Fast Isometric Parametrization of 3D Triangular Mesh

In this paper we describe a new mesh parametrization method that is both computationally efficient and yields minimized distance errors. The method has four steps. First, the multidimensional scaling is used to locally flatten each vertex. Second, an optimal method is used to compute the linear reconstructing weights of each vertex with respect to its neighbours. Thirdly, a spectral decomposition method is used to obtain initial 2D parametrization coordinates. Fourthly, we rotate and scale the initial coordinates to minimize the distance errors. Examples are provided to show the effectiveness of this parametrization method compared with alternatives.