Article Dans Une Revue International Journal of Computational Geometry and Applications Année : 2007

Parabola separation queries and their application to stone throwing

Résumé

Given two sets A and B of m non-crossing line segments in the plane, we show how to compute in O(mlogm) time a data structure that uses O(m) storage and supports the following query in O(logm) time: Given a parabola \p:y=ax2+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(log2n) time, using O(nlogn) storage and O(nlog2n) preprocessing time. This matches the best known bound for circular ray shooting in simple polygons.
Fichier principal
Vignette du fichier
ijcga-final.pdf (217.36 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

inria-00434090 , version 1 (20-11-2009)

Identifiants

Citer

Otfried Cheong, Hazel Everett, Hyo-Sil Kim, Sylvain Lazard, René Schott. Parabola separation queries and their application to stone throwing. International Journal of Computational Geometry and Applications, 2007, 17 (4), pp.349-360. ⟨10.1142/S0218195907002379⟩. ⟨inria-00434090⟩
266 Consultations
239 Téléchargements

Altmetric

Partager

More