Sensing Coverage in Three-Dimensional Space

Efficient sensor deployment has been one of the most challenging and interesting research areas. The importance and effectiveness of real-world sensing applications, such as underwater and atmospheric sensing, military applications, health systems, and alert systems, which target specific events, raise the need for adaptable design of Wireless Sensor Networks (WSNs). The main challenge in the design of such networks is the optimal sensor deployment, which helps extend the operational network lifetime. Indeed, by maintaining coverage and connectivity with the least number of active nodes and least communication cost, the operable time of the network is guaranteed to be prolonged. The study of two-dimensional (2D) WSNs introduced a significant advancement to the wireless sensor computing technology for different types of smart environments. Nevertheless, 2D WSNs were not sufficient concerning certain applications that require three-dimensional (3D) design. Previous work focused on the design and analysis of various approaches to cover a 3D field of interest, and expanded existing design from 2D to 3D space. Hence, the complexity of such approaches is a major stumbling block. To alleviate this problem, more efficient solutions for the design of WSNs for 3D space deployment have been introduced. By tessellation of the 3D space, which is one of the proposed solutions, researchers studied the partitioning of the space based on Voronoi tessellation by generating identical space-filling cells. Using space fillers cells, which are represented by polyhedra, to model the sensing range of the sensor nodes is assumed to be an optimal solution since these polyhedra can fill a 3D space without leaving gaps or overlaps among them. In the existing literature, the coverage problem in 3D space is concerned with finding the polyhedron that can best approximate the spherical sensing range and eliminates gaps without scarifying the network connectivity. Therefore, the latter is directly related to the sensor node placement strategy. This book chapter studies various proposed solutions for the design of 3D WSNs, with a focus on coverage and connectivity. More specifically, it presents several space filling polyhedra, including the cube, truncated octahedron, hexagonal prism, and rhombic dodecahedron. Also, it compares all these space filling polyhedra to cover a 3D space.