1 /* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
2 /* vim: set ts=8 sts=2 et sw=2 tw=80: */
3 /* This Source Code Form is subject to the terms of the Mozilla Public
4 * License, v. 2.0. If a copy of the MPL was not distributed with this
5 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
6
7 #include "AxisPhysicsModel.h"
8
9 namespace mozilla {
10 namespace layers {
11
12 /**
13 * The simulation is advanced forward in time with a fixed time step to ensure
14 * that it remains deterministic given variable framerates. To determine the
15 * position at any variable time, two samples are interpolated.
16 *
17 * kFixedtimestep is set to 120hz in order to ensure that every frame in a
18 * common 60hz refresh rate display will have at least one physics simulation
19 * sample. More accuracy can be obtained by reducing kFixedTimestep to smaller
20 * intervals, such as 240hz or 1000hz, at the cost of more CPU cycles. If
21 * kFixedTimestep is increased to much longer intervals, interpolation will
22 * become less effective at reducing temporal jitter and the simulation will
23 * lose accuracy.
24 */
25 const double AxisPhysicsModel::kFixedTimestep = 1.0 / 120.0; // 120hz
26
27 /**
28 * Constructs an AxisPhysicsModel with initial values for state.
29 *
30 * @param aInitialPosition sets the initial position of the simulation,
31 * in AppUnits.
32 * @param aInitialVelocity sets the initial velocity of the simulation,
33 * in AppUnits / second.
34 */
AxisPhysicsModel(double aInitialPosition,double aInitialVelocity)35 AxisPhysicsModel::AxisPhysicsModel(double aInitialPosition,
36 double aInitialVelocity)
37 : mProgress(1.0),
38 mPrevState(aInitialPosition, aInitialVelocity),
39 mNextState(aInitialPosition, aInitialVelocity) {}
40
~AxisPhysicsModel()41 AxisPhysicsModel::~AxisPhysicsModel() {}
42
GetVelocity() const43 double AxisPhysicsModel::GetVelocity() const {
44 return LinearInterpolate(mPrevState.v, mNextState.v, mProgress);
45 }
46
GetPosition() const47 double AxisPhysicsModel::GetPosition() const {
48 return LinearInterpolate(mPrevState.p, mNextState.p, mProgress);
49 }
50
SetVelocity(double aVelocity)51 void AxisPhysicsModel::SetVelocity(double aVelocity) {
52 mNextState.v = aVelocity;
53 mNextState.p = GetPosition();
54 mProgress = 1.0;
55 }
56
SetPosition(double aPosition)57 void AxisPhysicsModel::SetPosition(double aPosition) {
58 mNextState.v = GetVelocity();
59 mNextState.p = aPosition;
60 mProgress = 1.0;
61 }
62
Simulate(const TimeDuration & aDeltaTime)63 void AxisPhysicsModel::Simulate(const TimeDuration &aDeltaTime) {
64 for (mProgress += aDeltaTime.ToSeconds() / kFixedTimestep; mProgress > 1.0;
65 mProgress -= 1.0) {
66 Integrate(kFixedTimestep);
67 }
68 }
69
Integrate(double aDeltaTime)70 void AxisPhysicsModel::Integrate(double aDeltaTime) {
71 mPrevState = mNextState;
72
73 // RK4 (Runge-Kutta method) Integration
74 // http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
75 Derivative a = Evaluate(mNextState, 0.0, Derivative());
76 Derivative b = Evaluate(mNextState, aDeltaTime * 0.5, a);
77 Derivative c = Evaluate(mNextState, aDeltaTime * 0.5, b);
78 Derivative d = Evaluate(mNextState, aDeltaTime, c);
79
80 double dpdt = 1.0 / 6.0 * (a.dp + 2.0 * (b.dp + c.dp) + d.dp);
81 double dvdt = 1.0 / 6.0 * (a.dv + 2.0 * (b.dv + c.dv) + d.dv);
82
83 mNextState.p += dpdt * aDeltaTime;
84 mNextState.v += dvdt * aDeltaTime;
85 }
86
Evaluate(const State & aInitState,double aDeltaTime,const Derivative & aDerivative)87 AxisPhysicsModel::Derivative AxisPhysicsModel::Evaluate(
88 const State &aInitState, double aDeltaTime, const Derivative &aDerivative) {
89 State state(aInitState.p + aDerivative.dp * aDeltaTime,
90 aInitState.v + aDerivative.dv * aDeltaTime);
91
92 return Derivative(state.v, Acceleration(state));
93 }
94
LinearInterpolate(double aV1,double aV2,double aBlend)95 double AxisPhysicsModel::LinearInterpolate(double aV1, double aV2,
96 double aBlend) {
97 return aV1 * (1.0 - aBlend) + aV2 * aBlend;
98 }
99
100 } // namespace layers
101 } // namespace mozilla
102