Stabilize initial scroll simulation velocity on Android (#8543)

Previously, we would create a simulation whose initial velocity did not match
the requested parameters. We now compute the parameters for the simulation in a
way that ensures all the math works out.

Fixes #8255

packages/flutter/lib/src/widgets/scroll_simulation.dart

@@ -107,52 +107,41 @@ class BouncingScrollSimulation extends SimulationGroup {
 // simplifications have been made.
 class ClampingScrollSimulation extends Simulation {
   /// Creates a scroll physics simulation that matches Android scrolling.
-  //
-  // TODO(ianh): The incoming `velocity` is used to determine the starting speed
-  // and duration, but does not represent the exact velocity of the simulation
-  // at t=0 as it should. This causes crazy scrolling irregularities when the
-  // scroll dimensions change during a fling.
   ClampingScrollSimulation({
     @required this.position,
     @required this.velocity,
     this.friction: 0.015,
     Tolerance tolerance: Tolerance.defaultTolerance,
   }) : super(tolerance: tolerance) {
-    _scaledFriction = friction * _decelerationForFriction(0.84); // See mPhysicalCoeff
+    assert(_flingVelocityPenetration(0.0) == _kInitialVelocityPenetration);
     _duration = _flingDuration(velocity);
-    _distance = _flingDistance(velocity);
+    _distance = (velocity * _duration / _kInitialVelocityPenetration).abs();
   }
 
   final double position;
   final double velocity;
   final double friction;
 
-  double _scaledFriction;
   double _duration;
   double _distance;
 
   // See DECELERATION_RATE.
-  static final double _decelerationRate = math.log(0.78) / math.log(0.9);
+  static final double _kDecelerationRate = math.log(0.78) / math.log(0.9);
 
   // See computeDeceleration().
-  double _decelerationForFriction(double friction) {
+  static double _decelerationForFriction(double friction) {
     return friction * 61774.04968;
   }
 
-  // See getSplineDeceleration().
-  double _flingDeceleration(double velocity) {
-    return math.log(0.35 * velocity.abs() / _scaledFriction);
-  }
-
   // See getSplineFlingDuration(). Returns a value in seconds.
   double _flingDuration(double velocity) {
-    return math.exp(_flingDeceleration(velocity) / (_decelerationRate - 1.0));
-  }
+    // See mPhysicalCoeff
+    final double scaledFriction = friction * _decelerationForFriction(0.84);
 
-  // See getSplineFlingDistance().
-  double _flingDistance(double velocity) {
-    final double rate = _decelerationRate / (_decelerationRate - 1.0) * _flingDeceleration(velocity);
-    return _scaledFriction * math.exp(rate);
+    // See getSplineDeceleration().
+    final double deceleration = math.log(0.35 * velocity.abs() / scaledFriction);
+
+    return math.exp(deceleration / (_kDecelerationRate - 1.0));
   }
 
   // Based on a cubic curve fit to the Scroller.computeScrollOffset() values
@@ -170,13 +159,14 @@ class ClampingScrollSimulation extends Simulation {
   // Scale f(t) so that 0.0 <= f(t) <= 1.0
   // f(t) = (1165.03 t^3 - 3143.62 t^2 + 2945.87 t) / 961.0
   //      = 1.2 t^3 - 3.27 t^2 + 3.065 t
-  double _flingDistancePenetration(double t) {
-    return (1.2 * t * t * t) - (3.27 * t * t) + (3.065 * t);
+  static const double _kInitialVelocityPenetration = 3.065;
+  static double _flingDistancePenetration(double t) {
+    return (1.2 * t * t * t) - (3.27 * t * t) + (_kInitialVelocityPenetration * t);
   }
 
   // The derivative of the _flingDistancePenetration() function.
-  double _flingVelocityPenetration(double t) {
-    return (3.63693 * t * t) - (6.5424 * t) + 3.06542;
+  static double _flingVelocityPenetration(double t) {
+    return (3.6 * t * t) - (6.54 * t) + _kInitialVelocityPenetration;
   }
 
   @override
@@ -188,7 +178,7 @@ class ClampingScrollSimulation extends Simulation {
   @override
   double dx(double time) {
     final double t = (time / _duration).clamp(0.0, 1.0);
-    return _distance * _flingVelocityPenetration(t) * velocity.sign;
+    return _distance * _flingVelocityPenetration(t) * velocity.sign / _duration;
   }
 
   @override

packages/flutter/test/widgets/scroll_simulation_test.dart

@@ -0,0 +1,26 @@
+// Copyright 2017 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.
+
+import 'package:flutter_test/flutter_test.dart';
+import 'package:flutter/widgets.dart';
+
+void main() {
+  test('ClampingScrollSimulation has a stable initial conditions', () {
+    void checkInitialConditions(double position, double velocity) {
+      ClampingScrollSimulation simulation = new ClampingScrollSimulation(position: position, velocity: velocity);
+      expect(simulation.x(0.0), closeTo(position, 0.00001));
+      expect(simulation.dx(0.0), closeTo(velocity, 0.00001));
+    }
+
+    checkInitialConditions(51.0, 2866.91537);
+    checkInitialConditions(584.0, 2617.294734);
+    checkInitialConditions(345.0, 1982.785934);
+    checkInitialConditions(0.0, 1831.366634);
+    checkInitialConditions(-156.2, 1541.57665);
+    checkInitialConditions(4.0, 1139.250439);
+    checkInitialConditions(4534.0, 1073.553798);
+    checkInitialConditions(75.0, 614.2093);
+    checkInitialConditions(5469.0, 182.114534);
+  });
+}

packages/flutter/test/widgets/scrollable_fling_test.dart

@@ -91,6 +91,6 @@ void main() {
     expect(log, equals(<String>['tap 18']));
     await tester.tap(find.byType(Scrollable));
     await tester.pump(const Duration(milliseconds: 50));
-    expect(log, equals(<String>['tap 18', 'tap 43']));
+    expect(log, equals(<String>['tap 18', 'tap 42']));
   }, skip: Platform.isMacOS); // Skip due to https://github.com/flutter/flutter/issues/6961
 }