| 1 | /* | 
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| 2 | * Copyright 2018 Google Inc. | 
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| 3 | * | 
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| 4 | * Use of this source code is governed by a BSD-style license that can be | 
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| 5 | * found in the LICENSE file. | 
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| 6 | */ | 
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| 7 |  | 
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| 8 | #include "src/gpu/ccpr/GrCCStrokeGeometry.h" | 
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| 9 |  | 
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| 10 | #include "include/core/SkStrokeRec.h" | 
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| 11 | #include "include/private/SkNx.h" | 
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| 12 | #include "src/core/SkGeometry.h" | 
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| 13 | #include "src/core/SkMathPriv.h" | 
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| 14 |  | 
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| 15 | // This is the maximum distance in pixels that we can stray from the edge of a stroke when | 
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| 16 | // converting it to flat line segments. | 
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| 17 | static constexpr float kMaxErrorFromLinearization = 1/8.f; | 
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| 18 |  | 
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| 19 | static inline float length(const Sk2f& n) { | 
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| 20 | Sk2f nn = n*n; | 
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| 21 | return SkScalarSqrt(nn[0] + nn[1]); | 
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| 22 | } | 
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| 23 |  | 
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| 24 | static inline Sk2f normalize(const Sk2f& v) { | 
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| 25 | Sk2f vv = v*v; | 
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| 26 | vv += SkNx_shuffle<1,0>(vv); | 
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| 27 | return v * vv.rsqrt(); | 
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| 28 | } | 
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| 29 |  | 
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| 30 | static inline void transpose(const Sk2f& a, const Sk2f& b, Sk2f* X, Sk2f* Y) { | 
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| 31 | float transpose[4]; | 
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| 32 | a.store(transpose); | 
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| 33 | b.store(transpose+2); | 
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| 34 | Sk2f::Load2(transpose, X, Y); | 
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| 35 | } | 
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| 36 |  | 
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| 37 | static inline void normalize2(const Sk2f& v0, const Sk2f& v1, SkPoint out[2]) { | 
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| 38 | Sk2f X, Y; | 
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| 39 | transpose(v0, v1, &X, &Y); | 
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| 40 | Sk2f invlength = (X*X + Y*Y).rsqrt(); | 
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| 41 | Sk2f::Store2(out, Y * invlength, -X * invlength); | 
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| 42 | } | 
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| 43 |  | 
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| 44 | static inline float calc_curvature_costheta(const Sk2f& leftTan, const Sk2f& rightTan) { | 
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| 45 | Sk2f X, Y; | 
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| 46 | transpose(leftTan, rightTan, &X, &Y); | 
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| 47 | Sk2f invlength = (X*X + Y*Y).rsqrt(); | 
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| 48 | Sk2f dotprod = leftTan * rightTan; | 
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| 49 | return (dotprod[0] + dotprod[1]) * invlength[0] * invlength[1]; | 
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| 50 | } | 
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| 51 |  | 
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| 52 | static GrCCStrokeGeometry::Verb join_verb_from_join(SkPaint::Join join) { | 
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| 53 | using Verb = GrCCStrokeGeometry::Verb; | 
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| 54 | switch (join) { | 
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| 55 | case SkPaint::kBevel_Join: | 
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| 56 | return Verb::kBevelJoin; | 
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| 57 | case SkPaint::kMiter_Join: | 
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| 58 | return Verb::kMiterJoin; | 
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| 59 | case SkPaint::kRound_Join: | 
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| 60 | return Verb::kRoundJoin; | 
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| 61 | } | 
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| 62 | SK_ABORT( "Invalid SkPaint::Join."); | 
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| 63 | } | 
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| 64 |  | 
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| 65 | void GrCCStrokeGeometry::beginPath(const SkStrokeRec& stroke, float strokeDevWidth, | 
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| 66 | InstanceTallies* tallies) { | 
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| 67 | SkASSERT(!fInsideContour); | 
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| 68 | // Client should have already converted the stroke to device space (i.e. width=1 for hairline). | 
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| 69 | SkASSERT(strokeDevWidth > 0); | 
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| 70 |  | 
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| 71 | fCurrStrokeRadius = strokeDevWidth/2; | 
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| 72 | fCurrStrokeJoinVerb = join_verb_from_join(stroke.getJoin()); | 
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| 73 | fCurrStrokeCapType = stroke.getCap(); | 
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| 74 | fCurrStrokeTallies = tallies; | 
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| 75 |  | 
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| 76 | if (Verb::kMiterJoin == fCurrStrokeJoinVerb) { | 
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| 77 | // We implement miters by placing a triangle-shaped cap on top of a bevel join. Convert the | 
