Perspective: circles that are off-centre.

Abstraction

I recently asked this on Wetcanvas but no replies. I'm hoping someone here understands perspective better than I do.

To help me with perspective problems on my painting, which combined two photos of slightly different perspective which needed to be resolved, my son (a computer games programmer) created a 3D model of my source photo. It allowed me to move the horizon and move objects around. Here’s a section towards the left. The blue is the movable plane towards the horizon that shows everything in the same perspective. Impressive hey. (That's not my actual painting - he mocked it up and put bots in.)

I did enough homework to understand that to draw a circle in perspective you create a grid of squares and plot the circle within the square. To calculate where to put the back line for the square is half the angle, etc. but it’s beyond my technical ability. The 'squares' that are off to the side and above or below horizon become distorted.

But... I have this program he made, and the result is counter-intuitive.

The set up of the columns on each side and table is one point perspective. This image below is part of a column on RHS, above the Horizon. Naturally, it curves up in the middle because we are below it. What doesn't make sense to me is that the LHS of circle on column is lower than the RHS. If it's a round object then if I turned and faced it, the closest point to me should be the centre of the column that I see. That should mean that the LHS and RHS should be equidistant from me and the same height. ??? In my logic anyway. 

I don't understand why it's different? Is it a software flaw or am I confused and the software is correct? I just want to confirm it's correct or not to understand it and correct if needed and get on with painting.

tassieguy

I agree that the column doesn't look right, @Abstraction. I guess it's the software. 

dencal

Abstraction

Yep. You are right the flute inserts should be symmetrical around the centre of the column nearest to you.
In fact there is some sort of graphical distortion down the entire LHS of the column.
The whole image is a CGI mashup.

Here is p55 of Loomis Successful Drawing.



Denis

Abstraction

Firstly, I really appreciate the confirmation.

But now I'm stuck again. I don't know how to solve this. I can take the original photo of the columns and fix the vertical pattern of the flutes. Easy. But the circle from the end of the flutes? The original horizon was much lower. I had to shift it higher in my painting to match the second photo of my four children that I combined it with. So...

* I know where my horizon and VP is.

* I don't know how to draw the squares to build the circles. I kind of get the logic in the excerpt in terms of how the squares can be pulled into perspective - but how do I build the square from a circle?

I assume:

a) Find the top of the circle and draw a horizontal line for the front of the square. How wide? Don't know yet. 

b) Draw a line from vanishing point to that line the front of the square. Which part? How wide is the front of the square? I don't know how to determine that.

I will touch base with my son and see whether he drew a circle in his program or simply used the photo points as reference. Because if he can fix it, it's simple. This draftsmanship without proper training - just to fix a few curves - has been a struggle for months. I want to paint.

Abstraction

Ok. This is interesting. The comment at the end - 'Horizontal circles seen simultaneously, even the ones far to the left and right of center line of observer's vision, should all be drawn as true - despite... in rigorous mechanical perspective circles at far left and far right would come out as distorted ellipses.' (https://www.joshuanava.biz/perspective/info-ivu.html) 

Is he recommending that because it's true or because it's simpler? I've contacted the guy.

dencal

Abstraction

You are overthinking this. The column flute inserts are of no consequence. Just paint them in symmetrically about the column centre in an even upward curve. Do some pencil free hands to get it to look right.

Denis

Abstraction

I don't think I'm overthinking it. I'm underthinking it. There are two very convincing arguments that contradict each other.

Perspective is partly a blind spot for me - my initial image (from two shots) an artist online dismantled it due to incorrect perspective. I fixed most of it since. But I took this particular question to my son tonight who produced this in a matter of moments.

This seems fairly convincing that the modelling is correct and this matches the original photo. When the circle is above us, the circle edge that we see from viewer perspective is lower on the point closest to the vanishing  point. I don't understand why though. I suspect it's related to it being on the edge of our cone of vision.

tassieguy

Well, looks like your son is right then, @Abstraction.  Funny how it just looks wrong, though. Maybe it's that we're seeing the one column in isolation from the rest of the picture. Do you have a shot with both columns? 

