Ray shooting amidst convex polyhedra and polyhedral terrains in three dimensions

Published

Journal Article

We consider the problem of ray shooting in a three-dimensional scene consisting of m (possibly intersecting) convex polyhedra or polyhedral terrains with a total of n faces, i.e., we want to preprocess them into a data structure, so that the first intersection point of a query ray and the given polyhedra can be determined quickly. We present a technique that requires O((mn)2+ε) preprocessing time and storage, and can answer ray-shooting queries in O(log2 n) time. This is a significant improvement over previously known techniques (which require O(n4+ε) space and preprocessing) if m is much smaller than n, which is often the case in practice. Next, we present a variant of the technique that requires O(n1+ε) space and preprocessing, and answers queries in time O(m1/4n1/2+ε), again a significant improvement over previous techniques when m ≪ n.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Sharir, M

Published Date

  • January 1, 1996

Published In

Volume / Issue

  • 25 / 1

Start / End Page

  • 100 - 116

International Standard Serial Number (ISSN)

  • 0097-5397

Digital Object Identifier (DOI)

  • 10.1137/S0097539793244368

Citation Source

  • Scopus