Group of Supramolecular Structures,Institute of Chemical Kinetics and Combustion SB RAS
Novosibirsk State University
Russia

Title of Talk: Delaunay's impact on Voronoi DiagramVoronoi polyhedra and Delaunay simplexes, Voronoi tessellation and Delaunay triangulation are used in very different fields on science from the computer visualization to economics, from PDE to CIS, for structure investigations and for analysis of intermolecular voids in material sciences and molecular biology. G.F.Voronoi had studied these fundamental geometrical notions at length and proven their duality in 1909. However it was rather a pure mathematical result obtained in application of the quadratic forms for filling of space by parallelohedra. B.N. Delaunay had disclosed in 1929 that the geometrical constructions of Voronoi are generally valid, i.e. they can be determined not only for lattice systems of points, but for any discrete points. It turned out, that such systems become the main objects of the researches in Computer era, and the Delaunay’s contribution has promoted general geometrical basis for their investigations. The main ideas of B.N. Delaunay, in particular, the image of “Delaunay empty sphere” will be discussed. Delaunay proven correctness of the main theorems of Voronoi using this simple geometrical image. It is also a helpful tool for understanding (and development) of algorithms for calculation of the Voronoi-Delaunay tessellations.

A Short Biography of Delaunay

B.N. Delaunay is one of the notable mathematicians of the XX-th century. Many large achievements in different fields (algebra, theory of number, geometry, crystallography) are related with his name. The notions Delaunay triangulation, Delaunay simplex are known far beyond the bounds of the pure mathematics. He had proven that the decomposition of space on polyhedra and simplices, studied by G.F.Voronoi for lattice point systems, can be generalized on any disordered systems of discrete points. Just this generalization is the base of the numerous applications of the Voronoi decomposition.

B.N. Delaunay was born in 1890 in Petrburg in family of a professor of mathematics. The family moved to Kiev in 1906. In 1908 - 1913 he was studied in the University of Kiev, and then worked as an associate professor in the Polytechnic Institute of Kiev. In 1920 he was invited in Peterburg , and became a professor of the University of Peterburg since 1922. In 1935 he moved in Moscow to be the head of the department of higher geometry in the University of Moscow being a well-known scientist, and a Corresponding Member of Academy of Science of the USSR. The last years he worked in the Mathematical Institute of the Academy of Science. He died in Moscow at the age of ninety, in 1980.

B.N. Delaunay was an eminent teacher. There are a lot of known mathematicians among his pupils. However he is known not only as a scientist and a pedagogue, but also as a famous alpinist. He climbed all main peaks of the Caucasus. He went on travels in Altay Mountains. There is a peak of his name (Delaunay peak, 4300m) alongside with the mountain Belukha (4500m), the highest peak of Altay.

In 1926 he climbed this mountain (4300 m) on the way to the highest mountain of Altay - Belukha (4500). In 1936 this name had been inserted into a geographical map.The picture from site: http://www.skitalets.ru/ski/2009/altay09_belykh/