REVISITING INTEGRATION IN THE MATERIAL POINT METHOD
Transcript of REVISITING INTEGRATION IN THE MATERIAL POINT METHOD
![Page 1: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/1.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
YUN (RAYMOND) FEI
QI GUO
RUNDONG WU
LI HUANG
MING GAO
TENCENT GAME AI RESEARCH CENTER
REVISITING INTEGRATION IN
THE MATERIAL POINT METHODA SCHEME FOR EASIER SEPARATION AND LESS DISSIPATION
Β© 2021 TENCENT. ALL RIGHTS RESERVED.
![Page 2: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/2.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.2
![Page 3: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/3.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
MOTIVATION
WHY WE NEED A NEW INTEGRATION SCHEME?
Β© 2021 TENCENT. ALL RIGHTS RESERVED.3
![Page 4: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/4.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
A CASE IN PRODUCTION
β’ 93,014 strands
β’ 7,179,350 DoFs
β’ Required simulation cost
β ~ 6s per frame (based on 60
frame per simulated second)
β ~ 1h in total (10s simulation)
Β© 2021 TENCENT. ALL RIGHTS RESERVED.4
Simulate with GPU-MPM?
![Page 5: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/5.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
PRIOR WORK OF MPM WITH LAGRANGIAN FORCES
Β© 2021 TENCENT. ALL RIGHTS RESERVED.5
[Jiang et al. 2017][Jiang et al. 2015] [Guo et al. 2018] [Han et al. 2019]
![Page 6: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/6.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
AN MPM HAIR SIMULATOR
Β© 2021 TENCENT. ALL RIGHTS RESERVED.6
Init time stepping
Particle to grid mapping
Apply stress on grid
Grid to particle mapping
Plasticity projection
Add Lagrangianimpulses solved from discrete elastic rods
(DER)
Our MPM Hair SimulatorMPM for contact & friction
![Page 7: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/7.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
HAIRS SIMULATED WITH MLS-MPM + FLIP
Β© 2021 TENCENT. ALL RIGHTS RESERVED.7
![Page 8: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/8.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
HAIRS SIMULATED WITH MLS-MPM + FLIP
Β© 2021 TENCENT. ALL RIGHTS RESERVED.8
![Page 9: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/9.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
FLIP INTEGRATOR[BRACKBILL & RUPPEL 1986]
Β© 2021 TENCENT. ALL RIGHTS RESERVED.9
Positions they should be
Positions they end up with
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ Interpolated from
current nodal velocity
P2G G2P
Position update during grid-to-particle (G2P) transfer:
![Page 10: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/10.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
πππ+1 =
π
π€ππππβ
PIC/APIC/POLYPIC INTEGRATORS
PIC grid-to-particle:[Harlow et al. 1955]
Β© 2021 TENCENT. ALL RIGHTS RESERVED.10
APIC grid-to-particle: (moving-least-square version)[Jiang et al. 2015, Hu et al. 2018]
PolyPIC grid-to-particle:[Fu et al. 2017]
VelocityUpdate
PositionUpdate
πππ+1 =
π
π€ππππβ
πππ+1 =
π
π€ππππβ π₯π
π β π₯ππ π
πππ β1
πππ+1 =
π
π€ππππβ
πππ+1 = argmin
π
π
ππππ ππ
β β
π
πΌ
π π π₯π β π₯ππ ππΌππππΌ
π+1
2
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ ππ
π+1 = πππ + Ξπ‘
π
π€ππππβ ππ
π+1 = πππ + Ξπ‘
π
π€ππππβ
![Page 11: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/11.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
THE CONTINUUM ASSUMPTION
β’ FLIP/xPIC assumes material continuous in the
entire domain.
β’ Problem:
β Particle position is always interpolated from
deformed nodal positions
β If any movement is not capturable by grid, it
would be neither capturable by particles.
Β© 2021 TENCENT. ALL RIGHTS RESERVED.11
Continuous deformation Ξ¨
ππ
ππ‘=πΞ¨ π, π‘
ππ‘β
π
π€ππππβ
πππ+1 =
π
π€ππππβ
![Page 12: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/12.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
DISCREPANCY BETWEEN RENDERING, EXPECTATION AND SIMULATION
Β© 2021 TENCENT. ALL RIGHTS RESERVED.12
Sand Hairs Clothes
Expected behavior: separate immediately when pulled apart
Rendering: discrete & separated elements
Simulation: continuum that trap particles until they have no shared weights on a node
![Page 13: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/13.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
NFLIP
NATURALLY-MODIFIED FLIP
Β© 2021 TENCENT. ALL RIGHTS RESERVED.13
![Page 14: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/14.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
NFLIP: USE PARTICLE VELOCITY FOR ADVECTION
FLIP grid-to-particle:
πππ+1 =
π
π€ππππβ + πΌ ππ
π β
π
π€πππππ
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ
Β© 2021 TENCENT. ALL RIGHTS RESERVED.14
NFLIP grid-to-particle:
πππ+1 =
π
π€ππππβ + πΌ ππ
π β
π
π€πππππ
πππ+1 = ππ
π + Ξπ‘πππ+1
Completely ignore continuity.Assume material continuous everywhere.
