Complementary Dynamics

How to read this

Category

Method: a secondary-dynamics simulation technique

Contributions

• Adds elastodynamic secondary motion by optimizing displacements in the subspace orthogonal to those the rig can produce, so dynamics never undo the rig
• Constructs this high-dimensional complementary space algebraically without manual weights, segmentation, or tracking clusters
• Works model-agnostically with nonlinear FEM, as-rigid-as-possible energies, or mass-spring models, and across skeletal, cage, wire, mocap, and rigid-body rigs

Context

Reframes rig-aware physics, succeeding tracking-style approaches like Hahn et al.'s 'Rig-Space Physics', by making physics complement rather than compete with the artist's rig.Builds on: Rig-Space Physics

Correctness

Key assumption is that artist intent lives entirely in the rig subspace so dynamics should be confined to its orthogonal complement; broadly demonstrated across rig and physics-model types, though the result is only as expressive as the chosen rig parameterization and physical energy.

Clarity

Conceptually clean but mathematically dense; a first pass conveys the orthogonal-subspace idea, a second pass is needed for the constraint formulation.

How to read it

Focus on the orthogonal-complement construction and the 'complement, not compete' framing; a second pass into the optimization is worthwhile if you implement secondary dynamics.