Projective Comparisons, and One to One Correspondence —
The two photographs below are of the same object —
a Cartesian graph, on paper.
There is one-to-one correspondence of the
features in photograph 2
Thus, if line-pairs converge in one photograph
From the foregoing, we must have that,
So, either parallels meet,Essentially, we (and the camera) always see in Perspective, which compares our plotted ordinates (intervals) to the graph's axes
or there are no parallels.
in Perspectivities, centered on X and Y.
Drag the green ‘dash-dot’ lines on the graph below,
to bring these “meetings of parallels”, X and Y, into view.