CGAL users discussion list

[Andreas Fabri <>]

 wrote:
> Dear List,
>
> I have recently downloaded and installed CGAL and have run into a minor 
> problem. When I run the attached code, the finite cells include the 
> point (0.5,0.5,0.5), which I have not entered. I only want a delaunay 
> triangulation of the points I have entered. I have tried to remove that 
> point, which corresponds to vertices_begin(), but that results in an 
> exception.

Christopher,

As a newbie you probably have to read the user manual first.
CGAL triangulates the interir of the convex hull of your input
points, AND it also triangulates the unbounded space outside
the convex hull. Each of those cells has three vertices on
the convex hull and as fourth an "infinite vertex".
The triangulation has a member function to test whether a
vertex is the infinite one.

best regards,

andreas

> Secondly, is there a structure or method that allows me access to the 
> list of cells of which a given vertex is a member? The documentation of 
> cell() for a vertex has suggested no obvious way to me.
>
>     Christopher
>
> PS: Is there a complete class hierarchy diagram for CGAL in the 
> documentation? I haven't come across one so far.
>
> --
> C. Rinderspacher, Ph. D.
> Duke University
> Dept. of Chemistry
> Box 97
> Durham, NC 27705
> Tel.: (919) 660-1633
> E-Mail: 
>
>
> The faults of the burglar are the qualities of the financier.
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>
> ------------------------------------------------------------------------
>
> #include <iostream>
> #include <CGAL/basic.h>
> #include <CGAL/Delaunay_triangulation_3.h>
>
> #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
> #include <CGAL/Point_3.h>
> typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
> typedef CGAL::Delaunay_triangulation_3<Kernel>            Triangulation;
> typedef Triangulation::Point                              Point_3;
> typedef Triangulation::Cell_iterator                      Cell_iterator;
> typedef Triangulation::Vertex_iterator                    Vertex_iterator;
> //typedef CGAL::Point_3 Point_3;
>
> using namespace std;
>
> main()
> {
>   vector<Point_3> L;
>   L.push_back(Point_3(0.0,-0.1200944034,0.0));
>   L.push_back(Point_3(-1.4301799859,0.9529926662, 0.0000000000 ));
>   L.push_back(Point_3( 1.4301799859,0.9529926662, 0.0000000000 ));
>   L.push_back(Point_3(-1.4301799859,0.9529926662, 1.0000000000 ));
>   L.push_back(Point_3( 1.4301799859,0.9529926662,-1.2000000000 ));
>   L.push_back(Point_3( 1.4301799859,0.9529,-1.000000000 ));
>   Triangulation td(L.begin(),L.end());
>   Cell_iterator Cell;
>   /*
>     td.insert(Point_3(0.0,-0.1200944034,0.0));
>   td.insert(Point_3(-1.4301799859,0.9529926662, 0.0000000000 ));
>   td.insert(Point_3( 1.4301799859,0.9529926662, 0.0000000000 ));
>   td.insert(Point_3(-1.4301799859,0.9529926662, 1.0000000000 ));
>   td.insert(Point_3( 1.4301799859,0.9529926662,-1.2000000000 ));*/
>   Vertex_iterator Vertex=td.vertices_begin();
>   //  td.remove(td.vertex(1));
>   Vertex=td.finite_vertices_begin();
>   int k=0;
>   while(Vertex != td.vertices_end()) {
>     cout << " Vertex : " << k++ << endl;
>     cout << "X : " << Vertex->point().x() <<" Y : " << Vertex->point().y() <<" Z : " 
> << Vertex->point().z() << endl;
>     Cell=Vertex->cell();
>     //    td.index(Cell);
>     Vertex++;
>   }
>   int noc=td.number_of_finite_cells();
>   cout << "\n Number of cells    : " << noc;
>   cout << "\n Number of facets   : " << td.number_of_finite_facets();
>   cout << "\n Number of edges    : " << td.number_of_finite_edges();
>   cout << "\n Number of vertices : " << td.number_of_vertices() << endl;
>   Cell=td.finite_cells_begin();
>   for(int i=0;i<noc;i++, Cell++)
>     {
>       cout << "Cell " << i << " : \n";
>       for(int j=0;j<4;j++)
>         cout << "X : " << Cell->vertex(j)->point().x() << " Y : " << Cell->vertex(j)->point().y() << 
> " Z : " << Cell->vertex(j)->point().z() << endl;
>     }
> }