astridv | Drawing with perspective, part 1: Intro to parallel projection

Lots of interest in perspective construction, so, diving right in!

I figured I'd talk about parallel projection for a bit before moving on to perspective projection.

Perspective projection = the kind you'll see in drawings that aim for realism. For example 1-point-perspective, 2-point-perspective, 3-point-perspective, zero-point-perspective.

I'll get back to that later.
Perspective projection is the kind that's most interesting for illustrators but I think it helps to know how to construct an object with parallel projections first.

1. Parallel projection is much simpler and easier to construct but less realistic. All lines that are parallel in reality will be parallel in the drawing, they don't converge in the distance. You can't get an illusion of distance. But you can get an illusion of depth and they still have their use in pictorial drawings... things like technical drawings in furniture catalogues or hifi manuals - drawings that need to illustrate the dimensions and details of an object. Or architectural drawings. Or just the quick sketch a teacher might throw at the blackboard to illustrate a subject. So, really useful!

for example:

For the purpose of these posts I'm picking two common forms: cavalier projection

and isometric projection

. There are more but if you know these two you're set.

Cavalier Perspective
This is the crudest, easiest for of a perspective drawing. It can look like this

or this

You'll notice that what each of these have in common is: one plane of the object isn't distorted - a 90° angle in reality remains at 90° in the drawing. In the first two examples that plane is the one at the bottom, in the third one it's the front one.

Now, to construct one, first let's take a very simple object: a cube.
for this version let's start with the front plane. Then draw the receding lines at a 45° angle (you could vary the angle but 45° is easiest to work with). To enhance the 3-D effect, they can be arbitrarily foreshortened (usually by a factor of 1/2 since, again, that's easiest to work with).

... and that's it!

This form of cavalier perspective is also called cabinet perspective and is, for example, used in pictorial drawings of furniture (hence cabinet). It's well suited for that because you retain an undistorted view of the front plus an idea of the depth.

There's an alternate way of constructing a cavalier projection by starting with the ground plane (pic 1) In this case it needs to be turned at an angle so that the lines of the front and the side faces don't exactly overlay the ones of the ground plane (as they do in pic 2). To avoid that, the ground plane is turned; the angle is arbitrary, 30° is a common choice (pic 4). You can experiment a bit and see what looks good. In (pic 3) two lines still end up overlapping so I increased the angle.*

Okay, so let's construct it from scratch: starting with the ground plane (1), then adding the vertical lines of the side planes (2), then the top plane (3).

Note that in this kind of cavalier perspective all lines retain their original length, without any foreshortening.

*general tip: You don't want parallel lines in drawings to overlap if it can be avoided. If that happens in an illustration I twist it and move things around, because it's confusing to the viewer.

Okay, so these are the two ways you can construct a very simple object with cavalier projection. Whether you start off the front or the bottom plane kind of depends on what you want to draw. Like, for a building I'd probably work off the ground, unless I want to showcase the facade in which case I might go with cabinet projection.

Next up: let's ~~build a companion cube~~ construct some more complex objects. For this cube, the only information needed was the width of one plane, since all planes have the same shape and dimensions. That'd get boring real soon. But if you have complex objects, you need more information - front view, side view, and top view.

Gotta take a break, come up with some interesting shapes to construct...

(I got the terminology mostly from places like wikipedia; correct me if I'm wrong somewhere. But anyway, it doesn't matter so much what each method is called, what counts is how to do it.)

Oh, and let me know if any of this doesn't make sense!

part 2