Intersection of lines with endpoints

The lines are represented by their endpoints in a matrix. Each row in a matrix gives coordinates for a line like: (x1, y1, x2, y2).The problem is that Matlab makes a line from the endpoints and not a section of a line and still displays intersection although it's not there. (See the attached picture below)

lines = [
    1.9988    3.3693    5.3629    6.9431
    2.7362    6.3124    4.5334    3.6730
    4.8329    5.9387    4.3260    4.4204
];

a = lines;
b = a;
for line = 1:size(a,1)
    lineone = a(line, :);
    b(1,:) = [];
    for anotherline = 1:size(b,1)
       linetwo = b(anotherline, :);
       %line1
        %x1 =[from x1 value , to x2 value]
        %y1 =[from y1 value , to y2 value]
        x1  = [lineone(1) lineone(3)];
        y1  = [lineone(2) lineone(4)];
        %line2
        x2 = [linetwo(1) linetwo(3)];
        y2 = [linetwo(2) linetwo(4)];
        %fit linear polynomial
        p1 = polyfit(x1,y1,1);
        p2 = polyfit(x2,y2,1);
        %calculate intersection
        x_intersect = fzero(@(x) polyval(p1-p2,x),3);
        y_intersect = polyval(p1,x_intersect);
        intersectionpoint =[x_intersect , y_intersect]
        hold on
        plot(x1,y1)
        plot(x2,y2)
        plot(x_intersect,y_intersect,"*")
end

[Michal Dobai]

Why you just don't check if x value of found intersection is within range where (and only where) could possibly be the intersection between two lines?

if x_intersect >= max(min(x1),min(x2)) && ...
      x_intersect <= min(max(x1),max(x2))

      intersectionpoint =[x_intersect , y_intersect]
      plot(x_intersect,y_intersect,"*")

end

[Jan]

polyfit and fzero is an overkill for the occurring easy systems of equations. If you express the line in the form of a start point and a direction vector, it gets much easier to obtain the result and as a side effect it is trivial to limit the intersections to the line segment only. On demand I will post some code in the evening.

Answer 1

[KSSV]

Have a look on this code: https://www.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections?focused=5165138&tab=function