Update ClampingScrollSimulation to better match Android (#77497)

dev/tools/generate_android_spline_data.dart

+// Copyright 2014 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+const int _nbSamples = 100;
+final List<double> _splinePosition = List<double>.filled(_nbSamples + 1, 0.0);
+final List<double> _splineTime = List<double>.filled(_nbSamples + 1, 0.0);
+const double _startTension = 0.5;
+const double _endTension = 1.0;
+const double _inflexion = 0.35;
+
+// Generate the spline data used in ClampingScrollSimulation.
+//
+// This logic is a translation of the 2-dimensional logic found in
+// https://android.googlesource.com/platform/frameworks/base/+/master/core/java/android/widget/Scroller.java.
+//
+// The output of this program should be copied over to [_splinePosition] in
+// flutter/packages/flutter/lib/src/widgets/scroll_simulation.dart.
+void main() {
+  const double p1 = _startTension * _inflexion;
+  const double p2 = 1.0 - _endTension * (1.0 - _inflexion);
+  double xMin = 0.0;
+  double yMin = 0.0;
+  for (int i = 0; i < _nbSamples; i++) {
+    final double alpha = i / _nbSamples;
+    double xMax = 1.0;
+    double x, tx, coef;
+    while (true) {
+      x = xMin + (xMax - xMin) / 2.0;
+      coef = 3.0 * x * (1.0 - x);
+      tx = coef * ((1.0 - x) * p1 + x * p2) + x * x * x;
+      if ((tx - alpha).abs() < 1e-5) {
+        break;
+      }
+      if (tx > alpha) {
+        xMax = x;
+      } else {
+        xMin = x;
+      }
+    }
+    _splinePosition[i] = coef * ((1.0 - x) * _startTension + x) + x * x * x;
+    double yMax = 1.0;
+    double y, dy;
+    while (true) {
+      y = yMin + (yMax - yMin) / 2.0;
+      coef = 3.0 * y * (1.0 - y);
+      dy = coef * ((1.0 - y) * _startTension + y) + y * y * y;
+      if ((dy - alpha).abs() < 1e-5) {
+        break;
+      }
+      if (dy > alpha) {
+        yMax = y;
+      } else {
+        yMin = y;
+      }
+    }
+    _splineTime[i] = coef * ((1.0 - y) * p1 + y * p2) + y * y * y;
+  }
+  _splinePosition[_nbSamples] = _splineTime[_nbSamples] = 1.0;
+  print(_splinePosition);
+}

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

@@ -129,6 +129,8 @@ class BouncingScrollSimulation extends Simulation {
   }
 }
 
+const double _inflexion = 0.35;
+
 /// An implementation of scroll physics that matches Android.
 ///
 /// See also:
@@ -147,10 +149,9 @@ class ClampingScrollSimulation extends Simulation {
     required this.velocity,
     this.friction = 0.015,
     Tolerance tolerance = Tolerance.defaultTolerance,
-  }) : assert(_flingVelocityPenetration(0.0) == _initialVelocityPenetration),
-       super(tolerance: tolerance) {
-    _duration = _flingDuration(velocity);
-    _distance = (velocity * _duration / _initialVelocityPenetration).abs();
+  }) : super(tolerance: tolerance) {
+    _duration = _splineFlingDuration(velocity);
+    _distance = _splineFlingDistance(velocity);
   }
 
   /// The position of the particle at the beginning of the simulation.
@@ -165,7 +166,7 @@ class ClampingScrollSimulation extends Simulation {
   /// The more friction the particle experiences, the sooner it stops.
   final double friction;
 
-  late double _duration;
+  late int _duration;
   late double _distance;
 
   // See DECELERATION_RATE.
@@ -173,59 +174,186 @@ class ClampingScrollSimulation extends Simulation {
 
   // See computeDeceleration().
   static double _decelerationForFriction(double friction) {
-    return friction * 61774.04968;
+    return 9.80665 *
+        39.37 *
+        friction *
+        1.0 * // Flutter operates on logical pixels so the DPI should be 1.0.
+        160.0;
   }
 
-  // See getSplineFlingDuration(). Returns a value in seconds.
-  double _flingDuration(double velocity) {
-    // See mPhysicalCoeff
-    final double scaledFriction = friction * _decelerationForFriction(0.84);
-
   // See getSplineDeceleration().
-    final double deceleration = math.log(0.35 * velocity.abs() / scaledFriction);
-
-    return math.exp(deceleration / (_kDecelerationRate - 1.0));
+  double _splineDeceleration(double velocity) {
+    return math.log(_inflexion *
+        velocity.abs() /
+        (friction * _decelerationForFriction(0.84)));
   }
 
-  // Based on a cubic curve fit to the Scroller.computeScrollOffset() values
-  // produced for an initial velocity of 4000. The value of Scroller.getDuration()
-  // and Scroller.getFinalY() were 686ms and 961 pixels respectively.
-  //
-  // Algebra courtesy of Wolfram Alpha.
-  //
-  // f(x) = scrollOffset, x is time in milliseconds
-  // f(x) = 3.60882×10^-6 x^3 - 0.00668009 x^2 + 4.29427 x - 3.15307
-  // f(x) = 3.60882×10^-6 x^3 - 0.00668009 x^2 + 4.29427 x, so f(0) is 0
-  // f(686ms) = 961 pixels
-  // Scale to f(0 <= t <= 1.0), x = t * 686
-  // f(t) = 1165.03 t^3 - 3143.62 t^2 + 2945.87 t
-  // 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
-  static const double _initialVelocityPenetration = 3.065;
-  static double _flingDistancePenetration(double t) {
-    return (1.2 * t * t * t) - (3.27 * t * t) + (_initialVelocityPenetration * t);
+  // See getSplineFlingDuration().
+  int _splineFlingDuration(double velocity) {
+    final double deceleration = _splineDeceleration(velocity);
+    return (1000 * math.exp(deceleration / (_kDecelerationRate - 1.0))).round();
   }
 
-  // The derivative of the _flingDistancePenetration() function.
-  static double _flingVelocityPenetration(double t) {
-    return (3.6 * t * t) - (6.54 * t) + _initialVelocityPenetration;
+  // See getSplineFlingDistance().
+  double _splineFlingDistance(double velocity) {
+    final double l = _splineDeceleration(velocity);
+    final double decelMinusOne = _kDecelerationRate - 1.0;
+    return friction *
+        _decelerationForFriction(0.84) *
+        math.exp(_kDecelerationRate / decelMinusOne * l);
   }
 
   @override
   double x(double time) {
-    final double t = (time / _duration).clamp(0.0, 1.0);
-    return position + _distance * _flingDistancePenetration(t) * velocity.sign;
+    if (time == 0) {
+      return position;
+    }
+    final _NBSample sample = _NBSample(time, _duration);
+    return position + (sample.distanceCoef * _distance) * velocity.sign;
   }
 
   @override
   double dx(double time) {
-    final double t = (time / _duration).clamp(0.0, 1.0);
-    return _distance * _flingVelocityPenetration(t) * velocity.sign / _duration;
+    if (time == 0) {
+      return velocity;
+    }
+    final _NBSample sample = _NBSample(time, _duration);
+    return sample.velocityCoef * _distance / _duration * velocity.sign * 1000.0;
   }
 
