function []=prob_7_1_28()
%
% Written by:
% -- 
% John L. Weatherwax                2006-11-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----
  
clc; close all; 

A = [ 2 1; 1 2 ]; 
A = rand(2,2);

theta = [ 0:2*pi/50:2*pi ]; 
circle = [cos(theta); sin(theta)];
ellipse = A * circle; 

figure; axis( [ -4 4 -4 4 ] ); axis( 'square' );
plot( circle(1,:), circle(2,:), ellipse(1,:), ellipse(2,:) );
hold on; 

eyes = [ -0.5 +0.5; +0.5 +0.5 ]; 
plot( eyes(1,1), eyes(2,1), 'bo' ); 
plot( eyes(1,2), eyes(2,2), 'ro' ); 
smileAngles = linspace( -3*pi/4, -pi/4 ); 
smile = 0.5*[ cos(smileAngles); sin(smileAngles) ]; 
plot( smile(1,:), smile(2,:), '-g' ); 

mappedEyes = A*eyes; 
mappedSmile = A*smile; 
plot( mappedEyes(1,1), mappedEyes(2,1), 'bo' ); 
plot( mappedEyes(1,2), mappedEyes(2,2), 'ro' ); 
plot( mappedSmile(1,:), mappedSmile(2,:), '-g' );