fanf | Constructing a four-point egg (Reply)

https://dotat.at/@/2024-01-29-four-point-egg.html

For reasons beyond the scope of this entry, I have been investigating elliptical and ovoid shapes. The Wikipedia article for Moss's egg has a link to a tutorial on Euclidean Eggs by Freyja Hreinsdóttir which (amongst other things) describes how to construct the "four point egg". I think it is a nicer shape than Moss's egg.

a geometrical construction with 8 circles and 6 lines; there are 6 coloured spots marking the centres of the 6 correspondingly coloured circles, and thickened arcs of the circles join smoothly to make an egg shape

Freyja's construction uses a straight edge and compasses in classical style, so it lacks dimensions. My version is on my blog, because Dreamwidth doesn't like my embedded SVG diagrams.

At first this construction seems fairly rigid, but some of its choices are more arbitrary than they might appear to be. I have made an interactive four-point egg so you can drag the points around and observe how its shape changes.