How to find the point of interception between the two lines?

Prashant Kumar answered . 2024-12-21 15:12:34

I think this is more or less what your are looking for. The crossover indices are idx1 and idx2. Just for fun, and since you mentioned the integral, I added code to compute and show the area between the curves at the crossover points. The area was compute both using polyarea and trapz. The result is the same (187.85 in this case).

M = readmatrix('testdata.txt'); % this is your x_untrt and x_untrt_s data
y1 = M(:,1); % x_untrt
y2 = M(:,2); % x_untrt_s
x = 1:length(y1);

% find indices of crossover points
ydiff = y1 - y2;
idxCross = find(ydiff(1:end-1) < 0 & ydiff(2:end) > 0);
idxCross(end) = []; % ignore last crossover point (by inspection)
idx1 = idxCross(1); % 1st crossover point
idx2 = idxCross(2); % 2nd crossover point

% find area using trapz
a1 = trapz(x(idx1:idx2), y1(idx1:idx2));
a2 = trapz(x(idx1:idx2), y2(idx1:idx2));
area1 = abs(a2 - a1)

% find area using polyarea
px = [x(idx1:idx2) flip(x(idx1:idx2))];
py = [y2(idx1:idx2)' flip(y1(idx1:idx2))'];
p = polyshape(px, py);
area2 = polyarea(px,py)

plot(y1);
hold on;
plot(y2);
scatter(x(idxCross), y1(idxCross), 'k', 'filled');
plot(p);

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