The Diversity of Topological Applications within Computer‐aided Geometric Design

Abstract

ABSTRACT: Boolean algebras of regular closed sets, continuous functions, tame homeomorphisms, and Betti numbers are representative of the spectrum of topological tools that have been useful within computer aided geometric design (CAGD). The history of mathematics is rich with examples where the investigation of applications leads to extensions of existing theory. In that spirit, representative applications of topology to CAGD are presented. The intent is to present these examples in mathematical language within their larger mathematical context, so that other topologists might be encouraged to simultaneously enrich CAGD practice and mathematical theory. The authors' own research has benefited from such synergy, in that preparation of this article has resulted in new findings, which are presented herein.