Publications

2021

H. Edelsbrunner and A. Nikitenko. Average and expected distortion of Voronoi paths and shapes. Manuscript, IST Austria, Klosterneuburg, Austria, 2021. pdf-file

A. Akopyan, H. Edelsbrunner and A. Nikitenko. The beauty of random polytopes inscribed in the 2-sphere. Manuscript, IST Austria, Klosterneuburg, Austria, 2021. pdf-file

H. Edelsbrunner, A. Nikitenko and G. Osang. A step in the Delaunay mosaic of order k. J. Geometry (2021), accepted. pdf-file

G. Osang, H. Edelsbrunner and M. Saadatfar. Topological signatures and stability of hexagonal close packings and Barlow stackings. Manuscript, IST Austria, Klosterneuburg, Austria, 2021. pdf-file

H. Edelsbrunner and G. Osang. The multi-cover persistence of Euclidean balls. Discrete Comput. Geom. (2021), accepted. pdf-file

H. Edelsbrunner, T. Heiss, V. Kurlin, P. Smith and M. Wintraecken. The density fingerprint of a periodic set. In “Proc. 37th Ann. Sympos. Comput. Geom., 2021”, to appear. pdf-file

R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner and M. Saghafian. Counting cells of order-k Voronoi tessellations in R^3 with Morse theory. In “Proc. 37th Ann. Sympos. Comput. Geom., 2021”, to appear. pdf-file

R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner and M. Saghafian. Continuous and discrete radius functions on tessellations and mosaics. Manuscript, IST Austria, Klosterneuburg, Austria, 2021. pdf-file

2020

G. Osang, M. Rouxel-Labbe and M. Theillaud. Generalizing CGAL periodic Delaunay triangulations. In “28th Ann. Europ. Symbol. Algorithms, 2020”, 75:1-75:17. pdf-file

H. Edelsbrunner and G. Osang. A simple algorithm for computing higher order Delaunay mosaics. Manuscript, IST Austria, Klosterneuburg, Austria, 2020.  pdf-file

A. Akopyan and H. Edelsbrunner. The weighted Gaussian curvature derivative of a space-filling diagram. Comput. Math. Biophys. 8 (2020), 78-88. arXiv:1908.06777 [cs.CG] pdf-file

A. Akopyan and H. Edelsbrunner. The weighted mean curvature derivative of a space-filling diagram. Comput. Math. Biophys. 8 (2020), 51-67. arXiv:1908.06779 [cs.CG] pdf-file

H. Edelsbrunner, A. Nikitenko, K. Oelsboeck and P. Synak. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally.  In Topological Data Analysis, Abel Symposium 15, 2020, 181-218.  pdf-file

H. Edelsbrunner and K. Oelsboeck. Tri-partitions and bases of an ordered complex. Discrete Comput. Geom. 64 (2012), 759-775. arXiv:2103.10830 [math.CO] pdf-file

2019

H. Edelsbrunner and K. Oelsboeck. Holes and dependence in an ordered complex. Comput. Aided Geom. Des. 73 (2019), 1-15.  pdf-file

H. Edelsbrunner and A. Nikitenko. Weighted Poisson–Delaunay mosaics. Theory Probab. Appl., SIAM 64 (2019), 746-770. arXiv:1705.08735 [math.PR] pdf-file

H. Edelsbrunner and A. Nikitenko. Poisson–Delaunay mosaics of order kDiscrete Comput. Geom. 62 (2019), 865-878.  pdf-file