Relatively simple perspective question

[Ken Smith]

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

[Marvin Mattelson]

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.

[Ken Smith]

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?

[Allan Rahbek]

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

[Chuck Yokota]

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.

[Allan Rahbek]

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

[Geary Wootten]

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

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

-Gear (Just clowning w/ my 2

[Ken Smith]

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.

[Allan Rahbek]

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

[Chuck Yokota]

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.