Perspective, Interlude: How to draw a circle/ellipse with just a ruler and a pencil

[astridv]

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.)

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By the way, I found an interesting article comparing various kinds of graphical projection for use in RPGs