Local nonobtuse tetrahedral refinements around an edge

In this note we show how to generate and conformly refine nonobtuse tetrahedral meshes locally around and towards an edge so that all dihedral angles of all resulting tetrahedra remain nonobtuse. The proposed technique can be used e.g. for a numerical treatment of solution singularities, and also for various mesh adaptivity procedures, near the reentrant corners of cylindric-type 3D domains.