lec20.key
© 2017 Changxi Zheng
COMS W4160
Computer Graphics
Changxi Zheng
Spring 2017
Columbia CS W4160 Spring 2017
Lecture-20
© 2017 Changxi Zheng
Inverse Kinematics
© 2017 Changxi Zheng
How to Compute the Jacobian?
© 2017 Changxi Zheng
• Analytical differentiation
• Numerical computation
• Auto differentiation:
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• http://www.fadbad.com/fadbad.html
How to Compute the Jacobian?
http://www.fadbad.com/fadbad.html
© 2017 Changxi Zheng
IK Algorithm Outline
• user changes the positions of the effectors (character
bones)
• iteration:
• compute Jacobian
• construct
• solve for
• update
• update forward kinematics based on solved
s(✓ +�✓)� s(�) ⇡ J�✓
�✓
✓ ✓ +�✓
✓
© 2017 Changxi Zheng
IK Algorithm Outline
• user changes the positions of the effectors (character
bones)
• iteration:
• compute Jacobian
• construct
• solve for
• update
• update forward kinematics based on solved
s(✓ +�✓)� s(�) ⇡ J�✓
�✓
✓ ✓ +�✓
✓
© 2017 Changxi Zheng
Update
• Solve the linear system
• Might have multiple solution. Use regularization:
• This amounts to solving a squared linear system.
Minimize