% a wall of tiles, specified in terms of dilation=a, translation=b, chirp=c
%
% returns a gridwork
%
% USE:  contour(tilesabc(4,4,100,100,0,0,0))
%               tiles(u,v, M , N , dilation_and_zoom, translation, chirp_rate)
%               tiles(u,v, M , N ,a,b,c);
%
%       translation=1/N moves image one pixel to right
%       translation=i*1/M moves image one pixel DOWN    (FIX THIS???)
%       dilation_and_zoom = exp(i*30*o) causes 30deg rot CLOCKWISE (FIX THIS???)
%       dilation_and_zoom = 2     makes everything smaller; (more cycles appear)
%
%       X to right, Y up; that makes ROTATION (origin) ABOUT LOWER LEFT CORNER
%       for M down, N to right, use rot90(___,3), for example:
%       imagesc(rot90(tilesabc(3,3,100,100,exp(i*10*o),0),3)); axis square
%
% chirp_rate not yet implemented (take it from tiles.m: angle,f1,f2, and all...)


%function E = dummy(u,v,M,N,angle,f1,f2,X0,Y0);
%function E = dummy(u,v,M,N,dilation_and_zoom,translation,chirp_parameters);
function E = dummy(u,v,M,N,a,b,c);

if nargin >= 7
  disp('chirp parameters not yet implemented; modify tilesabc.m or use tiles.m')
end%if

if nargin<=6
  c = 0;              % identity chirp-rates
end%if
if nargin<=5
  b = 0;              % identity translation
end%if
if nargin<=4
  a = 1 + 0*i;        % identity zoom
end%if

if nargin < 4
  disp('need at least 4 input arguments (e.g. the frequencies and size)')
end%if

%x = cos(2*pi*u*((0:(N-1))/N));
%y = cos(2*pi*v*((0:(M-1))/M));

%[X, Y] = meshdom(u*((0:(N-1))/N),v*((0:(M-1))/M));
[X, Y] = meshdom((0:(N-1))/N,(0:(M-1))/M);

Z = X + i*Y;
Z2 = a*Z + b;
X2 = real(Z2);
Y2 = imag(Z2);

E = cos(2*pi*u*X2).*cos(2*pi*v*Y2);             % chessboard-like pattern
%E = abs(cos(2*pi*u*X2)).*abs(cos(2*pi*v*Y2));   % tile-like pattern