NDLI: An extension of manifold boundary representations to the r-sets

Content Provider	ACM Digital Library
Author	Desaulniers, H. Stewart, N. F.
Copyright Year	1992
Abstract	In this paper we study the relationship between manifold solids (r-sets whose boundaries are two-dimensional closed manifolds) and $\textit{r-sets}.$ We begin by showing that an r-set may be viewed as the limit of a certain sequence of manifold solids, where distance is measured using the Hausdorff metric. This permits us to introduce a minimal set of generalized Euler operators, sufficient for the construction and manipulation of r-sets. The completeness result for ordinary Euler operators carries over immediately to the generalized Euler operators on the r-sets and the modification of the usual boundary data structures, corresponding to our extension to nonmanifold r-sets, is straightforward. We in fact describe a modification of a well-known boundary data structure in order to illustrate how the extension can be used in typical solid modeling algorithms, and describe an implementation.The results described above largely eliminate what has been called an inherent mismatch between the modeling spaces defined by manifold solids and by r-sets. We view the r-sets as a more appropriate choice for a modeling space: in particular, the r-sets provide closure with respect to regularized set operations and a complete set of generalized Euler operators for the manipulation of boundary representations, for graphics and other purposes. It remains to formulate and prove a theorem on the soundness of the generalized Euler operators.
Starting Page	40
Ending Page	60
Page Count	21
File Format	PDF
ISSN	07300301
e-ISSN	15577368
DOI	10.1145/102377.111777
Volume Number	11
Issue Number	1
Journal	ACM Transactions on Graphics (TOG)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1992-01-02
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Euler operators Data structures Manifold object Nonmanifold objects R-set
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design

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