Group the vertices of a mesh into various mutually exclusive categories.

Input parameters:

1. Ms → Mesh whose vertices to categorise.

Output parameters:

1. Wv → Vertices with only welded edges.
2. Wi → Indices of vertices with only welded edges.
3. Uv → Vertices with at least one unwelded edge, and without any naked or non-manifold edges.
4. Ui → Indices of vertices with at least one unwelded edge, and without any naked or non-manifold edges.
5. Nv → Vertices with at least one naked edge, and without any non-manifold edges.
6. Ni → Indices of vertices with at least one naked edge, and without any non-manifold edges.
7. Xv → Vertices with at least one non-manifold edge.
8. Xi → Indices of vertices with at least one non-manifold edge.