3 papers
math.CO2024
On Spheres with Points Inside
Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian
We generalize the classic definition of Delaunay triangulation and prove that for a locally finite and coarsely dense generic point set, , the -simplic…
math.MG2023
On the metric spaces of lattices and periodic point sets
Alexey Garber, Žiga Virk, Nicolò Zava
Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals.…
math.CO2023
Order-2 Delaunay Triangulations Optimize Angles
Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian
The local angle property of the (order-) Delaunay triangulations of a generic set in asserts that the sum of two angles opposite a common edge is less than . T…