Presented at the Dagstuhl-Seminar No. 01421 Integration of Algebra and Geometry Software Systems, October 15th to 19th, 2001 organized by M. Joswig (TU Berlin) and N. Takayama (Kobe University)
Published in In Algebra, Geometry, and Software Systems, Ed. Michael Joswig and Nobuki Takayama. Springer Verlag, pp 239–253. (2003)
Algebraic surfaces, defined as the zero set of a polynomial function in three variables, present particular problem for visualizing, especially if the surface contains singularities. Most algorithms for constructing a polygonization of the surface will miss the singular points. We present an algorithm for polygonizing such surfaces which attempts to get accurate representations of the singular points. A client-server approach, with a java applet and a C program as backend, is used to enable the visualization of the polygonal mesh in a web browser. This system allows algebraic surfaces to be viewed in any web browser on any platform.