The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Physically-Based Visual Simulation on Graphics Hardware Mark J. Harris Greg Coombe Thorsten Scheuermann

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Physically-Based Visual Simulation on Graphics Hardware

Mark J. HarrisGreg CoombeThorsten ScheuermannAnselmo Lastra

2 The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

More, Better, Faster

Goal:Flexible, real-time visual simulation of diverse dynamic systemsFurther increase visual realism of interactive 3D applications•Fluids, gases, fire, etc.•Beyond canned texture animations


Visual Simulation?

Goal is visual realismAd hoc simulation methods can provide good visual results w/ less computation• But not necessarily high numerical accuracy

If the user is convinced, numbers aren’t so important


Coupled Map Lattice

Mapping:Continuous state lattice nodes

Coupling:Nodes interact with each other to produce new state according to specified rules


Coupled Map Lattice

CML introduced by Kaneko (1980s)Used CML to study spatio-temporal chaosOthers adapted CML to physical simulation:• Boiling [Yanagita 1992]• Convection [Yanagita 1993]• Clouds [Yanagita 1997; Miyazaki 2001]• Chemical reaction-diffusion [Kapral ‘93]• Saltation (sand ripples / dunes) [ Nishimori ‘93]• And more


CML vs. CA

CML extends cellular automata (CA)

CA CMLSPACE Discrete Discrete

TIME Discrete Discrete

STATE Discrete ContinuouContinuouss


CML vs. CA

Continuous state is more usefulDiscrete: physical quantities difficult• Must filter over many nodes to get “real” values

Continuous: physical quantities easy• Real physical values at each node• Temperature, velocity, concentration, etc.

8


CML Operations


Graphics Hardware

Why use it?Speed: up to 25x speedup in our simsGPU perf. grows faster than CPU perf.Cheap: GeForce 4 Ti 4200 < $140Load balancing in complex applications

Why not use it?Low precision computation (not anymore!)Difficult to program (not for long!)


Hardware Implementation


CML Operations

Implement operations as building blocks for use in multiple simulations

DiffusionBuoyancy (2 types)Latent HeatAdvectionViscosity / PressureGray-Scott Chemical ReactionBoundary ConditionsUser interaction (drawing)Transfer function (color gradient)


Results

Implemented multiple simulations

Boiling (2D and 3D)

Rayleigh-Bénard Convection (2D)

Reaction-diffusion (2D and 3D)


Boiling

[Yanagita 1992]State = TemperatureThree operations:

Diffusion, buoyancy, latent heat7 passes in 2D, 9 per 3D slice


Rayleigh-Bénard Convection[Yanagita & Kaneko 1993]State = temp. (scalar) + velocity (vector)Three operations (10 passes):

Diffusion, advection, and viscosity / pressure


Reaction-Diffusion

Gray-Scott reaction-diffusion model [Pearson 1993]State = two scalar chemical concentrationsSimple: just diffusion and reaction ops2 passes in 2D, 3 per 3D slice


Hardware Limitations

Precision, precision, precision!8 or 9 bits is far from enoughDiffusion is very susceptible to precision problems• All of our simulations use it!

High dynamic range simulations are very susceptible• Convection, reaction-diffusion• Not boiling – relatively small range of values


Hardware Limitations

3D texturingIt’s fast … unless you are doing dynamic texturing• Copy to slice of 3D texture is slow• We use a stack of 2D slices to

represent 3D volume

Not all 2D texture shaders have 3D analogs• Fixed with general purpose fragment

programs (NV30, ATI R300)


Future Work

Explore simulation techniques / issues on graphics hardware

Other PDE solution techniquesMore complex simulationsUse of HLSL, next-gen hardwareHigh dynamic range simulations

Applications:Interactive environments, gamesScientific ComputationDynamic painting / modeling applicationsDynamic procedural texture synthesisDynamic procedural model synthesis…


Conclusion

GPUs are a capable, efficient, and flexible platform for physically-based visual simulation


Acknowledgements

NVIDIA Developer RelationsHWW Paper ReviewersSponsors:

NVIDIA CorporationUS National Institutes of HealthUS Office of Naval Research US Department of Energy ASCI programUS National Science Foundation


For More Information

http://www.cs.unc.edu/~harrism/cmlEmail [email protected]


Extra Slides


CML Philosophy

Bottom-up approach.Don’t directly simulate macroscopic behavior:

Perform simple, local, “microscopic” lattice operations.


