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["Sebastien Loriot (GeometryFactory)" <>]

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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