/*
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* Copyright 2006 The Android Open Source Project
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#ifndef SkGeometry_DEFINED
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#define SkGeometry_DEFINED
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#include "SkMatrix.h"
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#include "SkNx.h"
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static inline Sk2s from_point(const SkPoint& point) {
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return Sk2s::Load(&point);
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}
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static inline SkPoint to_point(const Sk2s& x) {
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SkPoint point;
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x.store(&point);
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return point;
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}
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static Sk2s times_2(const Sk2s& value) {
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return value + value;
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}
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/** Given a quadratic equation Ax^2 + Bx + C = 0, return 0, 1, 2 roots for the
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equation.
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*/
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int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]);
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///////////////////////////////////////////////////////////////////////////////
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SkPoint SkEvalQuadAt(const SkPoint src[3], SkScalar t);
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SkPoint SkEvalQuadTangentAt(const SkPoint src[3], SkScalar t);
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/** Set pt to the point on the src quadratic specified by t. t must be
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0 <= t <= 1.0
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*/
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void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt, SkVector* tangent = nullptr);
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/** Given a src quadratic bezier, chop it at the specified t value,
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where 0 < t < 1, and return the two new quadratics in dst:
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dst[0..2] and dst[2..4]
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*/
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void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t);
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/** Given a src quadratic bezier, chop it at the specified t == 1/2,
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The new quads are returned in dst[0..2] and dst[2..4]
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*/
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void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]);
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/** Given the 3 coefficients for a quadratic bezier (either X or Y values), look
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for extrema, and return the number of t-values that are found that represent
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these extrema. If the quadratic has no extrema betwee (0..1) exclusive, the
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function returns 0.
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Returned count tValues[]
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0 ignored
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1 0 < tValues[0] < 1
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*/
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int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValues[1]);
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/** Given 3 points on a quadratic bezier, chop it into 1, 2 beziers such that
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the resulting beziers are monotonic in Y. This is called by the scan converter.
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Depending on what is returned, dst[] is treated as follows
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0 dst[0..2] is the original quad
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1 dst[0..2] and dst[2..4] are the two new quads
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*/
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int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]);
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int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]);
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/** Given 3 points on a quadratic bezier, if the point of maximum
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curvature exists on the segment, returns the t value for this
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point along the curve. Otherwise it will return a value of 0.
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*/
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SkScalar SkFindQuadMaxCurvature(const SkPoint src[3]);
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/** Given 3 points on a quadratic bezier, divide it into 2 quadratics
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if the point of maximum curvature exists on the quad segment.
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Depending on what is returned, dst[] is treated as follows
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1 dst[0..2] is the original quad
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2 dst[0..2] and dst[2..4] are the two new quads
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If dst == null, it is ignored and only the count is returned.
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*/
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int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]);
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/** Given 3 points on a quadratic bezier, use degree elevation to
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convert it into the cubic fitting the same curve. The new cubic
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curve is returned in dst[0..3].
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*/
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SK_API void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]);
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///////////////////////////////////////////////////////////////////////////////
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/** Set pt to the point on the src cubic specified by t. t must be
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0 <= t <= 1.0
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*/
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void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* locOrNull,
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SkVector* tangentOrNull, SkVector* curvatureOrNull);
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/** Given a src cubic bezier, chop it at the specified t value,
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where 0 < t < 1, and return the two new cubics in dst:
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dst[0..3] and dst[3..6]
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*/
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void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t);
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/** Given a src cubic bezier, chop it at the specified t values,
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where 0 < t < 1, and return the new cubics in dst:
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dst[0..3],dst[3..6],...,dst[3*t_count..3*(t_count+1)]
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*/
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void SkChopCubicAt(const SkPoint src[4], SkPoint dst[], const SkScalar t[],
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int t_count);
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/** Given a src cubic bezier, chop it at the specified t == 1/2,
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The new cubics are returned in dst[0..3] and dst[3..6]
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*/
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void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]);
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/** Given the 4 coefficients for a cubic bezier (either X or Y values), look
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for extrema, and return the number of t-values that are found that represent
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these extrema. If the cubic has no extrema betwee (0..1) exclusive, the
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function returns 0.