CML Philosophy

Macroscopic behavior is aggregate of simple operations.

e.g. Boiling simulation:• 3 operations: diffusion, thermal buoyancy,

latent heat.


CML Operations

Typically consist of four components:

1. Neighbor sampling2. Computation on Neighbors3. New state computation4. State update


Neighbor Sampling

Set a 1:1 mapping from pixels to texels:

Set view port resolution to texture resolution.Use orthographic projection.

To sample an immediate neighbor of each texel:

Draw a single quad filling the view port.Set texture coordinates at corners to {(0,0), (0,1), (1,1), (1,0)} plus the offset to the neighbor.• E.G. Offset to right is (w, 0), where is view space

texel width.


Neighbor Sampling

Neighbor sampling is easy with vertex programs.

Store table of offsets in vertex program memory.At run time, pass table index that represents the type of offset needed.Render a quad (with only a single set of base texcoords).Use vertex program to add offsets and generate texcoords for all texture units.


Computation on Neighbors

Use texture table lookups to compute arbitrary functions of sampled values.

Dependent texturing using texture shaders.


New State Computation

Combine sampled values and computations to compute new state.Implemented on GeForce 3 using register combiners.

Arithmetic: add, subtract, multiply, scale, bias and dot product.8 cascaded register combiners + 1 “final” combiner.9-bit signed arithmetic internally.8-bit unsigned on output (can clamp or scale and bias).


State Update

Store the newly computed state to texture.We use glCopyTexSubImage2D()

Fast copy from frame buffer to texture memory.

Render to texture OpenGL extension

Will reduce cost, but still in development.Already available in Direct3D.


Common Operations

Laplacian:

Discrete form:

Diffusion:

cd is the diffusion coefficient

.),(2

2

2

22

y

T

x

TyxT

jijijijijiji TTTTTT ,1,1,,1,1,2 4

.4 ,

2,

', ji

djiji Tc

TT


Common Operations

Directional forcesBuoyancy (used in convection simulation):

Thermal buoyancy with phase change:

• Uses dependent texture to compute tanh

• Tc is the boiling point

].2[)()( ,1,1,2,, yxyxyxc

yxyx TTTyvyv b

)],(tanh[)(

)],()([ 1,1,,2,,

c

yxyxyxyxyx

TTT

TTTTT


Boiling Simulation Performance

0

200

400

600

800

1000

1200

1400

1600

1800

2000

128x

128

256x

256

512x

512

1024

x102

4

32x3

2x32

64x6

4x64

128x

128x1

28

Lattice Resolution

Ite

rati

on

s P

er

Se

co

nd

Software

GeForce 3

GeForce 4

25x speedup


Interactive Framework

CMLlabFramework for building and testing CML simulations


Real Applications

Fast simulation integrated with 3D environments

Virtual environment in HMD w/ head trackingWildMagic Game Engine [Eberly 2001]


Graphics Hardware Performance

Peak Perf.

('s/sec)

Year

HP CRXSGI Iris

SGI GT

HP VRX

Stellar GS1000

SGI VGX

HP TVRX

SGI SkyWriter

SGI

E&SF300

One-pixel polygons (~10M polygons @ 30Hz)

SGIRE2

RE1

Megatek

86 88 90 92 94 96 98 00104

105

106

107

108

109

UNC Pxpl4

UNC Pxpl5

UNC/HP PixelFlow

Flat shading

Gouraudshading

Antialiasing

Slope ~2.4x/year (Moore's Law ~ 1.7x/year) SGI

IRE&SHarmony

SGI R-Monster

Division VPX

E&S Freedom

Accel/VSISVoodoo

Glint

DivisionPxpl6

PC Graphics

Textures

SGICobalt

Nvidia TNT

Graph courtesy of Professor John Poulton

GeForce 3& Radeon

3DLabs

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Physically-Based Visual Simulation on Graphics Hardware Mark J. Harris Greg Coombe Thorsten Scheuermann