Combinatorial 3-manifolds from sets of tetrahedra

We propose an algorithm to convert a tetrahedral mesh with singularities to a combinatorial 3-manifold using only local modifications. We outline sufficient conditions on the mesh to guarantee the feasibility of the approach and we show how singularities can be both identified and removed according to the configuration of their link. Furthermore, we demonstrate that the algorithm can be implemented using a flexible state-of-the-art data structure for manifold tetrahedral meshes suitable for efficient and general applications.