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6:31 PM, Friday November 5th 2021

I'm honestly still a little confused by what you're asking, because I don't really see why the relationship between the length/height would be relevant.

There are three aspects of the lid that we need to determine, once it has been rotated in space:

  • Its depth - so the distance from the front of the lid to the back of the lid. This is the edge we're rotating in the first place, so we maintain that distance by drawing an ellipse that represents a circle in 3D space, with the axis defined by the hinges serving as the ellipse's minor axis.

  • Its height. I eyeballed this in the video demo for the challenge, but to be more precise, you'd just repeat the step for the depth, but for the top-side edge (where for the depth we used the bottom-side edge). If your lid isn't a simple box (and therefore might not have a top-side edge), you'd just end up using a box to figure out the correct rotation, then build whatever fancy lid inside of it.

  • Its length - so the distance from one side to the other. This is achieved by simply repeating the same process on the other side. You'll see in the demo video that while I eyeballed the height (instead of adding two ellipses on either side), I did place an ellipse on both sides.

So, in essence, all three dimensions of the rotated lid can be determined by applying the same ellipse/circle based approach, and none of this has anything to do with the chest's height. The only dimension of the chest that actually matters here is the depth, since the depth is what becomes the radius of each of these circles in 3D space.

3:32 PM, Wednesday November 10th 2021

Ah, alright. I'm just wondering if there's a more precise way to draw a square around the minor axis that can work for chests of any dimension (chests with long/short depth), so I can draw a more precise ellipse. Since the depth is converging to the "horizontal" vanishing point, how do you measure the height part of the square, which is vertical?

4:26 PM, Wednesday November 10th 2021

The ellipse technique is basically the tool that is being used to transfer that depth measurement to the vertical axis. It is entirely precise. While there are other techniques (which I'm not particularly well versed in, as they rely more on looking far back to the vanishing points and horizon line), they aren't any more precise than this. I think what's been confusing me about your statements is the implication that what we're doing here is somehow less precise.

Admittedly, working with a more limited set of ellipse guides would make this technique trickier to employ (since you need an ellipse that'll match the desired criteria) - but again, that comes down more to the tools at your disposal.

There's definitely more to be learned in regards to perspective - lots more tools that we don't get into here simply because we're focusing on things that occur physically close to the object we're drawing, rather than relying on far-off vanishing points that may be way off the page. Scott Robertson's How to Draw is a good resource for that sort of thing, and people have generally enjoyed Marshall Vandruff's Perspective Lectures as well.

2:49 PM, Thursday November 11th 2021

No, I don't meant what we're doing here is less precise, maybe I'm doing it wrong and got less than expected result. I also stopped using ellipse guides for this challenge because they're too small.

Hmm, Scott Robertson's book, way to go then. Thank you for your guidance!

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