1
play

1 Articulated Figures Inverse Kinematics Articulated Figures - PDF document

Mar 10, 2023 •383 likes •433 views

Summary and Outline Summary and Outline Foundations of Computer Graphics Foundations of Computer Graphics Inverse Kinematics Lecture (Spring 2010) (Spring 2010) CS 294-13 Advanced Graphics in the fall CS 184, Lecture 25: Inverse

  1. Summary and Outline Summary and Outline Foundations of Computer Graphics Foundations of Computer Graphics  Inverse Kinematics Lecture (Spring 2010) (Spring 2010)  CS 294-13 Advanced Graphics in the fall CS 184, Lecture 25: Inverse Kinematics  Course Evaluations http://inst.eecs.berkeley.edu/~cs184  Best of luck for HW 5, Final Many slides courtesy James O’Brien Forward Kinematics Joints Forward Kinematics Joints  Joints (typically not 6 DOF)  Pin – rotate about one axis  Ball – arbitrary rotation  Prism – translate alone one axis Pin and Ball Joint Pin and Ball Joint Prism Joint Prism Joint  Translate inboard joint to local origin  Translate inboard joint to local origin  Rotate about axis (for pin), arbitrary (for ball)  Translate along axis  Translate origin to location of joint on outboard  Translate origin to location of joint on outboard 1

  2. Articulated Figures Inverse Kinematics Articulated Figures Inverse Kinematics  Composite transformations up the hierarchy Inverse Kinematics 2 Segment Arm in 2D Inverse Kinematics 2 Segment Arm in 2D Egon Pasztor Direct IK Direct IK Difficult Issues Difficult Issues  Analytically solve for parameters (not general)  Multiple configurations distinct in config space  Or connected in config space 2

  3. Infeasible Regions Numerical Solution Infeasible Regions Numerical Solution  Start in some initial config. (previous frame)  Define error metric (goal pos – current pos)  Compute Jacobian with respect to inputs  Use Newton’s or other method to iterate  General principle of goal optimization Back to 2 Segment Arm Back to 2 Segment Arm Jacobians and Configuration Space Jacobians and Configuration Space Solving for Joint Angles Solving for Joint Angles Issues Issues  Jacobian not always invertible  Use an SVD and pseudo-inverse  Iterative approach, not direct  The Jacobian is a linearization, changes  Practical implementation (see longer slides)  Analytic forms for prism, ball joints  Composing transformations  Or quick and dirty: finite differencing  Cyclic coordinate descent (each DOF one at a time) 3

  4. Next Semester Wrap Up Next Semester Wrap Up  CS 294-13 (maybe CS 283) Advanced Graphics  Good luck on HW 5 and Final  Follow-on of this course, discuss current research  Great teaching the course; hope to see more of  Take it if did well and enjoyed 184, want to learn more some of you next semester and beyond  Or are considering industry or graduate school in area  Course Evaluations  Tentative Topics / Assignments  Scores taken seriously in instructor evaluations  Path Tracer  Comments feedback important for future iterations  Real-Time or Image-Based Rendering  Subdivision Surfaces  Have a great end of semester  Physical Simulation  http://inst.eecs.berkeley.edu/~cs294-13/fa09  Daniel’s path tracer 4

Recommend

More recommend