Nef_3: e->incident_sface() != SFace_const_handle() assertion error.

[GilesBathgate]

Issue Details

Following on the investigation in #7205 here is an example which can be built using the facet cycles method, but not with the polyhedron incremental builder. This example isn't closed i.e the is_closed check was removed, but I think it's worth documenting here:

Polyhedron polyhedron = {{{0,0,0},{0,10,0},{10,10,0},{10,0,0},{10,-10,0}},{{0,1,2},{0,3,4}}};

CGAL error: assertion violation!
Expression : e->incident_sface() != SFace_const_handle()
File       : /usr/include/CGAL/Nef_S2/SM_const_decorator.h
Line       : 331
Explanation: 
Refer to the bug-reporting instructions at https://www.cgal.org/bug_report.html
terminate called after throwing an instance of 'CGAL::Assertion_exception'
  what():  CGAL ERROR: assertion violation!
Expr: e->incident_sface() != SFace_const_handle()
File: /usr/include/CGAL/Nef_S2/SM_const_decorator.h
Line: 331

Environment

• Operating system (Windows/Mac/Linux, 32/64 bits): Linux 64bit
• Compiler: clang++ version 14.0.0
• Release or debug mode: debug
• Specific flags used (if any):
• CGAL version: master
• Boost version: 1.74.0
• Other libraries versions if used (Eigen, TBB, etc.): None

[GilesBathgate]

Also reported in #4210 and #4666

[GilesBathgate]

This is a facet fan, that has a missing connecting facet leading to a non-manifold vertex.

A check for this condition can be written as follows (fans not fins):

bool all_vertices_manifold(const HalfedgeDS& hds)  {
	for(auto v=hds.vertices_begin(); v!=hds.vertices_end(); ++v) {
		if(v->vertex_degree()<=2) continue;
		unsigned borderEdges=0;
		auto b=v->vertex_begin(),e(b);
		CGAL_For_all(e,b) {
			if(e->is_border_edge())
				++borderEdges;
		}
		if(borderEdges>2) return false;
	}
	return true;
}

It doesn't check for fins, but Polyhedron_incremental_builder_3 doesn't allow them, So the test_facet function in builder can be used to detect them.