   @override
   bool isDone(double time) {
-    return time >= _duration;
+    return time * 1000.0 >= _duration;
+  }
+}
+
+class _NBSample {
+  _NBSample(double time, int duration) {
+    // See computeScrollOffset().
+    final double t = time * 1000.0 / duration;
+    final int index = (_nbSamples * t).clamp(0, _nbSamples).round();
+    _distanceCoef = 1.0;
+    _velocityCoef = 0.0;
+    if (index < _nbSamples) {
+      final double tInf = index / _nbSamples;
+      final double tSup = (index + 1) / _nbSamples;
+      final double dInf = _splinePosition[index];
+      final double dSup = _splinePosition[index + 1];
+      _velocityCoef = (dSup - dInf) / (tSup - tInf);
+      _distanceCoef = dInf + (t - tInf) * _velocityCoef;
     }
+  }
+
+  late double _velocityCoef;
+  double get velocityCoef => _velocityCoef;
+
+  late double _distanceCoef;
+  double get distanceCoef => _distanceCoef;
+
+  static const int _nbSamples = 100;
+
+  // Generated from dev/tools/generate_android_spline_data.dart.
+  static final List<double> _splinePosition = <double>[
+    0.000022888183591973643,
+    0.028561000304762274,
+    0.05705195792956655,
+    0.08538917797618413,
+    0.11349556286812107,
+    0.14129881694635613,
+    0.16877157254923383,
+    0.19581093511175632,
+    0.22239649722992452,
+    0.24843841866631658,
+    0.2740024733220569,
+    0.298967680744136,
+    0.32333234658228116,
+    0.34709556909569184,
+    0.3702249257894571,
+    0.39272483400399893,
+    0.41456988647721615,
+    0.43582889025419114,
+    0.4564192786416,
+    0.476410299013587,
+    0.4957560715637827,
+    0.5145493169954743,
+    0.5327205670880077,
+    0.5502846891191615,
+    0.5673274324802855,
+    0.583810881323224,
+    0.5997478744397482,
+    0.615194045299478,
+    0.6301165005270208,
+    0.6445484042257972,
+    0.6585198219185201,
+    0.6720397744233084,
+    0.6850997688076114,
+    0.6977281404741683,
+    0.7099506591298411,
+    0.7217749311525871,
+    0.7331784038850426,
+    0.7442308394229518,
+    0.7549087205105974,
+    0.7652471277371271,
+    0.7752251637549381,
+    0.7848768260203478,
+    0.7942056937103814,
+    0.8032299679689082,
+    0.8119428702388629,
+    0.8203713516576219,
+    0.8285187880808974,
+    0.8363794492831295,
+    0.8439768562813565,
+    0.851322799855549,
+    0.8584111051351724,
+    0.8652534074722162,
+    0.8718525580962131,
+    0.8782333271742155,
+    0.8843892099362031,
+    0.8903155590440985,
+    0.8960465359221951,
+    0.9015574505919048,
+    0.9068736766459904,
+    0.9119951682409297,
+    0.9169321898723632,
+    0.9216747065581234,
+    0.9262420604674766,
+    0.9306331858366086,
+    0.9348476990715433,
+    0.9389007110754832,
+    0.9427903495057521,
+    0.9465220679845756,
+    0.9500943036519721,
+    0.9535176728088761,
+    0.9567898524767604,
+    0.959924306623116,
+    0.9629127700159108,
+    0.9657622101750765,
+    0.9684818726275105,
+    0.9710676079044347,
+    0.9735231939498,
+    0.9758514437576309,
+    0.9780599066560445,
+    0.9801485715370128,
+    0.9821149805689633,
+    0.9839677526782791,
+    0.9857085499421516,
+    0.9873347811966005,
+    0.9888547171706613,
+    0.9902689443512227,
+    0.9915771042095881,
+    0.9927840651641069,
+    0.9938913963715834,
+    0.9948987305580712,
+    0.9958114963810524,
+    0.9966274782266875,
+    0.997352148697352,
+    0.9979848677523623,
+    0.9985285021374979,
+    0.9989844084453229,
+    0.9993537595844986,
+    0.999638729860106,
+    0.9998403888004533,
+    0.9999602810470701,
+    1.0
+  ];
 }

packages/flutter/test/widgets/list_wheel_scroll_view_test.dart

@@ -2,9 +2,9 @@
 // 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/rendering.dart';
 import 'package:flutter/widgets.dart';
+import 'package:flutter_test/flutter_test.dart';
 
 import '../rendering/mock_canvas.dart';
 import '../rendering/rendering_tester.dart';
@@ -1195,7 +1195,7 @@ void main() {
       await tester.fling(
         find.byType(ListWheelScrollView),
         const Offset(0.0, -50.0),
-        800.0,
+        100.0,
       );
 
       // At this moment, the ballistics is started but 50px is still inside the

packages/flutter/test/widgets/scroll_simulation_test.dart

@@ -2,8 +2,8 @@
 // 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';
+import 'package:flutter_test/flutter_test.dart';
 
 void main() {
   test('ClampingScrollSimulation has a stable initial conditions', () {
@@ -23,4 +23,21 @@ void main() {
     checkInitialConditions(75.0, 614.2093);
     checkInitialConditions(5469.0, 182.114534);
   });
+
+  test('ClampingScrollSimulation velocity eventually reaches zero', () {
+    void checkFinalConditions(double position, double velocity) {
+      final ClampingScrollSimulation simulation = ClampingScrollSimulation(position: position, velocity: velocity);
+      expect(simulation.dx(10.0), equals(0.0));
+    }
+
+    checkFinalConditions(51.0, 2000.0);
+    checkFinalConditions(584.0, 2617.294734);
+    checkFinalConditions(345.0, 1982.785934);
+    checkFinalConditions(0.0, 1831.366634);
+    checkFinalConditions(-156.2, 1541.57665);
+    checkFinalConditions(4.0, 1139.250439);
+    checkFinalConditions(4534.0, 1073.553798);
+    checkFinalConditions(75.0, 614.2093);
+    checkFinalConditions(5469.0, 182.114534);
+  });
 }

packages/flutter/test/widgets/scrollable_fling_test.dart

@@ -147,6 +147,6 @@ void main() {
     expect(log, equals(<String>['tap 21']));
     await tester.tap(find.byType(Scrollable));
     await tester.pump(const Duration(milliseconds: 50));
-    expect(log, equals(<String>['tap 21', 'tap 48']));
+    expect(log, equals(<String>['tap 21', 'tap 49']));
   });
 }

packages/flutter/test/widgets/scrollable_semantics_test.dart

@@ -4,10 +4,10 @@
 
 import 'dart:ui';
 
