Skinning improvement: Dual Quaternion

• Second idea: Use of dual quaternion
• • \(\hat q = q_0 + \epsilon \,q_\epsilon\;\), \(\;\;\epsilon\) dual element.

• Dual quaternion = generalization of quaternion to handle rigid transformation
• • Rotation + translation

• Unit dual quaternion models rigid transformation as screw motions
• • = rotation about an axis followed by a translation in the direction of this axis

LBS

\(\Rightarrow\)

DQS