CGAL users discussion list

[Mariette Yvinec <>]

Le 11/07/11 11:00, Nicholas Mario Wardhana a écrit :
> Hi all,
>
> I have a set of voxels associated to boolean values (either 0 or 1),
> and I wish to generate a mesh that approximates the voxels with value
> 1. The '1' voxels are the result of voxelising an input surface, so
> these voxels are relatively smooth (not scattered) but thin. I am able
> to generate the INR file which can be properly loaded by CGAL's
> surface mesher, but what confuses me is the configuration. So I would
> like to ask the questions below, referencing the corresponding manual:
>
> http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Surface_mesher/Chapter_main.html
>
> especially Section 46.3.
>
> 1) What is the coordinate system of the gray image? I notice that I am
> required to determine its centre which is inside the surface, such
> that the value of sign( f(centre) - isovalue ) = -1. Let isovalue =
> 0.5. I choose the centre to be the centre of an arbitrary voxel whose
> value is 0. I suppose I can get sign(0 - 0.5) = -1, but instead I got
> a 1. Am I right to assume that the mesher's coordinate system is
> different from mine? I also notice that the INR file lacks of notion
> of origin or anything related, so does it have to do with that?

Note that the coordinate system of a gray image is encoded in the image 
file.
You are  not required to determine the center of the coordinate system.
You are just required  to provide a bounding-sphere whose center
is a point inside the surface you want to mesh and whose radius is big 
enough
for the sphere to include the whole image.

> 2) Suppose I know the size of the whole voxelisation. What are the
> good range estimates for the radius and centre-centre distance upper
> bounds relative to the voxelisation size? I made some trial-and-error
> efforts and found that the result rarely changes with different
> parameters, but when it does, the change is very abrupt. For example,
> there is no face generated (only point set) if I use the bounds 0.602
> and 0.602, no face is generated, but if I use 0.601 and 0.601, the
> algorithm produces so many faces and does not stop after a few
> minutes.
The radius bound provide an upper bound on the size of the surface mesh 
elements.
If you decrease it, you will get a finer mesh with more  and smaller 
elements.
So the right value is function of the size (in terms of number of 
elements)  of the mesh
you want to generate.
The centre-centre  bound controls the accuracy of the surface approximation.
It will also has an influence on the granularity of the mesh.
Beware that this parameter should not be small
compared to the precision with which
points on the level set are computed
which is be default set to 1E-03 x the bounding sphere radius.
Typically the  centre-centre distance bound should be 10 times the
error bound.
> 3) Still related to the previous point, even if I use the same
> configuration, the results might differ. Sometimes the algorithm stops
> after a few seconds, sometimes it does not stop after a few minutes. I
> notice somewhere (sorry I forget) that the algorithm has a random
> element, but how is it possible that the results are distinctly
> different?
The surface_mesher has a randomized way of computing a few initial points
on the surface : it computes intersections with the surface of random rays
casted from the center of the bounding sphere.
Depending of these initial points, different connected components
of the level set can be discovered and meshed. This might explain
what you observe.
Hope this helps.


> Please let me know if more information is needed. Thank you.
>
> Best regards,
> Nicholas

--
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis