find intersection of 2 graphs in one plot with unknown function

So i have 3 sets of data each containing 25 rows and 3 columns. (first column are the data points for the x axis and the other 2 for the y axis)

When i plot the data in a single figure they intersect.

how can i find the interscetion without knowing the functions of each graph?

[darova]

do you have polyxpoly?

[cloutdrop]

no

Answer 1

[David Hill]

You could fit your data using polyfit or fit (sounds like your data is relatively smooth). Then run feval on the objects over the same x array (with steps as small as you like x=-5:.0001:5). Then subtract and look for the zeros (approximately zero).

a=fit(m(:,1),m(:,2),'smoothingspline');
b=fit(m(:,1),m(:,3),'smoothingspline');
x=min(m(:,1)):.0001:max(m(:,1));
A=feval(a,x);
B=feval(b,x);
c=find(abs(A-B)<.001,1);%may have to play with the number here (.001). If only 1 crossing specify.
pointOfintersection=[x(c),A(c)];

Answer 2

[Star Strider]

It would help to have the actual data.

This simply requires basic MATLAB functions:

A = [0:20; (0:20).^2; 100-(0:20).^1.5].';                           % Create Array

x_intersect = interp1(A(:,2)-A(:,3), A(:,1), 0);                    % X-Value At Intersection
y_intersect = interp1(A(:,1),A(:,2),x_intersect);                   % Y-Value At Intersection

figure
plot(A(:,1), A(:,2),    A(:,1), A(:,3))
hold on
plot(x_intersect, y_intersect, 'sk', 'MarkerSize',10)
hold off
grid
legend('Column 1','Column 2', 'Intersection', 'Location','best')

It may be necessary to experiment for it to work with your data, if there is more than 1 intersection or if the data are not monotonically increasing or decreasing with respect to the independent variable. Also, the rows must be sorted by the independent variable in column 1 for this to work.