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That's really interesting stuff. There's some expediency to this system to make it more practical for creating drawings and paintings. It's never been intended to be mathematically precise. I don't know that I'd give up the arcs -- having to plot sine curve sections instead of being able to use a compass I think would make this process so onerous I'd never use it. I wonder if there's a relatively elegant way to plot the distance between VPs other than equidistant. Thanks for writing, I enjoy talking about this stuff.

@@Jasoncm I completely get that, and what you do still seems to work very well for you which is the most important thing. I also admit that I don't know how to find out where the horizon arc should be located in a stereographic projection in any easy way (without using a calculator). The only way I have found to actually work in a stereographic projection when drawing is by using a Wulff net (a.k.a. stereonet), but from what I have seen those always have one vanishing point in COV. And of course, even if you could get a similar net where no vanishing point is in COV (which I think should be possible), having to use a computer to print a visual guide on a separate piece of paper would still be very cumbersome and make the process more complicated. I think you're process is elegant in its (relative) simplicity.

@@kristoferkrus thanks! It's largely taken from Flocon and Barre's book "Curvilnear Perspective"

Follow-up... *why* isn't it exact? Do we need to take any considerations for the angles between the vanishing points? vp1, vp2 seem to be chosen somewhat arbitrarily. Next step... how do we fill in a grid? Equidistant spacing along the first two axes we drew, same as in three point perspective to find the intersections on the surface of the sphere, and then draw arcs of increasing curvature passing through the poles orthogonal to the corresponding vp?

@@innovationsanonymous8841 there are some great tricks for equal spacing in 5-point, and some of them extrapolate pretty well to six-point. VP 1 and VP two are chosen in one sense arbitrarily, but it's really to give the angle of view you want. If your up VP is close to the edge of the circle, you're looking a little up, if it's closer to the center, you're looking WAY up.

@@innovationsanonymous8841 why isn't it exact? I honestly don't know. Flocon and Barre said it wasn't exact, and I read through their explanation years ago. I remember being convinced at the time, but I don't remember the exact explanation. You can probably find a pdf of their book "curvilinear perspective" if you want to read it. I THINK if you were to make this space with sine curves instead of arcs, it might be more exact.

excellent!

To show the metal beneath

@@Jasoncm Very cool result!

Maybe so! What sort of thing did you have in mind?

What I had in mind was, knowing how to draw something that’s 60° and 30° on the horizontal line for example, or how to draw things that are inclined and rotated while all in 5 point perspective. Is that something you can help us out with? It would be greatly appreciate. Thank you.

@@illiria2000 that's a great idea. I'll put it on my to-do list.

Thanks a ton!

Straight- line perspective only allows a narrow field of vision, curvilinear keys you draw a much larger view. Plus it's weird and fun (I might be biased on that last one)

thanks!

If you think of the lines that draw a cube, there are three sets of parallel lines. And a line points in two directions. For simplicity sake, let's turn the cube to point north. So there are lines that go up and down, lines that go north and south, and lines that go east and west. Six directions, six points!

Thanks! "Real" is a pretty interesting concept, and one that's important to me.

It's been so many years I don't remember and it's irrelevant. But if you google "Beam Compass" you'll find some suppliers.

Glad it was helpful!

You're most welcome!

Ha! Make sure you have a couple cookies on hand you can give the demon to keep him happy while you explain it was all just a mistake

Thanks!

Thanks so much! I'm glad you like it

I hadn't, no

Thanks!

Thank you so much! I wish you all the best in life!

7 points or more is definitely possible. First I should say that you could easily have 7 points or more in a standard 2-pt perspective drawing if there are multiple objects in the scene that don't line up with the main scene. If you have chairs around a circular table, each chair will use separate vanishing points. But that's not what I'm talking about here, I'm just talking about the primary scene's vanishing points. Each vp represents a direction. So you could have vps for up, down, left, right, forward, backward (that's six) and then another point for forward again, and up again, etc and your directions would show up multiple times in the same drawing (maybe with changes, maybe the same)

This is Part 1. There's more

So, the main circle that circumscribes the drawing represents a 90 degree cone of vision. So the radius of that circle is 90 degrees. So whatever size you draw your circle, the radius is your 90 degree measurement (that can only be applied with a ruler if it passes through the center of the circle, otherwise the line of measurement would curve and the measurement would change.

Lots of drawing stuff is fun and easy. Some stuff is complicated and has a lot of steps but is still worth it

You COULD build a system that did that, but it'd be weird (sometimes weird is perfect!). So, your lines that run north-south would still curve from the N and S VPs. The question is the east/west lines. What I usually do is set up another W vp over to the left of the N vp and get a neat rotating system where the blocks look the same no matter where you draw them. But you could have the E/W lines go straight when they're left of the E vp. Or even have them keep curving in arcs thar are larger than a half-circle, so go (for instance) up and diagonal to the left from the E vp, but then arc in a HUGE circle back around to the right, coming back to the W vp. The fixed foot of the compass stays on the same line, only now it's above the horizon rather than below it. This is a bit complicated, I know. It might take another video to explain. Or it's in my book "Vanishing Point: Perspective for Comics from the Ground Up"

@@Jasoncm i was thinking the same of introducing new W point left of North. Oh and thanks for the explanation. It was weird when I drew 2 point object inside a 4d. Again, Thanks for clearing up the doubt.

