Fitting freeform shapes with orthogonal bases

Orthogonality is exploited for fitting analytically-specified freeform shapes in terms of orthogonal polynomials. The end result is expressed in terms of FFTs coupled to a simple explicit form of Gaussian quadrature. Its efficiency opens the possibilities for proceeding to arbitrary numbers of polynomial terms. This is shown to create promising options for quantifying and filtering the mid-spatial frequency structure within circular domains from measurements of as-built parts.