Showing papers on "Delaunay triangulation published in 1981"

An O(n log n) Heuristic for Steiner Minimal Tree Problems on the Euclidean Metric

Abstract: An O(n log n) heuristic for the Euclidean Steiner Minimal Tree (ESMT) problem is presented. The algorithm is based on a decomposition approach which first partitions the vertex set into triangles via the Delaunay triangulation, then “recomposes” the suboptimal Steiner Minimal Tree (SMT) according to the Voronoi diagram and Minimum Spanning Tree (MST) of the point set. The ESMT algorithm was implemented in FORTRAN-IV and tested on a number of randomly generated point sets in the plane drawn from a uniform distribution. Comparison of the O(n log n) algorithm with an O(n4) algorithm clearly indicates that the O(n log n) algorithm is as good as the previous O(n4) algorithm in achieving reductions in the ratio SMT/MST of the given vertex set. This is somewhat surprising since the O(n4) algorithm considers more potential Steiner points and alternative tree configurations.

Lagrangian fluid dynamics using the Voronoi-Delauanay mesh

Abstract: A Lagrangian technique for numerical fluid dynamics is described This technique makes use of the Voronoi mesh to efficiently locate new neighbors, and it uses the dual (Delaunay) triangulation to define computational cells This removes all topological restrictions and facilitates the solution of problems containing interfaces and multiple materials To improve computational accuracy a mesh smoothing procedure is employed

A note on lee and schachter's algorithm for delaunay triangulation

Abstract: Lee and Schachter have presented an algorithm for the Delaunay triangulation of a set of points whose convex hull is a rectangular region. An addendum to that algorithm is presented which gives the Delaunay triangulation of a set of points with an arbitrary convex hull. Timing results are also given.