1. Depicting Fire and Other Gaseous Phenomena Using Diffusion Processes Jos Stam and Eugene Fiume Dept. of CS, University of Toronto Presentation ©2001 Brenden Schubert

2. Modeling Gasses Texture Parameterization –Vary parameters to get animation  Empirical  Hard to relate parameters to physical model Particle System –User-defined wind field displaces particles each frame  More correct (think molecular)  Computationally intense

3. “warped blobbies” Start with a particle system Use blobs instead of particles –Replace lots of particles with single blob Wind field advects and diffuses blobs –Key: diffusion is non-uniform

4. Diffusion Processes Toronto must require CS majors to take Differential Equations too Is applied to both particles (blobs), and temperature Simple enough to be understood by animators with “limited knowledge of physics” –What could be more simple than milk dissolving in a coffee cup..?

5. The Diffusion Equation u = wind field  = scalar field (density of the gas)  = gradient operator   = diffusion coefficient (like viscosity) S  = source field (producing gas) L  = sink field (sucking gas in)

6. The Diffusion Equation Diffusion depends on the (square of) the gradient of the scalar field *   Advection depends on the gradient of the scalar field * u Sources and sinks are like adding constant (over time) fields to the wind field Apply to both gas “density” and temperature

7. There’s no gluDiffEQ() function Approximate by convolving the exact solution with a smoothing function The Smoothing Function –Modified Gaussian: incorporates How much the blob has changed from original  = function of the wind field

8. There’s no gluDiffEQ() function Approximate by convolving the exact solution with a smoothing function The Smoothing Function –Modified Gaussian: incorporates  = original blob attributes  = function of the wind field

9. Light and Gas Internally produced light –Emission spectra known –Proportional to T 4 Externally produced light –Scattered: albedo (  ) contstant Phase function p –Absorbed (1 –  * absorption spectra

10. Shooting Operations Light sources are a field Discretize environment into patches Repeatedly shoot light from patch to patch, blob to patch, and patch to blob Eventually will converge to an intensity field

11. Fire Why I picked this paper (you can’t burn stuff with differential equations) The key: Temperature field –Define an activation temperature T a –When T reaches T a … –Render flames Smoke –When gas cools below T s render smoke particle

12. Conclusions Warping blobs is good Convolution must be slow –“typical resolutions for our simulations were 20 x 20” –Video res frame takes 20 min on SGI Indigo 2 Manipulation of wind field is key to usability Fire –still requires lots of tweaking –good movement, but coloration not addressed