CGAL users discussion list

[Camille Wormser <>]

[the list seems to have some troubles, I try to post my answer once  
more...]

> I then run the example with the “mesh_a_3d_gray_image.cpp” without  
> any modification made to the original code. The output “out.off” is  
> at attached.  After removing the third empty line in the off file,  
> the mesh is visualized as attached “out_grayimage.jpg”.  As can be  
> seen, there are a lot of holes on the mesh (I don't think they are  
> caused by back face culling since there is no triangle at the holws  
> if I show the mesh in the mode of wireframe).

Hi,
In fact, this is a visualization problem, due to the orientation of  
the triangles: as you can see in the OFF file, there are 5270 vertices  
and 10544 (triangular) faces. Assuming that it is manifold (which is  
in fact the case), so that the number of edges can be deduced, you can  
compute that

euler_characteristic = v - e + f = -2  = 2 - 2g,

so that the genus appears to be 2. If you fix your visualization tool,  
you will see that it is in fact the case: one loop is represented by  
the jawbone, and the other loop comes from the nose.

If you look carefully, you will also see that the skull has a hole on  
the left temple (not a missing triangle: the mesh is still a manifold  
without boundary). This happens because the feature size provided to  
the algorithm is a bit too high (in comparison to the width of the  
bone layer): the internal and external surfaces cannot be properly  
separated by the algorithm in this region. Setting a lower feature  
size would prevent that from happening.

Best,
--
Camille