Richard_P

I think you are right. If you take a cylinder like a can and move it around it quickly goes out of our centre of vision and we can't tell if it's distorted or not. On a flat image we can look directly at areas that we normally don't see from that angle and it looks wrong.

KingstonFineArt

@Abstraction
The 'camera' used in the 3d video is very wide angle causing distortion. 
For me perspective is essential to paint straight up realism. I did drafting at a high level when I was young. It's part of my DNA. I can't imagine having to learn it all over again.
 
Here's an amazon link to some starting books. I have a couple of these on my phone for refreshing my aging mind.

https://www.amazon.com/s?k=drawing+perspective+for+beginners&crid=1Y2Z1P5I9KCQG&sprefix=drawing+perspective%2Caps%2C211&ref=nb_sb_ss_ts-doa-p_4_19

There are 3d cgi apps that can help. Blender is free but tough to get through. I've use Strata3d for the past 30 years. CGI can help solve problems, invent and augment compositions.

I think Loomis's Books are the most approachable on many levels. They have mostly been republished and available on amazon.

There are other approaches to perspective. Layered vertical planes. Atmospheric and aerial perspective. Hans Hoffman developed what he called 'push pull' to create spacial depth using color. But not as realism. The principles can be applied to realism.

Mastering perspective means that you can control and manipulate it to your advantage.

Richard_P

As luck would have it, just found an article which directly addresses this:
https://www.treeshark.com/treeblog/?p=307

CBG

@Abstraction

I think in photography and 3d rendering, because they map a perspective view to a flat rectangular 2d plane there will be "distortions" if the viewer is not viewing that 2d plane in the exact same manner, field of view (FOV) wise, as the real or virtual camera. 


Imagine drawing lines from a point lens out to a very wide and tall flat rectangle...a large FOV context...at the far corners objects imaged and projected occupy much more canvas space along both x and y than objects in the center for them to look the same from that point. After all the corner of the canvas is farther away from your camera/projector/eye.

If you step back from the plane, so that your eye is almost the same distance from the corner and the center... a small FOV viewing context... this will cause the work to look distorted. 

Again...
Imagine taking a wide angle shot of a very wide and tall window you are standing very close to, and imagine that the photo just takes in the frame of the window.  Arguably, if you were to print that photo and blow it up to the size of just bigger than the window and stood in the spot you took the photo, the print might look pretty good.  However, if you printed that photo on an 5x7 card and looked at it from a few feet, it would not look right at all.

I think in your case, the cylinder would look right if you were to look at it at the same FOV as the render.  and it was in the corner of the work.

See the following:



Here two identical objects are A and B are at the exact same distance D from the viewpoint: camera (real or virtual), your eye, or the projector.  Observe how the finite size of the object's projections onto the plane A' and B' must be in order for these objects to be the same size from the viewpoint.  A' near the edge must be must larger than B' to appear the same size.  Image this occurring in 2D in a corner and it is quite clear that the finite 2d sizes and shapes will be very different in order to appear correctly from the viewpoint.


This is an extreme FOV case but the same principle applies to any perspective (non-parallel) projection.

Now a coin, to look correctly to the eye, if projected onto a canvas, with a wide FOV, will be distorted when looked at from a low FOV.  What particular distortions look like... is in the details of the shape and how it projects in a 2D plane over the multiple angles it spans.

Abstraction

@kingstonFineArt @Richard_P @CBG Thank you so much. In fact that link to 'The Problem with Columns' helped explain and helped me not feel like an idiot for struggling with it. If it's a problem that perplexed the Renaissance artists I'm in good company. I've been through so many youtube videos and sites and books that didn't explain what he did there. 

If I understand correctly (I might yet be an idiot) -

• It's distortion caused by nature of 'cameras' real or virtual. Things to either side are - 1. Hitting a flat plane at an oblique angle (1,2 point fixed perspective issues) and 2. Potentially distorted through the lens if it's wide angle.
  
• If we were staring straight ahead, the pillars would be in the periphery of our vision and we wouldn't see much detail. But if we looked at them directly the edges of the ellipse would be equidistant and even - because the vanishing point of course would then be directly behind the middle of the column as we saw it.
  
