Comparison of the corneal surface representations based on Chebyshev polynomials

Surface representations based on the even Chebyshev-polynomials of the second kind were proposed earlier for description of corneal surfaces. Two approaches were proposed. According to the first one, the representation in radial direction is based on unmodified even Chebyshev-polynomials, while according to the second one, an adequate, application induced argument transform is applied to the polynomials. The surface needs to be sampled, or re-sampled, over a well-defined set of grid points. Between these grid points, interpolation is achieved via the continuous Chebyshev-polynomials and their argument transformed versions, respectively. In the present paper, the precision of the second representation approach is looked at for common cornea-like mathematical surfaces.