The Strange Complexity of Constrained Delaunay Triangulation

The problem of determining whether a polyhedron has a constrained Delaunay tetrahedralization is NP-complete. However, if no five vertices of the polyhedron lie on a common sphere, the problem has a polynomial-time solution. Constrained Delaunay tetrahedralization has the unusual status (for a small-dimensional problem) of being NP-hard only for degenerate inputs.

• Type: Conference
• Year: 2003
• Where: CCCG
• Authors: Nicolas Grislain, Jonathan Richard Shewchuk
• Keywords: CCCG 2003, CCCG 2007, Constrained Delaunay Tetrahedralization, Polyhedron, Polyhedron Lie