[vtkusers] Polyhedral volume computation

[Jochen K.]

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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