function gradualfft2()

img = readImage('lighthouse.tif');

ffs = fftshift(fft2(img)); %the real fft shifted for simmetry

ffl = log(abs(ffs)); %the log of fft to be able to see it in good visible proportions

%this is a meshgrid to use with the calculation of the round filter
[x y] = meshgrid(-1:(2/size(img,1)):1-(2/size(img,1)), -1:(2/size(img,2)):1-(2/size(img,2)));
circledist = sqrt(x.^2+y.^2);

fimg = figure;
set(fimg,'position',[10,10,400,400]);
image(img);
colormap(gray(256));

ffilter = figure;
set(ffilter,'position',[10,420,400,400]);
mesh(ffl);

[x,y,but]=ginput(1);

while (but==1)
 for i=0:0.1:sqrt(2)
  filter = (circledist<i);
  figure(ffilter);
  mesh(ffl);
  hold on;
  mesh(filter*20);
  hold off;
  figure(fimg);
  image(real(ifft2(fftshift(ffs.*filter))));
  colormap(gray(256));
  pause(0.001);
 end;  
 [x,y,but]=ginput(1);
end;

figure(ffilter);
clf;
set(ffilter,'position',[350, 0, 350,900]);
figure(fimg);
clf;
set(fimg,'position',[0,0,350,900]);

for i=1:6
 figure(ffilter);
 subplot(6,1,i);
 mesh(ffl);
 hold on;
 filter=(circledist<(i/6))-(circledist<(i/6-1/6));
 mesh(filter*20);
 figure(fimg);
 subplot(6,2,2*i-1);
 im = real(ifft2(fftshift(ffs.*filter)));
 image(im);
 colormap(gray(256));
 axis image;
 subplot(6,2,2*i);
 image(256*im/max(max(im)));
 axis image;
 colormap(gray(256));
end