Solving pathfinding problems in cubic grids using 3D neighborhood extension

Pathfinding in three-dimensional environments is essential for solving various application problems. Pathfinding in 3D spaces presents significantly greater complexity than in two-dimensional environments, primarily due to the increased number of potential paths an agent can traverse. This complexity is further compounded by three-dimensional obstacles, which introduce an additional layer of difficulty to pathfinding and necessitate solutions capable of efficiently navigating complex scenarios. Additionally, when considering the third dimension, different movement directions become relevant for identifying low-cost and smooth routes in 3D space. To address these challenges, this work investigates an innovative technique called 3D Neighborhood Expansion, which uniformly expands the neighborhood search in three-dimensional space. The proposed 3D neighborhood expansion is then integrated into relevant path-smoothing algorithms. The primary goal is to analyze the impact of expanding the neighborhood search, controlled by the parameter $k$, on the performance of pathfinding algorithms in 3D environments. Specifically, this work examines whether increasing $k$ results in more direct and smoother paths. The technique is tested using voxel-based maps, which offer realistic representations of 3D space. Based on a statistical analysis of various path search metrics, experiments conducted with the A*, Theta*, and JPS algorithms demonstrate that expanding the neighborhood significantly improves the quality of the resulting paths as $k$ increases. These findings are crucial for enhancing practical applications in computer games, robotics, and simulation systems.