Showing papers on "Constrained Delaunay triangulation published in 1980"

Two algorithms for constructing a Delaunay triangulation

Abstract: This paper provides a unified discussion of the Delaunay triangulation. Its geometric properties are reviewed and several applications are discussed. Two algorithms are presented for constructing the triangulation over a planar set ofN points. The first algorithm uses a divide-and-conquer approach. It runs inO(N logN) time, which is asymptotically optimal. The second algorithm is iterative and requiresO(N 2) time in the worst case. However, its average case performance is comparable to that of the first algorithm.

Delaunay Triangulation of a Random Data Set for Isarithmic Mapping

Abstract: The problems of developing an efficient Delaunay triangulation algorithm are described and a number of modifications to existing algorithms suggested. The process of triangle creation is related to that of isarithmic mapping. Estimates of relative time savings are given using a grid versus a triangular data base.

An improvement of fixed point algorithms by using a good triangulation

Abstract: We consider measures for triangulations ofRn. A new measure is introduced based on the ratio of the length of the sides and the content of the subsimplices of the triangulation. In a subclass of triangulations, which is appropriate for computing fixed points using simplicial subdivisions, the optimal one according to this measure is calculated and some of its properties are given. It is proved that for the average directional density this triangulation is optimal (within the subclass) asn goes to infinity. Furthermore, we compare the measures of the optimal triangulation with those of other triangulations. We also propose a new triangulation of the affine hull of the unit simplex. Finally, we report some computational experience that confirms the theoretical results.