Linear BSP trees for sets of hyperrectangles with low directional density

We consider the problem of constructing of binary space partitions (BSP) for a set S of n hyperrectangles in space with constant dimension. If the set S ful lls the low directional density condition de ned in this paper then the resultant BSP has O(n) size and it can be constructed in O(n log2 n) time in R3 . The low directional density condition de nes a new class of objects which we are able to construct a linear BSP for. The method is quite simple and it should be appropriate for practical implementation