A simple model of ocean waves

We present a simple model for the surface of the ocean, suitable for the modeling and rendering of most common waves where the disturbing force is from the wind and the restoring force from gravity.It is based on the Gerstner, or Rankine, model where particles of water describe circular or elliptical stationary orbits. The model can easily produce realistic waves shapes which are varied according to the parameters of the orbits. The surface of the ocean floor affects the refraction and the breaking of waves on the shore. The model can also determine the position, direction, and speed of breakers.The ocean surface is modeled as a parametric surface, permitting the use of traditional rendering methods, including ray-tracing and adaptive subdivision. Animation is easy, since time is built into the model. The foam generated by the breakers is modeled by particle systems whose direction, speed and life expectancy is given by the surface model.To give designers control over the shape of the ocean, the model of the overall surface includes multiple trains of waves, each with its own set of parameters and optional stochastic elements. The overall "randomness" and "short-crestedness" of the ocean is achieved by a combination of small variations within a train and large variations between trains.Rendered examples of oceans waves generated by the model are given and a 10 second animation is described.