Cost distance is one of the fundamental functions in geographical information systems (GISs). 3D cost distance function makes the analysis of movement in 3D frictions possible. In this paper, we propose an algorithm and efficient data structures to accurately calculate the cost distance in discrete 3D space. Specifically, Dijkstra’s algorithm is used to calculate the least cost between initial voxels and all the other voxels in 3D space. During the calculation, unnecessary bends along the travel path are constantly corrected to retain the accurate least cost. Our results show that the proposed algorithm can generate true Euclidean distance in homogeneous frictions and can provide more accurate least cost in heterogeneous frictions than that provided by several existing methods. Furthermore, the proposed data structures, i.e., a heap combined with a hash table, significantly improve the algorithm’s efficiency. The algorithm and data structures have been verified via several applications including planning the shortest drone delivery path in an urban environment, generating volumetric viewshed, and calculating the minimum hydraulic resistance.

中文翻译：

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准确有效地计算三维成本距离

成本距离是地理信息系统（GIS）的基本功能之一。3D成本距离功能可以分析3D摩擦中的运动。在本文中，我们提出了一种算法和有效的数据结构，可准确计算离散3D空间中的成本距离。具体而言，Dijkstra的算法用于计算3D空间中初始体素与所有其他体素之间的最小成本。在计算过程中，将不断修正沿行进路径不必要的弯曲，以保持准确的最低成本。我们的结果表明，与几种现有方法相比，该算法可以在均质摩擦中生成真实的欧几里德距离，并且在异质摩擦中可以提供更准确的最小成本。此外，建议的数据结构，即 堆与哈希表结合使用，可显着提高算法的效率。该算法和数据结构已通过多种应用进行了验证，包括规划城市环境中最短的无人机输送路径，生成体积视域以及计算最小水力阻力。