  Smectic liquid crystals are remarkable, beautiful examples of materials
microstructure, with ordered patterns of geometrically perfect ellipses and
hyperbolas. The solution of the complex problem of filling three-dimensional
space with domains of focal conics under constraining boundary conditions
yields a set of strict rules, which are similar to the compatibility conditions
in a martensitic crystal. Here we present the rules giving compatible
conditions for the concentric circle domains found at two-dimensional smectic
interfaces with planar boundary conditions. Using configurations generated by
numerical simulations, we develop a clustering algorithm to decompose the
planar boundaries into domains. The interfaces between different domains agree
well with the smectic compatibility conditions. We also discuss generalizations
of our approach to describe the full three-dimensional smectic domains, where
the variant symmetry group is the Weyl-Poincar\'e group of Lorentz boosts,
translations, rotations, and dilatations.
