InforLorV4, Main, Exploration, bibRecord, 004A45

Parabola separation queries and their application to stone throwing

Identifieur interne : 004A45 ( Main/Exploration ); précédent : 004A44; suivant : 004A46

Parabola separation queries and their application to stone throwing

Auteurs : Otfried Cheong [Corée du Sud] ; Hazel Everett [France] ; Hyo-Sil Kim [Corée du Sud] ; Sylvain Lazard [France] ; René Schott [France]

Source :

International Journal of Computational Geometry and Applications [ 0218-1959 ] ; 2007.

RBID : Hal:inria-00434090

Abstract

Given two sets $A$ and $B$ of $m$ non-crossing line segments in the plane, we show how to compute in $O(m \log m)$ time a data structure that uses $O(m)$ storage and supports the following query in $O(\log m)$ time: Given a parabola $\p: y = ax^{2} + bx + c$, does $\p$ separate $A$ and $B$? This structure can be used to build a data structure that stores a simple polygon and allows ray-shooting queries along parabolic trajectories with vertical main axis. For a polygon of complexity~$n$, we can answer such ``stone-throwing'' queries in $O(\log^{2} n)$ time, using $O(n \log n)$ storage and $O(n \log^{2} n)$ preprocessing time. This matches the best known bound for circular ray shooting in simple polygons.

Url:

https://hal.inria.fr/inria-00434090

DOI: 10.1142/S0218195907002379

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 003A67
to stream Hal, to step Curation: 003A67
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Le document en format XML

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<idno type="DOI">10.1142/S0218195907002379</idno>
<series><title level="j">International Journal of Computational Geometry and Applications</title>
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<front><div type="abstract" xml:lang="en">Given two sets $A$ and $B$ of $m$ non-crossing line segments in the plane, we show how to compute in $O(m \log m)$ time a data structure that uses $O(m)$ storage and supports the following query in $O(\log m)$ time: Given a parabola $\p: y = ax^{2} + bx + c$, does $\p$ separate $A$ and $B$? This structure can be used to build a data structure that stores a simple polygon and allows ray-shooting queries along parabolic trajectories with vertical main axis. For a polygon of complexity~$n$, we can answer such ``stone-throwing'' queries in $O(\log^{2} n)$ time, using $O(n \log n)$ storage and $O(n \log^{2} n)$ preprocessing time. This matches the best known bound for circular ray shooting in simple polygons.</div>
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Parabola separation queries and their application to stone throwing

Parabola separation queries and their application to stone throwing

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