Lesson 1: Lines, Ellipses and Boxes

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). 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.

This lesson, and all my lessons, are very dense. I don't at all expect that you will absorb all of the information contained here in one sitting, or even after one read through. I encourage you to read through the whole lesson once, then whenever you sit down to do one of the many exercises listed here, go back and reread the exercise's description. Also, check out the self critique resources (both lessons 1 and 2 have these, they're the blue buttons at the top of the lesson pages), where common mistakes for each exercise are broken down. Once you're done the exercise, you should go back to those self-critique resources and try and pick up anything listed there that you may have done wrong. There will probably be a couple things.

This lesson has a homework section for each section, with minimum required amounts for each exercise. Doing only this amount won't make you a professional, but you should absolutely not sit here and grind away on one exercise until it's perfect. That's not how this works. Completing the minimum amount is meant to establish whether or not you understand what you should be aiming for. That's all we want to achieve for now - for you to understand the goals before you. Once you grasp the point of each exercise, you should be okay to move onto the next lesson.

Of course, you're not done with the exercises at that point, oh no. Every day, or every couple of days, or whenever you sit down to draw (ideally this should be frequent and regular), you will start by doing a 10-15 minute warmup. Each time you will choose two or three exercises (and once you've completed lesson 2, its exercises are also added to this pool) and you will do them for that time. The amount is not important - like I said, 10-15 minutes between them is fine. What matters is that you do this often. Grinding on a single challenge is not an effective approach to growing as an artist - investing time over a long period will result in compound interest, allowing you to both train both your muscles and your mind. Furthermore, applying those skills to actual drawings will help give them context and purpose, and giving yourself time to breathe and think will let you reflect upon what you've learned.

A little each day is far better than a lot all at once. As I explain here, this is not a sprint, and not a marathon.

So what tools should you use? Each lesson outlines the tools that suit its content best in its homework section(s) - keep in mind that I do not recommend certain tools because I want you to learn how to draw with that particular tool. Rather, it's that this tool suits the learning of that material best, and offers just the right challenges and promotes the right habits to make those lessons the most effective they can be. Lessons 1-7 recommend the use of a felt tip pen/fineliner - I explain why ink complements these lessons far better than pencil or digital in this short article.

As for paper, printer paper is just fine - and in fact, I generally recommend loose leaf sheets over sketchbooks. When working in sketchbooks, people tend to be far too precious with their work. They tend to be entirely unwilling to make the mistakes they need to make in order to improve. In order to grow as an artist (or really as anything), it's not that you have to conquer failure. You simply have to conquer your fear of it, and learn that failure is incredibly valuable. It's an asset that shows you your limitations - and in being aware of them, you can discover how to break past them. If you're caught up in trying to draw pretty pictures for these exercises, you're not going to exhibit the sort of boldness that will take you far. Working with individual sheets means that if something goes wrong, you can just toss it out when you're done.

That's all for now. Good luck, and I hope you're able to find something of value here.

A lot of you have probably looked at the lessons I post on /r/ArtFundamentals, on Reddit. What I presented there was more or less what I remembered from taking Peter Han's Vis Com: Dynamic Sketching course at Concept Design Academy in Pasadena, CA. Having learned from Peter for only one term, my understanding of the material definitely falls short. That said, over years of seeing how others have digested the material, I've learned a lot in regards to how to improve my delivery of the content. As such, I will be restructuring and rewriting many of the lessons - this will be the first of that series.

Many of you have already completed this lesson, and I don't expect you to go back and redo the homework. While there will be a few new or different exercises included here, if I've marked this lesson as complete for you, it means that I've seen that you have a decent understanding of the material. The core concepts have not changed at all.

The Basic Mechanics of Drawing: Lines, Ellipses and Boxes

In my experience, there are two major component skills involved in drawing.

If I had to assign a weight of importance to each component, I would say that mechanical skills contribute only 20%. The greater mastery comes from truly being able to break down what you see around you into their constructions. It's undeniable that you need to know how to draw a line or a circle in order to be able to capture anything on a page, but if you don't understand what it is you're trying to draw, then there isn't much good that'll come out of the ordeal.

So, in this first section - the basics - we are going to go over those general mechanics of drawing. The 'Dynamic Sketching' lessons, which will come later, will pertain to observing and understanding. A lot of people are bound to find these first couple of lessons tedious, and that's because a lot of them are. Still, regardless of what you think you know, and regardless of what prior experience you have, do these exercises.

