Dual Contouring - Normal Vectors of a Noise Function

Question

I'm currently working on a voxel engine that utilizes dual contouring to give the terrain a more organic/real-life look.

If you're not familiar with dual contouring, basically I need to supply a density function to denote whether a specific point is air or solid (in my case, I'm utilizing 3D Simplex Noise) and I need to be able to provide the normal vector at any point on the 3D noise function.

Normally, when calculating normals for a triangle, I take the cross product of two of the vectors that constitute the triangle; in this case, should I just apply a small delta to the noise function to achieve the same effect?

Thanks for any help!

Answer 1

I've found a simple approach using gradient for marching cubes algorithm (I'm working on a voxel engine too), but since you're still operating on a 3D grid and not directly on the triangles you could give it a try.

Answer 2

You may compute the gradient function of the noise function as normal vector at a point on the iso-surface.

In 3D Perlin noise case, you may use 3D Perlin noise analytical derivative.