Making waves

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Making waves
Alain Fournier, UBC
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Making Waves What is the goal

• Computable model
• Geometry in familiar form
• Realistic shape
• Realistic motion
• Depth effect, refraction, wind effects
• Foam, spray
• Level of details, control of complexity

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What the model is not

• Stochastic
• A fractal
• A height field
• Net transport of water
• A physical model

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Previous and following work

• Nelson Max Carlas Island (81)
• Ken Perlins noise (85)
• Darwin Peacheys waves (86)
• Tso and Barsky (85)
• Musgrave, Foster, Metaxas, and many dynamic
  models.

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The basic model

• Lagrangian a grid is created and each grid point
  moves, but relationship is kept
• Each point moves in a circular orbital
• x x0 r sin(k x0 - w t )
• z z0 - r cos(k x0 - w t )

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Parametric equation

• For t 0 and z0 0
• x -a / k - r sin (a)
• z - r cos(a)
• where a - k x0

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Wave characteristics

• Height H 2r
• Wavelength L 2 p / k
• Period T 2 p / w
• Phase speed c L/T w / k (eg speed at which
  crest travels)

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Shape parameter

• Steepness of the wave H/L is the shape parameter
• H/L k r / p

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Some relationships

• L g T2 / 2 p (in deep water)
• c g T / 2 p (in deep water)
• Group velocity U c/2 (speed at which energy
  carried travels)
• If average wind speed is V, under some
  conditions
• H 7.065 10-3 V 2.5

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Special effects

• Go to 2D (wave direction)
• Put wind effect (speed up orbital at top, slow
  down at bottom) l
• Depth effect at depth h k tanh(k h ) k0
• k0 is k at infinite depth
• can be approximated by
• k k0 / sqrt( tanh (k0 h))

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Effects of effects

• l (wind effect) affects shape
• k (depth effect) affects wavelength, therefore
  phase speed, so causes refraction
• depth effect has to be cumulative over depth
  history of wave

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Breakers, spray and foam

• Particle speed greater than phase speed
• Curvature has to be high
• In model, particle (foam) is generated is
  curvature above threshold, leaves the wave
  (spray) if speed is above threshold.
• Direction and speed of spray is known

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Trains

• Wave train is group of waves with same
  characteristics
• Implemented as rectangular boxes with same
  height, period, wavelength, direction and its own
  speed.
• For fun also has height envelope and holes to
  introduce more variations

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Trains (continued)

• Trains actually have their own grid (usually
  rather low resolution, eg 5x5 or 10x10) to gather
  own information (such as depth history)
• Time decay effect can be introduced
• Trains can be backed up for initialization
• Train files describe several trains.

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Typical train file
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Height data

• Some built-in (slope, platform, funnels)
• Some imported (will be adjusted to size of wave
  grid)

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Rendering

• Youre on your own
• Still to get nice foam and spray
• Speed? Nor worse than basic terrain object

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Conclusions

• Well, youve got waves
• Its pretty simple
• Its quite flexible
• It can look good
• Its fairly adaptable (OK, very adaptable).