The hierarchical representation of objects: the Delaunay tree

Authors:
J D Boissonnat;M Teillaud
Affiliations:
-;-
Venue:
SCG '86 Proceedings of the second annual symposium on Computational geometry
Year:
1986

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Abstract

We present, in this paper, a new hierarchical data structure called the Delaunay tree. It is defined from the Delaunay triangulation and, roughly speaking, represents a triangulation as a hierarchy of balls. The Delaunay tree provides efficient solutions to several problems such as building the Delaunay triangulation of a finite set of n points in any dimension, locating a point in the triangulation, defining neighborhood relationships in the triangulation and computing intersections. The algorithms are extremely simple and are analyzed from a theoretical and practical points of view.