M. Bubak et al. (Eds.): ICCS 2004, LNCS 3037, pp. 523–531, 2004. © Springer-Verlag Berlin Heidelberg 2004 A Method Based on Fuzzy Logic Technique for Smoothing in 2D Ahmet Çinar Fırat University, Faculty of Engineering, Computer Engineering, 23119 Elazig, Turkey acinar@firat.edu.tr Abstract. This paper describes a novel approach based on fuzzy logic technique for smoothing process on the unstructured meshes in 2D. The proposed method works local on triangulation. Therefore, remeshing does not require. It is known that other smoothing operations such as laplacian smoothing , optimization based smoothing, angle based smoothing, and hybrid smoothing operations work global. That is, in these methods, meshing is achieved, afterwards remeshing is done for smoothing. Whereas, the goal of presented method is to find the best fit location of node while meshing is done. However, remeshing process is avoided. 1 Introduction The basic element in unstructured mesh generation in 2D is triangle and quadrangle. Triangulation is known as creating mesh by using triangles[1]. For optimum triangulation, elements of the created unstructured mesh must be equal size. The often equilateral triangle or isosceles triangle are used. This process is called as smoothing[2],[3]. The goal of smoothing is to obtain regular elements in mesh. However, in the solving domain such as finite element method, the more corrected results can be achieved. There are many kinds of smoothing in the literature. These are; laplacian smoothing [4],[5],[6], optimization based smoothing, hybrid smoothing which is combining of laplacian and optimization based smoothing,, angle based smoothing, variations of laplacian smoothing[7], winslow smoothing,..., etc. Although laplacian smoothing need computational cost less than other methods, invalid elements can be generated in mesh. On the other hand, while optimization ]based smoothing is more likely to avoid invalid elements, the computational costs is higher than laplacian smoothing. Hybrid methods eliminate generating of invalid elements of laplacian smoothing and is decreased computational cost of optimization based smoothing. But, mesh quality of hybrid methods is not as good as pure optimization based smoothing. Angle based smoothing provides good mesh quality, but it needs computational cost less than optimization based smoothing. The common property of all methods is the working as global smoothing. That is, firstly mesh is created and then remeshing is done for smoothing. This situation causes more time and more computational cost. In this study, while creating a mesh, the smoothed mesh is produced in 2D. So, remeshing process does not need. Fuzzy logic technique based a method is applied to