Relatively simple perspective question
 

I'm going to show my public school art education here, but...

If I wanted to draw a 4x4x4 cube in two-point perspective, how can I accurately make the sides of the box (B&C) the same length as the height of the box (A), except drawn in perspective?

I understand I can do it with Plan perspective (which I have the barest grasp of), or just eyeball it, but I'm wondering if there might be a simple, but accurate method that I'm not aware of. The drawing I'm doing is somewhat more complicated than a cube, but this is the gist of the problem.

Thanks in advance.

Ken

The simple answer here is that you can't. As planes recede into the distance they get forshortened. So on a cube positioned such as yours The length of the vertical (A) will always exceed the length of horizontal (B or C) going into perspective. If you objectively look at the "cube" you illustrated, it looks more rectangular. Sorry.

This does look rectangular now that you mention it.

Just to make sure I'm explaining myself clearly, I understand that the B&C lines will always be shorter than the A line due to foreshortening. But what I'm wondering is: is there a method to precisely define the length of the B&C line in relation to the A line (while taking the foreshortening into account), since they're all supposed to be 4 inches long? All the perspective stuff I've read (except for plan perspective) seem to define the length of foreshortened lines only in relation to themselves (as in finding half distances).

I got into this question when I started to draw a rectangular background object (in perspective) that I knew was 46 inches tall and 6.5 ft. long. The 46 inches tall was no problem, but I couldn't figure how to draw the 6.5 ft. length accurately, in perspective, relative to the 46 inch height.

Is this still a "can't be done" situation?

The easy part of painting
 

Hi Ken,

This is easy. You draw your cube in scale 1:10 on a paper. Then you mark your point of view and draw the lines, and measure.
Allan

For those who found Allan's explanation a bit brief, I prepared an expanded explanation, with diagrams.

There are three parts to making a perspective view: the object (e.g. the box that Ken asked about), the drawing plane (the 2-dimensional representation as it would appear on your drawing), and the viewpoint (your eye position). You chose the positions of the drawing plane and the viewpoint to suit your artistic requirements.

Imagine that you carry around a large piece of glass. You set it up between yourself and your subject, and, holding your eye still, you trace on the glass what you see. The result is a perspective view.

To create the same view analytically, you would draw views of the side and top (to scale, not in perspective). Draw lines from the corners to the viewpoint. The place where the lines cross the drawing plane is the position of the corner in the drawing, the vertical position in the side view, and the horizontal position in the top view. You can put these together either graphically or by measurement to locate the corner on your drawing.

Chuck is right.

To get the measures right you will have to place the "glass plane" at the distance from "viewpoint" by the "A" line.

Allan

Ya gotta love it when guys say' , 'This is easy", and then go into partnership with geometric theory. LOL! :D

In 99% of my drawings and paintings, I FAKE it baby!

-Gear (Just clowning w/ my 2

I think that technique is called "plan perspective." (I read three different books on perspective last evening). And that seemed to be the only way to get the info I was looking for.

I was hoping for something simpler, because I'm not actually drawing a cube. I'm drawing the inside of a boat cockpit.

I've also heard this referred to as descriptive geometry. Keith Ferris, the aviation artist, says he uses it to draw exotic angles on fighter planes (from blueprints). One of my perspective books has an example of an airplane in a box drawn this way, but frankly I can't make heads or tails out of how they've explained it.

It has nothing to do with portraits, but if any of you know of any books that explain this technique in English (particularly as it applies to objects more complicated than a house), I'd like to read one.

Hi Ken,

I am, by no mean, interested in oversimplifying things. But I insist that you can draw anything by looking through an imaginary frame from a particular viewpoint. Just try it!

When I draw, I control my drawing by comparing the angles with the vertical and horizontal of the drawing paper.

Next, I often draw life size, to bee another control funktion .

This, of cause, are technical things that have to bee understood before you can take the advantage of them.

There are many topics that deal with these matters.

Ken, I am aware that you are the one that just asked the question, but I prefer to answer as precise and direct as I can.

