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Motion Synthesis By Example
A Tutorial in 3 and 3/2 parts
Michael Gleicher
Dept of Computer SciencesUniversity of Wisconsin - Madison
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How to Represent a Pose?
Foundations:
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Modeling Humans• Humans are complex!
Human motion can be understood at a very fine level
of detail!
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Abstractions
206 bones, muscles, fat,
organs, clothing, …
206 bones, complex joints
53 bonesKinematic joints
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Complexities of Skeletal Representation
• Abstraction• Don't know parameters• Need to know skeleton and relation of skeleton to
markers
Can't just measure
(even x-rays wouldn't help, no real "joints")
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Abstractions vs. Reality (skeletons vs. humans)
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Representations of 2 bodies
Hierarchical: Relative OrientationFixed Relative Position
Independent: Absolute OrientationAbsolute Position
Position Only
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Ease of manipulation
Hierarchical: Relative OrientationFixed Relative Position
Independent: Absolute OrientationAbsolute Position
Position Only
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Alternative Representations
An Aside…
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Mesh of points
Ho, Komura, Tai. Spatial Relationship Preserving Character Motion Adaptation. SIGGRAPH 2010.
Preserve Distances using Mesh Editing techniques
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MKM: A non-hierarchical approach
• Richard Kulpa, Franck Multon and others
• Several papers
• Multon, Kulpa, Bideau. MKM: A Global Framework for Animating Humans in Virtual Reality Applications. Presence. 17 (1) 2008.
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Points + Distances
• Others (particularly in the game industry)
• Cormac O'Brien, John Dingliana, Steven Collins. Spacetime Vertex Constraints for Dynamically-based Adaptation of Motion-Captured Animation. SCA 2011.
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• James, Twigg, Cove, Wang. Mesh Ensemble Motion Graphs: Data-driven Mesh Animation with Constraints. SIGGRAPH Asia 2008.
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Back to Skeletons
206 bones, muscles, fat,
organs, clothing, …
206 bones, complex joints
53 bonesKinematic joints
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Skelletal Representation
• One position
• One global orientation
• One relative orientation per joint
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Why hierarchical skeletons?
They are the standard
• Enforce constraints– Stretching
– Connection
• Methods for orientations– Compact
• Tie to fast drawing (skins)
• Easy forward kinematics
There are challenges
• Can’t go beyond constraints– Biomechanic adaptations
– Cartooning / Fudging
• Orientations are hard!– Some things tricky
• Not general controls
• Hard inverse kinematics
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Rigid Bodies
• Does not deform
• Idealization
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Rigid Kinematics
• Translation
• Rotation
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Rotations and Orientations
Orientations
• Configuration
Rotations
• Transformation
0 30 60 90 30 30 30
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Should we care?
No
• Rotation from zero
• It’s a mathematical detail
• People are usually sloppy
Yes – they are different
Rotations (not orientations)
• Wrap around
• Scalar multiply
• Addition
• Linear combinations
Use different parameterizations for each! (Jehee Lee)Representing Rotations and Orientations in Geometric Computing, CG&A. March 2008
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What is a Rotation Anyway?and how do we parameterize them?
• Transformation Rn -> Rn
• F(x) -> x’
• Rigid |a-b| = | F(a)-F(b) |
• Has a zero F(0) = 0
• Preserves Handedness
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Mathematics of Rotations
• Special Orthogonal Groups
• Rotation Vectors
• Rotation Matrices
• Logarithmic Maps / Exponential Maps
• Matrix Exponentials
• Quaternions
• Logarithmic Coordinates
• ….
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Attempt Dynamic Presentation
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