Very nice. this was the sign I was expecting.
Anyway for next time you can just give directions so that we can implement things the way you like, speeding up the improvements and needed changes.

At this point I suppose the C or Fortran implementations are not needed anymore.
So now the function can be included in geomtools.levelVolumes,
be called in Mesh.levelVolumes or just be called directly?

In b1a81c7 arraytools.vectorTripleProduct was changed to use a determinant formula, resulting in an important speedup on large datasets. Here are results for 1 to 10 million tetrahedrons.

# tet:        1; old: 0.000174s; new: 0.000109s; maxdiff: 0.0000e+00
# tet:       10; old: 0.000145s; new: 0.000109s; maxdiff: 0.0000e+00
# tet:      100; old: 0.000173s; new: 0.000097s; maxdiff: 0.0000e+00
# tet:     1000; old: 0.000529s; new: 0.000142s; maxdiff: 0.0000e+00
# tet:    10000; old: 0.003892s; new: 0.000369s; maxdiff: 0.0000e+00
# tet:   100000; old: 0.031370s; new: 0.002073s; maxdiff: 0.0000e+00
# tet:  1000000; old: 0.252968s; new: 0.030414s; maxdiff: 0.0000e+00
# tet: 10000000; old: 2.574564s; new: 0.379788s; maxdiff: 0.0000e+00

In commit 36adca0 the function meshQuality has been added to compute all vtk quality measures.

Now if we like we can call this function for some specific measures (like vtkVolumes ) as Gianluca suggested , but I think we should not add many.

For the volumes I still think we should find a way not to use vtk.

Benedict can you give a sign on this?

I would not do like you said

I have already implemented the mesh quality functions based on the jacobian and the norms. I will put them as soon as possible after I finish the tests and I write the paper on the mesh quality improvemnet based on that.

this vtk things would be just a temporary solution for some stuff not included in pyformex, a general evaluateMesh will be more compact and we will not add so many different functions. this way teh user ask directly what he needs otherwise eveytime we need something from the  _vtkCellQuality we will keep on adding specific functions that call it. beside I think it is a
easy way just to use a evaluateMesh(mesh, quality). and we keep it as you said with no converisons as teh user can do it outside the function.


For teh volumes in vtk I remember I read something once but I might be wrong or maybe it is not a problem anymore

I think with our own c++ functions with can have faster computation of volumes,

The correct results is the one in pyformex but
with the conversion to tet4 and then using the vtkTet* instead of the vtkHex* methods the results are the same. I did not cjheck for the quad

I think we can introduce this function in the vtk plugin for all the additional information still lacking in pyFormex.
Maybe we can introduce a function that wraps the vtk one like

evaluateQuality(mesh, targetQuality):

and make some due conversions of quad and hex first in pyformex to and tri3-x and  tet4

Still an improvement of the pyformex functions is needed.
Gianluca will you do the additin to vtk?

following the comment of Gianluca
indeed the computation with tet-5 will be accuarate only with plane faces so indeed we need another solution.

 Though I need this to be improved, if you can give me the input to improve it with additional libraries please do, I will work on it and send it back to you. I have a code that needs many calls to volumes and this call slows it down a lot. So please give mehints on how to proceed

Hi Francesco,

- Regarding the element volumes:

if you use hex8->tet4-5 and you sum up the element volumes you do not get the correct total volume. The reason is that the face shared by two face-adjacent hex elements could be split in 2 tets using two different diagonals, producing a non-conformal tri3 mesh at the interface. If the shared quad4 face would be warping the tri3 meshes of the two hex may have gaps or intersect each other. The only subdivision which guarantees conformity is the tet-24. Of course, if you need a fast computation of all volumes to assess the element quality you do not care about warping, so an approximated volume would suffice, using the hex8->tet4-5, but you should be aware that the sum of the volumes is not the total volume

- Regarding the mesh volume:

what Benedict suggested is already the standard in mesh.py and it is indeed very fast:
3dmesh -> getbordermesh -> convert to tri3 -> surface_volume

For the total volume, I would use

3dmesh -> getbordermesh -> convert to tri3 -> surface_volume

For individual volumes of elements, we can best implement direct formulas based on the shape functions. We have them available in calpy and calix(fortran), could be ported to pyformex, possibly even in accelerated form. Or we re-implement them in our C-library.