Geometry based parameter extraction and creeping wave evaluation for triangulated convex surfaces

Abstract

Asymptotic solutions based on the uniform geometrical theory of diffraction (UTD) are available for creeping waves traveling along geodesic paths between source and field points on convex surfaces. The application of these UTD solutions to discretized convex surfaces requires extraction of geometry based parameters such as path length, surface curvature, Fock parameter, surface torsion and divergence factor. As unique contributions of this study, accurate and efficient closed-form expressions and algorithms are proposed to extract these parameters from a triangulated conducting convex surface, and UTD surface fields are predicted using the extracted parameters. A quadratic surface mapping is used in barycentric coordinates to define a curved surface on each triangular facet, first. Then, closed-form expressions are obtained for path length, surface curvature and Fock parameter. Algorithms are developed for surface torsion and divergence factor as well. The extracted and actual values for these parameters are compared for primary and secondary paths between source and field points on a circular cylinder and a sphere. The results obtained by applying a UTD solution to triangulated conducting convex surfaces are also validated with the analytical UTD results for surface fields on a circular cylinder, a sphere and a prolate spheroid.