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首页> 外文期刊>Journal of Mechanical Design >Finding the Shortest Path on a Polyhedral Surface and Its Application to Quality Assurance of Electric Components
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Finding the Shortest Path on a Polyhedral Surface and Its Application to Quality Assurance of Electric Components

机译：在多面体表面上找到最短路径及其在电气元件质量保证中的应用

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摘要

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.
机译：本文提出了一种计算方法，可以找到沿多面体表面的最短路径。此方法可用于验证两个电气组件之间是否有足够的距离，以防止在产品设计中在它们之间产生火花。我们提出了一种基于Kanai-Suzuki方法的扩展算法，该算法通过减少在与多面体表面相对应的离散加权图中搜索最短路径的问题来找到近似最短路径。通过Kanai-Suzuki方法获得的解决方案的准确性有时不足以满足我们对产品设计的要求。为了在不大幅增加计算成本的情况下实现更高的准确性，我们通过采用两种附加方法来扩展算法：“几何改进”和“ K最短路径算法”。几何改进通过使用通过图方法获得的路径周围的几何信息来改善局部最优性。另一方面，K最短路径算法通过查找用于搜索最短路径的多个初始路径来提高全局最优性。对于某些代表性的多面体表面，我们进行了数值实验，并通过比较通过Chen-Han精确方法和Kanai-Suzuki近似方法获得的最短路径与通过我们的方法获得的最短路径，证明了该方法的有效性。

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