private static double K(int l, int m)
{
var lpm = Functions.Factorial(l + Functions.Abs(m));
var lmm = Functions.Factorial(l - Functions.Abs(m));
return(Functions.Sqrt(((2 * l + 1) * lmm) / (4 * Constants.Pi * lpm)));
}
/// <summary>
/// Interpolates between two unit complex numbers, using spherical linear interpolation.
/// </summary>
/// <param name="start">Start complex number.</param>
/// <param name="end">End complex number.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <returns>The spherical linear interpolation of the two complex numbers.</returns>
/// <remarks>
/// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
/// </remarks>
public Complex Slerp(Complex start, Complex end, double amount)
{
double cosTheta = Dot(start, end);
//Cannot use slerp, use lerp instead
if (Functions.Abs(cosTheta) - 1.0 < double.Epsilon)
{
return(Lerp(start, end, amount));
}
double theta = Functions.Acos(cosTheta);
double sinTheta = Functions.Sin(theta);
double t0 = Functions.Sin((1.0 - amount) * theta) / sinTheta;
double t1 = Functions.Sin(amount * theta) / sinTheta;
return(t0 * start + t1 * end);
}
public static Vector2sb Abs(Vector2sb value)
{
return(new Vector2sb(Functions.Abs(value.X), Functions.Abs(value.Y)));
}
/// <summary>
/// Returns the absolute value (per element).
/// </summary>
/// <param name="value">A matrix.</param>
/// <returns>The absolute value (per element) of value.</returns>
public static Matrix3x2d Abs(Matrix3x2d value)
{
return(new Matrix3x2d(Functions.Abs(value.M11), Functions.Abs(value.M21), Functions.Abs(value.M31), Functions.Abs(value.M12), Functions.Abs(value.M22), Functions.Abs(value.M32)));
}
/// <summary>
/// Returns the absolute value (per component).
/// </summary>
/// <param name="value">A vector.</param>
/// <returns>The absolute value (per component) of value.</returns>
public static Vector8l Abs(Vector8l value)
{
return(new Vector8l(Functions.Abs(value.V0), Functions.Abs(value.V1), Functions.Abs(value.V2), Functions.Abs(value.V3), Functions.Abs(value.V4), Functions.Abs(value.V5), Functions.Abs(value.V6), Functions.Abs(value.V7)));
}
/// <summary>
/// Returns the absolute value (per element).
/// </summary>
/// <param name="value">A matrix.</param>
/// <returns>The absolute value (per element) of value.</returns>
public static Matrix4x2f Abs(Matrix4x2f value)
{
return(new Matrix4x2f(Functions.Abs(value.M11), Functions.Abs(value.M21), Functions.Abs(value.M31), Functions.Abs(value.M41), Functions.Abs(value.M12), Functions.Abs(value.M22), Functions.Abs(value.M32), Functions.Abs(value.M42)));
}
/// <summary>
/// Returns the absolute value (per element).
/// </summary>
/// <param name="value">A matrix.</param>
/// <returns>The absolute value (per element) of value.</returns>
public static Matrix2x3f Abs(Matrix2x3f value)
{
return(new Matrix2x3f(Functions.Abs(value.M11), Functions.Abs(value.M21), Functions.Abs(value.M12), Functions.Abs(value.M22), Functions.Abs(value.M13), Functions.Abs(value.M23)));
}
/// <summary>
/// Returns the absolute value (per element).
/// </summary>
/// <param name="value">A matrix.</param>
/// <returns>The absolute value (per element) of value.</returns>
public static Matrix3x4d Abs(Matrix3x4d value)
{
return(new Matrix3x4d(Functions.Abs(value.M11), Functions.Abs(value.M21), Functions.Abs(value.M31), Functions.Abs(value.M12), Functions.Abs(value.M22), Functions.Abs(value.M32), Functions.Abs(value.M13), Functions.Abs(value.M23), Functions.Abs(value.M33), Functions.Abs(value.M14), Functions.Abs(value.M24), Functions.Abs(value.M34)));
}
public static Vector2ul Abs(Vector2ul value)
{
return(new Vector2ul(Functions.Abs(value.X), Functions.Abs(value.Y)));
}
/// <summary>
/// Returns the absolute value (per element).
/// </summary>
/// <param name="value">A matrix.</param>
/// <returns>The absolute value (per element) of value.</returns>
public static Matrix4x3d Abs(Matrix4x3d value)
{
return(new Matrix4x3d(Functions.Abs(value.M11), Functions.Abs(value.M21), Functions.Abs(value.M31), Functions.Abs(value.M41), Functions.Abs(value.M12), Functions.Abs(value.M22), Functions.Abs(value.M32), Functions.Abs(value.M42), Functions.Abs(value.M13), Functions.Abs(value.M23), Functions.Abs(value.M33), Functions.Abs(value.M43)));
}
