(from bruce donnelly)
If you look at the diagram of the Campidoglio and St. Peters' in
Hegemann and Peets's Civic Art, you'll probably wonder why the viewing angles
are calculated from certain apparently arbitrary positions. It doesn't fit
our assumption visual constancy will ensure we perceive space with almost
Cartesian clarity, does it?
Actually, it's exactly the opposite; it details an old conception of space based on particular sight angles from privileged positions or sweet spots. For example, the privileged bench in a Roman dining room might have a more classically balanced view of the peristyle court than would a position on a bench on axis to the door.
Or the frescoes on a wall might fall into perspective better from the
privileged end of the room (sort of like an anamorphic projection).
The problem isn't to create a square with some sort of ideal
proportion, it's to coordinate plan and elevation to artistic effect. Thus,
there's a spot at St. Peter's where the central column and the main façade both
top out at 27 degrees above the horizontal. That point coincides with the
threshold between the keystone-shaped part of the square and the
oval-shaped part. Now, one of my professors, Harris Forusz, proved to my class
during a field trip on urban design that above _approximately_ a 27-degree
cutoff we have trouble perceiving a whole façade at once. Thus, when we cross
the threshold at St. Peter's, we also approach so close to the façade that
we have entered the personal space, so to speak, of the building itself.