I'm looking for an efficient way to determine if two paths (sets of x,y coordinates) intersect at a point.
Input - (x,y) from a Mercator Projection (longitude,latitude) coordinates
Output - Intersection point
I looked at this question here: Solve for the intersection point, given two sets of data but there doesn't seem to be an answer.
Does anyone have any suggestions on where to start?
You can find the interpolation equation of p1=ax+b for x1,y1 points and p2=cx+d for x2,y2 points using "Least Squares method" . Then solve for p1=p2.
If you know that some intersections occurs between some "specific points inside the bound" and calculating intersection coordinates matters, you may fit the points you have in a polynomial (Using Newton's Limited Divided Differences method or Lagrange method). Then numerically solve for P1=P2 ( Caution: This interpolation may fail for points far out of bound of the given points)