Output-Sensitive Methods for Rectilinear Hidden Surface Removal

Mark H. Overmars§ We present an algorithm for the hidden-surface elimination problem for rectangles, which is also known as window rendering. The time complexity of OUI algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a hade-off between these two components, in that its running time is O(r(nI+l/T" + k», where 1 5 r :S log n is a tunable parameter. By using this method while adjusting the parameter r (Con the fly" one can achieve a running time that is O(nlog n+k{log n/ log(l+k/n))). Note that when k is 0(n), this achieves an G(nlog n) running time, and when k is 0(nl+l ) for any positive constant E, then this achieves an O(k) running time, both of which are optimal. •A preliminary version of this research appeared in the Proceedings of the 17th ICALP conference, July 1990. fThis author's research was supported by the National Science Foundation under Grant CCR-8810568 and by the NSF and DARPA under Grant CCR-8908092. Author's address: Department of Computer Science, The Johns Hopkins University, Baltimore, Maryland 21218. tThis author's research was supported by the Office of Naval Research under Grants NOOOl4-84-K-0502 and NOOOI4-86-K-0689, the Air Force Office of Scientific Research under Grant AFOSR-90-0107, the National Science Foundation under Grant DCRr8451393, and the National Library of Medicine under Grant R01LM05118. Part of this research was carried out while this author was visiting the Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, California. Author's address: Department of Computer Science, Purdue University, West Lafayette, Indiana 47907. §This author's research was partially supported by the ESPRIT II Basic Research Actions Program of the EC, under contract No. 3075 (project ALCOM). Author's address: Department of Computer Science, University of Utrecht, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands.