Abstract : This article introduces a method that generates a hexahedral-dominant mesh from an input tetrahedral mesh.
It follows a three-steps pipeline similar to the one proposed by Carrier-Baudoin et al.:
(1) generate a frame field; (2) generate a pointset P that is mostly organized on a regular
grid locally aligned with the frame field; and (3) generate the
hexahedral-dominant mesh by recombining the tetrahedra obtained from the constrained Delaunay triangulation of P.
For step (1), we use a state of the art algorithm to generate a smooth frame field. For step (2), we
introduce an extension of Periodic Global Parameterization to the volumetric case. As compared with
other global parameterization methods (such as CubeCover), our method relaxes some global constraints
and avoids creating degenerate elements, at the expense of introducing some singularities that are
meshed using non-hexahedral elements. For step (3), we build on the formalism introduced by
Meshkat and Talmor, fill-in a gap in their proof and provide a complete enumeration of all the
possible recombinations, as well as an algorithm that efficiently detects all the matches in a tetrahedral mesh.
The method is evaluated and compared with the state of the art on a
database of examples with various mesh complexities, varying from
academic examples to real industrial cases. Compared with the method
of Carrier-Baudoin et al., the method results in better scores
for classical quality criteria of hexahedral-dominant meshes
(hexahedral proportion, scaled Jacobian, etc.). The method
also shows better robustness than CubeCover and its derivatives
when applied to complicated industrial models.