Detecting Intersections of Functions: Is There a Foolproof Method?

[Physt]

Does anyone know of an algorithm to detect the intersection of any two functions - both for individual points within a fixed range of x values and determining whether or not total points of intersection are finite or infinite over an infinite range of x values? Also, is this possible to do this when you rotate the plot around a third axis (such as using a graph for each edge of a polygon).

 

[Erland]

Well, the simplest is probably to take the difference of the functions and find its zeros, by some numerical method such as Newton-Raphson. It works only for reasonably nice functions, though. There is certainly no general algorithm that always works.