Exploring Perspective

I don't find it obvious. The key phrase here is 'in a picture'. Had you said 'in a scene' I'd agree, but both cropping and shifting change the way in which the scene is projected onto the picture. As regards perspective, both affect the picture-relative positions of the vanishing points.
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Maybe I put it badly, I actually meant scene, but I think it can be both but scene and a picture in its uncropped form. Let's immagine I make a print with a wide angle lens. I then decide to crop the picture. I can change the apparent angle of view, or I can shift the convergence point, changing the angle of view, with the inevitable crop. The angular relationship of projection lines leading to the vanishing point or points remain unchanged.

Maybe these two quick sketches make my point clearer.

The convergence point has been shifted in the camera, using lens movements. The same effect could be achieved using a wider lens, and then cropping

We can change the focal length of the lens by zooming in, or crop a larger image but the lead lines remain constant.

The difference in heights (red 'circles') between the tops of the arches and the tops of the walls from front to back looks very unnatural to me because the differences are way more than what I would expect to see in real life in that scene.

The steepness of the lines (green 'circles') and the relative distance between them from front to back also looks very unnatural to me compared to what I would expect to see in real life in that scene.

I doubt very much that image represents what I would have seen, in terms of perspective, had I been standing at the same point.

You raise an interesting point and open a much bigger question.

Let's look at the "uneducated viewer". This is the most interesting. I have a whole series of books I bought over the years, concerning the architecture I am interested in. The books that date back into the last century, are illustrated almost without fail with pictures taken with a large format camera with movements. Many old magazines and periodicals would commission photographs where verticals are vertical and sometimes the optical axis is shifted to one side. I would venture to say that up until the massification of photography, via digital and above all the cell phone, the unwritten laws of architectural photography went out of the window. It is quite common now to see horrific keystoning even in glossy publications, and even in some more recent books I have bought.

I have a few recent books that some of my Architectural clients, where I have done the Structural Engineering have self published. There the attention to geometry is still very present.

The question is: have the viewers become less visually educated with the flood of photography, we are now deluged with?

Lastly, maybe my photographs, with their visual geometric language are more akin to a piece of classical music from the past, which hardly anybody understands or listens to now. My photographs are linked to the past I believe, rather than the present.

And similar to my previous post with the above image. The relative width of the roof from front to back looks very unnatural to me because the change in width in the image due to perspective is way more than I would expect to see had I been standing in the same position.

No, I don't think viewers are less visually educated now.

Imo if viewers interpret the intent of the image creator was to display a documentary version of the scene then the viewer would normally judge the image on how realistic it looks to them in terms of content and perspective.

Stand in an old major Gothic church or cathedral. The sensation is of towering height and perspective. The builders used several tricks to achive this, like narrowing the building towards the altar (Duomo di Fidenza). I now often use a 15mm lens to get the perspective I perceive.

The whole purpose of Baroque architecture is to transmit shock and awe. In the Baroque church above the purpose was to transmit a sensation rather than coldly document.

I try to photograph what I perceive and transmit the sensation the Architecture gives me.

I have stood in old cathedrals and my eyes at the time didn't see the extremes in perspective your images portray.

I posted in another thread that not everyone's eyes and brain interact in exactly the same way when it comes to perspective.

Your images are nice but I don't see the perspective some of them display as being very accurate compared to my experience in similar scenes.

That's all very well and I have no issue with that. But your intent behind creating and displaying an image is then clearly not obvious. I thought all your images in this thread were intended to be documentary displays and so I posted my opinions of them accordingly.

Now it seems there is at least a significant portion of artistic intent behind the intention your images. That's fine.

Once you make it clear that art is at least a significant portion behind the intent of an image then any discussion about perspective becomes far less technical and much more flexible in people's opinions.

You may have missed this important bit from my original post:

Quoting a pamphlet on the use of perspective in Renaissance painting, published by the British National Gallery, we can understand that sometimes we need to depart from pure geometric, or mathematical models:

“Optical illusion does not necessarily depend on mathematical absolutes and, with a few important exceptions such as Piero della Francesca, it seems that painters were more concerned with achieving a level of visual plausibility than with the rigorous application of theoretical models. Perspective was designed to fulfil the needs of the picture (not vice versa), and a series of other conditions and criteria were at stake: the knowledge, skill and aesthetic preferences of the artist, the demands of patrons, the ways in which the site might determine the viewpoint, and the requirements of the subject matter. Thus, a painting which has often been considered a perspectival manifesto, Masaccio’s ‘Trinity’ fresco, has been shown to bend the rules of one-point mathematical perspective, probably because it looked better that way”

Thank you for those two books.

I find it interesting that the description of perspective is done largely in terms of vanishing points. Personally, I find the more theoretical approach (the mathematics of perspective projection) simpler to understand, but that is probably due to my education in mathematics.

I notice that in Chapter 9 of Joseph D'Amelio's book, he talks about the perspective distortion caused by having the "Vanishing Points Too Far Apart" [Section 60], which he says is "wrong because it results in minimal convergence and hence a sense of flatness". This is, of course, just an alternative way of describing what photographers call telephoto compression. He says little more about it other than that it is something to avoid.

It is interesting how the same idea can be described in totally different ways according to your background and point of view.

The point I am making is that people will normally judge and interpret an image based on whether they see an image as meaning to be a documentary or artistic version or a mixture of the two.

If the image creator does not make their intent behind the creation of the image clear to viewers then viewers will make an assumption about the image's intent (as I showed in my previous post) and then interpret and judge it accordingly.

It seems to me some of your images in this thread are intended to be documentary and some are at least partly artistic as you indicated earlier.

Your thread title is "Exploring Perspective".

That's fine as it is an interesting topic but the way someone would go about exploring perspective displayed in an image depends to a large extent on the type of image in which perspective is being explored.

Is the image intended to be documentary, artistic or a mixture of both?

Once the intent behind the image has been agreed between those doing the exploring then a meaningful and consistent discussion can potentially take place.

If a given image is being interpreted by some as intended to be documentary and by others as being either artistic or a combination of artistic and documentary then any discussion about the perspective displayed in the image can quickly go pear-shaped and become convoluted, messy and confusing.

I find frames that place a scene's single viewpoint dead in the middle rather cliché. Going back over many pictures of my street, not one of them is framed that way.

This one is typical of my street shots:

Off-topic, but the Golden Ratio springs to mind ...

Viewers have undoubtedly become accustomed to new norms as photographic tools and methods have changed. One example is that some young people who have only used hand-held smartphones with wide lenses to photograph themselves say that the 'traditional portrait' perspective of a more distant viewpoint and a longer lens make their faces look weird.

Glad you liked the books.

I made this thread to put forward the graphic alternative, which I find easier to grasp. Also there is lot of mathematics in my job, and photography is my artistic alter ego. I also enjoyed technical drawing and geometry at school.

I seem to remember using graphic solutions to find the forces in roof trusses, back in the distant past, much quicker than doing the number crunching with a slide rule.