An area-preserving parameterization is a bijective mapping that maps a surface onto a specified domain and preserves the local area. This paper formulates the computation of disk area-preserving parameterization as an authalic energy minimization (AEM) problem and proposes a novel preconditioned nonlinear conjugate gradient method for the AEM 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：保面积参数化是一类将曲面映射到指定区域并保持局部面积的双射映射。本文将圆盘等积参数化的计算表述为保面积能量最小化（AEM）问题，并提出了一种具有理论收敛保证的新型预条件非线性共轭梯度法来求解该问题。数值实验表明，与另一类前沿算法相比，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实例，以阐明保面积映射作为曲面参数化的实际效用。