A simple model of ship wakes

While ocean waves were among the first natural phenomenon to be modeled satisfactorily in computer graphics, waves from ships—ship wakes—have been largely ignored. The model presented in this thesis is suitable for animating wakes created by a ship moving along an arbitrary course. Instead of the dynamic solution of a free-surface problem that can be computationally expensive and unstable, the approach presented is kinematic and while ad hoc, is efficient and simple to implement. The model superimposes circular waves emanating from points along the ship's path to determine the wake profile. In doing so, characteristics of the ship's hull are ignored. The approach is similar to the mathematical treatment of Kelvin's method of stationary phase, where curves of constant phase are obtained by integrating point impulses over the ship's course. Accuracy in obtaining an exact profile for the surface, as determined by the stationary phase method for closed-form solutions, is sacrificed for the ability to specify an arbitrary path. The problem then becomes one of generating circles with a height field associated with them. This is done by adopting two different methods; one that uses a midpoint circle algorithm based on Bresenham's incremental circle generator and another that efficiently determines a profile for the circles. The path of the ship is represented by parametric piecewise-cubic curves and the water surface by a height field. An animation is obtained by generating the height field for successive positions of the ship along the curve.

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