(L-R) Dr. Guido Gerig, Dr. Marcel Prastawa, Casey Goodlett, Sylvain Gouttard
Can the interior of every simply connected polyhedron whose surface is meshed by an even number of quadrilaterals be partitioned into a hexahedral mesh compatible with the surface meshing?The solution of Carbonera and Shepherd settles the practical aspects of the problem by demonstrating an explicit algorithm that extends a quadrilateral surface mesh to a hexahedral mesh where all the hexahedra have straight segment edges. This work did leave one aspect of the problem open. The authors did not resolve the question of achieving a hexahedral mesh with all planar faces. The collaborators are now working on a revision that should close this problem definitively.