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Ocean Wave Simulation Model for Realistic Effects

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  1. Making waves Alain Fournier, UBC

  2. 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

  3. What the model is not • Stochastic • A fractal • A height field • Net transport of water • A physical model

  4. Previous and following work • Nelson Max’ Carla’s Island (‘81) • Ken Perlin’s noise (‘85) • Darwin Peachey’s waves (‘86) • Ts’o and Barsky (‘85) • Musgrave, Foster, Metaxas, and many dynamic models.

  5. 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 )

  6. Parametric equation For t = 0 and z0 = 0 x = -a / k - r sin (a) z = - r cos(a) where a = - k x0

  7. 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)

  8. Shape parameter • Steepness of the wave H/L is the shape parameter • H/L = k r / p

  9. 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

  10. 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))

  11. 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

  12. 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

  13. 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

  14. 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.

  15. Typical train file

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

  17. Rendering • You’re on your own • Still to get nice foam and spray • Speed? Nor worse than basic terrain object

  18. Conclusions • Well, you’ve got waves • It’s pretty simple • It’s quite flexible • It can look good • It’s fairly adaptable (OK, very adaptable).

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