Problem Definition:

1. Problem Definition: • For any given 3D environment, setup a wireless sensor network using the least number of wireless sensor motes which provides full signal coverage in the 3D environment. • Design Specifications: • All free spaces within the environment must be covered by the wireless network • The lease number of wireless sensor motes must be used. • Description of 3D Environment: • The 3D Environment  “Cave” • Cave is divided into nodes which are separated by x,y and z paralleled planes (i.e a 3*3*3 cave will look like a Rubic’s cube) • Empty space nodes “FS Nodes” (refer to the center point of the cube area ) • Non-empty space nodes  “Rock” • Important Definitions: • Covered Nodes: FS nodes which are reachable by at least one sensor mote. • Occupied Nodes: FS nodes which has a wireless sensor placed on it. Senior Project – Electrical Engineering - 2005Wireless Sensor Placements in Arbitrary 3D EnvironmentBy: Ziji Song Advisor: Prof. Spinelli Step 1: Analyze the shape of the free space using neighbor density(ND). Definition of ND:For a given free space node in the cave, denote Q as the set of free space nodes which direct lines between p and Q maps only free space nodes. The neighbor density of p equals ∑1/dist2(p,q) for all q in Q. As shown in Fig.1, the higher value of ND indicates a FS node has, the more centered the FS node is. Step 2: Place motes using two algorithms The adding algorithm: place sensor motes to an empty cave based on the ND value of each FS node (High ND value FS nodes get higher priority). The subtracting algorithm: remove sensor motes from a fully occupied cave based on the ND value of each FS node (Low ND value FS nodes get higher priority). Java GUI implementing JOGL Simulation Results: Runtime: Adding algorithm runs significantly faster than subtracting algorithm. Motes usage: Subtracting algorithm is usually better than adding algorithm. However, this is not absolute. Both algorithms give heuristic solutions