[vtkusers] Polyhedral volume computation

[Andrew Parker]

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
>
>
>
> --
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-- 

__________________________________

   Dr Andrew Parker

   Em at il:  andrew.parker at cantab.net
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