Hexahedral-dominant mesh generation

As known in the literature, quadrilateral meshes can be created indirectly by recombining the elements of initial triangular meshes. Because triangular mesh generation is very well mastered, this type of approach has the advantage of being applicable to complex domains. Moreover, it allows the user to select a variable mesh size. The quality and orientation of the resulting quadrilaterals can be greatly improved by starting from an aligned vertices distribution. Methods capable of aligning vertices in precise directions were therefore sought. Two approaches were explored: the iterative one and the frontal one. The iterative method defines an objective function based on Voronoi cells that measures how well the vertices are aligned. The vertices are then progressively moved in order to minimize the objective function. On the contrary, the frontal method constructs the aligned vertices all at once. It is also possible to recombine tetrahedra into hexahedra. However, five, six or seven tetrahedra are necessary to construct a single hexahedron. The algorithms currently available in the literature are not capable of achieving a recombination rate of 100% in the general case. Final meshes inevitably contain hexahedra and a certain number of remaining tetrahedra. Some of these tetrahedra can be further merged into prisms and pyramids. The percentage of hexahedra is much higher when the vertices of the initial tetrahedral mesh are aligned in precise directions. As a consequence, methods capable of creating aligned vertices distributions in three dimensions were investigated.