Stochastic modeling in computer graphics

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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 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 proposed by B. 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 here a new, efficient algorithm for rendering realistic surfaces defined using the stochastic process mentioned above. A major advantage of this technique is that it allows us to compute the surface to arbitrary levels of detail without increasing the database. Thus objects with complex appearance 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.As examples of applications of the method, we show an artificial planet viewed at various levels of detail, and a piece of paper being uncrumpled.