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// Copyright 2014 The Chromium Authors
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#ifndef UI_GFX_GEOMETRY_CUBIC_BEZIER_H_
#define UI_GFX_GEOMETRY_CUBIC_BEZIER_H_
#include <array>
#include "base/component_export.h"
namespace gfx {
#define CUBIC_BEZIER_SPLINE_SAMPLES 11
class COMPONENT_EXPORT(GEOMETRY) CubicBezier {
public:
CubicBezier(double p1x, double p1y, double p2x, double p2y);
CubicBezier(const CubicBezier& other);
CubicBezier& operator=(const CubicBezier&) = delete;
double SampleCurveX(double t) const {
// `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
// The x values are in the range [0, 1]. So it isn't needed toFinite
// clamping.
// https://drafts.csswg.org/css-easing-1/#funcdef-cubic-bezier-easing-function-cubic-bezier
return ((ax_ * t + bx_) * t + cx_) * t;
}
double SampleCurveY(double t) const {
return ToFinite(((ay_ * t + by_) * t + cy_) * t);
}
double SampleCurveDerivativeX(double t) const {
return (3.0 * ax_ * t + 2.0 * bx_) * t + cx_;
}
double SampleCurveDerivativeY(double t) const {
return ToFinite(
ToFinite(ToFinite(3.0 * ay_) * t + ToFinite(2.0 * by_)) * t + cy_);
}
static double GetDefaultEpsilon();
// Given an x value, find a parametric value it came from.
// x must be in [0, 1] range. Doesn't use gradients.
double SolveCurveX(double x, double epsilon) const;
// Evaluates y at the given x with default epsilon.
double Solve(double x) const;
// Evaluates y at the given x. The epsilon parameter provides a hint as to the
// required accuracy and is not guaranteed. Uses gradients if x is
// out of [0, 1] range.
double SolveWithEpsilon(double x, double epsilon) const {
if (x < 0.0)
return ToFinite(0.0 + start_gradient_ * x);
if (x > 1.0)
return ToFinite(1.0 + end_gradient_ * (x - 1.0));
return SampleCurveY(SolveCurveX(x, epsilon));
}
// Returns an approximation of dy/dx at the given x with default epsilon.
double Slope(double x) const;
// Returns an approximation of dy/dx at the given x.
// Clamps x to range [0, 1].
double SlopeWithEpsilon(double x, double epsilon) const;
// These getters are used rarely. We reverse compute them from coefficients.
// See CubicBezier::InitCoefficients. The speed has been traded for memory.
double GetX1() const;
double GetY1() const;
double GetX2() const;
double GetY2() const;
// Gets the bezier's minimum y value in the interval [0, 1].
double range_min() const { return range_min_; }
// Gets the bezier's maximum y value in the interval [0, 1].
double range_max() const { return range_max_; }
private:
void InitCoefficients(double p1x, double p1y, double p2x, double p2y);
void InitGradients(double p1x, double p1y, double p2x, double p2y);
void InitRange(double p1y, double p2y);
void InitSpline();
static double ToFinite(double value);
double ax_;
double bx_;
double cx_;
double ay_;
double by_;
double cy_;
double start_gradient_;
double end_gradient_;
double range_min_;
double range_max_;
std::array<double, CUBIC_BEZIER_SPLINE_SAMPLES> spline_samples_;
#ifndef NDEBUG
// Guard against attempted to solve for t given x in the event that the curve
// may have multiple values for t for some values of x in [0, 1].
bool monotonically_increasing_;
#endif
};
} // namespace gfx
#endif // UI_GFX_GEOMETRY_CUBIC_BEZIER_H_
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