Dijkstra Algorithm Based Ray Tracing: A Case Study for Tunnel Structures

Abstract

This paper deals with ray tracing in a closed space such as tunnel or underground by using the numerical method based on Dijkstra algorithm (DA). The essence of the method is to modify the DA based proximity matrix in terms of three procedures, that is, path selection, path linearization and line of sight (LOS) check. This method has successively been applied to ray tracing in an open space such as a random rough surface. When we treat a closed space, however, more detailed discussions are required than in the case of an open space, because we must take account of the effects of floor, ceiling and side walls at the same time. In this paper we propose procedures for LOS check to solve this difficult situation. Numerical examples are shown for the traced rays and cost distributions in sinusoidal and cross type tunnels.