Crash-Course: Curvilinear perspective question: Four-Point Perspective

A quick walk-through of drawing in 4-pt perspective. The camera is at a bit of an angle to the table, so the circles look like ellipses, and the right angles don't look quite like right angles, so you've sort of got to trust what I'm saying. Using an Alvin beam compass (that I love) for drawing the circle sections.

[@anjhap]

Man, I'm literally paying $600 for an art class to explain to me the WHY and HOW of curvilinear perspective. Thank goodness I found this video!!

[@5ilver42]

For anyone interested in the math for the actual curve, it's effectively:
_f( x )_ = _height_ * sin( _x_ ) ^ cos( _height_ )
This will create the distortion for the cylindrical projection where straight up and strait down exist at all points horizontally at the top and bottom of the rendering plane.

[@kalpa_redon4043]

I didn't bother taking your time to explain how to draw this in the class, but this video clears thing up for me. Love the video, thanks for sharing this

[@Rafael-kb1ql]

THANK YOU. Your video answers another question-- what if there is a diagonal object in the middle.
The other videos I watched only teach it as if you're conveniently parallel/perpendicular to your scene.

[@dublinphotoart]

This object would simply have its own seperate set of vanishing points spread apart equal distance as the main ones

[@zomkila]

Hello Jason, what if you place a cube between N and E? Would it become 2 point perspective object?

[@Jasoncm]

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"

[@zomkila]

@@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.

[@AbiNomac]

So helpful. Thank you

[@Jasoncm]

I'm so glad it's helpful!

[@dublinphotoart]

So this is 'cylindrical perspective' as used in MC Escher 'house of stairs'? 😮🤔 and repeatable ad infinitum? 😮🤔

[@Jasoncm]

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.

[@dublinphotoart]

@@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.

[@Jasoncm]

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.

[@MultiMetalsnake]

He's four dimensions ahead of you.

[@3govideo]

Thanks for explaining how to draw. Can you explain why verticals, stay vertical?

[@Jasoncm]

Hi! I'm going to make another short video explaining that in a day or three. The basic answer is it's actually an artificial convention. We CHOOSE to make the verticals stay vertical so this particular system works. And there are reasons why that choice works well. But you could totally choose to make the horizontals stay horizontal instead. Or let the verticals converge top to bottom in five-point perspective.

[@Jasoncm]

This video is about your question: ua-cam.com/video/gdwHa-0CH7k/v-deo.html

[@PhilsDesignCorner]

Curvilinear perspective should only have 5 vanishing points. There are not 4 sets of vanishing points on a horizon line in this area....there should only be 3 from this view? You shouldn't need a compass to show this. That just complicates the drawing.

[@Jasoncm]

I put up another video about five-point perspective you might be interested in -- ua-cam.com/video/gdwHa-0CH7k/v-deo.html . As for the compass, I think it's useful, just like a straightedge is useful in rectilinear perspective. Do you think freehanding the curves is better?