article

Realization Spaces of Arrangements of Convex Bodies

Authors:

Michael Gene Dobbins,

Andreas Holmsen,

Alfredo HubardAuthors Info & Claims

Discrete & Computational Geometry, Volume 58, Issue 1

Pages 1 - 29

https://doi.org/10.1007/s00454-017-9869-8

Published: 01 July 2017 Publication History

Abstract

We introduce combinatorial types of planar arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial complexity of the bodies and the topological complexity of their realization space. First, we show that every combinatorial type is realizable and its realization space is contractible under mild assumptions. Second, we prove a universality theorem that says the restriction of the realization space to arrangements polygons with a bounded number of vertices can have the homotopy type of any primary semialgebraic set.

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Cited By

Koswara IPogudin GSelivanova SZiegler M(2023)Bit-complexity of classical solutions of linear evolutionary systems of partial differential equationsJournal of Complexity10.1016/j.jco.2022.10172776:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.jco.2022.101727

Realization Spaces of Arrangements of Convex Bodies
1. Computing methodologies
  1. Computer graphics
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 58, Issue 1

July 2017

253 pages

ISSN:0179-5376

Issue’s Table of Contents

Copyright © Copyright © 2017 Springer Science+Business Media New York.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 July 2017

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Cited By

Koswara IPogudin GSelivanova SZiegler M(2023)Bit-complexity of classical solutions of linear evolutionary systems of partial differential equationsJournal of Complexity10.1016/j.jco.2022.10172776:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.jco.2022.101727

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