Functionals on Triangulations of Delaunay Sets
Nikolay P. Dolbilin, Herbert Edelsbrunner, Alexey Glazyrin, Oleg R., Musin
TL;DR
This paper investigates the properties of functionals on triangulations of Delaunay sets, establishing that the Delaunay triangulation minimizes these functionals under certain conditions, extending finite set results to infinite sets.
Contribution
It proves that the Delaunay triangulation minimizes specific functionals for infinite Delaunay sets, generalizing finite set results.
Findings
Delaunay triangulation minimizes functionals on Delaunay sets
Extension of finite set results to infinite sets
Establishment of density minimization properties
Abstract
We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.