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Perspective, Interlude: How to draw a circle/ellipse with just a ruler and a pencil
This bit fell off the last post since it would’ve veered away too far from the main topic. So, taking a quick detour because I found an alternate way of creating a circle that comes in especially handy if one doesn't have any circle-creating tools at hand. It's also a bit more exact because it uses 12 points instead of 8.
The two methods in comparison:
So here's how one constructs a circle (as well as perspective projections thereof) without the appropriate tools:
- You start with a square
- draw the diagonals, which cross in the center (m)
- from that you get the lines (ac) and (bd) that divide the square in half
- by connecting dots a-b you get the point (x) you need to cut the square into quarter pieces.
- Luckily (I don't know why but no doubt there exists a neat mathematical formula that explains it) the red diagonal lines - of which I drew the first one in the left pic- each happen to cross a blue line in a point that's exactly on the circle.
(I'll keep using the first method here though because it needs a lot fewer subsidiary lines.)
By the way, I found an interesting article comparing various kinds of graphical projection for use in RPGs
The two methods in comparison:
So here's how one constructs a circle (as well as perspective projections thereof) without the appropriate tools:
- You start with a square
- draw the diagonals, which cross in the center (m)
- from that you get the lines (ac) and (bd) that divide the square in half
- by connecting dots a-b you get the point (x) you need to cut the square into quarter pieces.
- Luckily (I don't know why but no doubt there exists a neat mathematical formula that explains it) the red diagonal lines - of which I drew the first one in the left pic- each happen to cross a blue line in a point that's exactly on the circle.
(I'll keep using the first method here though because it needs a lot fewer subsidiary lines.)
By the way, I found an interesting article comparing various kinds of graphical projection for use in RPGs
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(I've got a feeling the red lines crossing the circle are in some way related to Thales' theorem but that's about as far as my memory of maths at school gets me.)
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Oh, that is great to hear, I'm glad you find it interesting!
Thales, possibly... maybe a subclause. I'll look around on Wikipedia, I'm curious.