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 IR 3 such that the aspect ratio of each rectangle in S is at most ff, for some constant ff 1. We present an n2 O( p log n ) -time algorithm to build a binary space partition of size n2 O( p log n ) for S. We also show that if m of the n rectangles in S have aspect ratios greater than ff, we can construct a BSP of size n p m2 O( p log n ) for S in n p m2 O( p log n ) time. The constants of proportionality in the big-oh terms are linear in log ff. We extend these results to cases in which the input contains non-orthogonal or intersecting objects. 1. Introduction How to render a set of opaque or partially transparent objects in IR 3 in a visually realistic way is a fundamental problem in computer graphics [12, 22]. A central component of this problem is hidden-surface removal: given a set of objects, a viewpo..