inverse kinematics for reduced deformable models
DESCRIPTION
Inverse Kinematics for Reduced Deformable Models. Our Goal: Interaction. mesh manipulation direct, intuitive control speed. Related Work. mesh editing [Zorin et al. 1997, Kobbelt et al. 1998, Sorkine 2005] Mesh-based inverse kinematics [Sumner et al. 2005] Skinning mesh animations - PowerPoint PPT PresentationTRANSCRIPT
Der, Sumner, and Popović
Inverse Kinematics for Reduced Deformable Models
Kevin G. Der Robert W. Sumner1 Jovan Popović
Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology
1ETH Zürich
Der, Sumner, and Popović
Our Goal: Interaction
• mesh manipulation• direct, intuitive control• speed
Der, Sumner, and Popović
Related Work
• mesh editing[Zorin et al. 1997, Kobbelt et al. 1998,
Sorkine 2005]
• Mesh-based inverse kinematics[Sumner et al. 2005]
• Skinning mesh animations[ James and Twigg 2005]
Der, Sumner, and Popović
Our Method
Reduced Deformabl
e Model
Mesh Examples
InverseKinematic
s
decouple deformation complexity from geometric complexity!
- completely automated animation pipeline
Der, Sumner, and Popović
Reduced Deformable Model
• expresses deformations compactly
• automatically constructed
Control parameters:
Examples Reduced Deformabl
e Model
[James and Twigg 2005]
• non-rigid• no hierarchy
Skinning weights:(Using mean-shift
clustering)
Der, Sumner, and Popović
RDM: Mesh Reconstruction
Control parameters:
Skinning weights:
20 to 50
huge number
different values estimate each example
x: before deformationv: after deformation
Der, Sumner, and Popović
Inverse Kinematics
• obtain natural poses by blending examples
• blend in which domain?– vertex positions ?– control parameters ?
• find a semantically proper shape
Desired
Blending function.
Der, Sumner, and Popović
Deformation Gradients• simple 3x3 transformation matrices• describe deformation of each example
Skinning equation.
Vertex deformation
gradient.
deformation function
Der, Sumner, and Popović
Deformation Gradients
flattened deformation gradients of vertices
constant matrix
flattened control matrices
for each example: have t → get f
Der, Sumner, and Popović
Shape Blending
• combine example deformation gradients
Blending function.
• recover the control parameters given deformation gradientsHas closed form
solution.
solving for reduced basis!but still slow
Der, Sumner, and Popović
Proxy Vertices
• evaluating deformation gradients at every vertex is undesirable
• summarize using a few vertices
same deformation gradient!
controlsvertex groups
weighted centroid of the group’s vertices
))(1(
))(1(
iVi
iiVi
X
XXf
Der, Sumner, and Popović
Inverse Kinematics
“ Find best natural pose that meets user constraints”
)( bCt
When there’s only a few constraints:
2
1,
**1 ))((minarg,
*1
bGCmGNttt
1NtbCt
Der, Sumner, and Popović
Results
0
1
2
3
4
MeshIK Our method
seconds
Solving time for interaction
Der, Sumner, and Popović
ResultsSolving time for interaction
Mesh Vertices Example Ct Pxy Total Solve MIK Efull(Eproxy)
Horse 8431 12 33 195 0.019 0.007 0.424 3.01(3.00)
Human 12500 10 42 471 0.031 0.013 0.675 6.01(5.95)
Mouse 13188 26 48 278 0.037 0.019 1.351 1.63(1.73)
Dragon 15560 7 72 380 0.046 0.023 0.590 0.96(0.97)
Gorilla 25436 27 28 198 0.045 0.013 2.962 4.38(4.33)
Elephant 42321 11 23 210 0.058 0.008 1.928 5.38(5.46)
Der, Sumner, and Popović
Conclusion
• interactive control of reduced deformable models
• future work– error correction for new poses– model transfer between meshes– other reduced deformable models