I have a curve (not a function) as a list of points and I would like to find the intersection of the curve with another curve (another set of points). To be more concrete about the problem I am solving :
The curve is a spiral, whose points are https://drive.google.com/file/d/1TtkKPgIxSKmdeWZDYQ1-Dd2aUvxqGDyF/view?usp=sharing. It looks like :
and I need to find intersection with another curve, say a straight line $y=x$. Is there a way to do this in Mathematica.
A canonical procedure is to find the interpolating function from the points (if this were a function) say $f(x)$ and solve $f-g=0$ to find intersection with the the curve $g(x)$.
How does one do the same for a curve where an interpolating function makes no sense? Other alternatives?
Thanks for reading and any help is appreciated.
Edit: I think one way is to check for intersection of all possible line segments, but the number of checks is $O(n^2)$. Maybe someone in the community could suggest a clever way to remove some of these checks, or suggest another method.