How to find intersection between two array line plots

The problem is the array is to plot a payload diagram so the array is made up of 4 x and y points. So basically 4 x,y coordinates but the lines intersect and I want to know at what point they intersect.

The first array has 3 lines horizontal then diagonal then diagonal again but steeper. And the other array has only 2 x,y coordinates and intersects the first diagnonal line! Can you help me find the value at that intersection AKA teh coordinates there.

Answer 1

[Star Strider]

It would help to have the actual data.

x = 1:4;
y1 = rand(size(x));
y2 = rand(size(x));

xi = linspace(min(x), max(x), numel(x)*10);                     % Increase 'x' Resolution
y1i = interp1(x,y1,xi);                                         % Increase 'y1' Resolution
y2i = interp1(x,y2,xi);                                         % Increase 'y2' Resolution

zxi = find(diff(sign(y1i-y2i)));                                % Appriximate Indices Of Intersections

for k = 1:numel(zxi)
    idxrng = max(1,zxi(k)-1) : min(numel(xi),zxi(k)+1);         % Index Range For Interpolation
    xix(k,:) = interp1(y1i(idxrng)-y2i(idxrng),xi(idxrng),0);   % 'x' Value At Intersection
    yix(k,:) = interp1(xi(idxrng),y1i(idxrng),xix(k));          % 'y' Value At Intersection
end
Intersections = table(xix,yix)

Intersections = 2×2 table
     xix        yix  
    ______    _______

    1.3419    0.35144
    2.4677    0.42242

figure
plot(x, y1,  x, y2)
hold on
plot(xix, yix, 'sm')
hold off
grid

This will be reliable if there is only one intersection between each pair of indices. It may fail to discriminate intersections that are close together, even with the increased point resolution.

EDIT — (6 Apr 2022 at 13:00)

Made ‘xi’ length a function of the original ‘x’ length.

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