On the topic of those of you with prior experience - for now, leave what you know at the door. Once you're done the exercises, you can take what you've learned and merge it back with what you know, keeping what you find valuable and tossing out what isn't.

Approach these exercises with a blank mind. Do not rush. Demonstrate patience. Spend the hours required to give each exercise the attention it requires and deserves. Do each exercise as it is prescribed in the lesson. Often times I see people stray a little, trying to spice things up and make things more fun. While creativity is lovely, you risk missing some of the core concepts that each exercise has been designed to convey. Just be patient - it'll be over soon, and then you'll be able to get to the fun stuff.

WARNING: Do NOT try to digest this entire lesson in one sitting. It is very information-dense.

Part 1: Lines

There are many different kinds of lines you'll find yourself needing to draw, but they tend to follow the same principles. Lines should be smooth and consistent. A lot of the time, you'll see beginners realizing that it's hard to draw a long line, and they'll end up drawing something like this:

A Sketchy Line

The reason for this is that when we start out, it's very likely that we've spent far more time writing than we have drawing - so, we draw the way we write. Similar tools, so the technique must be the same, right? Not quite.

In terms of drawing, we can move our arm using any one of three major points as a pivot: the wrist, the elbow and the shoulder. We mainly focus on the wrist and shoulder. Since we're pivoting around those points, this means that the most natural motion is an arc rather than a straight line.

The Pivots of the Arm
The Wrist
Having a small radius, the extent of the drawing motions we can do before lifting our hand and moving it over is quite limited, often leading us to draw "sketchy" lines composed of many smaller marks (like figure 1.1). Having such limited movement however does allow us to make very specific, fine marks. This makes it ideal for applying small details, but truly awful for any lines that need to be more than a few inches in length. Furthermore, due to the small radius, the 'arcing' of the lines becomes more obvious.
The Shoulder
Having such a large radius means that drawing from the shoulder can produce much longer, more consistent strokes. This tends to work better for most drawing, especially when you're dealing with the fundamentals. It's great for drawing lines that need to be straight (as the radius is much larger, so it's easier to counteract the natural arcing motion). You will also be able to draw these longer lines in a single, consistent motion without having to lift and reposition your arm.

The problem is that most people aren't used to drawing from their shoulders, so it feels awkward and unnatural. Often people will go back to drawing from the wrist without realizing it. You must consciously lock your wrist and force yourself to draw from the shoulder. Once you're used to it, and gain a greater understanding of its benefits and disadvantages through practice, you'll be able to decide on a case-by-case basis which pivot works better for any given task.

A Smooth Line

In the exercises, you're going to find one called "Ghosting Lines". It outlines the use of the ghosting technique, which should be applied to literally any and every line you draw. To be more succinct, I'm going to outline the three step process here, so you have some context when you encounter it below.

PAY ATTENTION TO THIS. These three steps are some of the most important things you'll learn here. It captures the essence of thinking before you draw.

  1. Identify - where does your line start and end? Is it straight or does it curve? Is it an ellipse?
  2. Prepare - find the most comfortable angle of approach (rotating your page if necessary) and ghost through the motion of drawing it. Don't just do this a couple times - the point is to make your arm and muscles feel that the motion is familiar and comfortable. Do it as much as is necessary.
  3. Execute - Now your brain has had its say, and has given your muscles their marching orders. Keeping the rhythm of your repeated ghosting, lower the pen to the page and draw the mark using that same motion. Your brain should not interfere - your pace should be steady and confident, and quick enough so that your muscles can take over.
  1. Superimposing Lines

    This one's pretty straightforward. You draw a line to use as a template. It's probably best to do this with a straight edge, to make sure it's perfectly straight. Then, you draw directly on top of that line, freehand, eight times.

    Superimposing Lines

    You'll notice that the example isn't perfect - that's because this is an exercise that should be done regularly. Chances are you won't even notice how it impacts your drawings, because of how gradual it all is. For now, all you should expect is to try to get as close to perfect as possible.

    See how there's fraying at one end of the example? This is because we tend to overshoot the end point. The opposite end (the starting point) is not frayed, however - because we consciously take the time to line up the pen where it needs to be. If you're seeing fraying on both sides, you're rushing and doing yourself no favours.

    Try this exercise with a variety of lines. Start with short, straight lines (2 inches or so), move up to half a page, then a full page width. Then try arcing lines, wavy lines, etc.

