I am currently implementing a 3D Perlin noise bump mapping using Shader Model 4 (DirectX 10 HLSL). Generating the noise itself is not a big problem (there are tons of tutorials and codes around) but what I have not found are analytical derivatives of 3D Perlin noise.
The only sites taking the derivatives into account are Ińigo Quilez's site and a related GameDev.net discussion. The problem is that in the first link the noise is value based, not gradient based (which is a requirement for me), in the second link, there's only 2D gradient noise derivative.
Note that I'm not looking for numerical derivatives as those require 4 neighboring noise samples to be generated and that's way too much overhead.
Has anyone calculated these derivatives? Is there a reference implementation that is using them?