How to generate local refinements of unstructured tetrahedral meshes satisfying a regularity ball condition

A simple algorithm that generates local refinements of tetrahedral meshes is proposed. Refinements are made by tetrahedra, which are subdivided into eight, four, three, or two smaller tetrahedra. We prove that a regularity ball condition is satisfied for the refined mesh. This guarantees that tetrahedra do not become flat when the mesh size tends to zero. © 1997 John Wiley & Sons, Inc.