A simple algorithm for computing positively weighted straight skeletons of monotone polygons

A Method for Generating the Centerline of an Elongated Polygon on the Example of a Watercourse

The centerlines of polygons can be generated with the use of various methods. The aim of this study was to propose an algorithm for generating the centerline of an elongated polygon based on the transformation of vector data. The proposed method involves the determination of base points denoting the direction of river flow. These points were also used to map two polygon boundaries. A Triangulated Irregular Network (TIN) was created based on the polygon’s breakpoints. Edges that intersect the river channel in a direction perpendicular to river flow (across) were selected from a set of TIN edges. The polygon was partitioned into segments with the use of the selected TIN edges. The midpoints of selected TIN edges were used to generate the polygon’s centerline based on topological relations. The presented methodology was tested on a polygon representing a 15-km-long section of a river intersecting the city of Olsztyn (a university center). The analyzed river is a highly meandering watercourse, and its channel is narrowed down by hydraulic structures. The river features an island and distributary channels. The generated centerline effectively fits the polygon, and, unlike the solution modeled with the Medial Axis Transformation (MAT) algorithm, it does not feature branching streams.

A Straight Skeleton Based Connectivity Restoration Strategy in the Presence of Obstacles for WSNs

Connectivity has significance in both of data collection and aggregation for Wireless Sensor Networks (WSNs). Once the connectivity is lost, relay nodes are deployed to build a Steiner Minimal Tree (SMT) such that the inter-component connection is reestablished. In recent years, there has been a growing interest in connectivity restoration problems. In previous works, the deployment area of a WSN is assumed to be flat without obstacles. However, such an assumption is not realistic. In addition, most of the existing strategies chose the representative of each component, which serves as the starting point of relay node deployment during the connectivity restoration, either in a random way or in the shortest-distance based manner. In fact, both ways of representative selection could potentially increase the length of the SMT such that more relay nodes are required. In this paper, a novel connectivity restoration strategy is proposed-Obstacle-Avoid connectivity restoration strategy based on Straight Skeletons (OASS), which employs both the polygon based representative selection with the presence of obstacles and the straight skeleton based SMT establishment. The OASS is proved to be a 3- o p t approximation algorithm with the complexity of O ( n log n ) , and the approximation ratio can reduce to 3 3 2 while it satisfies a certain condition. The theoretical analysis and simulations show that the performance of the OASS is better than other strategies in terms of the relay count and the quality of the established topology (i.e., distances between components, delivery latency and balanced traffic load) as well.