Use a bezier timing function for the overview mode animation

cc/animation/timing_function.cc

Index: cc/animation/timing_function.cc
diff --git a/cc/animation/timing_function.cc b/cc/animation/timing_function.cc
index 7fdb37fed962a48fa68a3e9b58252b694c50f4ca..bf11c20fe03a13f448f486ff600aef2005ea9d4c 100644
--- a/cc/animation/timing_function.cc
+++ b/cc/animation/timing_function.cc
@@ -2,67 +2,11 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
-#include <algorithm>
-#include <cmath>
-
 #include "base/logging.h"
 #include "cc/animation/timing_function.h"
 
 namespace cc {
 
-namespace {
-
-static const double kBezierEpsilon = 1e-7;
-static const int MAX_STEPS = 30;
-
-static double eval_bezier(double x1, double x2, double t) {
-  const double x1_times_3 = 3.0 * x1;
-  const double x2_times_3 = 3.0 * x2;
-  const double h3 = x1_times_3;
-  const double h1 = x1_times_3 - x2_times_3 + 1.0;
-  const double h2 = x2_times_3 - 6.0 * x1;
-  return t * (t * (t * h1 + h2) + h3);
-}
-
-static double bezier_interp(double x1,
-                            double y1,
-                            double x2,
-                            double y2,
-                            double x) {
-  DCHECK_GE(1.0, x1);
-  DCHECK_LE(0.0, x1);
-  DCHECK_GE(1.0, x2);
-  DCHECK_LE(0.0, x2);
-
-  x1 = std::min(std::max(x1, 0.0), 1.0);
-  x2 = std::min(std::max(x2, 0.0), 1.0);
-  x = std::min(std::max(x, 0.0), 1.0);
-
-  // Step 1. Find the t corresponding to the given x. I.e., we want t such that
-  // eval_bezier(x1, x2, t) = x. There is a unique solution if x1 and x2 lie
-  // within (0, 1).
-  //
-  // We're just going to do bisection for now (for simplicity), but we could
-  // easily do some newton steps if this turns out to be a bottleneck.
-  double t = 0.0;
-  double step = 1.0;
-  for (int i = 0; i < MAX_STEPS; ++i, step *= 0.5) {
-    const double error = eval_bezier(x1, x2, t) - x;
-    if (std::abs(error) < kBezierEpsilon)
-      break;
-    t += error > 0.0 ? -step : step;
-  }
-
-  // We should have terminated the above loop because we got close to x, not
-  // because we exceeded MAX_STEPS. Do a DCHECK here to confirm.
-  DCHECK_GT(kBezierEpsilon, std::abs(eval_bezier(x1, x2, t) - x));
-
-  // Step 2. Return the interpolated y values at the t we computed above.
-  return eval_bezier(y1, y2, t);
-}
-
-}  // namespace
-
 TimingFunction::TimingFunction() {}
 
 TimingFunction::~TimingFunction() {}
@@ -80,12 +24,12 @@ CubicBezierTimingFunction::CubicBezierTimingFunction(double x1,
                                                      double y1,
                                                      double x2,
                                                      double y2)
-    : x1_(x1), y1_(y1), x2_(x2), y2_(y2) {}
+    : bezier_(x1, y1, x2, y2) {}
 
 CubicBezierTimingFunction::~CubicBezierTimingFunction() {}
 
 float CubicBezierTimingFunction::GetValue(double x) const {
-  return static_cast<float>(bezier_interp(x1_, y1_, x2_, y2_, x));
+  return static_cast<float>(bezier_.Solve(x));
 }
 
 scoped_ptr<AnimationCurve> CubicBezierTimingFunction::Clone() const {
@@ -94,50 +38,11 @@ scoped_ptr<AnimationCurve> CubicBezierTimingFunction::Clone() const {
 }
 
 void CubicBezierTimingFunction::Range(float* min, float* max) const {
-  *min = 0.f;
-  *max = 1.f;
-  if (0.f <= y1_ && y1_ < 1.f && 0.f <= y2_ && y2_ <= 1.f)
-    return;
-
-  // Represent the function's derivative in the form at^2 + bt + c.
-  float a = 3.f * (y1_ - y2_) + 1.f;
-  float b = 2.f * (y2_ - 2.f * y1_);
-  float c = y1_;
-
-  // Check if the derivative is constant.
-  if (std::abs(a) < kBezierEpsilon &&
-      std::abs(b) < kBezierEpsilon)
-    return;
-
-  // Zeros of the function's derivative.
-  float t_1 = 0.f;
-  float t_2 = 0.f;
-
-  if (std::abs(a) < kBezierEpsilon) {
-    // The function's derivative is linear.
-    t_1 = -c / b;
-  } else {
-    // The function's derivative is a quadratic. We find the zeros of this
-    // quadratic using the quadratic formula.
-    float discriminant = b * b - 4 * a * c;
-    if (discriminant < 0.f)
-      return;
-    float discriminant_sqrt = sqrt(discriminant);
-    t_1 = (-b + discriminant_sqrt) / (2.f * a);
-    t_2 = (-b - discriminant_sqrt) / (2.f * a);
-  }
-
-  float sol_1 = 0.f;
-  float sol_2 = 0.f;
-
-  if (0.f < t_1 && t_1 < 1.f)
-    sol_1 = eval_bezier(y1_, y2_, t_1);
-
-  if (0.f < t_2 && t_2 < 1.f)
-    sol_2 = eval_bezier(y1_, y2_, t_2);
-
-  *min = std::min(std::min(*min, sol_1), sol_2);
-  *max = std::max(std::max(*max, sol_1), sol_2);
+  double min_d = 0;
+  double max_d = 1;
+  bezier_.Range(&min_d, &max_d);
+  *min = static_cast<float>(min_d);
+  *max = static_cast<float>(max_d);
 }
 
 // These numbers come from