    Superimposing Lines

    You'll find at times that when you're drawing, your hand will cover up some of the line, which will likely give you trouble. Each consistent, flowing line has a particular rhythm to it. Once you become familiar with the rhythm of a line, you'll find it easier to anticipate where the line goes even when you cannot follow it with your eyes.

    Superimposing Lines

    When doing this exercise, you'll spend some time trying to find the pace that's just right. It's very easy to go either too fast, or too slow. If you're too fast, your accuracy will be way off. If you're too slow, your brain will start micromanaging your muscles, which will result in a wobbly line that keeps correcting itself. The goal here is to let go and let your muscles take over.

    Ultimately, you won't be getting particularly close to perfect - so if you're a little inaccurate, that's fine. Just don't let your lines get wobbly.

  2. Ghosting Lines

    This technique is pulled from Scott Robertson's older DVDs, and works wonders for increasing control and accuracy when drawing lines. It's slower than the natural, intuitive matter of just making a mark on a page and hoping it comes out right, but its results are far better. It also encourages forethought and planning, two essential aspects of drawing.

    Ghosting Lines

    First, you draw a point where you want your line to begin, and one where you want it to end.

    Ghosting Lines

    Then, holding your pen some distance above the page, you go through the motion of drawing the line without actually letting the tip touch the paper. This is not to draw a line, but rather to get used to the action itself. Do this several times.

    Ghosting Lines

    You may find that the motion itself is awkward and uncomfortable. In that case, feel free to rotate your page. All you really need is to be able to draw a line smooth and straight from one angle - the rest can be a matter of "spinning the pad" as Scott Robertson puts it. Of course, there is serious advantage to the flexibility of being able to draw at most angles, but I'm merely exaggerating to make a point: Rotating the page to find a more comfortable angle is completely acceptable.

    Ghosting Lines

    Once you find a comfortable angle, and you've gone through the motion a few times, without missing a beat repeat the motion once more with the pen touching the page.

    Ghosting Lines

    Yeah, the first handful of times your pen might get away from you a bit, but in general this technique should seriously help you draw more accurately.

    Practice this exercise by simply dropping two points anywhere on a page and using the technique to draw a line between them. Try different lengths of lines, and experiment with different angles and different ways of orienting the page. Also play with holding the pen at different angles - having it upright (90 degrees to the drawing surface) will probably result in an optimal flow of ink, resulting in the best line quality.

  3. Planes

    This exercise is an extension of the ghosting exercise, with a little bit more purpose. It's intended to ease one into the idea of drawing things in perspective. Just a little bit.

    We're going to start off by laying down four points - really, they're two pairs of points. Like the points in the ghosting exercise, these will be connected, and will ultimately form a rectangle-like shape. You can choose to make the distance between the points of each pair the same, or you can make one a little bit smaller, which will start to feel like a square or rectangle drawn in perspective. Either way, I'll be referring to it as a plane from now on.

    Perspective Squares

    Now, connect the dots using the ghosting technique. Don't rush - slow and steady wins the race and all that.

    Perspective Squares

    Now that you've got your plane down, lets connect the diagonal points.

    Perspective Squares

    Now there's something interesting here - the point where the two diagonals cross. That point is the center of this plane, in perspective. You don't really need to worry about it right now, it's just a neat thing to know. Lets finish it off by drawing lines along the plane that cut through this "center" intersection point.

    Perspective Squares

    Since a lot of the later exercises involve things like drawing boxes (which I think are some of the best things to practice), you can see this exercise as being the beginnings of building a box. You've got a plane, in perspective, with one length smaller than the other (as it recedes into the distance).

These exercises should be done traditionally, using a felt tip pen (0.5mm is ideal). These are also referred to as fineliners or technical pens in some parts of the world. I use the Staedtler Pigment Liners, and sometimes the Faber Castell PITT artist pens (more expensive and higher quality), though there are plenty of other brands that work just as well.

Felt Tip Pens

In a pinch, ballpoint pens can be used, but I strongly advise against using pencils or working digitally for these exercises.

As homework, I recommend doing at least:

  • 2 filled pages of the superimposing lines exercise (examples)
  • 1 filled page of the ghosting lines exercise
  • 2 filled pages of the planes exercise

If you want a critique and some direction, you can submit your homework for review as a comment on this lesson's post on /r/ArtFundamentals. If you do choose to submit, please be sure to complete the homework in its entirety (all three parts as prescribed: lines, ellipses and boxes) in the required medium/media. While I am happy to help out, it does take a lot of time, and I'd greatly appreciate it if the time is taken to fully read and digest the material.

