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What would we see if we were inside a cube, looking around through a spherical glass surface?
I thought this would be a simple exercise. It wasn’t. Drawing the inside of a cube turned into a full-on brain gym session. But it was a blast and I learned a ton along the way.
Can’t wait to see what intellectual delights Marshall is preparing for us!
LESSON NOTES
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Explore how to use curvilinear perspective to capture wider views in a single image. You’ll learn how curved picture planes keep lines more natural at extreme angles, discover exercises for shooting labeled panoramas, and see how adding vertical and horizontal curves can transform your sense of space. These simple steps will help you widen your view, reduce distortion, and refine how you see and draw the world around you.
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panoramas-unlock-curvilinear-knowledge.mp4
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panoramas-unlock-curvilinear-knowledge-captions-spanish.txt
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panoramas-unlock-curvilinear-knowledge-captions-english.srt
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COMMENTS
Explore how to use curvilinear perspective to capture wider views in a single image. You’ll learn how curved picture planes keep lines more natural at extreme angles, discover exercises for shooting labeled panoramas, and see how adding vertical and horizontal curves can transform your sense of space. These simple steps will help you widen your view, reduce distortion, and refine how you see and draw the world around you.
It was really good to take your own panoramas. It makes it easier to understand whats going on when you can see how it looks in real life. But even with scenes that have straight lines, it's tricky to find where the vps are and exactly how the lines should curve. But I tried my best to draw it out.
I did several shoots of my door going closer and closer and then changing angle to see the difference. The closer you are the closer the vps are, which give a more extreme curving.
At first I wasn't so interested in curvilinear perspective because I didn't like the curving distortion that much. It just felt weird. But after playing around with this I actually like it, as long as it doesn't get too extreme. Now I looking forward to play around even more with this.
I also had a lot of fun drawing panoramas of my kitchen and living room. I did use a premade grid as help for this.
This panorama view was photographed in 'Bandits', a coffee bar in Saltash, Cornwall. My first line drawing I created using reference buildings in my high street, with a lot of liberties while I practised using the grid. I really like the using curvilinear perspective, although a few times I reverted back to straights unintentionally.
Here are my photo's and some basic drawings based of some of them!
So, if I'm correct, different objects can have their own vanishing points, even in four/five point perspective, right? I think this is the case for some buildings in the background. It complicates things.
This is a panorama picture I took of Castle Groeneveld in my little town.
It took a while before I found the grid.
Last week I took panorama pictures in the surrounding park where I bike and often take walks, but I couldn’t find any grids to lay underneath them. Of course, Marshall already said it already that you need more obvious right angles.
By the way about the Castle:
There used to live a family, but in 1941 it became in possession of State Forestry Department and it lays a wonderful park now.
That same year Escher moved to our town and would live here for 29 years.
I'm sure he took walks there too :)
The third image is The Pythagoras Tree, drawn by Escher's neighbour and friend here. I thought this was interesting :)
If you want to know more: https://alberternstbosman.nl/en/
Went on a bit of an outing to the shopping area below my office. I tried to look at 3 different kinds of scenes: 1 with dead-straight horizontal and vertical lines, the 2nd containing a concavely curved staircase and the third with a convexly curved building. What was most enlightening was how the concave staircase was almost perfectly flattened out. It was a great exercise trying to draw the receding lines in the first instance. What was also interesting to see was how much the convex building was made even more convex.
Haven't had the courage to draw an entire scene, but I'll try to cross that hurdle ASAP.
Awesome work! :D And yeah, get yourself out there. You could use some Pokemon Go or something for extra incentive lol
now as a certified shut-in, this is actually a good encouragement to drag my feet outside for once!
So a 360 deg curved picture plane is represented by four 180 deg grids…who’d of thought it…!
Is it a ‘rule’ for curvilinear perspective that the vanishing points must be spaced apart on the horizon line by a distance that represents 90 deg field of view?
It is confusing how you would deal with many objects that are not ‘aligned’ to the same VPs in a more complex scene using curvilinear perspective….
In my panoramas I drew grids with the vanishing points always at N, S, E, W. It worked ok for most but probably you should place the VPs based on where converging lines of the main subject of the frame meet. Not sure I’m approaching this in the right way.
Any feedback appreciated, my head is spinning 360 trying understand the details here
This is as far as I've got - I ran out of steam. The vertical lines are dead straight, so not exactly reflecting the lens. This building has too many angles!
What would we see if we were inside a cube, looking around through a spherical glass surface?
I thought this would be a simple exercise. It wasn’t. Drawing the inside of a cube turned into a full-on brain gym session. But it was a blast and I learned a ton along the way.
Can’t wait to see what intellectual delights Marshall is preparing for us!
