Complementary dynamics

Abstract

We present a novel approach to enrich arbitrary rig animations with elastodynamic secondary effects. Unlike previous methods which pit rig displacements and physical forces as adversaries against each other, we advocate that physics should complement artists' intentions. We propose optimizing for elastodynamic displacements in the subspace orthogonal to displacements that can be created by the rig. This ensures that the additional dynamic motions do not undo the rig animation. The complementary space is high-dimensional, algebraically constructed without manual oversight, and capable of rich high-frequency dynamics. Unlike prior tracking methods, we do not require extra painted weights, segmentation into fixed and free regions or tracking clusters. Our method is agnostic to the physical model and plugs into non-linear FEM simulations, geometric as-rigid-as-possible energies, or mass-spring models. Our method does not require a particular type of rig and adds secondary effects to skeletal animations, cage-based deformations, wire deformers, motion capture data, and rigid-body simulations.

Velocity Skinning for Real-time Stylized Skeletal Animation

“…An additional limitation of the current implementation is that motion applied to the end effectors of a character will not propagate backward within the hierarchy -this effect would require dynamic adaptation of the skeleton hierarchy. Therefore, our method cannot achieve contact-like effects and IK-guided motion (contrasting further with [ZBLJ20]).…”

Multi‐scale edge aggregation mesh‐graph‐network for character secondary motion

“…The methods that solve the secondary motion of the character in the full space (coordinate space) that fully comply with the physical laws are well known for their computational complexity. 4 In recent years, a series of methods that attempt to accelerate the computation process in the subspace have been proposed, among which the acceleration methods for the skinning weight subspace have developed rapidly, including: Le et al 9 proposed a method for precomputing optimized rotation centers for skinning vertices, enabling efficient deformation calculations at runtime using these centers; an efficient method for skeletal-driven elasticity computation 10 ; formulate motion equation in the binding weight subspace of the skinning skeleton, and solve the secondary motion by minimizing the static elastic energy 11,12 ; a complementary dynamics work that can be embedded in a nonlinear finite element simulation framework 13 ; Wu et al 14 introduced a 2-step solution method for complementary subspace skinning deformations using a position-based dynamics solver, enabling interactive dynamics simulation of skinned characters. As well as the recent impressive work, 15 which proposes skinning eigenmodes, a skinning mode that computes the joint eigenvalues of the model without requiring the artist to specify the skin configuration.…”

Voronoi Filters for Simulation Enrichment

“…Other works have also used ideas similar to kinematic filters to transfer data between representations, e.g, between grids and particles [JSS*15], or between grids and rigid modes [FLLP13]. Some recent works constrain motion to the null‐space of predefined reduced spaces; some use kinematic filters to implement the constraint efficiently [SYS*21, RCPO22], while others could replace Lagrange multiplier formulations with kinematic filters for higher performance [ZBLJ20].…”