How to determine the exact intersection between line and two curves

Data is attached.

Hi everyone,

I am trying to find the exact intersection between line and curve and I tried everything and all they gave me an approximate intersection. Can anyone help me to determine the exact intersection. Thanks in advance,

I used " intersect points=find(p1==p2)"

intersectionpoints =

0×1 empty double column vector

However, If i used intersectionpoints=find(p1>=p2)

intersectionpoints =

9 10 11 12 13 14 18 19 20 21 22

So 9 is not the exact point, it is the point after the intersection between p1 and p2, how to find the exact intersected point between the red line and the blue curve.

Answer 1

[Star Strider]

Try this —

LD = load(' matlab.mat');
p1 = LD.p1;
p2 = LD.p2;
x = linspace(0, numel(p1)-1, numel(p1));

idx = find(diff(sign(p1-p2)));                          % Approximate Indices Of The Intersections
for k = 1:numel(idx)
    idxrng = max(1,idx(k)-1) : min(numel(p1),idx(k)+1);
    xi(k) = interp1(p1(idxrng)-p2(idxrng), x(idxrng), 0);
    yi(k) = interp1(x(idxrng),p2(idxrng),xi(k));
end

Intersections = table(xi,yi)

figure
plot(x, p1,   x, p2)
hold on
plot(xi, yi, 'ms')
hold off
grid
legend('p_1','p_2','Intersections', 'Location','best')

Intersections =

4×2 table

xi yi

______ __________

7.5374 1.5534e+08

13.133 1.5534e+08

16.345 1.5534e+08

21.731 1.5534e+08

.

Answer 2

[Torsten]

Depending on how you interpolate between the points of the blue curve, you will get different intersection points.

So there is no "exact" intersection you can expect to get.

If (x,y) are the points of the blue curve and y0 is the y-value of the orange curve, you can do something like:

i = 0;
for j = 1:numel(x)-1
    xl = x(j);
    yl = y(j);
    xn = x(j+1);
    yn = y(j+1);
    if yl <= y0 & yn >= y0
        i = i+1;
        xi(i) = (y0*(xn-xl)+xl*yn-xn*yl)/(yn-yl);
    end
end
xi

This will give you an approximation for the x-coordinates of the intersection points.