# 3D projection that increases objects' size as they become more distant

tl;dr Is there a name for a type of (non-physical) projection that causes objects to become larger the farther they are from a camera?

1. With a fisheye projection, an object twice as far from the camera is less than half the size on screen. (I think; my understanding of fisheye math is fuzzy. I gather there are various projections/mapping functions.) There is massive foreshortening, objects shrink very quickly as they move away.

2. With a rectilinear projection, an object twice as far from the camera is always half the size on screen, regardless of FoV. This is how trigonometry works. Infinitely-far objects have zero size.

3. With an orthographic projection, an object twice as far from the camera is always the same size on screen. There is no foreshortening. Infinitely-far objects have the same size.

4. Now, go one step farther. I want negative foreshortening. I want to see an object get bigger the farther away it gets. Infinitely-far objects have infinite size.

After a quick google of 'Inverted perspective' I found out that you have five different names for it; Reverse perspective, inverse perspective, inverted perspective, divergent perspective and Byzantine perspective. https://en.wikipedia.org/wiki/Reverse_perspective

I think that if you want to use it in a render engine using a projection matrix, in the perspective divide, you use multiply by w instead of divide. This is because in a perspective projection, the divide by w is what actually gives the perspective. In a orthographic projection w is always 1, meaning that there is no actual perspective.

For a ray tracer you probably just need to scale the image plane up of course, but probably instead of having the origin of the ray to be the center of the camera, you have some kind of second image plane that is larger than the actual image plane. If both are the same size, the rays are straight and you have an orthographic projection, if the actual image plane is smaller then you have your Reverse perspective.

Quick extra note: If you have proper lenses, you might be able to get this effect in real life. Yes, you would need to have a lens that is a few meters in diameter, but I do not think it is impossible! :P

I hope this will help you and that I have not made any mistakes. Good luck with whatever you are doing!

• the video linked to the wiki page looks really interesting
– AMA
Commented Jun 13, 2017 at 18:35
• Yes lenses that do this are called pericentric. Commented Jun 14, 2017 at 5:42