Bezier Mesh

For finite-element (FEM) applications of NURBS and B-splines it is often required to introduce a cell-structure on the NURBS surfaces that is largely independent of the surface description. Especially, in isogeometric approaches B-splines are used to describe quantities such as currents or charges on the surface. To this end, it is customary to introduce on each NURBS patch a virtual mesh induced by the knot vectors of the B-splines: the Bezier mesh.

Per Patch Conventions

The local edges and corner points numbering as defined in the patch conventions is passed on to the Bezier cells. Moreover, the numbering of the cells follows

• starting at patch one, there is a consecutive number over all patches
• on each patch the numbering starts at $u=v=0$ and is increased first along the $v$ axes

Adjacency Information

Most importantly, adjacency information about the Bezier cells is extraced: for a given Bezier cell, what other Bezier cells:

• have a common edge at which local edge numbers
• have a common corner point at which local corner numbers