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| 78 | // "miter limit" to how tall that triangle cap can be. | 
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| 79 | float m = stroke.getMiter(); | 
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| 80 | fMiterMaxCapHeightOverWidth = .5f * SkScalarSqrt(m*m - 1); | 
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| 81 | } | 
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| 82 |  | 
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| 83 | // Find the angle of curvature where the arc height above a simple line from point A to point B | 
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| 84 | // is equal to kMaxErrorFromLinearization. | 
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| 85 | float r = std::max(1 - kMaxErrorFromLinearization / fCurrStrokeRadius, 0.f); | 
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| 86 | fMaxCurvatureCosTheta = 2*r*r - 1; | 
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| 87 |  | 
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| 88 | fCurrContourFirstPtIdx = -1; | 
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| 89 | fCurrContourFirstNormalIdx = -1; | 
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| 90 |  | 
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| 91 | fVerbs.push_back(Verb::kBeginPath); | 
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| 92 | } | 
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| 93 |  | 
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| 94 | void GrCCStrokeGeometry::moveTo(SkPoint pt) { | 
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| 95 | SkASSERT(!fInsideContour); | 
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| 96 | fCurrContourFirstPtIdx = fPoints.count(); | 
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| 97 | fCurrContourFirstNormalIdx = fNormals.count(); | 
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| 98 | fPoints.push_back(pt); | 
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| 99 | SkDEBUGCODE(fInsideContour = true); | 
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| 100 | } | 
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| 101 |  | 
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| 102 | void GrCCStrokeGeometry::lineTo(SkPoint pt) { | 
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| 103 | SkASSERT(fInsideContour); | 
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| 104 | this->lineTo(fCurrStrokeJoinVerb, pt); | 
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| 105 | } | 
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| 106 |  | 
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| 107 | void GrCCStrokeGeometry::lineTo(Verb leftJoinVerb, SkPoint pt) { | 
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| 108 | Sk2f tan = Sk2f::Load(&pt) - Sk2f::Load(&fPoints.back()); | 
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| 109 | if ((tan == 0).allTrue()) { | 
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| 110 | return; | 
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| 111 | } | 
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| 112 |  | 
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| 113 | tan = normalize(tan); | 
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| 114 | SkVector n = SkVector::Make(tan[1], -tan[0]); | 
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| 115 |  | 
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| 116 | this->recordLeftJoinIfNotEmpty(leftJoinVerb, n); | 
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| 117 | fNormals.push_back(n); | 
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| 118 |  | 
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| 119 | this->recordStroke(Verb::kLinearStroke, 0); | 
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| 120 | fPoints.push_back(pt); | 
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| 121 | } | 
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| 122 |  | 
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| 123 | void GrCCStrokeGeometry::quadraticTo(const SkPoint P[3]) { | 
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| 124 | SkASSERT(fInsideContour); | 
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| 125 | this->quadraticTo(fCurrStrokeJoinVerb, P, SkFindQuadMaxCurvature(P)); | 
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| 126 | } | 
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| 127 |  | 
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| 128 | // Wang's formula for quadratics (1985) gives us the number of evenly spaced (in the parametric | 
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| 129 | // sense) line segments that are guaranteed to be within a distance of "kMaxErrorFromLinearization" | 
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| 130 | // from the actual curve. | 
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| 131 | static inline float wangs_formula_quadratic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2) { | 
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| 132 | static constexpr float k = 2 / (8 * kMaxErrorFromLinearization); | 
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| 133 | float f = SkScalarSqrt(k * length(p2 - p1*2 + p0)); | 
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| 134 | return SkScalarCeilToInt(f); | 
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| 135 | } | 
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| 136 |  | 
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| 137 | void GrCCStrokeGeometry::quadraticTo(Verb leftJoinVerb, const SkPoint P[3], float maxCurvatureT) { | 
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| 138 | Sk2f p0 = Sk2f::Load(P); | 
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| 139 | Sk2f p1 = Sk2f::Load(P+1); | 
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| 140 | Sk2f p2 = Sk2f::Load(P+2); | 
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| 141 |  | 
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| 142 | Sk2f tan0 = p1 - p0; | 
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| 143 | Sk2f tan1 = p2 - p1; | 
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| 144 |  | 
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| 145 | // Snap to a "lineTo" if the control point is so close to an endpoint that FP error will become | 
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| 146 | // an issue. | 
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| 147 | if ((tan0.abs() < SK_ScalarNearlyZero).allTrue() ||  // p0 ~= p1 | 
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| 148 | (tan1.abs() < SK_ScalarNearlyZero).allTrue()) {  // p1 ~= p2 | 
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| 149 | this->lineTo(leftJoinVerb, P[2]); | 
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| 150 | return; | 
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| 151 | } | 
