Abstract
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 language | English |
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Pages (from-to) | 100-116 |
Number of pages | 17 |
Journal | SIAM Journal on Computing |
Volume | 25 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1996 |
Keywords
- Arrangements
- Data structures
- Parametric search
- Random sampling
- Range searching
- Ray shooting