### 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) |
---|---|

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 2008 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Computational Geometry: Theory and Applications*,

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

**Ray shooting and intersection searching amidst fat convex polyhedra in 3-space.** / Aronov, Boris; De Berg, Mark; Gray, Chris.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 41, no. 1-2, pp. 68-76. https://doi.org/10.1016/j.comgeo.2007.10.006

}

TY - JOUR

T1 - Ray shooting and intersection searching amidst fat convex polyhedra in 3-space

AU - Aronov, Boris

AU - De Berg, Mark

AU - Gray, Chris

PY - 2008/10

Y1 - 2008/10

N2 - 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( log2n) 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) log2n) 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.

AB - 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( log2n) 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) log2n) 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.

KW - Fat objects

KW - Geometric data structures

KW - Intersection searching

KW - Ray shooting

UR - http://www.scopus.com/inward/record.url?scp=84867992862&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867992862&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2007.10.006

DO - 10.1016/j.comgeo.2007.10.006

M3 - Article

VL - 41

SP - 68

EP - 76

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 1-2

ER -