How to rebuild a circle into superellipse?

[Quan_Li]

I am trying to make a controllable superellipse in Grasshopper.

I was taught the right way to do it in Rhino is as in the video, so I think that is the correct shape.
Now I like to do that in GH by manipulating the weight of the control points. The final shape is quite close but not equal to the one in Rhino.
I wonder which one is the right result and why.

perforated surface.gh (11.5 KB)

I uploaded the GH file.

[anon39580149]

You need to convert the circle to NurbsCurve

perforated surface.gh (13.0 KB)

[AndersDeleuran]

You could also plot the super ellipse formula and draw a curve through the points:

Super elipse, please

Here is a version using GHPython to plot the coordinates, seems to generate okay curvature: And the file: 170203_SuperEllipse_GHPython_00.gh (8.6 KB) Edit: You can change the sampling by setting the step parameter in the Python code (or hook it up to a slider). Edit II: Here’s version where you can extrude/cap the profile: 170203_SuperEllipse_GHPython_01.gh (8.5 KB)

[akilli (Ethan Gross)]

There’s also the Borromini Oval, used by Francesco Borromini’s in his dome of San Carlo alle Quattro Fontane 1646, and based on circular arcs. For certain values its pretty close to a super ellipse.

Borromini oval in rectangle.gh (102.7 KB)

[Quan_Li]

Thank you! Yes I have to change it to 3 degree and 8 CPs.

[Quan_Li]

Thank you! I never knew it, great to know there is this beautiful shape!

[Quan_Li]

Understood, Thanks!