Merging visibility maps

Mark H. Overmars, Micha Sharir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Let V be a set of objects in space for which we want to determine the portions visible from a particular point of view v. Assume V is subdivided in subsets V1, ... , Vz and the visibility maps M1, ... Mz of these subsets from point v are known. We show that the visibility map M for V can be computed by merging M1, ... , Mz in time O((n + k)z log2 n) where n is the total size (number of edges, vertices and faces) of the visibility maps M1, ... , Mz and k is the size of M. This result has important applications e.g. in animation where objects move with respect to a fixed environment. It also leads to efficient algorithms for special cases of the hidden-surface removal problem. For example, we obtain a method for hidden surface removal in a set of unit spheres, viewed from infinity, that runs in time O((n + k) log2 n).

Original languageEnglish
Title of host publicationProc Sixth Annu Symp Comput Geom
PublisherAssociation for Computing Machinery (ACM)
Number of pages9
ISBN (Print)0897913620, 9780897913621
StatePublished - 1990
Externally publishedYes
EventProceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA
Duration: 6 Jun 19908 Jun 1990

Publication series

NameProc Sixth Annu Symp Comput Geom


ConferenceProceedings of the Sixth Annual Symposium on Computational Geometry
CityBerkeley, CA, USA


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