% 
% Written by:
% -- 
% John L. Weatherwax                2006-12-31
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; clear; close all; 

a = 2; 

x_star = a * ( -1 + sqrt(2) ); 

x_upper = linspace( 0, x_star, 100 );
y_upper = (1/(2*a))*( a^2 - x_upper.^2 );

x_lower = linspace( x_star, +a/2, 100 );
y_lower = sqrt( a^2 - 2 * a * x_lower ); 

h_lower = plot( x_lower, y_lower, 'k-', 'LineWidth', 3 ); hold on; 
h_upper = plot( x_upper, y_upper, 'k-', 'LineWidth', 3 );
xlabel('x axis' ); ylabel('y axis'); 
legend( [h_lower,h_upper], 'lower curve','upper curve', 'location', 'northeast' ); 
axis( [0, a, 0, a] ); 
text( 0.05*a, 0.15*a, 'points closer to center than edge' )

saveas( gcf, '../WriteUp/Graphics/region_R', 'epsc' );