Abstract
Delaunay refinement is a technique for generating unstructured meshes of triangles for sensor network configuration engineering practice. A new method for solving Delaunay triangulation problem is proposed in this paper, which is called endpoint triangle’s circumcircle model (ETCM). As compared with the original fractional node refinement algorithms, the proposed algorithm can get well refinement stability with least time cost. Simulations are performed under five aspects including refinement stability, the number of additional nodes, time cost, mesh quality after intruding additional nodes, and the aspect ratio improved by single additional node. All experimental results show the advantages of the proposed algorithm as compared with the existing algorithms and confirm the algorithm analysis sufficiently.
Highlights
The concept of intelligent network system is very popular in the world
We give five assessment criteria as follows: (1) stability of refinement; (2) number of additional nodes, which means that, by using as small number of additional points as possible, we can change the original datum set as little as possible; (3) time cost; (4) the quality of the mesh after intruding additional nodes: when AAR is 0.5 approximately, it indicates a result of fine quality; (5) the average aspect ratio (AAR) improved by single additional point
The model is given by the following equation: AARp where AAR is the average of all aspect ratios of meshes, AARrefine is the AAR after refinement, AARCDT is the AAR after constrained Delaunay triangulation (DT), and n is the number of additional points
Summary
The concept of intelligent network system is very popular in the world. how can we deploy and optimize the sensor? It is still a difficult issue to scientists that affects both cost and detection capability, which are required considerations of both coverage and connectivity. Delaunay triangulation (DT) is an effective method to carve up a discrete data region, which is especially widely used in sensor network configuration engineering field [2,3,4,5]. There are two types of DT algorithm: constrained Delaunay triangulation [6, 7] and conforming Delaunay triangulation [8, 9] The former method is a best approximation of the Delaunay triangulation, given that it must contain all features in the graph. The DT property cannot be preserved and the quality of the mesh declines in constrained Delaunay triangulation, which will influence the stability and convergence of finite element numerical calculation.
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