1cs426-winter-2008

NotesNotes

If you’re interested, readBridson, Hourihan, Nordenstam, “Curl noise for procedural fluid flow”, SIGGRAPH ‘07

2cs426-winter-2008

Time integration woesTime integration woes

For rotational motion, immediately find serious flaw with Forward Euler: instability

Better off using a more accurate, more stable Runge-Kutta method• For example: 3rd order

k1 =v x( )

k2 =v x+ 12 Δtk1( )

k3 =v x+ 34 Δtk2( )

xnew =x+ 29 Δtk1 +

39 Δtk2 +

49 Δtk3

3cs426-winter-2008

Second order motionSecond order motion

Real particles move due to forces• Newton’s law F=ma• Need to specify force F (gravity, collisions, …)• Divide by particle mass to get acceleration a• Update velocity v by acceleration• Update position x by velocity

€

v inew = v i + Δt

F(x i,v i, t)

mi

x inew = x i + Δtv i

new

4cs426-winter-2008

Basic renderingBasic rendering

Draw a dot for each particle But what do you do with several particles per

pixel?• Add: models each point emitting (but not absorbing)

light -- good for sparks, fire, …• More generally, compute depth order, do alpha-

compositing (and worry about shadows etc.)• Can fit into Reyes very easily

Anti-aliasing• Blur edges of particle, make sure blurred to cover at

least a pixel Particle with radius: kernel function

5cs426-winter-2008

Motion blurMotion blur

One case where you can actually do exact solution instead of sampling

Really easy for simple particles• Instead of a dot, draw a line

(from old position to new position - the shutter time)• May involve decrease in alpha• More accurately, draw a spline curve• May need to take into account radius as

well…

6cs426-winter-2008

More detailed particle More detailed particle renderingrendering

Stick a texture (or even a little movie) on each particle: “sprites” or “billboards”• E.g. a noise function• E.g. a video of real flames

Draw a little object for each particle• Need to keep track of orientation as well, unless spherical• We’ll get into full-fledged rigid bodies later

Draw between particles• curve (hair), surface (cloth)

Implicit surface wrapped around virtual particles(e.g. water)