Blend shapes

• Represent deformation as a difference of coordinates with respect to neutral pose

• - Per-vertex formulation
• • \(\displaystyle p_i(t)=b^0_i+\sum_{k}^{N_{\scriptsize{poses}}} \omega_k(t)\, (\underbrace{b_{ki}-b^0_i}_{d_{ki}})\)
• - Matrix formulation \({\bf p}(t)={\bf b^0}+\mathrm{D}\,\mathbf{\omega}(t)\)

• Can add/substract local expressions (even extrapolate)
• • as long as they are not interfering/redundant

• Allows expression transfert (keep same \(\mathrm{D}\) for different faces \(b^0\)).
• • same connectivity required

• Note:
• • - \(D\) is not an orthogonal matrix (non unique combination, redundancies) \(\Rightarrow\) decomposition PCA, etc.
  • - How to directly manipulate blend shapes