## Abstract

We consider the problem of ray shooting in a 3-dimensional scene consisting of m (possibly intersecting) convex polyhedra 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(log n) time. This is a significant improvement over previously known techniques (which require O(n^{4+ε}) space and preprocessing) if m is much smaller than n, which is often the case in practice. We also present a variant of the technique that requires O(n^{1+ε}) space and preprocessing, and answers queries in time O(m^{1/4}n^{1/2+ε}), again a significant improvement over previous techniques when m≪n. Our algorithms also work when the given polyhedra intersect, and also apply to a collection of (possibly intersecting) polyhedral terrains.

Original language | English |
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Pages | 260-270 |

Number of pages | 11 |

State | Published - 1993 |

Externally published | Yes |

Event | Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms - Austin, TX, USA Duration: 25 Jan 1993 → 27 Jan 1993 |

### Conference

Conference | Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | Austin, TX, USA |

Period | 25/01/93 → 27/01/93 |