Linear Binary Space Partitions and the Hierarchy of Object Classes

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 that support the design of effective algorithms. We extend the existing de Berg hierarchy of classes [4] by defining new classes based on old ones and we show the desirability of such an extension. Moreover we propose a new algorithm that works on generalized Λ-low-density scenes [11] (defined in this paper) and provides BSP trees of linear size. The tree can be constructed in O(n log2 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.

• Type: Conference
• Year: 2003
• Where: CCCG
• Authors: Petr Tobola, Karel Nechvíle
• Keywords: Binary Space Partitions, BSP Tree, CCCG 2003, CCCG 2007, D-dimensional Objects