The Diversity of Topological Applications within Computer-aided Geometric Design
THOMAS J. PETERS
Department of Computer Science and Engineering University of Connecticut Storrs, Connecticut 06269–3155
The first and third authors acknowledge, with appreciation, partial funding for this work received under NASA Grant Number NGT 40037. The views expressed herein are of these authors, not of NASA.
Search for more papers by this authorDAVID W. ROSEN
The George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332–0405
Search for more papers by this authorSUZANNE M. DORNEY
Department of Computer Science and Engineering University of Connecticut Storrs, Connecticut 06269–3155
The first and third authors acknowledge, with appreciation, partial funding for this work received under NASA Grant Number NGT 40037. The views expressed herein are of these authors, not of NASA.
Search for more papers by this authorTHOMAS J. PETERS
Department of Computer Science and Engineering University of Connecticut Storrs, Connecticut 06269–3155
The first and third authors acknowledge, with appreciation, partial funding for this work received under NASA Grant Number NGT 40037. The views expressed herein are of these authors, not of NASA.
Search for more papers by this authorDAVID W. ROSEN
The George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332–0405
Search for more papers by this authorSUZANNE M. DORNEY
Department of Computer Science and Engineering University of Connecticut Storrs, Connecticut 06269–3155
The first and third authors acknowledge, with appreciation, partial funding for this work received under NASA Grant Number NGT 40037. The views expressed herein are of these authors, not of NASA.
Search for more papers by this authorBecause of the interdisciplinary nature of this paper, original mathematical references will not always be cited. Some citations will be to application articles, which, in turn, can provide reference to the original mathematical sources.
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.
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