1. FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation
Alec R. Rivers and Doug L. James
Cornell University
Presenter: 이성호

2. Prior work: Meshless Deformations Based on Shape Matching

3. Best fit Rigid Transformation
Q: What can be precomputed?

4. Best fit Rigid Transformation
Q: Which is the generalized one, between R and A?
Q: Prove the solution of A

5. Extracting Rotation

6. Particles position and velocities update

7. Linear shape matching

8. Linear shape matching

9. Quadratic shape matching

10. Best fit quadratic transformation
Q: Could it be precomputed Apq and/or Aqq, and what dimensions they are?

11. Cluster Based Deformation

12. FastLSM

13. Approach

14. Assumptions Construct regular lattice of cubic cells containing mesh
[James et al. 2004]

15. Computational cost

16. Naive sum

17. Bar-plate-cube sum

18. Constant-time sum

19. Center of mass

20. Rotations

21. Goal positions
Q: Prove this. (Recall in [Mueller et al. 2005], p6)

22. Pseudocode

23. 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
(Refer to p5)

24. Damping From [Mueller et al. 2006]
Apply damping per-region basis (See demo)

25. Fracture
Break by distance
[Terzopoulos and Fleischer 1988]

26. Hardware-accelerated rendering

27. Per-vertex normals
Precompute per each vertex

28. Constant memory restirction
Construct triangle batches

29. Statistics

30. 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