Finding the Shortest Path on a Polyhedral Surface and Its Application to Quality Assurance of Electric Components

Abstract

This paper presents a computational method for finding the shortest path along polyhedral surfaces. This method is useful for verifying that there is a sufficient distance between two electrical components to prevent the occurrence of a spark between them in product design. We propose an extended algorithm based on the Kanai-Suzuki method, which finds an approximate shortest path by reducing the problem to searching the shortest path on the discrete weighted graph that corresponds to a polyhedral surface. The accuracy of the solution obtained by the Kanai-Suzuki method is occasionally insufficient for our requirements in product design. To achieve higher accuracy without increasing the computational cost drastically, we extend the algorithm by adopting two additional methods: “geometrical improvement” and the “K shortest path algorithm.” Geometrical improvement improves the local optimality by using the geometrical information around a path obtained by the graph method. The K shortest path algorithm, on the other hand, improves the global optimality by finding multiple initial paths for searching the shortest path. For some representative polyhedral surfaces we performed numerical experiments and demonstrated the effectiveness of the proposed method by comparing the shortest paths obtained by the Chen-Han exact method and the Kanai-Suzuki approximate method with the ones obtained by our method.