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Returned count tValues[]
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0 ignored
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1 0 < tValues[0] < 1
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2 0 < tValues[0] < tValues[1] < 1
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*/
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int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
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SkScalar tValues[2]);
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/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
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the resulting beziers are monotonic in Y. This is called by the scan converter.
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Depending on what is returned, dst[] is treated as follows
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0 dst[0..3] is the original cubic
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1 dst[0..3] and dst[3..6] are the two new cubics
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2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics
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If dst == null, it is ignored and only the count is returned.
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*/
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int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]);
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int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]);
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/** Given a cubic bezier, return 0, 1, or 2 t-values that represent the
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inflection points.
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*/
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int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[2]);
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/** Return 1 for no chop, 2 for having chopped the cubic at a single
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inflection point, 3 for having chopped at 2 inflection points.
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dst will hold the resulting 1, 2, or 3 cubics.
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*/
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int SkChopCubicAtInflections(const SkPoint src[4], SkPoint dst[10]);
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int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]);
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int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
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SkScalar tValues[3] = nullptr);
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/** Returns t value of cusp if cubic has one; returns -1 otherwise.
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*/
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SkScalar SkFindCubicCusp(const SkPoint src[4]);
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bool SkChopMonoCubicAtX(SkPoint src[4], SkScalar y, SkPoint dst[7]);
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bool SkChopMonoCubicAtY(SkPoint src[4], SkScalar x, SkPoint dst[7]);
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enum class SkCubicType {
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kSerpentine,
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kLoop,
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kLocalCusp, // Cusp at a non-infinite parameter value with an inflection at t=infinity.
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kCuspAtInfinity, // Cusp with a cusp at t=infinity and a local inflection.
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kQuadratic,
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kLineOrPoint
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};
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static inline bool SkCubicIsDegenerate(SkCubicType type) {
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switch (type) {
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case SkCubicType::kSerpentine:
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case SkCubicType::kLoop:
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case SkCubicType::kLocalCusp:
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case SkCubicType::kCuspAtInfinity:
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return false;
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case SkCubicType::kQuadratic:
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case SkCubicType::kLineOrPoint:
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return true;
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}
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SK_ABORT("Invalid SkCubicType");
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return true;
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}
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static inline const char* SkCubicTypeName(SkCubicType type) {
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switch (type) {
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case SkCubicType::kSerpentine: return "kSerpentine";
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case SkCubicType::kLoop: return "kLoop";
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case SkCubicType::kLocalCusp: return "kLocalCusp";
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case SkCubicType::kCuspAtInfinity: return "kCuspAtInfinity";
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case SkCubicType::kQuadratic: return "kQuadratic";
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case SkCubicType::kLineOrPoint: return "kLineOrPoint";
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}
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SK_ABORT("Invalid SkCubicType");
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return "";
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}
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/** Returns the cubic classification.
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t[],s[] are set to the two homogeneous parameter values at which points the lines L & M
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intersect with K, sorted from smallest to largest and oriented so positive values of the
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implicit are on the "left" side. For a serpentine curve they are the inflection points. For a
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loop they are the double point. For a local cusp, they are both equal and denote the cusp point.
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For a cusp at an infinite parameter value, one will be the local inflection point and the other
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+inf (t,s = 1,0). If the curve is degenerate (i.e. quadratic or linear) they are both set to a
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parameter value of +inf (t,s = 1,0).
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d[] is filled with the cubic inflection function coefficients. See "Resolution Independent
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Curve Rendering using Programmable Graphics Hardware", 4.2 Curve Categorization:
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If the input points contain infinities or NaN, the return values are undefined.
