AnimationCS 551 / 651

Final ReviewFinal ReviewFinal ReviewFinal Review

Homework review

1)1) Big oh complexity of pseudoinverseBig oh complexity of pseudoinverse

• Compute JacobianCompute Jacobian

– Analytically… O(n)Analytically… O(n)

– Finite Differences… O(nFinite Differences… O(n22))

nn - Foreach joint - Foreach joint

11 - perturb joint - perturb joint

nn - compute new end effector pos by - compute new end effector pos bymultiplying down kinematic multiplying down kinematic

chainchain

1)1) Big oh complexity of pseudoinverseBig oh complexity of pseudoinverse

• Compute JacobianCompute Jacobian

– Analytically… O(n)Analytically… O(n)

– Finite Differences… O(nFinite Differences… O(n22))

nn - Foreach joint - Foreach joint

11 - perturb joint - perturb joint

nn - compute new end effector pos by - compute new end effector pos bymultiplying down kinematic multiplying down kinematic

chainchain

Homework review

Big oh complexity of pseudoinverseBig oh complexity of pseudoinverse

• Compute JacobianCompute Jacobian

– Analytically… O(n)Analytically… O(n)

– Finite Differences… Finite Differences… O(n)O(n)

n - Foreach jointn - Foreach joint

1 - perturb joint1 - perturb joint

1 - compute new end effector pos by1 - compute new end effector pos bysubstituting in precomputed substituting in precomputed

matrixmatrix

Big oh complexity of pseudoinverseBig oh complexity of pseudoinverse

• Compute JacobianCompute Jacobian

– Analytically… O(n)Analytically… O(n)

– Finite Differences… Finite Differences… O(n)O(n)

n - Foreach jointn - Foreach joint

1 - perturb joint1 - perturb joint

1 - compute new end effector pos by1 - compute new end effector pos bysubstituting in precomputed substituting in precomputed

matrixmatrix

Homework review

Computing pseudoinverseComputing pseudoinverse

• J = 3 x nJ = 3 x n

• JJ+ + = (J= (JTT J) J)-1-1 J JT T = O (n= O (n22))

• JJ++ = J = JTT (JJ (JJTT))-1 -1 = O (1)= O (1)

Matrix mult: [n x m] [ m x o] = O (n*m*o)Matrix mult: [n x m] [ m x o] = O (n*m*o)

Matrix invert: [n x n] = O (nMatrix invert: [n x n] = O (n33) ) O (n O (n2 2 log n)log n)

Computing pseudoinverseComputing pseudoinverse

• J = 3 x nJ = 3 x n

• JJ+ + = (J= (JTT J) J)-1-1 J JT T = O (n= O (n22))

• JJ++ = J = JTT (JJ (JJTT))-1 -1 = O (1)= O (1)

Matrix mult: [n x m] [ m x o] = O (n*m*o)Matrix mult: [n x m] [ m x o] = O (n*m*o)

Matrix invert: [n x n] = O (nMatrix invert: [n x n] = O (n33) ) O (n O (n2 2 log n)log n)

Assignments 3 and 4

DiscussionDiscussion

GradingGrading

Thursday 12:00 – 2:30Thursday 12:00 – 2:30

Friday 2:00 – 4:00Friday 2:00 – 4:00

DiscussionDiscussion

GradingGrading

Thursday 12:00 – 2:30Thursday 12:00 – 2:30

Friday 2:00 – 4:00Friday 2:00 – 4:00

Logistics

Exam will be released Monday at 7:00 p.m.Exam will be released Monday at 7:00 p.m.• Electronically available (not sure how yet so check your email)Electronically available (not sure how yet so check your email)

• Programming may be requiredProgramming may be required

Exam must be returned by following Monday at Exam must be returned by following Monday at 9:00 a.m.9:00 a.m.

You have 24 contiguous hours to work on the You have 24 contiguous hours to work on the examexam

Exam will be released Monday at 7:00 p.m.Exam will be released Monday at 7:00 p.m.• Electronically available (not sure how yet so check your email)Electronically available (not sure how yet so check your email)

• Programming may be requiredProgramming may be required

Exam must be returned by following Monday at Exam must be returned by following Monday at 9:00 a.m.9:00 a.m.

