Coherent Spherical Noise?

Question

Does anyone know how I might be able to generate the following kind of noise?

Three inputs, three outputs
The outputs must always result in a vector of the same magnitude
If it receives the same input as some other time, it must return the same output
It must be continuous (best if it appears smooth, like perlin noise)
It must appear to be fairly random

EDIT: It would also be nice if it were isotropic, but that's not entirely necessary.

What do you mean by continuous? As the input varies smoothly the output must also vary smoothly? As if these coordinates were the time parameter in a drunkard's walk algorithm or something? — sh1, Jun 16 '13 at 00:52
yes, I just mean that the first and second derivatives of the function with respect to each input is continuous. If we smoothly and randomly changed each of the inputs over time, I would expect the output vector to sort of wander, but smoothly. More like the drunkard's "perceived gravity" vector. — Miles, Jun 18 '13 at 17:38

score 0 · Accepted Answer · answered Jun 19 '13 at 22:12

I've found a way, and it might not be very fast, but it does the job (this is c-like pseudocode designed to make porting to other languages easy).

vec3 sphereNoise(vec3 input, float radius)
{
    vec3 result;
    result.x = simplex(input.x, input.y); //could use perlin instead of simplex
    result.y = simplex(input.y, input.z); //but I prefer simplex for its speed
    result.z = simplex(input.z, input.x); //and its lack of directional artifacts

    //uncomment the following line to make it a spherical-shell noise
    //result.normalize();
    result *= radius;
    return result;
}

Coherent Spherical Noise?

1 Answers1