Shade the encircled area

Hi. Can anyone please tell me how to shade the encircled area(in red)?

The graph is as follows

And the code is as follows

tx1=-7:0.1:-1;
tx2=-1:0.1:0.5;
tx3=0.5:0.1:3;
tx4=3:0.1:7;
tx=[tx1 tx2 tx3 tx4];
x1=zeros(size(tx1));
x2=0.6.*ones(size(tx2));
x3=0.3.*ones(size(tx3));
x4=zeros(size(tx4));
x=[x1 x2 x3 x4];
th1=-7:0.1:0;
th2=0:0.1:7;
h1=zeros(size(th1));
h2=ones(size(th2));
h3=[h1 h2];
th=[th1 th2];
h4=exp(-th);
h=h3.*h4;
t=0;
plot(tx,x,-th+t,h,'-','linewidth',2)
ylim([-0.1 1.1])
legend('x(\tau)','h(t-\tau)')
grid

Answer 1

[Star Strider]

After the original code in your Question (not your subsequent Comment), add these lines:

hold on
Ltx = (tx >= -1) & (tx <= 0);
Ltht = (-th+t >= -1) & (-th+t <= 0);
xh = min([x(Ltx); h(Ltht)]);
patch([tx(Ltx) flip(tx(Ltx))], [zeros(size(xh)) xh], 'g')
hold off

to get this plot:

.

[the cyclist]

When I recreate this plot, and zoom in, I see that the green-shaded region is not below the red line as I believe OP wants.

[Star Strider]

I will let Muhammad Sanwal determine whether my code meets the requirements.

[Muhammad Sanwal]

It worked. Thanks!

Also, Star Strider, can you please explain the lines of code that you sent? And can the area(x,y) command be used instead of patch command? If so, how?

[Star Strider]

As always, my pleasure!

The ‘Ltx’ and ‘Ltht’ logical vectors select the parts of the respective independent variable vectors between -1 and 0. he ‘xh’ vector selects the minimum of the two vectors defined by ‘x(Ltx)’ and ‘h(Ltht)’ to define the dependent variable value of the segment at each point. (It would have been necesary to interpolate them to a common set of independent variable values had they not both been easily defined.) The patch call then fills the defined segment.

This area call would work:

area(-th(Ltht)+t, xh)

It would require an additional line of code to define the colour, if you wanted to change it from the default.

I use patch because it allows me to control exactly what the code does, and I am used to using it.

[Muhammad Sanwal]

Thank you. Suppose that I now shift the h(t-tau) graph in the interval 0<tau<2 (since I'm convolving x(tau) and h(t-tau)). What changes should I make in the portion of the code you sent in order to get the shaded area within that interval?

(Please note that now, the shaded portion should be within the value of x(tau)=0.3 and within the tau domain of 0<tau<2)

[Bruno Luong]

See my annimation code bellow that plots plenty of different shifts

[Star Strider]

I had to re-write your code to make this work. I created anonymous functions for the exponential and the ‘steps’ function to make it easier to change later, if you want to:

tau=1;
tv = linspace(-7, 7, 1000);
hexp = @(t,tau) exp(t-tau).*((t-tau)<0);
hstep = @(t) (0.6).*((t>=-1) & (t<=0.5)) + (0.3).*((t>=0.5) & (t<=3));
hmin = @(t,tau) min([hexp(t,tau); hstep(t)]);

figure
patch([tv flip(tv)], [hmin(tv,tau) zeros(size(tv))], 'g')
hold on
plot(tv, hstep(tv), '-b', 'LineWidth',1)
plot(tv, hexp(tv,tau),'r', 'LineWidth',1)
hold off
legend('Filled Area','x(\tau)','h(t-\tau)')
title(sprintf('\\tau = %g', tau))

Note that τ can be anything, including . I did not animate this, however varying τ will demonstrate that it definitely does work.

For :

.

[Muhammad Sanwal]

Thank you very much!

[Star Strider]

As always, my pleasure!

Answer 2

[the cyclist]

Combining your new code that aligns the values of t (but not using your attempt at creating the patch), and the same basic idea of Star Strider and Image Analyst, this code accurately aligns the patch as I believe you want. But, as Star Strider says, you decide.

t1=-7:0.1:-1;
t2=-1:0.1:0;
t3=0:0.1:0.5;
t4=0.5:0.1:3;
t5=3:0.1:7;
t=[t1 t2 t3 t4 t5];
x1=zeros(size(t1));
x2=0.6.*ones(size(t2));
x3=0.6.*ones(size(t3));
x4=0.3.*ones(size(t4));
x5=zeros(size(t5));
x=[x1 x2 x3 x4 x5];
h1=zeros(size(t1));
h2=zeros(size(t2));
h3=ones(size(t3));
h4=ones(size(t4));
h5=ones(size(t5));
h6=[h1 h2 h3 h4 h5];
h7=exp(-t);
h=h6.*h7;

figure
hold on
plot(t,x,-t,h,'-','linewidth',2)
ylim([-0.1 1.1])
legend('x(\tau)','h(t-\tau)')
grid

lightGreen = [0.85, 1, 0.85];

xh = min([x; flip(h)]);
plot(t,xh)
patch([flip(t) t], [zeros(size(t)) xh], lightGreen)

[Muhammad Sanwal]

both methods work. thanks!

[the cyclist]

Glad it worked out. Be aware that the two solutions cover slightly different areas, and this is more evident with the relative large step size (0.1) you are using.

