Starting with your form intersections, it's at this lesson that this exercise really ends up showing its value. That is to say, when we assign it back in Lesson 2, it's really just to plant a seed - to give the student a task that will get the gears in their head turning. It plays an important role in that regard (although in the future we may reevaluate just how we handle this), but it definitely leaves a lot of students floundering, looking for explanations that simply won't make sense to them at that stage in the game. All we can do is give them some general information, and let them flail away.

Then, as they work through Lessons 3-5, they get more experience in thinking about how different forms can fit together and relate to one another in space - organic forms that aren't nearly as punishing as these clean-cut geometric forms - but it helps to develop their spatial reasoning skills to a point where, now, we can talk a little more about those intersections.

As a whole, you're definitely demonstrating that your understanding of the relationships between these forms is developing quite nicely, with a few little things I've called out here. Just a couple main takeaways:

• This isn't marked out on that image, but I would recommend drawing just the visible portion of the intersections. While throughout the course we definitely put a lot of emphasis on drawing all the way through our forms, as though we have x-ray vision, but I have found that focusing on the visible portion of the intersection helps take what still is a rather daunting, challenging exercise, and makes it a little easier to learn from.

• Always keep in mind that the intersections themselves occur between surfaces, rather than between forms. There's a cylinder-cylinder intersection towards the upper right where you've got the flat ends of the forms intersecting with one another, and you ended up going for a curving line. I can definitely understand that it's natural to think cylinder = curved, but a cylinder has different surfaces, some of which are flat, and others that are curved - and moreover, some of them can be flat in one direction and curved in another. Try to break the intersections into the pairs of surfaces that are touching one another, and then stitch them together.

While overall I do feel you're doing just fine as far as what I expect at this stage, here's an additional diagram that some students have found helped to solidify their understanding of how these forms interact with one another, and how to define those intersection lines.

Continuing onto your object constructions, this lesson is really the first one that focuses on the concept of 'precision'. Lessons 3-5 have us working in an inside-out, reactive fashion, where we're never really wrong (as long as we're respecting the 3D nature of what we're building up). We may draw a ribcage too big, but that simply means our result is going to have a bigger chest, and that we may move other things out accordingly. But there's no clear separation between good/bad, or correct/incorrect, as long as you're following those principles of construction. Here, we take a different turn, and start to actually look at working from outside-in, planning things out and making decisions ahead of time.

Precision is often conflated with accuracy, but they're actually two different things (at least insofar as I use the terms here). Where accuracy speaks to how close you were to executing the mark you intended to, precision actually has nothing to do with putting the mark down on the page. It's about the steps you take beforehand to declare those intentions.

So for example, if we look at the ghosting method, when going through the planning phase of a straight line, we can place a start/end point down. This increases the precision of our drawing, by declaring what we intend to do. From there the mark may miss those points, or it may nail them, it may overshoot, or whatever else - but prior to any of that, we have declared our intent, explaining our thought process, and in so doing, ensuring that we ourselves are acting on that clearly defined intent, rather than just putting marks down and then figuring things out as we go.

In our constructions here, we build up precision primarily through the use of the subdivisions. These allow us to meaningfully study the proportions of our intended object in two dimensions with an orthographic study, then apply those same proportions to the object in three dimensions, as demonstrated in the computer mouse demo. This kind of approach becomes very useful when we tackle more complex objects, though isn't strictly required for things that are much simpler.

Needless to say throughout your constructions, you've been very thorough, breaking down your subdivisions extensively throughout the process on many of these (this stove was especially impressive. I did however want to talk a bit more about the benefits of starting with those kinds of orthographic plans, so you can better understand how they might fit into your process when tackling objects like this. I believe doing so will help answer the last question.

Ultimately since the presence of precision in our approach comes down to decisions having been made ahead of time, we can presume that the more we end up eyeballing and approximating, the less precise our construction will be - since those eyeballed elements are done on the spur of the moment. Generally speaking, as much as possible we want to bring the number of things we're willing to eyeball/approximate down, and shift to making as many of those decisions ahead of time, so that when we actually go to draw a given mark, that there is a clear correct/incorrect. So we can effectively judge, whether or not the mark we put down matched what we required of it, or if it ended up being off.

There are however levels to this. Ideally, as things get more complicated, we'd do this separately from the construction, in the orthographic plan. That effectively means for every element present in the construction, defining where along each dimension that form would start and end - so for example, on this sink, we know that the drain is positioned in the dead-center of the width dimension, but we don't know specifically how wide it's meant to be. We could, if we were producing an orthographic plan from the top-down view, determine that (I'm just pulling numbers out of the air here), the drain spans from 7/16ths to 9/16ths along the width dimension - and of course you'd figure out the same in the depth dimension as well. This way we effectively have determined a footprint where that drain's going to fall - when constructing it in 3D, it merely becomes a matter of establishing a rectangle at the correct positioning, spanning between the predetermined points, and then putting an ellipse inside of it (then constructing the rest of the drain from that ellipse).

Given that in your approach, the drain was not given a specific size, just a particular point to center itself upon, so there was definitely some precision lost there.

Of course, there is a middleground - the act of putting down your subdivisions as you construct, even if not based on an orthographic plan, still involves making decisions ahead of time, it's just mixed in with the actual process of constructing the object. Not ideal, because we end up doing many things all at once (instead of breaking everything into separate steps, as per the core principles of constructional approach), but definitely still valuable. But, going forward, you should definitely push yourself to make as many of those decisions ahead of time, in a separate orthographic plan (or a couple orthographic plans, depending on the nature of the object, to capture different dimensions), to bring your threshold as high as possible, and avoid eyeballing anything.

Before I call this critique done, there's two last things I wanted to call out:

• In these notes, I talk about how we can think about curves, and how they have a tendency not to provide as strong a basis for solid construction as we'd like. I mention that in order to pin down a specific structure, it's best to first represent those curves as a chain of straight edges, or a chain of flat planes, then round them out towards the end. This provides us with a much more specific structure, and would definitely have helped with the sink and the toilet.

• I also noticed that you appear to have used a ruler for your initial subdivision, which is great, but not necessarily as much when drawing the later linework. I understand that using a ruler for all your straight lines has a tendency to increase how long each construction takes (as would doing more orthographic plans, and pretty much everything this lesson focuses on), but ultimately it is important that within the bounds of what you're allowed to use, and what you have access to, you should be giving yourself as much time as you require to execute each mark to the best of your ability. You appear to have a tendency to go back over your existing lines with visibly scratchy and shaky linework, which we can see quite prominently on this backpack. Either use a ruler or, if for whatever reason you're compelled to work freehand, the ghosting method to ensure your lines are smooth as per the principles of markmaking from Lesson 1.

Anyway, I'll go ahead and mark this lesson as complete.