I found some Euclidean eggs...

Triggered by Sergey Kuznetsov's very cool image from last year I decided to make an Egg (VB scriptable) component - obviously just for fun.

It can draw each of the seven Euclidean eggs as described by Robert Dixon.
The information I based it on I found on Takaya Iwamoto's website:

For neatness sake I incorporated a piece of Aidan Kurtz's InputTools class from his Intralattice plugin, so the 'egg type' parameter (T) will have an automatically populated value list attached:

Coming to (diagonally) revisit the component this week (I actually wrote it 11 months ago) I remembered it was mainly the result of my predilection for the PolyArc component. It seemed appropriate for the shapes in this exersize.

If you drag and drop the Egg.ghuser onto the grasshopper canvas, it will appear in the "Extra" tab.

Maybe someone thinks of an actual use for this ;)
Happy Easter~
A Sqrt327 egg populated with 350 Cundy & Rollett eggs

Inputs:
P = base plane
S = size
WH = size (in input 'S' is the eggs' width(False/0) or its height(True/1)
T = egg type

Outputs:
Egg = the egg surface
HW = if you defined the egg by height: HW returns the width, If you defined the egg by width, HW return the height.
PC = profile (the curve that gets revolved)
C = Circle around the egg at its 'widest point'

Comment

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Comment by MillieJordon on January 27, 2023 at 3:38am: The egg equation is a nonlinear, partial differential equation that describes the heat transfer within the egg. It takes into account the thermal conductivity of the egg, the heat of fusion, the heat of evaporation, and the specific heat of the egg. It also takes into account the rate at which heat is being transferred to the egg, as well as the rate at which heat is being lost from the egg. Well, now I want Ad-free Grammar assist for my essay and one of my friends suggested me https://fixgerald.com/ website as it is really helpful in detecting duplication in your content and also provides you grammar assistance.

Comment by Pieter Segeren on April 19, 2017 at 2:34pm: ...I meant to say "Tadao Itou" (sorry Tadao!)

Comment by Pieter Segeren on April 19, 2017 at 2:27pm: Thank you Laurent.
I guess I should have emphasised that these egg shapes are all constructed from arcs only. I see that I wasn't clear about that.

Also thanks for the hint for finding some useful equations! I liked (one of) Tadoa Itou's approach(es) best.

Comment by Laurent DELRIEU on April 16, 2017 at 1:10pm: Pieter, thanks for the plugin and the link. I will try to draw eggs with my daugthers. A good geometric exercice. I usually use an equation for my eggs

http://www.bsidneysmith.com/writings/JotsnDoodles/The-Egg-Equations

Happy Easter