Water Wave Animation via Wavefront Parameter Interpolation

Abstract

We present an efficient wavefront tracking algorithm for animating bodies of water that interact with their environment. Our contributions include: a novel wavefront tracking technique that enables dispersion, refraction, reflection, and diffraction in the same simulation; a unique multivalued function interpolation method that enables our simulations to elegantly sidestep the Nyquist limit; a dispersion approximation for efficiently amplifying the number of simulated waves by several orders of magnitude; and additional extensions that allow for time-dependent effects and interactive artistic editing of the resulting animation. Our contributions combine to give us multitudes more wave details than similar algorithms, while maintaining high frame rates and allowing close camera zooms.

An optimization on water wave diffraction approximation based on wave packets

“…In fact, the diffractive water waves have a tendency to stay away from the boundaries. Specifically, for the water wave after diffraction, its amplitude decreases as it gets closer to the boundary, which is consistent with the conclusion in one the aforementioned works …”

“…The closer the simulation performance is to these patterns, the higher the authenticity of the method is. As demonstrated in these patterns, different from the statement in the works of Jeschke and Wojtan, the diffractive water waves are not strictly “glued” to the boundaries. In fact, the diffractive water waves have a tendency to stay away from the boundaries.…”

“…Recently, Jeschke et al proposed an approach for diminishing the effect of Nyquist's limit via carrying out a simulation on a lower resolution instead of visualized resolution through a novel Gabor transformation. As stated in the work of Jeschke and Wojtan, compared to particle‐based approaches, artificial damping is often needed to keep stability in grid‐based approaches. In addition, without energy conservation, grid‐based approaches lack the ability to deal with waves propagating through a long distance.…”

“…However, this method suffers from the incapability to deal with partial diffraction. Jeschke and Wojtan have successfully handled approximations of wave behaviors mentioned above with the wavefront tracking approach in their previous work, in which water wavefronts were divided into segments and were treated and tracked as “particles.” Refraction was implemented according to the Snell's law, and diffraction was accomplished by adding another point which moves along the boundary between the start point and end point of a wavefront segment. Later, based on such approximation methods, they put forward the wave packets approach .…”

Ocean Wave Rendering with Whitecap in the Visual System of a Maritime Simulator

“…Horvath [22] used the TMA spectrum to construct a directional spectrum, and the Gerstner wave model was used to render sea swell. Some approaches were tried to animate the interaction between the ocean wave and solid body, such as wave front tracking algorithm [23] and wave particle [24].…”