Abstract

Many interesting surfaces can be written as polynomial functions of the spatial coordinates, often of low degree. We present a method based on a ray casting algorithm, extended to work in more than three dimensions, to produce pictures of these surfaces. The method uses a symbolic algebra system to automatically derive the equation of intersection between the ray and the surface and then solves this equa-tion using an exact polynomial root find-ing algorithm. Included are illustrations of the cusp catastrophe surface, and two unusu-ally shaped quartic surfaces, Kummer's quadruple and Steiner's surface.

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