The surface discretization is based on templates fitted into quadrants
of quad tree built on the surface or extracted from the octal tree of
the region bounded by the surface. The number of templates is
considerably reduced by the fact that only one node is allowed to be
on side of a quadrant. This is a direct consequence of ``1:2 rule''
applied during the parametric tree construction. The basic set of templates
currently used is displayed in Figure 12. Although
there are known templates yielding all-quadrilateral meshes, these
have not been used because of incompatibility with consequent region
discretization for which the all-hexahedral templates are not
available. This is the reason why triangular elements, treated as
degenerated quadrilateral elements, are accepted. After all quadrants
have been filled in with appropriate template the final surface mesh
is smoothed. The same technique as used in the sequential mesh
generator is used optionally extended by preserving symmetry (if any)
at somewhat higher computational cost.
However, the quality of the optimized mesh is a little bit deteriorated
by the irregularity of the mesh connectivity due to the common presence of
triangular and quadrilateral elements. Also the distribution of
boundary nodes arising from the less flexible curve smoothing has a
negative influence on the overall surface mesh quality.

*Daniel Rypl
2005-12-03*