Chapter 9 Animation Inverse Kinematics skinning 2001 11

Chapter 9. Animation Inverse Kinematics & skinning 2001. 11. 20 강신진 1

Contents Inverse Kinematics Skinning 2

Inverse Kinematics General Idea Forward Kinematics l Inverse Kinematics l Manipulator P 4 P 2 P 5 P 3 P 0 P 1 3

Inverse Kinematics General Idea Forward Kinematics l Inverse Kinematics l Manipulator End Effector P 4 P 2 P 5 P 3 P 0 P 1 4

Inverse Kinematics General Idea Forward Kinematics l Inverse Kinematics l Manipulator P 4 P 2 ? End Effector P 5 P 3 P 0 P 1 5

Inverse Kinematics General Idea Forward Kinematics l Inverse Kinematics l Manipulator P 2 ? P 0 ? ? ? P 4 ? End Effector P 5 P 3 P 1 6

Inverse Kinematics General Idea Forward Kinematics l Inverse Kinematics l Manipulator P 2 P 5 P 3 P 0 End Effector P 4 P 1 Many Solutions! ! 7

Typical Constraints Revolute Joint P 2 P 0 P 1 Prismatic Joint P 0 P 1 P 2 8

Manipulator Polyline starting point l Unit-length direction l Polyline terminating point l P 4 P 2 P 0 L 1 L 3 L 2 L 4 P 5 P 3 P 1 9

End Effect formula P 4 P 2 P 0 L 1 L 3 L 2 L 4 P 5 P 3 P 1 10

End Effect formula l Each direction l Calculated as as incremental rotation of the previous direction 11

Closed-Form Representation Difficult 12

Numerical Solution by Jacobian l Matrix of first-order partial Derivatives Less Difficult 13

Numerical Solution By Nonlinear Optimization Minimizing Squared Error 14

Numerical Solution by Cyclic Coordinate Descent Joint is optimized one at a time Approximation of global minimum of 15

List Manipulator with One End Effector Rotate to Point Goal: If rotation is constrained to the plane 16

List Manipulator with One End Effector Rotate to Line Goal: If rotation is constrained to the plane 17

List Manipulator with One End Effector Rotate to Plane Goal: 18

List Manipulator with One End Effector Slide to Point Goal: 19

List Manipulator with One End Effector Slide to Line Goal: Find closest point on the line Slide to Plane Goal: Find closest point on the plane 20

List Manipulator with Multiple End Effects Multiple Goal Shoulder P 2 Weighted Distance elbow hand P 0 P 1 GE GH 21

Skinning l Attaching a deformable mesh to a skeletal structure Medial Surface Medial Axis 22

Skinned Mesh attached to the bone with weight values 23

Skinned Mesh In 3 D MAX Studio 24

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