  The description of light diffraction using catastrophe optics is one of the
most intriguing theoretical invention in the field of classical optics of the
last four decades. Its practical implementation has faced some resistance over
the years, mainly due to the difficulty of mathematically decorating the
different, topologically speaking, types of optical singularities (caustics)
that concur to build up the skeleton on which diffraction patterns stem. Such a
fundamental {\em dressing problem} has been solved in the past only for the
so-called {\em fold}, which lies at the bottom of the hierarchy of structurally
stable caustics. Climbing this hierarchy implies considerably more challenging
mathematical problems to be solved.
  An ancient mathematical theorem is here employed to find the complete
solution of the dressing problem for the {\em cusp}, which is placed, in the
stable caustic hierarchy, immediately after the fold. The other ingredient used
for achieving such an important theoretical result is the paraxial version of
the boundary diffraction wave theory, whose tight connection with catastrophe
optics has recently been emphasized in [R. Borghi, Opt. Lett. {\bf 41,} 3114 -
3117 (2016)].
  A significant example of the developed algorithm aimed at demonstrating its
effectiveness and ease of implementation, is also presented.