• People looking at the painting will look directly at the columns at some point, the way we would if we were standing in the room. I'm ok with that. It makes more sense to the average person.
  
• So the most effective way to address it from painting perspective is to treat the columns as a round object that we are looking at directly. An even ellipse, not distorted.
  
• I just need to find the appropriate height of the curve above/ below the horizon to determine the shape of the ellipse. I can do that on my son's program easily.
  

@tassieguy Original uncorrected image. The lens distortion is clear. When 'corrected' in photoshop it still replicates the distorted view of the 3D model because it views it the same way. 

This is what happens when the camera looks directly at the column. It's even.

The grand house was in Bucharest, Romania. This stately house was taken over by the communist party for their own purposes back in the day and now sits idle. A guy took me there. I was standing in the front stairwell and experimenting with low light photography (complete amateur out of his depth) in other shots. I've used it as a dark background for portrait of my kids at table (really just a plastic table in a tin shed) but had to change perspective to match them. No, let's be honest, I changed their perspective as well for artistic purposes - just to raise the degree of difficulty.

tassieguy

Hi, @Abstraction. Yes, the solution seems to be to paint them as if they were being viewed straight on.

BTW, It's a wonderful space. The staircase, columns and parquetry are beautiful. and I love the cool blue light of the window contrasting with the mellow warmness of the room.

GTO

I have struggled with this problem too.  I understand the construction methods but I end up tweaking the ellipse until it feels correct.  Back in the day I went through Radu Vera’s book understanding perspective that helps visualize different perspective problems.  It’s a good book but difficult to work through.
BTW It’s Caravaggio’s birthday.  Fitting for this topi .

CBG

@Abstraction

When I display your original photo in a new Tab on its own, on my flat monitor... and when I place my eye at the right place in front of my monitor (where I guess the camera would have been), there is no distortion, no matter where I look, no matter what I directly look at, as long as I keep my eye in the right place.

In this sense, this photo is wholly correct in the most absolute of terms.


I think the main problem here is the attempt to "cheat" reality - the attempt to make a large field of view (projected onto 2D) look "right" to a viewer seeing it through small field of view (projected onto 2D).  Unfortunately, if the photo/subject really is a wide angle, and one intends for viewers to view it at a small angle, that is a contradiction with reality which cannot be "corrected"... squares are not circles, A is not B and A does not look like B...those distortions are what you get when you try to cheat reality.


One thing one could do, as the article above suggests, is to fabricate an illusion to make the appearance of those contradictions "reduce" in the eye of the viewer.  Essentially, to distort a correct image so that when incorrectly viewed, it will look "better" even though it is even less correct than the original.

Another option is to set out to make an image which is intended to be viewed at a field of view which is as close to the correct field of view as possible.

A final option is to leave it as is, and trust the viewer will simply recognize the fact that it is a wide angle shot she is viewing from too far away, and that those distortions are a natural consequence.


Note:  There are of course some kinds of lenses which introduce further "lens" specific distortions... that is a whole other ball of wax...

Abstraction

Really helpful discussion and contributions from all. I began this question months ago on another site before I joined this site. On so many youtubes or sites I read about perspective and they didn't solve it. My son brilliantly created the 3D model and it still was confusing. This is the first time I've had clarity on this issue. Some other learnings from this long process (so far):

- In combining multiple photos - this background was combined with several from the photoshoot of my kids - I originally did it by eye - the arrangement that looked right. I thought perspective looked ok. An artist on another site completely dismantled my perspective (and gave other helpful comments.) I immediately knew that I had a blind spot for perspective, that he was seeing things I thought were fine by eye. Like a person who draws a face with the eyes near the top of the head that we can instantly see is wrong. That was me with perspective. Lesson: Blindspots - you don't know what you don't know. Feedback from an art community can help you see what you can't see. (And humility is a gift and is always beautiful and humanising even though it counter-intuitively feels like the opposite.)

