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I've spent the last week or so rendering a simple ocean using gerstner waves but having issues with tiling, so I decided to start rendering them "properly" and dip my toes into the murky waters of rendering a heightfield using an iFFT.

There are plenty of papers explaining the basic gist -

1) calculate a frequency spectrum

2) use this to create a heightfield using ifft to convert from frequency domain to spatial domain - animating with time t

Since the beginning of this journey I have learned about things like the complex plane, the complex exponent equation, the FFT in more detail etc but after the initial steps of creating an initial spectrum (rendering a texture full of guassian numbers with mean 0 and sd of 1, filtered by the phillips spectrum) I am still totally lost.

My code for creating the initial data is here (GLSL):

float PhillipsSpectrum(vec2 k){
  //kLen is the length of the vector from the centre of the tex
  float kLen = length(k);
  float kSq = kLen * kLen;

  // amp is wave amplitude, passed in as a uniform
  float Amp = amplitude;

  //L = velocity * velcoity / gravity
  float L = (velocity*velocity)/9.81;

  float dir = dot(normalize(waveDir),normalize(k));

  return Amp * (dir*dir) * exp(-1.0/(kSq * L * L))/ (kSq * kSq) ;
}

void main(){

   vec3 sums;

   //get screenpos - center is 0.0 and ranges from -0.5 to 0.5 in both
   //directions
   vec2 screenPos = vec2(gl_FragCoord.x,gl_FragCoord.y)/texSize - vec2(0.5,0.5);

   //get random Guass number
   vec2 randomGuass = vec2(rand(screenPos),rand(screenPos.yx));

   //use phillips spectrum as a filter depending on position in freq domain
   float Phil = sqrt(PhillipsSpectrum(screenPos));
   float coeff = 1.0/sqrt(2.0);

   color = vec3(coeff *randomGuass.x * Phil,coeff * randomGuass.y * Phil,0.0);
}

which creates a texture like this: enter image description here

Now I am totally lost as how to : a) derive spectrums in three directions from the initial texture

b) animate this according to time t like mentioned in this paper (https://developer.nvidia.com/sites/default/files/akamai/gamedev/files/sdk/11/OceanCS_Slides.pdf) on slide 5

I might be completely stupid and overlooking something really obvious - I've looked at a bunch of papers and just get lost in formulae even after acquainting myself with their meaning. Please help.

Lloyd Crawley
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  • you should read some paper about this, those slides does not have enough info,... as I see it the texture is not texture at all but the statistical distribution of the waves wavelength and Amplitude (not sure what is the difference between k and bold k) this is a 2D spectrum so apply 2D IDFFT on it and you will obtain the `omega` and `A` parameters from it so now just add time to the wave equations and sum it for each position and that should be it (but I see this first time so I could also missing something) – Spektre Mar 18 '15 at 09:08
  • at slide `The Diagram of updating...` you got the equations if I get it right the texture is `H0(k)` , after IDFFT it is called `H(k,t)` so just compute the equations (combination of both) ... btw your output texture does not match theirs your is symmetrical in two axises theirs is rotated and symmetrical in single axis ... so your waves will look a bit differently – Spektre Mar 18 '15 at 09:16
  • @spektre Thank you for your comments, however you state the obvious in that yes, this is in fact the statistical distribution of the waves, which is updated before applying the fft to it. It is symmetrical due to me using different input vals to create the phillips spectrum. Thankfully, I have found the source code for the presentation and going through it now, however it is pretty crazy stuff. Thanks again. – Lloyd Crawley Mar 18 '15 at 15:01

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