Alpha Shape Theory Extended

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Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

A step in the Delaunay mosaic of order k

Author(s): H. Edelsbrunner, A. Nikitenko, G. Osang
Published in: Geometry, Issue 112, 2021, ISSN 0047-2468
Publisher: Birkhauser Verlag
DOI: 10.1007/s00022-021-00577-4

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
Publisher: De Gruyter
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
Publisher: Springer Verlag
DOI: 10.1007/s00454-020-00188-x

Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives

Author(s): Patrice Koehl; Arseniy Akopyan; Herbert Edelsbrunner
Published in: Journal of Chemical Information and Modeling, Issue 63, 3, 2023, Page(s) 973–985, ISSN 1549-9596
Publisher: American Chemical Society
DOI: 10.1021/acs.jcim.2c01346

Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics

Author(s): Ranita Biswas, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, Morteza Saghafian
Published in: Discrete & Computational Geometry, Issue 67, 2022, Page(s) 811–842, ISSN 1432-0444
Publisher: Springer Nature
DOI: 10.1007/s00454-022-00371-2

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
Publisher: Elsevier BV
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
Publisher: Springer Verlag
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
Publisher: Oxford University Press
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
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/s0040585x97t989726

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

Author(s): Herbert Edelsbrunner, Georg Osang
Published in: Algorithmica, Issue 85, 2022, Page(s) 277-295, ISSN 1432-0541
Publisher: Springer Nature
DOI: 10.1007/s00453-022-01027-6

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
Publisher: De Gruyter
DOI: 10.1515/cmb-2020-0100

The multi-cover persistence of Euclidean balls

Author(s): Herbert Edelsbrunner; Georg Osang
Published in: Discrete & Computational Geometry, Issue 65, 2021, Page(s) 1296-1313, ISSN 0179-5376
Publisher: Springer Verlag
DOI: 10.1007/s00454-021-00281-9

Topological signatures and stability of hexagonal close packing and Barlow stackings.

Author(s): Georg Osang; Herbert Edelsbrunner; Mohammad Saadatfar
Published in: Soft Matter, Issue 17(40), 2021, Page(s) 9107-9115, ISSN 1744-6848
Publisher: Royal Society of Chemistry
DOI: 10.1039/d1sm00774b

The beauty of random polytopes inscribed in the 2-sphere

Author(s): Arseniy Akopyan, Herbert Edelsbrunner, Anton Nikitenko
Published in: Experimental Mathematics, 2021, ISSN 1944-950X
Publisher: Taylor & Francis Online
DOI: 10.1080/10586458.2021.1980459

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, ISBN 978-3-030-43407-6
Publisher: Springer, Cham
DOI: 10.1007/978-3-030-43408-3_8

Counting Cells of Order-k Voronoi Tessellations in ℝ³ with Morse Theory

Author(s): Biswas, Ranita ; Cultrera di Montesano, Sebastiano ; Edelsbrunner, Herbert ; Saghafian, Morteza
Published in: 37th International Symposium on Computational Geometry (SoCG 2021), Issue LIPIcs, Volume 189, 2021, Page(s) 16:1-16:15, ISBN 978-3-95977-184-9
Publisher: Schloss Dagstuhl
DOI: 10.4230/lipics.socg.2021.16

The Density Fingerprint of a Periodic Point Set

Author(s): Edelsbrunner, Herbert; Heiss, Teresa; Kurlin, Vitaliy; Smith, Philip; Wintraecken, Mathijs
Published in: 37th International Symposium on Computational Geometry (SoCG 2021), Issue Article No. 19, 2021, Page(s) pp. 19:1-19:16
Publisher: Schloss Dagstuhl
DOI: 10.48550/arxiv.2104.11046

Generalizing CGAL Periodic Delaunay Triangulations

Author(s): Georg Osang, Mael Rouxel-Labbé, Monique Teillaud
Published in: Leibniz International Proceedings in Informatics - ESA 2020, Issue 75, 2020, Page(s) 1-17
Publisher: Dagstuhl Publishing
DOI: 10.4230/lipics.esa.2020.75

The hole system of triangulated shapes

Author(s): Katharina Ölsböck
Published in: 2020
Publisher: IST Austria
DOI: 10.15479/at:ista:7460

Average and Expected Distortion of VoronoiPaths and Scapes

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

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