Evaluation of the Contour Integral on Curved Edges in Time Domain Equivalent Edge Currents

The closed-form evaluation of the radiation integral in time domain physical theory of diffraction (PTD) equivalent edge currents (EECs) on quadratic edges of quadratic triangular surfaces, is presented. The radiation integral is interpreted as a Radon transform and the closed-form expressions are obtained by finding the intersection of the plane, which is formed by the propagation direction of the incident wave and the observation direction, and quadratic edge. A numerical example that shows the accuracy and validity of the scheme is presented.