A line-integral asymptotic representation of the PO radiation from NURBS surfaces

Computer aided geometric design (CAGD) tools use non-uniform rational B-spline (NURBS) surfaces to describe the geometrical shape of an object. A NURBS-based description is particularly useful when treating problems of EM scattering from large conducting surfaces in the framework of high-frequency techniques like physical optics (PO). When dealing with large and complex bodies, PO requires the computation of double integrals with fast oscillating kernels. The use of basic building blocks (e.g. NURBS) for describing complex surfaces can alleviate the numerical problems. The presented approach provides a field representation in terms of line-integrals for the near-field PO radiation from a general NURBS surface. The surface is illuminated by a point source located in arbitrary position. The numerical computation of geometrical parameters is more conveniently performed if each NURBS surface is transformed into a set of rational Be´zier patches. The final physically meaningful outcome provides a representation of the PO field from the Be´zier surface in terms of line integrals. The results are compared with those obtained with classical PO surface integration, by discussing the computational improvements and asymptotic limitations.