If its a random position on just one side of the mesh and not a 360. Assuming this is a random spot on a map. Cast a ray from the sky to the land at random positions within the max boundaries of the mesh. as in if the highest X position of the mesh is 100 then that will be your max x. There will be areas near the max X that might not be a position on the mesh, but if that happens just instantly recast the ray. Rays are fairly cheap and I’m gonna assume if you put the mesh within a square it covers a majority of the surfaces. And so more than 50% of the time it’ll cast somewhere on the mesh and if not recast.
I understand this is 2D drawing, but understand I said mesh, in scope of 3D similar to sphere, the drawing is just highlighting regardless of the uniqueness to the shape and surface it must be random yet inside the mesh