CGAL users discussion list

[Mariette Yvinec <>]

You might
look at the alpha_spectrum to see if all the alpha-values
you have been trying are relevant or not.

Le 23/09/13 19:40, evantong623 a écrit :

I have a 3D point cloud, and need to determine whether there is a big hole or
not. So I extract its convex hull and alpha shape, and measure their
volumes. If the volume of convex hull is much larger than the one of alpha
shape, I say there exist big hole(s) in the point cloud.
To compute the volume of convex hull, I first triangulate the convex hull
and then sum up the volumes of the tetrahedrons. To compute the volume of
alpha shape, I just sum up the volumes of its cells. Here is the code:

//generating convex hull
Polyhedron_3 poly;
CGAL::convex_hull_3(_bundlePoints[ib].begin(), _bundlePoints[ib].end(),
poly);

//convex hull volume
std::vector<Triangulation::Point> L;
for (Polyhedron_3::Vertex_const_iterator  it = poly.vertices_begin(); it !=
poly.vertices_end(); it++)
	L.push_back(Triangulation::Point(it->point().x(), it->point().y(),
it->point().z()));
Triangulation T(L.begin(), L.end());
float hull_volume = 0;
for(Triangulation::Finite_cells_iterator it = T.finite_cells_begin(); it !=
T.finite_cells_end(); it++)
{
	Tetrahedron_3 tetr = T.tetrahedron(it);
	hull_volume += tetr.volume();
}
cout<<"hull volume:"<< hull_volume << endl;

//generating alpha shape
Alpha_shape_3 as(_bundlePoints[ib].begin(),
_bundlePoints[ib].end(),10000,Alpha_shape_3::GENERAL);

//alpha shape volume
float alpha_volume = 0;
for(Alpha_shape_3::Finite_cells_iterator it = as.finite_cells_begin(); it !=
as.finite_cells_end(); it++)
{
	Tetrahedron_3 tetr = as.tetrahedron(it);
	alpha_volume += tetr.volume();
}
cout<<"alpha volume:"<< alpha_volume << endl;

I tried different alpha values, but the volumes of convex hull and alpha
shape are always almost the same. Is my volume computation not correct? I am
very new to CGAL, hope someone could give me a clue for my problem. Thanks,



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-- 
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis