A novel approach in the determination of visible surfaces in 3D vector geometries for ray-optical wave propagation modelling

Image theory as a ray-tracing method is a well known but cumbersome tool for propagation modelling. A promising way to enhance its efficiency is a prior reduction of complexity of the scenario under consideration. Only the visible surfaces from the receiver and transmitter locations are potential ray interceptors. Thus, only they have to be subject to the imaging algorithm. The determination of the visible surfaces is discussed. The proposed algorithm is based on a successive dimensional reduction of the problem. In the first step the whole 3D scenario is projected perspectively in several 2D planes. The spatial information is hereby preserved. The resulting 2D polygons, which represent the surfaces, are tested for overlap. This is efficiently done by applying a sweep-line algorithm. With the knowledge of the relative surface positions a graph theory based polygon subtraction is applied to determine the visible surfaces. An inverse projection into 3D space yields the actual visible 3D polygons