SEPARATING POINT SETS IN POLYGONAL ENVIRONMENTS-Reference-Cited by-同舟云学术

SEPARATING POINT SETS IN POLYGONAL ENVIRONMENTS

Published:2005-08 Issue:04 Volume:15 Page:403-419
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

DEMAINE ERIK D.¹,ERICKSON JEFF²,HURTADO FERRAN³,IACONO JOHN⁴,LANGERMAN STEFAN⁵,MEIJER HENK⁶,OVERMARS MARK⁷,WHITESIDES SUE⁸

Affiliation:

1. MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA

2. Department of Computer Science, University of Illinois at Urbana-Champaign, 1304 W. Springfield Avenue, Urbana, IL 61801, USA

3. Departement de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain

4. Department of Computer and Information Science, Polytechnic University, 5 MetroTech Center, Brooklyn, NY 11201, USA

5. Département d'Informatique, Université Libre de Bruxelles, ULB CP212, 1050 Bruxelles, Belgium

6. School of Computing, Queen's University, Kingston, Ontario, K7L 3N6, Canada

7. Institute of Information and Computing Sciences, Utrecht University, P.O.Box 80.089, 3508 TB Utrecht, The Netherlands

8. School of Computer Science, McGill University, 3480 University St. room 318, Montreal, Quebec H3A 2A7, Canada

Abstract

We consider the separability of two point sets inside a polygon by means of chords or geodesic lines. Specifically, given a set of red points and a set of blue points in the interior of a polygon, we provide necessary and sufficient conditions for the existence of a chord and for the existence of a geodesic path that separate the two sets; when they exist we also derive efficient algorithms for their obtention. We also study the separation of the two sets using the minimum number of pairwise non-crossing chords.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195905001762

Reference15 articles.

1. On the geodesic voronoi diagram of point sites in a simple polygon

2. The furthest-site geodesic voronoi diagram

3. COMPUTING LARGEST CIRCLES SEPARATING TWO SETS OF SEGMENTS

4. How to draw a planar graph on a grid

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