Delaunay refinement

[2] Chew's second algorithm is guaranteed to terminate and produce a local feature size-graded meshes with minimum angle up to about 28.6 degrees.

Moreover, any previously inserted circumcenters inside the diametral ball of the original segment (before it is split) are removed from the triangulation.

Ruppert's algorithm takes a planar straight-line graph (or in dimension higher than two a piecewise linear system) and returns a conforming Delaunay triangulation of only quality triangles.

Without modification Ruppert's algorithm is guaranteed to terminate and generate a quality mesh for non-acute input and any poor-quality threshold less than about 20.7 degrees.

[7] Ruppert's algorithm can be naturally extended to three dimensions, however its output guarantees are somewhat weaker due to the sliver type tetrahedron.