Download - Animation of 3D surfaces - Inria
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Motivations
• When character animation is controlled by “skeleton”…– set of hierarchical joints
– joints oriented by rotations
• the character shape still needs to be visible:– visible = to be rendered as a continuous shape– typically, a surface is rendered
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Motivations
• Animation of 3D surface is actually the most “practical” thing:– direct connection with modeling phase
• shape and texture
– light structure, easy to animate• possibly real-time
– works will be focused on workarounds to cope with this approximation of reality
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Overview
• “Skinning”
• Non-linear deformers
• Shape morphing
• Mesh edition
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Overview
• “Skinning ”
• Non-linear deformers
• Shape morphing
• Mesh edition
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Skinning
• Goal: bind a skeleton and a shape
P1
P2
P P
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Skinning
• Linear blend skinning
P P2 P1
P = w1*P1 + w2*P2
P
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Skinning
• Linear blend skinning
P
P
A AB
B
P = w1*P1 + w2*P2wi : [0..1], skin weights
QQ P2 P1
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Skinning
• Linear blend skinning
P0 P2P1
P = w1*P1 + w2*P2
with Pi = M0,i Mi(θ)M-10,i P0
P
M0,1 M0,2 M1
M2(θ)
θ
M : R and T
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Skinning
• Linear blend skinning
P0
P
A AB
B
P = Σi wi* M0,i Mi(θ)M-10,i P0
QQ0
Implemented as “Skin>Smooth bind” in Maya
M0,1 M0,2 M1
M2(θ)
θ
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Skinning
• Linear blend skinning
P P(θ)A AB
B
Q(θ)
θ
Q
λ λ
δ
δ
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Skinning
• Limitations
P = Σi wi* M0,i Mi M-10,i P0
= ( Σi wi* M0,i Mi M-10,i ) P0
Non-rigid transformation
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Skinning
• Improvements– Skinning as a prediction function from joint
configuration to 3D shapes
[Lewis et al., 2000]
[ θ1, V1]
[ θi, Vi]
[ θn, Vn]θ in Rm, with m joints dofV in Rp, with p mesh verticesai in Rp, n parameters
V = fa(θ) = Σi ai f(||θ - θi||)
a = argmin Σi || Vi – fa(θi) ||2
fa(θ) = Σi ai f(||θ - θi||)Radial Basis Function (RBF)
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Skinning
• Improvements– Incorporate user-defined examples of shapes and
automatically add some joints and weights in LBS
[Mohr et Gleicher, 2003]
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Skinning
• Improvements– Compute the matrix interpolation while maintaining
correct rotations, using dual quaternions
[Kavan et al., 2007]
P = Σi wi* M0,i Mi M-10,i P0
= ( Σi wi* M0,i Mi M-10,i ) P0
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Overview
• “Skinning”
• Non-linear deformers
• Shape morphing
• Mesh edition
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Non-linear deformers
• Global modification of 3D shapesthe transformation matrix is a function of R3 point
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Non-linear deformers
• Non-uniform rotation (twisting)
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Non-linear deformers
• Free-Form Deformation (FFD)
Object embedded in “3D rubber”
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Non-linear deformers
• FFD– applications to non-characters objects
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Non-linear deformers
• Preserving volume
Influence object combined with skinning
[Scheepers et al., 97]
V = 4/3 π abc
b = ¾ V / ( π ac)
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Non-linear deformers
• Preserving volume
[Angelidis et Singh, 2007]
Motion of “Muscles” induces a displacement field
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Overview
• “Skinning”
• Non-linear deformers
• Shape morphing
• Mesh edition
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Shape blending• a 3D shape is a linear combination of
reference shapes– a linear interpolation for each vertex,
• S = S0+Σiwi(Si-S0)• animation is controlled by blend coefficient wi
– typical application is facial animation
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Shape blending
• Facial animation : two main domains
– Emotion• any expression is combination of basic expression:
fear, disgust, joy, surprise, anger [Ekman, 75]
– Talking• visual perception of speech production
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Lip-synching
• Difficult task– how to post-synchronized video onto audio track– one common solution :
• a phoneme = a 3D shape• several visually equivalent phonemes as a “viseme”
[p,b,m], [f,v], etc.
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Lip-synching
• Problem of the co-articulation effect– audio-visual speech signal is continuous
– audio and visual are not synchronized by nature (anticipation and latency)
– gesture vs shape
[Reveret et Essa, 2001]
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Overview
• “Skinning”
• Non-linear deformers
• Shape morphing
• Mesh edition
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Barycentric coordinates
• Low-resolution « cage » controlling a high-resolution mesh– each vertex is a linear combination w.r.t cage vertices and
normals => local coordinates or weights– difficulty: getting the right weights, leading to little artefacts
Mean value coordinates,Harmonic coordinates,Green coordinates, etc
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Laplacian mesh edition
• Character animation without a skeleton• Group of vertices are locally deformed
while preserving surface details• Based on discrete differential geometry
[Sorkine et al., 2004]
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Laplacian mesh edition
• Each vertex coordinate is replaced by the difference to the average of its neighborsD = L V : di = Vi-(1/|Ni|)ΣkϵNiVk
• Deformation by adding constrainsadd some rows to L => L* and D => D*
• Reconstruction of V by approximationV* = argminV( || L’V – D’ || )
More details on:http://igl.ethz.ch/projects/Laplacian-mesh-processing/STAR/STAR-
Laplacian-mesh-processing.pdf
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Laplacian mesh edition
• Application to key-frame animation
[Xu et al., 2006]