# Web-based Client-Server System for the Calculation of Algebraic
Surfaces

**Richard Morris **

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)

## Abstract

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.

PDF version of the full paper