UI GFX Geometry: Make UnitBezier a wrapper for gfx::CubicBezier

ui/gfx/geometry/cubic_bezier.h

 // Copyright 2014 The Chromium Authors. All rights reserved.
 // 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 "base/macros.h"
 #include "ui/gfx/gfx_export.h"
 
 namespace gfx {
 
 class GFX_EXPORT CubicBezier {
  public:
-  CubicBezier(double x1, double y1, double x2, double y2);
-  ~CubicBezier();
+  CubicBezier(double p1x, double p1y, double p2x, double p2y);
 
-  // Returns an approximation of y at the given x.
+  double SampleCurveX(double t) const {
+    // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
+    return ((ax_ * t + bx_) * t + cx_) * t;
+  }
+
+  double SampleCurveY(double t) const {
+    return ((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 (3.0 * ay_ * t + 2.0 * by_) * t + cy_;
+  }
+
+  // Given an x value, find a parametric value it came from.
+  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.
+  double SolveWithEpsilon(double x, double epsilon) const {
+    if (x < 0.0)
+      return 0.0 + start_gradient_ * x;
+    if (x > 1.0)
+      return 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.
-  double Slope(double x) const;
+  double SlopeWithEpsilon(double x, double epsilon) const {
+    double t = SolveCurveX(x, epsilon);
+    double dx = SampleCurveDerivativeX(t);
+    double dy = SampleCurveDerivativeY(t);
+    return dy / dx;
+  }
 
   // Sets |min| and |max| to the bezier's minimum and maximium y values in the
   // interval [0, 1].
-  void Range(double* min, double* max) const;
+  void Range(double* min, double* max) const {
+    *min = range_min_;
+    *max = range_max_;
+  }
 
  private:
-  void InitGradients();
+  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);
 
-  double x1_;
-  double y1_;
-  double x2_;
-  double y2_;
+  double ax_;
+  double bx_;
+  double cx_;
+
+  double ay_;
+  double by_;
+  double cy_;
 
   double start_gradient_;
   double end_gradient_;
 
+  double range_min_;
+  double range_max_;
+
   DISALLOW_ASSIGN(CubicBezier);
 };
 
 }  // namespace gfx
 
 #endif  // UI_GFX_GEOMETRY_CUBIC_BEZIER_H_