/// <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);
}