FFT_NOISE.h

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// This file is part of Wavelet Turbulence.
// 
// Wavelet Turbulence is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// 
// Wavelet Turbulence is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
// 
// You should have received a copy of the GNU General Public License
// along with Wavelet Turbulence.  If not, see <http://www.gnu.org/licenses/>.
// 
// Copyright 2008 Theodore Kim and Nils Thuerey
// 
//

#ifndef FFT_NOISE_H_
#define FFT_NOISE_H_

#ifdef WITH_FFTW3
#include <iostream>
#include <fftw3.h>
#include <MERSENNETWISTER.h>

#include "WAVELET_NOISE.h"

#ifndef M_PI
#define M_PI 3.14159265
#endif

// shift spectrum to the format that FFTW expects
static void shift3D(float*& field, int xRes, int yRes, int zRes)
{
  int xHalf = xRes / 2;
  int yHalf = yRes / 2;
  int zHalf = zRes / 2;
 // int slabSize = xRes * yRes;
  for (int z = 0; z < zHalf; z++)
    for (int y = 0; y < yHalf; y++)
      for (int x = 0; x < xHalf; x++)
      {
        int index = x + y * xRes + z * xRes * yRes;
        float temp;
        int xSwap = xHalf;
        int ySwap = yHalf * xRes;
        int zSwap = zHalf * xRes * yRes;
        
        // [0,0,0] to [1,1,1]
        temp = field[index];
        field[index] = field[index + xSwap + ySwap + zSwap];
        field[index + xSwap + ySwap + zSwap] = temp;

        // [1,0,0] to [0,1,1]
        temp = field[index + xSwap];
        field[index + xSwap] = field[index + ySwap + zSwap];
        field[index + ySwap + zSwap] = temp;

        // [0,1,0] to [1,0,1]
        temp = field[index + ySwap];
        field[index + ySwap] = field[index + xSwap + zSwap];
        field[index + xSwap + zSwap] = temp;
        
        // [0,0,1] to [1,1,0]
        temp = field[index + zSwap];
        field[index + zSwap] = field[index + xSwap + ySwap];
        field[index + xSwap + ySwap] = temp;
      }
}

static void generatTile_FFT(float* const noiseTileData, std::string filename)
{
    if (loadTile(noiseTileData, filename)) return;
    
    int res = NOISE_TILE_SIZE;
    int xRes = res;
    int yRes = res;
    int zRes = res;
    int totalCells = xRes * yRes * zRes;
    
    // create and shift the filter
    float* filter = new float[totalCells];
    for (int z = 0; z < zRes; z++)
        for (int y = 0; y < yRes; y++)
            for (int x = 0; x < xRes; x++)
            {
                int index = x + y * xRes + z * xRes * yRes;
                float diff[] = {abs(x - xRes/2), 
                abs(y - yRes/2), 
                abs(z - zRes/2)};
                float radius = sqrtf(diff[0] * diff[0] + 
                diff[1] * diff[1] + 
                diff[2] * diff[2]) / (xRes / 2);
                radius *= M_PI;
                float H = cos((M_PI / 2.0f) * log(4.0f * radius / M_PI) / log(2.0f));
                H = H * H;
                float filtered = H;
                
                // clamp everything outside the wanted band
                if (radius >= M_PI / 2.0f)
                    filtered = 0.0f;
                
                // make sure to capture all low frequencies
                if (radius <= M_PI / 4.0f)
                    filtered = 1.0f;
                
                filter[index] = filtered;
            }
    shift3D(filter, xRes, yRes, zRes);
    
    // create the noise
    float* noise = new float[totalCells];
    int index = 0;
    MTRand twister;
    for (int z = 0; z < zRes; z++)
    for (int y = 0; y < yRes; y++)
      for (int x = 0; x < xRes; x++, index++)
        noise[index] = twister.randNorm();
    
    // create padded field
    fftw_complex* forward = (fftw_complex*)fftw_malloc(sizeof(fftw_complex) * totalCells);
    
    // init padded field
    index = 0;
    for (int z = 0; z < zRes; z++)
    for (int y = 0; y < yRes; y++)
      for (int x = 0; x < xRes; x++, index++)
      {
        forward[index][0] = noise[index];
        forward[index][1] = 0.0f;
      }
    
    // forward FFT 
    fftw_complex* backward = (fftw_complex*)fftw_malloc(sizeof(fftw_complex) * totalCells);
    fftw_plan forwardPlan = fftw_plan_dft_3d(xRes, yRes, zRes, forward, backward, FFTW_FORWARD, FFTW_ESTIMATE);  
    fftw_execute(forwardPlan);
    fftw_destroy_plan(forwardPlan);
    
    // apply filter
    index = 0;
    for (int z = 0; z < zRes; z++)
        for (int y = 0; y < yRes; y++)
            for (int x = 0; x < xRes; x++, index++)
            {
                backward[index][0] *= filter[index];
                backward[index][1] *= filter[index];
            }
    
    // backward FFT
    fftw_plan backwardPlan = fftw_plan_dft_3d(xRes, yRes, zRes, backward, forward, FFTW_BACKWARD, FFTW_ESTIMATE);  
    fftw_execute(backwardPlan);
    fftw_destroy_plan(backwardPlan);
    
    // subtract out the low frequency components
    index = 0;
    for (int z = 0; z < zRes; z++)
        for (int y = 0; y < yRes; y++)
            for (int x = 0; x < xRes; x++, index++)
                noise[index] -= forward[index][0] / totalCells;

    // save out the noise tile
    saveTile(noise, filename);
    
    fftw_free(forward);
    fftw_free(backward);
    delete[] filter;
    delete[] noise;
}

#endif

#endif /* FFT_NOISE_H_ */