Calculating perspective for off-page vanishing point

[Senira]

A professor of mine taught us a way to draw lines to vanishing points that went off the page without having to tape together three or four rulers to locate it. The first step was to draw a horizontal line, then on top of it draw a line at the angle you wanted; after that, my memory of the technique is extremely fuzzy.

I think part of it was to calculate the distance between the horizon and the corner formed by the horizontal/angle, then to find the distance between the horizon and some other part of the angle, then divide the answer at some point. I wish I could remember, because it's a very handy trick when you don't know perspective well enough to guess at extending lines from a VP.

Does anyone know what I'm talking about? Or, do you have a better way of doing this?

[deepbluehue]

What I do is put down my horizon line, and place a line that defines the angle I want either below or above the horizon line. I measure the distance between the lines on both sides of my paper. I'll use that measurement to make equidistant marks on both sides of my paper and then draw lines to connect the marks so that I have lines that recede to a vanishing point off the page. I'll repeat the process so that I have a second vanishing point going in the other direction. You can do that for three point perspective as well.

[Senira]

That's exactly it! A friend of mine who took the professor in question's class also confirmed this. I swear, I've been trying to remember that forever. Thanks a lot!

[deepbluehue]

You're welcome.

[Jack the R]

Can one of you guys post an illustration of this technique?

[Barber]

some people just eyeball it,or "guesstimate" ,see Scott Robertson Dvd's.

[Flake]

Can one of you guys post an illustration of this technique?

I think we're talking about the same technique and this is how I've best seen it explained. (Image from a poster on GurneyJurney)

http://img87.imageshack.us/img87/1626/perspectqg8.jpg (http://imageshack.us)

[deepbluehue]

Flake, that's exactly what I meant.

[Paulie]

Sorry to bring this thread back from the dead but hopefully someone can help me with this.

I understand how to calculate the perspective of an object such as a box when the vanishing points are off the page and when the object is completely below the horizon line like in the example below.

However, if the bottom of the box starts below the horizon line and the top of it is above the horizon line, how to do you go about doing that?

Since the initial angles are done by eye, how do you make sure that the angles above the horizon line correct? (ie, to ensure that the top of a building is not sloping).

Hopefully I haven't worded this too confusingly.

[QueenGwenevere]

I think you just keep ticking off more marks above the horizon line as well, using the same measurements... So, if you have marks 1mm apart on one side and 5mm apart on the other, just add more marks 1mm apart and 5mm apart all the way up the page... (And all the way down, if you need to go further down.)

(My memory of this is hazy, too, but I think I've seen it done that way... I could be totally wrong. I suppose you could try it and see what happens.)

[Elwell]

Yeah, it's the same process. If the units are uniform, they'll recede to the same VP whether they're above or below the horizon.

[Paulie]

Sweeeeeet.

Thanks!

[Jie Kageshinzo]

I think we're talking about the same technique and this is how I've best seen it explained. (Image from a poster on GurneyJurney)

http://img87.imageshack.us/img87/1626/perspectqg8.jpg (http://imageshack.us)

Just a question, if I may: the equal measurements for each side, does that have to be measured off the page/canvas? Or can I use a measurement on the edge of the canvas itself? The reason I'm asking is because if it's set off-canvas, that'd be hard if your workspace is not big enough, am I right?

[QueenGwenevere]

Just a question, if I may: the equal measurements for each side, does that have to be measured off the page/canvas? Or can I use a measurement on the edge of the canvas itself? The reason I'm asking is because if it's set off-canvas, that'd be hard if your workspace is not big enough, am I right?

They can be on the edge of the canvas, or as close to or far from the edge as you like... The whole point of that method is to be able to do perspective in a small workspace.

[eezacque@xs4all.nl]

They can be on the edge of the canvas, or as close to or far from the edge as you like... The whole point of that method is to be able to do perspective in a small workspace.

Good point. I used to tape perspective stuff to the wall and bought a 50cm ruler to make it to the vanishing points. Not happy.

[QueenGwenevere]

Good point. I used to tape perspective stuff to the wall and bought a 50cm ruler to make it to the vanishing points. Not happy.

Only 50cm? :P When I do big drawings I use a 48-inch ruler (about 122cm) plus a hockey stick as an extension... plus lots of tape... usually on the floor and running out into the hallway...

Seriously considering using this grid trick instead.

[eezacque@xs4all.nl]

Only 50cm? :P When I do big drawings I use a 48-inch ruler (about 122cm) plus a hockey stick as an extension... plus lots of tape... usually on the floor and running out into the hallway...

Seriously considering using this grid trick instead.

I heard that at the top schools they do their homework in the parking lot, using lasers, just to make sure their vanishing points are not too close.

[Jie Kageshinzo]

They can be on the edge of the canvas, or as close to or far from the edge as you like... The whole point of that method is to be able to do perspective in a small workspace.

So essentially, the whole trick is just measuring equal distance from the horizon line for each side. Neat. Each side's equal measurement can be independent from each other, right?

[Jie Kageshinzo]

Sorry for the bump, but I found this while looking up perspectives with off-screen VPs:

http://scientificartist.blogspot.com/2005/09/perspective-tips-1.html

Just as I thought when I tried it, the method doesn't work when you're trying to foreshorten something. Is there any way I can use a similar technique for foreshortening? :/

[eezacque@xs4all.nl]

Sorry for the bump, but I found this while looking up perspectives with off-screen VPs:

http://scientificartist.blogspot.com/2005/09/perspective-tips-1.html

Just as I thought when I tried it, the method doesn't work when you're trying to foreshorten something. Is there any way I can use a similar technique for foreshortening? :/

Why doesn't it work? It is a shortcut for using vanishing points, which are used to construct the distortion caused by perspective, but both methods do not give you foreshortening for free. Foreshortening is usually eye-balled, although there are more exact methods available, using measure points.

[Elwell]

I think he's referring to what Paul Rivoche says in the link posted:
A couple of things to note: the lines which you generate will be spaced evenly across the flat surface of the paper. They will not be successively closer together as they go away into the distance, the way a checkerboard pattern spaces more tightly on a floor as it is seen in perspective.

In other words, don’t rely on these lines to show spacing in depth (foreshortening), just use them to guide the angles of your lines.

This is an important point, not necessarily a drawback if it's understood, but something to be aware of.

[nofu]

Only 50cm? :P When I do big drawings I use a 48-inch ruler (about 122cm) plus a hockey stick as an extension... plus lots of tape... usually on the floor and running out into the hallway...

If you wanna go at it this way why not use builders tape measure, makes a whole lot easier.

[eezacque@xs4all.nl]

I think he's referring to what Paul Rivoche says in the link posted:

This is an important point, not necessarily a drawback if it's understood, but something to be aware of.

I think the construction lines are meant to construct vertical planes, like the walls of a building. As such, it is really no different from using vanishing points. I'm pretty sure the construction can be easily adapted for horizontal planes, like the checkerboard mentioned.

[Jie Kageshinzo]

I tried using this last night while making a piece:

http://www.khulsey.com/perspective_foreshortened.html

Tried making it work with the method above. I wasn't quite successful because you need to know the exact VP (which the method above can't be used). But I still get a feeling they can be used together somehow. >_<x