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| 152 |  | 
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| 153 | SkPoint normals[2]; | 
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| 154 | normalize2(tan0, tan1, normals); | 
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| 155 |  | 
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| 156 | // Decide how many flat line segments to chop the curve into. | 
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| 157 | int numSegments = wangs_formula_quadratic(p0, p1, p2); | 
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| 158 | numSegments = std::min(numSegments, 1 << kMaxNumLinearSegmentsLog2); | 
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| 159 | if (numSegments <= 1) { | 
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| 160 | this->rotateTo(leftJoinVerb, normals[0]); | 
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| 161 | this->lineTo(Verb::kInternalRoundJoin, P[2]); | 
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| 162 | this->rotateTo(Verb::kInternalRoundJoin, normals[1]); | 
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| 163 | return; | 
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| 164 | } | 
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| 165 |  | 
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| 166 | // At + B gives a vector tangent to the quadratic. | 
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| 167 | Sk2f A = p0 - p1*2 + p2; | 
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| 168 | Sk2f B = p1 - p0; | 
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| 169 |  | 
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| 170 | // Find a line segment that crosses max curvature. | 
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| 171 | float segmentLength = SkScalarInvert(numSegments); | 
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| 172 | float leftT = maxCurvatureT - segmentLength/2; | 
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| 173 | float rightT = maxCurvatureT + segmentLength/2; | 
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| 174 | Sk2f leftTan, rightTan; | 
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| 175 | if (leftT <= 0) { | 
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| 176 | leftT = 0; | 
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| 177 | leftTan = tan0; | 
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| 178 | rightT = segmentLength; | 
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| 179 | rightTan = A*rightT + B; | 
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| 180 | } else if (rightT >= 1) { | 
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| 181 | leftT = 1 - segmentLength; | 
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| 182 | leftTan = A*leftT + B; | 
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| 183 | rightT = 1; | 
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| 184 | rightTan = tan1; | 
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| 185 | } else { | 
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| 186 | leftTan = A*leftT + B; | 
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| 187 | rightTan = A*rightT + B; | 
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| 188 | } | 
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| 189 |  | 
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| 190 | // Check if curvature is too strong for a triangle strip on the line segment that crosses max | 
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| 191 | // curvature. If it is, we will chop and convert the segment to a "lineTo" with round joins. | 
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| 192 | // | 
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| 193 | // FIXME: This is quite costly and the vast majority of curves only have moderate curvature. We | 
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| 194 | // would benefit significantly from a quick reject that detects curves that don't need special | 
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| 195 | // treatment for strong curvature. | 
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| 196 | bool isCurvatureTooStrong = calc_curvature_costheta(leftTan, rightTan) < fMaxCurvatureCosTheta; | 
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| 197 | if (isCurvatureTooStrong) { | 
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| 198 | SkPoint ptsBuffer[5]; | 
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| 199 | const SkPoint* currQuadratic = P; | 
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| 200 |  | 
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| 201 | if (leftT > 0) { | 
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| 202 | SkChopQuadAt(currQuadratic, ptsBuffer, leftT); | 
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| 203 | this->quadraticTo(leftJoinVerb, ptsBuffer, /*maxCurvatureT=*/1); | 
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| 204 | if (rightT < 1) { | 
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| 205 | rightT = (rightT - leftT) / (1 - leftT); | 
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| 206 | } | 
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| 207 | currQuadratic = ptsBuffer + 2; | 
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| 208 | } else { | 
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| 209 | this->rotateTo(leftJoinVerb, normals[0]); | 
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| 210 | } | 
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| 211 |  | 
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| 212 | if (rightT < 1) { | 
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| 213 | SkChopQuadAt(currQuadratic, ptsBuffer, rightT); | 
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| 214 | this->lineTo(Verb::kInternalRoundJoin, ptsBuffer[2]); | 
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| 215 | this->quadraticTo(Verb::kInternalRoundJoin, ptsBuffer + 2, /*maxCurvatureT=*/0); | 
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| 216 | } else { | 
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| 217 | this->lineTo(Verb::kInternalRoundJoin, currQuadratic[2]); | 
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| 218 | this->rotateTo(Verb::kInternalRoundJoin, normals[1]); | 
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| 219 | } | 
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| 220 | return; | 
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| 221 | } | 
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| 222 |  | 
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| 223 | this->recordLeftJoinIfNotEmpty(leftJoinVerb, normals[0]); | 
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| 224 | fNormals.push_back_n(2, normals); | 
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| 225 |  | 
