# Intersection algorithim for finding the intersection points of two arbitrary mathematical curves

I'm looking for an intersection algorithm for finding the intersection points of two arbitrary mathematical curves. Websites like Desmos, GeoGebra, and WolframAlpha allow you to graph and/or input two(Or more but I'm only interested in two) curves to find their intersection points. I know all of the services I've listed have some form of API, my problems with those APIs are the technical and practical restrictions. Therefore, I'd like to just use the algorithms they use under the hood. Problem comes when I don't even know the names of those algorithms or even whether they're public domain. I've done some searching around but I can't seem to find what I'm looking for. So I guess what I'm asking for are some basic design descriptions/requirements for these algorithms so I can implement one of them. I figured this problem wasn't really a question for the mathematics StackExchange or StackOverflow So I decided to place it here. Let me know if that's a problem.

• What, for the purpose of this question, is a mathematical curve, an intersection point? – greybeard Mar 17 at 5:45
• @greybeard A mathematical curve, in my case, is an equation in two variables or a function of one variable. It's an exceedingly general definition but the actual definition given by Wikipedia appears to be even more general. An intersection point would be that exact location[s] where the two curves overlap. – video_error Mar 17 at 8:14