Using Wavelet Transform to Speedup RealTime Cloth Simulation

1
Using Wavelet Transform to Speedup Real-Time
Cloth Simulation

• Student ??? Advisor ???
• Chia-Ying Chi Prof. Zen-Chung Shih
• Institute of Multimedia and EngineeringNational
  Chiao Tung University

2
Abstract original method
Time t
Time t 1
3
Abstract our method
4
Outline

• Introduction
• Related works
• System overview
• Our Speeding Approach
• Fast and Stable Integrator
• Implementation Results
• Conclusion and Future Works

5
Introduction
6
Introduction

• Regions with low curvature often occur
• Bending forces
• Not always moved in VR environment
• To deal with problems
• Time consuming framework
• Stable simulation
• Our approach
• Pre-processing of segmentation
• Modified integrator

7
Related works

• Mass-spring system
• Adaptive mesh

8
Mass-spring system
9
Adaptive Mesh (multi-level mesh)
10
Mesh adaptation
Choi and Hong using surface wavelet VSMM 2002
v3 refinement rule used by Volkov ACSC 2005
11
Mesh adaptation

• Features
• Construction and destruction (FILO)
• Change mesh topology
• For accurate result mainly when collision occurs
• Segmentation rule

12
Integration method
13
Integration method

• The Verlet method
• Proposed early by Verlet in 1997
• For experiment on fluid
• Desbrun use it for cloth simulation
• Because sometimes position changed rapidly (ex
  collision response)
• Changed in position directly effect velocities

14
Our Speeding Approach

• Segmentation
• Interpolation

15
Segmentation

• Method requirement
• Fast
• Nodes in the same cluster must be connected
• Not all nodes should be classified into a cluster

16
Wavelet transform

• Used in digital signal processing
• CWT (continuous wavelet transform)
• DWT (discrete wavelet transform)
• The Haar wavelet
• proposed in 1909 by Alfred Haar
• the simplest possible wavelet
• 2D Haar wavelet transform

17
The Haar wavelet transform
?-average-?
?-difference?
18
The Haar wavelet transform
average
difference
19
The Haar wavelet transform
average
difference
20
The Haar wavelet transform
21
Segmentation
Normal differences
Average normal
Vertex normal
Vertex normal
a
b
22
Interpolation
23
Bilinear Interpolation
24
Following benefit (1)

• Over-stretch springs

25
Following benefit (2)

• Over-stretch spring

26
Fast and Stable Integrator

• Explicit/Implicit Euler method
• Approximate implicit method
• our integration method

27
Integration method

• Explicit Euler method
• The oldest and most simple method
• Direct linear extrapolation

v
t-h t th
28
Explicit method
?Error
v
t-h t th
29
Integration method (cont)

• Implicit Euler method (The backward Euler method)
• introduced by Baraff at 1998
• Consider all nodes when calculating each node
• Compute a N?N matrix H for N mass points
• Prediction for the next time step
• Stability is the most advantage
• larger simulation time steps
• Total computation time decreased

30
Implicit method

• ?F/?x is denoted as H

H
If i ?j and i,j is linked
From Desbrun(1999)
31
Integration method

• Approximated implicit method
• Hij0 when node i and node j are not connected
• Compute only non-zero elements
• Desbrun splits the forces into two parts
• the linear one and nonlinear one.
• Cho and Choi makes the model working in O(n)
• simplified the formula of ?v

32
Approximated implicit method
FromChoi and Cho (2000)
33
Verlet integrator

• Calculating position without computing velocities

34
Our integration method

• Modified for our speedup approach
• Ideas from combining Verlet method
• Basically use approximated implicit method
• Not use it to calculate ?v
• To predict velocity for the next time step
• Calculate position use explicit method
• Errors from interpolation should not be propagate

35
Implementation Results

• Simulation
• Stretch correction
• Enhancement

36
Implementation

• Environment
• Pentium 4 PC with 3.4GHz CPU
• 2Gbyte RAM
• NVIDIA GeForce 6600 GT graphic card
• Cloth object
• 3232 and 6464
• Spring constant 2000

37
Result (3232)
38
Result (6464)
39
Over-stretch correction
Original simulation
With our approach
40
Enhancement

• Stability and efficiency enhanced
• Our system can perform simulation at timestep
  0.06
• While original method only performs at timestep
  no over than 0.023
• That means less simulation frequency and time
  costs.

41
Conclusion
42
conclusion

• for simulating cloth in real-time
• a time-saving approach
• a suitable algorithm
• advantage
• Less time for each frame calculation
• Less frequency to simulation
• Higher stability
• Bending and over-stretch correction

43
limitation

• Accuracy is not the point
• interpolation
• Cloth resolution must be 2n
• 2D wavelet transform

44
Future Works
45
Future Works

• Temporal coherence
• No need to rebuild hierarchical structure every
  time
• Feature vector
• Forces, velocities
• Better interpolation method
• Interpolate smoothly

46
Questions?