Hey I'm a perception researcher.

In the real world we call this visual angle or retina angle

You can calculate the visual angle of an object based on its distance from the eye and dimensions.

If you want to create another object that "looks" the same size but is at a different distance, you use the same formula but instead you input the distance and visual angle and then it gives you the new dimensions needed for both objects to "look" the same size. (Project into the retina at the same size)

This is actually part of an experiment I did for my dissertation where two cylinders were shown to participants. One was 90cm away. The other 80cm. But the "looked" identical in size. (They had to tell me which was closer without size influencing their judgment).

When it comes to movement. The math for this might be a little more tricky as I'm pretty sure it's proportional changes.

I'll be honest, my knowledge of this is lacking (calculus). But I'm open to helping you figure it out.

I also am not familiar enough with blender to help you do this on blender. Only in real life. I mostly use blender for sculpting 3d models for printing. So you would have to figure out how to translate my help to blender.

Honestly this sounds like a pretty cool optical illusion.

I do have an excel sheet I created that I put the formulas in that make it easy to make two objects at different distances have the same retina angle.

So let's say I have a cube that's 2x2x2cm. And it's 50cm away. I first calculate the visual angle of 2cm height at 50cm.

Then I use this information and make it so the object would be at 100cm away. How big does the cube now need to be , to still have the same visual angle. ?

My formula will tell you.

If you are interested I can give it for you and explain how to use it.

There are online calculators for visual angle but none let you use a secondary one to create a matching (in retina angle) item at a different distance. So mine will be very useful to you for that purpose.

There is also some discrepancy issue with what is called lens length. And this factors heavily into virtual spaces.

I'll go into that later with you.

People are influenced by slight changes in size.

And bigger is interpreted in one specific way. "It's closer". Which in your situation would make the object appear to get closer to the camera. So this is actually a big deal to make sure it's projected perfectly.

Here is a photo depicting visual angle. Basically the big E and the smaller E that is closer will project at the same size. The small E that is farther will project smaller in angle than the same dimensions small E that's closer.

https://encrypted-tbn0.gstatic.com/images?q=tbn%3AANd9GcQjwyDmu1E2UPMVdPzTO3IBUvzW-ieOmw580A&s=

Another image. This shows how two objects that are the same dimensions will project different visual angles based on distance.

https://cdn.cambridgeincolour.com/images/tutorials/wa_narrow-angle-of-view.png

Here is a photo of the formula. And shows that both a human and the Eiffle tower can project at same size.

https://i.ytimg.com/vi/83kLc5WkO6I/maxresdefault.jpg?sqp=-oaymwEmCIAKENAF8quKqQMa8AEB-AG-B4AC0AWKAgwIABABGGUgZShlMA8%3D&rs=AOn4CLD3d56taVe6fL3cI2jIf4VO4wroHw

I don't want to overload you with info. I'll try to remember to check my Lemmy later. I'm also in the middle of moving but I'll help if I can.

Send me a DM if you want to chat more one on one.

What you're looking for is called a Dolly Zoom, though it usually involves moving the camera away while zooming in (or vice versa) instead of the object size, which makes sense in traditional filmography, where the object size can't be changed

Quick example, create an empty at camera’s coordinates, parent objects to said empty and scale the empty. (Alternatively snap 3d cursor to active camera and use that as the transform centre while scaling environment)

To do this with a moving camera, I don’t know if there is a simple way..

You could do some math :D

Or you could clone your object so that you have two, one far away and one close to the camera, this way you can tweak their sizes so that they align visually. Finally, you animate the object on the back to make it move towards the camera and scale it down so that it occupies the same space as the object near the camera. Then you delete the reference object