### Abstract

We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in ^{R3}. The data structure uses O(n2 ^{+}) storage and preprocessing time, and queries can be answered in O( ^{log2}n) time. A trade-off between storage and query time is also possible: for any m with n<m< ^{n2}, we can construct a structure that uses O(m1 ^{+}) storage and preprocessing time such that queries take O((n/m) ^{log2}n) time. We also describe a data structure for simplex intersection queries in a set of n convex fat constant-complexity polyhedra in ^{R3}. For any m with n<m< ^{n3}, we can construct a structure that uses O(m1 ^{+}) storage and preprocessing time such that all polyhedra intersecting a query simplex can be reported in O((n/m1 ^{/3})logn+k) time, where k is the number of answers.

Original language | English (US) |
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Pages (from-to) | 68-76 |

Number of pages | 9 |

Journal | Computational Geometry: Theory and Applications |

Volume | 41 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 2008 |

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### Keywords

- Fat objects
- Geometric data structures
- Intersection searching
- Ray shooting

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computational Geometry: Theory and Applications*,

*41*(1-2), 68-76. https://doi.org/10.1016/j.comgeo.2007.10.006