Abstract-High frequency methods resort to numerical ray tracing for application to complex environments. A new method based on the geometrical projection performed by a ray-congruence has been developed as a preconditioning of the ray tracing procedure. It builds a visibility tree, i.e., a database, storing information on all possible ray paths inside a scenario. The method gives a solution to a class of open problems of ray tracing techniques: ray missing, double (multiple) counting, termination criterion, calculation upgrade. Other features of the method are the multipath map and the multipath classification that allow the user to know the relevance of multipath at any point of the scenario in advance, before ray-tracing calculation.The method can be systematically applied to scenarios pertaining to different applications provided that the objects belong to the class of polyhedrons. Reflected and diffracted contributions in a scene are modelled as secondary sources which are handled with an off-line electromagnetic field calculation.Numerical analysis is provided showing the efficiency of the method.