Short version: An object moving away to infinity along the Horizon, never actually drops *below* the horizon yes? No matter how you try to interpret the laws of perspective, that's just the way things are observed.

Where do we observe an infinite plane where bodies perpetually approach, but never touch, the horizon line?

If you've never seen an infinite plane, how can you know what would happen on one?

The only infinite plane I know of is the earth. So therefore there is a pretense for bodies intersecting with the vanishing point after a finite distance.

Ok, is it just me... or did you completely contradict yourself. According to you, we all see an infinite plane each and every day on the good Flat Earth. Therefore that point is moot.

As far as physical bodies intersecting after a finite distance - are you saying the sun actually 'does' drop down and somehow 'collide' with the planet? No matter how you slice it, two objects that are travelling in true parallel will never touch right? Therefore, no matter what kind of refraction you come up with, the suns light is not going to get 'below' the clouds during a sunset if it is hundreds of miles above them.

Even if you try to say it's somehow bouncing up off of the infinite plane of ice, the concentrated area of sunlight from the sun itself as it sets is just basic observational "duh". Also, no amount of refraction is going to keep the Sun from getting smaller, and smaller, and smaller - if you are to use your intersecting vanishing point theory. If it has to get so far away to do this strange feat, then you've lost perspective, as it would also for some strange reason seem to be moving north by then as it continued on it's orbit around the Earth.

Edit: Sorry cpt. I got to writing my own post and didn't see you already pointed out the light concentration and posed the east-west / north-south path issue already.