Surface-ray tracing based on the property of geodesic on arbitrary NURBS surfaces

An accurate and efficient 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 UTD surface diffracted fields on NURBS surfaces is due to the difficulty in determining the geodesic paths which the creeping rays propagate along. In this paper, an efficient method is developed based on the property of geodesic to compute geodesic paths on NURBS surfaces. And the algorithm can extend the applicability of UTD for practical engineering. The validity and efficiency of the algorithm is verified by numerical results.