+import 'package:flutter/gestures.dart' show DragStartBehavior;
 import 'package:flutter/material.dart';
-import 'package:flutter_test/flutter_test.dart';
 import 'package:flutter/rendering.dart';
-import 'package:flutter/gestures.dart' show DragStartBehavior;
+import 'package:flutter_test/flutter_test.dart';
 
 import 'semantics_tester.dart';
 
@@ -232,7 +232,7 @@ void main() {
 
     expect(semantics, includesNodeWith(
       scrollExtentMin: 0.0,
-      scrollPosition: 380.2,
+      scrollPosition: 394.3,
       scrollExtentMax: 520.0,
       actions: <SemanticsAction>[
         SemanticsAction.scrollUp,
@@ -281,7 +281,7 @@ void main() {
 
     expect(semantics, includesNodeWith(
       scrollExtentMin: 0.0,
-      scrollPosition: 380.2,
+      scrollPosition: 394.3,
       scrollExtentMax: double.infinity,
       actions: <SemanticsAction>[
         SemanticsAction.scrollUp,
@@ -293,7 +293,7 @@ void main() {
 
     expect(semantics, includesNodeWith(
       scrollExtentMin: 0.0,
-      scrollPosition: 760.4,
+      scrollPosition: 788.6,
       scrollExtentMax: double.infinity,
       actions: <SemanticsAction>[
         SemanticsAction.scrollUp,

packages/flutter/test/widgets/scrollable_test.dart

@@ -9,7 +9,6 @@ import 'package:flutter/material.dart';
 import 'package:flutter/rendering.dart';
 import 'package:flutter/scheduler.dart';
 import 'package:flutter/services.dart';
-
 import 'package:flutter_test/flutter_test.dart';
 
 Future<void> pumpTest(
@@ -890,8 +889,8 @@ void main() {
     expect(find.byKey(const ValueKey<String>('Box 0')), findsNothing);
     expect(find.byKey(const ValueKey<String>('Box 52')), findsOneWidget);
 
-    expect(expensiveWidgets, 38);
-    expect(cheapWidgets, 20);
+    expect(expensiveWidgets, 40);
+    expect(cheapWidgets, 21);
   });
 
   testWidgets('Can recommendDeferredLoadingForContext - override heuristic', (WidgetTester tester) async {
@@ -933,9 +932,9 @@ void main() {
     expect(find.byKey(const ValueKey<String>('Box 0')), findsNothing);
     expect(find.byKey(const ValueKey<String>('Cheap box 52')), findsOneWidget);
 
-    expect(expensiveWidgets, 18);
-    expect(cheapWidgets, 40);
-    expect(physics.count, 40 + 18);
+    expect(expensiveWidgets, 17);
+    expect(cheapWidgets, 44);
+    expect(physics.count, 44 + 17);
   });
 
   testWidgets('Can recommendDeferredLoadingForContext - override heuristic and always return true', (WidgetTester tester) async {
@@ -976,7 +975,7 @@ void main() {
     expect(find.byKey(const ValueKey<String>('Cheap box 52')), findsOneWidget);
 
     expect(expensiveWidgets, 0);
-    expect(cheapWidgets, 58);
+    expect(cheapWidgets, 61);
   });
 
   testWidgets('ensureVisible does not move PageViews', (WidgetTester tester) async {

packages/flutter/test/widgets/slivers_appbar_floating_pinned_test.dart

@@ -2,9 +2,9 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
+import 'package:flutter/material.dart';
 import 'package:flutter/rendering.dart';
 import 'package:flutter_test/flutter_test.dart';
-import 'package:flutter/material.dart';
 
 import 'semantics_tester.dart';
 
@@ -151,7 +151,7 @@ void main() {
     );
     expect(semantics, hasSemantics(expectedSemantics, ignoreTransform: true, ignoreId: true, ignoreRect: true));
 
-    await tester.fling(find.text('Tile 2'), const Offset(0, -600), 2000);
+    await tester.fling(find.text('Tile 2'), const Offset(0, -600), 1950);
     await tester.pumpAndSettle();
 
     expectedSemantics = TestSemantics.root(