Smith, Philip and Kurlin, Vitally 
ORCID: 0000-0001-5328-5351
(2022)
A Practical Algorithm for Degree-<i>k</i> Voronoi Domains of Three-Dimensional Periodic Point Sets.
In: International Symposium on Visual Computing, 2022-10-3 - 2022-10-5, San Diego, US.
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Abstract
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. The paper describes the first algorithm to compute all degree-k Voronoi domains up to any degree k≥ 1 for any two or three-dimensional periodic point set.
| Item Type: | Conference or Workshop Item (Unspecified) |
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| Uncontrolled Keywords: | Degree-k Voronoi Domains, Periodic point sets, Crystals |
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 16 Jan 2023 10:31 |
| Last Modified: | 25 Nov 2023 11:04 |
| DOI: | 10.1007/978-3-031-20713-6_29 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3167050 |
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