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)

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... and provides BSP trees 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.