> > 1) Is there any particular reason why there are no implementations for
> > calculating barycenter/measure for faces in 3d?
>
> Not really -- I was just too lazy to compute the formulas for that back when I
> wrote most of these functions, and nobody has needed them since. I think it
> should be pretty clear how to implement them if you look at how the measure
> and barycenter functions are computed for 3d cells, for example.

I don't think that's true, non-planar faces are not as easy as general bricks 
in 3D. I tried that some time ago, but neither maple nor myself were able to 
find an explicit expression for the measure of a general quadrilateral face. We 
could use some numerical quadrature formula, though. That's what we usually do 
now.
 
Best, Tobias
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