论文标题
实用的最低失真映射
Practical lowest distortion mapping
论文作者
论文摘要
最佳变形的构建是计算数学长期存在的问题之一。我们考虑以最小可能的准静电法常数计算准静电变形的问题（相对长度变化的全球估计值）。我们在[Garanzha等人的[Garanzha等。 2021a]，一种最近提出的数值优化方案，通过部分解决有限数量的最小化问题，可以证明与倒数元素解开2D和3D网格。在本文中，我们显示了网状堵塞的延续问题与达到规定的变形质量阈值之间的相似性。这两个问题都可以通过有限数量的优化问题的部分解决方案来解决，这些解决方案基于参数依赖性超弹性功能的有限元近似值。我们的方法基于一个供应良好的变分问题的多型孔功能。总而言之，我们可靠地构建了最小的已知失真估计值（准等级常数）以及稳定的准准共形参数化，可靠地构建2D和3D网格变形。
Construction of optimal deformations is one of the long standing problems of computational mathematics. We consider the problem of computing quasi-isometric deformations with minimal possible quasi-isometry constant (global estimate for relative length change).We build our technique upon [Garanzha et al. 2021a], a recently proposed numerical optimization scheme that provably untangles 2D and 3D meshes with inverted elements by partially solving a finite number of minimization problems. In this paper we show the similarity between continuation problems for mesh untangling and for attaining prescribed deformation quality threshold. Both problems can be solved by a finite number of partial solutions of optimization problems which are based on finite element approximations of parameter-dependent hyperelastic functionals. Our method is based on a polyconvex functional which admits a well-posed variational problem. To sum up, we reliably build 2D and 3D mesh deformations with smallest known distortion estimates (quasi-isometry constants) as well as stable quasi conformal parameterizations for very stiff problems.
