Perspective: focal length v. subject distance or "zooming with your feet"

Sure, I saw the above, and I had a feeling you would extend it to the human retina as a 2D plane. However, I have three dictionaries in the house, which all include the same additional definition seen here:

www.merriam-webster.com/dictionary/perspective

'the appearance to the eye of objects in respect to their relative distance and positions'

If you write your own dictionary, you might prefer to leave it out.

But for now, I'm not even sure in what way you and TomAxford actually disagree. Can that be concisely stated?

I'm sorry if I'm still not making myself clear here, I thought I was. From your own link:

3: the appearance to the eye of objects in respect to their relative distance and positions

4a: the technique or process of representing on a plane or curved surface the spatial relation of objects as they might appear to the eye
specifically : representation in a drawing or painting of parallel lines as converging in order to give the illusion of depth and distance

b: a picture in perspective

None of that contradicts the science and none of that is actually the science. Looking in dictionaries for the meaning of words does not constitute understanding perspective. Niether does it contradict the definition I gave, which is also there twice, in both 3 and 4a.

I am quite clear here and everywhere before:

You can describe how the shape of a cube is projected on a 2D surface. And perspective is always a projection on a 2D surface because perspective is also defined as the distortion caused by viewing from a unique point in space. A cube is defined by equal sides and all 90 degree angles, which is it's 3D shape. It's perspective is NEVER all equal sides and every angle at 90 degrees.

As per your definitions above.

I'm sorry you can't see this, as I said, I though I was being quite plain. But so far we have Tom whose op suggests that when zooming with your feet you have to move the scenery proportionally with distance when to the eye it's clear that it's inversely proportional. This was derived by taking pictures of 2D signs, we formulate about 3D rendering by considering a case void of 3D information.

Then Dan wanders off into his argumentative fallacies, "whats important to you..."

The you come along and quote dictionaries at me as though it provides the missing insight into understanding perspective.

2a: the interrelation in which a subject or its parts are mentally viewed
places the issues in proper perspective

Aye, sure does. I can't be bothered with this anymore. Soz but I'm off as well.

I'm still not sure.

You still seem to be struggling to cope with the fact that something important to you is not always important to everyone else.

Can sombody in simple terms, tell me what the point of the OP is.

I see two pictures of a two dimensional reproduction of a two dimensional sign. To make such a picture, you just fill the frame with any focal length lens. Zooming with a zoom lens or moving backwards or forwards with the camera and lens to fill the frame have the same effect.

So what!

The op clearly explains under what circumstances in a 2D scene zooming with your feet and zooming with your lens will produce the same image. He then goes on to explain how that relates to 3D scenes.

I quess there is some esoteric technical reasoning, way beyond the understanding of us common mortals.

In the circumstances described in the op yes, otherwise no.

The point was to draw attention to the fact that sometimes zooming with your feet and zooming with your lens have exactly the same effect. Of course, most experienced photographers are already well aware of this, and most other photographers quickly realise that it makes sense and fits with their own experience.

A further point was to show that it is a simple illustration of the basic rule of perspective that the size of the image varies in inverse proportion to the object distance. Again, this is probably obvious to most.

I also hoped that many might also realise that it is a simple further step to conclude that magnifying the image of a 3D scene (e.g. by zooming the lens) has the same effect as moving every part of the scene towards the camera (using the basic rule of perspective). Hence telephoto compression. This should be obvious, but apparently isn't to everybody!

By the way, there is nothing here about how our eyes see and perceive depth in 2D images. All I am doing is showing that there are different ways of getting the same image. Whatever you see in one copy of that image you are likely to see in another copy. If you see depth in one, you will see the same depth in the other.

Of course, you may not be interested in thinking about perspective and how to explain it, in which case, why are you contributing to this thread?

It might be easier and more easily understood, if you explained Leon Battista Alberti's work on pictorial perspective. It is this and the further explorations of two and three point perspective that interest us a photographers.

Sorry but the Op is just a source of confusion for most. Pictorial perspective is pretty easy to understand and implement, without mystification. It took about ten minutes for the chief draughtsman to show me how to create perspective drawings, back in the early days of my engineering career.

