  It is argued that the high energy semiclassical wave functions (SWF) in an
arbitrary billiards can be built by approximating the billiards by a respective
polygon one. The latter billiards is determined by a finite number of periodic
orbits of the original one limited by their lengths beginning with the shortest
ones and which are common for both the billiards. The phenomenon of scars and
superscars (Heller, E.J., {\it Phys. Rev. Lett.} {\bf 53},(1984) 1515) are then
naturally incorporated into such a construction being a limit of periodic orbit
channels (POCs) considered by Bogomolny and Schmit ({\it Phys. Rev. Lett.} {\bf
92} (2004) 244102). The Bunimovich stadium billiards is considered as an
example of such an approach.
