Correcting the Amplitude Malformation of Ocean Wave Rendering with Wave Number Spectrum

Because the rendered ocean wave of the inverse fast Fourier transform(IFFT) Gerstner wave is malformed, we raise a method using the wave number spectrum to correct the amplitude malformation. First, the IFFT Gerstner wave including the elementary wave amplitude is re-deduced. Then, we employ the right Riemann sum to discretize the definite integral of the wave number spectrum. The boundary value of the discrete integral domain depends on the sample mode for the wave number vector in IFFT. An approximate solution of the elementary wave amplitude is gotten. Finally, substituting the solution into the re-deduced expression, we get another IFFT Gerstner wave. Its Fourier coefficient contains the wave number spectrum and the area of the discrete integral domain. The experimental results show the method of the paper can precisely calculate the wave potential and the amplitude, keep the shape of the rendered wave stable, and correct the malformation.