Automatic Skinning using the Mixed Finite Element Method

TL;DR

This work tackles physics-based character skinning without laborious weight painting by introducing a mixed finite element skinning (MFEM) framework that adds per-element rotation $R_k$ and symmetric deformation $S_k$ variables. By coupling these variables to rig handles and formulating a constrained energy, the method yields a condensed, linear system solvable in a single step per frame for quadratic energies such as ARAP and Co-rotated elasticity, enabling interactive performance. Key contributions include processor-efficient, artifact-reducing skinning, support for heterogeneous materials and collision response, and a practical rotation-clustering strategy that integrates seamlessly with artist workflows. The approach offers a flexible, physics-based alternative to traditional weight-driven skinning with potential for GPU acceleration to close remaining performance gaps while enabling detailed, volume-preserving deformations in real-time pipelines.

Abstract

In this work, we show that exploiting additional variables in a mixed finite element formulation of deformation leads to an efficient physics-based character skinning algorithm. Taking as input, a user-defined rig, we show how to efficiently compute deformations of the character mesh which respect artist-supplied handle positions and orientations, but without requiring complicated constraints on the physics solver, which can cause poor performance. Rather we demonstrate an efficient, user controllable skinning pipeline that can generate compelling character deformations, using a variety of physics material models.

Figures (8)

• Figure 1: Pinning vertices without offset vector will introduce undesired deformation in neutral shape (left) - and Pinning vertices with offset produce a fine result.
• Figure 2: Left: Flour sack pose in our interactive preview application. Right: Flour sack surface mesh overlaid with wrapped rendering surface.
• Figure 3: Using vertex constraints to couple standard finite element method to a rig leads to artifacts due to under- (left) or over-constraining (center) the discretization. Our method avoids these issues with the additional advantage of requiring only a single linear system solve.
• Figure 4: Clustering rotations of tetrahedron by the closest distance to joint produces unnatural deformation at hip and left-leg (left) - using closest distance to each bone segment for rotation clusters gives plausible result (middle) - user can also define rotation clusters on their own (right) which produces similar result as closest bone distance.
• Figure 5: Using different material models with our method yields signficantly more natural deformations for the back, shoulders and lower body than standard linear blend skinning.