Part 2: Ellipses

So, what is an ellipse? Is it just a fancy word for an oval?

An ellipse is a circle - once that circle has been turned in 3D space. If you take a CD or some other circular disc-type object in your hand and you look at it straight on, you see a circle. If you start to turn it away from you, however, it becomes narrower in one dimension, becoming an ellipse. Eventually it becomes a line, once it's been turned away completely.

Circles in Perspective

Ellipses are extremely important and notoriously annoying to draw. You'll find them all over the place in mechanical drawings. Cars, space ships, tanks, machines - anything man made will probably make extensive use of ellipses.

An ellipse has two major axes - the major axis, which is largely unimportant, and the minor axis (which is always the shorter of the two). The length of its minor axis is its width, or what we refer to as its degree.

Anatomy of an Ellipse

Now this is a bit of a guess on my part, but I'm guessing that we refer to the width as its degree, because it relates directly to the angle of the circle it represents. When we are looking at the ellipse full-on, its ellipse has a degree of 90°. When the circle is rotated 45° away from us, its degree is 45°. When it is turned away from us completely, it has a degree of 0°.

The minor axis is very important when we start talking about perspective, as it aligns to a vanishing point, which makes it critical for the construction of cylinders. You don't need to worry about this too much for now, I am only mentioning it so that you can begin to familiarize yourself with the general idea.

Minor Axis in Perspective

One thing to be clear on here is that the minor axis aligns with the vanishing point in the depth-direction of the circle in perspective. In Figure 2.3, this would be the right vanishing point. The easiest way to think about it is if you treat the minor axis as the center line of a cylinder.

  1. A Whole Lot of Ellipses

    The first exercise is relatively straight forward, and involves drawing a lot of ellipses. These are not, however, simply free ellipses with no real goals. Instead, it is pinned on the idea of setting out criteria and targets for the ellipses we intend to draw, before drawing them. Therefore, when you draw your ellipse, it is either correct, or it isn't.

    Start off by taking your piece of paper and dividing it into a table with two columns and a bunch of rows.

    Each of these sections will contain a different variation on the exercise - here you can experiment with different approaches, but here's a few that you can try out first.

    For this one, you draw a circle starting from the far left of the box. Then, draw another beside it. Keep repeating it until you fill in the whole box. Strive to make your circles touch the top and bottom of the box, as well as the line to the left of it.

    Same idea, but with ellipses. Within the same box, you should aim to draw ellipses of the same degree. You can also play with the angle of the ellipse, and this should also be consistent within the same box.

    This one's a little different. Draw a wave through the box, dividing it into irregular pockets of space. Then fill these spaces with circles, trying to keep your circles touching the bounds of the box as well as the curve. Everything should fit in there snugly, and nothing should be floating around not touching anything.

    I've seen lots of people do these in the past. This is my opinion of course, but I don't think they're terribly useful, since they don't give a concrete target to aim for. I understand that it definitely is tricky to draw a circle inside of another circle and keeping it centered, but I still don't feel like it's as effective as other more concrete exercises.

    Absolutely read the notes in the image below - people generally start approaching ellipses in a manner that results in uneven, bumpy or incomplete shapes. Be sure to draw through every single ellipse you draw for any of the lessons on this website. That means drawing around the elliptical shape two or three times (no more, no less) before lifting your pen. This will let you draw with more speed and confidence, smoothing out any wobbling. Make sure you keep your mind on the kind of ellipse you're trying to draw, however - that is, the position, angle, degree and size.

    In figure 2.9, you'll see three ways of approaching drawing ellipses. In my experience, the top is probably what you're doing right now. Instead, the middle is what you should try doing, ultimately aiming long-term to achieve the bottom. The reason is that when you go around the ellipse once, it's very approximate. If you haven't had much practice with this before, it can be all kinds of awful. If you go around twice, the second time your muscles automatically start to correct some of the mistakes from the first approximation, rounding things out nicely. Not only does this result in a better shape, but it also gives your muscles the chance to record that in their muscle-memory. All of these mechanical exercises are intended to train muscle memory, so your brain can be freed up to worry about the big picture, instead of micromanaging the smaller tasks.

    Of course, don't go overboard with this. Try to be as clean as you can, but remember that the shape takes precedence.

  2. Ellipses inside of Planes

    This one's an extension of the 3rd line exercise - in fact, you can simply take those pages and draw on top of them.

