We present a novel approach to enrich rig animations
with dynamic secondary effects.
Artists can use low-dimensional rigs
to control the primary motion,
and our system will enrich the results with dynamics.
The main idea is that, with a given rig deformation,
our complementary dynamics are computed
in the space orthogonal to the rig subspace.
Our method can be applied to any rig type.
The bird in this example is rigged with three bones.
Notice our method adds high frequency motions to the feathers.
They could not be achieved by moving the bones.
Here, we show a various walrus rigged with a cage
using Harmonic Coordinates.
Notice the rich details of dynamics on the body.
Our method can also add secondary effects
to non-linear rigs.
Here, we show a bar twisting and bending
with dual-quaternion skinning.
Here, we show another nonlinear rig example
of a daisy rigged with a wire deformer.
Notive how it becomes more cheerful.
Our method shows rich detail without
requiring extra rigging.
This hedgehog is rigged with two point handles 
handle with our method,
and with two additional handles for 
the Rig-Space Dynamics method.
With a smaller number of handles, our
method shows rich detail of dynamics.
Previous "embedded rigid bar" dynamics methods 
require meaningful geometric bones.
For example, with this input motion of
an elephant trunk,
the "embedded rigid bar" dynamics show
awkward kinks around the joint.
Whereas our method interprets the rig as
an action on the shape.
Our method can respond to external forces.
Here, we show an affinely rigged amoeba
reacting to wind forces. 
Even with this simple input motion
our method enriches it.
Here we show a keyframed "plumber"
reacting to contact forces with the ground.
Notice the deformation when he hits the ground.
Here we show two rigged arms punching
each other with collision forces.
Here we show how StayPuft deforms
correspondingly when it's poked by a stick.
Our method is not restricted to a specific data structure.
Here we show a simulation of a roller
coaster modeled with mass-springs.
Here we show another mass-spring example
of a flying carpet
with a keyframed animation.
Our method can be applied to heterogeneous material.
Here we show a worm with
homogeneous material in the middle row
and heterogeneous material with soft body
and stiff propeller in the bottom row.
Here we show a skeleton-rigged elephant
driven by motion capture.
Notice the deformation around the ears
and nose, and how it becomes more
energetic after our method.
Here's with a softer material. Even more energetic!
Our method can enrich rigid body simulation.
We compare our method with TRACKS simulation.
TRACKS simulation method shows poor
tracking when the cluster number is small,
but shows too stiff results when it has
too many clusters.
Our method can also enrich
rigid multi-body simulation.
We can achieve this without requiring expensive
soft-body contact simulation.
Our method can be applied to complex rigs in the wild. 
This dinosaur model is
rigged with a complex set of bones.
Despite the large rig-space, our method
still finds room for interesting secondary dynamics.
Thank you, for watching!
