As Rigid As Possible (ARAP) Solution
- Minimize the following term
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- \(\displaystyle E = \sum_{i=0}^{N-1} \|\delta(q_i)- R(q_i) \,\delta(p_i)\|^2 + \omega\,\sum_{i\in C} \|q_i-c_i\|^2\)
- Problem: \(R(q_i)\) is a non linear function of \(q_i\)
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- \(E\) is non quadratic, cannot use least square.
- Idea: Interleave and iterate on these two steps
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- Find optimal rotation \(R(q_i)\) with fixed \(q_i\)
- Find \(q_i\) optimizing \(E\) with fixed \(R(q_i)\)
- Gain: Surface rotates during deformation
- Limit: Slightly more costly
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- Iterations + polar decomposition