    Take your squares and draw ellipses inside of them. Don't worry if you mess up, this is rather difficult to do.

  3. Funnels

    For this one, you draw a straight line, and on either side of it, a curving line, creating a sort of funnel shape like on the left side of figure 2.11. Then you draw a series of ellipses in the funnel, with large degrees on the outside and narrow degrees (0°) in the very middle, with all of their minor axes aligned to that center line. This basically means that the center line should bisect the ellipses symmetrically.

These exercises should be done traditionally, using a felt tip pen (0.5mm is ideal). These are also referred to as fineliners or technical pens in some parts of the world. I use the Staedtler Pigment Liners, and sometimes the Faber Castell PITT artist pens (more expensive and higher quality), though there are plenty of other brands that work just as well.

Felt Tip Pens

In a pinch, ballpoint pens can be used, but I strongly advise against using pencils or working digitally for these exercises.

As homework, I recommend doing at least:

  • 2 filled pages of the tables of ellipses (examples)
  • 2 filled pages of the ellipses in planes exercise
  • 1 filled page of funnels (examples)

If you want a critique and some direction, you can submit your homework for review as a comment on this lesson's post on /r/ArtFundamentals. If you do choose to submit, please be sure to complete the homework in its entirety (all three parts as prescribed: lines, ellipses and boxes) in the required medium/media. While I am happy to help out, it does take a lot of time, and I'd greatly appreciate it if the time is taken to fully read and digest the material.

Part 3: Boxes

So, we've tried to avoid it, but we can't any longer. If you want to draw a box, you're going to have to get your head around some basic perspective concepts. The most basic concept is that when a 3D world is rendered or drawn on a 2D piece of paper, things closer to the viewer are bigger and things further away are smaller. Or, to be a little more specific about it, if two objects are the same size in 3D space, when rendered in 2D the one that is further away will be smaller than the one that is closer to the viewer.

An extension of this is the idea of vanishing points. In 3D space, two lines can be completely parallel - meaning the distance between them at any point is equal. Due to the rules of perspective, once rendered in 2D, those "equal" distances between them steadily get smaller as they get further from the viewer, so lines that are essentially parallel, do what no two parallel lines should ever; they converge. This is at the very core of perspective drawing. The idea that any set of lines that are parallel will converge at a single vanishing point.

Now you may have heard of terms such as one point, two point or three point perspective. These are all simplifications. Since you can have an infinite number of different sets of parallel lines, there are technically an infinite number of potential vanishing points. The reason we can simplify this whole idea to three, two, or a single vanishing point is because of boxes.

Things in our world tend to be pretty boxy. Buildings are boxes. Furniture is boxy. Cars are boxy. Hell, even wheels, when you really think about it, are fairly boxy. You can represent any cylinder as a box and as long as it doesn't have to roll, you're fine. Because of this, people like to teach those who are new to perspective that the world can be summarized with a maximum of 3 vanishing points.

Honestly, this confused me for years. So instead, I will teach you how a single object can be approximated to a maximum of three vanishing points. Each different object may require a different set of vanishing points altogether.

Now, what's all this business about one, two or three VPs? Well, the number of vanishing points you use when drawing a particular object is governed by the orientation of that object relative to the viewer. In the following explanation, we will refer to three sets of lines:

  • Width Lines (X axis)
  • Height Lines (Y axis)
  • Depth Lines (Z axis)
Box in 3 Point Perspective

This is a box with 3 vanishing points. None of its axes are parallel to any of the viewing angles - of which there are 3, one for each dimension:

The 3 Viewing Angles

We can remove vanishing points by aligning the axes of the object (our box) to viewing angles 2 and/or 3.

Aligning to Viewing Angle 2

When we align to viewing angle 2, all the width-lines of the box become parallel to the horizon - these lines will not converge, they'll simply go on infinitely, so this eliminates one of the vanishing points.

The horizon line represents the viewing angle. Think of it as always being parallel to a line that connects the viewer's eyes. If the viewer's head tilts to the side, so does the horizon line.

Aligning to Viewing Angle 3

Now, if you align to the viewing angle 3 instead, all of the height lines become perpendicular to the horizon line. They'll go on forever, so this eliminates a vanishing point.

Aligning to Both Viewing Angles (2 & 3)

If you align to both viewing angles 2 and 3 as shown in figure 3.5, you eliminate two vanishing points simultaneously, leaving only one. This is one point perspective, where only your depth lines converge at a vanishing point.

