curve a and b are two great circle segments that lie on a sphere. How can I decide whether these two circle segments intersect with each other?

CodePudding user response：

I assume you need only a fact of intersection, not intersection point (in the second case just look at Intersection of two paths given start points and bearings section of link below)

Let we have points a1, a2, b1, b2 in lat/lon coordinates.

Paths a1a2 and b1b2 do intersect, if both b1 and b2 lie in different hemispheres relative to a1a2 big circle, and a1 and a2 lie in different hemispheres relative to b1b2 big circle.

To determine hemisheres, we can calculate signs of cross-track distances as described in Cross-track distance of