Computing the overlapping area of curves

I have a set of datapoints corresponding to 5 curves.

scale =  1.5;
x1 = [0,4,6,10,15,20]*scale;
y1 =  [18,17.5,13,12,8,10];
x2 = [0,10.5,28]*scale;
y2= [18.2,10.6,10.3];
x3 = [0,4,6,10,15,20]*scale;
y3 = [18,13,15,12,11,9.6];
x4 = [9,17,28]*scale;
y4 = [5,5.5,7];
x5 = [1,10,20]*scale;
y5 = [3,0.8,2];

plot(x1,y1, '*-', x2, y2,  '*-', x3, y3,  '*-', x4, y4,  '*-', x5, y5,  '*-')

I want to find the overlapping area under these curves.

Suggestions on the functions that could be uded to find the intersecting area and the x limits of the intersecting area will be really helpful.

[Deepa Maheshvare]

Any suggestions?

[Chunru]

Which curves do you mean? How the overlapping area is defined?

[Deepa Maheshvare]

Thank you for the reply. I am interested in finding the area under each of the curve and visualize the area that overlaps.

Answer 1

[Chunru]

scale =  1.5;
x{1} = [0,4,6,10,15,20]*scale;
y{1} =  [18,17.5,13,12,8,10];
x{2} = [0,10.5,28]*scale;
y{2}= [18.2,10.6,10.3];
x{3} = [0,4,6,10,15,20]*scale;
y{3} = [18,13,15,12,11,9.6];
x{4} = [9,17,28]*scale;
y{4} = [5,5.5,7];
x{5} = [1,10,20]*scale;
y{5} = [3,0.8,2];
figure; hold on
xmin = -inf; xmax=inf;
for i=1:length(x)
    area(x{i}, y{i}, 'FaceAlpha', 0.5);     % visualize area with transparancy
    a(i) = trapz(x{i}, y{i});       % compute area
    xmin = max(xmin, min(x{i}));
    xmax = min(xmax, max(x{i}));
end
xline([xmin xmax], 'LineWidth', 2)
legend

a

a = 1×5

369.7500 501.1125 379.5000 166.1250 46.6500

[Deepa Maheshvare]

Thanks so much. Could we find/highlight the area that is intersected by all curves?

[Chunru]

See the update.