Perspective: circles that are off-centre.

edited September 28 in Drawing
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.


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


  • 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.

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

  • 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.


  • 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.

  • 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? 
  • 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.
  • @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.

    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.
  • As luck would have it, just found an article which directly addresses this:
  • CBGCBG -
    edited September 28

    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 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. 

    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.

  • edited September 29
    @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.
  • 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.
  • 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 .
  • CBGCBG -
    edited September 29

    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...
  • edited September 29
    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. )
    - 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.
  • 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?
  • 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.
  • 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.  :)
  • 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.

  • edited September 30
    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.  :)
  • 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.
  • 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!
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