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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)