Starting with the form intersections, the goal with introducing this exercise back in Lesson 2 is really just to plant a seed and get the student's brain-gears to start turning in a particular way. The turning at that point is slow, and it isn't until we go through Lessons 3-5, where we're forced to think about a bunch of simpler combination of forms in 3D space, with the overall context of the form intersections exercise hanging over our heads, that our underlying 3D spatial skills improve enough for us to be able to really discuss the mechanics of intersection more fruitfully.

So, at this point I don't expect students to have a perfect grasp of the exercise, merely that we're in a better position to talk about how it all works. Your work meets that expectation quite readily, but there are certainly still mistakes, as I've called out here on your work.

One key point that helps to understand the manner in which these form intersections work is to keep in mind that an intersection is something that happens not between two whole forms, but rather between pairings of surfaces. A box is made up exclusively of flat surfaces - six of them in fact - whereas a sphere consists of just one rounded surface. A cylinder and a cone on the other hand are made up of a combination, with the cylinder having two flat surfaces and one rounded surface between them, and a cone having one flat and one rounded. Thinking about the intersections in this manner - as a line that runs along these surfaces, effectively trying to find that one path that allows it to run along both surfaces simultaneously - helps a fair bit, but we can take that a step further by looking at how the intersection line changes as the forms in question are modified.

This diagram demonstrates this, by using contour lines to kind of analyze the paths along the sphere's surface that are relevant (based on the alignment of the relevant faces from the box), and then modifying the nature of the box - turning a straight edge that would result in a sharp corner where the intersection line jumps from following one plane to following an entirely different plane into a rounded, more gradual transition, resulting in a softer transition on the part of the intersection line.

The diagram may not make complete sense right off the bat - but just like the form intersections exercise as a whole, you may need to revisit it periodically as you push forwards, and we'll have another chance to look at your work for this exercise in Lesson 7.

Before we move on, I wanted to note that your linework here is very good. Confident strokes, excellent control, and wonderfully subtle use of line weight. It's crazy how far these kinds of things go towards fooling people into thinking that the more technical aspects are indeed correct - at a glance I would have assumed the intersections were right just by the sheer confidence of the linework.

Continuing onto your object constructions, by and large you've done a good job here, although I do have some suggestions that'll help you continue to push your work even further. This lesson is really the first major point in the course where we really start focusing on the concept of precision. Prior to this point, we've largely operated on a basis of working inside-out, in a sort of reactive fashion. That is to say, if we were drawing animal and made its cranial ball too big, then we'd simply draw a head that proportionally larger than the reference showed, without devaluating the exercise as a whole or undermining its goals.

Here however, we end up working outside-in, with clearer boundaries for where objects will be placed, prior to actually putting them down, which allows us to work with greater 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.

To summarize this point, it comes down to breaking the process of making a given mark down into smaller steps, allowing for the decisions to be made first, rather than in the same moment that we actually execute the stroke. Throughout your constructions you make good use of subdivision to that end. Subdivision allows us to determine where a given element will start and end along a given dimension - so we can decide that the handle of a drawer will span from the 1/4th mark to the 3/4ths mark along the width of its face, use subdivision to identify those locations, block a little "footprint" out for the handle, then finally construct the handle coming out of that footprint. We can see an example of this on your pencil sharpener, in how you tackled the big hole the pencil enters through.

That said, there are certainly places where you've taken some more liberties that diminished this precision - for example, for the screw that secures the razor blade on the same pencil sharpener. It appears to buttress against the center line of the bounding box's top plane on one side, and along the edge of the razor blade that separates its "sharp" section from its main body, but the other two sides aren't determined. Instead, you would have been deciding on how big that screw's footprint was going to be as you drew it, rather than making that decision more specifically based on specific proportions.

So, in this manner, precision is a spectrum - there are lots of things we can do to increase precision. Furthermore, it's not always required that we have to work with as much precision as possible - it's more that more is better, given your other considerations. In this course though, and especially when you get into the last lesson, it is going to be important that you keep pushing yourself on this front.

One tool we can use to push that precision farther (and this will certainly be very helpful in Lesson 7) are the orthographic plans introduced in the computer mouse demo. While the example there was very simple and merely had us divide the plan into quadrants to provide us with some manner of grid but without specific relationships to our object's landmarks, we can instead use subdivision to hammer out exactly where we want each element to be.

Like in the drawer example, we can find those quarter subdivisions to identify the specific points at which the handle starts and ends - and we can do this for as many elements in the construction as we can manage. This allows us to have those decisions made, effectively having a formula for the object before ever drawing a single stroke in three dimensions. Once we do move into 3D, we can then simply translate those decisions, rather than having to make them as we work.

Of course situations may arise where we realize we didn't identify the specific location for an element. We don't have to identify everything, because again, it's a spectrum. Any choice we make that increases precision is good, even if we aren't working at the absolute most precision we could. Though, of course, we can always go back to the orthographic plan and build it out alongside building the object in 3D, adding elements we may have forgotten in order to think through those decisions in a simpler 2D state, before applying them in 3 dimensions.

The last thing I wanted to mention on this front is that this act of making decision is really just that - it's an expression of control over the thing you're going to draw. Don't confuse it with the pursuit of accuracy, where we're trying to identify the "correct" proportions from our reference image. That is important to a point - at least insofar as exhibiting good, patient, meticulous observation of the object we're studying - but there will inevitably be situations where that drawer handle might span from 19/50ths to 31/50ths, which would be a huge pain to subdivide properly. We can however choose to "round" these positions, as long as it doesn't conflict with any other elements of the construction. In other words, we could decide to have the handle span from 2/5ths to 3/5ths.

So! As a whole, you've done a great job. I know I didn't talk entirely specifically abut most of your object constructions, but I felt that overall you were doing well, and I could offer more value by focusing on how these tools can be leveraged for continued growth. That said - and this is just the last point - I do think you could stand to be more mindful of maintaining consistent convergences for your sets of parallel edges. This starts with your bounding boxes (which are generally OK but not without their issues), but also comes down to adding additional edges that would run parallel in 3D space with any of the box's major axes.

The exercise introduced in the 250 box challenge - specifically, constructing arbitrarily rotated boxes and then analyzing them with line extensions - is very useful for this, and should still be present in your pool of warmup exercises. In addition to this, I get the impression that you're freehanding a lot of your linework here. If that is the case, it's certainly impressive - but not necessarily the best choice for our purposes here. The lesson does give you permission to use a ruler, not to be kind, but to help students focus on the core of the lesson as much as possible, eliminating additional difficulties that are addressed in a more targeted fashion by earlier exercises in the course.

Another big benefit of using a ruler is that it functions as a live extension of the line we wish to draw, and thus allows us to gauge exactly how it's going to converge with those other edges without actually having to commit to a stroke. Using a ruler, it thus becomes much easier to maintain more consistent convergences - as long as you're using it to that end, and giving yourself the time required to achieve it.

So! I'll go ahead and mark this lesson as complete, and will leave you to absorb and apply what I've shared with you here.