Representing geometric structures in d dimensions: topology and order

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Representing geometric structures in d dimensions: topology and order

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Annual Symposium on Computational Geometry archive
Proceedings of the fifth annual symposium on Computational geometry table of contents

Saarbruchen, West Germany

Pages: 218 - 227

Year of Publication: 1989

ISBN:0-89791-318-3

Author

E. Brisson

Department of Computer Science, University of Washington, Seattle, Washington

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 33, Citation Count: 21

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ABSTRACT

We develop a representation for the topological structure of subdivided manifolds (with and without boundary) of dimension d ≥ 1 which allows straightforward access of the available order information. It is shown that there exists a large amount of ordering information in subdivided manifolds: given a (k-2)-cell in the boundary of a (k+1)-cell, 1 ≤ k ≤ d, all of the k- and (k-1)-cells 'between them' can be ordered 'around' the (k-2)-cell. This includes the usual orderings in 2- and 3-dimensional objects. We introduce the 'cell-tuple structure', a simple, uniform representation of the incidence and ordering information in a subdivided manifold. It includes the quad-edge data structure of Guibas and Stolfi [GS 85] and the facet-edge data structure of Dobkin and Laszlo [DL 87] as special cases in dimensions 2 and 3, respectively.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	Br 88	Brisson, Erik, "Representing Geometric Structures in d Dimensions: Topology and Order," Tech. Report 88-11-07, Dept. of Computer Science, Univ. of Washington, 1988.
	DL 87	D. P. Dobkin , M. J. Laszlo, Primitives for the manipulation of three-dimensional subdivisions, Proceedings of the third annual symposium on Computational geometry, p.86-99, June 08-10, 1987, Waterloo, Ontario, Canada [doi>10.1145/41958.41967]
	GS 85	Leonidas Guibas , Jorge Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi, ACM Transactions on Graphics (TOG), v.4 n.2, p.74-123, April 1985 [doi>10.1145/282918.282923]
	LW 69	Lundell, Albert T. and Weingram, Stephen, The Topology of CW Complexes, Van Nostrand Reinhold, 1969.
	Mu 75	Munkres, James R., Topology: A First Course, Prentice-Hall, 1975.
	Mu 84	Munkres, James R., Elements of Algebraic Topology, Addison-Wesley, 1984.
	PR 77	F. P. Preparata , S. J. Hong, Convex hulls of finite sets of points in two and three dimensions, Communications of the ACM, v.20 n.2, p.87-93, Feb. 1977 [doi>10.1145/359423.359430]

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