A frontal delaunay quad mesh generator using the L∞ norm

Abstract

A new indirect way of producing all-quad meshes is presented. The method takes advantage of a well known algorithm of the graph theory, namely the Blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time. Then, the triangulation itself is taylored with the aim of producing right triangles in the domain. This is done using the infinity norm to compute distances in the meshing process. The alignement of the triangles is controlled by a cross field that is defined on the domain. Meshes constructed this way have their points aligned with the cross field direction and their triangles are almost right everywhere. Then, recombination with our Blossom-based approach yields quadrilateral meshes of excellent quality.