# How vanishing point and centre of projection both are same?

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?

• No, simply because there is one COP in a ideal pinhole camera model, but there are any nymber of wanishing points for any set of coplanar lines. This sentence in it self is enough to disprove them being the same. But yes they are caused by the same thing. Oct 21, 2021 at 9:45
• – D.W.
Nov 8, 2021 at 3:55

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.

• 287001 this statement is right "we know that parallel lines that are not parallel to the viewing plane converge to a vanishing point." ---? Oct 20, 2021 at 18:19
• @N-Sat that statement is right, but it tells something about the images of the lines which are parallel in the 3d space. It tells nothing of the observing point i.e. of the center of projection
– user82991
Oct 20, 2021 at 21:57
• @user287001 "The observer of A can be in image B and just in a vanishing point."---could you explain little bit, what you mean? Oct 28, 2021 at 16:38
• @user please explain easily. Oct 28, 2021 at 17:32
• Imagine a painting like this previews.123rf.com/images/keifer/keifer1307/keifer130700040/… and you are just making the final touches to it on a real canvas in front of you. A person behind the canvas punches a small hole to the vanishing point of the railroad to see better. He is painting to the backside of the same canvas another painting. That painting contains you and the landscape behind you as seen through the hole.
– user82991
Oct 28, 2021 at 18:08