Quadrilateral Meshing with Directionality Control through the Packing of Square Cells

This paper proposes a computational method for fully automated quadrilateral meshing. Unlike previous methods, this new scheme can create a quadrilateral mesh whose directionality is precisely controlled. Given as input: (1) a 2D geometric domain, (2) a desired node spacing distribution as a scalar function deened over the domain, and (3) a desired mesh directionality as a vector eld deened over the domain, the proposed method rst packs square cells closely in the domain. The centers of the squares are then connected by Delaunay triangulation, yielding a triangular mesh topology. The triangular mesh is further converted into a quad-dominant mesh or an all-quad mesh that satisses the given mesh directionality. Since the closely packed square cells mimic a pattern of Voroni polygons corresponding to a well-shaped graded quadrilateral mesh, the proposed method generates a high quality mesh whose element sizes and mesh directionality conform well to the given input.