Radius functions on Poisson–Delaunay mosaics and related complexes experimentally

Edelsbrunner, Herbert; Nikitenko, Anton; Ölsböck, Katharina; Synak, Peter

Radius functions on Poisson–Delaunay mosaics and related complexes experimentally

Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. Topological Data Analysis. , Abel Symposia, vol. 15, 181–218.

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2020-B-01-PoissonExperimentalSurvey.pdf 2.21 MB [Submitted Version]

DOI

10.1007/978-3-030-43408-3_8

Conference Paper | Published | English

Scopus indexed

Author

Edelsbrunner, Herbert^ISTA ; Nikitenko, Anton^ISTA ; Ölsböck, Katharina^ISTA ; Synak, Peter^ISTA

Department

Edelsbrunner Group

Grant

Alpha Shape Theory Extended
Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales
Persistence and stability of geometric complexes

Series Title

Abel Symposia

Abstract

Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics.

Publishing Year

2020

Date Published

2020-06-22

Proceedings Title

Topological Data Analysis

Publisher

Springer Nature

Acknowledgement

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 78818 Alpha and No 638176). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).

Volume

Page

181-218

ISBN

9783030434076

ISSN

21932808

eISSN

21978549

IST-REx-ID

8135

Cite this

Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In: Topological Data Analysis. Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8

Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8

Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.

H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological Data Analysis, 2020, vol. 15, pp. 181–218.

Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” Topological Data Analysis, vol. 15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.

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