1:59 PM, Friday September 3rd 2021
Hi! To try to answer your questions:
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I believe that only a cylinder by itself is open to interpretation in that way. In a box, if the contact points of the ellipses at the end of the cylinder (along with its minor axis) go towards the respective vanishing points of the box, then the cylinder has circular ends, and the box has square ends. In all other cases, the cylinder does not have circular ends. I think the box in this case is technically open to interpretation, but since creating these cases is not the goal of the exercise, I don't think it helps much.
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While cylinders do have this property, I do believe it is a property of perspective in general. For example, this note on the 250 box challenge states that the further box side has a greater proportional width compared to the closer side. The corresponding property in ellipses would be a wider degree, or a larger minor to major axis ratio. On a more personal note, I didn't really use this property to construct my cylinders in boxes.
If I may offer some advice, I think one major thing that helped me in this challenge is realizing that while it's impossible to draw a circle that touches all 4 sides of a rectangle, it's perfectly possible to draw an oval that touches all 4 sides of a square. Therefore I found that figuring out "ideal" contact points after drawing the box (and later on, while plotting out points for the box), and trying to align the ellipses to those points, helped me create circular ended cylinders. It's still not going to work if the boxes don't have square ends, but the error shown in the line extensions were more useful to me.
Hope this helps!