%  mk3Dcosine(N,T, kx,ky,omega)
%
%  This program displays a travelling 3D cosine wave (kx,ky,omega)
%
%     cos( 2 pi / N * (kx x + ky y) +  2 pi / T * omega t)
%  
%  where kx,ky are in 0,1,.. N-1  and omega is in 0,1,..T-1
%
%  You need to have Mike Langer's program "showmovie" in the same directory.
%


function mk3Dcosine(N,T,kx,ky,omega)

Ihat = zeros(N,N,T);

%
%  MATLAB indexes the matrix I(x,y) using indices from 1 to N, 
%  whereas, in the course notes,  we have been indexing from 0 to N-1.   
%  This is the reason why we subtract 1 from the indices when 
%  computing the x,y coordinates in Ihat() below.
%  (Similarly for the time variable.)


Ihat(ky+1,kx+1,omega+1) = 1;

if (kx * ky * omega == 0)
   ['ERROR:  This code only works kx,ky,omega are all > 0']
else
   Ihat(N-ky+1,N-kx+1,T-omega+1) = 1;
end

I =  real(ifftn(Ihat));    

% The small imaginary error is due to numerical imprecision off fft.

showmovie