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.

翻译：拉伸能量最小化（SEM）被广泛认为是计算保面积映射最有效的方法之一。本文提出了一种新颖的预处理非线性共轭梯度方法用于SEM，并保证了理论收敛性。数值实验表明，与另一种先进算法相比，我们的新方法在保面积精度和计算效率上均有显著提升。此外，我们展示了曲面配准的应用，以说明保面积映射作为曲面参数化的实际效用。