** Next:** Implementation
**Up:** Top
** Previous:** Surface Representation

The discretization is carried out in a hierarchical manner. Firstly, the
model vertices are discretized. Then the curves are segmented using
the mass curve of the required element density along that
curve. And finally, the individual surfaces are triangulated.
In the presented implementation, the surfaces are discretized by the
advancing front technique constrained directly to the surface and
modified to allow for surface curvature [4].
The generated mesh is then subjected to optimization in order to
improve the quality of the final mesh. The Laplacian smoothing technique
in combination with topological transformations (diagonal edge
swapping) is adopted. This yields the optimized grid after only a few
cycles of smoothing (typically up to six). Note that, contradictory to
the smoothing carried out in 2D, the repositioning of a node
is likely to
shift the node out of the surface. Therefore, the point-to-surface
projection has to be employed to satisfy the surface constraint.

** Next:** Implementation
**Up:** Top
** Previous:** Surface Representation
*Daniel Rypl *

2005-12-03