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| 226 | this->recordStroke(Verb::kQuadraticStroke, SkNextLog2(numSegments)); | 
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| 227 | p1.store(&fPoints.push_back()); | 
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| 228 | p2.store(&fPoints.push_back()); | 
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| 229 | } | 
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| 230 |  | 
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| 231 | void GrCCStrokeGeometry::cubicTo(const SkPoint P[4]) { | 
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| 232 | SkASSERT(fInsideContour); | 
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| 233 | float roots[3]; | 
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| 234 | int numRoots = SkFindCubicMaxCurvature(P, roots); | 
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| 235 | this->cubicTo(fCurrStrokeJoinVerb, P, | 
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| 236 | numRoots > 0 ? roots[numRoots/2] : 0, | 
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| 237 | numRoots > 1 ? roots[0] : kLeftMaxCurvatureNone, | 
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| 238 | numRoots > 2 ? roots[2] : kRightMaxCurvatureNone); | 
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| 239 | } | 
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| 240 |  | 
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| 241 | // Wang's formula for cubics (1985) gives us the number of evenly spaced (in the parametric sense) | 
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| 242 | // line segments that are guaranteed to be within a distance of "kMaxErrorFromLinearization" | 
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| 243 | // from the actual curve. | 
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| 244 | static inline float wangs_formula_cubic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, | 
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| 245 | const Sk2f& p3) { | 
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| 246 | static constexpr float k = (3 * 2) / (8 * kMaxErrorFromLinearization); | 
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| 247 | float f = SkScalarSqrt(k * length(Sk2f::Max((p2 - p1*2 + p0).abs(), | 
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| 248 | (p3 - p2*2 + p1).abs()))); | 
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| 249 | return SkScalarCeilToInt(f); | 
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| 250 | } | 
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| 251 |  | 
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| 252 | void GrCCStrokeGeometry::cubicTo(Verb leftJoinVerb, const SkPoint P[4], float maxCurvatureT, | 
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| 253 | float leftMaxCurvatureT, float rightMaxCurvatureT) { | 
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| 254 | Sk2f p0 = Sk2f::Load(P); | 
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| 255 | Sk2f p1 = Sk2f::Load(P+1); | 
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| 256 | Sk2f p2 = Sk2f::Load(P+2); | 
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| 257 | Sk2f p3 = Sk2f::Load(P+3); | 
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| 258 |  | 
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| 259 | Sk2f tan0 = p1 - p0; | 
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| 260 | Sk2f tan1 = p3 - p2; | 
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| 261 |  | 
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| 262 | // Snap control points to endpoints if they are so close that FP error will become an issue. | 
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| 263 | if ((tan0.abs() < SK_ScalarNearlyZero).allTrue()) {  // p0 ~= p1 | 
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| 264 | p1 = p0; | 
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| 265 | tan0 = p2 - p0; | 
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| 266 | if ((tan0.abs() < SK_ScalarNearlyZero).allTrue()) {  // p0 ~= p1 ~= p2 | 
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| 267 | this->lineTo(leftJoinVerb, P[3]); | 
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| 268 | return; | 
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| 269 | } | 
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| 270 | } | 
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| 271 | if ((tan1.abs() < SK_ScalarNearlyZero).allTrue()) {  // p2 ~= p3 | 
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| 272 | p2 = p3; | 
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| 273 | tan1 = p3 - p1; | 
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| 274 | if ((tan1.abs() < SK_ScalarNearlyZero).allTrue() ||  // p1 ~= p2 ~= p3 | 
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| 275 | (p0 == p1).allTrue()) {  // p0 ~= p1 AND p2 ~= p3 | 
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| 276 | this->lineTo(leftJoinVerb, P[3]); | 
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| 277 | return; | 
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| 278 | } | 
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| 279 | } | 
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| 280 |  | 
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| 281 | SkPoint normals[2]; | 
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| 282 | normalize2(tan0, tan1, normals); | 
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| 283 |  | 
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| 284 | // Decide how many flat line segments to chop the curve into. | 
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| 285 | int numSegments = wangs_formula_cubic(p0, p1, p2, p3); | 
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| 286 | numSegments = std::min(numSegments, 1 << kMaxNumLinearSegmentsLog2); | 
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| 287 | if (numSegments <= 1) { | 
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| 288 | this->rotateTo(leftJoinVerb, normals[0]); | 
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| 289 | this->lineTo(leftJoinVerb, P[3]); | 
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| 290 | this->rotateTo(Verb::kInternalRoundJoin, normals[1]); | 
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| 291 | return; | 
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| 292 | } | 
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| 293 |  | 
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| 294 | // At^2 + Bt + C gives a vector tangent to the cubic. (More specifically, it's the derivative | 
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| 295 | // minus an irrelevant scale by 3, since all we care about is the direction.) | 
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| 296 | Sk2f A = p3 + (p1 - p2)*3 - p0; | 
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| 297 | Sk2f B = (p0 - p1*2 + p2)*2; | 
