//Test if all halfedges of the new face
//are possibly consecutive border halfedges in the HDS.
//Possibly because it may be not directly encoded in the HDS
//(using next() function ). This situation can occur when one or
//more facets share only a vertex: For example, the new facet we try to
//would make the vertex indices[i] a manifold but this should be
//if a facet only incident to that vertex has already been inserted.
//We check this for each vertex of the sequence.
Can you explain please what this means or maybe provide a small example?
I think it checks for a non-manifold vertex. More specifically, consider a
vertex incident to two triangle fans. If you add a facet that would close
one of the fans into a cone, then it's definitely going to be a non-manifold
vertex. For example, the last facet: