Efficient Octree-based 3 Dimensional Pathfinding

Three-dimensional virtual environments are commonplace in modern games.Nonplayer character (NPC) character movement planning, however, is still largely 2D, with off-plane or vertical movement modeled through limited, and frequently custom connections between 2D surfaces.Naive extension of 2D pathfinding methods to 3D by building a full 3D grid (voxelization) is possible but easily becomes too expensive for non-trivial 3D spaces.In this thesis we develop an efficient solution to 3D pathfinding by building a reduced, hierarchical grid representation within which we can extend traditional 2D navigation mesh (navmesh) pathing.Our design begins with an octree representation, which already provides more flexibility than a more traditional voxelization.By merging adjacent cells while preserving their convexity, we obtain a coarser representation that greatly reduces path computation costs.We then build a navigation graph from this octree within which we can search for paths using the popular A* search algorithm.To increase the quality of the paths we obtain we implemented two forms of path refinement: a visibility-based path pruning heuristic, and a novel implementation of the classic "funnel" algorithm that computes minimal homotopic paths, in our case extended to our 3D environment.We further extend our work to handle dynamic environments with local and efficient updates to the octree and the movement graph.Experiments on a variety of scenarios show that our approach remains fast and efficient even for very large 3D maps and could be used for real-time pathfinding in video i games.We implemented our work in Unity, one of the most popular game engines, as an effort to make pathfinding in 3D environments accessible to game developers.First and foremost I want to thank my supervisor, Clark Verbrugge, for his invaluable help and support throughout these last two years.This thesis would not exist without him.I also thank Thomas Nobes for providing his results and code on the 3D JPS algorithm and his openness to discuss his work.

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