The goal of terrain viewshed point selection is to identify multiple viewpoints within a specific area that offer optimal visibility. However, as the resolution of terrain data becomes finer, the number of data points to be processed grows significantly, leading to a sharp rise in computational demands for viewshed point selection. This paper introduces the Efficient Precise Viewshed Point Selection (EPVPS) algorithm, which provides an important reference for multi-viewpoint planning. First, the Empty Circles based K-means (ECKM) algorithm is utilized to determine the initial centers for candidate viewpoint clustering. Second, a new viewpoint evaluation metric, Weighted Coverage Overlap Metric (WCOM), is proposed. This metric divides the viewshed of candidate points into coverage contribution points and overlap contribution points, computes WCOM based on this division, and stores the values in a min-heap. Finally, viewpoints are added and deleted from clusters by adjusting the sets of coverage contribution points and overlap contribution points. The EPVPS algorithm is compared with the Candidate Viewpoints Filtering (CVF) algorithm and the Simulated Annealing (SA) algorithm. Experimental results demonstrate that the EPVPS algorithm outperforms the others in computational efficiency, coverage rate, and overlap rate.

Viewshed analyses using Digital Elevation Models (DEMs) can provide decision support information in a variety of areas. Traditional viewshed analyses are mainly based on a circular visual range centred on an observation point, and lack the ability to dynamically adjust the visual range by view angle. In addition, these algorithms face challenges in achieving a balance between computational efficiency and accuracy. To solve the above problems, this study proposes a field-of-view (FOV) angular range based partitioning strategy to realise dynamic range proximity-direction-elevation reference lines (DPDERL), which improves the adaptability to complex terrains and the flexibility of viewpoint application environments. After partitioning, the algorithm is optimised for grid point search and reference line update. Experimental results show that the algorithm takes less than half the time of the Xdraw algorithm for a variety of terrain regions, has an error of no more than 5% compared to the R3 algorithm, and has less aggregation of error points than the PDERL and the XPDERL. The DPDERL approach provides an effective solution for large-scale dynamic range viewshed analysis by balancing speed and accuracy.