function out=lt2d(A,p)
%
% LT2D(A,p) overlays a polygon p in the plane and
% its image A*p defined by multiplication by a
% 2 x 2 matrix A that is passed as a parameter.
%
% The function is self-demonstrating -- it uses the
% cat's face and a geometrically simple matrix A if
% no (or only one) paramter(s) are provided.
%
% The function call typically is preceded by the
% commands
%
% p=drawfig  % Create a polygon
% twoDexa    % Define typical matrices
%
% Then repeatedly call this function with predefined
% matrices lt2d(A1,p), lt2d(A2,p), lt2d(B3,p),  ...
% and twofold/threefold products like lt2d(A2*C3) or 
% lt2d(inv(C5)*A3*C5,p) or enter matrices by hand
% lt2d([1 2; 3 -4],p)
%
% Typical task: Precisely describe the effect of 
% the linear transformation. Systematically organize
% the observations with the goal of KNOWING the 
% effects of any of these matrices....
%
% Author: Matthias Kawski. July 2000.
%         http://math.la.asu.edu/~kawski
%
% Update July 24, 00: Correction of help paragraph.
%                     Pass polygon p as 2nd parameter.                         
if nargin < 2 
   topx=[1 .98 .8  .83 .8  .77  .5 .25 0 -.25 -.5 -.8 -.8 -.98 -1];
   topy=[0 .15 .7 1.15 1.03 1.15 .85 .95 1  .95 .85 1.2  .7  .15  0];
   botx=-cos(pi*[1:10]/10);
   boty=-sin(pi*[1:10]/10);
   wiskx=[.2 1.3 .2 1.4 .2 1.4 .2 1.3 .2 .17 .13 .08 .03 0];
   wisky=[ 0  .3  0  .1  0 -.1  0 -.3  0  .1 -.1 .1  -.1 0]-.2;
   xeye=[0  .2  .3 .4 .43 .45 .43 .4 .37 .35 .37 .4  .5 .6 .5  .4 .3  .2  0];
   yeye=[.5 .5 .43 .4 .42 .5  .58 .6 .58 .5  .42 .4  .43 .5 .57 .6 .57 .5 .5]-.2;
   x=[topx,botx,wiskx,xeye,-xeye,fliplr(-wiskx)];
   y=[topy,boty,wisky,yeye, yeye,fliplr(wisky)];
   p=[x;y];
end
if nargin < 1 
   A = [57 26; 26 27]/24
end
clf
axis([-5 5 -5 5])
hold on
axis equal
plot([-5 5],[0,0],'k')
plot([0,0],[-5 5],'k')
pplot(p,'r')
disp('Strike any key to continue')
pause
ffill(A*p,'c')
pplot(p,'r')
text(-4.5,4,'A=','FontSize',14)
text(-3.5,4,num2str(A,2),'FontSize',14)
text(-4.5,2,'det A=','FontSize',14)
text(-2,2,num2str(det(A),2),'FontSize',14)
axis([-5 5 -5 5])