Realistic Simulation and Rendering of Smoke CSE Class Project Presentation Oleksiy Busaryev TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.:
Project Goals and Methods Realistic visualization of smoke behavior Simulation: inviscid incompressible fluid flow Rendering: high albedo, multiple scattering Visual Simulation of Smoke Fedkiw, Stam, Jensen SIGGRAPH 01 Efficient Simulation of Light Transport in Scenes with Participating Media using Photon Maps Jensen, Christensen, SIGGRAPH 98 Fluid Simulation for Computer Graphics Bridson 08
Eulerian vs Lagrangian Eulerian approach (we use) – fixed space tesselation (grid) – quantities defined on a grid – good for gas & fluid simulation Lagrangian approach – particle-based simulation – granular materials (sand) & fluid
Computational Grid Staggered arrangement Scalar values in centers Vector components in faces Allows O( x 2 ) accurate central differences:
Fluid Equations (Eulerian) Inviscid Navier-Stokes (Euler) equations: Density & temperature: Advection Incompressibility Pressure difference External forces
Fluid Equations (Lagrangian) Inviscid Navier-Stokes (Euler) equations: Density & temperature: Incompressibility Pressure difference External forces
Splitting Advection (move quantities with the flow): External forces (e.g. gravity, buoyancy): Pressure difference/mass conservation:
Numerical Algorithm Find a suitable time step t Advect and T in the divergence-free field u Self-advect the velocity field u Apply external forces f to u Enforce incompressibility in u by projection, producing divergence-free velocity field
Semi-Lagrangian Advection Trace density and temperature back in time: More accurate 2 nd order Runge-Kutta: Each velocity component is advected separately
External Forces & Vorticity Gravity & buoyancy: Vorticity confinement (combats dissipation): Vorticity Vorticity gradient
Pressure Projection Project u to the space of divergence-free fields Subtract pressure gradient p: Pressures are obtained from linear system that enforces zero divergence for each cell:
Simulation Results OpenGL rendering of density & temperature 64 x 64 x 64 grid Semi-transparency Color: temperature 75 frames = 9.81, = 350 = 0.01
Light Transport Equation Volume rendering of density field required Absorption, scattering, emission affect light: Emitted radiance Absorption + Scattering = Extinction coefficient Radiance change Phase function Scattering coefficient Absorption coefficient
Rendering Algorithm Discretize LTE using ray marching algorithm: How to compute in-scattered radiance? Emitted radiance New radiance In-scattered radiance Previous radiance
Single Scattering Only rays from light sources are scattered Smoke volume looks somewhat flat with emission no emission
Multiple Scattering Any light rays can be scattered in media Environment affects how media is shaded Global illumination needed
Multiple Scattering Computation Direct scattering + indirect scattering: Indirect part estimated by photon mapping: surface photon mappingvolume photon mapping
Volume Photon Mapping Shoot enough photons from light sources Photons are absorbed or scattered by media Interacting photons stored in the volume map
Video: Single Scattering 75 frames 10 frames / sec 800 x 800 px 5-10 min / frame
Video: Single Scattering + Emission 75 frames 10 frames / sec 800 x 800 px 5-10 min / frame
Video: Multiple Scattering 75 frames 10 frames / sec 800 x 800 px 3-6 hours / frame Noise! 100K photons is not enough! Add emission