Efficient geometric routing algorithms have been studied extensively in two-dimensional ad hoc networks, or simply 2D networks. These algorithms are efficient and they have been proven to be the worst-case optimal, localized routing algorithms. However, few prior works have focused on efficient geometric routing in 3D networks due to the lack of an efficient method to limit the search once the greedy routing algorithm encounters a local-minimum, like face routing in 2D networks. In this paper, we tackle the problem of efficient geometric routing in 3D networks. We propose routing on hulls, a 3D analogue to face routing, and present the first 3D partial unit Delaunay triangulation (PUDT) algorithm to divide the entire network space into a number of closed subspaces. The proposed greedyhull-greedy (GHG) routing is efficient because it bounds the local-minimum recovery process from the whole network to the surface structure (hull) of only one of the subspaces.