🤩 And that's how it's done! 👏🏼 I'm saving all of these to study. They answer many questions on the topic. Thank you!
Brilliant - and the drawings are kept beautifully simple :)
I might be making a big deal over nothing, but were exactly is the third point in this pano?
None of the lines really seem to go towards any single vanishing point in the center of the image. I made a little irl pano with a piece of paper folded into a cylinder to help me understand all this madness. It makes sense for the third point to be on the absolute dead center of the image, but I don't know how correct that is...
Out of curiosity, I tried fitting an equirectangular spherical grid, like the one that seems to be used by cameras to create panoramas, to your image. It seems to fit quite nicely. It even explains why the black pothole patches in the foreground appear to bend away from us as they get closer. The buildings on the right converge toward the east vanishing point. And the building just to the right of center should converge to the north vanishing point, but it’s probably not facing us, so it has its own, different vanishing point.
Source of the grid: https://www.araujoab.com/equirectangular.html#grid.
I love the paper cylinder you made to help explain things to yourself.
Although, since we're supposed to view the world from inside a transparent sphere, maybe you could make it larger, glue it with the drawing facing inward and view it from inside? Or, come to think of it, maybe you should make a paper sphere and look at it from the inside? 😀
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5mo
Isn't that large grey area on the ground, just left of center, pointing to a center vanishing point?
Remember that a vanishing point doesn't happen unless there is something in the picture to make it happen. An organic landscape may have no VP's.
That's why the number of points is not the issue in curvilinear. The issue is what that expanded view does to the straight lines.
There are some amazing photos and drawings posted here.
I see some references to using technology outwith the course,
to compare drawing accuracy. I'm wondering if there is a more basic
means for the beginner to understand all this within the course without / before all the
advanced technology?
I bought the wrong (new mastering perspective) course but hope to get into some of this in the new one. I made a thread where artists can take on a plein air painting/drawing in equirectangular perspective if anyone's interested. I uploaded these to Google street view. Would be cool to see more artists contribute.
https://www.proko.com/community/topics/360-spherical-panorama-challenge
Second attempt, from imagination. I watched the vids from the link that Stepka sent to Lin and copied the grids. Also tried to use the sliding trick he shows there.
Do I understand it now?
No. 😂
While experimenting I added music to playlists on Spotify, so had a good time with it all. Hope there are not too many errors.
Sita, you’ve been a speed demon with that drawing! 🚀
It looks spot-on to me. Nice job! Either you’ve mastered perspective, or you’ve made a secret deal with the vanishing points. 😄
Found a wide open spot to answer a question I had last week. The horizon does indeed take precedence over the lense distortion.
I also found that the distortion was way less dramatic than I was anticipating, I had to be almost touching the subject to get the super warped effect I default to when drawing!
I like your photos, what make of camera did you use?
I only have a small bridge camera Pentax X90, I'm not sure it's
suitable for these panoramic shots.
First attempt. One of the rooms in the building. There are far more chairs and easels than I drew, but I wanted to simplify (and felt impatient) hoping to understand a bit more of this topic. I don’t see the underlying grid exactly yet.
Marshall, there’s one thing that confuses me when doing our exercise - why is it that once you get far enough to the top and bottom the lines stop being gradual circles and become squareish? Look at how the ceiling lines start distorting - I see it in professional drawings too. Is there a way to know where to “bend” correctly when it’s not yet intuitive? You can’t just go VP to VP gradually like in the grids we make. Does it have something to do with the lens? Thanks :3
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5mo
There are exact ways to project the curves. David Chelsea, in his book EXTREME PERSPECTIVE FOR ARTISTS, takes it up. It's quite mathematical and requires a good deal of energy and commitment — so in case you want more, go there — I'm not going to attempt it!
This is an amazing image! Can you tell us more about it?
I uploaded my drawings to google street view using teleport (Ipad). The app allows you to view your drawing in a 3D ball while you move the screen and you can also upload to google street view. That helped me understand those lines better. I also found practicing in a boxed room or alley helped sort the grid. Going at it at a 45 degree is tricky!
https://www.proko.com/community/topics/360-spherical-panorama-challenge
The squarish shape of the lines is due to the equirectangular spherical perspective. This format appears to be a natural choice for cameras and for apps that support 360-degree views, such as Koola, e.g https://kuula.co/post/7xPwt.
Some interesting example videos can be found here:
https://www.youtube.com/watch?v=Bf9569yyli8&list=PLlfj5HYIafD4UInN7GKNd9nbBgerZXG2k.
Seeing the West-North-East panoramic view was super helpful. Realizing that these curvilinear views work by essentially adding an element of depth to (I guess?) what you'd call the x-axis left to right as well as the y-axis if you pan up and down was a lightbulb moment for me. Thank you for the video, Marshall.
