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The Diversity of Topological Applications within Computer‐aided Geometric Design
Author(s) -
PETERS THOMAS J.,
ROSEN DAVID W.,
DORNEY SUZANNE M.
Publication year - 1994
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1994.tb44145.x
Subject(s) - context (archaeology) , topology (electrical circuits) , computer science , betti number , computer aided design , mathematics , algebra over a field , pure mathematics , paleontology , combinatorics , biology , operating system
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.