TY - GEN
T1 - Linear data structures for fast ray-shooting amidst convex polyhedra
AU - Kaplan, Haim
AU - Rubin, Natan
AU - Sharir, Micha
PY - 2007/1/1
Y1 - 2007/1/1
N2 - We consider the problem of ray shooting in a three-dimensional scene consisting of k (possibly intersecting) convex polyhedra with a total of n facets. That is, 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 describe data structures that require Õ(npoly(k)) preprocessing time and storage, and have polylogarithmic query time, for several special instances of the problem. These include the case when the ray origins are restricted to lie on a fixed line ℓ0, but the directions of the rays are arbitrary, the more general case when the supporting lines of the rays pass through ℓ0, and the case of rays orthogonal to z-axis with arbitrary origins. In all cases, this is a significant improvement over previously known techniques (which require Ω(n2) storage, even when A: ≪ n).
AB - We consider the problem of ray shooting in a three-dimensional scene consisting of k (possibly intersecting) convex polyhedra with a total of n facets. That is, 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 describe data structures that require Õ(npoly(k)) preprocessing time and storage, and have polylogarithmic query time, for several special instances of the problem. These include the case when the ray origins are restricted to lie on a fixed line ℓ0, but the directions of the rays are arbitrary, the more general case when the supporting lines of the rays pass through ℓ0, and the case of rays orthogonal to z-axis with arbitrary origins. In all cases, this is a significant improvement over previously known techniques (which require Ω(n2) storage, even when A: ≪ n).
UR - http://www.scopus.com/inward/record.url?scp=38049063119&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-75520-3_27
DO - 10.1007/978-3-540-75520-3_27
M3 - Conference contribution
AN - SCOPUS:38049063119
SN - 9783540755197
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 287
EP - 298
BT - Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings
PB - Springer Verlag
T2 - 15th Annual European Symposium on Algorithms, ESA 2007
Y2 - 8 October 2007 through 10 October 2007
ER -