--- res: bibo_abstract: - The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Ranita foaf_name: Biswas, Ranita foaf_surname: Biswas foaf_workInfoHomepage: http://www.librecat.org/personId=3C2B033E-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-5372-7890 - foaf_Person: foaf_givenName: Sebastiano foaf_name: Cultrera Di Montesano, Sebastiano foaf_surname: Cultrera Di Montesano foaf_workInfoHomepage: http://www.librecat.org/personId=34D2A09C-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-6249-0832 - foaf_Person: foaf_givenName: Herbert foaf_name: Edelsbrunner, Herbert foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Morteza foaf_name: Saghafian, Morteza foaf_surname: Saghafian bibo_doi: 10.1007/s00454-022-00371-2 bibo_volume: 67 dct_date: 2022^xs_gYear dct_identifier: - UT:000752175300002 dct_isPartOf: - http://id.crossref.org/issn/0179-5376 - http://id.crossref.org/issn/1432-0444 dct_language: eng dct_publisher: Springer Nature@ dct_title: Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics@ ...