The Delaunay refinement algorithm DelTetPLC in the previous chapter requires that the input PLC satisfy the projection condition, which rules out linear cells adjoining each other at dihedral angles or plane angles less than 90◦. For many engineering applications, this restriction is not acceptable. Unfortunately, DelTetPLC, like Ruppert’s original algorithm, can fail to terminate because of ping-pong encroachment (recall Figure 6.12). Ruppert’s “modified segment splitting using concentric circular shells,” described in Section 6.6, extends easily to spherical shells, and it copes reasonably well with segments that meet at small plane angles in tetrahedral meshes. It is not a complete solution, because of the seditious edges discussed in Section 6.6.