SphericalHarmonics

Spherical harmonics are a system that blend values using an integer Order using the Coder<T> library.

A simple way of explaining spherical harmonics is that they are areas on a sphere that increase in number (and decrease in size) depending on it's complexity order (L1-L4). These areas can represent any value. When sampling them a direction is used to sample from the areas. When between areas, there is blending between their values. This finally outputs a value.

How this works mathematically is outside the scope of this wiki, and is better explained on it's wikipedia page [1].

Technical Notes

Spherical harmonics are blended using the code below

public static T Evaluate<T>(this ISphericalHarmonics<T> harmonics, float3 dir) where T : unmanaged
{
    T val = default(T);
    dir = new float3(0f - dir.x, 0f - dir.y, dir.z);
    for (int i = 0; i <= harmonics.Order; i++)
    {
        for (int j = -i; j <= i; j++)
        {
            T t = harmonics[CoefficientIndex(i, j)];
            float s = EvaluateScale(i, j, in dir);
            val = Coder<T>.Add(val, Coder<T>.Scale(t, s));
        }
    }
    return val;
}

The EvaluateScale(i, j, in dir) uses precalculated values that would take much longer to evaluate if done on the fly. How to calculate these values are also explained on the spherical harmonics wikipedia page [2].