This is a completely wrong diagram of what a vanishing point it.
In the world of perspective a vanishing point is exactly what it says it is. A vanishing point. Items become so small in the distance that they "vanish". However, while an item that is parallel to another item might appear to "vanish" it would never cross over the other item. Train tracks might appear to converge but they will never cross each other. Just as the sun cannot cross the horizon line if it's circling parallel to the flat earth surface.
Your diagram is incorrect. Whoever made it has zero knowledge of perspective.
The reason the sun crosses the horizon line is because the earth is a sphere and it is spinning. As it spins the curvature of the earth covers the sun from our point of view. But people to the west of me still can see the sun (at least until it set s for them).
Dave watch this time lapse and be honest with yourself.
Do you honestly believe the sun is disappearing due to the fact it's getting too far away?? And if so... why doesn't the sun "vanish" all at once?? Who does it vanish as if it's goin under the horizon line?
Not everything vanishes at the vanishing point.
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The tops of trees mountains, etc. that are larger/taller in elevation will appear but the base or bottoms will not.
The sun will simply have that effect which is why the bottom will be blocked before the top but the sun will continue to move away from us until it disappears entirely.
In the pick with with the sun we see the perspective of tracks, clouds and sun, as per prediction of how all three work on a flat plane.
--Dave