Medial axis construction and applications in 3D wireless sensor networks

The medial axis of a shape provides a compact abstraction of its global topology and a proximity of its geometry. The construction of medial axis in two-dimensional (2D) sensor networks has been discussed in the literature, in support of several applications including routing and navigation. In this work, we first reveal the challenges of constructing medial axis in a three-dimensional (3D) sensor network. With more complicated geometric features and complex topology shapes, previous methods proposed for 2D settings cannot be extended easily to 3D networks. Then we propose a distributed algorithm with linear time complexity and communication cost to build a well-structured medial axis of a 3D sensor network without knowing its global shape or global position information. Furthermore we apply the computed medial axis for safe navigation and distributed information storage and retrieval in 3D sensor networks. Simulations are carried out to demonstrate the efficiency of the proposed medial axis-based applications in various 3D sensor networks.