Details of rotations that we didn’t get to last time
Quaternions
- multiply
- single axis
- anti-podal equivalence
- multiple different zeros
Log Map
- the derivative of a unit quaternion is a vector in 3 space
- S(3) –> R(3)
- Local linearization
Interpolation
- SLERP
- NLERP
- log map interpolation
- Multi-Way averaging?
- using the log map
- how to pick the center?
- iterate?
- optimize?
Quaternion Splines
- Construction by SLERP
- Bezier construction
- Doesn’t work (not commutative)
- do in log map space?
- need to be careful about choice of “center”
Filtering Quaternions Curves
- Jehee Lee and Sung Yong Shin, General Construction of Time-Domain Filters for Orientation Data, IEEE Transactions on Visualization and Computer Graphics, volume 8, number 2, 119-128, 2002.
PDF (214K) - find the deltas between steps (q^-1 (j) * q(j+1))
- log map those (since they are velocities)
- center of filter is the zero point
- filter of the log map of the deltas gives how to change the center point
- needs a little bit of redesign to the filters
Human Motion
- Levels of Abstraction
- Skeletons vs. Rigid Segments vs. Joint Clouds vs. Point Clouds
- more anatomical joints
- degrees of freedom per joint
Issues in skeletal structures
- Describing hierarchies with offsets
- zero poses
- T-Pose vs. Frankenstein vs. Dress Pose vs. …
- ZXY Euler angles
Motion
- Representations
- Ways to create
- Artistic
- Pure Hack (a form of artistry)
- From Example (a different form of artistry)
- From Physics / Control / Principles
- Usefulness of motions in different settings
- Usefulness with different skeletons
- Different environments
- Re-Targeting
Conceptual Math
- Latent spaces
- Pose space vs. “natural pose space”
- Motion space
- Metrics for pose space / Metrics for motion space
- a little off the ground (is far)
- just distance only works in some cases (and close by)
