An Efficient Algorithm for the Computation of the UTD $T$ Transition Function

We present an efficient algorithm for the numerical calculation of the T canonical transition function, which is encountered in the uniform geometrical theory of diffraction (UTD). Such a transition function allows the uniform ray field description of various high-frequency diffraction mechanisms, such as double wedge or vertex diffraction. The proposed algorithm is valid for both real and imaginary arguments as required to deal with the general case in UTD applications.