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

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

doi:10.1007/978-3-540-75520-3_57

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

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

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

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 language	English
Title of host publication	Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings
Publisher	Springer Verlag
Pages	645-656
Number of pages	12
ISBN (Print)	9783540755197
DOIs	https://doi.org/10.1007/978-3-540-75520-3_57
State	Published - 2007
Event	15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel Duration: 8 Oct 2007 → 10 Oct 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4698 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th Annual European Symposium on Algorithms, ESA 2007
Country/Territory	Israel
City	Eilat
Period	8/10/07 → 10/10/07

Access to Document

10.1007/978-3-540-75520-3_57

Cite this

Berberich, E., Fogel, E., Halperin, D., Mehlhorn, K., & Wein, R. (2007). Sweeping and maintaining two-dimensional arrangements on surfaces: A first step. In Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings (pp. 645-656). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4698 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-75520-3_57

Berberich, Eric ; Fogel, Efi ; Halperin, Dan et al. / Sweeping and maintaining two-dimensional arrangements on surfaces : A first step. Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings. Springer Verlag, 2007. pp. 645-656 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

author = "Eric Berberich and Efi Fogel and Dan Halperin and Kurt Mehlhorn and Ron Wein",

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Berberich, E, Fogel, E, Halperin, D, Mehlhorn, K & Wein, R 2007, Sweeping and maintaining two-dimensional arrangements on surfaces: A first step. in Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4698 LNCS, Springer Verlag, pp. 645-656, 15th Annual European Symposium on Algorithms, ESA 2007, Eilat, Israel, 8/10/07. https://doi.org/10.1007/978-3-540-75520-3_57

Sweeping and maintaining two-dimensional arrangements on surfaces: A first step. / Berberich, Eric; Fogel, Efi; Halperin, Dan et al.
Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings. Springer Verlag, 2007. p. 645-656 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4698 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Berberich E, Fogel E, Halperin D, Mehlhorn K, Wein R. Sweeping and maintaining two-dimensional arrangements on surfaces: A first step. In Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings. Springer Verlag. 2007. p. 645-656. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-75520-3_57

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

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