Ray shooting amidst convex polyhedra and polyhedral terrains in three dimensions

Pankaj K. Agarwal*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish
Pages (from-to)100-116
Number of pages17
JournalSIAM Journal on Computing
Issue number1
StatePublished - Feb 1996


  • Arrangements
  • Data structures
  • Parametric search
  • Random sampling
  • Range searching
  • Ray shooting


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