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["Laurent Rineau (GeometryFactory)" <>]

Le jeudi 19 janvier 2012 15:12:16 Juan Carlos Lopez Alfonso a écrit :
> 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);
> ........

That way of detecting coplanarity is subject to rounding errors. Probably you 
have almost-coplanar points in your data set, but in reality, using a 
certified arithmetic, there are not coplanar.

-- 
Laurent Rineau, PhD
R&D Engineer at GeometryFactory           http://www.geometryfactory.com/
Release Manager of the CGAL Project       http://www.cgal.org/