How can i fill the common areas of two curves?

I can draw two cureves as below.

y1 = @(x) 3*x.^2 + 2*x +1;

y2 = @(x) -5*x.^2 + x + 20;

x=-5:0.1:5;

figure(3),plot(x,y1(x),x,y2(x));

Then, now i would like to fill the common areas with red color but i have no idea.

How can i do that?

And what about if i would like to fill the common areas of three different curves?

Answer 1

[Akira Agata]

Another possible solution:

y1 = @(x) 3*x.^2 + 2*x +1;
y2 = @(x) -5*x.^2 + x + 20;
x = -5:0.1:5;

pgon1 = polyshape(x,y1(x));
pgon2 = polyshape(x,y2(x));

figure
plot(x,y1(x),x,y2(x))
hold on
plot(intersect(pgon1,pgon2),'EdgeColor','none')

[byungkeuk cho]

Thank you so much.

This is more like i want it to be.

[byungkeuk cho]

What about three curves?

how can i shade the common area with three lines?

[Akira Agata]

Same approach works. The following is an example.

y1 = @(x) 3*x.^2 + 2*x +1;
y2 = @(x) -5*x.^2 + x + 20;
y3 = @(x) -10*x.^2 + 20*x + 30;
x = -5:0.1:5;

pgon1 = polyshape(x,y1(x));
pgon2 = polyshape(x,y2(x));
pgon3 = polyshape(x,y3(x));

figure
plot(x,y1(x),x,y2(x),x,y3(x))
hold on
plot(intersect([pgon1,pgon2,pgon3]),'EdgeColor','none')

[byungkeuk cho]

Thank you very much :)

[byungkeuk cho]

One more question plz.

How can i change the colar of the shade?

[Akira Agata]

You can change the color by setting FaceColor option, like:

...
plot(intersect([pgon1,pgon2,pgon3]),'EdgeColor','none','FaceColor','m')

More details can be foun in the documentation page.

https://jp.mathworks.com/help/matlab/ref/polyshape.plot.html

Answer 2

[byungkeuk cho]

I am trying to shade the triangle between three lines.

but it is not working.

y1 = @(x) x ;

y2 = @(x) sqrt(3)/2*x ;

y3 = @(x) -x + 1 ;

x = 0:0.1:2;

pgon1 = polyshape(x,y1(x));

pgon2 = polyshape(x,y2(x));

pgon3 = polyshape(x,y3(x));

figure

plot(x,y1(x),x,y2(x),x,y3(x))

hold on

plot(intersect([pgon1,pgon2,pgon3]),'EdgeColor','none ')

[Akira Agata]

You need to make a polyshape object correctly. In this case, target area shall be lower than y1, lower than y3 and higher than y2. Also, since these shapes are line, you would better setting 'Simplify' option to false.

Regarding how to change the color of the shade, you should set 'FaceColor' option when plotting.

Here is an example.

y1 = @(x) x; 
y2 = @(x) sqrt(3)/2*x; 
y3 = @(x) -x + 1; 
x = 0:0.1:2;

pgon1 = polyshape([x(1) x x(end)],[-10 y1(x) -10],'Simplify',false); 
pgon2 = polyshape([x(1) x x(end)],[10 y2(x) 10],'Simplify',false); 
pgon3 = polyshape([x(1) x x(end)],[-10 y3(x) -10],'Simplify',false); 

figure 
plot(x,y1(x),x,y2(x),x,y3(x)) 
hold on 
plot(intersect([pgon1,pgon2,pgon3]),...
  'EdgeColor',  'none',...
  'FaceColor',  'c') % change shade color to cyan

[byungkeuk cho]

I really appreciate it.

[Rahman]

Mr. Akira Agata, I've a code that generates 2 curves and have an intersection point. How can I show the area on the right of the intersection as 'hatched grey'?

M = [0.54, 0.7, 0.74, 0.78];
X1 = [0.007856, 0.008394, 0.008607, 0.012584];      %X1 values
X2 =  [0.007901, 0.008461, 0.008739, 0.011302];      %X2 values
xq = linspace(M(1), M(end), 1000);   %adding intervals to make line smoother
X3 = interpn(M,X1,xq,'pchip');  %other type: pchip, makima, spline etc.
X4 = interpn(M,X2,xq,'pchip');  %other type: pchip, makima, spline etc.

set(0,'defaulttextinterpreter','latex')

figure(1)
hold all; 
plot(xq, X3,'r-','LineWidth',2);
plot(xq, X4,'b--','LineWidth',2);
X=[xq,fliplr(xq)];           %create continuous x value array for plotting
Y=[X3,fliplr(X4)];           %create y values for out and then back
fill(X,Y,'g');    %plot filled area
xlabel('X','FontSize',12); % Label the x axis
ylabel('Y','FontSize',12); % Label the y axis

The code above generates following figure: (the whole area between 2 curves is shaded as green)

However, I'd like to have the right area after intersection (roughly from X = 0.75 to 0.78) shaded only. Also, in the plot above, I need to change the shaded area on the right after intersection (roughly from X = 0.75 to 0.78) as 'hatched grey'.

Any help will be appreciated.