fastlsm: fast lattice shape matching for robust real-time deformation

Alec R. Rivers and Doug L. James

Cornell University

Presenter: 이성호

FastLSM: Fast Lattice Shape Matching for Robust

Real-Time Deformation

Prior work: Meshless Deformations Based on Shape Matching

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Best fit Rigid Transformation

Q: What can be precomputed?3

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

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)

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

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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