Students frequently don't feel good about their homework, but it's usually not the result of the work itself, but rather this idea that we need to always be hyper-critical of ourselves, otherwise we won't grow. It teaches us to always downplay our achievements, as a false form of integrity, and more broadly it trains us to look not at the facts before us (facts we may not yet be fully equipped to judge for ourselves - which is why this course relies so heavily on getting feedback from other people, even outside of official critique, and not relying on one's own assessment), but rather about ideals of how one ought to feel. It's normal, but it's not something to feed and fuel if you can help it.

To put it lightly, you've undoubtedly invested a great deal of effort and attention to the work throughout this lesson, and you've applied the lesson material quite well. I have some suggestions and advice to offer in how to continue getting the most out of these exercises, but the biggest is that your self-assessment doesn't appear to be particularly trustworthy right now, so while it is unavoidable that you will attempt to self-assess, try to remind yourself that, like criticisms from a stranger on the street, they should not be heeded.

Anyway! Jumping in with your form intersections, as this is an exercise that relies upon spatial reasoning (the skill this course as a whole seeks to develop) in its purest form, even this late in the course we don't expect students to be nailing it in its entirety. Rather, our expectation at this stage is that students are demonstrating a fair bit of comfort with those intersections involving flat surfaces only, but while still having some trouble when curved surfaces are added to the mix. You're absolutely meeting this expectation, so I think you're at a point where additional advice on how to think about them will be able to have a meaningful impact.

I've noted some points directly on your work here, but one of the main points I want to stress is that intersections occur between the specific surfaces that are present. It's easy to fixate more on the idea of what a form is (one form is made up of flat surfaces, another form is made up of curving surfaces, and yet another may have a mixture of the two), but in order to properly resolve the relationship between two forms, in their specific orientations, we have to look at how the surfaces themselves sit in space in order to figure out which direction in which our curves should be oriented (this is particularly relevant to those cases where you choose the right tool, like a C-curve or an S-curve, but where the orientation of those curves is reversed, as we see here).

This diagram may help. On your homework, I usually drew arrows alongside the corrected intersections - these arrows show the curvature of the form that is relevant to a given part of an intersection (so like in the sphere-cone intersection at the end of the previous paragraph, the arrow to the left shows the curvature along the sphere that is relevant along the left side of the intersection, and the arrow to the right shows the curvature along the cone that is relevant along the right side of the intersection. These are the ones that allow our intersection line to remain along the surface of both forms simultaneously, whereas the ones you'd chosen (following the cone along the left and the sphere along the right) resulted in an intersection that actually cut into the volume of both forms, rather than remaining along their surfaces - but this is a very difficult thing to wrap our heads around, especially at this stage.

The diagram tries to take a step back in terms of complexity by looking at how we can consider which of the sphere's cross-sections are relevant by looking at the planes of the box that are part of the intersection, one at a time. The top plane aligns to one potential slice of the sphere, and the side plane aligns to another. Our resulting intersection is then stitched together, with the edge of the box demarking where we change from one set of surfaces to a different one, creating a sharp corner consistent with just how dramatically that trajectory changes. But of course, when we're dealing with two rounded surfaces intersecting, we don't have the benefit of that hard edge (something I've seen you leverage correctly elsewhere in your work).

But, as shown in the lower part of the diagram, a curving surface can itself be seen as doing the job of a hard edge, just over a longer measure of space, and more gradually. Thinking about how we can express these spatial relationships, or aspects of forms, in different ways can help us focus more on the surfaces themselves, and ultimately develop our capacity to apply them in more novel situations. But like I said - this is spatial reasoning at its core, and as it stands you're meeting our expectations and developing that this understanding of space has developed well thus far. So, keep at it, and we'll take another look at these as part of Lesson 7.

One last thing - don't draw through your intersection lines. You don't do this all over, but I see it occurring in a number of places. As you'll notice in the demonstrations for this exercise, I specifically only draw the visible portion of the intersection. This is because, while drawing through our forms in general gives us a lot of benefits in terms of our understanding of how they sit in 3D space, while only minimally increasing the complexity of the task, drawing through our intersections has the inverse effect - it increases the complexity a lot, but doesn't actually give enough of a benefit. As a result, it can make things more difficult than they need to be.

Continuing onto your object constructions, you've done a fantastic job here, especially in the sheer volume of patience and care you've demonstrated throughout the development of your orthographic plans, and their application to the 3D constructions. In this, you've done a phenomenal job of taking to hear the concepts espoused throughout this lesson, which focus primarily on the concept of precision and the choices we can make in how we tackle problems to increase it.

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.

I have just a few points of feedback to offer:

• Firstly, I noticed that your bounding boxes tend to be very shallow in their foreshortening, to the point of the edges remaining roughly parallel on the page at times, and even sometimes diverging slightly. This charging dongle is a good example. While the size of these objects (being smaller) does make shallower foreshortening a good choice, do keep in mind that we can't arbitrarily force our vanishing points to infinity and have those edges be represented as parallel on the page - that only happens when the edges in question actually run perpendicularly to our viewer's angle of sight, which is not the case for any of these constructions. That said, there's a good chance that this wasn't intentional - in which case, our use of a ruler can actually help with this in an unexpected way. Basically the issue comes down to it being hard to gauge whether we're drawing lines that converge slightly, as opposed to being parallel or diverging, by eye, until we've actually drawn the marks - and at that point, we're committed to them. What a ruler gives us beyond simply making it easier to draw straight lines reliably is that they provide us with a visible extension of that line, telling us how it's oriented and how it's behaving relative to other marks on the page, without first committing to the mark. So, we can check how the edge we're about to draw will behave relative to those other already marked on the page, and make adjustments accordingly, before the mark is drawn - if we take advantage of the tool in this manner.

• Be sure to review these notes on how to build up curves and curving structures. I saw some minor applications of it for rounding out specific corners, but when it came to larger curves that could have benefitted from being built up from a chain of straight edges (like the top structure of your hole punch, which has a curve in profile, the bell structures of your alarm, which you constructed in pyramids instead, and so forth. Basically you tend to use singular straight edges as the basis of your curves, which doesn't actually give you the added control of building up a more complex chain of straight edges to better fit to your intended curve.

And with that, I'll go ahead and mark this lesson as complete. Keep up the good work.