Ray Shooting Amidst Spheres in Three Dimensions and Related Problems (1997)
| Venue: | SIAM J. Comput |
| Citations: | 10 - 3 self |
BibTeX
@ARTICLE{Mohaban97rayshooting,
author = {Shai Mohaban and Micha Sharir},
title = {Ray Shooting Amidst Spheres in Three Dimensions and Related Problems},
journal = {SIAM J. Comput},
year = {1997},
volume = {26},
pages = {26--654}
}
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Abstract
We consider the problem of ray shooting amidst spheres in 3-space: given n arbitrary (possibly intersecting) spheres in 3-space and any " ? 0, we show how to preprocess the spheres in time O(n 3+" ), into a data structure of size O(n 3+" ), so that any ray-shooting query can be answered in time O(n " ). Our result improves previous techniques (see [3, 5]), where roughly O(n 4 ) storage was required to support fast queries. Our result shows that ray shooting amidst spheres has complexity comparable with that of ray shooting amidst planes in 3-space. Our technique applies to more general (convex) objects in 3-space, and we also discuss these extensions. 1 Introduction The ray shooting problem can be defined as follows: Given a collection S of n objects in IR d , preprocess S into a data structure, so that one can quickly determine the first object of S intersected by a query ray. The ray shooting problem has received considerable attention in the past few years beca...
