Sweeping and maintaining two-dimensional arrangements on surfaces: A first step

Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to them. A major goal of our work is to maximize code reuse by generalizing the prevalent sweep-line paradigm and its implementation so that it can be employed on a large class of surfaces and curves embedded on them. We have realized our approach as a prototypical CGAL package. We present experimental results for two concrete adaptations of the framework: (i) arrangements of arcs of great circles embedded on a sphere, and (ii) arrangements of intersection curves between quadric surfaces embedded on a quadric.

Original languageEnglish
Title of host publicationAlgorithms - ESA 2007 - 15th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Pages645-656
Number of pages12
ISBN (Print)9783540755197
DOIs
StatePublished - 2007
Event15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel
Duration: 8 Oct 200710 Oct 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4698 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th Annual European Symposium on Algorithms, ESA 2007
Country/TerritoryIsrael
CityEilat
Period8/10/0710/10/07

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