Defining and rendering of textured objects through the use of exponential functions

Abstract

We present a method for modeling and rendering various surface textures by actually defining them over the entire three-dimensional space. Once this is done any surface representable by an implicit function can be rendered. We do not do any volume rendering; instead the surfaces are ray traced directly. The implicit functions used to define various surfaces are taken to be exponential functions with exponents with large magnitudes. Use of such functions allows us to define even such surfaces as the surface (entire) of a rectangular solid or a truncated cone as precisely as we want. It also allows us to model complex surfaces through piecewise modeling and blending of different analytical surfaces. Even for simple surfaces, it allows us to calculate the ray-surface points of intersection and the normals at those points very precisely because of the large relative variation of the implicit functional density in the entire three-dimensional space. Both regular and stochastic textures can be modeled and rendered. A complete methodology together with several examples is presented.