Animation of Algebraic Surfaces

Dietmar Saupe and Matthias Ruhl

Visualization and Mathematics
H.-C. Hege, K. Polthier (eds.), Springer Verlag, July 1997

A preliminary version appeared in:
International Workshop on Visualization and Mathematics (VisMath '95)
Berlin, June 1995

[Postscript, gzip'ed, 3410KB]


This contribution is a practise-and-experience report on the visualization of parameter dependent algebraic surfaces. An important example of a deformation of algebraic surfaces was proposed by Kummer in the last century. The techniques in computer graphics algorithms, software and hardware for the animated real-time display of many types of surfaces have been established in recent years. We present an application of this technology and a raytracer to the Kummer family and others. The purpose of this report is to demonstrate the feasibility of such studies by combining several pieces of readily available software and off-the-shelf hardware with only a minimal investment of extra programming. Raytracing produces high quality renderings, however, the method requires much processing time. Faster alternatives are methods yielding polygonalizations or using physically-based approaches. These provide less quality but allow near real-time user interaction. We present some examples for them.

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