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[Bear <>]

I used the typical way to construct the constrained triangulation. Please see
the code bellow, i also attached the full code  test_cgal_CT.cpp
<http://cgal-discuss.949826.n4.nabble.com/file/n4657896/test_cgal_CT.cpp>  .

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Triangulation_vertex_base_2<K> VB;
typedef CGAL::Constrained_triangulation_face_base_2<K> FB;
typedef CGAL::Triangulation_face_base_2<K, FB> FBWI;
typedef CGAL::Triangulation_data_structure_2<VB, FBWI> TDS;
typedef CGAL::Exact_predicates_tag PT;
typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, PT> CDT;

typedef CGAL::Constrained_triangulation_plus_2<CDT> Triangulation;
typedef CGAL::Polygon_2<K> Ring;
typedef Triangulation::Point Point;

void test_cgal_ct()
{
        vector<Ring> rings = importPolygons();
        Triangulation triangulation;
        Triangulation::Face_handle startingSearchFace;
        Triangulation::Vertex_handle sourceVertex, targetVertex;

        for (vector<Ring>::iterator itrRing=rings.begin(); 
itrRing!=rings.end();
itrRing++)      {
                for (Ring::Edge_const_iterator itrEdge = 
itrRing->edges_begin(); itrEdge
!= itrRing->edges_end(); ++itrEdge) {
                        sourceVertex = triangulation.insert(itrEdge->source(),
startingSearchFace);
                        startingSearchFace = 
triangulation.incident_faces(sourceVertex);
                        targetVertex = triangulation.insert(itrEdge->target(),
startingSearchFace);
                        triangulation.insert_constraint(sourceVertex, 
targetVertex);
                        startingSearchFace = 
triangulation.incident_faces(targetVertex);
                } 
        }


        exportTriangulation(triangulation, "constrainted_d_t.edg");
}



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