If you use something smaller (e.g. 0.01), both solutions will more sharply align with your lines, visually.

Answer 3

[Bruno Luong]

Use polyshape and let polyshape do the work. Replace plot(P1, ...) with normal plot if you don't like the artefact on x-axis.

t1=-7:0.1:-1;
t2=-1:0.1:0;
t3=0:0.1:0.5;
t4=0.5:0.1:3;
t5=3:0.1:7;
t=[t1 t2 t3 t4 t5];
x1=zeros(size(t1));
x2=0.6.*ones(size(t2));
x3=0.6.*ones(size(t3));
x4=0.3.*ones(size(t4));
x5=zeros(size(t5));
x=[x1 x2 x3 x4 x5];
h1=zeros(size(t1));
h2=zeros(size(t2));
h3=ones(size(t3));
h4=ones(size(t4));
h5=ones(size(t5));
h6=[h1 h2 h3 h4 h5];
h7=exp(-t);
h=h6.*h7;

warning('off','MATLAB:polyshape:repairedBySimplify');
P1=polyshape(t,x);
P2=polyshape(-t,h);

close all
figure
hold on
plot(P2,'facecolor','none','edgecolor','r','linewidth',1)
plot(P1,'facecolor','none','edgecolor','b','linewidth',1)
plot(intersect(P1,P2), 'Facecolor', [0.5, 1, 0.5],'linestyle','none');
ylim([-0.1 1.1])
legend('h(t-\tau)','x(\tau)','whatever')
grid

[Bruno Luong]

Shift annimation:

t1=-7:0.1:-1;
t2=-1:0.1:0;
t3=0:0.1:0.5;
t4=0.5:0.1:3;
t5=3:0.1:7;
t=[t1 t2 t3 t4 t5];
x1=zeros(size(t1));
x2=0.6.*ones(size(t2));
x3=0.6.*ones(size(t3));
x4=0.3.*ones(size(t4));
x5=zeros(size(t5));
x=[x1 x2 x3 x4 x5];
h1=zeros(size(t1));
h2=zeros(size(t2));
h3=ones(size(t3));
h4=ones(size(t4));
h5=ones(size(t5));
h6=[h1 h2 h3 h4 h5];
h7=exp(-t);
h=h6.*h7;

warning('off','MATLAB:polyshape:repairedBySimplify');

close all
figure
for tau=0:0.1:4
    cla
    hold on
    t1 = t;
    t2 = tau-t;
    P1=polyshape(t1,x);
    P2=polyshape(t2,h);
    
    plot(t1,x,'color','r','linewidth',1)
    plot(t2,h,'color','b','linewidth',1)
    plot(intersect(P1,P2), 'Facecolor', [0.5, 1, 0.5],'linestyle','none');
    xlim([-6 12]);
    ylim([-0.1 1.1])
    legend('h(t-\tau)','x(\tau)','whatever')
    grid on
    drawnow
end

[Muhammad Sanwal]

Yes, this code works too. Thankyou!

Answer 4

[Image Analyst]

See the FAQ and adapt as needed.

FAQ How_do_I_shade_the_region_between_two_curves?

[the cyclist]

@muhammad:

Note that the solution that @ImageAnalyst posted makes this statement:

% Assume y1 and y2 have the same number of elements located at the same x values.

Your curves do not obey this assumption, which makes your problem significantly more difficult (I think).

If you can define data in a way that they use the same t (number of elements and same values), this will be an easier task.

Next best would be using at least the same number of elements (if not at the same values).

[Muhammad Sanwal]

I made my vector t of the same length, but the graph I get is as follows

Please help me make changes to the program so that I can get the original encircled area (in red), as mentioned in my question.

The code is as follows

t1=-7:0.1:-1;
t2=-1:0.1:0;
t3=0:0.1:0.5;
t4=0.5:0.1:3;
t5=3:0.1:7;
t=[t1 t2 t3 t4 t5];
x1=zeros(size(t1));
x2=0.6.*ones(size(t2));
x3=0.6.*ones(size(t3));
x4=0.3.*ones(size(t4));
x5=zeros(size(t5));
x=[x1 x2 x3 x4 x5];
h1=zeros(size(t1));
h2=zeros(size(t2));
h3=ones(size(t3));
h4=ones(size(t4));
h5=ones(size(t5));
h6=[h1 h2 h3 h4 h5];
h7=exp(-t);
h=h6.*h7;
plot(t,x,-t,h,'-','linewidth',2)
ylim([-0.1 1.1])
legend('x(\tau)','h(t-\tau)')
grid
% Shade the area between in light green using the patch() function.
lightGreen = [0.85, 1, 0.85];
% Create the boundaries of the upper points and the lower points.
% Assume x and h have the same number of elements located at the same x values.
upperBoundary = max(x, h);
lowerBoundary = min(x, h);
% Now do the actual display of the shaded region.
patch([t fliplr(t)], [upperBoundary  fliplr(lowerBoundary)], lightGreen); 
% Plot x and h AFTER the patch so the patch does not cover any of those curves.
hold on;
plot(t, x, 'r-', 'LineWidth', 2); % Plot curve 1 in red.
plot(t, h, 'b-', 'LineWidth', 2); % Plot curve 2 in blue.
legend('Patch', 'y1', 'y2');
% Maximize the figure window
g = gcf; % Setting the WindowState  on gcf directly doesn't work for some reason.
g.WindowState = 'maximized'