Surface Triangulation

Surface triangulation is an important milestone in 3D mesh generation as it forms the input for the tetrahedralisation of volumes which is a 3D analog of triangulation in 2D. Efficient methods like Delaunay triangulation cannot be applied to surfaces as the Delaunay criterion is not defined for surfaces like it is for planar domains (2D) or volumes (3D).

The following two methods can be employed for surface triangulation -

1.

Triangulation in Parametric Domain - One-to-one mapping of the surface component onto a 2D parametric domain is done. Graded triangulation is then applied to the parametric plane taking into consideration the actual edge lengths and curvature in 3D. The generated grid is then transformed back to 3D surface. Since the basic triangulation takes place in the 2D (u,v) plane, this method is just an extension of the 2D algorithm described earlier, and is expected to provide quality grids for various applications.

2.

Direct Triangulation - Triangulation done in 2D can be extended to a surface by performing direct triangulation (i.e., attempting to triangulate the surface as it is) [NS95]. The graded triangulation as is cannot be applied here, as Delaunay criterion is not defined for surfaces, hence initial triangulation cannot be carried out as described.