Starting with your cylinders around arbitrary minor axes, you've done a pretty solid job here. I'm seeing a lot of variation in the rates of foreshortening, a clear grasp of the relationships between the different manifestations of foreshortening (that is, how the shift in degree from one end to the other and the shift in scale of those ellipses work in tandem - the more the scale shifts, the more the degree shifts to match), and I'm quite pleased to see a pretty fastidious use of the error checking method here to identify your true minor axis alignments. I can see that you haven't allowed yourself to get too comfortable, and continued catching even fairly minor discrepancies to ensure that you don't plateau as your cylinders get into the "close enough" territory.

Continuing onto your cylinders in boxes, your work is similarly well done. 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.

While your work has been done well, I do have a few suggestions of things to pay attention to as you practice this exercise in future warmups.

• Keep an eye on the lengthwise-axis of your cylinders. As your boxes get longer, you're more and more prone to having the line extensions for the plane on either side converge in pairs rather than having all 4 of each set (2 from each side) converge together.

• When you're picking which colour to use when extending certain lines, it's easy to focus more on the direction in which they extend. This has a certain risk however - when our boxes end up squashed in one dimension (meaning, the ends don't end up being proportionally square by a pretty wide margin), it can cause the minor axis of the ellipses to align fairly convincingly towards a completely different dimension. This isn't something that comes up in your work in any one clean example (because you were quite good at judging those proportions throughout), but if we look at examples like 94, where the box is a little more squashed, we can basically end up in a situation where we confuse the minor axis line with one of the contact point lines, where the minor axis line might get defined in blue (up and to the right), when it's actually supposed to be grouped with the purple lines (down to the left). If however we purposely choose the colour based on what we're extending relative to cylinder itself, it becomes a lot easier to catch mistakes (like if you end up with a purple line amongst many blues).

• I noticed that your earlier boxes were more prone to widely deviating their convergences, which makes me suspect you might not be practicing the boxes as frequently in your warmups as you should. This is pretty common, as there are a lot of exercises throughout this course and some just end up left by the wayside. You did get back up to speed pretty quickly, but if my suspicion there is correct, do be sure to incorporate it into your warmup rotation with the line extensions included.

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