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Lesson 1: Lines, Ellipses and Boxes
Boxes: Simplified Guidelines
Rules of thumb
In the last page, I explained that 1, 2, and 3 point perspective are simplifications that can when used without proper understanding, have a negative impact on how a student understands the manner in which perspective can be used as a tool. That does not however mean that it is without its uses. Below, I will explain situations where one can simplify the approach to constructing a box, based on how it's oriented in space.
Just keep in mind  these are loose guidelines, and depend very much on the circumstances of what you're drawing. Additionally, they only really apply to single boxes. That may not seem particularly useful, but you'll be surprised just how often you end up drawing boxes  not as the final goal, but as a tool to help define a chunk of space in which to construct a given object.
Each of the cases below involve drawing a singular box. The simplified guidelines will help you decide whether this box should be drawn in:

1 point perspective (meaning, if the box's orientation is close enough to perpendicular to the viewer on two axes, allowing for 2 vanishing points at infinity)

2 point perspective (meaning, if the box's orientation is close enough to perpendicular to the viewer on one axis, allowing for 1 vanishing point at infinity)

or 3 point perspective (meaning, the box's orientation would not allow for any of the vanishing points to be at infinity)
In doing so, each one will have you consider the general silhouette of the box you wish to draw  that is, the 2D shape it will result in when drawn on the page.
These guidelines are suggestions for you to use outside of this course. Do not employ them for any of the exercises you're doing here  especially not ones like the box challenge and cylinder challenge, which have us drawing forms that are randomly rotated in space.
1 point perspective simplified
Consider the box you wish to draw, and the general silhouette its orientation will result in when drawn on the page. If the center of this silhouette is roughly over one of the box's faces (and is not too close to an edge or corner), then you can likely get away with drawing this box in 1 point perspective. This means that one vanishing point will be inside of or very close to the box's silhouette, but the other two can be placed at infinity, allowing you to draw those edges as parallel on the page.
The closer the silhouette's center drifts to an edge or corner, the more "off" this will end up appearing, so do not try to force it.
2 point perspective simplified
If the general silhouette of your box once drawn is centered close to an edge, you can get away with drawing it in 2 point perspective  meaning, with two sets of parallel edges drawn as lines that converge towards concrete vanishing points, and one set of parallel edges whose vanishing point is at infinity, allowing them to be drawn as parallel on the page.
The closer the silhouette's center drifts to a corner, the more it'll start to look distorted.
3 point perspective simplified
And lastly, if you find that the box's silhouette is centered close to one of the box's corners, then there's not much that can be done. Attempting to force any of the vanishing points to infinity will result in a ton of distortion, so that should absolutely be avoided in these situations.
Staedtler Pigment Liners
These are what I use when doing these exercises. They usually run somewhere in the middle of the price/quality range, and are often sold in sets of different line weights  remember that for the Drawabox lessons, we only really use the 0.5s, so try and find sets that sell only one size.
Alternatively, if at all possible, going to an art supply store and buying the pens in person is often better because they'll generally sell them individually and allow you to test them out before you buy (to weed out any duds).