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| 298 | Sk2f C = p1 - p0; | 
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| 299 |  | 
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| 300 | // Find a line segment that crosses max curvature. | 
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| 301 | float segmentLength = SkScalarInvert(numSegments); | 
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| 302 | float leftT = maxCurvatureT - segmentLength/2; | 
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| 303 | float rightT = maxCurvatureT + segmentLength/2; | 
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| 304 | Sk2f leftTan, rightTan; | 
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| 305 | if (leftT <= 0) { | 
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| 306 | leftT = 0; | 
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| 307 | leftTan = tan0; | 
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| 308 | rightT = segmentLength; | 
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| 309 | rightTan = A*rightT*rightT + B*rightT + C; | 
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| 310 | } else if (rightT >= 1) { | 
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| 311 | leftT = 1 - segmentLength; | 
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| 312 | leftTan = A*leftT*leftT + B*leftT + C; | 
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| 313 | rightT = 1; | 
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| 314 | rightTan = tan1; | 
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| 315 | } else { | 
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| 316 | leftTan = A*leftT*leftT + B*leftT + C; | 
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| 317 | rightTan = A*rightT*rightT + B*rightT + C; | 
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| 318 | } | 
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| 319 |  | 
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| 320 | // Check if curvature is too strong for a triangle strip on the line segment that crosses max | 
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| 321 | // curvature. If it is, we will chop and convert the segment to a "lineTo" with round joins. | 
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| 322 | // | 
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| 323 | // FIXME: This is quite costly and the vast majority of curves only have moderate curvature. We | 
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| 324 | // would benefit significantly from a quick reject that detects curves that don't need special | 
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| 325 | // treatment for strong curvature. | 
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| 326 | bool isCurvatureTooStrong = calc_curvature_costheta(leftTan, rightTan) < fMaxCurvatureCosTheta; | 
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| 327 | if (isCurvatureTooStrong) { | 
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| 328 | SkPoint ptsBuffer[7]; | 
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| 329 | p0.store(ptsBuffer); | 
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| 330 | p1.store(ptsBuffer + 1); | 
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| 331 | p2.store(ptsBuffer + 2); | 
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| 332 | p3.store(ptsBuffer + 3); | 
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| 333 | const SkPoint* currCubic = ptsBuffer; | 
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| 334 |  | 
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| 335 | if (leftT > 0) { | 
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| 336 | SkChopCubicAt(currCubic, ptsBuffer, leftT); | 
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| 337 | this->cubicTo(leftJoinVerb, ptsBuffer, /*maxCurvatureT=*/1, | 
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| 338 | (kLeftMaxCurvatureNone != leftMaxCurvatureT) | 
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| 339 | ? leftMaxCurvatureT/leftT : kLeftMaxCurvatureNone, | 
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| 340 | kRightMaxCurvatureNone); | 
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| 341 | if (rightT < 1) { | 
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| 342 | rightT = (rightT - leftT) / (1 - leftT); | 
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| 343 | } | 
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| 344 | if (rightMaxCurvatureT < 1 && kRightMaxCurvatureNone != rightMaxCurvatureT) { | 
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| 345 | rightMaxCurvatureT = (rightMaxCurvatureT - leftT) / (1 - leftT); | 
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| 346 | } | 
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| 347 | currCubic = ptsBuffer + 3; | 
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| 348 | } else { | 
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| 349 | this->rotateTo(leftJoinVerb, normals[0]); | 
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| 350 | } | 
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| 351 |  | 
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| 352 | if (rightT < 1) { | 
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| 353 | SkChopCubicAt(currCubic, ptsBuffer, rightT); | 
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| 354 | this->lineTo(Verb::kInternalRoundJoin, ptsBuffer[3]); | 
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| 355 | currCubic = ptsBuffer + 3; | 
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| 356 | this->cubicTo(Verb::kInternalRoundJoin, currCubic, /*maxCurvatureT=*/0, | 
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| 357 | kLeftMaxCurvatureNone, kRightMaxCurvatureNone); | 
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| 358 | } else { | 
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| 359 | this->lineTo(Verb::kInternalRoundJoin, currCubic[3]); | 
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| 360 | this->rotateTo(Verb::kInternalRoundJoin, normals[1]); | 
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| 361 | } | 
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| 362 | return; | 
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| 363 | } | 
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| 364 |  | 
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| 365 | // Recurse and check the other two points of max curvature, if any. | 
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| 366 | if (kRightMaxCurvatureNone != rightMaxCurvatureT) { | 
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| 367 | this->cubicTo(leftJoinVerb, P, rightMaxCurvatureT, leftMaxCurvatureT, | 
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| 368 | kRightMaxCurvatureNone); | 
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| 369 | return; | 
