Accessing internal and external faces using the unique_cell iterator

[CristinaGL]

Hi!

I'm working with a periodic triangulation and trying to identify the faces located at the periodic boundary as well as the interior faces. Currently, I'm using the following approach, but it's extremely inefficient:

std::vector<Facet> interior_faces;
for (auto ocit = T.unique_cells_begin(); ocit != T.unique_cells_end(); ++ocit) {
    Cell_handle cell = ocit;

    // Loop over the 4 faces (facets) of the tetrahedron
    for (int face_index = 0; face_index < 4; ++face_index) {
        Facet facet = std::make_pair(cell, face_index);

        bool is_periodic = is_periodic_face(facet, target_offset, extended_box_size, T);

        if (is_periodic) {
            continue;
        }

        interior_faces.push_back(facet);
    }
}

bool is_periodic_face(const Facet& face,
                      const Rt::Offset& target_offset,
                      const box_size& extended_box_size,
                      const CGAL::Periodic_3_regular_triangulation_3<Gt>& T) {
    Cell_handle cell = face.first;
    int face_index = face.second;

    // Get the neighboring cell across this facet
    Cell_handle neighbor_cell = cell->neighbor(face_index);

    // Loop over the unique cells and check if the neighbor_cell is in this list
    for (auto ocit = T.unique_cells_begin(); ocit != T.unique_cells_end(); ++ocit) {
        Cell_handle unique_cell = *ocit;
        
        // Compare neighbor_cell with unique_cell
        if (neighbor_cell == unique_cell) {
            return false;  // Neighbor cell is in the list of unique cells, not a periodic face
        }
    }

    // Neighbor cell is not in the list of unique cells, hence the face is periodic
    return true;
};

As you can see, the algorithm involves checking all unique cells for each face, which is very slow for large datasets.

Is there a more efficient way to identify periodic boundary faces without having to loop over all unique cells for each face? I would greatly appreciate any suggestions or improvements to this approach.

Thanks!