Bregman Delaunay Triangulations Satisfy the Bregman Empty Sphere Property

FrnkNlsn · x · 2026-09-12

A concise explainer on Delaunay triangulations (DT): they are the dual of Voronoi diagrams of a site set and satisfy the empty sphere property—every circumscribing sphere of a triangle (or d-dimensional simplex) contains no other sites.

The author then notes that Bregman DT satisfies the analogous Bregman empty sphere property, extending this classical computational geometry structure to spaces measured by Bregman divergences (e.g., KL divergence, Euclidean distance), which are widely used in machine learning.

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