Starting with your form intersections, your work here is really solid. Both in terms of drawing each mark with care, to yield solid, believable structures, and in terms of the intersection lines themselves, which declare a strong understanding of how each of these forms relate to one another in 3D space. You're handling both flat-on-flat intersections (like boxes with other boxes) as well as curved-on-curved intersections (cylinders and spheres, which are especially tricky) very well.

Now, continuing onto your object constructions, as a whole you've done an excellent job here. While I understand your concerns about tools, my choices take in a lot of factors. There's the purpose of the exercise which determines whether the use of rulers and other such tools would be appropriate (since we have exercises that allow us to focus on our linework already, there's no sense piling it on here). There's also a question of how such an allowance would impact the way in which students engage with the entire course. I do, at least at this time, feel that allowing digital tools on any of the mandatory lessons/challenges (we do allow it in the treasure chest challenge) would call our reasoning into question enough to be problematic.

After all, one of the most important reasons we have for working with ink and paper is that it bypasses the natural tendency for digital tools to make us less patient. Sure - at this point, students should generally be more inclined to take their time, exhibit patience and discipline and all that good stuff - but not all students do.

This lesson serves a very specific purpose - it takes us from working on organic construction, which is quite forgiving when it comes to precision, and instead throws us in a situation where for each of these constructions, we really have to push ourselves to the limits of our patience and willingness to step through things granularly. Not all students at this stage are willing - not just yet, at least - to commit all the time they require.

That word - precision - has a specific meaning in our use here, which separates it from simple accuracy. Rather, precision speaks to the steps we take before the execution of a mark to define what our intent specifically is for a given mark. For example, in the ghosting method's planning phase, we'll put down points to mark out the start and end for a straight line. Doing so - declaring our intent - increases the precision with which we work, because we know precisely where our line should start and end. This is our focus here - accuracy itself is not really as important, and as with all of the drawings throughout this course, the focus is always going to be on the exercise. Meaning, getting our proportions wrong, and otherwise deviating from the reference image is not a problem. We're simply using the reference as a source of information to help us build something solid and three dimensional on the page.

Similarly, the act of subdividing our constructions here, to identify the specific location where specific elements should sit in relation to others, also increases the precision of our intentions here. So for example, with your light switch, taking the time to break everything down so each screw has a specific plane in which to exist before ever drawing a single screw, is what we're after. All about making decisions and figuring things out ahead of time. This requires patience, and given that, I want to put students in as conducive a position to exhibit that patience. While the majority of people will certainly do fine with these lessons digitally, they too are not really harmed in being made to take the long road around.

To that point, your work throughout these constructions is extremely well done. You've exhibited considerable precision and patience throughout the set, and while there may be some cases where your initial box is a little skewed, (like the initial bounding box for your bottle in number 7, or on the clock you pointed out), I am very pleased to see that you stuck through it, committing to the choices and decisions that had been made previously. If anything, having a student make mistakes like this (or frankly more obvious ones), and continue to roll with it helps them gain a better overall understanding of the nature of the exercise that we're practicing. Making decisions, and committing to them, every step of the way.

To that same point - the fact that you decided to keep the rod of your toilet paper holder down to a simpler cylinder rather than incorporating the larger cylinder along the right side, speaks again to the fact that we're not worried about reproducing our reference perfectly. Despite leaving this part out, you still did an excellent job with the study, focusing on the arrangement and relationships between your forms in 3D space.

Since your work is largely very well done, I'll finish up by addressing your questions:

• For the toilet paper holder, if I understand your question correctly, the issue arises from the fact that the green plane is tapered - and therefore if you simply draw another plane inset within it, it too will be tapered. Being that the green plane's longer edges are indeed diverging in 3D space, then we know that they are not governed by the same vanishing point - but we do already have structure with many lines that do in fact converge towards the same vanishing point as the plane we actually wish to draw - the edges of the bounding box itself. As shown here, we can draw the top and bottom edges of our plane by keeping them in consistent convergence with the side edges of our bounding box. We already have one of the vertical edges of the plane that will enclose our ellipse, so from there it's a matter of drawing an ellipse that touches the edges above and below at points that align towards the vertical vanishing point, while also having a minor axis that aligns to the left-side vanishing point. While these are concepts we covered in the cylinder challenge, we dip back into it further in some of Lesson 7's videos - including how to use the ellipses to transfer equal measurements from one dimension to another.

• For the first question on your electric shaver, this is one of those areas where without specific, plotted, and technical perspective (which this course does not attempt to explore) would be necessary for high technical accuracy - but that also isn't really what we're after in most cases. Rather, we do precisely what you did - rely on your existing spatial reasoning skills to infer, based on the existing lines in the scene and their own vanishing points, how the lines of this new structure would converge. This is where the box challenge as well as the form intersections help a great deal, because we're training our brain to better understand the relationships between those forms in space. So while we do not know the correct answer for how those pink lines should be oriented, you made an educated guess based on your spatial reasoning skills, and to my eye it looks acceptably correct. Keep in mind - not once in my career as a concept artist and illustrator have I needed more technical accuracy than what you've demonstrated here. If anything, what we're doing in this lesson already is overkill.

• For the base of your electric shaver, keep in mind that the reason we have so many rules for what is/isn't correct when it comes to circles, is because circles are a very specific case. All of the rules of what the minor axis aligns to, for example, apply only for when we're drawing ellipses to specifically represent a circle in 3D space. If we're not trying to do that, then we don't actually adhere to the alignment of the minor axis. Furthermore, there's no reason to assume that an ellipse in 3D space would be represented as an ellipse in 2D space either - rather, it would be impacted by perspective that would distort its shape. Technically this occurs with circles in certain extreme perspectives too, though the ellipse approach is still used to approach them because again, the results are "close enough" and the technique is extremely useful all the same. So, in this case I'd just draw each quadrant of my "ellipse" separately, keeping them within my predefined rectangular plane, and relying on that plane to provide the bulk of the structure.

Hopefully I've answered your questions as satisfactorily as I can - obviously most of those answers did not provide specific solutions to the problems, as this course does have a specific scope (and I myself am only versed as well in perspective as I have needed to be in my career).

So, I'll go ahead and mark this lesson as complete. Keep up the fantastic work - and, fair warning, I'm sorry but Lesson 7 is going to be a fresh hell for you (given your concerns with not being able to use digital tools). But, looking at your work, it is very clearly a fresh hell that I expect you will knock straight out of the park.