Proceedings of 37th Conference on Foundations of Computer Science (1996)

Burlington, VT

Oct. 14, 1996 to Oct. 16, 1996

ISBN: 0-8186-7594-2

pp: 482

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

ABSTRACT

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.

INDEX TERMS

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

CITATION

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.

doi:10.1109/SFCS.1996.548507

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