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https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf
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*/
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SkCubicType SkClassifyCubic(const SkPoint p[4], double t[2] = nullptr, double s[2] = nullptr,
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double d[4] = nullptr);
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///////////////////////////////////////////////////////////////////////////////
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enum SkRotationDirection {
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kCW_SkRotationDirection,
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kCCW_SkRotationDirection
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};
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struct SkConic {
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SkConic() {}
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SkConic(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, SkScalar w) {
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fPts[0] = p0;
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fPts[1] = p1;
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fPts[2] = p2;
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fW = w;
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}
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SkConic(const SkPoint pts[3], SkScalar w) {
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memcpy(fPts, pts, sizeof(fPts));
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fW = w;
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}
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SkPoint fPts[3];
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SkScalar fW;
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void set(const SkPoint pts[3], SkScalar w) {
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memcpy(fPts, pts, 3 * sizeof(SkPoint));
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fW = w;
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}
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void set(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2, SkScalar w) {
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fPts[0] = p0;
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fPts[1] = p1;
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fPts[2] = p2;
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fW = w;
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}
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/**
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* Given a t-value [0...1] return its position and/or tangent.
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* If pos is not null, return its position at the t-value.
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* If tangent is not null, return its tangent at the t-value. NOTE the
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* tangent value's length is arbitrary, and only its direction should
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* be used.
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*/
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void evalAt(SkScalar t, SkPoint* pos, SkVector* tangent = nullptr) const;
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bool SK_WARN_UNUSED_RESULT chopAt(SkScalar t, SkConic dst[2]) const;
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void chopAt(SkScalar t1, SkScalar t2, SkConic* dst) const;
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void chop(SkConic dst[2]) const;
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SkPoint evalAt(SkScalar t) const;
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SkVector evalTangentAt(SkScalar t) const;
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void computeAsQuadError(SkVector* err) const;
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bool asQuadTol(SkScalar tol) const;
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/**
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* return the power-of-2 number of quads needed to approximate this conic
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* with a sequence of quads. Will be >= 0.
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*/
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int SK_API computeQuadPOW2(SkScalar tol) const;
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/**
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* Chop this conic into N quads, stored continguously in pts[], where
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* N = 1 << pow2. The amount of storage needed is (1 + 2 * N)
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*/
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int SK_API SK_WARN_UNUSED_RESULT chopIntoQuadsPOW2(SkPoint pts[], int pow2) const;
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bool findXExtrema(SkScalar* t) const;
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bool findYExtrema(SkScalar* t) const;
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bool chopAtXExtrema(SkConic dst[2]) const;
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bool chopAtYExtrema(SkConic dst[2]) const;
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void computeTightBounds(SkRect* bounds) const;
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void computeFastBounds(SkRect* bounds) const;
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/** Find the parameter value where the conic takes on its maximum curvature.
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*
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* @param t output scalar for max curvature. Will be unchanged if
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* max curvature outside 0..1 range.
