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[Iasonm <>]

I found the following:
volume(const TriangleMesh& tmesh, const CGAL_PMP_NP_CLASS& np)
{
   ......

  typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT volume =
0.;
  typename CGAL::Kernel_traits<typename property_map_value<TriangleMesh,
    CGAL::vertex_point_t>::type>::Kernel::Compute_volume_3 cv3;

*  BOOST_FOREACH(face_descriptor f, faces(tmesh))
  {
    volume += cv3(origin,
      get(vpm, target(halfedge(f, tmesh), tmesh)),
      get(vpm, target(next(halfedge(f, tmesh), tmesh), tmesh)),
      get(vpm, target(prev(halfedge(f, tmesh), tmesh), tmesh)));
    exact(volume);
  }
  return volume;*
}

and about cv3:

class Compute_volume_3
  {
    ....
    result_type
 *   operator()(const Point_3& p0, const Point_3& p1,
               const Point_3& p2, const Point_3& p3) const
    {
      return determinant<FT>(p1.x()-p0.x(), p1.y()-p0.y(), p1.z()-p0.z(),
                             p2.x()-p0.x(), p2.y()-p0.y(), p2.z()-p0.z(),
                             p3.x()-p0.x(), p3.y()-p0.y(), p3.z()-p0.z())/6;
    }
*
    ...
};

The above determinant compute the volume of a tetrahedron with vertices
p0,p1,p2,p3.
So if I get it right the volume of the mesh is the sum of all its pyramids
formed by every face and the origin. 
I don't understand what the negative sign of the above determinant means
geometrically though..



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