Vertical decomposition of a single cell in a three-dimensional arrangement of surfaces and its applications

Otfried Schwarzkopf*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

Abstract

Let Σ be a collection of n algebraic surface patches of constant maximum degree in R3. We show that the combinatorial complexity of the vertical decomposition of a single cell in the arrangement A(Σ) is O(n2+ε), for any ε > 0, where the constant of proportionality depends on ε and on the maximum degree of the surfaces and of their boundaries. As an application, we obtain a near-quadratic motion planning algorithm for general systems with three degrees of freedom.

Original languageEnglish
Pages20-29
Number of pages10
DOIs
StatePublished - 1996
Externally publishedYes
EventProceedings of the 1996 12th Annual Symposium on Computational Geometry - Philadelphia, PA, USA
Duration: 24 May 199626 May 1996

Conference

ConferenceProceedings of the 1996 12th Annual Symposium on Computational Geometry
CityPhiladelphia, PA, USA
Period24/05/9626/05/96

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