An optimal parameterization algorithm for discrete surface

Parameterization of discrete surface is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, for a surface patch on a smooth, two-dimensional surface in R³, low-distortion Parameterizations are achieved by an optimal parameterization algorithm. Our proposed algorithm is described by initial parameterization, domain discretization and numerical optimization. The parameterization can be optimized with respect to the varying importance of conformality, length preservation and area preservation. The initial parameterization is provided for the subsequent optimization of the parameter domain. The domain discretization is introduced and a constrained Newton method is used to minimize a corresponding discrete energy. The numerical optimization method is provided for the optimal deformation to generate the final, optimal parameterization. Experiment results prove that our proposed algorithm is effective and robust.