fluid simulation and control for computer graphics
DESCRIPTION
Physically accurate computer simulations of fluids such as water, gasses and air have for many years been a valuable complement to experimental methods in examining the flow around airplanes, cars, wind turbines etc. Recently physically based simulation of fluids has also been adopted in computer graphics, where such techniques are required to faithfully reproduce the visually complex motion of fluids that is very hard to animate in a traditional sense. However, the demands are different in graphics where the visual properties of the fluid have to impose character on the fluid in addition to adhering to the vision of an artist or a director. This poses entirely new research challenges for fluid simulation in computer graphics where artistic control, low simulation cost and visual richness are in focus. In this presentation I will motivate the use of physically based fluid simulation for computer graphics, show examples of state of the art and go into more depth with a recent fluid control framework developed at Aarhus University in collaboration with DreamWorks Animation and Digital Domain. I will elaborate both on the final technique and results as well as on the process that took us there, including challenges faced and approaches that turned out not to be successful.TRANSCRIPT
Fluid Simulation and Control forComputer Graphics
Michael Bang NielsenAarhus University
What is Computer Graphics?
• Modeling– Geometry– Appearance
• Animation– Keyframes– Motion Capture– Simulation/Synthesis
• Rendering– Offline– Realtime
What is Physically BasedAnimation?
• Rigid bodies• Deformable objects• Cloth• Hair• Fluids
– Water– Smoke– Fire– Air
Important for games, but what about movies and commercials?
Why Computer Generated Effectsfor Movies and Commercials?
Real world smoke and water phenomena are very complex
Why Computer Generated Effectsfor Movies and Commercials?
Ivan Aivazovsky, ”The Ninth Wave”, 1850.
It requires remarkable talent and a lot of time to do..
Why Computer Generated Effectsfor Movies and Commercials?
And real phenomena have scale…From Rikitt: Special Effects
Why Computer Generated Effectsfor Movies and Commercials?
And real phenomena have scale…From Rikitt: Special Effects
Why Computer Generated Effectsfor Movies and Commercials?
But sometimes physical effects work.Copyright Cinefex.
State of the Art in Fluid Simulation for Computer Graphics
1: http://www.scanlinevfxla.com/la/en/reels.html
2: Sequence from Golden Compass
Molemaker et al.
State of the Art in Fluid Simulation for Computer Graphics
But don’t be fooled: Artists spenda lot of time making raw simulations look good
Copyright Twentieth Century Fox.
Sequence from Day After Tomorrow:
How do we Simulate Fluids for Computer Graphics?
Math, Physics, Computer Science, Fluid Dynamics and Computational Fluid Dynamics (CFD)
From John D. Anderson: Computational Fluid Dynamics
Fluid Simulation for Computer Graphics
• Should be visually plausible
• Physical accuracy not paramount
• Animators/directorwant a certainvisual style
Demands are different than in CFD:
Fluid Simulation for Computer Graphics
• Simulation speed –deadlines and interactive preview
• The fluid should have character
• The artists want control – it should be possible to sculpt the fluid
From Inkheart. Image by Double Negative
Production designs by Jon Brooks
Collaboration between
• Michael Bang Nielsen• Brian Bunch Christensen• Nafees Bin Zafar• Doug Roble• Ken Museth
Guided Fluid Simulation
I will share both our successes and frustrations with you!
Guided Fluid Simulation MotivationCoarse Simulation
Fine Simulation
Our Contribution:Guided Fine Simulation
Guided Fluid Simulation Motivation
Low Res Low Res UpsampledHigh Res
Guided Fluid Simulation Problem Statement
• Mathematical model• Algorithms• Data structures
That make it possible to guide a high resolution fluid simulation using a low resolution simulation
Develop
Guided Fluid SimulationThe Fundamental Idea
The low frequencies of the fine simulation should be equal to the
frequencies of the coarse simulation
Challenge: Formulate this mathematically
The One-Slide Fluid MechanicsCourse
Volma
VolF
=maF = aVolF
=ρ1
Net force = mass x acceleration⇒ ⇒
The One-Slide Computational Fluid Mechanics Course
In computer graphics we apply Operator Splitting:
Advection
Body forces
Incompressibility
Guided Fluid SimulationHow do we attack the problem?
The low frequencies of the fine simulation should be equal to the
frequencies of the coarse simulation
Advection
Body forces
Incompressibility
Guided Fluid SimulationThe Force-Based Approach
• Forces (all or low frequencies)
• Blending of divergence free velocity fields– Leads to results that are too smooth
Thuerey et al.
Guided Fluid SimulationHow do we attack the problem?
The low frequencies of the fine simulation should be equal to the
frequencies of the coarse simulation
Advection
Body forces
Incompressibility
Guided Fluid SimulationThe Modified Pressure Projection
ApproachObservationSolving for Incompressibility
subject to the constraint
is identical to the minimization of
Guided Fluid SimulationThe Modified Pressure Projection
ApproachWe add the constraint
to the minimization of
subject to the constraint
Guided Fluid SimulationThe Modified Pressure Projection
Approach
Calculus of variations leads to the equations
Does it work?
Guided Fluid SimulationThe Modified Pressure Projection
Approach
Problems:• Matrix singular when filter is wide• Where should we place the constraints?
Test-simulations in Matlab
Guided Fluid SimulationThe Modified Pressure Projection
Approach
Fundamental question:
Does our approach fail completely,or can we modify it somehow?
Guided Fluid SimulationThe Modified Pressure Projection
Second Approach
The low frequencies of the fine simulation should be as close as possible to the frequencies of the
coarse simulation
Challenge: Formulate this mathematically
Guided Fluid SimulationThe Modified Pressure Projection
Second ApproachWe add the minimization term
to the minimization of
subject to the constraint
Guided Fluid SimulationThe Modified Pressure Projection
Second Approach
Calculus of variations leads to the equations
Does it work?
Guided Fluid SimulationThe Modified Pressure Projection
Second ApproachVerification in 2D
Guided Fluid SimulationThe Modified Pressure Projection
Second Approach
Fast to solve, but 1602 requires roughly 2GB and we want to do it in 2563…
Computational challenges: • Sparse entries take up 4.04TB in resolution 2563
• We reduced this to 208MB• Linear system is a-symmetric
• Solution: Improved multigrid solver• Linear system is slow to solve
• Solution: Parallel solver using separable lowpass filters
Guided Fluid SimulationThe Modified Pressure Projection
Second Approach
Guided Fluid SimulationThe Modified Pressure Projection
Second Approach
• Boundaries traditionally hard to use withmultigrid
• Which lowpass filter should be used?• How do we handle non-physically based
guiding velocity fields?
More computational challenges:
ResultsInterpolation between strictly guided and unguided simulation
Low res High Res
Links to More Information
• http://cs.au.dk/research/areas/computer-graphics-and-scientific-computing/
• http://cg.alexandra.dk/2009/05/15/smoke-rendering-demo/
