Normal vector generation for sampled data using fourier filtering

A three-dimensional surface is a useful graphic representation of a two-dimensional function which has been sampled on a regular grid. Shading the surface to simulate the effects of direct lighting makes visible small changes in the surface orientation, and enhances realism when the data represents a physical surface such as terrain. Shading interpolation calculations and surface patch generation techniques require the specification of a surface normal vector (or related slope information) at each sample point. These normal vectors are usually generated by averaging local data such as the normal vectors of the surfaces of a triangular mesh connecting the points. This paper describes a technique which uses Fourier filtering to generate normal vectors for two-dimensional sampled data. Images and analysis of frequency spectra are included to show how this technique preserves detail which is lost using the averaging method. Performance figures show that this enhancement of detail in the final image can be achieved for only a small increase in computation time.