You have a long list of line segments. Not lines, unless you mean the extension of those lines to infinity in each direction. But the distinction is of course crucial.
Next, what do you mean by "in the middle"? Note that it is trivial to create a set of line segments such that it is impossible for any single line to pass in a way that the line intersects ALL line segments between their end points. The simple counter-example is to choose 5 points, at the corners of a regular pentagon. There is no line that can intersect more than 4 of the line segments, even if the line passes through 2 of the vertices. Thus, choose these line segments:
t = linspace(0,2*pi,6);
px = cos(t);
py = sin(t);
plot(px,py,'o-')
No line can intersect all 5 line segments, so case closed.
If you have a set of lines such that a common intersecting line does exist, then it is not that difficult to find. For example, given the following set of line segments, are you asking to find a line that intersects all of them?
x = rand(2,10) + [0;2];
y = rand(2,10);
plot(x,y,'o-')
Of course, as I constructed it, the simple solution is just the line defined by
x = 1.5
If you actually want a programmatic solution, I would ask that you confirm what you are trying to do. Note that almost always, even if a solution does exist, that it will not be unique.
