How to calculate vertex normals of a cylinder?

Question

I have the following cylinder, I am drawing a worm in opengl and I want to calculate the vertex normals.

Answer 1

Calculate normals for every face (triangle) and save it somewhere. Now for every vertex you have several faces that share the vertex (typicaly 6 on your picture). Your final vertex normal is an average of the faces' normals. For 6 faces, you calculate:

int faceCount = 6;
float sum = 0.0f;
for(int face = 0; face < faceCount; ++face)
    sum += faceNormals[face].x;
normal.x = sum / faceCount;
// and so on for y and z

Don't forget to normalize the resulting vector, so that its length is 1.

NOTE: Don't put faceNormals in an array like this. In a real code you probably want to have a single vector-like container of all normals and some logic saying which normals are relevant for which vertex.

Answer 2

For every point on a cylinder ring, vertexNormal = normalize(vertexPosition - ringCenter);

Or you could calculate them normally, where normal is normalized sum of all face normals for every face that contains this vertex.