Need advice to sketch Squircle

[travis.designer.vn]

Hi
I find way to sketch Squircle.

Refer link:
https://en.wikipedia.org/wiki/Squircle

I search google and find a video using Conic to sketch. However I do not know Is it right or wrong.

Need advice to sketch precise Squircle

Thank
Travis

[MichaelT_123]

Hi Mr TravisDesigner,

There is no way to implement the curve in F360 generatively... so approximation of it is a necessity.

FittedSpline approximation would be my preferable choice. Approximation - generation of fitted points can be done externally or by a simple F360 script. Look at the built-in method useful in the estimation of an error and creation the curve as light as possible.

(returnValue, vertexCoordinates) = curveEvaluator3D_var.getStrokes(fromParameter, toParameter, tolerance).

Regards

MichaelT

[g-andresen]

Hi,

depending on your requirements, you could do it with a conical curve or (alternatively) with a conrolpoint spline.

günther

[travis.designer.vn]

I also try use Conic, but not sure Is it right or wrong?

[TrippyLighting]

Either one is a good approximation.

In industrial design 3-degree and 5-degree control point splines and resulting surfaces are the prevalent design tools. 

This image and the attached model include both versions.

[TrippyLighting]

I have to revise my judgement. I downloaded the .svg from Wikipedia and tried to match the curvature with both, the conic curve and the 5-degree control point spline. The 5-degree control point spline clearly wins!

[MichaelT_123]

Hi Mr TravisDesigner,

Squircle is undoubtedly a fascinating topological object ... and not trivial, both mathematically and philosophically.

Here is my effort to harness it in F360 (extended) environment.

The file Squircle_Fusculator.f3d contains squircylinder. A planar xy intersection of it represents a squircircle curve:

(x/a)**n+(y/b)**n = 1

… so, in essence, it can be used as a respective squircle curve calculator. Note… n does not need to be a natural number! Just … change the model’s user parameter n, and the curve will … recalculate itself at the front of your eyes. The fusculator is a little wired… but it is what it is! Anyway, there are far more strange phenomena in F360 😉.

The file can be freely used in your and others' projects without restrictions.

Attached files:

Squircle_mono.png         4K_mono        ( 4MB)    https://a360.co/3P32Tx7 

Squircle_mono.mp4        4K_mono        (  7MB)    https://a360.co/3I8A3sC 

Squircle _arcd.png           4K_stereo      (  8MB)   https://a360.co/3nBDjU9 

Squircle_arcd.mp4           4K_stereo      ( 37MB)  https://a360.co/3nziXek 

Squircle_al.mp4               4K_stereo       ( 14MB)  https://a360.co/3OCfHKJ 

Squircle_Fusculator.f3d  F360 model    (14MB)    https://a360.co/3I9yKtC 

To be viewed on 4K media devices (monitors, UHD TVs, projectors...) of reasonable performance. For the best experience, use stand-alone media applications (WMP, VLC) and the native resolution 3840x2160 - full screen. The '_arcd' files require an anaglyph red/cyan glasses, while '_al' is for an active shutter glasses 3D hardware (~30 deg viewing angle is recommended). Download the files over a network, where the cost of doing so is not a concern. The files are to be used for private, non-commercial purposes only.

Regards

MichaelT

[MichaelT_123]

Hi Fellows,

As the Squircle object is fascinating, I have decided to update the domain of its rendering. So, the domain was extended from <2,10> to <0.1,10>.

One might ask why not to <0,∞>?

These are the reasons:

• The solution at 0 does not exist as based on the GAAP (Generally Accepted Algebra Principles) limit of function x**x when x→0 does not exist. It plays with intuition, as by looking at the rendering of the function, a cross looks like a sensible solution!? I could not manage to render such topology at 0 and also in the region (0,0.1> though, as the F360 was getting … crazy!
• Calculations of (x/a)**n+(y/b)**n = 1 in the region (0,0.1> encounter significant numerical challenges, even when done with extended precision.
• Why not to go to ∞? … Well, perhaps this is obvious! It is the place where the circle subscribed square is! … and squaring the circle is obligatory, not allowed! Contrary to that, the circle inscribed square is perfectly legal (n=1).

Please find updated files. Additional conditions are as in my previous post.

Attached files:

Squircle_mono.png         4K_mono        ( 2MB)    https://a360.co/3SgnKiH 

Squircle_mono.mp4        4K_mono        (18MB)   https://a360.co/3Sg8Itu 

Squircle _arcd.png           4K_stereo      (  4MB)   https://a360.co/3vwOwcV 

Squircle_arcd.mp4           4K_stereo      ( 50MB)  https://a360.co/3vS8xen 

Squircle_al.mp4               4K_stereo       ( 37MB)  https://a360.co/3zK2Scw 

Squircle_Fusculator.f3d  F360 model    (66MB)   https://a360.co/3JrDX0E 

To be viewed on 4K media devices (monitors, UHD TVs, projectors...) of reasonable performance. For the best experience, use stand-alone media applications (WMP, VLC) and the native resolution 3840x2160 - full screen. The '_arcd' files require an anaglyph red/cyan glasses, while '_al' is for an active shutter glasses 3D hardware (~30 deg viewing angle is recommended). Download the files over a network, where the cost of doing so is not a concern. The files are to be used for private, non-commercial purposes only.

Regards

MichaelT