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Multi-Band Fourier Synthesis of Ocean Waves

Realistic simulations of the ocean surface based on statistical wave models typically rely on very large Fourier grids. Real-time requirements severely limit the size of the grids that can be used, even if the FFT is implemented on the GPU. Moreover, none of the grids used so far are sufficient for capturing the entire dynamic range of ocean waves, which can easily span four to five orders of magnitude. Adaptive approaches that do not require the wave number samples to be equidistantly spaced offer greater flexibility, but they are not able to benefit from the computational efficiency of the FFT.

The multi-band approach we propose removes the FFT as the computational bottleneck of sea surface simulations. By splitting the wave number range into a small number of non-overlapping, relatively narrow bands within which the samples are equidistantly spaced allows making use of the FFT while having some of the flexibility of the adaptive approaches that concentrate wave number samples in high-energy regions of the spectrum. A wide range of wave numbers can be modelled at a small fraction of the computational costs of the single-band approach, making the algorithm highly suitable for real-time applications, such as computer games and naval and flight simulators.

Seen on the right is an example of a multi-band simulation employing four 64×64 grids that span a dynamic range of more than four orders of magnitude. On current hardware, simulation and display proceed at 200 frames per second. Also shown are single-band simulations that share the smallest and the largest wave numbers, respectively, with the multi-band approach. The simulations using 128×128 grids are approximately as fast as the multi-band one; those using 1024×1024 grids run over one hundred times slower.

Publication

G. LeBlanc, A. Shouldice, D. V. Arnold, and S. Brooks
Multi-band Fourier synthesis of ocean waves
Journal of Graphics Tools, 16(2):57-70, 2012.

Code

A Matlab/Octave script that implements the multi-band approach can be found here.

Support

This research is supported through grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Foundation for Innovation (CFI).