What I'll cover:

• Basic approach
• How it works
• Cool examples

  Noise

• Controlled pseudo-random texture primitive
• Can be used for displacement

  Some things you do with noise

• Modify color
   

  Some things you do with noise

• Use a fractal sum
  T(x) = N(x) + N(2x)/2 + N(4x)/4 ...

  Some things you do with noise

• Use a fractal sum of abs value:
  T'(x) = |N(x)| + |N(2x)/2| ...

  Some things you do with noise

• Domain displacement:
  color(x) = sin ( x + T'(x) )

  When you use it for time-varying noise

• There is time component:

  Our goal

• Make things "flow" better

• Pure evaluation:

  Require only one place on the domain

  We introduce several tricks

• Swirling trick

• Fake advection trick

  Swirling trick

• Noise is a sum of overlapping wavelets

• Each is a linear gradient × a dropoff kernel

Trick: rotate all the gradients over time

  Swirling trick

• Noise is a sum of overlapping wavelets

• Each is a linear gradient × a dropoff kernel

  Make sure directions stay uncorrelated

• Rotate all gradients (don't look at them)

  Advection

• No advection:
  • Small features independent of large features
  • Eg: billowing
• Lots of advection:
  • Small features carried along by large features
  • Eg: foam

  Face advection trick

• Constraint:
  • Color(x) = func( x + T(x + time) )
  • Only look at one domain point per noise eval

• Idea:
  • As fractal sum progresses:
    • Use value displacement at step i
    • To create domain displacement at step i+1

  Face advection trick

• Follow along noise derivative at step i

• Move "downhill" in domain to eval step i+1

  Displacing value up is like shifting domain downhill

  Iterate from coarse to fine

1. Eval noise for scale 2ⁱ

2. Shift domain downhill, following noise derivative

3. Iterate

  To vary amount of advection

• Maintain weight of how much to shift domain
  • Weight = 1 : Foam

  • Weight = 0 : Billowing

  Examples

  Examples

  Examples

  Examples

  Examples

  Examples

  What's it useful for

• Only pure evaluation needed
• A tool to use in a texturing bag of tricks
• Good for parallel / hardware accelaration:

  Only need to know one domain point

  Future work/blue sky

Apply to volume models, real time hardware