Fast Accurate Normal Calculation for Heightfield Lighting on a Non-Isometric Grid

Heightfields are two-dimensional arrays of height values, commonly used to store terrain or water surface data, and are also commonly used for calculating bump maps. It is necessary to calculate normal vectors for heightfield when shading it. A traditional way to obtain a vertex normal is to compute it as a weighted sum of the normals of facets sharing that vertex. In this paper, instead of the classical approach and based on finite difference formulae, we give a fast and more accurate normal calculation scheme for heightfield over a non-isometric grid. Numerical and experimental results that support the theoretical analysis are given.