The 3D surface to be discretized is represented by an unstructured triangular control grid. Only manifold surfaces are considered, thus the surface is not allowed to be self-intersecting (in terms of sharing nodes by different parts of the grid). Such a representation is general enough to describe complex realistic geometries. Note that non-manifold domains can be represented by a set of manifold surfaces.
The boundary edges of the control grid (i.e. the edges shared just by a single triangular facet of the grid) form the boundary curves of the surface. The end nodes of each curve represent vertices. Nodes not representing vertices are called curve nodes if they form a curve, otherwise they are called surface nodes. A surface node with valence 6 is called regular, otherwise it is called irregular.