Computer rendering of stochastic models

TLDR

Generating realistic computer graphics requires efficient modeling of natural irregular objects, and fractional Brownian motion has emerged as a useful stochastic process for representing terrains, making algorithmic efficiency crucial. The authors propose modeling objects as stochastic process sample paths to solve realistic rendering challenges. They present an algorithm that rapidly approximates fractional Brownian motion, enabling realistic rendering without exact calculations. The algorithm permits arbitrary detail surfaces and complex motion from a small database, with surface characteristics adjustable by a few parameters.

Abstract

A recurrent problem in generating realistic pictures by computers is to represent natural irregular objects and phenomena without undue time or space overhead. We develop a new and powerful solution to this computer graphics problem by modeling objects as sample paths of stochastic processes. Of particular interest are those stochastic processes which previously have been found to be useful models of the natural phenomena to be represented. One such model applicable to the representation of terrains, known as “fractional Brownian motion,” has been developed by Mandelbrot. The value of a new approach to object modeling in computer graphics depends largely on the efficiency of the techniques used to implement the model. We introduce a new algorithm that computes a realistic, visually satisfactory approximation to fractional Brownian motion in faster time than with exact calculations. A major advantage of this technique is that it allows us to compute the surface to arbitrary levels of details without increasing the database. Thus objects with complex appearances can be displayed from a very small database. The character of the surface can be controlled by merely modifying a few parameters. A similar change allows complex motion to be created inexpensively.