Realization Spaces of Arrangements of Convex Bodies

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.
Publisher
SPRINGER
Issue Date
2017-07
Language
English
Keywords

ORIENTED MATROIDS; ORDER TYPES; CONFIGURATIONS; SETS; POLYTOPES; FAMILIES; PLANE

Citation

DISCRETE & COMPUTATIONAL GEOMETRY, v.58, no.1, pp.1 - 29

ISSN
0179-5376
DOI
10.1007/s00454-017-9869-8
URI
http://hdl.handle.net/10203/224774
Appears in Collection
MA-Journal Papers(저널논문)
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