About Some Localization Problems in Delaunay Triangulations

N. F. Dyshkant

M. V. Lomonosov Moscow State University

Abstract: We study some problems of nodes localization in a Delaunay triangulation and problem-solving procedures. For the problem of the set of nodes the computationally efficient approach that uses Euclidean minimum spanning tree of Delaunay triangulation is proposed. Efficient estimations for computational comlexity of the proposed methods in the average and in the worst cases are proved.

Keywords: computational geometry, geometric search, Delaunay triangulation, merging of overlapping triangulations, unregular discrete mesh, computational complexity.

UDC: 519.17+510.52

Received: 15.09.2012