##### 5:52 AM, Wednesday May 24th 2023

Thanks so much for letting me know!

Does this work?

##### 5:28 AM, Friday May 26th 2023

Sorry for the delay in replying - I've been traveling and attending a funeral, so I've been a bit behind on my usual work.

Diving right into the critique and starting with your cylinders around arbitrary minor axes, I'm very pleased to see the general trend towards improvement over this set. For the first bit, you were definitely a lot less certain about what you were doing and how to set out the relationship between the ellipses on either side - but as you progressed through it, you became more comfortable and familiar with the basic mechanics of how the circles in 3D space change as we slide along the length of the form. You demonstrated the degree shift more consistently, and also demonstrated an understanding - either conscious or subconscious - of how the shift in degree works in tandem with the shift in scale from one end to the other. This can easily be overlooked, but because both function as a manifestation of the foreshortening applied to the form as seen by the viewer, and thus conveys just how much of the cylinder's length is visible right there on the page, and how much exists in the "unseen" dimension of depth.

I'm also pleased to see that you're identifying the minor axis lines carefully and fastidiously, being careful not to get too comfortable with cases where you're just a little bit off. Continuing to identify those small mistakes as you have been will ensure you avoid plateauing your skills in this area in the future.

Continuing onto the cylinders in boxes, you've similarly done a pretty good job here, especially when it comes to applying the line extensions. Essentially this exercise is really about the boxes themselves - the cylinders function as an additional "error analysis" step, allowing us to add additional line extensions. In testing how consistently they converge towards the box's vanishing points, we can identify how much we need to adjust the proportions of the box in order to achieve boxes with ends which are proportionally squared. So, by doing this repeatedly, we gradually hone our internal sense of those proportions, and improve upon our ability to construct boxes with squared ends.

One thing I would push for however is to try your best to have the ellipses touch each edge of their enclosing plane, to ensure that the line extensions applied to each ellipse accurately describe the proportions of that plane. I did notice a tendency to have the ellipse fall a little short on one side in many cases. This is of course something that you may end up doing even while intending to have it touch all sides (mistakes certainly happen, and you'll get better with continued practice), but just make sure that your intent is first and foremost to have it touch all four sides. Secondary to that would be to have it align to the minor axis defined by the line passing through the centers of the two planes, leaving the two contact point lines to be the main discrepancies that can be addressed by shifting the width of the plane in one dimension in subsequent pages. In other words, it cuts down on how many variables we have at play down to just one dimension of the box. If the ellipses touch all four sides and align to the minor axis line, then if our contact points are off, the solution is to make the box wider or narrower on that one dimension.

Anyway, all in all you're making great progress, and are clearly demonstrating a good sense of how to apply these two exercises going forward. I'll go ahead and mark this challenge as complete.

Next Steps:

Feel free to move onto Lesson 6.

This critique marks this lesson as complete.
##### 6:21 PM, Friday May 26th 2023

No worries at all man!

Thanks for the throrough feedback as always and my condolences to you.

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