An important thing to remember is that scenes can have tens, or hundreds of vanishing points, depending on their complexity. Even a single object - given that it is more interesting than a box - can have more than three. It all depends on the number of sets of parallel lines. You could potentially plot out every different line in perspective with every single vanishing point, but that just feels excessive and slow. On top of that, often times if you plot out perspective fully, everything will come out *too* perfect. Yes, that's a thing. The world around us is flawed to varying degrees, and when everything lines up perfectly, it can be a little jarring to the viewer.

So, in most of my lessons, I insist that you get used to approximating perspective. At the very beginning, we will play with plotting things out, but we will quickly remove those training wheels once you have a general sense of how things work.

  1. Plotted 2 Point Perspective

    We'll start off with getting accustomed to what perspective plotting is. As long as you follow the steps, things should come out correctly. Just a few things to remember:

    • All vertical lines are straight up and down, perpendicular to your horizon line.
    • All other lines go to either one of the vanishing points.
    • Use a ruler for this - we're not dealing with your drawing technique in this exercise, just your understanding of perspective
    Draw a horizon line

    Draw a horizon line on a page. Take up the full page. Draw a vanishing point on either side of the horizon line. If you picture those vanishing points as being points on opposite ends of a circle, any boxes you plot outside of that circle will start to have some distortion. That circle would represent the field of view. You don't really need to worry too much about what that means for now.

    Draw a horizon line

    Draw a vertical line. Each box you draw for this exercise will start off with an arbitrary vertical line.

    2 Point Perspective Steps

    **Update** It was brought to my attention that I leave a huge gap between figures 3.7 and 3.8 (I have no idea why upon writing this lesson I thought it was a reasonable jump, it's definitely not), so I've added a quick description of how to construct a box in 2 point perspective.

    Draw lines back to the vanishing points

    Start drawing lines back to the vanishing points. Then draw the rest of your verticals, and plot the lines back from them. This will build out your box.

    Repeat

    Repeat these steps until your page is full of boxes.

  2. Rough Perspective Boxes

    Now that you have a solid grasp on how perspective and vanishing points work, we're going to take off the training wheels. Everything from here on in is freehand except for the horizon line and the frames. Instead of one drawing taking up the whole page, you will put several on a single sheet, each one contained within its own rectangular frame.

    It is important that you strive to be clean and careful. The first step towards that is to draw your frame with a straight edge. If you start off sloppy here, you'll only go down hill.

    Draw a horizon line

    Draw your horizon, and mark a single vanishing point on it. I usually do this exercise as one point perspective. This means your horizontal and vertical lines will all be either straight across or straight up and down. Makes things a little easier.

    Draw some boxes

    Beyond this, you just draw boxes. Do it carefully, using the ghosting technique. Also, refrain from plotting your lines back to the vanishing point. Try to visualize them in your mind without actually drawing them on the page. If you make a mistake, fight the urge to correct it, as that will often only lead to darkening the area and drawing the viewer's attention to your mistakes. Keep things as clean as you can - one mark per line initially, though you can go back afterward to reinforce some line weights if you like.

    Now, when I say clean, I don't mean that your focus needs to be a pretty picture. Feel free to draw through boxes (drawing lines that would otherwise be blocked by other forms) to better understand what you're drawing. You can see that in the top left corner of figure 3.11. By clean, I simply mean that every mark you make must be done so with purpose, intent and forethought.

    You do not need to add shading, but sometimes it helps to separate out the planes, especially when you draw through forms - which I encourage you to do. If you do decide to add hatching, do so cleanly. I've seen a lot of people apply it very sloppily, and it makes everything look awful. Apply it as consistent, separate, parallel lines stretching from one end of a surface to the other. No randomness, no scribbling.

    You should be able to fit three or four of these frames on a single page. Be careful not to draw too small though, as the smaller you draw, the larger the tip of your pen will be in relation to your drawing, making all your lines seem oddly thick and clumsy.

  3. Rotated Boxes

    As you might have noticed, we've started with something really rigid and grounded in the rules of perspective, strictly using vanishing points and a ruler. Then we set the ruler aside and worked towards building a natural awareness of our vanishing points without explicitly drawing each line back to them. We are working towards a goal of having a general sense of 3D space, even when there are no explicit vanishing points present. This exercise is the next step on that road.

