Algorithm for Delaunay triangulation and convex-hull computation using a sparse matrix

Abstract

A direct algorithm for computing the Delaunay triangulation of 2D data points is presented. The algorithm is based on a sparse-matrix data structure and on a circular-triangulation strategy, called shelling, that guarantees that the triangulation is complete and correct, and allows the dynamic update of the internal sparse-matrix data structure during triangulation. An edge list is used to govern the shelling procedure, and to output edges of the convex hull of the data set. The algorithm is numerically stable, i.e. degeneracies such as collinear or coincident points are automatically handled.