Calculating the least-cost path (LCP) is a fundamental operation in raster-based geographic information systems (GIS). The LCP is applied to raster cost surfaces, in which it determines the most cost-effective path. Increasing the raster resolution results in a longer computation time to obtain LCP. This paper proposes a method for calculating the LCP using a multi-resolution raster cost surface model to enhance computational performance for large-scale grids. The original raster cost surface is progressively downsampled to generate grids of decreasing resolutions. Subsequently, the path is determined on the low-resolution raster. By performing operations such as filtering directional points and mapping path points, the final path on the high-resolution raster can be obtained. The method enables a parallel computation of paths. Therefore, it significantly improves the efficiency for synthetic raster cost surfaces with continuous or discrete characteristics, as well as for raster cost surfaces generated from real terrain datasets, while also providing an end-to-end path output. The experiments show that 80% of the results are very close to the original LCP, and the accuracy of the remaining paths falls within an acceptable range. At the same time, our method greatly improves the efficiency of path solving on a large-scale raster, fulfilling practical application requirements.
Terrain viewshed analysis based on the digital elevation model (DEM) is of significant application value. A lot of viewshed analysis algorithms have been proposed, including R3 as the accurate one and others as efficient ones. The R3 algorithm is accurate because of its comprehensive but time-consuming computation, while the others are efficient due to proper approximation. However, no algorithm is capable of taking advantage of both until one algorithm is proposed, which is based on a ‘proximity-direction-elevation’ (PDE) coordinate system and named the PDE spatial reference line (PDERL) algorithm. The original research proves the PDERL algorithm is perfectly accurate by theory and experimental results, in comparison with R3 as standard, and even more efficient than R3. However, the original research does not mention the cases where the observer is placed on grid points, and the original implementation does not produce very accurate results in practice. It is important to find out and correct the errors. In this paper, a checking algorithm for PDERL is proposed to allow further investigation of errors. With the fundamental ideas of PDERL unchallenged, an improved implementation of the PDERL algorithm is proposed, named HiPDERL. By experimental results, this paper proves HiPDERL utilizes the potential of PDERL on accuracy at the cost of a little efficiency when the observer is placed on grid points.
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