论文标题
扩展能量最小化的理论基础
Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings
论文作者
论文摘要
拉伸能是一种完全非线性的能量功能，已应用于区域保护映射的数值计算。但是，这种方法缺乏理论支持，由于功能的全部非线性，分析变得复杂。在本文中，我们为伸展能量最小化的理论基础用于计算区域保护映射，包括功能的梯度的整洁配方，以及功能最小化的证明功能是保护面积映射的。此外，还提供了拉伸能量的几何解释，以更好地理解这种能量功能。此外，证明了数值实验，以验证拉伸能量最小化的有效性和准确性，以计算正方形保护区域的简单表面映射。
The stretch energy is a fully nonlinear energy functional that has been applied to the numerical computation of area-preserving mappings. However, this approach lacks theoretical support and the analysis is complicated due to the full nonlinearity of the functional. In this paper, we provide a theoretical foundation of the stretch energy minimization for the computation of area-preserving mappings, including a neat formulation of the gradient of the functional, and the proof of the minimizers of the functional being area-preserving mappings. In addition, the geometric interpretation of the stretch energy is also provided to better understand this energy functional. Furthermore, numerical experiments are demonstrated to validate the effectiveness and accuracy of the stretch energy minimization for the computation of square-shaped area-preserving mappings of simplicial surfaces.
