/// <summary>
/// Returns the instantaneous velocity given by 4 points and a time value.
/// </summary>
/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">The end point.</param>
/// <param name="t">A value between 0 and 1.</param>
public static Vector3 Velocity(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
{
ArgumentChecker.CheckT(t);
return((3f * (1f - t) * (1f - t) * (p1 - p0)) +
(6f * (1f - t) * t * (p2 - p1)) +
(3f * t * t * (p3 - p2)));
}
/// <summary>
/// Returns the curve coordinate given by 4 points and a time value.
/// </summary>
/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">The end point.</param>
/// <param name="t">A value between 0 and 1.</param>
public static Vector3 Point(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
{
ArgumentChecker.CheckT(t);
return(((1f - t) * (1f - t) * (1f - t) * p0) +
(3f * (1f - t) * (1f - t) * t * p1) +
(3f * (1f - t) * t * t * p2) +
(t * t * t * p3));
}
/// <summary>
/// Returns the instantaneous velocity given by 4 points and a normalized time value.
/// </summary>
/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">The end point.</param>
/// <param name="t">A value between startTime and endTime.</param>
/// <param name="startTime"></param>
/// <param name="endTime"></param>
public static Vector3 Velocity(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t, float startTime, float endTime)
{
ArgumentChecker.CheckT(t, startTime, endTime);
return(Velocity(p0, p1, p2, p3, TimeHelper.Normalized(t, startTime, endTime)));
}