Forward and Inverse Kinematics Seamless Matching Using Jacobian
  In this paper the problem of matching Forward Kinematics (FK) motion of a 3 Dimensional (3D) joint chain to the Inverse Kinematics (IK) movement and vice versa has been addressed. The problem lies at the heart of animating a 3D character having controller and manipulator based rig for animation within any 3D modeling and animation software. The seamless matching has been achieved through the use of pseudo-inverse of Jacobian Matrix. The Jacobian Matrix is used to determine the rotation values of each joint of character body part such as arms, between the inverse kinematics and forward kinematics motion. Then moving the corresponding kinematic joint system to the desired place, automatically eliminating the jumping or popping effect which would reduce the complexity of the system. 
Zeeshan Bhatti, Asadullah Shah, Farruh Shahidi, Mostafa Karbasi
cs.GR