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

2

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

4

Extracting Rotation

5

Particles position and velocities update

6

Linear shape matching

7

Linear shape matching

8

Quadratic shape matching

9

Best fit quadratic transformation

Q: Could it be precomputed Apq and/or Aqq, and what dimensions they are?

10

Cluster Based Deformation

11

FastLSM

12

Approach

13

Assumptions

• Construct regular lattice of cubic cells containing mesh– [James et al. 2004]

14

Computational cost

15

Naive sum

16

Bar-plate-cube sum

17

Constant-time sum

18

Center of mass

19

Rotations

20

Goal positions

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

Pseudocode

22

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

23

(Refer to p5)

Damping

From [Mueller et al. 2006]

Apply damping per-region basis (See demo)

24

Fracture

• Break by distance– [Terzopoulos and Fleischer 1988]

25

Hardware-accelerated rendering

26

Per-vertex normals

Precompute per each vertex27

Constant memory restirction• Construct triangle batches

28

Statistics

29

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

30