%Chapter 10, Example 10.3, Fig 10.10
%Eric Dubois, updated 2018-12-20
%Illustration of the frequencies involved in the halftone attenuation
%Required functions: Lattice_Points_2d, ds2nfu
close all; clear all;

%requires ds2nfu by Michelle Hirsch
clear all
close all

%sampling matrices and portion of R^2 to plot
VG = [.1474 .1614; .1614 -.1474];
UL = [-.5 -.5]';
LR = [.5 .5]';

%get the points of the lattice in the desired region 
xoutG = Lattice_Points_2d(VG,UL,LR);

%create the plot
%set the plot size and font
figure

%plot the points
points = plot(xoutG(:,1),xoutG(:,2),'k.');
points.MarkerSize= 9;

axis equal
axis off
set(gca,'ydir','reverse'); 

hold on

%create the axes
%u axis from -.52 to +.52
[xaxx,xaxy] = ds2nfu([-.52 .54], [0 0]);
annotation('arrow',xaxx,xaxy,'headlength',5,'headwidth',5);
%v axis from -.52 to .52
[yaxx,yaxy] = ds2nfu([0.0 0.0],[.52 -.54]);
annotation('arrow',yaxx,yaxy,'headlength',5,'headwidth',5);
text(.52,-.04,'\itu','FontName','times')
text(-0.04, .52, '\itv','FontName','times')

rectangle('Position',[-.5,-.5,1,1]);

%Label the modulation frequencies
str1 = '$$\mathbf{u}_{m,1}$$';
text(0.14,.185,str1,'Interpreter','latex');
str2 = '$$\mathbf{u}_{m,2}$$';
text(.14,-.12,str2,'Interpreter','latex');
str3 = '$$\mathbf{u}_{m,3}$$';
text(.28,.05,str3,'Interpreter','latex');
str4 = '$$\mathbf{u}_{m,4}$$';
text(.01,.33,str4,'Interpreter','latex');
str5 = '$$\mathbf{u}_{m,5}$$';
text(0.28,.35,str5,'Interpreter','latex');
str6 = '$$\mathbf{u}_{m,6}$$';
text(0.3,-.26,str6,'Interpreter','latex');
str7 = '$$\mathbf{u}_{m,7}$$';
text(0.42,.2,str7,'Interpreter','latex');
str8 = '$$\mathbf{u}_{m,8}$$';
text(0.14,.45,str8,'Interpreter','latex');
str9 = '$$\mathbf{u}_{m,9}$$';
text(0.41,-.11,str9,'Interpreter','latex');
str10 = '$$\mathbf{u}_{m,10}$$';
text(0.14,-.43,str10,'Interpreter','latex');

set(gcf,'Color',[1 1 1]);