Abstract: The high frequency surface wave starts propagating from the shadow boundary of the arbitrary curved surface along the geodesic path. The diffracted field contributed by the surface wave could be computed by the integral of the Fock current along the geodesic. In this paper, we improve the traditional shadow boundary algorithm and propose an improved geodesic tracing method based on projection angle method(PAM). The patch adaptive reconstruction method to optimize the shadow boundary of the triangular patch is proposed and adjudge precise shadow boundaries which divide light and shadow patches on the curved surface. Furthermore, an improved method for geodesic tracing based on the projection angle method is presented, which can accurately identify the propagation patch of the geodesic path. Based on direction and distance parameters, the barycentric coordinate method is applied to optimize the propagation point to form an accurate geodesic path. Numerical examples verify that the proposed method could calculate the geodesic path of the arbitrary curved surface with a 10⁻³ geodesic curvature such as body of aircraft and missile, which could meet the engineering requirements for computing the creeping wave scattered field.