Abstract: To overcome the drawback that the method of the uniform geometrical theory of diffraction can not be applied to arbitrary curved targets, the method of the uniform geometrical theory of diffraction based on models constructed by arbitrary curved surfaces is studied and the algorithm that traces the creeping rays which are in the highest flight in the shadow region is presented where the numerical differential geometry method is introduced in the process of ray-tracing. What is studied here makes the method of the uniform geometrical theory of diffraction able to be applied to analyze complex electromagnetic targets which can not be dealt with before. The algorithm can be applied to models constructed by arbitrary curved surfaces including the board, cylinder and cone that are already used and the validity and usefulness can be seen from numerical results.

Key words: non-uniform rational B-spline, uniform geometrical theory of diffraction, creeping ray, ray tracing