Math @ Duke

Publications [#235403] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Sharir, M, Ray shooting amidst convex polyhedra and polyhedral terrains in three dimensions,
SIAM Journal on Computing, vol. 25 no. 1
(1996),
pp. 100116
(last updated on 2018/02/18)
Abstract: We consider the problem of ray shooting in a threedimensional 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 rayshooting 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.


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