Vulnerability assessment is a systematic process to identify security gaps in the design and evaluation of physical protection systems. Adversarial path planning is a widely used method for identifying potential vulnerabilities and threats to the security and resilience of critical infrastructures. However, achieving efficient path optimization in complex large-scale three-dimensional (3D) scenes remains a significant challenge for vulnerability assessment. This paper introduces a novel \(A^*\) -algorithmic framework for 3D security modeling and vulnerability assessment. Within this framework, the 3D facility models were first developed in 3ds Max and then incorporated into Unity for \(A^*\) heuristic pathfinding. The \(A^*\) -heuristic pathfinding algorithm was implemented with a geometric probability model to refine the detection and distance fields and achieve a rational approximation of the cost to reach the goal. An admissible heuristic is ensured by incorporating the minimum probability of detection ( \(P_\text{D}^\text{min}\) ) and diagonal distance to estimate the heuristic function. The 3D \(A^*\) heuristic search was demonstrated using a hypothetical laboratory facility, where a comparison was also carried out between the \(A^*\) and Dijkstra algorithms for optimal path identification. Comparative results indicate that the proposed \(A^*\) -heuristic algorithm effectively identifies the most vulnerable adversarial pathfinding with high efficiency. Finally, the paper discusses hidden phenomena and open issues in efficient 3D pathfinding for security applications.
