Multi-target blending and blend shapes
- The standard for facial animation
- Full blend shape
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- - Per-vertex formulation \(p^i(t)=\sum_k \omega_k(t) \, b^i_k\)
- - Matrix formulation \({\bf p}(t)=\mathrm{B}\,{\bf \omega}(t)\)
- Differential representation
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- - Per-vertex formulation \(p^i(t)=b_0^i+\sum_k \omega_k(t)\, (\underbrace{b_k^i-b_0^i}_{d_k^i})\)
- - Matrix formulation \({\bf p}(t)={\bf b_0}+\mathrm{D}\,\mathbf{\omega}(t)\)
- \(\Rightarrow\) Allows expression transfert (keep same \(\mathrm{D}\) for different \({\bf b_0}\)).
- Problems:
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- - \(D\) is not an orthogonal matrix (non unique combination, redundancies) \(\Rightarrow\) decomposition PCA, etc.
- - How to directly manipulate blend shapes
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