Open 3D mesh parameterization based on edge ratio preservation

In this paper we introduce a new 3D planar parameterization algorithm. After presenting a brief overview of the state of the art, we introduce a new barycentric mapping method, based on the edge length ratio preservation. Our proposed approach demonstrate higher performances with respect to all main techniques developed so far in this direction, reducing both area and length distortions with more than 78% and 57% respectively, maintaining in the same time a low value for the angular distortion. Moreover, our method ensures valid embeddings for any arbitrary open 3D mesh, regardless its complexity.