Finding compact coordinate representations for polygons and polyhedra

Victor Milenkovic, Lee R. Nackman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

A standard technique in solid modeling is to represent planes (or lines) by explicit equations and to represent vertices and edges implicitly by means of combinatorial information. Numerical problems that arise from using floating-point arithmetic to implement operations on solids can be avoided by using exact arithmetic . Since the execution time of exact arithmetic operators increases with the number of bits required to represent the operands, it is important to avoid increasing the number of bits required to represent the plane (or line) equation coefficients. Set operations on solids do not increase the number of bits required. However, rotating a solid greatly increases the number of bits required, thus adversely affecting efficiency. One proposed solution to this problem is to round the coefficients of each plane (or line) equation without altering the combinatorial information. We show that such rounding is NP-complete.

Original languageEnglish (US)
Title of host publicationProc Sixth Annu Symp Comput Geom
PublisherPubl by ACM
Pages244-252
Number of pages9
ISBN (Print)0897913620, 9780897913621
DOIs
StatePublished - Jan 1 1990
Externally publishedYes
EventProceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA
Duration: Jun 6 1990Jun 8 1990

Publication series

NameProc Sixth Annu Symp Comput Geom

Conference

ConferenceProceedings of the Sixth Annual Symposium on Computational Geometry
CityBerkeley, CA, USA
Period6/6/906/8/90

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Milenkovic, V., & Nackman, L. R. (1990). Finding compact coordinate representations for polygons and polyhedra. In Proc Sixth Annu Symp Comput Geom (pp. 244-252). (Proc Sixth Annu Symp Comput Geom). Publ by ACM. https://doi.org/10.1145/98524.98579