it also depends a lot on whether there are other lines crossing the one you are interested in or not, and e.g. which "k real" value the lines have. Making a programming solution yourself for this would be straightforward, but if you are unable to write the code, it's very difficult for someone else to write a general code that works in all cases.
Take the Si example in the tutorial (Fig. 3) - if we just want the line connecting the CB min at G and the VB max at G (the red line), we have to somehow exclude the line which originates at the Delta minimum (blue). Besides, in the code we are talking about (referenced above), the goal is to make a 3D plot - I'm not sure want that, you just want the data points. So the code has to be modified to print out the data in a format you can import elsewhere. All this is easy if you have control of the data and code, but very difficult to make generic.
You may be better off just exporting all the data, and picking out the points by hand.