![Page 15: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/15.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
NFLIP: USE PARTICLE VELOCITY FOR ADVECTION
Β© 2021 TENCENT. ALL RIGHTS RESERVED.15
dissipated, difficult to separate
slow to separate, then accelerated
dissipated, easy to separate
![Page 16: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/16.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
IGNORING CONTINUITY LEADS TO ERROR
Β© 2021 TENCENT. ALL RIGHTS RESERVED.16
Ignoring continuity
Wrong deformation gradient
Wrong stress
Wrong contacts and frictions
![Page 17: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/17.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
SFLIP
A SEPARABLE FLIP
Β© 2021 TENCENT. ALL RIGHTS RESERVED.17
![Page 18: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/18.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
A SEPARABLE FLIP
FLIP grid-to-particle:
πππ+1 =
π
π€ππππβ + πΌ ππ
π β
π
π€πππππ
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ
Β© 2021 TENCENT. ALL RIGHTS RESERVED.18
SFLIP grid-to-particle:
πππ+1 =
π
π€ππππβ + πΌ ππ
π β
π
π€πππππ
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ + π½ππΌ ππ
π β
π
π€πππππ
π½π: the trap-breaking ratio
FLIP: βπ, π½π = 0
NFLIP: βπ, π½π = 1
![Page 19: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/19.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
THE TRAP-BREAKING RATIO π·p
Β© 2021 TENCENT. ALL RIGHTS RESERVED.19
π½p = π½min, mostly use interpolated nodal velocity to advect this particle
Un
se
pa
rate
d
ApplyForce
Se
pa
rate
d
π½p = π½max, mostly use particle velocity to advect this particle
P2G
ApplyForce
(zero when separated)
P2G
G2P
G2P
![Page 20: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/20.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
DETERMINE SEPARATION THROUGH VOLUME RATIO
Β© 2021 TENCENT. ALL RIGHTS RESERVED.20
π1, π2: stress
π½π: volume ratio
ππ: pressure
π : bulk modulus
π½ππ: critical volume ratio
![Page 21: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/21.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
DETERMINE SEPARATION THROUGH VOLUME RATIO
Β© 2021 TENCENT. ALL RIGHTS RESERVED.21
π1, π2: stress
π½π: volume ratio
ππ: pressure
π : bulk modulus
π½ππ: critical volume ratio
![Page 22: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/22.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
A SEPARABLE FLIP - SUMMARIZED
SFLIP grid-to-particle:
πππ+1 =
π
π€ππππβ + πΌ ππ
π β
π
π€πππππ
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ + π½ππΌ ππ
π β
π
π€πππππ
π½π = ΰ΅
0, in boundary
π½min, π½π < π½ππ
π½max, π½π β₯ π½ππ
Β© 2021 TENCENT. ALL RIGHTS RESERVED.22
![Page 23: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/23.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
SFLIP
DIDACTIC EXAMPLES
Β© 2021 TENCENT. ALL RIGHTS RESERVED.23
![Page 24: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/24.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
TWO PERFECTLY SMOOTH FINITE ELEMENT SQUARESNO FORCE APPLIED FROM ONE SQUARE TO ANOTHER
Β© 2021 TENCENT. ALL RIGHTS RESERVED.24
Ground Truth
![Page 25: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/25.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
2D FIBERS
Β© 2021 TENCENT. ALL RIGHTS RESERVED.25
![Page 26: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/26.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
2D HOURGLASS
Β© 2021 TENCENT. ALL RIGHTS RESERVED.26
![Page 27: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/27.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
2D CLAY FRACTURE
Β© 2021 TENCENT. ALL RIGHTS RESERVED.27
![Page 28: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/28.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
ASFLIP
AFFINE-AUGMENTED SEPARABLE FLIP
Β© 2021 TENCENT. ALL RIGHTS RESERVED.28
![Page 29: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/29.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
NAΓVE MODIFICATION TO IMPROVE APIC
Β© 2021 TENCENT. ALL RIGHTS RESERVED.29
APIC grid-to-particle transfer:
πππ+1 =
π
π€ππππβ
πππ+1 =
π
π€ππππβ π₯π
π β π₯ππ π
πππ β1
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ
Particle-to-grid transfer:
πππππ
π =
π
π€ππππ πππ + ππ
π πππ β ππ
π
ASPIC grid-to-particle transfer:
πππ+1 =
π
π€ππππβ
πππ+1 =
π
π€ππππβ π₯π
π β π₯ππ π
πππ β1
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ + π½ππΌ ππ
π β
π
π€πππππ
π½π = ΰ΅
0, in boundary or source
π½min, π½π < π½ππ
π½max, π½π β₯ π½ππ
Add positional adjustment
![Page 30: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/30.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
Assume zero force applied (i.e., ππβ = ππ
π):
πππ+1 = ππ
π + Ξπ‘
π
π€πππ ππ
β + π½ππΌ πππ β
π
π€πππ ππ
π
πππ+1 =
π
π€πππ ππ
β
ASPICAPIC + POSITIONAL ADJUSTMENT
Β© 2021 TENCENT. ALL RIGHTS RESERVED.30
ASPIC doesnβt work.
