Problem 567. Crossing to Kissing - Untangle the Lines

Turn lines that cross into lines that kiss.

You will be given two lines that cross at some point. Your job is to untangle them in the following way. Imagine two line segments, L1 and L2. L1 goes from (0,0) to (2,2). L2 goes from (0,1) to (2,1). We can specify them like so.

 L1 = [0 0; 
       2 2]

 L2 = [0 1; 
       2 1]

We want to transform these into two non-crossing segmented lines that look the same when plotted. To do this, we need to introduce a new point in each line. Both lines share this point, so now they "kiss" instead of crossing.

 L3 = [0 0; 
       1 1;
       2 1]

 L4 = [0 1;
       1 1;
       2 2]

            * L1               * L4
           /                  /
          /                  /
   L2 *--/--* L2      L4 *--*--* L3
        /                  /
       /                  /
   L1 *               L3 *

Your function should take the form

 [L3,L4] = cross2kiss(L1,L2)

The lines L3 and L4 should be ordered by the y coordinate of their first point. So in the case above, the first point in L3 is [0 0], so it comes first.