Suppose I have considered example of perspective projection.I have one railway track with two lines meets at point say,$X$ at infinity which is theoretical approach.And this X is called vanishing point.But practically this $X$ doesn't exists.
My first question is how we can say it doesn't exist, but when we see real image of railway track they intersects at $X?$
My second question is if it exists then during projection how this $X$ is projects in projection plane? Is it projecting like normal point projection $(x, y,z)$ to in view plane $(x_p, y_p, z_p)?$
N. B- I don't want that answer which is in details manner. I want just intuition which is brief and easy to understand.
X doesn't exist in reality, since the railroad tracks are parallel, but it exists in the projection plane.
In the following link, you have the explanation :
https://en.wikipedia.org/wiki/Vanishing_point
Projections of two sets of parallel lines lying in some plane πA appear to converge, i.e. the vanishing point associated with that pair, on a horizon line, or vanishing line H formed by the intersection of the image plane with the plane parallel to πA and passing through the pinhole.
Mateo.