Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method

Abstract

Although the uniform theory of diffraction (UTD) could be theoretically applied to arbitrarilyshaped convex objects modeled by nonuniform rational B-splines (NURBS), one of the great challenges in calculation of the UTD surface diffracted fields is the difficulty in determining the geodesic paths along which the creeping waves propagate on arbitrarilyshaped NURBS surfaces. In differential geometry, geodesic paths satisfy geodesic differential equation (GDE). Hence, in this paper, a general and efficient adaptive variable step Euler method is introduced for solving the GDE on arbitrarilyshaped NURBS surfaces. In contrast with conventional Euler method, the proposed method employs a shape factor (SF) ξ to efficiently enhance the accuracy of tracing and extends the application of UTD for practical engineering. The validity and usefulness of the algorithm can be verified by the numerical results.