On the number of views of polyhedral scenes

Boris Aronov, Hervé Brönnimann, Dan Halperin, Robert Schiffenbauer

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


It is known that a scene consisting of A- convex polyhedra of total complexity n has at most 0(n4 k2) distinct orthographic views, and that the number of such views is Ω((nk2 + n2)2) in the worst case. The corresponding bounds for perspective views are 0(n6 k3) and Ω((nk2+n2)3), respectively. In this paper, we close these gaps by improving the lower bounds. We construct an example of a scene with Ө(n4 k2) orthographic views, and another with Ө(n6 k3) perspective views. Our construction can also be used to improve the known lower bounds for the number of silhouette views and for the number of distinct views from a viewpoint moving along a straight line.

Original languageEnglish
Title of host publicationDiscrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers
EditorsJin Akiyama, Mikio Kano, Masatsugu Urabe
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783540477389
StatePublished - 2001
EventJapanese Conference on Discrete and Computational Geometry, JCDCG 2000 - Tokyo, Japan
Duration: 22 Nov 200025 Nov 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceJapanese Conference on Discrete and Computational Geometry, JCDCG 2000


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