Delone

Delone is a surname of Russian origin that appears in mathematics and crystallography. In Western literature the name is often rendered Delaunay, reflecting transliteration differences. The most prominent figure associated with the name is Boris Nikolaevich Delone, a Soviet geometer who made foundational contributions to the geometry of numbers and discrete geometry. His work laid the groundwork for several concepts that bear his name in modern geometry and its applications.

In discrete and computational geometry, several terms carry the Delone name. A Delone set (or Delone set) in Euclidean space is a point set that is both uniformly discrete and relatively dense; informally, there exists a minimum separation between points and every region of space contains some point from the set. Related to this is the Delaunay triangulation, a triangulation of a set of points in the plane or higher dimensions such that no point lies inside the circumcircle of any triangle. The Delaunay triangulation is the geometric dual of the Voronoi diagram and is widely used in mesh generation, computer graphics, geographic information systems, and finite element methods.

Delone concepts have had a broad impact beyond pure geometry, including crystallography and the study of quasicrystals, where Delone sets provide a mathematical framework for describing ordered but nonperiodic structures. In some texts, the same ideas are referred to by the French-derived spelling Delaunay, but they refer to the same underlying constructs.

See also: Delaunay triangulation, Voronoi diagram, Delone set.