/// <summary>
/// gets the first derivative for a cubic bezier
/// </summary>
/// <returns>The first derivative.</returns>
/// <param name="start">P0.</param>
/// <param name="firstControlPoint">P1.</param>
/// <param name="secondControlPoint">P2.</param>
/// <param name="end">P3.</param>
/// <param name="t">T.</param>
public static Vector2 GetFirstDerivative(Vector2 start, Vector2 firstControlPoint, Vector2 secondControlPoint, Vector2 end, float t)
{
t = NumericHelper.Clamp01(t);
var oneMinusT = 1f - t;
return(3f * oneMinusT * oneMinusT * (firstControlPoint - start) +
6f * oneMinusT * t * (secondControlPoint - firstControlPoint) +
3f * t * t * (end - secondControlPoint));
}
/// <summary>
/// evaluate quadratic bezier
/// </summary>
/// <returns>The point.</returns>
/// <param name="p0">P0.</param>
/// <param name="p1">P1.</param>
/// <param name="p2">P2.</param>
/// <param name="t">T.</param>
public static Vector2 GetPoint(Vector2 p0, Vector2 p1, Vector2 p2, float t)
{
t = NumericHelper.Clamp01(t);
var oneMinusT = 1f - t;
return(oneMinusT * oneMinusT * p0 +
2f * oneMinusT * t * p1 +
t * t * p2);
}
/// <summary>
/// evaluate a cubic bezier
/// </summary>
/// <returns>The point.</returns>
/// <param name="start">P0.</param>
/// <param name="firstControlPoint">P1.</param>
/// <param name="secondControlPoint">P2.</param>
/// <param name="end">P3.</param>
/// <param name="t">T.</param>
public static Vector2 GetPoint(Vector2 start, Vector2 firstControlPoint, Vector2 secondControlPoint, Vector2 end, float t)
{
t = NumericHelper.Clamp01(t);
var oneMinusT = 1f - t;
return(oneMinusT * oneMinusT * oneMinusT * start +
3f * oneMinusT * oneMinusT * t * firstControlPoint +
3f * oneMinusT * t * t * secondControlPoint +
t * t * t * end);
}
/// <summary>
/// helper that gets the bezier point index at time t. t is modified in the process to be in the range of the curve segment.
/// </summary>
/// <returns>The index at time.</returns>
/// <param name="t">T.</param>
private int PointIndexAtTime(ref float t)
{
int i;
if (t >= 1f)
{
t = 1f;
i = points.Length - 4;
}
else
{
t = NumericHelper.Clamp01(t) * curveCount;
i = (int)t;
t -= i;
i *= 3;
}
return(i);
}