[vtkusers] Polyhedral volume computation

[Jeff Lee]

You usually have to triangulate the polyhedron faces anyways because the
they will likely be nonplanar, nonconvex, etc.  You could either steal the
code in vtkMassProperties which computes the volume on the triangle set, or
convert to triangles and use an internal instance of vtkMassProperties - I
would probably opt for the former, but it depends on whether you are doing
a one-off or trying to compute volumes for an entire mesh.

On Tue, Jun 12, 2012 at 9:05 AM, Andrew Parker <
andy.john.parker at googlemail.com> wrote:

> I would have used it except this put me off in the docs:
>
> " vtkMassProperties<http://www.vtk.org/doc/nightly/html/classvtkMassProperties.html> estimates
> the volume, the surface area, and the normalized shape index of a triangle
> mesh. "
>
>
> On 12 June 2012 13:56, Jeff Lee <jlee1549 at gmail.com> wrote:
>
>> did you look at vtkMassProperties?  it uses divergence theorem to compute
>> volume which is face based and works on arbitrary polyhedra.
>> Jeff
>>
>>
>> On Tue, Jun 12, 2012 at 8:48 AM, Andrew Parker <
>> andy.john.parker at googlemail.com> wrote:
>>
>>> Hi,
>>>
>>> Many thanks, yes, linear only but an arbitrary number of faces.  I would
>>> have bet there was another way of doing this, and that I've used it, I just
>>> can't remember how I did it.
>>>
>>> Do you not think it's rather odd there is a lack of support for simple
>>> metrics like this given an arbitrary polyhedra?  One needs only the faces
>>> and nodes.  Under the assumption each face is planer then this sort of
>>> thing is quite easy, and would at least make the vtk support for this for
>>> type of metric with planer faces much more applicable to a significantly
>>> larger number of users.  See the following as a good example which is used
>>> in CFD and has been for many years:
>>>
>>> http://www.public.iastate.edu/~zjw/papers/1999-AIAAJ.pdf
>>>
>>> I appreciate in the non-planer case something else needs to be done, but
>>> all of this could be hidden behind a wrapper class that provides metrics
>>> regardless of cell type.  If this is indeed in vtk and anybody can point me
>>> to it then that would be really helpful.
>>>
>>> Cheers,
>>> Andy
>>>
>>>
>>> On 12 June 2012 12:59, Jochen K. <jochen.kling at email.de> wrote:
>>>
>>>> Hi Andy,
>>>>
>>>> do you address only linear elements with arbitrary polyhedrons?
>>>> Or should support be given to quadratic, biquadratic, triquadratic and
>>>> even
>>>> convexPointSets elements too?
>>>>
>>>> In any case all cells must be traversed, right?
>>>>
>>>> While traversing all cells I would check the celltype and store the
>>>> cellid
>>>> (for cell assignment of the calculated volume later on).
>>>>
>>>> If the current cell is a primitve type like tetrahedron etc. calculate
>>>> the
>>>> volume and traverse next cell.
>>>>
>>>> In case it's a more complicated element I would tetrahedralize it, and
>>>> sum
>>>> up the volume of each given tetrahedron.
>>>>
>>>> That's it.
>>>>
>>>> If the grid consists of a lot of nonlinear elements the result will
>>>> probably
>>>> deviate a bit from the correct value. The questionis how exactly you
>>>> want
>>>> the result to be.
>>>>
>>>> For a cross-check I would apply a surfacefilter to the whole grid,
>>>> tetrahedralize it, and sum up the tetrahedron volumes.
>>>> Then compare the volume of both approaches. They should be more or less
>>>> identical.
>>>>
>>>>
>>>> with best regards
>>>> Jochen
>>>>
>>>>
>>>>
>>>> --
>>>> View this message in context:
>>>> http://vtk.1045678.n5.nabble.com/Polyhedral-volume-computation-tp5713778p5713792.html
>>>> Sent from the VTK - Users mailing list archive at Nabble.com.
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>>>
>>>
>>>
>>> --
>>>
>>> __________________________________
>>>
>>>    Dr Andrew Parker
>>>
>>>    Em at il:  andrew.parker at cantab.net
>>>
>>>
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>>
>
>
> --
>
> __________________________________
>
>    Dr Andrew Parker
>
>    Em at il:  andrew.parker at cantab.net
>
>
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