Iterative Method for Edge Length Equalization

This paper presents a method for triangular surface remeshing to obtain new faces whose edge lengths are as close as possible to a target value m. The process uses as input a 2-manifold mesh with arbitrary geometry and topology. The proposed algorithm runs iteratively, automatically adjusting the necessary amount of vertices, and applies a global relaxation process using a variation of Laplace-Beltrami discrete operator. We introduce geometry constraints in order to preserve salient features of the original model. The method results on a grid with edge lengths near to m with low standard deviation, i.e. the vertices are uniformly distributed over the original surface. The dual space of the final triangular surface results in a trivalent, mostly hexagonal mesh, suitable for several applications.