Shader Math: Normals from non-texture height?

mAlkAv!An

I'm currently testing various methods of recalculating normals for an ocean shader with some vertex displacement waves.

One of these approaches uses sine - cosine correcelations to calculate the normal components, as described here:
http://www.antongerdelan.net/opengl/vertex_displacement.html
What I'd like to know is, how would you modify this method for waves that are not linear like in the example but irregular or circular shaped?

CrazyButcher

you could mathematically create the derivative of the position function

or use something like forward differencing

// Use forward differencing to compute the normal:
float du = 0.0001; float dv = 0.0001;
vec3 C = SurfaceFunc(p.x + du, p.y);
vec3 B = SurfaceFunc(p.x, p.y + dv);
vec3 A = tePosition;
teNormal = normalize(cross(C - A, B - A));

http://github.prideout.net/sympy-surfaces/

mAlkAv!An

Yes that's possible, and that's what I've already done. At first I thought that sine/cosine appraoch described in the linked article is a different method but in fact it's just a derivative for the special case of waves moving along a single axis only?

Thanks for the help and the code sample. Forward differencing is a term I never heard of, although I've been using it for generating normals from height before.