Starting with your cylinders around arbitrary minor axes, your work here is by and large quite well done. You're taking your time as you work through the various stages of freehanding each mark to achieve a confident, smooth execution, you're checking the alignment of your minor axes quite fastidiously, catching even minor discrepancies that'll ultimately help you avoid plateauing as you get into the territory of being "close enough", and you've varied the rate of foreshortening a fair bit over the set.

I really have just two points to call out, both being quite minor:

• While it is required that you draw through your freehanded ellipses in this course, remember that we want to aim to do so twice - three times max - before lifting our pen. Going around it too many times can cause us to lose track of the ellipse we were intending to draw, and can generally just get messy.

• There were cases where you were either applying foreshortening that was extremely shallow - to the point of having no real visible convergence for those side edges as they move back in space - or your intent was to force those vanishing points to infinity. While I don't think it's the latter, I do want to outline why that would be incorrect. Vanishing points only go to infinity when the set of edges in 3D space they govern run perpendicular to the angle at which the viewer looks out into the world. Basically, if those edges are going straight across their field of view, without slanting towards or away from the viewer through the depth of the scene. Since we're rotating our cylinders randomly throughout this challenge, the chances of aligning so perfectly as to have vanishing points at infinity is very unlikely, so it's best to include at least a minimal amount of visible convergence to those side edges. I do really think that it was just that the convergence was there, or intended, but you got too close to parallel to be discernible - but either way, a good thing to keep in mind.

Continuing onto your cylinders in boxes, your work here is fantastic - or at least, very close to fantastic. This exercise is really all about helping develop students' understanding of how to construct boxes which feature two opposite faces which are proportionally square, regardless of how the form is oriented in space. We do this not by memorizing every possible configuration, but rather by continuing to develop your subconscious understanding of space through repetition, and through analysis (by way of the line extensions).

Where the box challenge's line extensions helped to develop a stronger sense of how to achieve more consistent convergences in our lines, here we add three more lines for each ellipse: the minor axis, and the two contact point lines. In checking how far off these are from converging towards the box's own vanishing points, we can see how far off we were from having the ellipse represent a circle in 3D space, and in turn how far off we were from having the plane that encloses it from representing a square.

In being as attentive as you have been to applying the line extensions largely correctly, you've been giving yourself plenty of information on which to base adjustments to your approach from page to page, gradually honing those proportional instincts. The only area where I feel you may have fallen a little short is in identifying your ellipses' minor axis. There are some cases where I'm either not able to identify the minor axis line or it's not there at all (which definitely should be identified), but more frequently it's that you're only applying a limited extension more similarly to what's asked in the previous section of the challenge. Remember that here we want to extend both minor axes all the way back with the other lines so we can more easily judge how they converge with them. If we're not able to check this, it is possible for little errors to accumulate where we aren't checking for them as attentively.

Anyway! All in all, very good work. I'll go ahead and mark this challenge as complete.