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Alec R. Rivers and Doug L. James
Cornell University
Presenter: 이성호
FastLSM: Fast Lattice Shape Matching for Robust
Real-Time Deformation
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Prior work: Meshless Deformations Based on Shape Matching
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Best fit Rigid Transformation
Q: What can be precomputed?3
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Best fit Rigid Transformation
Q: Which is the generalized one, between R and A?Q: Prove the solution of A
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Extracting Rotation
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Particles position and velocities update
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Linear shape matching
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Linear shape matching
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Quadratic shape matching
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Best fit quadratic transformation
Q: Could it be precomputed Apq and/or Aqq, and what dimensions they are?
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Cluster Based Deformation
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FastLSM
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Approach
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Assumptions
• Construct regular lattice of cubic cells containing mesh– [James et al. 2004]
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Computational cost
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Naive sum
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Bar-plate-cube sum
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Constant-time sum
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Center of mass
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Rotations
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Goal positions
Q: Prove this. (Recall in [Mueller et al. 2005], p6)21
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Pseudocode
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Fast polar decomposition
• Cold start (V=I)– 1.9 Jacobi sweeps/solution– 2500ns/decomposition
• Warm start (V=V from the last timestep)– 0.4 Jacobi sweeps/solution– 450ns/decomposition
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(Refer to p5)
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Damping
From [Mueller et al. 2006]
Apply damping per-region basis (See demo)
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Fracture
• Break by distance– [Terzopoulos and Fleischer 1988]
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Hardware-accelerated rendering
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Per-vertex normals
Precompute per each vertex27
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Constant memory restirction• Construct triangle batches
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Statistics
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Conclusion and Discussion• Lattice Shape Matching
– Fast summation algorithm– Allows large deformation
• Maintaining speed and simplicity– Orientation sensitive smoothing
• Not physically accurate– But reasonably plausible and fast
• Future works– Try different particle frameworks
• Tetrahedral, irregular samplings– Adaptive particle resolution
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