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["Sebastien Loriot (GeometryFactory)" <>]

Panagiotis Foteinos wrote:
> Hello.
>
> I have encountered a problem with the Delaunay_d class, where d=4.
>
> I am reading the manual for Delaunay_d (
> http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Convex_hull_d_ref/Class_Delaunay_d.html#Cross_link_anchor_983
> ), and it seems that there is no way to test if a simplex is infinite
> or not. So, I am guessing that there are no infinite simplices.
> Therefore, after the insertion of 5 (linearly independent) Point_d
> points, I expect to see just one simplex.
>
> However, when I get the simplices in Delaunay_d::simplices_begin()
> ---> Delaunay_d::simplices_end(), I count 6 simplices. Are the 5 extra
> simplices the infinite simplices? If so, how do I check whether a
> simplex is infinite or not?
>
> The problem is observed with the insertion of the following sequence
> of 4D points:
>
> (1.0/sqrt(10), 1.0/sqrt(6), 1.0/sqrt(3), 1)
> (1.0/sqrt(10), 1.0/sqrt(6), 1/sqrt(3), -1)
> (1.0/sqrt(10), 1.0/sqrt(6), -2.0/sqrt(3), -0)
> (1.0/sqrt(10),-sqrt(3.0/2), 0, 0)
> (-2*sqrt(2.0/5), 0, 0, 0)
>
>
> Best Regards,
> Panagiotis Foteinos

On my machine the result is fine (one simplex). How did you construct
the 4D points? You should use the constructor
template <class InputIterator>
Point_d<Kernel> p ( int d, InputIterator first, InputIterator last);

the one with four arguments builds 3D points with homogeneous coordinates.

Sebastien.

#include <CGAL/Cartesian_d.h>
#include <CGAL/Gmpq.h>
#include <CGAL/Delaunay_d.h>
#include <iostream>

typedef CGAL::Gmpq FT;
typedef CGAL::Cartesian_d<FT> Kernel;
typedef CGAL::Delaunay_d<Kernel> Delaunay_d;
typedef Delaunay_d::Point_d Point_d;
typedef Delaunay_d::Simplex_handle Simplex_handle;
typedef Delaunay_d::Vertex_handle Vertex_handle;

int main()
{
  Delaunay_d T(4);
  FT points[5][4]={
    {FT(1.0/sqrt(10)), FT(1.0/sqrt(6)), FT(1.0/sqrt(3)), FT(1)},
    {FT(1.0/sqrt(10)), FT(1.0/sqrt(6)), FT(1/sqrt(3)), FT(-1)},
    {FT(1.0/sqrt(10)), FT(1.0/sqrt(6)), FT(-2.0/sqrt(3)), FT(-0)},
    {FT(1.0/sqrt(10)),FT(-sqrt(3.0/2)), FT(0), FT(0)},
    {FT(-2*sqrt(2.0/5)), FT(0), FT(0), FT(0)}
  };

  T.insert(Point_d(4,points[0],points[0]+4));
  T.insert(Point_d(4,points[1],points[1]+4));
  T.insert(Point_d(4,points[2],points[2]+4));
  T.insert(Point_d(4,points[3],points[3]+4));
  T.insert(Point_d(4,points[4],points[4]+4));

  int index=0;
  Delaunay_d::Simplex_iterator it=T.simplices_begin();
  for(;it!=T.simplices_end();++it,++index);

  std::cout << index << std::endl;
}