Find Crossovers for multiple contours drawn over a lake

I am new to MapBasic and wanting to help out with this problem. I have some ideas on what the algorithm might be to start this problem but I have never written anything in MapBasic. I do have some Java knowledge. Here is the problem: There are several contours drawn over a lake and is created through interpolation of points collected from surveys. But during the course there are several contours which cross over each other and cause problem. Sometimes there are lots of them. I was trying to find out where different lines cross. Probably, the script should show me a marker of where they cross. Basic algorithm that I think should hold this concept is using intercept form where a intersection point can be found out using slope and equation of two lines. But as I understand, the lines cannot be vertical. But contours that are drawn can be vertical. In fact, they can be anything. So, have you guys worked on something like this before? Please suggest. Thank you!