public static StateDerivative EulerEvaluate(ObjectState initial, float t, float dt, StateDerivative der, Func<ObjectState, float, Vector4> acceleration )
{
ObjectState state;
state.Value = initial.Value + der.Velocity * dt;
state.Velocity = initial.Velocity + der.Acceletaion * dt;
StateDerivative output;
output.Velocity = state.Velocity;
output.Acceletaion = acceleration(state, t + dt);
return output;
}
/// <summary>
/// Uses Runge-Kutta fourth order integration
///
/// </summary>
/// <remarks>Reference: Integration Basics by Glenn Fiedler
/// http://gafferongames.com/game-physics/integration-basics/</remarks>
/// <param name="state">Physics state</param>
/// <param name="t">Time</param>
/// <param name="dt">Time derived (step)</param>
/// <param name="acceleration">Acceleration function</param>
public static void RK4Integrate(ref ObjectState state, float t, float dt, Func <ObjectState, float, Vector4> acceleration)
{
StateDerivative a = EulerEvaluate(state, t, 0.0f, new StateDerivative(), acceleration);
StateDerivative b = EulerEvaluate(state, t + dt * .5f, dt * .5f, a, acceleration);
StateDerivative c = EulerEvaluate(state, t + dt * .5f, dt * .5f, b, acceleration);
StateDerivative d = EulerEvaluate(state, t + dt, dt, c, acceleration);
Vector4 dxdt = 1f / 6 * (a.Velocity + 2 * (b.Velocity + c.Velocity) + d.Velocity);
Vector4 dvdt = 1f / 6 * (a.Acceletaion + 2 * (b.Acceletaion + c.Acceletaion) + d.Acceletaion);
state.Value = state.Value + dxdt * dt;
state.Velocity = state.Velocity + dvdt * dt;
}
public static StateDerivative EulerEvaluate(ObjectState initial, float t, float dt, StateDerivative der, Func <ObjectState, float, Vector4> acceleration)
{
ObjectState state;
state.Value = initial.Value + der.Velocity * dt;
state.Velocity = initial.Velocity + der.Acceletaion * dt;
StateDerivative output;
output.Velocity = state.Velocity;
output.Acceletaion = acceleration(state, t + dt);
return(output);
}