Squircle

[leoheck]

Hello guys!

I have no idea how to create a squircle*.
Anyone has an idea on how to do this with a sketch?

* Squircle Reference
https://en.wikipedia.org/wiki/Squircle

Or even better, how can I create a box with all corners with this shape instead of fillet.
Toughts?

[TheMarkster]

These squircles are precise parametric curves. We can produce them with the following macro code:

Code: Select all

import FreeCAD
from math import *
import Draft

if not App.ActiveDocument:
    App.newDocument()

r = 10
s = 2

wirePoints=[]

for ii in range(0,628):
    t = ii/100.0
    p0 = (r/(2*s))
    p1 = sqrt(abs(2+2*s*sqrt(2)*cos(t)+s**2*cos(2*t)))
    p2 = sqrt(abs(2-2*s*sqrt(2)*cos(t)+s**2*cos(2*t)))
    p3 = sqrt(abs(2+2*s*sqrt(2)*sin(t)-s**2*cos(2*t)))
    p4 = sqrt(abs(2-2*s*sqrt(2)*sin(t)-s**2*cos(2*t)))
    x = p0*p1-p0*p2
    y = p0*p3-p0*p4
    wirePoints.append(FreeCAD.Base.Vector(x,y,0))

Draft.makeBSpline(wirePoints)

The "s" value in the above code defense (Edit: defines) the squareness or roundness of the shape. s=0 gives us a perfect circle (except we can't use s=0 or we get divide by zero error, so we can use something like s = 0.001). s=1 gives up a square. In the image below I used different s values between 0 and 1 to produce the various curves. The green one in the middle was produced with s=2.

The r value is the radius.

squircles.png (26.46 KiB) Viewed 1337 times

In the attached freecad file each of the bsplines is named according to the s value used to create it. For example, BSpline_s0_9 was produced with s=0.9.

If you wanted to make a box one way would be to extrude one of the profiles in the x, y, and z directions. Extrude, make copy, rotate the copy 90 degrees along the x axis. Extrude the copy, make another copy. Extrude that copy after rotating it 90 degrees on the y axis. Take the common of all 3 extrudes. All 3 extrudes should be symmetrical and long enough that each one sticks out along its extruded direction. When I did this I had to move on the extruded objects by 1 nanometer in the x,y, and z directions or else the common operation failed due to coplanar edges, I guess.

To extrude on of the bsplines make sure its closed property is set to true.

[leoheck]

TheMarkster, thanks for teaching me this thecnique and also for the explanation, this was great. And also thank you for sharing the freecad model.

[leoheck]

TheMarkster, I am playing here with the file you shared, and I see that one of its corners is not well-formed like the others. Do you have any idea on how to fix it?

[chrisb]

squircle3d.png

It's not a squircle, it's a sphubic .

[leoheck]

How did you do to extrude creating a solid? Freecad is complaining that it is not a closed object.

Edit: Oh, you already told that!

To extrude on of the bsplines make sure its closed property is set to true.

[leoheck]

I was able to reproduce your shape, it is awesome. The issue I saw is that the intersection didn't work properly, I guess. Then I moved the objects 0.01 mm to the direction of each extrusion and I was able to make the common from all the shapes. (Maybe this is also something you said but I couldn't understand properly). But AWESOME. This new shape is actually something good without the strange corner that I saw before.

[TheMarkster]

Another attempt, this time using curved shapes workbench. With this tool one of the shapes is the profile. The other 2 act as boundaries. The original profile gets resized according to the boundary shapes as it is arrayed. I don't like the squared off ends I end up with, but I think it's an improvement. I tried using the small profiles at the ends, but I didn't like how that lofted either. It might be possible to split with a plane one of the good sides and polar array the good side around 4 times to end up with a nicer looking model.

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