This research focuses on distributed and localized algorithms for precise boundary detection in 3D wireless networks. Our objectives are in two folds. First, we aim to identify the nodes on the boundaries of a 3D network, which serve as a key attribute that characterizes the network, especially in such geographic exploration tasks as terrain and underwater reconnaissance. Second, we construct locally planarized 2-manifold surfaces for inner and outer boundaries, in order to enable available graph theory tools to be applied on 3D surfaces, such as embedding, localization, partition, and greedy routing among many others. To achieve the first objective, we propose a Unit Ball Fitting (UBF) algorithm that discovers a set of potential boundary nodes, followed by a refinement algorithm, named Isolated Fragment Filtering (IFF), which removes isolated nodes that are misinterpreted as boundary nodes by UBF. Based on the identified boundary nodes, we develop an algorithm that constructs a locally planarized triangular mesh surface for each 3D boundary. Our proposed scheme is localized, requiring information within one-hop neighborhood only. Our simulation results demonstrate that the proposed algorithms can effectively identify boundary nodes and surfaces, even under high measurement errors. As far as we know, this is the first work for discovering boundary nodes and constructing boundary surfaces in 3D wireless networks.

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