Geometric Simplifications of Natural Caves in Ray-Tracing-Based Propagation Modelling

Natural caves show some similarities to human-made tunnels, which have previously been the subject of radio-frequency propagation modelling using deterministic ray-tracing techniques. Since natural caves are non-uniform because of their inherent concavity and irregular limestone formations, detailed 3D models contain a large number of small facets, which can have a detrimental impact on the ray-tracing computational complexity as well as on the modelling accuracy. Here, we analyse the performance of ray tracing in repeatedly simplified 3D descriptions of two caves in the UK, i.e., Kingsdale Master Cave (KMC) Roof Tunnel and Skirwith Cave. The trade-off between the size of the reflection surface and the modelling accuracy is examined. Further, by reducing the number of facets, simulation time can be reduced significantly. Two simplification methods from computer graphics were applied: Vertex Clustering and Quadric Edge Collapse. We compare the ray-tracing results to the experimental measurements and to the channel modelling based on the modal theory. We show Edge Collapse to be better suited for the task than Vertex Clustering, with larger simplifications being possible before the passage becomes entirely blocked. The use of model simplification is predominantly justified by the computational time gains, with the acceptable simplified geometries roughly halving the execution time given the laser scanning resolution of 10 cm.