The superellipse2d script is from 2013, and includes a squircle, I think as a subset.

https://moi3d.com/forum/index.php?webtag=MOI&msg=5616.1

About February 2022, a different squircle, using a different math formula, was created, the Fernandez-Guasti squircle. (Later in above link.)
This version is not a subset of superellipse2d. (?)

- Brian

I looked up the pronunciation of squircle. Combine the rodent squirrel with ircle.
(still hasn't made it into spellchecker :-)

On the first picture of this thread and in the video we see, the Sugarloaf Cabochon have 4 faces with edges.
With the video, I discover the render of this cut, that I see very rarely in stores.
Very nice cut...

Thank you Disovered lots if scripts at the link you posted and will give them a try.

Hi Tom,
Brian is the creator of these scripts. He has made several of the "mathematical formula" scripts that create well known geometrical shapes.

He is best to answer about them and if there is any difference (or similarity)

Since this impossible word "Squircle" nauseated my mind it mixes up the names Burrmen Benfarmer and Brian -sorry ;-)

Hey Tom... makes it harder to have to translate everything. Hang tough!

"Squircle"

Square + circle

Squ ircle

... another elegant way

Mik

This link shows a side view of a cabochon:
https://www.rockngem.com/filling-an-empty-space-and-enhancing-a-cabochon/
I had thought that it is a sugarloaf, but now think it is a "slab" for a pendant. ?

Learned a new word: "vug"
https://en.wikipedia.org/wiki/Vug



- Brian

Very nice Mik

Due to your kind collaboration this thread turned into a nice
compilation of how to achieve one goal by different means -
thank you all !!

As one contributor wrote, the shape of a "squircle" is aesthetically
very appealing. I wanted to apply this theme of "squaring the circle"
to the whole shape, starting with a circle at the bottom morphing
into a slightly rounded square at the top. The how to is attached
below.

Cool result! :)

Reproduced a close copy of Toms cab, using his images to reproduce curves.
Note that the two "acorn" shaped curves must be trimmed apart at the North and South poles, into 4 curves, for network to work. (Or kept separate during their creation.)
One-half "acorn" curve was created with two blends. A horizontal line segment was placed at the North pole, and a vertical line segment was placed at the squircle intersect point, and a blend done between. A second blend was done from said curve, down to a horizontal line segment at the south pole. Join for one curve.
Mirror and rotate for other 3 acorn half curves.
Rounded square, squircle, and lower circle curves were also created. The lower circle had to be a bit larger than the sketch IMHO.
Select all 7 curves, and do network.

Still attempting to load my old purchased copy of Keyshot 6.

- Brian

Hi Brian,

I attached my approach to the profile curve - MOI works so great
for stuff like that.