Creating a subField, even if just accessing one element
like in

  f.centering(0).read(1, 2);

is very costly.  This can hurt badly if used in a ScalarCode
or FieldStencil functor (or in a CppTran loop).

This is caused by the field Centering being copied and
this containing std::vector<> whose creation/destruction
cannot be optimized away while being standard conform.

There are several ways to improve this situation, the
most important and straight-forward being a cut down
in features of the (overdesigned) Centering class:
 - do not allow arbitrary positions/orientations
 - do not allow an arbitrary centering size
=> orientations could get a Dim-d bitfield of
   centering size size
=> positions could get a Dim-d bitfield of
   centering size size allowing only vertex or center
   values, not an arbitrary number [0.0, 1.0]
=> the centering size could be limited to 32
   (unsigned int bitfield).  This way a 3d edge
   centered field with discontinuous data would
   still be supported (i.e. all available canonical
   centerings).

Workaround available, use:

   f.fieldEngine().engine(0, 0).read(1, 2);