Allan

Ken,

Um, I guess I thought it *was* the simple way. I got my stuff from a course in geometric modelling, a graduate-level engineering class in the mathematics behind how computers generate real-time 3D scenes onto your monitor. The course started out assuming you were familiar with matrix algebra, vector and tensor calculus, and differential equations, and then got into the complicated stuff. Plan perspective was tossed out as a simple, intuitive way to picture what was going on when the computer was crunching bits.

As Allan says, you can paint any scene by painting through an imaginary frame, from life.

I suppose the next simplest way is to use a reference photo and accept whatever distortions are created by the camera lens.

Limiting this response to the desired representation that was described

:o ......Qww - ya wanna bet? LOL.

Steven, Ken..et al,

Thanks for taking the time in doing this. In spite of my yucking it up, I actually learned some things today.

G. (reeling from left brain hook to right brain. :( )

So, okay, I added the supporting illustrations above. That

Steven

There is no "true" perspective, all of them are theoretical, fulfilling different needs. I try to avoid the use of linear perspective.

How did you place the two vanishing points ? Did you measured them to the right place or how ?

I think Ken will have troubles drawing in a small boat cabin. It is tempting to take a broader view when drawing in a small room. When seeing the drawing from a longer distance (than it was done) you will see distortions.

I will attach a drawing that, hopefully, will explain the perspective consequence of doing the wide angle view.

Allan

Wow!

I'm suitably amazed. I never thought of myself as particularly left-brained, but this sure cinches it.

Last evening I actually was able to do the drawing using the plan perspective thing, and surprisingly (to me, anyway), it actually worked. Except that I made the horizon too low.

The reason I'm exploring this is that I'm doing a painting of 3 guys in the cockpit of a LCVP (a WWII landing craft). I have some 1/24 scale blueprints of the boat and a very poor plastic model and a bunch of photos (but of course none from the angle I need). I need to place these guys accurately to get the scale of the boat and a realistic view of the various angles.

After reading all this, and trying my own descriptive geometry session, I've decide to solve it this way:

I've taped out the layout of the cockpit full-size on the floor of my studio. I'm going to roughly mockup the sides and deck heights and so forth with some corrugated cardboard sheets, and then place the models where they belong, light them, sketch them, photograph them, and let that be that (and just be glad they weren't on an aircraft carrier!).

This has been a supremely informative discussion; I really appreciate all the info (and I actually sort of understand it, which I certainly didn't beforehand).

Allan,

You are astute to ask this question. In fact, in my quick sketch, I just located the vanishing points where it was convenient to do so. More correctly, one would have to establish a so-called "circle of view", the radius of which is the distance from the viewer to the image plane (or drawing). From any point, then, on that circle, the vanishing points would be 90 degrees apart (using the point on the circle as the vertex of that angle.) This gives you an infinite number of available perspectives, though a relatively small number of them will produce aesthetically pleasing results, which for our purposes here is the primary consideration.

A caveat, that this is the procedure for the cubic polyhedron. Other forms require modification of this approach.

All of which is why I suggested that Ken focus on what he could see, with an eye to aesthetic considerations, rather than worry about precision in perspective.

Hi, I just stumbled over this old tread and thought that I should try to make my point less brief by adding a practical example to show how the viewpoint, and angle of the view, affects the perspective in the final painting.
As you see, on the left illustration, the angle of view is about 75 degrees out of the full circle of 360 degrees. To project the correct drawing one would have to straiten out the curve before projecting the lines, but I cheated.

My 2 cents.
 

Hi there,

Nice thread!

If anybody wants, I can email the pages in a larger size.

All the best.

These are all from the book "Successful Drawing" by Andrew Loomis.

I've got many more pages about it.

One might ask: "Why should I study about it? I paint what I see!"
First of all, painting is 90 % drawing.
Second of all, most painters paint what they "think" they see and not what the actually see.
Last of all, sometimes you need to paint a posthumous portrait, and in that case, the model cannot sit for you, so you have to use these rules to make a better job. Sometimes the lighting in a photograph is horrible, but you liked the pose, so, you can change the values, lighting, etc, if you master perspective.

Hope it helps.