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[redpearl <>]

I am trying to use CGAL to compute the Power Diagram. My code is as follows.
It can correctly compute the Regular Triangulation (with 4 vertices and 1
hidden vertex). However, the computed Power Diagram is incorrect, which has
5 faces instead of 4. And more, its dual has 5 vertices and 0 hidden vertex.

Can anyone point out where the problems is? Thanks a lot!

====================================================
#include <iostream>

#include <CGAL/basic.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Regular_triangulation_filtered_traits_2.h>
#include <CGAL/Regular_triangulation_2.h>
#include <CGAL/Regular_triangulation_adaptation_traits_2.h>
#include <CGAL/Regular_triangulation_adaptation_policies_2.h>
#include <CGAL/Voronoi_diagram_2.h>

typedef CGAL::Exact_predicates_inexact_constructions_kernel                   
                          K;
typedef CGAL::Regular_triangulation_filtered_traits_2<K>                      
                          RT_Traits;
typedef CGAL::Regular_triangulation_2<RT_Traits>                              
                                  RT;
typedef CGAL::Regular_triangulation_adaptation_traits_2<RT>                   
                          AT;
typedef CGAL::Regular_triangulation_caching_degeneracy_removal_policy_2<RT>   
  
AP;
typedef CGAL::Voronoi_diagram_2<RT,AT,AP>                                     
                                          PD;

typedef CGAL::Point_2<K>              Point_2;
typedef RT::Weighted_point                        RT_Weighted_point;

RT rt;
PD pd;
int     num_sites=5;
double sites[5][2];

void main(void)
{
        sites[0][0] = 0.0;
        sites[0][1] = 0.0;

        sites[1][0] = 0.8;
        sites[1][1] = 0.0;

        sites[2][0] = 0.0;
        sites[2][1] = 1.0;

        sites[3][0] = -0.8;
        sites[3][1] = 0.0;

        sites[4][0] = 0.0;
        sites[4][1] = -1.0;

        for (int i=0; i<num_sites; i++)
        {
                double x, y, weight;
                x = sites[i][0];
                y = sites[i][1];
                if (i==0)
                        weight = 0;
                else
                        weight = 1.44;

                pd.insert(RT_Weighted_point(Point_2(x, y), weight));
                rt.insert(RT_Weighted_point(Point_2(x, y), weight));
        }

        std::cout << "number of vertices in RT:  " << rt.number_of_vertices() 
<<
std::endl;
        std::cout << "number of hidden vertices in RT:  " <<
rt.number_of_hidden_vertices() << std::endl << std::endl;

        std::cout << "num of faces in PD: " << pd.number_of_faces() << 
std::endl <<
std::endl;

        RT dual = pd.dual();
        std::cout << "number of vertices in Dual:  "  << 
dual.number_of_vertices()
<< std::endl;
        std::cout << "number of hidden vertices in Dual:  " <<
dual.number_of_hidden_vertices() << std::endl;
}
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