Calculate volumes for arbitrary tetrahedra and hexahedra about r2s-act HOT 7 CLOSED

See MOAB/iTaps methods for this: I think they are called ''measure"

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Looks like the relevant code is measure_volume() in MOAB/src/trunk/tools/dagmc/DagMC.cpp. This function supports only triangular-faceted polyhedra.

For now, I will use the code I have working within Fortran (a local branch), which makes testing and inclusions simpler to deal with.

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I'm not sure why it lives in MOAB/src/trunk/tools/ but measure.[hc]pp does it all (I think).

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Ahh, I see that now. I was tracing from what DAG-MCNP calls, and so did not stumble upon measure().

The challenge in my case is that measure() is not part of the iTaps API, and is thus trickier to call from Fortran.

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Current implementation for hexahedra duplicates the approach in measure() - calculate volumes of 5 tetrahedra within the hex. Since the hexahedra are limited to being parallelepipeds (#46), there may be a slightly more efficient volume method to be found, since parallelepipeds are a specific subset of quad-faceted hexahedra.

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Determined today that the tetrahedral volume formula from Wikipedia, V=abs( (a-d) . ((b-d) x (c-d)) ) / 6 seems to work except when it gives a volume of zero (namely a=1,0,0; b=0,1,0; c=0,0,1; d=1,1,1;). I will look more closely at the method used in measure.cpp. I got Mathematica's cross product operator confused, and so was incorrectly calculating the volume.

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In Python, the PyTaps example gives us the necessary code:
http://pythonhosted.org/PyTAPS/tutorial/example.html?highlight=volume

The three relevant functions have been added to write_alara_geom.py.

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