/// <summary>
/// Calculates average movement time to the point
/// </summary>
/// <returns>The average time.</returns>
/// <param name="velocity">Velocity.</param>
/// <param name="maxVelocity">Max velocity.</param>
/// <param name="position">Position.</param>
/// <param name="target">Target.</param>
public static float GetAverageMoveTime(Vector velocity, float maxVelocity, float damping, float acceleration, Vector position, Vector target, float epsilon)
{
Vector direction = (target - position);
float distance = direction.Normalize();
float v = Vector.Dot(velocity, direction);
float dampingDistance = maxVelocity * maxVelocity * s_oneMinusLog2 / damping;
float t;
if (distance > dampingDistance)
{
t = (distance - dampingDistance) / maxVelocity + (maxVelocity - v) / acceleration; // rought acceleration time, will be smaller than actual time
}
else
{
t = 0.1f;
}
float ndistance;
float u;
int iterations = 10; // limit the cycle
do
{
float exp = (float)Math.Exp(-acceleration * t / maxVelocity);
u = maxVelocity - (maxVelocity - v) * exp;
ndistance = maxVelocity * (t - (u - v) / acceleration) + GetDampingDistance(u, maxVelocity, damping);
if (ndistance >= distance + epsilon) // average goal
{
break;
}
t += 0.1f;
} while(ndistance < distance && --iterations >= 0);
return(t + maxVelocity * (float)Math.Log(1.0f + u / maxVelocity) / damping);
}
/// <summary>
/// Calculates the time untill full stop with specified speed and damping
/// </summary>
/// <returns>The damping time.</returns>
/// <param name="velocity">Velocity.</param>
/// <param name="maxVelocity">Max velocity.</param>
/// <param name="damping">Damping.</param>
public static float GetDampingTime(float velocity, float maxVelocity, float damping)
{
float speedPct = velocity / maxVelocity;
return(maxVelocity * (speedPct - (float)Math.Log(1 + speedPct)) / Math.Abs(damping));
}