  We propose a method of measuring approximate quantum eigenfunctions in
polygonalized billiard geometries, based on a quasiclassical evolution operator
having a (smoothened) Perron-Frobenius kernel modulated by a phase arising from
quantum considerations. We show that quasiclassical evolution differs from
semiclassical (or quantum) evolution but the operators have the same set of
eigenfunctions. We demonstrate this by determining the quasiclassical
eigenfunctions of the polygonalized stadium billiard using arbitrary
trajectories and comparing this with the exact quantum stadium eigenfunctions.
