Skinning is a popular way to rig and deform characters for animation, to compute reduced-order simulations, and to define features for geometry processing. Methods built on skinning rely on weight functions that distribute the influence of each degree of freedom across the mesh. Automatic skinning methods generate these weight functions with minimal user input, usually by solving a variational problem on a mesh whose boundary is the skinned surface. This formulation necessitates tetrahedralizing the volume inside the surface, which brings with it meshing artifacts, the possibility of tetrahedralization failure, and the impossibility of generating weights for surfaces that are not closed. We introduce a mesh-free and robust automatic skinning method that generates high-quality skinning weights comparable to the current state of the art without volumetric meshes. Our method reliably works even on open surfaces and triangle soups where current methods fail. We achieve this through the use of a Lagrangian representation for skinning weights, which circumvents the need for finite elements while optimizing the biharmonic energy.

翻译：蒙皮是动画中角色绑定与变形、计算降阶仿真以及定义几何处理特征的常用方法。基于蒙皮的方法依赖于权重函数，这些函数将每个自由度的影响分布到网格上。自动蒙皮方法通过最小化用户输入来生成这些权重函数，通常通过求解一个变分问题实现，该问题的定义域是以蒙皮表面为边界的网格。这种表述需要对表面内部的体积进行四面体剖分，这会带来网格伪影、四面体剖分失败的可能性，并且无法为非封闭表面生成权重。我们提出了一种无需网格且鲁棒的自动蒙皮方法，该方法无需体网格即可生成与当前最优技术相媲美的高质量蒙皮权重。即使在当前方法失效的开放表面和三角面片集上，我们的方法也能可靠工作。我们通过采用拉格朗日表示法描述蒙皮权重来实现这一目标，从而在优化双调和能量的同时规避了对有限元的需求。