Direct Skinning Methods and Deformation Primitives Ladislav Kavan - PowerPoint PPT Presentation

Stretchable and twistable bones [Jacobson and Sorkine 2011] Standard skinning transforms don’t stretch well 74

Stretching results in shape explosion 75

Twisting must be packed at joints 76

Solution: endpoint weights [Jacobson and Sorkine 2011] 0 1 77

Stretchable and twistable bones [Jacobson and Sorkine 2011] 78

Stretchable and twistable bones [Jacobson and Sorkine 2011] 79

How to fix dual quaternion bulging? 80

Joint-based deformers [Kavan and Sorkine 2012] x z y 81

Joint-based deformers [Kavan and Sorkine 2012] 𝑆 3 → 𝑆 3 82

Joint-based deformers [Kavan and Sorkine 2012] 𝑇𝑃 3 × 𝑆 3 → 𝑆 3 83

Joint-based deformers [Kavan and Sorkine 2012] Γ: 𝑇𝑃 3 × 𝑆 3 → 𝑆 3 Γ 𝑹, 𝒚 = 𝒚′ 84

Individual deformers blended linearly x z Γ 𝑓𝑚𝑐𝑝𝑥 y 85

Individual deformers blended linearly x z Γ 𝑓𝑚𝑐𝑝𝑥 y 86

Individual deformers blended linearly x z Γ 𝑡ℎ𝑝𝑣𝑚𝑒𝑓𝑠 y 87

Weights of bone-based deformers 88

Weights of bone-based deformers 89

Weights of joint-based deformers 90

Weights of joint-based deformers 91

Swing/twist deformer [Kavan and Sorkine 2012] LBS DQS 92

Swing/twist deformer [Kavan and Sorkine 2012] Γ 𝑹, 𝒚 𝑹 = 𝑹 𝑡𝑥𝑗𝑜𝑕 𝑹 𝑢𝑥𝑗𝑡𝑢 x x z’ z z y y swing twist 93

Swing/twist deformer [Kavan and Sorkine 2012] LBS DQS Swing/twist def. 94

Skinning normals 𝐍 −𝑈 𝐨 𝐨 𝐍 95

Classical solution Inverse transpose the linear part of the blended transformation 𝑛 𝑥 𝑗,𝑘 𝐔 𝑘 𝑘=1 96

This leads to inaccurate normals [Merry et al. 2006; Tarini et al. 2014] True normal Skinned normal 97

We can re-compute the normals … … but that’s not ideal, esp. on the GPUs 98

Correct skinned normals [LBS&DQS] [Merry et al. 2006; Tarini et al. 2014] Take weight gradients into account 𝑛 𝑛 𝑈 𝑥 𝑗,𝑘 𝐔 𝑘 + 𝐔 𝑘 𝐰 𝑗 𝛼𝑥 𝑗,𝑘 𝑘=1 𝑘=1 Inverse transposition can be avoided 99

Correct skinned normals [LBS&DQS] [Tarini et al. 2014] 100