  We analyze actual methods that generate smooth frame fields both in 2D and in
3D. We formalize the 2D problem by representing frames as functions (as it was
done in 3D), and show that the derived optimization problem is the one that
previous work obtain via "representation vectors." We show (in 2D) why this non
linear optimization problem is easier to solve than directly minimizing the
rotation angle of the field, and observe that the 2D algorithm is able to find
good fields.
  Now, the 2D and the 3D optimization problems are derived from the same
formulation (based on representing frames by functions). Their energies share
some similarities from an optimization point of view (smoothness, local minima,
bounds of partial derivatives, etc.), so we applied the 2D resolution mechanism
to the 3D problem. Our evaluation of all existing 3D methods suggests to
initialize the field by this new algorithm, but possibly use another method for
further smoothing.
