Rendering falling snow using an inverse Fourier transform

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Rendering falling snow using an inverse Fourier
transform

• Michael Langer Linqiao Zhang
• School of Computer Science
  McGill University

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Falling snow
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(No Transcript)
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Particle systems methodfor rendering falling snow

• W. Reeves, ACM Trans. Graphics 83
• K. Sims, SIGGRAPH 90
• M. Shinya and A. Fournier, Eurographics 92
• T. Nishita et al. Eurographics 97
• P. Fearing, SIGGRAPH 00

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Rendering falling snow using an inverse Fourier
transform
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Spectral Synthesis

• noise, turbulence (Perlin, 85)
• clouds (Gardner,84, 85)
• terrains (Voss, 85)
• ocean waves (Mastin et al, 87)
• wind, fluids and smoke (Stam and Fiume, 93,
  Nishita and Fournier 92)

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Spectral Synthesis method

• Model the power spectrum
• Compute the inverse Fourier transform
• Render

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Fourier transform of motion
Any video can be written as the sum of moving
sine waves.
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Fourier transform of motion
f , f are spatial frequencies f
is temporal frequency (v , v ) is
image velocity
x y
t
x y
v f v f f 0
x x y y t
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Two observations about falling snow

1. Far snowflakes are smaller.
2. Far snowflakes are slower.

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Observation 1

• Far snowflakes correspond to higher spatial
  frequencies.
• distance d

2 2
f f
x y
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Observation 2

• Fall snowflakes are slower.
• v

1
d
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Observations 1 2

• Thus,
• v

1
2 2
f f
x y
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Observation 3

• For vertically falling snow
• v

f
t
y
f
y
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Observations 1, 2, 3 imply

• dispersion relation for motion parallax

f
y
f
t
2 2
f f
x y
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Spectral Synthesis method

• Model the power spectrum
• Restrict the spectrum to the dispersion surface
  in (f , f , f )
• set 1/f amplitude and random phase over upper 3
  octaves of spatial frequencies
• Compute the inverse Fourier transform
• Render

x y z
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Inverse Fourier transform of dispersion surface
Bigger stuff moves faster.
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Spectral Synthesis method

• Model the power spectrum
• Compute the inverse Fourier transform
• Render
• Treat synthetic snow as a time-varying opacity
  function a(x, y, t)
• Composite the snow with a background image or
  video

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Composite with background image

• I(x,y,t) a(x, y, t) I
• (1 - a(x, y, t)) I (x,y)

amb
bg
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Background image
Jimmys place, painting by Gary Johnson
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Composite snow on top of background image