Abstract: Path planning is an active topic in the literature, and efficient navigation over non-planar surfaces is an open research question. In this work we present a novel technique for navigation of multiple agents over arbitrary triangular domains. The proposed solution uses a fast hierarchical computation of geodesic distances over triangular meshes to allow interactive frame rates, and a GPU-based collision avoidance technique to guide individual agents. Unlike most previous work, the method imposes no limitations on the surface over which the agents are moving, and can naturally deal with non-planar meshes of arbitrary genus and curvature. Moreover, the implementation is a hybrid CPU/GPU algorithm that explores the current trend of increasing the number of CPU cores and GPU programmability. This approach exploits the best qualities in each processor, thus achieving very high performance.