Iterative method for edge equalization of triangular meshes

Abstract

This work presents a method for remeshing triangular surfaces. This method obtains a new mesh in such a way that any edge is within a predefined interval [emin, emax]. The input of the process is a 2-manifold mesh with arbitrary geometry and topology. The proposed algorithm is iterative and is able to automatically adjust the number of vertices and polygons through stellar operations. A low pass filter is also applied to remove higher frequencies. This algorithm generates a triangular 2-manifold mesh, with the vertices spreaded almost uniform over the input surface. At the end of the process, almost all edges are within the interval. The dual mesh of this triangular mesh is a trivalent mesh also very uniform. This kind of mesh has many applications in simulations of carbon nano structures.