OpenGL - How to calculate normals in a terrain height grid?

Question

My approach is to calculate two tangent vectors parallel to axis X and Y respectively. Then calculate the cross product to find the normal vector.

The tangent vector

Answer 1

You can actually calculate it without a cross product, by using the "finite difference method" (or at least I think it is called in this way).

Actually it is fast enough that I use it to calculate the normals on the fly in a vertex shader.

  // # P.xy store the position for which we want to calculate the normals
  // # height() here is a function that return the height at a point in the terrain

  // read neightbor heights using an arbitrary small offset
  vec3 off = vec3(1.0, 1.0, 0.0);
  float hL = height(P.xy - off.xz);
  float hR = height(P.xy + off.xz);
  float hD = height(P.xy - off.zy);
  float hU = height(P.xy + off.zy);

  // deduce terrain normal
  N.x = hL - hR;
  N.y = hD - hU;
  N.z = 2.0;
  N = normalize(N);