# Thread: Spherical perspective

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## Spherical perspective

Weird.

I'm not quite sure I understand it, but it seems to work well. Can anyone enlighten me a bit more about this? His main page is down right now, my link is to a mirror.

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3. We always assume that what we are taught about perspective is the way we actually see. But it's not.
Yeah that's from that site and possibily the most common mistake made when starting out. That's to assume once you set things right on a perspective grid then you're set. It may be "mathematically" correct but visually wrong.

Someone mentioned a couple years ago here about the curvature of the eye surface and how it affects the way we see things in peripheral vision. I'm sure the more experienced artists here can go into further detail.

4. Wow! I love how THIS turns into THIS! And, here I thought all verticals were always vertical, but once the cubes are placed, it looks way better than if they were all purely vertical.

5. Good thing i stayed up an extra few minutes to see this.. I never heard about it, but I always wondered how escher did some of his drawings.

Ill be having a shot at using this tommorow since I've got viscom, perfect opportunity then.

-edit- < 3 for the nfo

6. This is 4pt Perspective!

This small pic might help you to see itin a different light.

I did several imgs in this for my perspective class that you can see in my sketchbook.

7. here i was thinking there could be no more than 3 points of perspective. the world is not flat after all. thanks for the great info guys.

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Originally Posted by otherside
This is 4pt Perspective!
Don't you mean 5pt? It could be reduced to just three points along the horizon for simplicity as well.

I wonder how many points you could actually use...

9. Originally Posted by glikster
thanks glikster, intresting read.

10. how would i go about drawing a grid like that, i thought about it and im not sure how to start. I think i could start out with the normal perspective and work my way out, but I dont know how to do the curves right.

Another thing, do many professionals use this kind of perspective? i see some that use the normal 1-3 point but never this kind, seems like its more acurate and would alow for a larger view of enviroments.

EDIT:http://www.termespheres.com/perspective.html Seems like this is 5pt instead of 4, I think i can do 4pt, but what about 5pt? Do i just add anothter vanishing point in the middle?
Last edited by s.ketch; May 3rd, 2006 at 08:10 PM.

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Originally Posted by BuckWeisel
how would i go about drawing a grid like that, i thought about it and im not sure how to start. I think i could start out with the normal perspective and work my way out, but I dont know how to do the curves right.
Draw a horizon line. Put three points on the line, two on the edges and one in the middle. Draw curving lines connecting the two edge points (the apex of the curves should be over the center point), then draw curved lines that reach their apex at the same height as the other curves, but with their apexes over the edge points. That's acceptable, but if you want to go further, draw two more points, one above and one below the centre point. Connect them with curved lines in the same way. I don't think the top and bottom points are really necessary though.

Something else to keep in mind, you don't have to have only three points on the horizontal axis. Every time you add a point along the horizon line, just connect it with curved lines to the second point away from it on either side.

If you're having trouble following my directions, look at the grids on the page I linked earlier. They ought to help you.

12. This does sorta make my head hurt, but thanks for posting it.

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Draw a horizon line. Put three points on the line, two on the edges and one in the middle. Draw curving lines connecting the two edge points (the apex of the curves should be over the center point), then draw curved lines that reach their apex at the same height as the other curves, but with their apexes over the edge points. That's acceptable,
You're kidding right? The shape of those 'curved lines' is the whole problem. You don't just stick your tongue out one side of your mouth, squint, and draw some curvy lines that look sorta right. Or were you parodying Python?

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Originally Posted by YVerloc
You're kidding right? The shape of those 'curved lines' is the whole problem. You don't just stick your tongue out one side of your mouth, squint, and draw some curvy lines that look sorta right. Or were you parodying Python?
How do you mean? If you have a start point and an end point for a curve, and you know where the apex is, there's only one way you can draw the line.

15. thanks for your help 6.

YVerloc: when you have the start/endpoints and an apex all you have to do is draw a curve that passes through the apex, its really not that hard, if youre having trouble keeping yoru pencil straight, use a compass.

16. This was vry informative, for me anyways, it brings a whole new light to perspective for me.

Many thanks for posting it.

Hyperion

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I've been fiddling around with an idea for some time - instead of drawing a picture straight in curved perspective, draw 2-3 pics in ordinary perspective and then stitch them together with a computer to achieve a curved effect. Should get round to trying that soon.

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Originally Posted by dogyears
I've been fiddling around with an idea for some time - instead of drawing a picture straight in curved perspective, draw 2-3 pics in ordinary perspective and then stitch them together with a computer to achieve a curved effect. Should get round to trying that soon.
Do you mean kind of like this or this?

I tried combining the pictures from the second link in the GIMP using the change perspective tool, but I couldn't get it right. How would you do it?

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How do you mean? If you have a start point and an end point for a curve, and you know where the apex is, there's only one way you can draw the line
You seem to be assuming that it's a circular arc. How do you know this? How do you know it's not an elliptical arc with a very specific degree? Or a parabola, hyperbola, catenary, or a polynomial curve like a catmull-rom or bezier spline. There's not such thing as 'just a curve'.

Whatever it is, it's shape is specified by the math of the perspective projection involved. Not the sort of thing you can just freehand.

20. Originally Posted by YVerloc
You seem to be assuming that it's a circular arc. How do you know this? How do you know it's not an elliptical arc with a very specific degree? Or a parabola, hyperbola, catenary, or a polynomial curve like a catmull-rom or bezier spline. There's not such thing as 'just a curve'.

Whatever it is, it's shape is specified by the math of the perspective projection involved. Not the sort of thing you can just freehand.
did you look at the grids that were posted above? no complex mathmatics there. Youre reading way too far into this. When we draw, it dosnt have to be mathmatically correct, its not like we're draftsmen. Spherical perspective is visually correct, not mathmatically (as stated in the links posted above, how bout giving them a read). You can free hand it if you try, trust me.

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Really old thread, but just in case you come through here:

You seem to be assuming that it's a circular arc. How do you know this?

Excellent question. Find your answer below:

A.Araujo, 2018, Ruler, compass, and nail: constructing a total spherical perspective, Journal of Mathematics and the Arts

Never stop asking the though questions. Perspective is more than just following grids. Making a perspective grid is the pons asinorum of learning a perspective - it shows you have understood the basics; settling for *using* someone else's grids means you have given up on ever understanding.

Hope you see this. Happy trails!
Antonio

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