2026-07-21T20:03:33Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13831 2024-03-06T10:52:49Z ddc:004 open_access

The Density Fingerprint of a Periodic Point Set Edelsbrunner, Herbert Heiss, Teresa Kurlin, Vitaliy Smith, Philip Wintraecken, Mathijs Lattices periodic sets isometries Dirichlet-Voronoi domains Brillouin zones bottleneck distance stability continuity crystal database Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functions that facilitates the efficient search for new materials and material properties. We prove invariance under isometries, continuity, and completeness in the generic case, which are necessary features for the reliable comparison of crystals. The proof of continuity integrates methods from discrete geometry and lattice theory, while the proof of generic completeness combines techniques from geometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and related inclusion-exclusion formulae. We have implemented the algorithm and describe its application to crystal structure prediction. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Herbert Edelsbrunner and Teresa Heiss and Vitaliy Kurlin and Philip Smith and Mathijs Wintraecken 2021 Is Part Of LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2021.32 urn:nbn:de:0030-drops-138310 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.32 eng https://creativecommons.org/licenses/by/4.0/legalcode