- Camera distortion: When I compared the sizes of people from my photoshoot, I realised the person on closer side of the table was giant. I learnt it's because the camera was too close. Sigh. I resized that person in photoshop - but of course changes everything. I had hired a photographer for equipment and support although I took the photos - so no reshoot affordable. Lesson: To make people or objects closer in size, shoot from further back. (I've discovered Mark addresses this and camera use in significant detail. https://www.drawmixpaint.com/classes/online/advanced-photography-guide.html )

- Horizon and vanishing points: In my subsequent learning about perspective I realised that horizon is  the viewer's eye level. On flat ground if you take a photo of a crowd from eye level, everyone the same height as you would have their eyes exactly level with the horizon. Since I also wanted to make my son in foreground lower than the others because it looked better, I had to work out where the camera/ viewing point would be to make him look the correct size and move his head below the others. This meant viewing point needed to be slightly higher than their eye level. If I was their eye level all eyes would be level. That shifts the entire horizon and everything in the room. So I had to select the vanishing point for the (thank goodness just one point) perspective of the table and columns, and I marked that on the board. I now know exactly where horizon and vanishing points are. Frankly, there was so much going on in the photoshoot this was one detail too many - i failed to see it until later. Lesson: Importance of deciding position of viewer and horizon (during photoshoot and during painting.) And vanishing points. Mark them if necessary and use them to check and resolve all items.

- Preparing painting boards: After sealing with pH neutral PVA I used Gamblin Ground for first time, thinned as per instructions. Not enough, apparently. Didn't realise that if too thick grounds can settle and leave a film of oil on top. I noticed it didn't have tooth but lacked experience to know what to do so continued painting. When I eventually contacted Gamblin technical dept they quickly gave me a helpful response which I'll post if anyone wants to see it. It needed sanding. I had already blocked in a number of sections, though, which created later problems. Lessons: thin the Gamblin ground adequately. Sand if it lacks tooth with 150 grit wet and dry.

- Glazing and best practice paint use: I had already attempted to glaze some darks as part of block in using liquin - so ended up with a ripple pattern from the oil on unsanded oil ground. I've had to sand sections back to remove the pattern. In investigating best practice, iIt turns out that use of solvents and mediums that is so widely recommended is unnecessary and compromises the paint film formation or adhesion. Lessons: Best techniques for conservation - paint from the tube always. Don't use solvents or mediums at all, even for glazing or underpainting. No, really.

- Major works: Since this is only my 9th original painting, I had always simply just painted and solved problems as I went. I've seen artists do mock up sketches, but seriously, that seemed like too much work. I work full time and paint in rare spare moments. But this is a large sized important work, and I've had to step out of the techniques and approach I understand because of all the architectural details in the background above. I've made a lot of errors. (I did do a lot of photoshop mock-ups and even practice table shots before the photoshoot, but not a mockup with paint.) Lesson: Important work that is a) not very clear in your mind and b) will take significant investment of time may deserve a smaller sketch to resolve issues.

toujours

Yes, it is all a learning curve.   I have unconsciously battled with some of the issues you describe @Abstraction.   You are much better at recognising them as issues which need solutions and how to go about solving these problems.
I discovered 140 year old photographs can have terrible effects on the angles of buildings.  Add to that putting your own images in front of these and the angles of the buildings need to match the angles of the foreground, as well as the heights of humans at different depths into the distance.  Also, the angle of the circles for wheels on carts is very tricky.  Not only do they go from circles side on to a straight line front on, but carriage wheels are champered (?) so the spokes by the axle are on a different plane to the rim.   Add to that the fact that the wheel is then tilted inwards at the bottom by having a convex curve to the axle and wheels can be the thing of nightmares.   I ended up just doing my best and tried to make each one look right on its own merit.   Sometimes I failed.  I am afraid I am not patient enough, nor mathematical enough to find the best solution (hats off to you) and I ended up just "fudging" these issues as best I could.
  I think, possibly, you could turn yourself inside out, upside down and go quite insane trying to perfect it all, unless your are a person blessed in life to have one of those brains that just understands how to make the eye and hand work to produce something mathematically correct for the viewer.

Would speaking with an architect help?

Abstraction

Wow, I thought my problem was complex. I will definitely think twice before taking on things like architecture or similar. Normal 1, 2, 3 point perspective is ok and can interesting. But then you get vertical distortion from cameras as well, and these curves are a conundrum...

