Alpha Shape Theory Extended

Project Period: 2018-07-01 – 2023-06-30
Externally Funded
Acronym
ALPHA
Principal Investigator
Herbert Edelsbrunner
Department(s)
Edelsbrunner Group
Grant Number
788183
Funding Organisation
EC/H2020

24 Publications

2020 | Journal Article | IST-REx-ID: 7791 | OA
When different norms lead to same billiard trajectories?
A. Akopyan, R. Karasev, European Journal of Mathematics (2020).
View | Files available | DOI | arXiv
 
2020 | Conference Paper | IST-REx-ID: 8135 | OA
Radius functions on Poisson–Delaunay mosaics and related complexes experimentally
H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.
View | Files available | DOI
 
2020 | Journal Article | IST-REx-ID: 8338 | OA
On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs
A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2020) 938–976.
View | DOI | Download Preprint (ext.) | arXiv
 
2020 | Journal Article | IST-REx-ID: 8538 | OA
Billiards in ellipses revisited
A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020).
View | DOI | Download Preprint (ext.) | arXiv
 
2019 | Journal Article | IST-REx-ID: 5678 | OA
Poisson–Delaunay Mosaics of Order k
H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.
View | Files available | DOI | arXiv
 
2020 | Journal Article | IST-REx-ID: 7554 | OA
Weighted Poisson–Delaunay mosaics
H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.
View | DOI | Download Preprint (ext.) | arXiv
 
2020 | Journal Article | IST-REx-ID: 7666 | OA
Tri-partitions and bases of an ordered complex
H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.
View | Files available | DOI
 
2019 | Journal Article | IST-REx-ID: 6608 | OA
Holes and dependences in an ordered complex
H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.
View | Files available | DOI
 
2019 | Journal Article | IST-REx-ID: 6793 | OA
The Regge symmetry, confocal conics, and the Schläfli formula
A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.
View | DOI | Download Preprint (ext.) | arXiv
 
2020 | Conference Paper | IST-REx-ID: 8703 | OA
Generalizing CGAL periodic Delaunay triangulations
G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
View | Files available | DOI
 
2020 | Journal Article | IST-REx-ID: 9156 | OA
The weighted Gaussian curvature derivative of a space-filling diagram
A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.
View | Files available | DOI | arXiv
 
2020 | Journal Article | IST-REx-ID: 9157 | OA
The weighted mean curvature derivative of a space-filling diagram
A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.
View | Files available | DOI
 
2020 | Journal Article | IST-REx-ID: 9249 | OA
Digital objects in rhombic dodecahedron grid
R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.
View | Files available | DOI
 
2021 | Journal Article | IST-REx-ID: 9317 | OA
The multi-cover persistence of Euclidean balls
H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.
View | Files available | DOI
 
2021 | Conference Paper | IST-REx-ID: 9345 | OA
The density fingerprint of a periodic point set
H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.
View | Files available | DOI
 
2021 | Conference Paper | IST-REx-ID: 9604 | OA
Counting cells of order-k voronoi tessellations in ℝ3 with morse theory
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.
View | Files available | DOI
 
2021 | Conference Paper | IST-REx-ID: 9824
Body centered cubic grid - coordinate system and discrete analytical plane definition
L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.
View | DOI
 
2021 | Journal Article | IST-REx-ID: 10204
Topological signatures and stability of hexagonal close packing and Barlow stackings
G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.
View | DOI | PubMed | Europe PMC
 
2022 | Book Chapter | IST-REx-ID: 11440 | OA
The persistent homology of dual digital image constructions
B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V. Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer Nature, Cham, 2022, pp. 1–26.
View | DOI | Download Preprint (ext.) | arXiv
 
2022 | Journal Article | IST-REx-ID: 11658 | OA
Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).
View | Files available
 
2022 | Journal Article | IST-REx-ID: 11660 | OA
A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).
View | Files available
 
2022 | Conference Paper | IST-REx-ID: 11428 | OA
A cautionary tale: Burning the medial axis is unstable
E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc, M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.
View | Files available | DOI
 
2023 | Journal Article | IST-REx-ID: 12086 | OA
A simple algorithm for higher-order Delaunay mosaics and alpha shapes
Edelsbrunner, Herbert, A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica 85. 2023
View | Files available | DOI
 
2021 | Journal Article | IST-REx-ID: 10222 | OA
The beauty of random polytopes inscribed in the 2-sphere
Akopyan, Arseniy, The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. 2021
View | DOI | Download Published Version (ext.) | arXiv