Starting with your cylinders around arbitrary minor axes, there are things here that you've done well, and areas where you somewhat misstepped.

The good:

• You're doing a great job of executing your straight lines for the edges of your cylinders - the lines are smooth and fairly straight, and also quite accurate.

• Your ellipses have been drawn fairly confidently - though there is still some hesitation, especially when you get to ellipses of larger degrees. Remember to use the ghosting method for your ellipses (specifically to separate out the preparation/planning from a confident, hesitation-free execution), as for all your marks, and engage your whole arm from the shoulder. That will help you continue to smooth out your ellipses.

• You appear to be demonstrating an understanding - whether instinctual based on experience, or conscious based on understanding - of the fact that the two "shifts" from one end to the other (one being the shift in scale where the far end is smaller due to the convergence of the side edges, the other being the shift in degree where the far end has is wider) that occur as a result of foreshortening, and the fact that they operate in tandem. That is to say, you wouldn't have a cylinder with limited shift in scale, but a more dramatic shift in degree, or vice-versa. Both are manifestations of foreshortening, and so they both play a role in conveying to the viewer just how much of the cylinder's length exists in the unseen dimension of depth.

• You've been quite fastidious in identifying your "true" minor axis alignments, even pointing out fairly small errors. As we get better at aligning our ellipses, it becomes increasingly important to identify even these tiny mistakes, so that we can continue to grow and improve.

The less good:

• Towards the beginning, and sporadically throughout the set, you do have a tendency to eliminate the scale shift/foreshortening altogether, placing the vanishing point "at infinity" in the manner discussed back in Lesson 1. This is actually incorrect - we cannot actively choose where the vanishing point goes. Rather, we decide how the form is oriented, and it is the orientation of the lines governed by each vanishing point that determines where it needs to be. Basically what this means is that we can't just arbitrarily place our vanishing points at infinity to simplify the problem at hand. Vanishing points will only go to infinity when the lines they govern run perpendicularly to the viewer's angle of sight, rather than slating towards or away from them through the depth of the scene. Given that this challenge has us rotating our cylinders freely and randomly in space, we can pretty much assume that they'd never align so perfectly. Thus, we should always include some convergence to those side edges.

Continuing onto your cylinders in boxes, you definitely made the same extent through the first chunk of this one as well, though it's not quite as consistent. That is, you did start to sneak in a little bit of convergence more and more, which does allow you to skate by. When doing this exercise in the future, I would definitely encourage you to incorporate more convergence, to the tune of what you were doing towards the end of the challenge, rather than the beginning.

That aside, 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.

To that point, you've done a pretty good job. You've been consistent in extending all of the ellipses' additional lines, including extending the minor axis lines as far back as the others (often students only identify them, similarly to the first part of the challenge, rather than extending them all the way back to where they can be compared to the others). As a result, your sense of the proportions of those boxes as they rotate in space is certainly showing improvement. As you continue to practice this exercise as part of your regular warmup routine, it will continue to do so.

Anyway, I'll go ahead and mark this challenge as complete.