The topological cleanup consists of several sets of topological operations that are performed in an appropriate order. The following sets of operations have been implemented
While the merge and transform operations attempt to remove as many triangles as possible, the swap, refine, and coarse operations try to optimize the valence of individual nodes by decreasing the difference between the actual and the ideal valence (see Eq. (14)). The split operations are adopted to remove non-convex quadrilaterals by splitting them into two triangles. A particular topological transformation is accomplished only if violation of the following geometrical criteria does not occur:
Theoretically, all triangles could be removed, if the domain is bounded by an even number of edges. In practice, however, individual triangles are topologically so far from each other that the adopted transformation schemes are not capable to remove them.
Note that the nodes newly introduced during the refine operation must satisfy the surface constraint.