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Fast Complementary Dynamics via Skinning Eigenmodes
Otman Benchekroun, Jiayi Eris Zhang, Siddhartha Chaudhuri, Eitan Grinspun, Yi Zhou, Alec Jacobson
Fast complementary dynamics simulation using skinning eigenmodes as a reduced subspace for secondary jiggle effects on skinned characters.
Abstract
We propose a reduced-space elastodynamic solver that is well suited for augmenting rigged character animations with secondary motion. At the core of our method is a novel deformation subspace based on Linear Blend Skinning that overcomes many of the shortcomings prior subspace methods face. Our skinning subspace is parameterized entirely by a set of scalar weights, which we can obtain through a small, material-aware and rig-sensitive generalized eigenvalue problem. The resulting subspace can easily capture rotational motion and guarantees that the resulting simulation is rotation equivariant. We further propose a simple local-global solver for linear co-rotational elasticity and propose a clustering method to aggregate per-tetrahedra nonlinear energetic quantities. The result is a compact simulation that is fully decoupled from the complexity of the mesh.
How to read this
- Category
- Method: reduced-space elastodynamics for secondary motion
- Contributions
- A reduced-space solver that adds secondary motion to rigged character animation
- A Linear Blend Skinning deformation subspace from a material-aware, rig-sensitive generalized eigenvalue problem, giving rotation equivariance
- A local-global solver for co-rotational elasticity plus per-tet clustering for a compact simulation decoupled from mesh complexity
- Context
- Advances complementary/secondary dynamics, building on Complementary Dynamics (zhang-complementary-dynamics-2020) and the skinning-subspace ideas of Fast Automatic Skinning Transformations (jacobson-fast-auto-skinning-2012).Builds on: Fast Automatic Skinning Transformations · Complementary Dynamics
- Correctness
- The subspace is parameterized by scalar skinning weights, which yields rotation equivariance and compactness; as a reduced model it trades full-space accuracy for speed, so fidelity is bounded by the chosen eigenmode subspace and clustering.
- Clarity
- Technical; a first pass conveys the subspace-and-secondary-motion idea, but the eigenproblem and local-global solver need a second and likely third pass.
- How to read it
- Focus first on what the skinning-eigenmode subspace buys (rotation equivariance, mesh-decoupled cost); plan a second pass on the generalized eigenvalue problem and a third on the local-global solver if you intend to implement it.
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