Método iterativo para geração de malhas triangulares com distribuição uniforme

Abstract

The approximation of continuous surfaces by polygonal meshes is very important in several areas. In recent years we have seen the use of this kind of mesh in various industrial applications such as computer simulations, geometric modeling and animation. Often, the input models have poor quality, i.e., bad elements distribution and inconsistent polygon shape. One important feature of poligonal surfaces is vertex distribution and sometimes it is necessary to control the vertices distance with an uniform edge lentgh. This work presents a method for triangular remeshing given a target edge length m. The input is a 2-manifold triangular surface with arbitrary geometry and topology. The proposed algorithm removes and inserts vertices adjusting the amount of necessary elements. Then, the model enters in a global relaxation process using a variation of Laplace-Beltrami discrete operator, which uses the k nearest neighbors of each vertex. This is done in an iteratively fashion until the algorithm reaches the maximum iteration number. At the end, one have a grid with edge length near to m and low standard deviation (vertices uniformly distributed). The triangles also presents good connectivity and high isotropy; the results shown that our remeshing scheme quantitatively improved the mesh quality. The dual space of the final triangular surface can be used for trivalent remeshing. These models are important for physical simulations of nano-carbon surfaces and we dedicated a chapter of our work to discuss this subject.