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| 370 | } | 
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| 371 | if (kLeftMaxCurvatureNone != leftMaxCurvatureT) { | 
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| 372 | SkASSERT(kRightMaxCurvatureNone == rightMaxCurvatureT); | 
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| 373 | this->cubicTo(leftJoinVerb, P, leftMaxCurvatureT, kLeftMaxCurvatureNone, | 
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| 374 | kRightMaxCurvatureNone); | 
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| 375 | return; | 
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| 376 | } | 
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| 377 |  | 
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| 378 | this->recordLeftJoinIfNotEmpty(leftJoinVerb, normals[0]); | 
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| 379 | fNormals.push_back_n(2, normals); | 
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| 380 |  | 
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| 381 | this->recordStroke(Verb::kCubicStroke, SkNextLog2(numSegments)); | 
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| 382 | p1.store(&fPoints.push_back()); | 
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| 383 | p2.store(&fPoints.push_back()); | 
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| 384 | p3.store(&fPoints.push_back()); | 
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| 385 | } | 
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| 386 |  | 
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| 387 | void GrCCStrokeGeometry::recordStroke(Verb verb, int numSegmentsLog2) { | 
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| 388 | SkASSERT(Verb::kLinearStroke != verb || 0 == numSegmentsLog2); | 
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| 389 | SkASSERT(numSegmentsLog2 <= kMaxNumLinearSegmentsLog2); | 
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| 390 | fVerbs.push_back(verb); | 
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| 391 | if (Verb::kLinearStroke != verb) { | 
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| 392 | SkASSERT(numSegmentsLog2 > 0); | 
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| 393 | fParams.push_back().fNumLinearSegmentsLog2 = numSegmentsLog2; | 
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| 394 | } | 
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| 395 | ++fCurrStrokeTallies->fStrokes[numSegmentsLog2]; | 
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| 396 | } | 
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| 397 |  | 
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| 398 | void GrCCStrokeGeometry::rotateTo(Verb leftJoinVerb, SkVector normal) { | 
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| 399 | this->recordLeftJoinIfNotEmpty(leftJoinVerb, normal); | 
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| 400 | fNormals.push_back(normal); | 
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| 401 | } | 
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| 402 |  | 
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| 403 | void GrCCStrokeGeometry::recordLeftJoinIfNotEmpty(Verb joinVerb, SkVector nextNormal) { | 
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| 404 | if (fNormals.count() <= fCurrContourFirstNormalIdx) { | 
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| 405 | // The contour is empty. Nothing to join with. | 
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| 406 | SkASSERT(fNormals.count() == fCurrContourFirstNormalIdx); | 
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| 407 | return; | 
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| 408 | } | 
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| 409 |  | 
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| 410 | if (Verb::kBevelJoin == joinVerb) { | 
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| 411 | this->recordBevelJoin(Verb::kBevelJoin); | 
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| 412 | return; | 
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| 413 | } | 
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| 414 |  | 
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| 415 | Sk2f n0 = Sk2f::Load(&fNormals.back()); | 
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| 416 | Sk2f n1 = Sk2f::Load(&nextNormal); | 
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| 417 | Sk2f base = n1 - n0; | 
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| 418 | if ((base.abs() * fCurrStrokeRadius < kMaxErrorFromLinearization).allTrue()) { | 
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| 419 | // Treat any join as a bevel when the outside corners of the two adjoining strokes are | 
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| 420 | // close enough to each other. This is important because "miterCapHeightOverWidth" becomes | 
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| 421 | // unstable when n0 and n1 are nearly equal. | 
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| 422 | this->recordBevelJoin(joinVerb); | 
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| 423 | return; | 
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| 424 | } | 
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| 425 |  | 
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| 426 | // We implement miters and round joins by placing a triangle-shaped cap on top of a bevel join. | 
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| 427 | // (For round joins this triangle cap comprises the conic control points.) Find how tall to make | 
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| 428 | // this triangle cap, relative to its width. | 
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| 429 | // | 
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| 430 | // NOTE: This value would be infinite at 180 degrees, but we clamp miterCapHeightOverWidth at | 
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| 431 | // near-infinity. 180-degree round joins still look perfectly acceptable like this (though | 
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| 432 | // technically not pure arcs). | 
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| 433 | Sk2f cross = base * SkNx_shuffle<1,0>(n0); | 
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| 434 | Sk2f dot = base * n0; | 
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| 435 | float miterCapHeight = SkScalarAbs(dot[0] + dot[1]); | 
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| 436 | float miterCapWidth = SkScalarAbs(cross[0] - cross[1]) * 2; | 
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| 437 |  | 
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| 438 | if (Verb::kMiterJoin == joinVerb) { | 
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| 439 | if (miterCapHeight > fMiterMaxCapHeightOverWidth * miterCapWidth) { | 
