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Accurate and Efficient Calculation of Three-Dimensional Cost Distance

Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Key Laboratory for Land Satellite Remote Sensing Applications of Ministry of Natural Resources, School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China
Jiangsu Center for Collaborative Innovation in Novel Software Technology and Industrialization, Nanjing 210023, China
Department of Geography & Atmospheric Science, University of Kansas, Lawrence, KS 66045, USA
College of Geomatics, Xi‘an University of Science and Technology, Xi’an 710054, China
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2020, 9(6), 353;
Received: 16 March 2020 / Revised: 16 May 2020 / Accepted: 25 May 2020 / Published: 27 May 2020
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. View Full-Text
Keywords: voxel; Dijkstra’s algorithm; minimum heap; route planning; viewshed; hydraulic resistance voxel; Dijkstra’s algorithm; minimum heap; route planning; viewshed; hydraulic resistance
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Chen, Y.; She, J.; Li, X.; Zhang, S.; Tan, J. Accurate and Efficient Calculation of Three-Dimensional Cost Distance. ISPRS Int. J. Geo-Inf. 2020, 9, 353.

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