Preconditioned Nonlinear Conjugate Gradient Method of Stretch Energy Minimization for Area-Preserving Parameterizations

Stretch energy minimization (SEM) is widely recognized as one of the most effective approaches for the computation of area-preserving mappings. In this paper, we propose a novel preconditioned nonlinear conjugate gradient method for SEM with guaranteed theoretical convergence. Numerical experiments indicate that our new approach has significantly improved area-preserving accuracy and computational efficiency compared to another state-of-the-art algorithm. Furthermore, we present an application of surface registration to illustrate the practical utility of area-preserving mappings as parameterizations of surfaces.