A new ray tracing algorithm for creeping waves on NURBS surfaces

Abstract

A new accurate numerical algorithm is presented for creeping ray tracing on the arbitrarily shaped surfaces modeled by the Non-Uniform Rational B-spline (NURBS) surfaces. The main problem in calculating the uniform geometrical theory of diffraction (UTD) surface diffracted fields on NURBS surfaces lies in the difficulty in determining the geodesic paths which the creeping rays propagate along. In this paper, a novel method is developed based on the property of geodesic to compute geodesic paths on NURBS surfaces. Actually a complex object generally needs to be modeled as a combination of several connected NURBS patches. Therefore a transition method is presented to handle the transition of the creeping rays when the rays propagate from one patch to another. The proposed creeping ray tracing algorithm is efficient and accurate for ray tracing on arbitrarily shaped complex shapes. And the algorithm can also extend the applicability of UTD for practical engineering. The validity and efficiency of the algorithm is verified by numerical results.