flame animation team : fire! 20061237 lee, ho-jin 20071229 kim, young soo
TRANSCRIPT
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Flame Animation
Team : Fire!20061237 Lee, Ho-Jin
20071229 Kim, Young Soo
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Objective
• Modeling the flame physically and realistically
• Rendering of the result of simulated flame
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Physical Modeling Function
• INPUT : Temperature, Pressure, Den-sity, Velocity, Material in specific time
• OUTPUT : RGB Color Value
• Physically simulate the flame and make data for rendering
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Fluid Simulation
• Get variables of each cell in next time step from data of given time
Picture from [S-tam99]
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Navier-Stokes Equation
• Equation to describe the state of vis-cous fluid
• Navier-Stokes Eq. for incompressible fluids was used for simulation
2 2 2
2 2 2 x
u u u u p u u uu v w g
t x y z dx x y z
Velocity
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Fluid Modeling
• Amount of moved fluid depends on density and velocity
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Fluid Modeling
• Derivative of density is proportional to the amount of transferred gas
• From equation of ideal gas state
P T
1 1( ) ( )ii i i iu u
t
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Fluid Modeling
• Because internal energy of gas is time derivative of Temperature is
3
2U nRT
1 1 1 1( ) ( ) ( ) ( )ii i i i i i i i
Tu T T u T T
t
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Material Modeling
• Like the thermal flow, oxygen and fuel flow is
,, 1 , , , 1( ) ( )oxygen i
oxygen i oxygen i oxygen i oxygen i
mm m u m m u
t
,, 1 , , , 1( ) ( )fuel i
fuel i fuel i fuel i fuel i
mm m u m m u
t
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Material Modeling
• According to Chemical Kinetics and Arrhenius’s Equation, the amount of burned fuel is
• Then energy conservation law gives
, , /,
oxygen i fuel i Tburned i
i i
m mm e
,i
burned i
Tm
t
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Get RGB Value from Vari-ables
• Emitted energy proportional to the amount of burned fuel
• RGB Values depends on temperature– In the basic case, it changes form red in
low temperature to yellow in high tem-perature
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Simulation Scheme
Calculate Velocity•From Navier-Stokes Equa-tion
Calculate Variables•Computational Fluid Dynam-ics
• Include pressure, density and temperature
Compute Fuel’s Burn-ing Effect•Temperature Change•Emitting Energy
Get Light form Cell•Get RGB Value•Spectrum depends on mate-rial property and tempera-ture
• Intensity depends on emit-ted energy
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Volume Rendering
• 각각의 Cell 을 Volume Rendering 을 사용
• Volume 감 있는 Fire Animation 을 표현
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Volume Rendering
• 반투명한 GLUT 의 Cube 를 이용해 그리드의 각 Cell 들의 색상 랜더링
• Alpha Blending 시에는 Z-Buffering에만 의존할 수 없으므로 시점에 따라 뒤에서부터 그려주게 코드 작성
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Example [RGB Cube]• Different Alpha Channel Value (A= 120, 60,
30, 5)
• Different Cell Grid Size (N = 10, 20, 50)
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Demo
GRIDSIZE = 10
GRIDSIZE = 10
GRIDSIZE = 10
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Conclusion
• Successfully modeled flame physi-cally– But couldn’t find realistic and stable so-
lution– Navier-Stokes Equation Solver should be
more stable
• Rendered explosion
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Future works
• Develop more stable CFD Solver
• Implement Solver for GPGPU
• Volume Rendering using Ray Casting with GPU
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Reference
• Wikipedia : Navier-Stokes Equations (http://en.wikipedia.org/wiki/Navier_Stokes, 2009.06.22 현재 )
• Jos Stam, "Stable Fluids", SIGGRAPH 1999, 121-128, 1999
• Jos Stam, "Real-Time Fluid Dynamics for Games", Game Developer Conference 2003
• Wikipedia : Arrhenius Equation (http://en.wikipedi-a.org/wiki/Arrhenius_equation, 2006.06.22 현재 )
• Keenan Crane et al, Real-Time Simulation and Ren-dering of 3D Fluids, GPU Gems 3, 633-675, Addison-Wesley Professional, 2007
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Thank You