I believe I have the answer above. So based on that I'm currently using my son's program and adjusting the camera angle so that I'm in front of the pillar to avoid the inherent distortion - taking screen grabs. If I make any adjustments to that they will only be miniscule.

tassieguy

Oh, boy. That does it - no architecture for me. I have a photo I took of Melbourne from about the 40th floor of a hotel near the old conference center. It has the river flowing through the center of the picture with sky scrapers and lower, older buildings along each side. I thought that, one day, I'd like to try painting it but you guys have put the fear of god into me. Being so high up things should narrow in towards river level and diverge outwards as the buildings get higher than my vantage point. Too difficult.  I think it's on the back burner. 

CBG

tassieguy said:

Oh, boy. That does it - no architecture for me. I have a photo I took of Melbourne from about the 40th floor of a hotel near the old conference center. It has the river flowing through the center of the picture with sky scrapers and lower, older buildings along each side. I thought that, one day, I'd like to try painting it but you guys have put the fear of god into me. Being so high up things should narrow in towards river level and diverge outwards as the buildings get higher than my vantage point. Too difficult.  I think it's on the back burner. 

cmon… the above exercise in analysis should not daunt you….

paint what you see and you will see it again in your painting… don’t second guess yourself… dispense with any analysis … it’s only 2d shapes after all.

I have every confidence in you.

tassieguy

Thanks, @CBG. The discussion above does make it sound daunting, though. But, as you say, it's just 2D shapes on a flat canvas. How hard can it be?  Brushstrokes of the right shape, of the right value/colour, in the right place and you're there. When I get past my current  "Mountain" series I'll pull that photo of Melbourne out again and see what I can do with it. 

Abstraction

I combined multiple photos - not just two - and therefore created problems for myself. Then I changed perspective of every photo to achieve my design. Amazingly, I think I've pulled it off now.

It's a practice that doesn't hurt on landscape/seascape, so I had always gotten away with it. Ok, you can get into trouble. That's photos mostly taken in same lighting, etc.

toujours

Yes, I probably used up an average of 4 reference photos on my series and up to about 6 or 7 on one picture, getting various buildings, horses, people, carts, and other animals as well as signs on shops etc...    Getting the perspective and sizing right on them to gel in one picture takes a bit of time.    What I was referring to as "the fiddle factor" when I mapped out each painting!

CBG

As a follow up, the best rule of thumb is to take a photo with the same angle you intend for a viewer of your painting.

You can determine an ideal size for your painting or an ideal viewing distance as follows:


 

Desertsky

@CBG - this is very useful. BTW, could you please post a "Dummies Guide" version of this for those of us who may be, er, trigonometrically challenged?

Asking for a friend. 

CBG

Desertsky said:

@CBG - this is very useful. BTW, pcould you please post a "Dummies Guide" version of this for those of us who may be, er, trigonometrically challenged?

Asking for a friend. 

You mean like add a few illustrations to help with understanding?  

I suppose if there was enough demand I could.

Abstraction

Am responding but need to make coffee.

Abstraction

@CBG Amazing - thanks for sharing. Serious question: do you actually use this formula when you take a photo? Or do you use it after you've taken the photo to edit the image for painting? Or did you post it for interest?  Maths can describe so much, although I couldn't translate that into taking a photo.  

* Single glance rule: I think(?) I noted elsewhere you consider a painting should represent a frozen moment glance of the viewer. It's what I was also taught by my original teacher. I respect and use that at times, but I don't subscribe to it as a rule. It's absolutely not the way we experience the world - it's the way a camera operates. Stare straight ahead, click. We, on the other hand, drink in a scene we love. So I consciously choose at times to create a grander perspective. eg, My seascape creates the sense of being surrounded, bigness, which I wanted to communicate. You have to look around, you want to look around, I hope. It's an experience of place.

* Rounded objects solution: In painting referred to here - to solve the centuries-old challenge of distortion of off-centre round objects created by both cameras/visual devices and perspective formulas - I have chosen to allow people to move their eyes around the painting - which I want them to do and they will do. So I am portraying the pillars as they would appear to someone who looks in that direction, which they would and they will. It makes far more sense (to me  ).

