Starting with your form intersections, as already know, we really only introduce the exercise in Lesson 2, planting a seed in the student's mind and leaving them to play with it alongside their work through Lessons 3-5. In that time, students spend a lot of time trying to work in 3D, which gradually nurtures the seed, developing how we think about the relationships between forms in that 3D space - but at the end of the day, the form intersections exercise is still by far the most difficult manifestation of this problem.

We are however, now at a point where we can talk about how to think about these kinds of intersections. By and large you're moving in the right direction, but you do tend to struggle a great deal with dealing with curving intersections. As you progress through the pages, you definitely get a better sense of what you're doing - especially with the sphere-cylinder intersection towards the bottom right of the last page, but there is advice I can offer to help you along.

Firstly, here are some corrections for your first page. The sphere-cylinder in the bottom right of that one is an especially weird one. If we shove a cylinder right into a sphere, normally we get some variation of an ellipse defining how the cylinder plunges into the cylinder - but you incorporated some extra weirdness along the side, where I did try to play along, although I think a simple ellipse probably would have worked. Either way, we won't be focusing much on that one.

Rather, let's break down how to think about the intersection between a sphere's rounded surfaces, and a box's flat ones. Ultimately that's what an intersection is - it's a sum of parts, with each part being intersections between different surfaces of the same form. As shown in this diagram, the spheres themselves are basically made up of an infinite set of individual circular slices - but when we bring the box into play, which has 6 distinct planes (only 2 of which are involved in the visible portion of this intersection), it immediately narrows down the number of slices of the sphere that we need to worry about. Each plane has its own corresponding circular slice, and it's at the corner between the box's planes where we get a sharp corner in our intersection, since we're now moving from one to the other.

It's not always as simple as this, but it does generally follow this premise. The more complex form would be an intersection between a sphere and a cylinder's curving surface, as you tackled quite well here. We can see here that you're transitioning from following the curvature of the cylinder, to the curvature of the sphere, and back to the cylinder. The only difference is that without distinct edges, we have to rely on more gradual transitions, merging two C curves into a sort of S curve, so to speak.

Anyway, I'll leave you to wrestle with that a bit more - it will come up again in Lesson 7, so we can look at it again at that time. Moving onto your object constructions, you have by and large done a great job of holding to the core premise of this lesson, which focuses above all else on the concept of 'precision'.

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.

Through your conscientious use of subdivision, you've done quite well. That said, there are a few points that I want to call out, that could improve this further:

• This one's not a mistake, more of a suggestion. I'm not seeing any orthographic studies of your objects (that is, plans from the side/top/front/etc - there's an example of this here). That doesn't mean you didn't do them - not all students include them, and you were never strictly told to do so anyway. That all said, these can be very useful, specifically in identifying how far along a given dimension a particular element might lie. For example, if we look at this pencil sharpener, you made a clear decision to place that lid flap down the center with one third of the object's width on either side, taking the middle third for the flap. That's great - it shows you analyzed your object, decided what proportions to employ, and then executed them. But if we look at exactly where along the length of that flap the circular impressions are situated, this is more arbitrary, and could benefit from more precision. A plan view of the top, breaking down where things go would help with this.

• I should also mention that while this pencil sharpener is, at least based on that reference image, quite cylindrical, you ended up building it more as a box with rounded corners. This is not a bad thing. Not exactly, anyway. If the goal were to capture that object perfectly, then immediately constructing a cylinder inside of a box would have been a good start. But what you did here does not deviate from the core of the lesson, and if anything, it actually makes for a very interesting design challenge, to take something that is made from a specific set of primitives, and then changing them into another in order to alter the design - while maintaining its other elements. Very neat, even if it wasn't strictly intentional.

• For this wall plug, similarly to the positioning of the circular impressions in the pencil sharpener lid, here there's no clear decision being made on how tall the vertical elements are meant to be. Here you started with a box, but then quickly decided that it was too tall, and arranged the forms inside such that they did not touch the top plane. This is incorrect, because it results in a considerable loss of precision in that dimension. Instead, we have two options - either we draw a shorter box within that big one (this doesn't necessarily need a lot of precision, so you don't need to have specific subdivisions for it). This would provide us with an even, consistent top plane that both of those prongs can touch equally, whilst being the same length (although that depends on how even that slice was - but again, precision is not about things being right, it's about taking the steps to plan them out). Or, we could simply use the box we have, and have the prongs stretch all the way to the top. The benefit of making a plan is that they are proportional - stretch the vertical axis, and you'll still have the same landmarks, because they'd exist in terms of fractions - halves, thirds, quarters, fifths, etc. Sure, the end result won't match your object perfectly - but you'd still be maintaining the solidity of your result.

That about covers it! So, you've definitely made big strides in the right direction, but there's more room for increasing that precision. I'll go ahead and mark this lesson as complete - for the purposes of this lesson, you're doing great. Lesson 7 however will be more demanding in this regard - as those constructions become more and more complex, with more steps in between, maintaining as much precision as possible becomes imperative. You do of course still have one last step before you get there, however.