I disagree. It's fairly straight forward and I would think most are capable of understanding what Tom described.

In any case, anyone very interested in the topic can easily go out the next time they have a bit of free time and go through the example situation Tom described and see for themselves practically.

They can then change one parameter at a time and see what effect it has on the image.

This is not rocket science and reasonably easy to pick up if you use Tom's example situation as a starting point.

You selected and example where there is no 3D information and used focal length vs distance to produce images of the same size then tried to apply those results to explain some of the effects of 3D rendering. Any mathematical connection must therefore be pure assumption on your part as there is no 3D information in your example with which to make any observation of perspective.

Zooming with your feet and zooming with your lens create different effects when you consider how a 3D scene is rendered on a 2D surface (purely the maths of geometry). There is no exception to this unless you dispense completely with 3D information, but you will find that if you zoom with your feet it has little effect on how distant objects are rendered on a 2D plane.

What?

No, the magnification of an image is all about the distance between the lens and the 2D plane you're rendering the scene on, not the distance between the object and the lens. If you change the distance between the lens and the object you change the relationships in all objects in a 3D scene and so also must change how that scene is rendered on a 2D plane. This is basic perspective, not what you said above. Of course if you remove any 3D information in the actual scene and start projecting 2D scenes through a lens onto a 2D plane then the maths becomes somewhat symmetrical and you can start making all sorts of false assumptions and assertions.

Well, if you read the paragraph you will see that you contradict your opening statement with the closing one where you talk about our perception of depth (" If you see depth") in a 2D image. but you continually mix the two. Earlier in this conversation:

Here you even state that perspective is all about how we perceive and decode the 2D information we are presented with. Remember scientifically all we "see" are a series of impulses from the cones and rods in our eyes, there is no other information attached. If your human brain relates that back to a 3D scene by the rules of geometry then it MUST know those rules as a precondition of being able to do it. It dictates that you must learn the maths. If you can construct a 3D understanding without the maths then you must accept the possibility that the understanding, or image, you see in your head is not identical to the true mathematically derived perspective of the real world. Which is where we are with observational data and current scientific thought. The division is clear, how an image is rendered on a 2D plane/how we make sense of that.

One thing I do notice is that your theories do not change but your examples of how you justify them do. Your thinking here seems back to front and is flawed.

Absolutely! The thing about banging your head against a brick wall is that it's so nice when you stop. Ciao.

It is good to see some sound common sense. It seems to be in short supply around here.

I don't think so. I think there are only some very restrictive circumstances under which it is true. I specifically described one earlier.

But if you have 3D objects in the scene at various distances, especially ones that appear off center, it will become impossible to recreate the scene exactly by changing the focal length because of differences in volume deformation when they're repositioned. Do you agree?

Yes, I agree, volume deformation of objects is required. I was thinking mathematically, in that every point in the scene must be moved by the specified amount. Every point can be thought of as having 3 coordinates. It is convenient to take one axis as the optical axis of the camera (i.e. perpendicular to the plane of the sensor). It is only this axial coordinate that gets compressed, the other two remain the same.

I usually gloss over these details because they are not essential (or helpful) to understanding the principles. Also many people get turned off by rigorous mathematical arguments with all the messy details. However, mathematicians can usually reconstruct the details themselves, without having them spelled out.

So we are quite literally discussing the mathematical model of how we physically change the landscape, or a human face in order to make "zoom with feet" the same as "zoom with lens". In order to understand that "zoom with lens" is a simple mathematical magnification (increasing the distance between focal point and 2D screen) where as "zoom with feet" changes the spacial relationships between objects and also how perspective distorts them. A quite complex model to visualise, made more so because it's clearly also impossible and therefore we have no real memory or experience in order to allow us to do it.

Just checking that we are still in the realms of common sense...

My fav?

LOL...

I assumed you would agree, so I still am not sure in what way you and Andrew546 actually disagree. Can that be concisely stated?

Glossing over the details in this case caused some issues.