How vanishing point and centre of projection both are same?

Question

We know that in perspective projection object positions are transformed to the view plane along lines that converge to the projection reference (center) point like this:

But many websites say that COP(Centre of projection) and vanishing point both are the same. But we know that parallel lines that are not parallel to the viewing plane converge to a vanishing point. In the above picture, if I draw the parallel line through the point $A, B, C$, then they intersect at infinity which is the vanishing point.

My question is: How are COP and vanishing point both the same?

Answer 1

The center of projection cannot be a vanishing point except in useless cases.

The center of projection is the place of observer's eye in 3D space. Vanishing points are on the imaging plane.

The useless case 1: The center of the projection is on the imaging plane. Everything will be projected to that single point.

Not asked: If an already world famous artist happens to invent that idea the paintings which apply it and have his signature may be sold for a million dollars; no matter who did the actual painting - he or a fly.

Useless case 2: There can be in the same 3d space going on 2 making a perspective image -jobs, say imaging A and imaging B. The observer of A can be in image B and just in a vanishing point.