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Alpha Shape Theory Extended

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Publications

The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram

Author(s): Arsenyi Akopyan, Herbert Edelsbrunner
Published in: Computational and Mathematical Biophysics, Issue 8/1, 2020, Page(s) 74-88, ISSN 2544-7297
DOI: 10.1515/cmb-2020-0101

Tri-partitions and Bases of an Ordered Complex

Author(s): Herbert Edelsbrunner, Katharina Ölsböck
Published in: Discrete & Computational Geometry, Issue 64/3, 2020, Page(s) 759-775, ISSN 0179-5376
DOI: 10.1007/s00454-020-00188-x

Holes and dependences in an ordered complex

Author(s): Herbert Edelsbrunner, Katharina Ölsböck
Published in: Computer Aided Geometric Design, Issue 73, 2019, Page(s) 1-15, ISSN 0167-8396
DOI: 10.1016/j.cagd.2019.06.003

Poisson–Delaunay Mosaics of Order k

Author(s): Herbert Edelsbrunner, Anton Nikitenko
Published in: Discrete & Computational Geometry, Issue 62/4, 2019, Page(s) 865-878, ISSN 0179-5376
DOI: 10.1007/s00454-018-0049-2

The Regge symmetry, confocal conics, and the Schläfli formula

Author(s): Arseniy Akopyan, Ivan Izmestiev
Published in: Bulletin of the London Mathematical Society, Issue 51/5, 2019, Page(s) 765-775, ISSN 0024-6093
DOI: 10.1112/blms.12276

Weighted Poisson--Delaunay Mosaics

Author(s): H. Edelsbrunner, A. Nikitenko
Published in: Theory of Probability & Its Applications, Issue 64/4, 2020, Page(s) 595-614, ISSN 0040-585X
DOI: 10.1137/s0040585x97t989726

The Weighted Mean Curvature Derivative of a Space-Filling Diagram

Author(s): Arsenyi Akopyan, Herbert Edelsbrunner
Published in: Computational and Mathematical Biophysics, Issue 8/1, 2020, Page(s) 51-67, ISSN 2544-7297
DOI: 10.1515/cmb-2020-0100

Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally

Author(s): Herbert Edelsbrunner, Anton Nikitenko, Katharina Ölsböck, Peter Synak
Published in: Topological Data Analysis - The Abel Symposium 2018, Issue 15, 2020, Page(s) 181-218
DOI: 10.1007/978-3-030-43408-3_8

A simple algorithm for computing higher order Delaunay mosaics and Alpha shapes

Author(s): Herbert Edelsbrunner, Georg Osang
Published in: arxiv preprint repository, 2020

Average and Expected Distortion of VoronoiPaths and Scapes

Author(s): Herbert Edelsbrunner, Anton Nikitenko
Published in: arxiv pre-print repository, 2020

The beauty of random polytopes inscribed in the 2-sphere

Author(s): Arseniy Akopyan, Herbert Edelsbrunner, Anton Nikitenko
Published in: arxiv pre-print repository, 2020