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| 440 | // This join is tighter than the miter limit. Treat it as a bevel. | 
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| 441 | this->recordBevelJoin(Verb::kMiterJoin); | 
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| 442 | return; | 
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| 443 | } | 
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| 444 | this->recordMiterJoin(miterCapHeight / miterCapWidth); | 
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| 445 | return; | 
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| 446 | } | 
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| 447 |  | 
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| 448 | SkASSERT(Verb::kRoundJoin == joinVerb || Verb::kInternalRoundJoin == joinVerb); | 
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| 449 |  | 
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| 450 | // Conic arcs become unstable when they approach 180 degrees. When the conic control point | 
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| 451 | // begins shooting off to infinity (i.e., height/width > 32), split the conic into two. | 
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| 452 | static constexpr float kAlmost180Degrees = 32; | 
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| 453 | if (miterCapHeight > kAlmost180Degrees * miterCapWidth) { | 
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| 454 | Sk2f bisect = normalize(n0 - n1); | 
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| 455 | this->rotateTo(joinVerb, SkVector::Make(-bisect[1], bisect[0])); | 
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| 456 | this->recordLeftJoinIfNotEmpty(joinVerb, nextNormal); | 
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| 457 | return; | 
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| 458 | } | 
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| 459 |  | 
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| 460 | float miterCapHeightOverWidth = miterCapHeight / miterCapWidth; | 
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| 461 |  | 
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| 462 | // Find the heights of this round join's conic control point as well as the arc itself. | 
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| 463 | Sk2f X, Y; | 
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| 464 | transpose(base * base, n0 * n1, &X, &Y); | 
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| 465 | Sk2f r = Sk2f::Max(X + Y + Sk2f(0, 1), 0.f).sqrt(); | 
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| 466 | Sk2f heights = SkNx_fma(r, Sk2f(miterCapHeightOverWidth, -SK_ScalarRoot2Over2), Sk2f(0, 1)); | 
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| 467 | float controlPointHeight = SkScalarAbs(heights[0]); | 
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| 468 | float curveHeight = heights[1]; | 
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| 469 | if (curveHeight * fCurrStrokeRadius < kMaxErrorFromLinearization) { | 
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| 470 | // Treat round joins as bevels when their curvature is nearly flat. | 
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| 471 | this->recordBevelJoin(joinVerb); | 
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| 472 | return; | 
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| 473 | } | 
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| 474 |  | 
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| 475 | float w = curveHeight / (controlPointHeight - curveHeight); | 
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| 476 | this->recordRoundJoin(joinVerb, miterCapHeightOverWidth, w); | 
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| 477 | } | 
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| 478 |  | 
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| 479 | void GrCCStrokeGeometry::recordBevelJoin(Verb originalJoinVerb) { | 
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| 480 | if (!IsInternalJoinVerb(originalJoinVerb)) { | 
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| 481 | fVerbs.push_back(Verb::kBevelJoin); | 
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| 482 | ++fCurrStrokeTallies->fTriangles; | 
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| 483 | } else { | 
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| 484 | fVerbs.push_back(Verb::kInternalBevelJoin); | 
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| 485 | fCurrStrokeTallies->fTriangles += 2; | 
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| 486 | } | 
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| 487 | } | 
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| 488 |  | 
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| 489 | void GrCCStrokeGeometry::recordMiterJoin(float miterCapHeightOverWidth) { | 
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| 490 | fVerbs.push_back(Verb::kMiterJoin); | 
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| 491 | fParams.push_back().fMiterCapHeightOverWidth = miterCapHeightOverWidth; | 
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| 492 | fCurrStrokeTallies->fTriangles += 2; | 
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| 493 | } | 
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| 494 |  | 
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| 495 | void GrCCStrokeGeometry::recordRoundJoin(Verb joinVerb, float miterCapHeightOverWidth, | 
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| 496 | float conicWeight) { | 
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| 497 | fVerbs.push_back(joinVerb); | 
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| 498 | fParams.push_back().fConicWeight = conicWeight; | 
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| 499 | fParams.push_back().fMiterCapHeightOverWidth = miterCapHeightOverWidth; | 
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| 500 | if (Verb::kRoundJoin == joinVerb) { | 
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| 501 | ++fCurrStrokeTallies->fTriangles; | 
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| 502 | ++fCurrStrokeTallies->fConics; | 
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| 503 | } else { | 
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| 504 | SkASSERT(Verb::kInternalRoundJoin == joinVerb); | 
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| 505 | fCurrStrokeTallies->fTriangles += 2; | 
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| 506 | fCurrStrokeTallies->fConics += 2; | 
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| 507 | } | 
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| 508 | } | 
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| 509 |  | 
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| 510 | void GrCCStrokeGeometry::closeContour() { | 
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| 511 | SkASSERT(fInsideContour); | 
