I'm not a deal.II expert, and while studying step-6 I was reading the documentation of the MappingQ1 class in the deal.II documentation. At some point in the description (https://www.dealii.org/current/doxygen/deal.II/classMappingQ1.html) , there's written:
Note, however, that in 3D the faces of a general, trilinearly mapped cell may be curved, even if the edges are not
I have two main issues with this:
I don't see why this is mathematically true. I don't see how the image of a trilinear map $\phi(x,y,z)$ gives some curved boundary.
Considering the case of an hyper_ball, i.e. a ball in 3D. I see indeed that boundary faces are not straight quadrilaterals (see the attached image). How can I retrieve the "curved" part of the face, from a software standpoint? I mean, I can of course ask to the Mapping object the vertices of the cell or face, but this are not enough to describe the curvature... I don't see how one can query the "curved part" in terms of Points!
I understand somehow this has to do with the concept of
Manifold, but I'd like to see how in the code one can actually got this "curved" information.
Any help is highly appreciated.