Constructing Delaunay triangulation on the Intel Paragon

Abstract

In this paper, we develop a parallel algorithm on the Intel Paragon supercomputer for constructing the two-dimensional Delaunay triangulation (called 2-d DT) of a point set with N points on the plane. The time complexity of the best sequential algorithm for 2-d DT is O(N log N). Our parallel algorithm improves it to constant or O(1) time by using N processors in the Paragon. The 2-d DT has many practical applications on sciences and technologies, such as unstructured mesh generation on computational fluid dynamics, geometric modeling on computer-aided design, volume rendering on scientific visualization, and Voronoi diagram on robotics and image processing.