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Animation
CS 551 / 651
Final Review
Homework review
1) Big oh complexity of pseudoinverse
•
Compute Jacobian
–
Analytically… O(n)
–
Finite Differences… O(n2)
n - Foreach joint
1 - perturb joint
n - compute new end effector pos by
multiplying down kinematic chain
Homework review
Big oh complexity of pseudoinverse
•
Compute Jacobian
–
Analytically… O(n)
–
Finite Differences… O(n)
n - Foreach joint
1 - perturb joint
1 - compute new end effector pos by
substituting in precomputed matrix
Homework review
Computing pseudoinverse
• J=3xn
• J+ = (JT J)-1 JT = O (n2)
• J+ = JT (JJT)-1 = O (1)
Matrix mult: [n x m] [ m x o] = O (n*m*o)
Matrix invert: [n x n] = O (n3)  O (n2 log n)
Assignments 3 and 4
Discussion
Grading
Thursday 12:00 – 2:30
Friday
2:00 – 4:00
Logistics
Exam will be released Monday at 7:00 p.m.
• Electronically available (not sure how yet so check your email)
• Programming may be required
Exam must be returned by following Monday at
9:00 a.m.
You have 24 contiguous hours to work on the
exam
Test-taking materials
You can use any materials except your
classmates during the exam
Be mindful that others may be taking the
exam later than you and you shouldn’t be
overheard talking about your answers
Content
Everything during the semester
• The class web page is very complete
• Emails I’ve sent to the class
– Through the lens
– Q & A about specific papers
• Programming Assignments
General nature of exam
Open-ended questions are impossible to grade
because there is no one right answer and
allocating partial credit is difficult
• How would you implement this…
• Why is technique A better than technique B
Questions will be more focused on details
• Explain what effect a has in paper Foo
• What technical element sets papers Foo and Bar apart?
Why is that important?
Major topics
Physical Simulation
• Hecker articles (Assignment 1)
• Numerical integration
• Sources of error (class lectures)
• Speedup (Mirtich, Chenney-99, Popovic)
Major topics
Controllers
• Optimal (Chenney-00, Gleicher-92, Witkin, Grzeszczuk,
Popovic,)
• Learning reactive controllers
– Offline trial and error (Stone, Sims)
– User-guided (Metoyer)
• Design methodologies (Blumberg)
• Multiagent (Reynolds, Helbing)
• Assignments 3-4
Major topics
Data-driven Animation
• Markov chain (Schodl, Kovar, Lee)
• Reusing (Gleicher-98, Metoyer)
• Generalizing (Grzeszczuk)
• Clean-up (O’Brien)
Major topics
Inverse Kinematics
• Class lectures (Brogan and O’Brien)
• Handouts (Parent and Numerical Recipes)
• Assignment 2
Major Topics
Optimization
• Spacetime constraints (Gleicher-92, Witkin, Popovic,
Gleicher-98)
• Neural Networks (Grzeszczuk, Chenney-99)
• Markov Chain Monte Carlo (Chenney-00)
• Least squares (O’Brien)
• Lagrangian (Gleicher-92)
• Genetic algorithms (Kass)
Major topics
Optimization (cont.)
• Dynamic Programming (Schodl)
• Strongly Connected Components (Kovar, Lee)
• Bayesian Classification (Metoyer)
• A* (Pinter)
• Reinforcement Learning (Stone)
Major topics
Perception
• Human motion (Hodgins)
• Using head-mounted displays (Banton, Thompson)
Major Topics
Biomechanics
• Swinging (Walker)
• Bicycling (Jones)
• Walking (articles from Nature)