    One thing to keep in mind though is that it is meant to be really difficult, and you're not really expected to be able to nail it on your first try. It's really intended as one's first exposure to the idea of constructing and manipulating arbitrarily rotated boxes in 3D space without having explicit vanishing points in frame to rely upon for most of your boxes. That said, drawing through your boxes (mentioned on figure 3.15) goes a long way to help you understand how each box sits in 3D space, so while it results in a whole lot of extra linework, it's really important - especially as a beginner.

    Draw your axes

    In principle, this exercise is very straight forward, but it can be daunting. So take a deep breath, and just focus on the step you're on. Don't think ahead.

    To start, draw two intersecting axes on your page - one horizontal (the horizon) and one vertical (which will serve the same purpose as the horizon, just.. rotated 90°). You'll understand its purpose in a bit.

    Draw the central box

    In this exercise, we're going to draw boxes that are gradually rotated on all three axes. We'll start with a single box - we're looking at it dead on, so if you remember from the lesson notes, it's going to have only a single vanishing point, and that vanishing point is going to be in the dead centre of the box itself. Because of this, all we see is a simple orthographic rectangle or square.

    Keep in mind that this vanishing point is ONLY for this box. I've seen people make the mistake of trying to use it for the other boxes we draw - that is incorrect.

    Draw the extremities

    One problem a lot of people encounter is that our brains, especially when we're starting out, don't want to rotate forms. Our brains like everything to sit on a nice grid with everything at a right angle. Because of this, when we try to rotate our boxes, we often find that our brain fights against us, resulting in very small rotations. In this exercise, we want to achieve a wide range of roughly 180 degrees from the far left to the far right. If we start out from the center though, there's a good chance we'll end up with much less.

    One way to mitigate this is to lay out the extremities we want first. Draw a box just like the central one (though smaller, since it's going to be a bit further back) on the far left, far right, far top and far bottom. By defining what you expect to do, you're forcing your brain to comply. You've set out the task - there are gaps between these boxes, and now you must fill them. Now, you'll notice that we've drawn these side boxes in one point perspective as well. This isn't technically correct, but it simplifies things in an advantageous way, so we'll leave it like that.

    Our first rotated box

    Now we draw our first rotated box. Pick either the left or the right side, immediately beside the central box. This box will be drawn in two point perspective, and you'll find that one vanishing point will be very far off to the side (off the page), while the other will be very close to the center point, but it will have moved slightly. As a box rotates, its vanishing points will slide in this manner along the horizon axis. You can see this in the abstracted animation in figure 3.16

    Sliding Vanishing Points

    You can see more information about this in the Self Critique Resources for this exercise.

    Next we simply fill in the rest along the horizon line as well as the vertical axis (which behaves in the same way as the horizon), filling the gaps between center and extremity with two boxes each (figures 3.17 and 3.18).

    Constructing a diagonal box

    And now comes the most challenging part of this exercise - the diagonals. These boxes are rotated on two axes (both horizontal and vertical) and as a result are drawn in 3 point perspective.

    There's a particular reason that we've progressed through this in the way that we have, starting with the center box, building up all the horizontal boxes, then all the verticals. Doing so has given us certain points of reference that will help us construct our diagonal boxes. Be sure to start with one of the diagonals with several neighbours. Basically, for some of the edges, we have edges on neighbouring boxes that are more or less identical in orientation, and close enough such that we can copy their orientations completely without things looking off. By pinning down the orientation of these edges, we can start to find grounding with which to construct the rest of the box.

    Always keep in mind that there are vanishing points floating around somewhere in or out of frame, and that your lines should be converging towards them, but these neighbouring points of reference can give you the same kind of information, in terms of how a given line should be drawn. You'll find that in the future when you're constructing more complex objects from a series of simple geometric forms, this approach will be very handy.

    Next, it's just a matter of repeating with the rest of the boxes (figures 3.20 and 3.21)

    Touchups

    At this point, we're pretty much done. I've gone a bit further to clean things up, though this isn't pertinent to the exercise itself. Keep in mind that even when working in ink, there are still ways to organize and clean up a drawing after the fact - so there's no reason to be timid about drawing through your forms. As long as a line helps you understand the forms you're putting on the page, you should draw it with confidence.

    Here you can see how reinforcing the line weights around the silhouettes, and adding tight, consistent hatching to certain faces of the boxes, you can organize and clarify your drawing. Of course, the other lines don't ever go away, but under the right circumstances you can make them much less noticeable. Lastly, while presentation is important, we're not here to draw pretty pictures. We're here to learn how to manipulate form and construct objects in 3D space. If your drawing comes out terribly, but you learned a lot from the process, then I consider that a win.

