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>
/// Returns the square root of a specified complex number.
/// </summary>
/// <param name="value">A complex number.</param>
/// <returns>The square root of value.</returns>
public static Complex Sqrt(Complex value)
{
double magnitude = Functions.Sqrt(value.A * value.A + value.B * value.B);
return(new Complex(
Functions.Sqrt((magnitude + value.A) / 2.0),
(value.B < 0 ? -1.0 : 1.0) * Functions.Sqrt((magnitude - value.A) / 2.0)));
}
/// <summary>
/// Returns the refraction of a vector off a surface that has the specified normal, and refractive index.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="normal">Normal of the surface.</param>
/// <param name="index">The refractive index, destination index over source index.</param>
/// <returns>The refracted vector.</returns>
/// <remarks>Refract only gives the direction of a refraction off a surface, it does not determine
/// whether the original vector was close enough to the surface to hit it.</remarks>
public static Vector2f Refract(Vector2h vector, Vector2h normal, float index)
{
var cos1 = Dot(vector, normal);
var radicand = 1 - (index * index) * (1 - (cos1 * cos1));
if (radicand < 0)
{
return(Vector2f.Zero);
}
return((index * vector) + ((Functions.Sqrt(radicand) - index * cos1) * normal));
}
public static PolarCoordinate CartesianToPolar(Vector2sb value)
{
double theta = Functions.Atan2(value.Y, value.X);
if (theta < 0)
{
theta += 2 * Constants.Pi;
}
return(new PolarCoordinate(
theta,
(double)Functions.Sqrt(value.X * value.X + value.Y * value.Y)));
}
public static float Absolute(Vector2sb value)
{
return(Functions.Sqrt(AbsoluteSquared(value)));
}
/// <summary>
/// Computes the absolute value (or modulus or magnitude) of a vector and returns the result.
/// </summary>
/// <param name="value">A vector.</param>
/// <returns>The absolute value of value.</returns>
public static double Absolute(Vector8l value)
{
return(Functions.Sqrt(AbsoluteSquared(value)));
}
/// <summary>
/// Computes the absolute value (or modulus or magnitude) of a complex number and returns the result.
/// </summary>
/// <param name="value">A complex number.</param>
/// <returns>The absolute value of value.</returns>
public static double Absolute(Complex value)
{
return(Functions.Sqrt(value.A * value.A + value.B * value.B));
}