You have 24 contiguous hours to work on the You have 24 contiguous hours to work on the examexam

Test-taking materials

You can use any materials except your You can use any materials except your classmates during the examclassmates during the exam

Be mindful that others may be taking the Be mindful that others may be taking the exam later than you and you shouldn’t be exam later than you and you shouldn’t be

overheard talking about your answersoverheard talking about your answers

You can use any materials except your You can use any materials except your classmates during the examclassmates during the exam

Be mindful that others may be taking the Be mindful that others may be taking the exam later than you and you shouldn’t be exam later than you and you shouldn’t be

overheard talking about your answersoverheard talking about your answers

Content

Everything during the semesterEverything during the semester

• The class web page is very completeThe class web page is very complete

• Emails I’ve sent to the classEmails I’ve sent to the class

– Through the lensThrough the lens

– Q & A about specific papersQ & A about specific papers

• Programming Assignments Programming Assignments

Everything during the semesterEverything during the semester

• The class web page is very completeThe class web page is very complete

• Emails I’ve sent to the classEmails I’ve sent to the class

– Through the lensThrough the lens

– Q & A about specific papersQ & A about specific papers

• Programming Assignments Programming Assignments

General nature of exam

Open-ended questions are impossible to grade Open-ended questions are impossible to grade because there is no one right answer and because there is no one right answer and allocating partial credit is difficultallocating partial credit is difficult

• How would you implement this…How would you implement this…

• Why is technique A better than technique BWhy is technique A better than technique B

Questions will be more focused on detailsQuestions will be more focused on details

• Explain what effect Explain what effect has in paper has in paper FooFoo

• What technical element sets papers What technical element sets papers Foo Foo and and Bar Bar apart? apart? Why is that important?Why is that important?

Open-ended questions are impossible to grade Open-ended questions are impossible to grade because there is no one right answer and because there is no one right answer and allocating partial credit is difficultallocating partial credit is difficult

• How would you implement this…How would you implement this…

• Why is technique A better than technique BWhy is technique A better than technique B

Questions will be more focused on detailsQuestions will be more focused on details

• Explain what effect Explain what effect has in paper has in paper FooFoo

• What technical element sets papers What technical element sets papers Foo Foo and and Bar Bar apart? apart? Why is that important?Why is that important?

Major topics

Physical SimulationPhysical Simulation

• Hecker articles (Assignment 1)Hecker articles (Assignment 1)

• Numerical integrationNumerical integration

• Sources of error (class lectures)Sources of error (class lectures)

• Speedup (Mirtich, Chenney-99, Popovic)Speedup (Mirtich, Chenney-99, Popovic)

Physical SimulationPhysical Simulation

• Hecker articles (Assignment 1)Hecker articles (Assignment 1)

• Numerical integrationNumerical integration

• Sources of error (class lectures)Sources of error (class lectures)

• Speedup (Mirtich, Chenney-99, Popovic)Speedup (Mirtich, Chenney-99, Popovic)

Major topics

ControllersControllers

• Optimal (Chenney-00, Gleicher-92, Witkin, Grzeszczuk, Optimal (Chenney-00, Gleicher-92, Witkin, Grzeszczuk, Popovic,)Popovic,)

• Learning reactive controllersLearning reactive controllers

– Offline trial and error (Stone, Sims)Offline trial and error (Stone, Sims)

– User-guided (Metoyer)User-guided (Metoyer)

• Design methodologies (Blumberg)Design methodologies (Blumberg)

• Multiagent (Reynolds, Helbing) Multiagent (Reynolds, Helbing)

• Assignments 3-4Assignments 3-4

ControllersControllers

• Optimal (Chenney-00, Gleicher-92, Witkin, Grzeszczuk, Optimal (Chenney-00, Gleicher-92, Witkin, Grzeszczuk, Popovic,)Popovic,)

• Learning reactive controllersLearning reactive controllers

– Offline trial and error (Stone, Sims)Offline trial and error (Stone, Sims)

– User-guided (Metoyer)User-guided (Metoyer)

• Design methodologies (Blumberg)Design methodologies (Blumberg)

• Multiagent (Reynolds, Helbing) Multiagent (Reynolds, Helbing)

• Assignments 3-4Assignments 3-4

Major topics

Data-driven AnimationData-driven Animation

• Markov chain (Schodl, Kovar, Lee)Markov chain (Schodl, Kovar, Lee)

