Delaunay Triangular Meshes in Convex Polygons

Abstract

An algorithm for producing a triangular mesh in a convex polygon is presented. It is used in a method for the finite element triangulation of a complex polygonal region of the plane in which the region is decomposed into convex polygons. The interior vertices of the mesh are chosen to be on a quasi-uniform grid, different mesh spacings are specified for the edges of the polygon, and the mesh is a Delaunay triangulation. The correctness of the algorithm is proved and the expected time complexity is shown to be linear in the number of triangles in the mesh.