CGAL users discussion list

[Juan Carlos Lopez Alfonso <>]

Hi Sebastian:

I have done this test (CGAL::orientation(p1,p2,p3,p4)==CGAL::COPLANAR) and I still have thetraedra with its 4 points in the same plane and in my first email, I have sent my header and I use (CGAL::Exact_predicates_inexact_constructions_kernel).

Please, could you give me more suggestions to solve this problem?

Thank you again

Juan Carlos

On Thu, Jan 19, 2012 at 3:18 PM, Sebastien Loriot (GeometryFactory) <> wrote:

On 01/19/2012 03:12 PM, Juan Carlos Lopez Alfonso wrote:

Hi Sebastien:

To detect that points are coplanar, I have computed the jacobian of each
thetraedra:

//for each thetraedra !!!
........
Tetrahedron t = T[i];

Vertex p1 = cit->vertex(0);
Vertex p2 = cit->vertex(1);
Vertex p3 = cit->vertex(2);
Vertex p4 = cit->vertex(3);

Can you try with this test instead:
CGAL::orientation(p1,p2,p3,p4)==CGAL::COPLANAR

and  CGAL::Exact_predicates_inexact_constructions_kernel as Kernel for the triangulation.

Sebastien.

double Jacobian =
(p2.x - p1.x) * (p3.y - p1.y) * (p4.z - p1.z) + (p3.x - p1.x) * (p4.y -
p1.y) * (p2.z - p1.z) + (p4.x - p1.x) * (p2.y - p1.y) * (p3.z - p1.z)
 - (p4.x - p1.x) * (p3.y - p1.y) * (p2.z - p1.z) - (p3.x - p1.x) *
(p2.y - p1.y) * (p4.z - p1.z) - (p2.x - p1.x) * (p4.y - p1.y) * (p3.z -
p1.z);
........

where p1, p2, p3 and p4 are the 4 points of each thetraedra, and when
Jacobian is equal to 0 the thetraedra has its 4 points in the same plane.
Could you help me to solve this problem? I need a triangulation
where all tetrahedra has no its 4 points in the same plane.

Thank you in advance
Juan Carlos

On Thu, Jan 19, 2012 at 3:04 PM, Sebastien Loriot (GeometryFactory)

< <mailto:>> wrote:

   On 01/19/2012 03:01 PM, Juan Carlos Lopez Alfonso wrote:

       Hi there:

       I have a problem with a 3D triangulation. I have the following code:

       #include <CGAL/Delaunay_triangulation___3.h>
       typedef CGAL::Delaunay_triangulation___3<K, Tds>  Delaunay;

       typedef Delaunay::Cell_handle    Cell_handle;
       typedef Delaunay::Vertex_handle  Vertex_handle;
       typedef Delaunay::Locate_type    Locate_type;
       typedef Delaunay::Point          Point;
       typedef Delaunay::size_type      size_type;

       typedef Delaunay::Finite_vertices___iterator
         Finite_vertices_iterator;
       typedef Delaunay::Finite_cells___iterator Finite_cells_iterator;

       ...

       Delaunay T;
       T.insert(L.begin(), L.end());

       for(Finite_cells_iterator cit = T.finite_cells_begin(), end =
       T.finite_cells_end(); cit != end; ++cit)
       {


   How do you detect that points are coplanar?

   Sebastien.


             ... coplanar points ...
       }

       ...

       where L is a list of 3D points. When I run my code, I have
       detected that
       there are several tetrahedra which its 4 points are coplanar.
       Could anyone help me to solve this problem? I need a
       triangulation where
       all tetrahedra has no its 4 points in the same plane.

       Thank you in advance and waiting for a suggestion
       Juan Carlos



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