Quad mesh generation for k-sided faces and hex mesh generation for trivalent polyhedra

Two mesh generation methods are presented in this paper: one for quadrilateral meshing of faces with convex vertices but an arbitrary number of sides, the other hexahedral meshing of polyhedra with convex edges, vertices connected to three edges and an arbitrary number of faces each of which has at least three sides. Efficient mapping methods for determining nodal positions are developed based on an extension to transfinite mapping and it is shown that these are identical to those obtained by iterative isoparametric smoothing.