Similar to the rotated boxes and organic perspective boxes exercises, this one is challenging, and is meant to be. While the name suggests that we're focusing on your ability to handle the intersections between the forms, that's icing on the cake, and I expect that you will struggle with it.

What I'm interested in most of all is your ability to draw these forms as being solid, within the same space, in a way that feels cohesive and consistent.

Before we start, here's a hint: stick to equilateral forms. That is to say, try and keep your forms roughly equal in all their three dimensions: length, width, height, and avoid any that are overly stretched in any one of these. This will keep dramatic perspective distortion out of the equation, so we can focus on the core of the exercise.

Before we actually get to the exercise itself, we're going to discuss how forms intersect - or more specifically, how we come up with the lines we draw to represent those intersections. People have inordinate amounts of trouble with this, and I don't expect you to be able to do this correctly right at lesson 2, but I do want you to give it a shot.

If I were to summarize how these intersections work, it would be this: Intersection lines sit exactly where they are able to run along the surfaces of both forms simultaneously.

To understand what this means, lets step back a little and look at this diagram depicting three kinds of intersections.

1. An intersection between two lines occurs at a point. This is a point in space that happens to sit on both lines simultaneously. The yellow point on the diagram sits only on the blue line, the purple point sits only on the green line, and the pink point sits on neither and is just floating arbitrarily in space. The red point however sits on both lines at the same time, and is therefore the intersection between them.

2. An intersection between two planes in 3D space occurs instead in a line - or more accurately, at any points that sit on both planes simultaneously. This also applies to any 2D shapes sitting in 3D space, even if those 2D shapes are bent or warped.

3. Finally, An intersection between two 3D forms can be represented by a 2D shape (that can be bent/deformed in space). The edges of this shape run along the surfaces of the two forms simultaneously. You'll never find an edge of this shape that exist only on the surface of one of the forms at a time.

This intersection shape can be quite difficult to figure out, and a big reason for this difficulty is that when we draw two forms in space, we decide where exactly they are. The intersections themselves allow us to describe these specific positions to others, but until we actually draw these intersections, how those forms relate to one another is not yet defined.

If you ignored the red intersection line in this diagram, you could argue that the blue box was floating completely in front of the cylinder, or behind it, or you could claim that they were intersecting in a different manner altogether. Once that red shape is drawn however (or more specifically the red line - the fainter red section is the part we wouldn't be able to see without x-ray vision), their relationship is cemented.

This is why form intersections are so critical, and why they become an extremely important tool for you - because it's your job to explain to your audience how the forms you've drawn relate to one another in the space you've created.

You start off with a box. Well, you can choose whichever simple form you like, but in honour of the name of this website, we're going to use a box. It also helps that it's the most versatile form we've got, and it effectively summarizes 3D space by its very nature.

If you're having trouble drawing boxes without explicitly drawing your vanishing points, you should look into the 250 Box Challenge before attempting this exercise.

Be sure to draw through your forms - that is, include the lines that exist on the opposite side of the form, that we technically wouldn't be able to see. This will help you get a clearer understanding of how that form sits in 3D space. I will warn you however that this WILL make your boxes harder to understand visually, so you should absolutely thicken the "visible" lines to make things a little clearer. Adding a little line weight to the silhouette of the form also helps.

Now, draw another. This is where the meat of the exercise comes in. Your primary goal here is to draw a bunch of forms that all look and feel consistent. That is to say, they all feel like they belong together in the same space and scene.

When two forms don't feel consistent, it's because their rate of foreshortening - how quickly a form shrinks or grows as it moves further away or closer to the viewer - are not the same. One box may get smaller REALLY quickly (dramatic perspective or foreshortening) and another may barely change over the length of its form (shallow perspective or foreshortening).

So, the goal of this exercise is to learn how to make your forms look and feel as though they should exist together in the same scene.

For now, I strongly encourage you to avoid forms that are stretched in any one dimension. For example, long tubes, long boxes, and so on. At this point it is far better to stick to fairly "equilateral" forms. That is, forms that are roughly the same size in every dimension. This was of course mentioned at the top of this page, and will be mentioned again.

Now we can explore other forms. If you're still feeling shaky with your boxes (which is perfectly acceptable), you can do entire sheets of only boxes. In fact, that's actually a pretty good idea, since as I said before, a box is the most versatile form. If you can draw boxes consistently, then you can construct any other form within the space enclosed by that box.

