Constructing a four-point egg

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.

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.

Joining ellipses with matching tangents

https://dotat.at/@/2024-02-05-joining-ellipses.html

In my previous entry I wrote about constructing a four-point egg, using curcular arcs that join where their tangents are at 45°. I wondered if I could do something similar with ellipses.

As before, I made an interactive ellipse workbench to experiment with the problem. I got something working, but I have questions...

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