Geodesic Computation on NURBS Surfaces for UTD Analysis

One of the great challenges in calculating the uniform geometrical theory of diffraction (UTD) surface diffracted fields on NURBS surfaces is due to the difficulty in determining the geodesic paths along which the creeping waves propagate. On one single parametric surface patch, the geodesic computation needs to be performed by solving the geodesic equations numerically. Furthermore, realistic objects are generally modeled as the union of several connected NURBS patches. Due to the discontinuity of parameter between patches, it is more complicated to compute geodesic paths on several connected patches than on one single patch. Therefore, this letter develops an adjustable modeling scheme that can adjust the parameterizations of several connected patches to support the geodesic computation throughout these patches. Based on the geodesic computation, the UTD diffractions by NURBS models can be analyzed.