* Lessons about photos: Most of the challenges in reconciling multiple photos for this painting weren't related to that formula. After I examined the photos and tried to compose the painting I decided:

• The person in the foreground was originally too big - giant actually. (lesson: camera further back reduces size distortion effect. I didn't notice it during photoshoot, and for ages afterwards - my blindspot.)
• For composition I now wanted the person in foreground below those in background (Had I known I wanted that the camera should have been above everyone's eye-level which puts eye level of person in foreground below the others. I had to figure that out afterwards.) 
• Background photo perspective now needed altering. Since it was shot in Romania years ago, I had to simply solve it.
  

All these created multiple perspective challenges.

Desertsky

CBG said:

Desertsky said:

@CBG - this is very useful. BTW, pcould you please post a "Dummies Guide" version of this for those of us who may be, er, trigonometrically challenged?

Asking for a friend. 

You mean like add a few illustrations to help with understanding?  

I suppose if there was enough demand I could.

Yes, please. I think this would be really useful!

CBG

@Abstraction

I haven't used these calculations as of yet as I have not tried painting a wide angle shot.

As long as the expected field of view (when someone looks at a painting) is roughly the same as the field of view of the photo taken by the camera, there is little to worry about.  Things will look just fine.

If and when I try to paint a grand scene which has a wide field of view, I will keep in the mind the fact that only a large canvas would do it justice, and mostly, only at the right viewing distance.

Re. Rounded objects: there is a difference between a stationary person turning their eyes to look directly all around a painting including areas near the edge (which are at an angle to the unmoving viewer), and a viewer who constantly looks straight ahead and shifts/slides laterally his position to look at the painting at each location perpendicular to the painting... the former is more natural, while the latter, is somewhat laborious and less common.

 

Desertsky

@CBG and @Abstraction - you both have described the problems and solutions in great detail for which I am grateful and will apply to my own work. I too have struggled with these viewing perspectives and combining multiple photos. 

CBG, please don't bother with the Dummies version of trig formulas. It would only mean I would have to dig out my old trig books and swot away. 

CBG

@Desertsky

I will post something ... someday.

I will indulge  you to visualize something here... but no math.

IMHO, a quick guide for taking pictures with a proper level of zoom (field of view) is to imagine your camera IS a viewer of your artwork, and that your painting is literally hovering in midair, between your camera and the scene, as a sort of virtual window coinciding with what is seen in your camera view.

HOW FAR is your virtual window from the camera?  WHAT SHAPE does it have? and HOW BIG is it?

If all of these match a canvas you plan to paint, you have set your camera zoom to something workable.

Desertsky

CBG said:

IMHO, a quick guide for taking pictures with a proper level of zoom (field of view) is to imagine your camera IS a viewer of your artwork, and that your painting is literally hovering in midair, between your camera and the scene, as a sort of virtual window coinciding with what is seen in your camera view.

HOW FAR is your virtual window from the camera?  WHAT SHAPE does it have? and HOW BIG is it?

If all of these match a canvas you plan to paint, you have set your camera zoom to something workable.

Thanks, CBG. This description is what I would call sight-size. I struggle working with photos, and this is part of the problem. When I take photos outdoors as painting references, I always bracket it with different depths of field. Even if I want to just use a small part of the photo, the depth of field on the painting works better when I blow up a distance shot, because the volume of space seems more dimensionally realistic than with a close up shot with a shallow depth of field. 

The WHAT SHAPE you mention is brilliant - the outer dimensions of the painting establish the proportions for all the internal flow, and yet this is hardly mentioned, apparently, in a lot of art classes. 

Now, when I take photos as references for painting, I always think when composing with the camera about what I want the painting to look like. It has really reduced my mistakes with converting the photo to a painting. 

tassieguy

So, @CBG, 

let's say I have a canvas that is 20" X 30" which I want to use. So, I go out on a shoot and take lots of photos. A few of which I like. Do I need to zoom or can I not crop an image I like to get it to fit nicely into the size of the canvas I have available without ending up with some sort of perspectival distortion? Or must I first somehow set the camera to take a 2:3 size shot? (Not sure how to do this) Sorry, but I'm a bit confused and any clarification you can give will be greatly appreciated. 

