So in the past, you've definitely run into a fair bit of trouble working through these lessons. Your homework here marks something of a change, and I wanted to mention up-front that you've done a great job with the object constructions themselves. You've demonstrated a lot of care and patience, and it's paid off a great deal. Perhaps the manner in which we work for this kind of material (we'll talk about how it differs from previous lessons in a moment) resonates more with how you think, or perhaps you've made a marked improvement overall. Either way, even if it's just the former, these later lessons still have a notable impact on students' understanding of space and construction as a whole, so this is definitely a good thing regardless.

Anyway! Getting right into your form intersections, at their core you're demonstrating a pretty well developing grasp of how these forms relate to one another in space. That said, there are a few things to keep in mind going forward:

• Be sure to use the ghosting method for the execution of all your marks! I'm definitely seeing some hesitation here which suggests that you might not be using it as consistently as you ought to.

• I'm seeing a lot of faint marks, and then darker ones - while this is likely the result of your scanner blasting the fainter ones out in its attempt to increase contrast (for this reason photos taken with a camera phone are better, although scanners can generally have settings that are designed for photos which don't mess with the contrast), the fact that you've got those fainter marks does suggest that you might have some areas where you get tempted to trace back over existing linework. Remember that tracing back over lines should be avoided - it makes us focus on how the mark we're drawing goes across the page in two dimensions, rather than how it represents an edge moving through 3D space.

• Also, I'm noticing that you ended up tackling the form intersections in clusters/groups, which is specifically mentioned as something not to do here in the instructions.

• Among those fainter marks, I'm definitely seeing a number of minor axis lines - but there are some cones and cylinders where it looks like you didn't use a minor axis line. Could be that the scanner just blasted it out, but just in case I wanted to give a reminder to always construct forms with circular cross-sections around a minor axis.

Now, while we introduce this exercise back in Lesson 2, it's really here - once the students have had a chance to work through constructional drawing exercises, and consider the relationships between those 3D forms, even just organic ones - that they really develop more comfort and familiarity with this kind of thing. It's that which puts us in a better position to actually provide more information in regards to how the intersections work. Admittedly, like I said already, you are demonstrating a good grasp of how these forms interact with one another, but I wanted to provide this diagram anyway, just in case it helps push things further for you.

Continuing onto the object constructions themselves, as I said - you've done a fantastic job. I do have some pointers on how you can continue getting the most out of these, but all in all I'm quite pleased with how you've come along. This lesson, unlike those preceding it, focuses on the concept of precision. Where lessons 3-5 have us working reactively, laying down forms and then arranging the forms that follow according to where the previous ones fell (so if a head is drawn bigger than it needs to be, we simply account for that and end up drawing a bigger head overall), which one could describe as a sort of inside-out approach, what we do here is very much the reverse - working from outside in. It's this which makes this lesson, along with Lesson 7, a very different way of exploring the 3D space in which we work, and it's approach that allows us to work more precisely, increasing our control over the end result in a way that works really well with geometric constructions.

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.

Now one of the really big points that I think you took from this lesson and ran with is the benefit of working with orthographic plans first, and using them to make all the big decisions ahead of time. That lines up super well with the whole "precision" dogma, and you've done an excellent job with it. Looking at your lighter ortho for example, there's you've not only analyzed the object itself, but you've made a number of important decisions, authoritatively taking control over what it is you wish to draw.

It's easy for students to get caught up in trying to figure out how to match everything in a given object perfectly, and thinking they need to drill down their subdivisions to a crazy degree - but there's nothing wrong with "rounding", in the sense of positioning something at 4/5ths instead of 39/50ths.

That said, there are some decisions you left undefined. As shown here, we don't actually know how far along the width of the lighter you want each of these landmarks to be positioned. That said, not all of them are equal - while the purple ones don't have a clear distance defined, there is some more precision in the fact that you've picked an arbitrary distance on one side, then mirrored it across the center to the other side. It's not perfect, but it does meaningfully increase the precision by creating a relationship between different measurements across the structure.

On the topic of precision, I did want to mention that this construction is really nicely done. The extra line weight on those internal lines does do it a bit of a disservice (the viewer's brain is inevitably going to assume, given our particular tool restrictions and limitations to strict black and white, that filled areas are meant to be cast shadows, which is why we generally try and keep our line weight more limited and subtle), but all in all it's still exceptionally well done and is a real testament to your overall patience and care. It's also not the only one that demonstrates this, but it did stand out as being especially complex - and that you rose to the challenge of that complexity.

The last thing I wanted to mention is that I can see that you had definite trouble with the lid on this water bottle, and that is perfectly okay. What you tackled there is actually a very complicated problem - how do we take a form and rotate it around an axis, while maintaining all the right relationships with the un-rotated version of the form? It's definitely not something I'd expect a student at this stage to be comfortable with, and it's not something we've discussed yet. The trick to this is to use ellipses - I demonstrate it in the video for the Treasure Chest Challenge (and there's a quick illustration of it here), if you're curious, but there's no need to worry about it right now.

And that about covers it! All in all, great work. I would however recommend that when you get into Lesson 7, that you use a ballpoint pen instead of a fineliner. You've done very well with the fineliner here, but it would make your life easier and help you focus your energy on the core elements of the lesson.

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