Fast Generation and Surface Structuring Methods for Terrain and Other Natural Phenomena

Abstract

Fractal geometry has proven to be a powerful tool for modeling natural phenomena. Using discrete approximations to fractional Brownian motion over a finite grid plane, computer graphics terrain-rendering algorithms are able to generate highly realistic topographical displays. Similar procedures can be applied to model other natural phenomena, such as clouds and water. Two important considerations in these algorithms are computational efficiency and the ability to control macroscopic surface features. Here we introduce a technique for structuring surface features so as to conform to a specified"elevation" envelope. We also present methods for implementing this technique using a recursive random midpoint-displacement procedure.