Dual Quaternion Skinning (DQS)

• 1- Encode rigid transformation \((q^i,t^i)\) into dual quaternion
• • \(\displaystyle \hat q^i = q^i_0 + \frac{\epsilon}{2} q^i_t\,q^i_0 \) , \(\;\;q^i_t=(t^i_x,t^i_y,t^i_z,0)\)

• 2- Compute blending in the dual quaternion space (ScLERP)
• • \(\displaystyle \hat q' = \sum_i\,\omega_i\;\hat q^i = q'_0+\epsilon\, q'_\epsilon\)

• 3- Extract components \((q,t)\) from \(\hat q'\)
• • - \(q=q'_0/\|q_0'\|\)
  • - \((t_x,t_y,t_z,0)=2\,q'_\epsilon\,q^\star\)

• 4- Apply finaly the transformation \((q,t)\) to position \(p_0\)

• Skinning with Dual Quaternions. Kavan et al. I3D, 2007

LBS

DQS

LBS

DQS