Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#235403] of Pankaj K. Agarwal

Papers Published

  1. 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. 100-116
    (last updated on 2017/12/14)

    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.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320