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A quadrature technique for evaluating physical optics (PO) scattering from biquadratic surfaces with associated quadratic phase variation is developed via an extension of Filon quadrature. This involves incorporating a quadratic polynomial amplitude function into the integrand of a Fresnel integral to account for both quadratic phase and amplitude variation of the currents on a curved surface. A 3-D application of this technique for direct PO scattering analysis of curved surfaces, which are defined by a set of biquadratic patches, is presented. Accuracy and computational efficiency of the resulting algorithms are included.