Allow explicitly setting tolerances on simulations

packages/newton/lib/newton.dart

@@ -8,6 +8,7 @@ import 'dart:math' as math;
 
 part 'src/simulation.dart';
 part 'src/simulation_group.dart';
+part 'src/tolerance.dart';
 part 'src/utils.dart';
 
 part 'src/friction_simulation.dart';

packages/newton/lib/src/friction_simulation.dart

@@ -22,5 +22,5 @@ class FrictionSimulation extends Simulation {
   double dx(double time) => _v * math.pow(_drag, time);
 
   @override
-  bool isDone(double time) => dx(time).abs() < 1.0;
+  bool isDone(double time) => dx(time).abs() < this.tolerance.velocity;
 }

packages/newton/lib/src/scroll_simulation.dart

@@ -27,7 +27,7 @@ class ScrollSimulation extends SimulationGroup {
   }
 
   @override
-  void step(double time) => _chooseSimulation(
+  bool step(double time) => _chooseSimulation(
       _currentSimulation.x(time - _offset),
       _currentSimulation.dx(time - _offset), time);
 
@@ -37,7 +37,7 @@ class ScrollSimulation extends SimulationGroup {
   @override
   double get currentIntervalOffset => _offset;
 
-  void _chooseSimulation(
+  bool _chooseSimulation(
       double position, double velocity, double intervalOffset) {
 
     /// This simulation can only step forward.
@@ -47,19 +47,21 @@ class ScrollSimulation extends SimulationGroup {
         _offset = intervalOffset;
         _currentSimulation = new SpringSimulation(
             _springDesc, position, _trailingExtent, velocity);
-        return;
+        return true;
       } else if (position < _leadingExtent) {
         _isSpringing = true;
         _offset = intervalOffset;
         _currentSimulation = new SpringSimulation(
             _springDesc, position, _leadingExtent, velocity);
-        return;
+        return true;
       }
     }
 
     if (_currentSimulation == null) {
       _currentSimulation = new FrictionSimulation(_drag, position, velocity);
-      return;
+      return true;
     }
+
+    return false;
   }
 }

packages/newton/lib/src/simulation.dart

@@ -15,9 +15,8 @@ abstract class Simulatable {
 /// The base class for all simulations. The user is meant to instantiate an
 /// instance of a simulation and query the same for the position and velocity
 /// of the body at a given interval.
-///
-/// Note: All operations on subclasses of Simulation are idempotent.
 abstract class Simulation implements Simulatable {
+  Tolerance tolerance = toleranceDefault;
 
   /// Returns if the simulation is done at a given time
   bool isDone(double time);

packages/newton/lib/src/simulation_group.dart

@@ -19,7 +19,8 @@ abstract class SimulationGroup extends Simulation {
 
   /// Called when a significant change in the interval is detected. Subclasses
   /// must decide if the the current simulation must be switched (or updated).
-  void step(double time);
+  /// The result is whether the simulation was switched in this step.
+  bool step(double time);
 
   double x(double time) {
     _stepIfNecessary(time);
@@ -31,6 +32,12 @@ abstract class SimulationGroup extends Simulation {
     return currentSimulation.dx(time - currentIntervalOffset);
   }
 
+  @override
+  void set tolerance(Tolerance t) {
+    this.currentSimulation.tolerance = t;
+    super.tolerance = t;
+  }
+
   @override
   bool isDone(double time) {
     _stepIfNecessary(time);
@@ -39,11 +46,13 @@ abstract class SimulationGroup extends Simulation {
 
   double _lastStep = -1.0;
   void _stepIfNecessary(double time) {
-    if (_nearEqual(_lastStep, time)) {
+    if (_nearEqual(_lastStep, time, toleranceDefault.time)) {
       return;
     }
 
     _lastStep = time;
-    step(time);
+    if (step(time)) {
+      this.currentSimulation.tolerance = this.tolerance;
+    }
   }
 }

packages/newton/lib/src/spring_simulation.dart

@@ -58,5 +58,6 @@ class SpringSimulation extends Simulation {
 
   @override
   bool isDone(double time) =>
-      _nearEqual(x(time), _endPosition) && _nearZero(dx(time));
+      _nearEqual(x(time), _endPosition, this.tolerance.distance) &&
+          _nearZero(dx(time), this.tolerance.velocity);
 }

packages/newton/lib/src/tolerance.dart

@@ -0,0 +1,17 @@
+// Copyright (c) 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.
+
+part of newton;
+
+class Tolerance {
+  final double distance;
+  final double time;
+  final double velocity;
+
+  const Tolerance({this.distance: epsilonDefault, this.time: epsilonDefault,
+      this.velocity: epsilonDefault});
+}
+
+const double epsilonDefault = 1e-3;
+const Tolerance toleranceDefault = const Tolerance();

packages/newton/lib/src/utils.dart

@@ -4,9 +4,7 @@
 
 part of newton;
 
-const double _simulationEpsilon = 0.2;
+bool _nearEqual(double a, double b, double epsilon) =>
+    (a > (b - epsilon)) && (a < (b + epsilon));
 
-bool _nearEqual(double a, double b) =>
-    (a > (b - _simulationEpsilon)) && (a < (b + _simulationEpsilon));
-
-bool _nearZero(double a) => _nearEqual(a, 0.0);
+bool _nearZero(double a, double epsilon) => _nearEqual(a, 0.0, epsilon);

packages/newton/test/newton_test.dart

@@ -12,6 +12,8 @@ void main() {
   test('test_friction', () {
     var friction = new FrictionSimulation(0.3, 100.0, 400.0);
 
+    friction.tolerance = const Tolerance(velocity: 1.0);
+
     expect(friction.isDone(0.0), false);
     expect(friction.x(0.0), 100);
     expect(friction.dx(0.0), 400.0);
@@ -84,6 +86,9 @@ void main() {
   test('crit_spring', () {
     var crit = new SpringSimulation(new SpringDescription.withDampingRatio(
         mass: 1.0, springConstant: 100.0, ratio: 1.0), 0.0, 500.0, 0.0);
+
+    crit.tolerance = const Tolerance(distance: 0.01, velocity: 0.01);
+
     expect(crit.type, SpringType.criticallyDamped);
 
     expect(crit.isDone(0.0), false);
@@ -106,6 +111,9 @@ void main() {
   test('overdamped_spring', () {
     var over = new SpringSimulation(new SpringDescription.withDampingRatio(
         mass: 1.0, springConstant: 100.0, ratio: 1.25), 0.0, 500.0, 0.0);
+
+    over.tolerance = const Tolerance(distance: 0.01, velocity: 0.01);
+
     expect(over.type, SpringType.overDamped);
 
     expect(over.isDone(0.0), false);
@@ -145,6 +153,8 @@ void main() {
 
     var scroll = new ScrollSimulation(100.0, 800.0, 0.0, 300.0, spring, 0.3);
 
+    scroll.tolerance = const Tolerance(velocity: 0.01, distance: 0.01);
+
     expect(scroll.isDone(0.0), false);
     expect(scroll.isDone(3.5), true);
 
@@ -159,6 +169,8 @@ void main() {
     var scroll =
         new ScrollSimulation(100.0, 400.0, 0.0, double.INFINITY, spring, 0.3);
 
+    scroll.tolerance = const Tolerance(velocity: 1.0);
+
     expect(scroll.isDone(0.0), false);
     expect(scroll.x(0.0), 100);
     expect(scroll.dx(0.0), 400.0);