This IS repeatable ad infinitum. I don't know it's EXACTLY what Escher used in "house of stairs." I'd need to take some time to examine that. My off-the-top guess is that he was using the sinusoid version of this. Where I'm using sections of a circle, he's using sine waves.

@@Jasoncm i don't know why youtube keeps deleteing my comments i'm trying to share a blog post Post is on Treeshark blog for April 17 - 2011 Cylindrical/Spherical perspictives And yes it seems Escher used some weird wave which I have no clue how to draw outside of digital and print. Great videos.

the weird wave is a sine curve -- mathematically easy to plot, but nowhere near as easy as a circle section. And remember most of those drawings he made were HUGE. Several feet long, reproduced at several inches long. The reduction in the reproduction makes him look even more mechanically precise than his very skilled hands were.

It's currently only available as an e-book, and I don't know of any plan to re-print it, I'm afraid.

Yes I have the ebook, it's truly a great book thank you so much for sharing all that information, some of the technical details I found in this book I've not ever found in another, it truly is an awesome book.... Thank you Sir for writing it , it's truly a treat

@@mohithooda8216 I'm so glad you're finding it useful! Thanks for taking the time to say so

I'm glad you liked it

I'm so glad it's helpful!

One of my first jobs in the comic book field had huge motorcycle chases, so I totally feel for you! Motorcycles are so tough to draw if you want to capture their energy and how they interact with their riders!

That's very kind of you to say, thank you!

my pleasure!

It's a beam compass made by Alvin. I believe the model is marketed as "Alvin Speed-set beam compass"

83 mm is the radius of the circle, and the radius of the circle is 90 degrees. So for this circle, 90 degrees is 83 mm (on a line that passes through the center). If your circle was 100mm, you'd use 100mm as your 90 degree measurement to place the distance from a VP to it's opposite horizon line.

@@Jasoncm ​ I had the same question as the original person about how you arrived at this, and I must honestly tell you that I found this explanation incomprehensible. "and the radius of the circle is 90 degrees"??? Relative to what? I feel like you're using mm and radius interchangeably here, but one is a measurement of length (i.e. the radius is the length of a ray emanating from the centerpoint of a circle out to its perimeter, or half the diameter), and the other is a measurement of an angle (implying two lines orginating at a common point). There's a piece of important info missing. Not trying to be difficult here---I would really like to understand this and keep going with your videos. But you've lost me very early on with this one point that Luke brought up about where 83mm is coming from (in the video you said centimeters). Any further clarification would be most welcome. Thank you.

@@anahata2009 Hi! Thanks for explaining your question. It's tricky, and I'll try to do it in a comment, but if that doesn't work, maybe a little video answer would be best. It's about the "cone of vision," or "what width of scene can you see in the picture?" In this perspective system, you are seeing a 180 degree field of vision. So the center of the circle is looking straight ahead, the top of the circle is straight up (90degrees away from straight ahead), the rightmost edge of the circle is straight to the viewer's right (90 degrees away from straight ahead) etc. The whole circumference of the circle represents 90 degrees away from looking straight ahead. So in this system, the radius of the circle represents a 90 degree change in the direction you're looking (as long as it's on a straight line that passes through the center of the circle). Let me know if this doesn't clear things up!

@@Jasoncm Hi Jason. Thanks for taking the time to try to further clarify. I'm still bewildered, like some crucial piece of information to orient myself is missing . . .but maybe getting closer? I understand the cone of vision representing everything in front of the viewer from left to right (arc of 180 degrees), and up and down. So when you say "The whole circumference of the circle represents 90 degrees away from looking straight ahead" I guess what you're describing is essentially a flat plane (picture a round plate) that is oriented perpendicular to the viewer's straight-ahead line of vision? Maybe? Even if I've understood that correctly, what you said next is still confusing to me: "in this system, the radius of the circle represents a 90 degree change in the direction you're looking (as long as it's on a straight line that passes through the center of the circle)" There are an extraordinary number of angles such a 'straight line through the center of the circle" on that plane could pass through. Are you talking about a straight line on the aforementioned perpendicular plane at the viewer's eye level, paralell to the ground? And I still don't know where a measurement of 88mm comes into play . . . A little video answer would be great, but at this point I feel like I'm going to need an elaborate 3D animation to untwist my neurons. ;-)

@@anahata2009 exactly! And that round picture plate, your eye itself is right at the center of it, because that 90 degree cone (or 180, depending on if you're thinking radius or diameter) lets you look straight up and straight down and fully to the left and fully to the right, just not behind you.