Shortest-path tree-based method for calculating visible area with time- and memory-saving preprocessing

Abstract

Visibility has extensive application in areas such as architecture, urban planning, and security. This study proposes a novel approximation method, called the shortest-path tree-based method (SPT-based method), for calculating the visible area using a random Delaunay network on a 2D plane. Various methods are available for calculating the visible area, including exact and approximation methods. However, it is difficult to calculate the visible area repeatedly in a space that has a vast number of obstacles while achieving efficient time and memory usage. The SPT-based method focuses on time- and memory-saving preprocessing. To achieve an efficient calculation of the visible area, we discretised a plane using a random Delaunay network and approximated the visible area using Dijkstra’s method. To evaluate the efficiency of the proposed method, we compared the calculation time, accuracy, and memory usage of the plane-sweep, ray-trace, brute-force, and SPT-based methods while considering the influence of the number of obstacles. This study provides valuable insights for researchers and practitioners for choosing the most suitable approach for their specific needs. Overall, the proposed method offers a time- and memory-efficient solution for calculating the visible area, making it suitable for a detailed analysis of the visual environment and providing a heuristic solution to the art gallery problem requiring repetitive calculations.