Degree-k Voronoi domains of periodic point sets.

7^th October 2022, 14:00
Vitaly Kurlin
MIF

Abstract

The talk is based on a joint paper with Phil Smith. Degree-k Voronoi domains of a periodic point set are concentric regions around a fixed centre consisting of all points in Euclidean space that have the centre as their k-th nearest neighbour. Periodic point sets generalise the concept of a lattice by allowing multiple points to appear within a unit cell of the lattice. Thus, periodic point sets model all solid crystalline materials (periodic crystals), and degree-k Voronoi domains of periodic point sets can be used to characterise the relative positions of atoms in a crystal from a fixed centre. We describe the first algorithm to compute all degree-k Voronoi domains up to any degree k>0 for any two or three-dimensional periodic point set.