  Most genuine multi-sided surface representations depend on a 2D domain that
enables a mapping between local parameters and global coordinates. The shape of
this domain ranges from regular polygons to curved configurations, but the
simple circular domain - to the best of our knowledge - has not been
investigated yet.
  Here we fill this gap, and introduce a parameter mapping ideal for use with
periodic boundaries. It is based on circular arcs and satisfies constraints
often needed in actual surface formulations. The proposed method is
demonstrated through a corner-based variant of Generalized B\'ezier patches.
