Binary Space Partitions for Fat Rectangles

We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in IR3 such that the aspect ratio of each rectangle in S is at most , for some constant 1. We present an n2O(plogn )-time algorithm to build a binary space partition of size n2O(plogn ) for S. We also show that if m of the n rectangles in S have aspect ratios greater than , we can construct a BSP of size npm2O(plogn ) for S in npm2O(plogn ) time. The constants of proportionality in the big-oh terms are linear in log . We extend these results to cases in which the input contains non-orthogonal or intersecting objects.