Bisecting with Optimal Similarity Bound on 3D Unstructured Conformal Meshes

We propose a new method to mark for bisection the edges of an arbitrary three-dimensional unstructured conformal mesh. For these meshes, the approach conformingly marks all the tetrahedra with coplanar edge marks. To this end, the method needs three key ingredients. First, we propose a specific edge ordering. Second, marking with this ordering, we guarantee that the mesh becomes conformingly marked. Third, we also ensure that all the marks are coplanar in each tetrahedron. To demonstrate the marking method, we implement an existent marked bisection approach. Using this implementation, we mark and then locally refine three-dimensional unstructured conformal meshes. We conclude that the resulting marked bisection features an optimal bound of 36 similarity classes per tetrahedron.