  We construct an orthogonal basis of functions defined over the unit circle as
the product of the common sinusoidal functions of the azimuth angle by radial
functions which are essentially sines of a polynomials of the radial distance
to the origin. The main impetus of this approach is to generate basis functions
where the minima and maxima along both coordinates, the azimuth and the
distance r to the center, have the same amplitude, akin to the Chebyshev
polynomial basis of the one-dimensional unit interval. The construction is
based on numerical evaluation of the overlap integrals, which have the format
of generalized Fresnel integrals.
