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## Flame Animation

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**Flame Animation**Team : Fire! 20061237 Lee, Ho-Jin 20071229 Kim, Young Soo**Objective**• Modeling the flame physically and realistically • Rendering of the result of simulated flame**Physical Modeling Function**• INPUT : Temperature, Pressure, Density, Velocity, Material in specific time • OUTPUT : RGB Color Value • Physically simulate the flame and make data for rendering**Fluid Simulation**• Get variables of each cell in next time step from data of given time Picture from [Stam99]**Navier-Stokes Equation**• Equation to describe the state of viscous fluid • Navier-Stokes Eq. for incompressible fluids was used for simulation Velocity**Fluid Modeling**• Amount of moved fluid depends on density and velocity**Fluid Modeling**• Derivative of density is proportional to the amount of transferred gas • From equation of ideal gas state**Fluid Modeling**• Because internal energy of gas istime derivative of Temperature is**Material Modeling**• Like the thermal flow, oxygen and fuel flow is**Material Modeling**• According to Chemical Kinetics and Arrhenius’s Equation, the amount of burned fuel is • Then energy conservation law gives**Get RGB Value from Variables**• 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 temperature**Volume Rendering**• 각각의 Cell을 Volume Rendering을 사용 • Volume감 있는 Fire Animation을 표현**Volume Rendering**• 반투명한 GLUT의 Cube를 이용해 그리드의 각 Cell들의 색상 랜더링 • Alpha Blending 시에는 Z-Buffering에만 의존할 수 없으므로 시점에 따라 뒤에서부터 그려주게 코드 작성**Example [RGB Cube]**• Different Alpha Channel Value (A= 120, 60, 30, 5) • Different Cell Grid Size (N = 10, 20, 50)**Demo**GRIDSIZE = 10 GRIDSIZE = 10 GRIDSIZE = 10**Conclusion**• Successfully modeled flame physically • But couldn’t find realistic and stable solution • Navier-Stokes Equation Solver should be more stable • Rendered explosion**Future works**• Develop more stable CFD Solver • Implement Solver for GPGPU • Volume Rendering using Ray Casting with GPU**Reference**• Wikipedia : Navier-Stokes Equations (http://en.wikipedia.org/wiki/Navier_Stokes, 2009.06.22 현재) • JosStam, "Stable Fluids", SIGGRAPH 1999, 121-128, 1999 • JosStam, "Real-Time Fluid Dynamics for Games", Game Developer Conference 2003 • Wikipedia : Arrhenius Equation (http://en.wikipedia.org/wiki/Arrhenius_equation, 2006.06.22 현재) • Keenan Crane et al, Real-Time Simulation and Rendering of 3D Fluids, GPU Gems 3, 633-675, Addison-Wesley Professional, 2007