Minimal roughness property of the Delaunay triangulation: A shorter approach
{S. Rippa} [ibid. 7, No. 6, 489-497 (1990; Zbl 0714.65009)] has shown that the Delaunay triangulation constructed from a set of vertices is of minimial roughness measured by the Euclidean norm of \(\nabla g\) where \(g\) is the piecewise linear function describing the triangulation. A basic tool in the proof was an inequality estimating the difference of the squares of the norms for the two triangulations possible for a quadrilateral in geometric terms. The author gives an inequality yielding the same result but with a much shortened proof.
scientific article; zbMATH DE number 85952