# Thread: Alex Vicat Cole... sun from behind

1. ## Alex Vicat Cole... sun from behind

In the attachment below is an approximate reproduction an image in perspective from Alex Vicat Cole's book on perspective. It shows the "Pseudo sun" and a sun from behind. My question is, how does he know where to put the true position of the sun as from behind the viewer, on the horizon line? I can't seem to find how the pseudo sun relates to the placement of the sun from behind.

Here is the book at google books, the page in question is page 192:
Last edited by Vay; July 18th, 2011 at 11:18 PM.

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3. Firstly, let me thank you for alerting me that my copy of Rex Vicat Cole's "Perspective for Artists" is missing. I'll have to tear the house apart sometime this weekend.

Now then, as for your question...

Typically, you plot out shadows from the sun directly by plotting a line downward from the sun where it is tangent with the top of the object and continue it until it intersects the corresponding line you have drawn out from the base to the horizon.

In the case of where the sun is behind the viewer, you instead use the "pseudo sun". To do this, you draw out your line from the base of the object to the horizon. Where that line meets the horizon, you draw a vertical line downward as far as the sun is high in the sky. From this point, you may draw a line tangent to the top of the object and if you wish continue it out to where the sun would be were it in front of the viewer.

In short, the pseudo sun is where a "mirror image" of the sun would be. That is, if there were another sun exactly opposite (in relation to the viewer) of the first sun... it would be where the pseudo sun is.

Now, I know that all sounds like a bunch of gobble-de-gook, so I made a drawing that will hopefully show better what took so many confusing words to describe.

In my drawing the sun in green is actually behind you, and is only included to show the relationship between it and the pseudo sun.

P.S. Your Google link does not offer the whole book, particularly page 192 is not available. Also the Archive.org version, via a mistake with whomever uploaded it, is actually a book about the Greek language. So only someone who has or had a physical copy of the book could answer your question, which is why you had to wait a few days. :)

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5. Originally Posted by Anid Maro
Firstly, let me thank you for alerting me that my copy of Rex Vicat Cole's "Perspective for Artists" is missing. I'll have to tear the house apart sometime this weekend.

Now then, as for your question...

Typically, you plot out shadows from the sun directly by plotting a line downward from the sun where it is tangent with the top of the object and continue it until it intersects the corresponding line you have drawn out from the base to the horizon.

In the case of where the sun is behind the viewer, you instead use the "pseudo sun". To do this, you draw out your line from the base of the object to the horizon. Where that line meets the horizon, you draw a vertical line downward as far as the sun is high in the sky. From this point, you may draw a line tangent to the top of the object and if you wish continue it out to where the sun would be were it in front of the viewer.

In short, the pseudo sun is where a "mirror image" of the sun would be. That is, if there were another sun exactly opposite (in relation to the viewer) of the first sun... it would be where the pseudo sun is.

Now, I know that all sounds like a bunch of gobble-de-gook, so I made a drawing that will hopefully show better what took so many confusing words to describe.

In my drawing the sun in green is actually behind you, and is only included to show the relationship between it and the pseudo sun.

P.S. Your Google link does not offer the whole book, particularly page 192 is not available. Also the Archive.org version, via a mistake with whomever uploaded it, is actually a book about the Greek language. So only someone who has or had a physical copy of the book could answer your question, which is why you had to wait a few days.
I have to question your sketch. If the sun is directly above the gate and from behind, then why is the shadow slanted to the right in perspective? It seems that Alex Vicat Cole's version looks more right, but at the same time I cannot figure out why the sun is placed where it is in the picture below.

Odd, because the page shows on my computer. I scrolled down to that page. With the picture in Alex Vicat Cole's book, the trangent line doesn't go to "the sun as from behind". The picture of the page is below:

Last edited by Vay; July 18th, 2011 at 11:28 PM.

6. It would seem I misspoke slightly, in my first response.

Originally Posted by Anid Maro
In my drawing the sun in green is actually behind you...
Should've been more like:

"In my drawing, the green is where one might approximate the real sun behind the viewer relative to that corner of the object."

That is to say, projecting the sun that is behind the viewer towards the front but not below (into the pseudo sun) is inherently inaccurate since... well it's behind you and not in front of you.

That projection is an estimate based upon a single sun ray and shifts depending on which sun ray you use. The true sun lies at a point where each and every one of those sun rays would converge, and that point is behind you and thereby out of view*.

In Rex Vicat Cole's example, the line drawn between pseudo sun and point 4 does not lead to his "real" sun as it would in mine. However, were you to draw a line between pseudo sun and point 1 it would lead to his "real" sun.

The short of it is that you'll get different projected "real" suns depending on what sun rays you reference because that projection is only a half-step. It also doesn't matter because the real sun and pseudo sun, both the only points of relevance, are in precise locations.

I drew another example, better constructed this time to be thorough, showing multiple possibilities for a projected "real" sun.

*Technically, you could see it with a curvilinear perspective as then the sun rays would curve appropriately and converge behind you.
Last edited by Anid Maro; July 19th, 2011 at 09:26 AM.

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8. Since I didn't want to leave you hanging, I made a very crude curvilinear diagram from a birds-eye view.

Briefly, if you aren't familiar, curvilinear perspective is when one uses arcs for their perspective grid in order to encompass a larger field of view offered by traditional linear perspective. The result will look similar to what you get when taking a picture with a wide-angle lens.

Anyhow the pseudo sun is up top and would be somewhere below the ground, the sun is at bottom and is elevated in the sky. To the bottom left and right are the projected suns, that is the estimation of the "real sun" shown in both Rex Vicat Cole and my own images.

The shifting of the projected sun is due to applying a linear method to what is essentially a curvilinear problem.

There, clear as mud now? :)

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10. Originally Posted by Anid Maro
Since I didn't want to leave you hanging, I made a very crude curvilinear diagram from a birds-eye view.

Briefly, if you aren't familiar, curvilinear perspective is when one uses arcs for their perspective grid in order to encompass a larger field of view offered by traditional linear perspective. The result will look similar to what you get when taking a picture with a wide-angle lens.

Anyhow the pseudo sun is up top and would be somewhere below the ground, the sun is at bottom and is elevated in the sky. To the bottom left and right are the projected suns, that is the estimation of the "real sun" shown in both Rex Vicat Cole and my own images.

The shifting of the projected sun is due to applying a linear method to what is essentially a curvilinear problem.

There, clear as mud now?
Yes, vacuum clear. You should write a book on perspective or something. Where did you learn this stuff? Can't find these answers in the usual perspective for artists books.

11. Glad to hear I helped.

As for where I learned this stuff, pretty much I started with questions similar to yours and read and drew until I could answer them.

Maybe one day I'll try my hand at a condensed perspective manual (in the vein of what Rex Vicat Cole was attempting) since I've spent quite a bit of time on it, but for just raw information have you ever read the perspective articles over at Handprint? Lots and lots of good info there.

12. Originally Posted by Anid Maro

As for where I learned this stuff, pretty much I started with questions similar to yours and read and drew until I could answer them.

Maybe one day I'll try my hand at a condensed perspective manual (in the vein of what Rex Vicat Cole was attempting) since I've spent quite a bit of time on it, but for just raw information have you ever read the perspective articles over at Handprint? Lots and lots of good info there.
I couldn't read it because the sentences are broken up by the alignment. I found myself going over the same sentence a few times, sometimes I get lost and find myself on another line, and etc. Especially for something so complicated.

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