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| 512 | SkASSERT(fPoints.count() > fCurrContourFirstPtIdx); | 
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| 513 | if (fPoints.back() != fPoints[fCurrContourFirstPtIdx]) { | 
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| 514 | // Draw a line back to the beginning. | 
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| 515 | this->lineTo(fCurrStrokeJoinVerb, fPoints[fCurrContourFirstPtIdx]); | 
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| 516 | } | 
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| 517 | if (fNormals.count() > fCurrContourFirstNormalIdx) { | 
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| 518 | // Join the first and last lines. | 
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| 519 | this->rotateTo(fCurrStrokeJoinVerb,fNormals[fCurrContourFirstNormalIdx]); | 
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| 520 | } else { | 
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| 521 | // This contour is empty. Add a bogus normal since the iterator always expects one. | 
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| 522 | SkASSERT(fNormals.count() == fCurrContourFirstNormalIdx); | 
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| 523 | fNormals.push_back({0, 0}); | 
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| 524 | } | 
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| 525 | fVerbs.push_back(Verb::kEndContour); | 
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| 526 | SkDEBUGCODE(fInsideContour = false); | 
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| 527 | } | 
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| 528 |  | 
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| 529 | void GrCCStrokeGeometry::capContourAndExit() { | 
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| 530 | SkASSERT(fInsideContour); | 
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| 531 | if (fCurrContourFirstNormalIdx >= fNormals.count()) { | 
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| 532 | // This contour is empty. Add a normal in the direction that caps orient on empty geometry. | 
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| 533 | SkASSERT(fNormals.count() == fCurrContourFirstNormalIdx); | 
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| 534 | fNormals.push_back({1, 0}); | 
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| 535 | } | 
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| 536 |  | 
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| 537 | this->recordCapsIfAny(); | 
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| 538 | fVerbs.push_back(Verb::kEndContour); | 
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| 539 |  | 
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| 540 | SkDEBUGCODE(fInsideContour = false); | 
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| 541 | } | 
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| 542 |  | 
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| 543 | void GrCCStrokeGeometry::recordCapsIfAny() { | 
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| 544 | SkASSERT(fInsideContour); | 
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| 545 | SkASSERT(fCurrContourFirstNormalIdx < fNormals.count()); | 
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| 546 |  | 
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| 547 | if (SkPaint::kButt_Cap == fCurrStrokeCapType) { | 
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| 548 | return; | 
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| 549 | } | 
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| 550 |  | 
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| 551 | Verb capVerb; | 
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| 552 | if (SkPaint::kSquare_Cap == fCurrStrokeCapType) { | 
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| 553 | if (fCurrStrokeRadius * SK_ScalarRoot2Over2 < kMaxErrorFromLinearization) { | 
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| 554 | return; | 
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| 555 | } | 
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| 556 | capVerb = Verb::kSquareCap; | 
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| 557 | fCurrStrokeTallies->fStrokes[0] += 2; | 
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| 558 | } else { | 
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| 559 | SkASSERT(SkPaint::kRound_Cap == fCurrStrokeCapType); | 
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| 560 | if (fCurrStrokeRadius < kMaxErrorFromLinearization) { | 
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| 561 | return; | 
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| 562 | } | 
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| 563 | capVerb = Verb::kRoundCap; | 
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| 564 | fCurrStrokeTallies->fTriangles += 2; | 
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| 565 | fCurrStrokeTallies->fConics += 4; | 
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| 566 | } | 
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| 567 |  | 
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| 568 | fVerbs.push_back(capVerb); | 
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| 569 | fVerbs.push_back(Verb::kEndContour); | 
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| 570 |  | 
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| 571 | fVerbs.push_back(capVerb); | 
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| 572 |  | 
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| 573 | // Reserve the space first, since push_back() takes the point by reference and might | 
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| 574 | // invalidate the reference if the array grows. | 
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| 575 | fPoints.reserve(fPoints.count() + 1); | 
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| 576 | fPoints.push_back(fPoints[fCurrContourFirstPtIdx]); | 
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| 577 |  | 
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| 578 | // Reserve the space first, since push_back() takes the normal by reference and might | 
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| 579 | // invalidate the reference if the array grows. (Although in this case we should be fine | 
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| 580 | // since there is a negate operator.) | 
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| 581 | fNormals.reserve(fNormals.count() + 1); | 
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| 582 | fNormals.push_back(-fNormals[fCurrContourFirstNormalIdx]); | 
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| 583 | } | 
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| 584 |  | 
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