Realization Spaces of Arrangements of Convex Bodies

@article{Dobbins2017RealizationSO,
  title={Realization Spaces of Arrangements of Convex Bodies},
  author={Michael Gene Dobbins and Andreas F. Holmsen and Alfredo Hubard},
  journal={Discrete \& Computational Geometry},
  year={2017},
  volume={58},
  pages={1-29}
}
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… 

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