Starting with your cylinders around arbitrary minor axis, I think it's obvious that you struggled a great deal in aligning your ellipses properly. You did improve with this over the course of this exercise as a whole, but it wasn't until the last 20 or so that the improvement started to become more consistent. You were applying the corrections after the fact with reasonable accuracy, so I think the solution in improving your results falls with two main things:

• Taking more time in applying the ghosting method when executing your ellipses

• If you're not rotating your page to find a more comfortable angle of approach, or perhaps the angle of your choice is not the most comfortable - try testing out a few different angles and see how it impacts your accuracy.

Another issue with this exercise that I'd like to point out is something that wasn't spelled out for students, as I wanted to give them an opportunity to figure this out on their own. It has to do with foreshortening as applied to your cylinders, and how that foreshortening impacts the shift in scale from the near ellipse to the far ellipse, as well as the shift in degree. You clearly understand that the farther ellipse needs to be smaller in scale, as well as wider in degree than the nearer one, but what you may not fully grasp yet is the idea that both of these are manifestations of foreshortening. Specifically, as the farther end gets farther away, perspective dictates that this ellipse needs to get smaller and smaller relative to the nearer end. This is basic stuff that you already know - but what you may not consider is that the same applies to the degree shift. The farther away that end is, the greater the shift in its degree.

What this means is that if we look at cylinder 128, you'll see that you've got a situation where the farther ellipse's scale has changed a noticeable amount, but the degree of this ellipse hasn't changed quite as much, resulting in something that looks a little off. It looks this way because the shift in scale is telling us that this far end is pretty far away from the near end (meaning it's a longer cylinder), but the shift in degree is telling us that the far end is pretty close (meaning a shorter cylinder). It's a contradiction that the brain has trouble processing.

So, long story short - they shifts need to correspond to one another. We'll never end up in a situation where the shift in scale is more or less dramatic than the shift in degree. The smaller the far end, the wider it should be, and vice versa.

Moving onto the cylinders in boxes, these are definitely tricky, and they're largely meant to be. I'm not actually entirely understanding what you mentioned in your question in regards to the minor axis aligning to the same VP as the contact points. I'm confused because that statement is incorrect (there are 3 vanishing points for a given box - one for each pair of contact points, and one for the minor axis), but the cylinder you pointed out was indeed correct. So perhaps you just phrased the statement incorrectly.

Anyway, the thing about this exercise is that it's actually not really about the cylinders themselves. It certainly is in part about learning how to construct a cylinder within a box, as this is a very useful skill we can use when having to orient a cylinder in a specific way in a scene, but more importantly this exercise is about learning how to intuitively estimate our proportions when drawing a box. To put it simply, it's about training our ability to draw boxes that have one pair of faces that is proportionally square.

Similarly to how back in the box challenge we use line extensions to check whether or not our boxes have consistent convergences towards their vanishing points, this exercise uses the cylinder as a further correction technique that determines whether or not those pairs of faces are square (as opposed to having one dimension be larger than the other). If the face is more rectangular, then the contact point and minor axis alignments of the ellipse that fits within it will definitely be off. So, as you work through the exercise, you subconsciously start focusing more and more on drawing boxes that will yield better results, ultimately improving your ability to estimate those proportions.

All things considered, I think you've done a pretty good job with this, and I see a great deal of improvement over the set as you sort through this particularly difficult problem. Just keep in mind that the reason you're struggling with the ellipses is simply that the box itself wasn't set up correctly in every case.

So! I'll go ahead and mark this challenge as complete.