| Abstract: | Find a connection of two points in the plane with minimal cost, the cost per length unit depending on the location, and the curvature of the curve being limited. For simple cases, as a necessary condition, the known optical law of refraction is supplemented by a “circular law of refraction”. For the general case, a practicable numerical procedure is developed on the foundation of graph theory. This procedure is able to additionally take into consideration the given directions of the curve in the end points. Several examples demonstrate fundamental solution structures for classical basic problems and also solutions for routing problems in planning traffic ways. |
