Vertical decompositions for triangles in 3-space

Mark de Berg, Leonidas J. Guibas, Dan Halperin

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

Abstract

We prove that, for any constant ε > 0, the complexity of the vertical decomposition of a set of n triangles in three-dimensional space is O(n2+ε + K), where K is the complexity of the arrangement of the triangles. For a single cell the complexity of the vertical decomposition is shown to be O(n2+ε). These bounds are almost tight in the worst case. We also give a deterministic output-sensitive algorithm for computing the vertical decomposition that runs in O(n2 log n + V log n) time, where V is the complexity of the decomposition. The algorithm is reasonably simple (in particular, it tries to perform as much of the computation in two-dimensional spaces as possible) and thus is a good candidate for efficient implementations.

Original languageEnglish
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery (ACM)
Pages1-10
Number of pages10
ISBN (Print)0897916484, 9780897916486
DOIs
StatePublished - 1994
Externally publishedYes
EventProceedings of the 10th Annual Symposium on Computational Geometry - Stony Brook, NY, USA
Duration: 6 Jun 19948 Jun 1994

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

ConferenceProceedings of the 10th Annual Symposium on Computational Geometry
CityStony Brook, NY, USA
Period6/06/948/06/94

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