πππ+1 = ππ
π + Ξπ‘
π
1 β π½ππΌ π€πππ ππ
π + π½ππΌπ€πππβ1ππ
πβ1
Nodal velocity at π‘πβ1Nodal velocity at π‘π
Only depends on nodal velocity
Root cause: PIC-style velocity update never preserves particle velocity from previous steps
![Page 31: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/31.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
AFFINE-AUGMENTED FLIP (AFLIP)
Β© 2021 TENCENT. ALL RIGHTS RESERVED.31
AFLIP grid-to-particle transfer (G2P):
πππ+1 =
π
π€ππππβ + πΌ ππ
π β
π
π€πππππ
πππ+1 =
π
π€ππππβ π₯π
π β π₯ππ π
πππ β1
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ
AFLIP particle-to-grid transfer (P2G):
πππππ
π =
π
π€ππππ πππ + ππ
π πππ β ππ
π Preserves affine momentum during P2G
Preserves high-frequency momentum during G2P(damped through Ξ± < 1)
![Page 32: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/32.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
2D WEAKLY-COMPRESSIBLE LIQUID
Β© 2021 TENCENT. ALL RIGHTS RESERVED.32
![Page 33: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/33.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
ASFLIPAFFINE-AUGMENTED SEPARABLE FLUID-IMPLICIT PARTICLE
Β© 2021 TENCENT. ALL RIGHTS RESERVED.33
ASFLIP grid-to-particle transfer (G2P):
πππ+1 =
π
π€ππππβ + πΌ ππ
π β
π
π€πππππ
πππ+1 =
π
π€ππππβ π₯π
π β π₯ππ π
πππ β1
πππ+1 = ππ
π + Ξπ‘
π
π€ππππβ + π½ππΌ ππ
π β
π
π€πππππ
π½π = ΰ΅
0, in boundary or source
π½min, π½π < π½ππ
π½max, π½π β₯ π½ππ
ASFLIP particle-to-grid transfer (P2G):
πππππ
π =
π
π€ππππ πππ + ππ
π πππ β ππ
π Preserves affine momentum during P2G
Preserves high-frequency momentum during G2P(damped through Ξ± < 1)
Improves upon cases where continuum assumption no longer applies, preserving sub-grid movements
![Page 34: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/34.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.34
![Page 35: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/35.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
2D FINITE ELEMENT SQUARES
Β© 2021 TENCENT. ALL RIGHTS RESERVED.35
Ground Truth
![Page 36: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/36.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
MORE EXAMPLES
WATER, SAND, HAIRS AND CLOTHES
Β© 2021 TENCENT. ALL RIGHTS RESERVED.36
![Page 37: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/37.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.37
![Page 38: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/38.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.38
![Page 39: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/39.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.39
![Page 40: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/40.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.40
![Page 41: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/41.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES41
Grid-resolution dependent wrinkling[Guo et al. 2018]
![Page 42: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/42.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.42
![Page 43: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/43.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.43
![Page 44: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/44.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
SUMMARY
IntegratorsHigh-
frequency motion
Undamped affine motion
Handle Boundary Condition
Easy Separation
Energetic Level
PIC β β β β β
APIC β β β β ββ
FLIP β β β β ββ
NFLIP β β β β ββ
SFLIP β β β β ββ
AFLIP β β β β βββ
ASFLIP β β β β βββ
Β© 2021 TENCENT. ALL RIGHTS RESERVED.44
![Page 45: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/45.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUES
FUTURE WORK
β’ Numerical volume gain
β’ Simulators based on Chorinβs projection
β’ Determine separation through fracture mechanics
β’ More accurate (self-) contact resolution
β’ Coupling with principled, discrete physics
Β© 2021 TENCENT. ALL RIGHTS RESERVED.45
![Page 46: REVISITING INTEGRATION IN THE MATERIAL POINT METHOD](https://reader030.fdocuments.in/reader030/viewer/2022013005/61cc3e80074e11294051d6fa/html5/thumbnails/46.jpg)
THE PREMIER CONFERENCE & EXHIBITION IN
COMPUTER GRAPHICS & INTERACTIVE TECHNIQUESΒ© 2021 TENCENT. ALL RIGHTS RESERVED.46
TENCENT GAME AI RESEARCH CENTER
PRE-PRINT, VIDEO, SOURCE CODE
http://yunfei.work/asflip/