Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
P.K. Agarwal , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
E.F. Grove , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
T.M. Murali , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
J.S. Vitter , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
The authors consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in R/sup 3/ such that the aspect ratio of each rectangle in S is at most /spl alpha/, for some constant a /spl alpha//spl ges/1. They present an n2/sup O(/spl radic/logn)/-time algorithm to build a binary space partition of size n2/sup O(/spl radic/logn)/ for S. They also show that if m of the n rectangles in S have aspect ratios greater than /spl alpha/, they can contact a BSP of size n/spl radic/m2/sup O(/spl radic/logn)/ for S in n/spl radic/2/sup O(/spl radic/logn)/ time. The constants of proportionality in the big-oh terms are linear in log /spl alpha/. They extend these results to cases in which the input contains non-orthogonal or intersecting objects.
computational complexity; fat rectangles; binary space partitions; orthogonal nonintersecting two-dimensional rectangles; aspect ratio; algorithm; proportionality constants; intersecting objects; nonorthogonal objects; computation time; hidden surface removal
E. Grove, T. Murali, P. Agarwal and J. Vitter, "Binary space partitions for fat rectangles," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 482.