- Linear Blend Skinning (LBS): Linear interpolation of positions between associated frames
- Example at middle vertex position of a bending cylinder
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- \(p=0.5\,p_{|b1}+0.5\,p_{|b2}\)
- \(p=0.5\,\underbrace{\mathrm{T}_1\,(\mathrm{T}_1^0)^{-1}}_{\mathrm{M}_1}\, p^0+0.5\,\underbrace{\mathrm{T}_2\,(\mathrm{T}_2^0)^{-1}}_{\mathrm{M}_2}\,p^0\)
- \(p=(0.5\,\mathrm{M}_1+0.5\,\mathrm{M}_2)\,p^0\)
- Can be generalized to arbitrary interpolation between two bones
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- \(p = \alpha\, p_{|b1} + (1-\alpha)\,p_{|b2}= \left(\alpha \mathrm{M}_1 + (1-\alpha)\,\mathrm{M}_2\right)\,p^0\)
- \(\alpha\): skinning weights
- Can be generalized to any number of bones
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\(\displaystyle p = \sum_{k=0}^{N-1} \alpha_k\;p_{|bk} = \left(\sum_{k=0}^{N-1} \alpha_k \, \mathrm{M}_k\right)\,p^0 \)\(\,\), \(\;\;\displaystyle \sum_k \alpha_k=1\)
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