The spatial localization, intersection checking and front
management, in terms of edge or face selection and searching, are considered
to be the general bottlenecks of the advancing front procedure.
All aspects are addressed in the presented approach. The intersection
check exploits the underlying parametric space if possible. Also the
number of involved mesh entities is significantly reduced. The spatial
localization is implemented using the octree. This exhibits the
computational complexity which becomes nearly constant for reasonable
octree depth . This is due to the fact that only negligible percentage of the total
generation time is consumed by the octree traversal. Since gradual
size variation is ensured (by the use of octree constrained at maximum to one level difference) no special
algorithm for the edge or face selection strategy is required. Therefore the
simplest approach was chosen which always uses the first available
edge or face in the front. This obviously leads to the constant computational
complexity. The remaining procedures are similar to the conventional
advancing front method and thus the overall computational complexity
approaches with being the number of elements, which makes
the proposed methodology very competitive for practical use.

*Daniel Rypl
2005-12-03*