Collars and Intestines: Practical Conforming Delaunay Refinement

While several existing Delaunay refinement algorithms allow acute 3D piecewise linear complexes as input, algorithms producing conforming Delaunay tetrahedralizations (as opposed to constrained or weighted Delaunay tetrahedralizations) often involve cumbersome constructions and are rarely implemented. We describe a practical construction for both “collar” and “intestine”-based approaches to this problem. Some of the key ideas are illustrated by the inclusion of the analogous 2D Delaunay refinement algorithms, each of which differs slightly from the standard approach. We have implemented the 3D algorithms and provide some practical examples.