程序代写代做代考 algorithm lec20.key

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:
• FadBad++
• 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