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.
Comments
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
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
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.
https://www.treeshark.com/treeblog/?p=307
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.
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.
BTW It’s Caravaggio’s birthday. Fitting for this topi .
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...
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?
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.
You can determine an ideal size for your painting or an ideal viewing distance as follows:
Asking for a friend.
I suppose if there was enough demand I could.
- 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.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.
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.
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.
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.
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.
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.