I was trying to create a volume mesh using the CGAL::Polyhedron_3 data structure when, doing some tests, I noticed that the make_tetrahedron function duplicates the vertices already present in the polyhedron.

Example: Two tetrahedra that share a common face

this is the code I tried:

#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polyhedron_3.h>
#include <iostream>

typedef CGAL::Simple_cartesian<double>     Kernel;
typedef Kernel::Point_3                    Point_3;
typedef CGAL::Polyhedron_3<Kernel>         Polyhedron;
typedef Polyhedron::Vertex_iterator        Vertex_iterator;

int main(void) {
    // common points
    Point_3 p( 1.0, 0.0, 0.0 );
    Point_3 q( 0.0, 1.0, 0.0 );
    Point_3 s( 0.0, 0.0, 0.0 );

    // the other two
    Point_3 r( 0.0, 0.0, 1.0 );
    Point_3 d( 0.0, 0.0,-1.0 );

    Polyhedron P;
    P.make_tetrahedron( p, q, r, s );
    P.make_tetrahedron( p, q, s, d );

    CGAL::IO::set_ascii_mode( std::cout );
    
    // printing out the vertices
    for ( Vertex_iterator v = P.vertices_begin(); v != P.vertices_end();   v )
        std::cout << v->point() << std::endl;

    return 0;
}

and this is the output I expected to see:

1 0 0
0 1 0
0 0 1
0 0 0
0 0 -1

1 0 0
0 1 0
0 0 1
0 0 0
1 0 0
0 1 0
0 0 0
0 0 -1

Now, the question is:
Is it possible to store a point as a vertex only once in CGAL::Polyhedron_3 using the make_tetrahedron function?

CodePudding user response：

You cannot store non-manifold features in a polyhedron, you need something like a linear cell complex. See here