When dealing with any ellipse-based forms, always start with the minor axis. If you don't remember what a minor axis is, jump back to the ellipse section of lesson 1 for a quick refresher.

This image includes a really quick breakdown on how to draw a cylinder, along with points to keep in mind (always keep your minor axis centred in the cylinder, and keep the degree of your far end ellipse larger (wider) than the end that is closer to the viewer). If you feel you need more practice (and I assure you, you probably do) with cylinders and ellipses, don't worry - you'll get plenty more from the 250 Cylinder Challenge later on (after Lesson 5, ideally). You can look at those notes to get a sense of how to construct your cylinders around a minor axis as well.

Now, fill up the whole page with forms. I mean it, fill up the whole damn page. People tend to submit homework that has tiny groupings of two or three intersecting forms. I want to see an ENTIRE page of forms all layered on top of each other. It will get visually confusing, but push through it, and use line weight to emphasize certain lines over others. Remember that you have a repertoire of 5 simple forms - boxes, tubes, balls, pyramids and cones.

Also, don't forget to draw through your ellipses, and to apply the ghosting method. The ellipse thing goes double for spheres, because if your circle is at all uneven, it will not read as a sphere.

Lastly, avoid drawing forms that are half off the page, because they don't end up teaching us a whole lot. So, I expect to see a heavy concentration of forms around the center.

Now that you have filled in your page with forms, you can now try giving some thought to how those forms intersect. In the lesson section above, I discuss how we approach intersections between forms - specifically using rounded forms, because they're tricky. Be sure to check that out.

Just remember - I do not expect you to nail this. Form intersections are not simple by any stretch, and they take time and work to truly understand. Give it a shot, and even if it doesn't turn out well, keep moving forwards. I fully expect you to continue practicing this even after I've marked the lesson as complete, so you will have the opportunity to continue working at it as you move forwards.

Luckily, this stuff doesn't come into play until lesson 6 and 7, and in those lessons the intersections we use are considerably simpler than these.

Students sometimes get a little overzealous with their hatching, so here's a quick guide on how to approach it within this course. Outside of Drawabox, hatching is a wonderful skill that can be used for capturing the formshading on an object. In Drawabox, however, we do not use hatching as shading and instead have it serve a very specific purpose - to help demonstrate which side of a form is facing the viewer.

The area students struggle with most is how to approach rounded surfaces. Because hatching lines function as contour lines (as do any marks along the surface of an object), to have them run along those surfaces, they have to curve just so, which is painfully difficult when you've got a lot of very short marks.

Here, because it's not really relevant to the core concepts I want students to learn, our solution is to simply not bother with curving hatching lines. Instead, we either draw hatching lines that run along the flat portion of a form (lengthwise on a cylinder, for example, instead of wrapping around it).

In the case of a sphere, where there are no "straight" surfaces, I instead either leave it blank, or I'll add a little contour ellipse on one of the "poles" of the sphere (basically just an arbitrary area you can choose for yourself). This is very similar to how we use contour ellipses in the organic forms with contour curves exercise to denote when the tip of a sausage form is pointing towards the viewer. A sphere is, after all, just the shortest sausage form you can have.

I promised I'd mention this again - don't draw stretched forms! It increases the complexity of the foreshortening in the scene and is going to distract you from the main focus of the exercise.

I don't want you drawing individual groupings on a single page. Students will often do this when they're not feeling quite as confident about what they're doing. No matter how you feel about it, I want you to draw one big network of forms that are all overlapping and interconnecting.

Mentioned this one in the instructions as well, and it had its own little section! Some of you with prior experience drawing may be familiar with the idea of roughing things in, or drawing them lightly/faintly before going back over the lines with a nice, rich, dark line.

Don't do that. I want you to draw each and every line you put down with the same kind of confidence as you would afford any part of this drawing. Don't worry about hiding things or organizing your strokes.

Once you're done all of your forms, you can add line weight to help develop a hierarchy to your drawing, but line weight should only be added to local sections of existing lines to emphasize them and clarify overlaps. Don't go applying line weight to the entirety of a line, ESPECIALLY not to your ellipses. This way the bits of weight you do add here and there can all be drawn confidently, using the ghosting method in order to keep them smooth and confident.

Students going back over their work with a slow, belabored stroke trying to be careful generally causes their drawings to become stiff and undermines the solidity of their forms.

This applies to the Drawabox course in general, and to all of its lessons.