An algorithm is presented for the rapid evaluation of certain functionals of three-point correlation functions, measured in a plane. This simplifies the estimation of effective physical properties of composite materials from cross-sectional photographs via bounds. More precisely, Fourier coefficients of a reduced three-point correlation function are expressed as inner products of polyharmonic fields. The polyharmonic fields are evaluated with a polyharmonic version of the fast multipole method with a CPU requirement proportional to the number (p) of fields included and to the number (N) of points in a discretization of the component interfaces. The Fourier coefficients are related to structural parameters which are used in third-order bounds on conductivity and elastic properties. Inclusion of (p) polyharmonic fields gives structural parameters with an error decaying at least as (1 / p^{3}). In a simple application for disks with (p=) 10 , superalgebraic convergence in (1 / N), and a high-order Gaussian quadrature rule for the inner products, the algorithm gives an error of typically (0.05 %). A previous algorithm, involving Monte Carlo integration, gives structural parameters with an error of typically (2 %). (c) 1995 Acadernic Press, Inc.