Dual Quaternion Skinning (DQS)

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

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

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

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

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

LBS

DQS

LBS

DQS