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[Juan Carlos Lopez Alfonso <>]

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);

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) <> 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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