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Arrangements of double pseudolines: extended abstract

Published: 08 June 2009 Publication History

Abstract

Define an arrangement of double pseudolines as a finite family of at least two separating simple closed curves embedded in a projective plane, with the property that any two meet transversally in exactly four points and induce a cell structure on the projective plane. We show that any arrangement of double pseudolines is isomorphic to the dual family of a finite family of pairwise disjoint convex bodies of a projective plane endowed with a topological point-line incidence geometry and we provide a simple axiomatic characterization of the class of isomorphism classes of indexed arrangements of oriented double pseudolines.

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Cited By

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  • (2013)LR Characterization of Chirotopes of Finite Planar Families of Pairwise Disjoint Convex bodiesDiscrete & Computational Geometry10.1007/s00454-013-9532-y50:3(552-648)Online publication date: 1-Oct-2013
  • (2012)Computing Pseudotriangulations via Branched CoveringsDiscrete & Computational Geometry10.5555/3116673.311715248:3(518-579)Online publication date: 1-Oct-2012

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cover image ACM Conferences
SCG '09: Proceedings of the twenty-fifth annual symposium on Computational geometry
June 2009
426 pages
ISBN:9781605585017
DOI:10.1145/1542362
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 08 June 2009

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Author Tags

  1. arrangements
  2. axiomatization
  3. convexity
  4. double pseudolines
  5. duality
  6. pseudolines

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View all
  • (2013)LR Characterization of Chirotopes of Finite Planar Families of Pairwise Disjoint Convex bodiesDiscrete & Computational Geometry10.1007/s00454-013-9532-y50:3(552-648)Online publication date: 1-Oct-2013
  • (2012)Computing Pseudotriangulations via Branched CoveringsDiscrete & Computational Geometry10.5555/3116673.311715248:3(518-579)Online publication date: 1-Oct-2012

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