Congrats on completing the cylinder challenge! I'll do my best to give you feedback so that you can improve.

Starting with your cylinders on an arbitrary axis I'll start by saying that you've been correctly checking your ellipses and catching even minor discrepancies that'll ultimately help you avoid plateauing as you get into the territory of being "close enough". Though there is no need to check the other minor axis of the ellipse (the green line) as there is nothing to check it against. You've also varied the rate of foreshortening a fair bit over the set which is good to see. However there are a fair number of errors present which still hold you back.

• Firstly, the thing that stands out most to me is that you seem to not be following the ghosting method closely enough which causes unconfident, wobbly lines and ellipses. While I did notice an improvement at the end of the set there are still far too many wobbly lines.This comic by uncomfortable summarises the ghosting method well but you should also go over the lesson 1 notes on markmaking. Additionally for your ellipses you seem to only draw them once and be done. Remember that we should also ghost our ellipses and draw through them 2 or 3 times max to not only ensure a confident ellipse but to also get more practice in for drawing them. Drawing more than 3 times makes our ellipses messy because we end up losing track of the original ellipse so it should also be avoided.

• Secondly, Although you did vary the rate of foreshortening across the set you still ended up with "impossible" cylinders near the end of the set so I'll explain how foreshortening manifests in two different ways and how we can correctly apply it to cylinders. One is the shift in scale from one end to the other, which we inevitably get by having the side edges of our cylinders converge, and the other is the shift in degree where the farther end gets wider. The thing is, because they both represent the same thing - how much foreshortening is being applied - they also must operate in tandem. The more that far end gets smaller, the wider it should also become as a result. If we take a look at cylinder 146 you started with a big ellipse for one side and correctly shrunk it down on the other side, however the degree would end up larger than the large ellipse you started with which is explained here. Therefore it would end up looking something like this.

• Finally you ended up with some cylinders that were parallel (109, 111, 31, 32 etc.) which isn't possible in the context of this challenge. As it has us rotating cylinders freely and randomly in space (as we did for the box challenge), and unfortunately a vanishing point would only go to infinity (resulting in lines parallel on the page) if the set of edges they represent are running perfectly perpendicular to the angle at which the viewer is looking out into the world. In other words, we only draw them with parallel lines on the page if the edges themselves aren't slanting towards or away from the viewer through the depth of the scene, but rather running straight across their field of view. Given the random rotations we use in this challenge, this perfect of an alignment is not something that would happen often, if at all, and so forcing those vanishing points to infinity would be incorrect. You do fortunately have many cylinders that don't have parallel side edges like that so they are exceptions but still it's something to keep in mind nonetheless.

Continuing onto your cylinders in boxes, overall you've done pretty decently here, although there are some points to pay closer attention to. 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 fastidious as you have been in applying the line extensions as instructed, I can see that you've been giving yourself ample opportunity to assess where your approach could be adjusted to bring those convergences together from one page to the next. As a result, your awareness of those proportions have improved, and while there is of course still plenty of room for improvement, you should be well equipped to tackle the related issues that arise as we tackle Lesson 6.

The only thing you would want to pay attention to is making sure all the lines converge towards a vanishing point. I can see that some of your boxes ended up diverging or isometric which isn't possible. But just like the cylinders around a random axis you've also improved in this regard as well.

Overall while there certainly are a lot of issues which you can work on, you've done the challenge correctly so there's no need to do revisions. Though I would strongly recommend going back through the ghosting notes as well as some other notes from the early lessons to familiarize yourself with the core concepts of the course. Hope this helps and if you have any questions don't hesitate to ask.