Singularities in structured meshes are vertices that have an irregular valency. The integer
irregularity in valency is called the singularity index of the vertex of the mesh. Singularities in
cross-fields are closely related which are isolated points where the cross-field vectors are
defined in its limit neighbourhood but not at the point itself. For a closed surface the genus
determines the minimum number of singularities that are required in a structured mesh or in
a cross-field on the surface. Adding boundaries and forcing conformity of the mesh or …