# Why is the line from the camera to vanishing point parallel to the other parallel lines?

When trying to find the vanishing point of an image, why is it that the vector from the center of the camera to the vanishing point is parallel to the parallel lines of the image?

What's the mathematical reasoning behind this?

• What are "original lines"? Oct 29, 2017 at 4:08
• Sorry for not being clear, I fixed that now. I hope its clear now Oct 29, 2017 at 4:35
• This diagram simply shows how in perspective projection the parallel lines are not parallel in the resulting image (image plane). They would only be parallel in orthogonal projection. The author of the diagram could project any lines he wanted to on the image plane. They don't have to be parallel with the line going through the vanishing point. Oct 29, 2017 at 4:47
• @AndrewWilson, absolutely. And the OP phrase to the parallel lines of the image is invalid, because there is no such thing that "THE" parallel lines. It's only meant to mean that some cubic looking, well aligned geometry, like architecture and streets, will tend to display lots of parallel lines that "engenders" the presence of a virtual vanishing point. Do anybody speaks of vanishing points in image of trees and ponds ? Oct 30, 2017 at 2:23
• This question seems nonsensical as it currently stands. Perhaps a photo showing which parallel lines you mean would clarify? Oct 30, 2017 at 3:28