Alpha Shape Theory Extended

Project Information

ALPHA

Grant agreement ID: 788183

DOI

10.3030/788183

Project closed

EC signature date 8 June 2018

Start date 1 July 2018

End date 30 June 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 678 432,00

EU contribution

€ 1 678 432,00

Coordinated by

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Austria

CORDIS provides links to public deliverables and publications of HORIZON projects.

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

Peer reviewed articles (16)

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

Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications

Author(s): Ranita Biswas; Sebastiano Cultrera di Montesano; Herbert Edelsbrunner; Morteza Saghafian
Published in: Journal of Applied Computational Topology, 2023, ISSN 2367-1734
Publisher: Springer Nature
DOI: 10.1007/s41468-024-00173-w

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

On angles in higher-order Brillouin tessellations and related tilings in the plane

Author(s): Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian
Published in: Discrete & Computational Geometry, 2023, ISSN 1432-0444
Publisher: Springer Nature
DOI: 10.48550/arXiv.2204.01076

Conference proceedings (4)

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

Thesis and dissertations (1)

The hole system of triangulated shapes

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

Other (1)

Average and Expected Distortion of VoronoiPaths and Scapes

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