastSegment = SkPath::kMove_Verb; |
| |
| for (;;) { |
| SkPoint pts[4]; |
| switch (iter.next(pts)) { |
| case SkPath::kMove_Verb: |
| stroker.moveTo(pts[0]); |
| break; |
| case SkPath::kLine_Verb: |
| stroker.lineTo(pts[1], &iter); |
| lastSegment = SkPath::kLine_Verb; |
| break; |
| case SkPath::kQuad_Verb: |
| stroker.quadTo(pts[1], pts[2]); |
| lastSegment = SkPath::kQuad_Verb; |
| break; |
| case SkPath::kConic_Verb: { |
| stroker.conicTo(pts[1], pts[2], iter.conicWeight()); |
| lastSegment = SkPath::kConic_Verb; |
| } break; |
| case SkPath::kCubic_Verb: |
| stroker.cubicTo(pts[1], pts[2], pts[3]); |
| lastSegment = SkPath::kCubic_Verb; |
| break; |
| case SkPath::kClose_Verb: |
| if (SkPaint::kButt_Cap != this->getCap()) { |
| /* If the stroke consists of a moveTo followed by a close, treat it |
| as if it were followed by a zero-length line. Lines without length |
| can have square and round end caps. */ |
| if (stroker.hasOnlyMoveTo()) { |
| stroker.lineTo(stroker.moveToPt()); |
| goto ZERO_LENGTH; |
| } |
| /* If the stroke consists of a moveTo followed by one or more zero-length |
| verbs, then followed by a close, treat is as if it were followed by a |
| zero-length line. Lines without length can have square & round end caps. */ |
| if (stroker.isCurrentContourEmpty()) { |
| ZERO_LENGTH: |
| lastSegment = SkPath::kLine_Verb; |
| break; |
| } |
| } |
| stroker.close(lastSegment == SkPath::kLine_Verb); |
| break; |
| case SkPath::kDone_Verb: |
| goto DONE; |
| } |
| } |
| DONE: |
| stroker.done(dst, lastSegment == SkPath::kLine_Verb); |
| |
| if (fDoFill && !ignoreCenter) { |
| if (SkPathPriv::ComputeFirstDirection(src) == SkPathFirstDirection::kCCW) { |
| dst->reverseAddPath(src); |
| } else { |
| dst->addPath(src); |
| } |
| } else { |
| // Seems like we can assume that a 2-point src would always result in |
| // a convex stroke, but testing has proved otherwise. |
| // TODO: fix the stroker to make this assumption true (without making |
| // it slower that the work that will be done in computeConvexity()) |
| #if 0 |
| // this test results in a non-convex stroke :( |
| static void test(SkCanvas* canvas) { |
| SkPoint pts[] = { 146.333328, 192.333328, 300.333344, 293.333344 }; |
| SkPaint paint; |
| paint.setStrokeWidth(7); |
| paint.setStrokeCap(SkPaint::kRound_Cap); |
| canvas->drawLine(pts[0].fX, pts[0].fY, pts[1].fX, pts[1].fY, paint); |
| } |
| #endif |
| #if 0 |
| if (2 == src.countPoints()) { |
| dst->setIsConvex(true); |
| } |
| #endif |
| } |
| |
| // our answer should preserve the inverseness of the src |
| if (src.isInverseFillType()) { |
| SkASSERT(!dst->isInverseFillType()); |
| dst->toggleInverseFillType(); |
| } |
| } |
| |
| static SkPathDirection reverse_direction(SkPathDirection dir) { |
| static const SkPathDirection gOpposite[] = { SkPathDirection::kCCW, SkPathDirection::kCW }; |
| return gOpposite[(int)dir]; |
| } |
| |
| static void addBevel(SkPath* path, const SkRect& r, const SkRect& outer, SkPathDirection dir) { |
| SkPoint pts[8]; |
| |
| if (SkPathDirection::kCW == dir) { |
| pts[0].set(r.fLeft, outer.fTop); |
| pts[1].set(r.fRight, outer.fTop); |
| pts[2].set(outer.fRight, r.fTop); |
| pts[3].set(outer.fRight, r.fBottom); |
| pts[4].set(r.fRight, outer.fBottom); |
| pts[5].set(r.fLeft, outer.fBottom); |
| pts[6].set(outer.fLeft, r.fBottom); |
| pts[7].set(outer.fLeft, r.fTop); |
| } else { |
| pts[7].set(r.fLeft, outer.fTop); |
| pts[6].set(r.fRight, outer.fTop); |
| pts[5].set(outer.fRight, r.fTop); |
| pts[4].set(outer.fRight, r.fBottom); |
| pts[3].set(r.fRight, outer.fBottom); |
| pts[2].set(r.fLeft, outer.fBottom); |
| pts[1].set(outer.fLeft, r.fBottom); |
| pts[0].set(outer.fLeft, r.fTop); |
| } |
| path->addPoly(pts, 8, true); |
| } |
| |
| void SkStroke::strokeRect(const SkRect& origRect, SkPath* dst, |
| SkPathDirection dir) const { |
| SkASSERT(dst != nullptr); |
| dst->reset(); |
| |
| SkScalar radius = SkScalarHalf(fWidth); |
| if (radius <= 0) { |
| return; |
| } |
| |
| SkScalar rw = origRect.width(); |
| SkScalar rh = origRect.height(); |
| if ((rw < 0) ^ (rh < 0)) { |
| dir = reverse_direction(dir); |
| } |
| SkRect rect(origRect); |
| rect.sort(); |
| // reassign these, now that we know they'll be >= 0 |
| rw = rect.width(); |
| rh = rect.height(); |
| |
| SkRect r(rect); |
| r.outset(radius, radius); |
| |
| SkPaint::Join join = (SkPaint::Join)fJoin; |
| if (SkPaint::kMiter_Join == join && fMiterLimit < SK_ScalarSqrt2) { |
| join = SkPaint::kBevel_Join; |
| } |
| |
| switch (join) { |
| case SkPaint::kMiter_Join: |
| dst->addRect(r, dir); |
| break; |
| case SkPaint::kBevel_Join: |
| addBevel(dst, rect, r, dir); |
| break; |
| case SkPaint::kRound_Join: |
| dst->addRoundRect(r, radius, radius, dir); |
| break; |
| default: |
| break; |
| } |
| |
| if (fWidth < std::min(rw, rh) && !fDoFill) { |
| r = rect; |
| r.inset(radius, radius); |
| dst->addRect(r, reverse_direction(dir)); |
| } |
| } |
