[Android] Add phone progress bar animation behind a flag.

chrome/android/java/src/org/chromium/chrome/browser/widget/ProgressAnimationSmooth.java

+// Copyright 2015 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.
+
+package org.chromium.chrome.browser.widget;
+
+/**
+ * Progress bar animation logic that smoothly accelerates in the beginning and smoothly decelerates
+ * towards the end. The model is applying a constant acceleration followed by a constant
+ * deceleration.
+ */
+class ProgressAnimationSmooth implements ToolbarProgressBar.AnimationLogic {
+    // The (de)acceleration unit is progress per second squared where 0 <= progress <= 1.
+    private static final float FINISHING_ACCELERATION = 7.0f;
+    private static final float ACCELERATION = 0.15f;
+    private static final float DECELERATION = 0.15f;
+
+    // Precomputed constants
+    private static final float CONSTANT_1 = -1.0f / ACCELERATION;
+    private static final float CONSTANT_2 = 2.0f * DECELERATION
+            / ((DECELERATION + ACCELERATION) * ACCELERATION);
+    private static final float CONSTANT_3 = DECELERATION
+            / ((DECELERATION + ACCELERATION) * ACCELERATION * ACCELERATION);
+
+    private float mProgress;
+    private float mVelocity;
+
+    @Override
+    public void reset() {
+        mProgress = 0.0f;
+        mVelocity = 0.0f;
+    }
+
+    @Override
+    public float updateProgress(float targetProgress, float frameTimeSec, int resolution) {
+        assert mProgress <= targetProgress;
+
+        final float acceleratingDuration = computeAcceleratingDuration(
+                targetProgress, frameTimeSec);
+        final float deceleratingDuration = frameTimeSec - acceleratingDuration;
+
+        if (acceleratingDuration > 0.0f) {
+            float velocityChange = (targetProgress == 1.0f ? FINISHING_ACCELERATION : ACCELERATION)
+                    * acceleratingDuration;
+            mProgress += (mVelocity + 0.5f * velocityChange) * acceleratingDuration;
+            mVelocity += velocityChange;
+        }
+
+        if (deceleratingDuration > 0.0f) {
+            float velocityChange = -DECELERATION * deceleratingDuration;
+            mProgress += (mVelocity + 0.5f * velocityChange) * deceleratingDuration;
+            mVelocity += velocityChange;
+        }
+
+        mProgress = Math.min(mProgress, targetProgress);
+        if (targetProgress - mProgress < 0.5f / resolution) {
+            mProgress = targetProgress;
+            mVelocity = 0.0f;
+        }
+
+        return mProgress;
+    }
+
+    /**
+     * Computes and returns accelerating duration.
+     *
+     * Symbol              Description    Corresponding variable
+     *    v_0         Initial velocity                 mVelocity
+     *      A             Acceleration              ACCELERATION
+     *      D             Deceleration              DECELERATION
+     *    d_A    Accelerating duration
+     *    d_D    Decelerating duration
+     *
+     * Given the initial position and the initial velocity, we assume that it accelerates constantly
+     * and then decelerates constantly.
+     *
+     * We want to stop smoothly when it reaches the end. Thus zero velocity at the end:
+     * v_0 + A d_A - D d_D = 0
+     * Equation image: http://www.HostMath.com/Show.aspx?Code=v_0%20%2B%20A%20d_A%20-%20D%20d_D%20%3D%200
+     *
+     * The traveled distance should be (targetProgress - mProgress):
+     * targetProgress - mProgress =
+     *         \int_0^{d_A} (v_0 + A t) dt + \int_0^{d_D} (v_{0} + A d_A - D t) dt
+     * Equation image: http://www.HostMath.com/Show.aspx?Code=targetProgress%20-%20mProgress%20%3D%20%5Cint_0%5E%7Bd_A%7D%20(v_0%20%2B%20A%20t)%20dt%20%2B%20%5Cint_0%5E%7Bd_D%7D%20(v_%7B0%7D%20%2B%20A%20d_A%20-%20D%20t)dt
+     *
+     * This function solves d_A from the above equations.
+     */
+    private float computeAcceleratingDuration(float targetProgress, float frameTimeSec) {
+        if (targetProgress == 1.0f) {
+            return frameTimeSec;
+        } else {
+            float maxAcceleratingDuration = CONSTANT_1 * mVelocity + (float) Math.sqrt(
+                    CONSTANT_2 * (targetProgress - mProgress) + CONSTANT_3 * mVelocity * mVelocity);
+            maxAcceleratingDuration = Math.max(maxAcceleratingDuration, 0.0f);
+            if (frameTimeSec <= maxAcceleratingDuration) {
+                return frameTimeSec;
+            } else {
+                return maxAcceleratingDuration;
+            }
+        }
+    }
+}