I cannot add points with infos at construction, as far as I understand, which is something I can do will all other CGAL triangulations. Here is an example of what I would like to be able to do:

#include <vector>
#include <utility>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Triangulation_vertex_base_with_info_3.h>
#include <CGAL/Triangulation_cell_base_with_info_3.h>
#include <CGAL/Triangulation_3.h>
#include <CGAL/Conforming_constrained_Delaunay_triangulation_3.h>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Triangulation_vertex_base_with_info_3<std::size_t, K> Vb;
typedef CGAL::Conforming_constrained_Delaunay_triangulation_vertex_base_3<K, Vb> CVb;
typedef CGAL::Triangulation_cell_base_with_info_3<bool, K> Cb;
typedef CGAL::Conforming_constrained_Delaunay_triangulation_cell_base_3<K, Cb>  CCb;

typedef CGAL::Triangulation_data_structure_3<CVb, CCb> Tds;
typedef CGAL::Triangulation_3<K, Tds> Trig_3;
typedef CGAL::Conforming_constrained_Delaunay_triangulation_3<K, Trig_3> CstrDelaunayTrig_3;

int main()
{
    std::vector<std::pair<K::Point_3, std::size_t>> pointsList;
    std::vector<std::vector<std::size_t>> polygons;

    //Initialize the point list

    CstrDelaunayTrig_3 cdt(pointsList, polygons);

    return 0;
}

CDT_3: point cell with infos #8955

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