Robust Biharmonic Skinning Using Geometric Fields

TL;DR

This work addresses automatic skinning in scenarios where volume meshing is problematic or infeasible by introducing mesh-free geometric fields that directly optimize the bounded biharmonic weights energy. The approach uses a geometry-aware kernel representation, enforcing nonnegativity, partition of unity, and Lagrange constraints while supporting Dirichlet and Neumann boundary conditions through a reparameterization near the boundary. Optimization proceeds via stochastic estimation of the biharmonic energy, augmented with generalized winding numbers to handle non-watertight domains and a multiscale strategy to ensure stable convergence. The results show robust performance on open surfaces and triangle soups, offering practical advantages over traditional FEM-based BBW and QHW in challenging geometries, and enabling user-guided control through boundary conditioning. Overall, the method delivers high-quality skinning weights without volumetric meshes, expanding the applicability of automatic skinning to a broader class of geometries in computer graphics and geometry processing.

Abstract

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 bounded by 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.

Figures (16)

• Figure 1: An illustrative example on the low-poly Shiba Inu mesh, with the skeleton depicted in purple (a). The skinning weight function of the ear bone determines the region of influence of that bone (b). Our method for skinning weight computation produces smooth-looking deformations (c).
• Figure 2: Our method for bounded biharmonic weights BBW:2011 works on poorly behaved geometry such as the challenging Gear mesh (a). We visualize quantities as colors on a planar slice through the volume. The mesh does not self-intersect, as evidenced by the generalized winding number Jacobson2013Winding (b). Solving for BBW using on a tetrahedral mesh from FastTetWildftetwild with default parameters results in weights bleeding over boundaries and discretization artifacts (c). Modifying FastTetWild's parameters to respect boundaries increases computation time to $\mathbf{1.78}$hours. In comparison, our weights are smooth, respect boundaries, and can be computed without tetrahedralization in $\mathbf{32.2}$ seconds (d).
• Figure 3: On well behaved meshes, our method is faster than BBW and somewhat slower than QHW (left). On meshes requiring robust tetrahedralization, our method succeeds in all test cases, whereas existing alternatives either fail to produce a solution or are up to orders of magnitude slower (right).
• Figure 4: We demonstrate the effects of our visibility-aware kernel on the Crocodile mesh. On the left, skinning weights optimized using $k_\textsc{e}$ exhibit undesirable bleeding artifacts. On the right, we can see that optimizing for skinning weights using $k_\textsc{rt}$ mitigates the issue.
• Figure 5: We combine the popular painting interface with our optimization method via Dirichlet boundary conditions. Our method quickly generates an initial solution (a). The ears and eyes of the Goosemoose mesh are disconnected as there is no path through the shape's interior that reaches them from any of the control handles. After inspection, the user can paint on skinning weights on a small subset of the boundary (b). The optimization then resumes, incorporating user-specified weights as Dirichlet boundary conditions (c, d).

Theorems & Definitions (4)

• Remark : Barycentric coordinates
• proposition 1
• proof
• Remark : bias