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*
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* @return true if max curvature found inside 0..1 range, false otherwise
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*/
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// bool findMaxCurvature(SkScalar* t) const; // unimplemented
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static SkScalar TransformW(const SkPoint[3], SkScalar w, const SkMatrix&);
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enum {
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kMaxConicsForArc = 5
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};
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static int BuildUnitArc(const SkVector& start, const SkVector& stop, SkRotationDirection,
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const SkMatrix*, SkConic conics[kMaxConicsForArc]);
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};
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// inline helpers are contained in a namespace to avoid external leakage to fragile SkNx members
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namespace { // NOLINT(google-build-namespaces)
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/**
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* use for : eval(t) == A * t^2 + B * t + C
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*/
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struct SkQuadCoeff {
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SkQuadCoeff() {}
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SkQuadCoeff(const Sk2s& A, const Sk2s& B, const Sk2s& C)
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: fA(A)
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, fB(B)
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, fC(C)
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{
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}
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SkQuadCoeff(const SkPoint src[3]) {
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fC = from_point(src[0]);
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Sk2s P1 = from_point(src[1]);
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Sk2s P2 = from_point(src[2]);
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fB = times_2(P1 - fC);
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fA = P2 - times_2(P1) + fC;
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}
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Sk2s eval(SkScalar t) {
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Sk2s tt(t);
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return eval(tt);
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}
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Sk2s eval(const Sk2s& tt) {
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return (fA * tt + fB) * tt + fC;
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}
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Sk2s fA;
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Sk2s fB;
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Sk2s fC;
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};
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struct SkConicCoeff {
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SkConicCoeff(const SkConic& conic) {
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Sk2s p0 = from_point(conic.fPts[0]);
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Sk2s p1 = from_point(conic.fPts[1]);
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Sk2s p2 = from_point(conic.fPts[2]);
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Sk2s ww(conic.fW);
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Sk2s p1w = p1 * ww;
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fNumer.fC = p0;
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fNumer.fA = p2 - times_2(p1w) + p0;
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fNumer.fB = times_2(p1w - p0);
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fDenom.fC = Sk2s(1);
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fDenom.fB = times_2(ww - fDenom.fC);
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fDenom.fA = Sk2s(0) - fDenom.fB;
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}
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Sk2s eval(SkScalar t) {
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Sk2s tt(t);
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Sk2s numer = fNumer.eval(tt);
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Sk2s denom = fDenom.eval(tt);
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return numer / denom;
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}
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SkQuadCoeff fNumer;
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SkQuadCoeff fDenom;
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};
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struct SkCubicCoeff {
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SkCubicCoeff(const SkPoint src[4]) {
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Sk2s P0 = from_point(src[0]);
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Sk2s P1 = from_point(src[1]);
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Sk2s P2 = from_point(src[2]);
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Sk2s P3 = from_point(src[3]);
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Sk2s three(3);
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fA = P3 + three * (P1 - P2) - P0;
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fB = three * (P2 - times_2(P1) + P0);
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fC = three * (P1 - P0);
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fD = P0;
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}
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Sk2s eval(SkScalar t) {
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Sk2s tt(t);
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return eval(tt);
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}
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Sk2s eval(const Sk2s& t) {
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return ((fA * t + fB) * t + fC) * t + fD;
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}
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Sk2s fA;
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Sk2s fB;
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Sk2s fC;
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Sk2s fD;
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};
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}
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#include "SkTemplates.h"
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/**
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* Help class to allocate storage for approximating a conic with N quads.
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*/
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class SkAutoConicToQuads {
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public:
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SkAutoConicToQuads() : fQuadCount(0) {}
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/**
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* Given a conic and a tolerance, return the array of points for the
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* approximating quad(s). Call countQuads() to know the number of quads
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* represented in these points.
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*
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* The quads are allocated to share end-points. e.g. if there are 4 quads,
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* there will be 9 points allocated as follows
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* quad[0] == pts[0..2]
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* quad[1] == pts[2..4]
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* quad[2] == pts[4..6]
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* quad[3] == pts[6..8]
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*/
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const SkPoint* computeQuads(const SkConic& conic, SkScalar tol) {
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int pow2 = conic.computeQuadPOW2(tol);
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fQuadCount = 1 << pow2;
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SkPoint* pts = fStorage.reset(1 + 2 * fQuadCount);
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fQuadCount = conic.chopIntoQuadsPOW2(pts, pow2);
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return pts;
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}
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const SkPoint* computeQuads(const SkPoint pts[3], SkScalar weight,
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SkScalar tol) {
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SkConic conic;
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conic.set(pts, weight);
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return computeQuads(conic, tol);
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}
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int countQuads() const { return fQuadCount; }
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private:
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enum {
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kQuadCount = 8, // should handle most conics
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kPointCount = 1 + 2 * kQuadCount,
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};
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SkAutoSTMalloc<kPointCount, SkPoint> fStorage;
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int fQuadCount; // #quads for current usage
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};
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#endif
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