Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations

Abstract

An area-preserving parameterization of a surface is a bijective mapping that maps the surface onto a specified domain and preserves the local area. This paper formulates the computation of disk area-preserving parameterization as an improved optimization problem and develops a preconditioned nonlinear conjugate gradient method with guaranteed theoretical convergence for solving the problem. Numerical experiments indicate that our new approach has significantly improved area-preserving accuracy and computational efficiency compared to other state-of-the-art algorithms. Furthermore, we present an application of surface registration to illustrate the practical utility of area-preserving mappings as parameterizations of surfaces.