Diffraction calculation of arbitrarily curved wedge modeled with NURBS surfaces

Abstract

In this paper, we present an equivalent current-based numerical routine for calculating the diffraction of arbitrarily curved wedge modeled with non-uniform rational B-spline (NURBS) curves and surfaces. The NURBS curves and surfaces obtained from CAD systems need to be parameterized for numerical calculation; however, available parameterizing approaches in rendering computer graphics, which use straight line segments and flat facets for tessellation, are not suitable for the computation of the wedge diffraction. To make the full use of NURBS modeling technique in high-frequency asymptotic approaches, the proposed numerical routine utilizes a curvature adaptive tessellation scheme to parameterize the edge curve of the wedge with varying curvature as well as the method of parameter alignment to maintain the C0 continuity between the edge curve and the wedge surfaces, which is essential in evaluating the diffraction coefficients. Based on the proposed parameterizing method, the equivalent edge current can be implemented for diffraction computation of arbitrarily curved wedge modeled with NURBS curves and surfaces, complementing with the NURBS based physical optics (PO) as a fully NURBS-based high-frequency approach, which provides high geometrical accuracy and computational efficiency for calculating diffraction of electrically large curved wedges. Numerical examples are presented to validate the proposed method.