Reference on the Lack of Uniqueness of the Cell Volume
Good afternoon to all of you,
I have for a while been looking for a reference, which discuss the volume of a general hexahedral cell, i.e. nonplanar faces. I have found some references which hint that the volume of such a hexahedral cell is not uniquely defined, and based on some practical tests with different methods to compute the volume, I have reached the same conclusion. Nonetheless, I would be grateful if anyone of you know about an article, which directly addresses the nonuniqueness in evaluating the volume of a general hexahedral cell. Thank you and Merry Christmas, Niels 
Why just hexahedral cells? Any general (nonsimplical) polyhedral cell with nonplanar faces would apply.
It depends on how you decompose the cell during the calculation. I've seen that a faceandcell decomposition gives the best results. 
If every face is decomposed consistently, I believe the errors in volume will at least cancel out globally.

Good evening,
Thanks for your replies. Right now I am working on an article, where I have found myself in the need to compute the volume of a general hexahedral in order to prove a conservation property, however, since the volume appears to be nonuniquely defined, I find myself unable to give a full proof. Therefore, I would like to be able to refer to a firm/nonarguable statement/proof/article that the volume is indeed nonunique. Kind regards, Niels 
Hi Niels,
This paper: http://citeseerx.ist.psu.edu/viewdoc...0.1.1.226.4098 mentions that without an expression for the surface that comprises a nonplanar face, there is no information available to define it (pg. 5) and you need to make something up and approximate before decomposition. The fact that you need to base your decomposition on some approximation, and volume is a function of that decomposition, tell me that it is not unique. This paper (sec. 4.2): http://dl.acm.org/citation.cfm?id=614335 Mentions that you need to be consistent in decomposition. Since you have different options when decomposing a polyhedra, I'm thinking this implies that you can get different volume calculations. If you search around for "tetrahedral subdivisions" or words like that you should find some more useful info. Sorry I can't give you a concrete answer on this. Cheers! Kyle 
Hi Kyle,
Thank you, I think those references should do the trick  at least they lend sufficient support to my arguments :) Merry Christmas, Niels 
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