Technical Reports

The report FIMU-RS-2003-02

Linear Binary Space Partitions and Hierarchy of Object Classes

by Petr Tobola, Karel Nechvíle, April 2003, 21 pages.

FIMU-RS-2003-02. Available as Postscript, PDF.

Abstract:

We consider the problem of constructing binary space partitions for the set P of d-dimensional objects in d-dimensional space. There are several classes of objects defined for such settings, which support design of effective algorithms. We extend the existing the de Berg hierarchy of classes by the definition of new classes derived from that one and we show desirability of such an extension. Moreover we propose a new algorithm, which works on generalized lambda-low density scenes (defined in this paper) and provides BSP tree of linear size. The tree can be constructed in O(n log^2 n) time and space, where n is the number of objects. Moreover, we can trade-off between size and balance of the BSP tree fairly simply.