How to interpolate vertex normals?

Question

I am trying to render a 3D model (from volvis.org) with Gouraud shading using the marching cubes algorithm. So far I have the normals for each vertex with:

GetNormalForVertex(vertex &b, vertex &a, vertex &c) {
    u.X = a.X - b.X;
    u.Y = a.Y - b.Y;
    u.Z = a.Z - b.Z;
    v.X = c.X - b.X;
    v.Y = c.Y - b.Y;
    v.Z = c.Z - b.Z;

    return  Cross(u,v);
}

I can see a nice flat shading when its rendered. Now, far as I know I need to interpolate those vertex normals to find normal at the intersection point to get Gouraud shading. How could I interpolate the vertex normals?

Answer 1

First of all, you are not computing vertex normals. You are computing face normals. This is step 1 in the process of computing vertex normals.

The next step is not interpolating anything. What you do is compute the (unnormalized) face normal for each face attached to a vertex. Then add them all together and normalize the result. That is the vertex normal.

How you determine which faces are attached to a vertex is another matter. In your case, because you're building this data via marching cubes, it shouldn't be too difficult to generate or retrieve the triangles from adjacent cubes. But if you're pass the generation step and just have a bag of triangles, then you're going to need an appropriate mesh topology data structure. Winged-edge or Quad-edge are both good choices.