1 // Copyright 2014 The Chromium Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style license that can be 3 // found in the LICENSE file. 4 5 #ifndef UI_GFX_GEOMETRY_CUBIC_BEZIER_H_ 6 #define UI_GFX_GEOMETRY_CUBIC_BEZIER_H_ 7 8 #include "base/macros.h" 9 #include "ui/gfx/gfx_export.h" 10 11 namespace gfx { 12 13 class GFX_EXPORT CubicBezier { 14 public: 15 CubicBezier(double p1x, double p1y, double p2x, double p2y); 16 CubicBezier(const CubicBezier& other); 17 SampleCurveX(double t)18 double SampleCurveX(double t) const { 19 // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule. 20 return ((ax_ * t + bx_) * t + cx_) * t; 21 } 22 SampleCurveY(double t)23 double SampleCurveY(double t) const { 24 return ((ay_ * t + by_) * t + cy_) * t; 25 } 26 SampleCurveDerivativeX(double t)27 double SampleCurveDerivativeX(double t) const { 28 return (3.0 * ax_ * t + 2.0 * bx_) * t + cx_; 29 } 30 SampleCurveDerivativeY(double t)31 double SampleCurveDerivativeY(double t) const { 32 return (3.0 * ay_ * t + 2.0 * by_) * t + cy_; 33 } 34 35 static double GetDefaultEpsilon(); 36 37 // Given an x value, find a parametric value it came from. 38 // x must be in [0, 1] range. Doesn't use gradients. 39 double SolveCurveX(double x, double epsilon) const; 40 41 // Evaluates y at the given x with default epsilon. 42 double Solve(double x) const; 43 // Evaluates y at the given x. The epsilon parameter provides a hint as to the 44 // required accuracy and is not guaranteed. Uses gradients if x is 45 // out of [0, 1] range. SolveWithEpsilon(double x,double epsilon)46 double SolveWithEpsilon(double x, double epsilon) const { 47 if (x < 0.0) 48 return 0.0 + start_gradient_ * x; 49 if (x > 1.0) 50 return 1.0 + end_gradient_ * (x - 1.0); 51 return SampleCurveY(SolveCurveX(x, epsilon)); 52 } 53 54 // Returns an approximation of dy/dx at the given x with default epsilon. 55 double Slope(double x) const; 56 // Returns an approximation of dy/dx at the given x. 57 // Clamps x to range [0, 1]. 58 double SlopeWithEpsilon(double x, double epsilon) const; 59 60 // These getters are used rarely. We reverse compute them from coefficients. 61 // See CubicBezier::InitCoefficients. The speed has been traded for memory. 62 double GetX1() const; 63 double GetY1() const; 64 double GetX2() const; 65 double GetY2() const; 66 67 // Gets the bezier's minimum y value in the interval [0, 1]. range_min()68 double range_min() const { return range_min_; } 69 // Gets the bezier's maximum y value in the interval [0, 1]. range_max()70 double range_max() const { return range_max_; } 71 72 private: 73 void InitCoefficients(double p1x, double p1y, double p2x, double p2y); 74 void InitGradients(double p1x, double p1y, double p2x, double p2y); 75 void InitRange(double p1y, double p2y); 76 77 double ax_; 78 double bx_; 79 double cx_; 80 81 double ay_; 82 double by_; 83 double cy_; 84 85 double start_gradient_; 86 double end_gradient_; 87 88 double range_min_; 89 double range_max_; 90 91 DISALLOW_ASSIGN(CubicBezier); 92 }; 93 94 } // namespace gfx 95 96 #endif // UI_GFX_GEOMETRY_CUBIC_BEZIER_H_ 97