CBG

tassieguy said:

So, @CBG, 

let's say I have a canvas that is 20" X 30" which I want to use. So, I go out on a shoot and take lots of photos. A few of which I like. Do I need to zoom or can I not crop an image I like to get it to fit nicely into the size of the canvas I have available without ending up with some sort of perspectival distortion? Or must I first somehow set the camera to take a 2:3 size shot? (Not sure how to do this) Sorry, but I'm a bit confused and any clarification you can give will be greatly appreciated. 

I will post something more... with illustrations... soonish.


For now, imagine your painting is complete and is mounted in what you deem to be an ideal position for viewing it.  Ask yourself where do you imagine your ideal viewer to be "taking in" the work from?  e.g. Four feet in front of it?  Three feet? Seven?

Imagine also what kind of experience you want your viewer to have looking at your painting, and try to think of that painting as a window, through which they are viewing your vision.  Since they essentially see your world through that frame of your painting, it cannot hurt to think of that painting, metaphorically, as a window.


This exercise might be useful.  Stand in front of a wall at a distance you would want someone to view your paintings at.  Mark the floor where you stand with an X.  Mount a canvas on that wall aligned so its center is directly in front of your eyes when you are on the X.  Now, while standing on the X with your camera directly above it, and pointing at the center of the canvas compare your camera's field of view  (the outer frame of a resulting picture you would take) at different zooms with the outer edge of your canvas.

An oversized canvas (i.e. a tighter zoom) normally is fine since it presents a "magnified" view of the world we rarely interpret as looking "distorted".  If your canvas is much smaller than the zoom you used for a picture upon which the painting is based, that is when a viewer will tend to feel there are wide angle distortions, and the only cure for which (the painting at that point being of a fixed size) is to step closer to the work.  To make an expansive work viewed from the X look good, one needs to use a sufficiently large canvas which spans the frame of the camera, i.e. one that matches the field of view through the camera that was used to take the picture upon which the painting is based.


Anywho... hope this provides food for thought.

Abstraction

Optimal viewing distance for a painting - I was taught by my (non-science) tonal impressionist teacher it is 2.5 times the diagonal - I assumed it has a basis in art somewhere. On googling that it produced this discussion on HDTV viewing distance that talks about different viewing angles in relation to diagonal measurement and human visual systems. I need to get back to it when I'm not just taking a break from work. But it shows 2.5 times diagonal has some validity as one option (for TV viewing) but also depends on what you want.

https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance

For a painting it all relates to what you want to achieve. Like most of us, I expect, I don't calculate paintings or follow composition rules, I fiddle until I like what I see. But being one of those people who combines creative with analytical - I then sometimes go back and analyse it. Not just for curiosity, but also because we have blind spots. The 'rules' help us analyse and fix problems in painting, writing, etc. We can then choose to change or ignore. A lot of paintings are clearly from cameras - bokeh (the way a limited depth of field blurs the background) is an example.

We are in a generation where we are so used to viewing through lenses and their distortions that we often don't realise it is happening. I have a vague awareness, but I still don't have a full handle on it. I want to understand it so that I can choose, not simply have a blind spot.

ASCooperband

A simple way of thinking about it is that the farther away an object not on the horizon is, the closer to the horizon vertically it will appear to be.  Since the far edge of the column top is farther away than the near edge, it will appear to be closer to the horizon line.

Abstraction

@ASCooperband Agree. But the challenge occurs when the column is off-centre. Both a camera and perspective drawing techniques distort rounded objects that are not central. The further you move from the centre, the more ridiculous the distortion. @Richard_P above provided the most definitive answer I found on any forum online and explains why and illustrates this distortion. https://www.treeshark.com/treeblog/?p=307

The camera and traditional perspective drawing creates something that they eye does not experience because it presumes a flat plane and oblique angle. In our peripheral vision we cannot make out such detail. Instead our eyes move or we turn our head and experience the perspective as if it was directly in front of us (which it has become). The decision I took for my painting was to use the eye, not the camera, to define the perspective.