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Binary Space Partitions for 3D Subdivisions (2003)
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| Venue: | The Challenge of Community Policing: Testing the Promises. Thousand Oaks, CA: Sage |
| Citations: | 6 - 1 self |
BibTeX
@INPROCEEDINGS{Hershberger03binaryspace,
author = {John Hershberger and Subhash Suri},
title = {Binary Space Partitions for 3D Subdivisions},
booktitle = {The Challenge of Community Policing: Testing the Promises. Thousand Oaks, CA: Sage},
year = {2003},
pages = {100--108},
publisher = {Press}
}
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Abstract
We consider the following question: Given a subdivision of space into n convex polyhedral cells, what is the worst-case complexity of a binary space partition (BSP) for the subdivision? We show that if the subdivision is rectangular and axis-aligned, then the worstcase complexity of an axis-aligned BSP is #(n ) and O(n n), where # = 1+log 2 (4/3) = 1.4150375 . . . . By contrast, it is known that the BSP of a collection of n rectangular cells not forming a subdivision has worstcase complexity #(n ). We also show that the worstcase complexity of a BSP for a general convex polyhedral subdivision of total complexity O(n) is #(n ).