• Reusing (Gleicher-98, Metoyer)Reusing (Gleicher-98, Metoyer)

• Generalizing (Grzeszczuk)Generalizing (Grzeszczuk)

• Clean-up (O’Brien)Clean-up (O’Brien)

Data-driven AnimationData-driven Animation

• Markov chain (Schodl, Kovar, Lee)Markov chain (Schodl, Kovar, Lee)

• Reusing (Gleicher-98, Metoyer)Reusing (Gleicher-98, Metoyer)

• Generalizing (Grzeszczuk)Generalizing (Grzeszczuk)

• Clean-up (O’Brien)Clean-up (O’Brien)

Major topics

Inverse KinematicsInverse Kinematics

• Class lectures (Brogan and O’Brien)Class lectures (Brogan and O’Brien)

• Handouts (Parent and Numerical Recipes)Handouts (Parent and Numerical Recipes)

• Assignment 2Assignment 2

Inverse KinematicsInverse Kinematics

• Class lectures (Brogan and O’Brien)Class lectures (Brogan and O’Brien)

• Handouts (Parent and Numerical Recipes)Handouts (Parent and Numerical Recipes)

• Assignment 2Assignment 2

Major Topics

OptimizationOptimization• Spacetime constraints (Gleicher-92, Witkin, Popovic, Spacetime constraints (Gleicher-92, Witkin, Popovic,

Gleicher-98)Gleicher-98)

• Neural Networks (Grzeszczuk, Chenney-99) Neural Networks (Grzeszczuk, Chenney-99)

• Markov Chain Monte Carlo (Chenney-00)Markov Chain Monte Carlo (Chenney-00)

• Least squares (O’Brien)Least squares (O’Brien)

• Lagrangian (Gleicher-92)Lagrangian (Gleicher-92)

• Genetic algorithms (Kass)Genetic algorithms (Kass)

OptimizationOptimization• Spacetime constraints (Gleicher-92, Witkin, Popovic, Spacetime constraints (Gleicher-92, Witkin, Popovic,

Gleicher-98)Gleicher-98)

• Neural Networks (Grzeszczuk, Chenney-99) Neural Networks (Grzeszczuk, Chenney-99)

• Markov Chain Monte Carlo (Chenney-00)Markov Chain Monte Carlo (Chenney-00)

• Least squares (O’Brien)Least squares (O’Brien)

• Lagrangian (Gleicher-92)Lagrangian (Gleicher-92)

• Genetic algorithms (Kass)Genetic algorithms (Kass)

Major topics

Optimization (cont.)Optimization (cont.)

• Dynamic Programming (Schodl)Dynamic Programming (Schodl)

• Strongly Connected Components (Kovar, Lee)Strongly Connected Components (Kovar, Lee)

• Bayesian Classification (Metoyer)Bayesian Classification (Metoyer)

• A* (Pinter)A* (Pinter)

• Reinforcement Learning (Stone)Reinforcement Learning (Stone)

Optimization (cont.)Optimization (cont.)

• Dynamic Programming (Schodl)Dynamic Programming (Schodl)

• Strongly Connected Components (Kovar, Lee)Strongly Connected Components (Kovar, Lee)

• Bayesian Classification (Metoyer)Bayesian Classification (Metoyer)

• A* (Pinter)A* (Pinter)

• Reinforcement Learning (Stone)Reinforcement Learning (Stone)

Major topics

PerceptionPerception

• Human motion (Hodgins)Human motion (Hodgins)

• Using head-mounted displays (Banton, Thompson)Using head-mounted displays (Banton, Thompson)

PerceptionPerception

• Human motion (Hodgins)Human motion (Hodgins)

• Using head-mounted displays (Banton, Thompson)Using head-mounted displays (Banton, Thompson)

Major Topics

BiomechanicsBiomechanics

• Swinging (Walker)Swinging (Walker)

• Bicycling (Jones)Bicycling (Jones)

• Walking (articles from Nature)Walking (articles from Nature)

BiomechanicsBiomechanics

• Swinging (Walker)Swinging (Walker)

• Bicycling (Jones)Bicycling (Jones)

• Walking (articles from Nature)Walking (articles from Nature)