Comparison study between the Fourier and the Hartley transforms for the real-time simulation of the sea surface elevation

The paper presents the results of a comparison study between the Fourier and the Hartley transforms for the real-time simulation of the sea surface elevation in 3D. Fourier transforms are currently the most used and efficient method for obtaining realistic ocean scenes in interactive Virtual Environments. Although the Fast Fourier Transform has been the preferred choice for this type of simulations, the study reveals that the Fast Hartley Transform can be a valid alternative, and even have some advantages compared to the former. The study mainly focuses on the performance and memory aspects, which are decisive factors for real-time applications with ocean scenes, such as ship bridge simulators. The methodology to obtain the sea surface elevation in time domain from a sea state defined by a directional wave spectrum is also described.