  4. Organic Perspective Boxes

    Here's a short video demo on how to draw boxes

    This exercise can be somewhat difficult, as in order to accomplish it, it requires some skills that may be beyond what someone at this level should have. It focuses heavily on the ability to understand 3D space, and more specifically to rotate a simple object (a box) arbitrarily. Give it a shot, and try your best. I do not expect this to come out perfectly for everyone at this stage.

    Draw a curve

    Start by marking out your frame (with a straight edge) and draw an organic, curving path through the composition. Instead of treating it like a line cutting through a 2D rectangle, try and picture it as though this line is beginning far off in the distance and swooping closer to the viewer. Looking at figure 3.22, you can see the line starting off in the upper left section. It has far more turning and twisting in that small area, but as it comes forward, it makes a much larger sweep. This is naturally due to perspective - a part of a line that is further away, but occupies the same space on the composition as a part that is much closer, will be much longer in 3D space.

    Draw some boxes

    Now, along this 3D path, draw some boxes. These boxes won't be oriented against any particular horizon line, or any specific vanishing points. Instead, you'll draw them organically, rotated arbitrarily in 3D space. This is difficult, but I think it is an important exercise to help shake off a lot of the rigidity that traditional perspective education emphasizes.

    Furthermore, not only does this exercise explore rotating boxes, but it also looks at building compositions. What you're building is essentially an extremely rudimentary illustration. When illustrating, artists will play with the density of detail and the scale of objects to create areas of interest (focal points, where you have a lot of information crammed into a small area to attract the eye) and areas of rest (with larger open spaces where the eye can relax and wander). In this exercise, using the density of the population of boxes, as well as their scale, you can lead the eye around the path you've created.

    Now, there are a few common pitfalls when it comes to drawing boxes that have been oriented so arbitrarily. So here's a few things to keep in mind:

    • Perspective. Each box has three pairs of near planes (that are closer to the viewer) and far planes, positioned across from one another. For example, the top and the bottom planes of the box are a pair.

      Draw some boxes

      One of those planes will generally block the other. It is this visible, blocking one that is the near plane, while the one being blocked is the far plane. The near plane is always larger than the far plane. This does not mean that it needs to be significantly or even noticeably bigger. Just that it should never be smaller. It's a common mistake that a lot of people make.

    • When you're drawing a lot of boxes together, it's very easy to make the amount of perspective distortion (how much smaller those far planes are compared to their near planes) inconsistent across all the boxes. Read these notes to get a better idea of what I mean. When dealing with a lot of objects like this, I like to put very little perspective distortion on each individual box - meaning that the near and far planes are almost the same size. Then, I show more of my perspective distortion on all the boxes as a whole - making the further boxes smaller than the closer ones. This brings the whole scene together and allows those boxes to relate to one another in a way that makes more visual sense.
    • Be mindful of the angles in your boxes. Because of perspective, you have a bit of leeway with the correctness of the angles of the lines that make up each box - however, after a certain point, it becomes obvious when the lines of a box aren't perpendicular to each other in 3D space.

    As with before, try and fit three or four compositions to a single page, but don't draw too small.

These exercises should be done traditionally, using a felt tip pen (0.5mm is ideal). These are also referred to as fineliners or technical pens in some parts of the world. I use the Staedtler Pigment Liners, and sometimes the Faber Castell PITT artist pens (more expensive and higher quality), though there are plenty of other brands that work just as well.

Felt Tip Pens

In a pinch, ballpoint pens can be used, but I strongly advise against using pencils or working digitally for these exercises.

As homework, I recommend doing at least:

  • 2 filled pages of plotted 2 point perspective exercise (using a straight edge or ruler)
  • 2 filled pages of the rough perspective exercise (freehand except for the horizon and frame, stick to regular boxes, nothing fancy)
  • 1 page of the rotated box exercise (completely freehand except the horizontal and vertical axes, using the ghosting method)
  • 2 filled pages of the organic perspective exercise (freehand except for the frame) (examples)

If you want a critique and some direction, you can submit your homework for review as a comment on this lesson's post on /r/ArtFundamentals. If you do choose to submit, please be sure to complete the homework in its entirety (all three parts as prescribed: lines, ellipses and boxes) in the required medium/media. While I am happy to help out, it does take a lot of time, and I'd greatly appreciate it if the time is taken to fully read and digest the material.