12 Length Ratio Preserving Parameterization of Triangular 3D Meshes

In this paper we propose an enhanced 3D object planar parameterization method. After presenting a comprehensive and critical overview of the state of the art, we introduce a new barycentric mapping algorithm, based on the length ratio preservation. The proposed approach shows superior performances with respect to all state of the art techniques by reducing both area and length distortion with more than 77% and 55% respectively. Moreover, the computational complexity is equivalent with the faster technique implemented so far. A major advantage of our method, concerns the bijectivity property, which holds in all cases, and ensures valid and shape preserving embeddings for arbitrary open and triangular 3D meshes, regardless their complexity.