Abstract
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.
Highlights
Cost distance is a fundamental function in geographical information systems (GISs) which calculates the least accumulative cost from each cell to its nearest source cell in a raster friction surface
In contrast to other methods based on lines of sight [43,44], we propose a novel method for calculating the viewshed using the 3D cost distance function
An efficient method for calculating accurate 3D cost distance is proposed, which uses Dijkstra algorithm to calculate the least cost from some starting voxels to every other voxel in 3D space
Summary
Cost distance is a fundamental function in geographical information systems (GISs) which calculates the least accumulative cost from each cell to its nearest source cell in a raster friction surface. Boroujerdi et al [12] proposed an approach that imposed turn constraints on least cost paths, and Gonçalves [13] and Shirabe [14] considered least cost paths that were wider than a pixel. Compared with 2D cost distance function, three-dimensional (3D) cost distance function facilitates the analysis of movement in 3D frictional problems and can take into account underground tunnels and overpasses while calculating the least cost paths. It can be applied in many domains that deal with 3D geospatial data such as atmospheric science, oceanography, and environmental science
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