Combinatorial complexity of hyperplane transversals

Sylvain Cappell, Richard Pollack, Jacob E. Goodman, Micha Sharir, Janos Pach, Rephael Wenger

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

Abstract

We show that the maximum combinatorial complexity of the space of hyperplane transversals to a family of n separated and strictly convex sets in Rd is Θ(nd/2), which generalizes results of Edelsbrunner and Sharir in the plane. As a key step in the argument, we show that the space of hyperplanes tangent to k ≤ d separated and strictly convex sets in Rd is a topological (d - k)-sphere.

Original languageEnglish (US)
Title of host publicationProc Sixth Annu Symp Comput Geom
PublisherPubl by ACM
Pages83-91
Number of pages9
ISBN (Print)0897913620
StatePublished - 1990
EventProceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA
Duration: Jun 6 1990Jun 8 1990

Other

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

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Cappell, S., Pollack, R., Goodman, J. E., Sharir, M., Pach, J., & Wenger, R. (1990). Combinatorial complexity of hyperplane transversals. In Proc Sixth Annu Symp Comput Geom (pp. 83-91). Publ by ACM.

Combinatorial complexity of hyperplane transversals. / Cappell, Sylvain; Pollack, Richard; Goodman, Jacob E.; Sharir, Micha; Pach, Janos; Wenger, Rephael.

Proc Sixth Annu Symp Comput Geom. Publ by ACM, 1990. p. 83-91.

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

Cappell, S, Pollack, R, Goodman, JE, Sharir, M, Pach, J & Wenger, R 1990, Combinatorial complexity of hyperplane transversals. in Proc Sixth Annu Symp Comput Geom. Publ by ACM, pp. 83-91, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/6/90.
Cappell S, Pollack R, Goodman JE, Sharir M, Pach J, Wenger R. Combinatorial complexity of hyperplane transversals. In Proc Sixth Annu Symp Comput Geom. Publ by ACM. 1990. p. 83-91
Cappell, Sylvain ; Pollack, Richard ; Goodman, Jacob E. ; Sharir, Micha ; Pach, Janos ; Wenger, Rephael. / Combinatorial complexity of hyperplane transversals. Proc Sixth Annu Symp Comput Geom. Publ by ACM, 1990. pp. 83-91
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