This time I'm trying hard to be as specific as I can. Please don't close the thread, help me to make a specific question. Thanks.

The description of formula with formula itself:

The fft-based representation of a wave height ﬁeld expresses the wave height **h(x, t)** at the horizontal position **x = (x, z)** as the sum of sinusoids with complex, time-dependent amplitudes:

(36)

where **t** is the time and **k** is a two-dimensional vector with components **k = (kx, kz)**, **kx = 2πn/Lx**, **kz = 2πm/Lz**, and **n** and **m** are integers with bounds **−N/2 ≤ n < N/2** and **−M/2 ≤ m < M/2**. The fft process generates the height ﬁeld at discrete points **x = (nLx/N,mLz/M)**. The value at other points can also be obtained by switching to a discrete fourier transform, but under many circumstances this is unnecessary and is not
applied here. The height amplitude Fourier components, **˜ h(k, t)**, determine the structure of the surface.

Another vesrion of the same formula:

Here **X** is a horizontal position of a point whose height we are evaluating. The wave vector **K** is a vector pointing in the direction of travel of the given wave, with a magnitude k dependent on the length of the wave (l):

**k =2p /lamda**

And the value of **h (K,t)** is a complex number representing both amplitude and phase of wave **K** at time **t**. Because we are using discrete Fourier transformation, there are only a finite number of waves and positions that enters our equations. If **s** is dimension of the heightfield we animate, and **r** is the resolution of the grid, then we can write:

**K = (kx,kz) = (2pn / s,2pm /s)**

where **n** and **m** are integers in bounds **–r/2 £ n,m < r/2**. Note that for FFT, **r** must be power of two.

Questions:

How many

**k**do I need? Does it mean, that**k**takes all possible values (on the grid I mean)?And what do I get as a result - complex number that shows height and (what?) in

**concrete point**so I need make computations for all points on the grid or the**whole grid itself**?How to apply fft to this formula?

research questionfor mathematicians; this is animplementation questionfor those who routinely do computational fluid dynamics as part of their job (but NOT applied mathematicians, who study the theoretical basis for methods) - I would suggest some kind of engineer or experimental physicist could help you, rather than a mathematician. All these numerical calculations/methods will be well-documented and implemented in standard hydrodynamics computer packages, and very familiar to those sorts of people (but not me). – Zen Harper Sep 10 '10 at 2:58