Finding an intersection between one data points curve and one linear curve (ax+b)

Hi, I work on these two curves. One is a linear data curve of expression y=ax+b, with a and b known, and the other is a curve of experimental points x_exp and y_exp. I want to find the smaller x for which this curve intersect, or at least are close enough so that we can say that they intersect. x_exp is a vector ordinated from the smaller x to the bigger x.

To do so, for each x_exp rank i from the smallest to the biggest, I calculate "delta", the gap between the coordinate y_calc (given by the linear expression ycalc=ax_exp(i)+b) and y_exp. I keep in a vector intersections all the ranks i of the gaps x(i) for which the gap delta between y_calc and y_exp is smaller than 50. However, the code doesn't work. The gap values calculated are odds, and the intersections are not the values i should find. Do anyone know where my logic/code is flawed ? Do anyone has an idea regarding how to find the intersection of these curves ? Thank you very much. Here is my code:

u=1; %used to build the intersections vector
nb_exp_value=size(x_exp);
for i=1:nb_exp_value

      y_calc= a*x_exp(i)+b;

      delta= abs(y_exp( i )) - abs(y_calc);
      if delta < 50
          intersections(u)=i
          u=u+1;

      end
end

Answer 1

[Sam Cook]

I think that the polyxpoly function is what you're looking for. It's part of the Mapping Toolbox.

X1 = -5:0.1:2;
Y1 = 3*X1 + -2; % Your linear data

X2 = -5:2;
Y2 = atan(X2) * 10; % Your experimental data

[Xi, Yi] = polyxpoly(X1, Y1, X2, Y2); % Intersection points

hold on
plot(X1, Y1);
plot(X2, Y2);
scatter(Xi, Yi, 'r*');

[Image Analyst]

Lucille, attach your data in a .mat file if you want any more help.