As of October 8th 2016, after roughly two years of offering free critiques, I will now be limiting my own critiques to patreon supporters ($3 or more for this lesson specifically). But don't fret - you are still welcome to freely submit your work and questions directly to the /r/ArtFundamentals subreddit to be reviewed by the community.
If you haven't yet completed Lesson 1, go back and do that first. This exercise is best done between lessons 1 and 2.
This is a great bit of practice for those who are having trouble with estimating perspective, or understanding the difference between a form that is solid and weighty, and one that is flimsy and unsubstantial.
I want you to draw 250 boxes. Big boxes, small boxes, long boxes, squat boxes, boxes tilted up, boxes tilted down, boxes boxes boxes. Number those boxes, too, so people don't have to count each one! With each box, take your time. Don't try and do them all in one sitting, if your hand gets tired, go do something else. Try your best to make each box correct. Mistakes may occur, they don't all have to be perfect - but they should all be the result of your best effort.
Also, it's best not to have these boxes overlap - draw each one separately. Overlapping would add complication, so lets just tackle one thing at a time.
When you finish a page, go back with a red pen, or a highlighter, or whatever, and mark out your mistakes. Half the battle is being able to quickly pick up what you've done right and what you've done wrong.
Lastly, remember - this should be done in ink, preferably with a fineliner/felt tip pen.
NOTE: THIS DOES NOT MEAN CIRCLING YOUR MISTAKES. Basically you want to focus on perspective errors - find where the angles of your lines are off and draw in the correct line with your differently coloured pen. You may find that your mistakes are harder to detect and everything looks correct to you (this can happen for complete beginners who haven't yet developed any real spatial awareness, as well as those who are much further along whose mistakes are much more subtle). For that, I recommend the following approach:
Each box consists of three sets of four parallel lines, each set having its own vanishing point. When going over a box in the correction phase, you can extend these lines two to three times their original length towards their implied vanishing point. This will give you a better sense of how these lines behave as they converge. Ideally all four lines of a given set will converge towards a single point at roughly the same rate. By extending these lines, you will start to notice how some lines within a set converge more quickly than others, which implies several points of convergence instead of just one. By being able to spot these mistakes, you should be able to learn from them that much more effectively.
As stressed in lesson 1, every single mark you draw from here on in - straight lines, curved lines, ellipses, everything is to be drawn using the three-step ghosting method. Those three steps are as follows:
This will help you develop the habit of thinking through every mark you put down, rather than just drawing on instinct and thinking on the page. When you think through your problems right on the page, you end up with chicken-scratchy, rough drawings with plenty of wasted lines. When you apply the ghosting method, the result is a greater respect for line economy and a more carefully executed drawing.
The laws of perspective state that as an object moves farther away from the viewer, it gets smaller. This is because all lines that are parallel to one another in 3D space converge towards a point in the distance when drawn in 2D.
So, a box is made up of 3 pairs of identical planes, each pair consisting of a near plane and of a far plane. The only difference between them is the position - the near plane is closer to the viewer, and the far plane is farther.
So, by this logic, far planes must be smaller than their near-plane counterparts.
I will admit that at times this is much harder to see, especially if you are not drawing through your boxes. By drawing through the boxes, you include the lines that are otherwise hidden by the box itself, allowing the far plane to be defined clearly by a full 4 lines rather than just 3. So, if you're not drawing through your boxes, you can accidentally make mistakes like reversing that size relationship.
I mentioned this above when talking about near/far planes, but it's worth mentioning twice: Draw through your boxes.
By "draw through" I mean draw all of the lines that make up the box construction, including those that are hidden by the box itself. Draw it as though you have x-ray vision. This will allow you to define all of the planes of the box with a full 4 lines, giving you a better sense of how they all sit in 3D space. It will also make certain kinds of mistakes more apparent.
As you get more confident with drawing your forms, you can start to play with line weight. By default, we draw all of the lines of a box with the same thickness. This results in a box that feels somewhat more like a collection of lines, rather than a single cohesive form.
The first thing we can do to make it feel more cohesive is to add weight to the outer lines of the box - that is, the lines that define the silhouette of the box. Turn off your 3D-thinking for a second and look at the box as a 2D shape. Imagine if it were completely filled in with black - that would be the silhouette.
By thickening the lines that define the edges of this silhouette, we start to establish a hierarchy of importance. The heavier outer lines establish a grouping, and the lighter internal lines become subordinate to that. It starts to feel as though the overall box is a single cohesive unit, rather than a collection of barely-related marks on the page.
Now, thickening the line all around the box is definitely good, but it also causes our box to flatten out somewhat. We're focusing heavily on the 2D silhouette that it suppresses the 3D nature of the form.
Luckily there's something we can do about this - we can thicken the silhouette-edges of the box, but we can do so more in some places and less in others. Think of it as though the lines of the box are actually little shadows, and you have a light bulb hanging somewhere near your box. The lines that face away from the light source are going to have larger shadows - so they'll come out a little thicker than the lines that on the side of the box that faces towards the light.
It's no doubt a simplistic way to think about it, but it will help you develop more dynamic line weights.
Line weight is an extremely useful tool to establish a hierarchy in your drawings. Often times it is this notion of organizing your lines that sets apart a very boring, stiff piece of line art and one that feels dynamic and alive.
If you've taken a look at lesson 2's form intersection section, you'll notice that we discuss the concept of "dominance" between two forms. To put it simply, we're talking about one form overlapping another. Line weight is extremely useful in this situation, as a thicker line automatically feels like it is in front of a thinner line. So, in this example you'll notice that the long box's bottom side has a very thick line to it, which gets thicker as it passes over the other box. This variance implies to the viewer that it has dominance, and that it is closer to the viewer.
Remember that line weight is a very flexible thing - even the same segment of line can gradually grow thicker or thinner over the course of its length, and this tapering effect gives a sense of fluidity and flow to your strokes that helps keep your drawings from looking stiff.