Amplitude malformation in the IFFT ocean wave rendering under the influence of the fourier coefficient

Abstract

Although Tessendorf's IFFT Gerstner wave model has been widely used, the value of A, a constant of the Fourier coefficient, is not given. A will strongly influence the shape of the rendered ocean wave and even cause amplitude malformation. We study the algorithm of the IFFT Gerstner wave, and give the method of A calculating. The method of the paper can guarantee there is no amplitude malformation in rendered ocean waves. The expression of the IFFT Gerstner wave with the amplitude of the cosine wave is derived again. The definite integral of the wave number spectrum is discretized. Further, another expression of the IFFT Gerstner wave is gotten. The Fourier coefficient of the expression contains the wave number spectrum and the area of the discrete integral domain. The method makes the shape of the generated wave stable. Comparing Tessdendorf's method with the method of the paper, we find that the expression of A should contain the area of the discrete integral domain and the spectral constant of the wave number spectrum. If A contains only the spectral constant, the amplitude malformation may occur. By reading some well known open source codes, we find that the code authors adopted some factitious methods to suppress the malformed amplitude Obviously, the code authors have already noticed the phenomenon of the malformation, but not probed the cause. The rendering results of the codes are close to that of the method of the paper. Furthermore, the wave potential is computed using the Gerstner wave model directly, the author find it is quite close to that of the paper. The experimental results and comparisons show that the method of the paper correctly computes the wave potential and effectively solves the problem of amplitude malformation.