While researching Cones and developable surface, came across an Oloid.
The Oloid shape is used in mixers, and as a toy which I never got to play with.
Have to get a 3d printer some day.

There are additional remarks in the script .js, regarding loft, mirror, and boolean union.

http://www.heldermann-verlag.de/jgg/jgg01_05/jgg0113.pdf

May try a torse "unwrap".


Here is a script to create an Oloid, based upon portions adapted from Lineweb script, and ToroidHelix script.

Using a higher line number will improve the Oloid "accuracy."
500 lines almost looks like a surface. Loft makes them a surface.





- Brian

Thanks Brian!!!

oloid (“oh-loh-weed”)

Not very exciting, but here is a script to make the 2d path, (unroll), of the oloid.

- Brian

This last one can be made by a simple 2 arcs circle + Transform / Array/ Dir ;)

Hi Pilou.
I cannot get a 3 point circle to match the curves, although it is pretty close, which
suggests that the track is not quite of circular arcs?
:-)

- Brian

Yes you right max gap following middle along the circumference between a circle of 1 m radius and the oloidtorse is something like 0,0129 m so like 1/100 so sure not exactly the same!

But for illustration that can be used ;)

:-)

I copy pasted an oloid to Geomagic Design, stitched it, and exported to .bip, for keyshot3 (/4).


I would try to do a "gomboc," but there apparently isn't any parametric equation.
One link said it was "Constructive Solid Geometry."
Did locate an .stl reduced version.
There is a US design patent granted April 20, 2010, which lasts for 14 years.


- Brian

seems all is there :)
http://www.gomboc.eu/site.php?inc=0&menuId=8

Hi Brian,

here's an interesting 4 side screenshot from Rhino, of a gomboc. (please scroll down to the end of the page)
Maybe it's useful for reconstructing the shape in MoI...

http://totallyepic.net/mossy.html

Regards
Stefan

Thankyou Pilou and Stephan.
There is supposed to be an infinite number of such shapes, but they are all also
supposed to be within a few percent of spherical.

The torse of the oloid is the unwrapped oloid.
Here is a re-creation of the paper model shown in several papers of Hellmuth Stachel, which I did, based upon the script for the torse
of the oloid, with the glue tabs added on.
http://www.iste-c.net/keynote_speech/inte2016/Hellmuth_Stachel.pdf
The top mirrored curve of the torse script was not quite tangent.
The mirror of the bottom initial quarter torse curve seemed to be smooth and tangent. The two curve formulas are different.
The tabs took quite a lot of time to do in MoI. Max's pattern selection script may have helped, and was used for the 4 "dashed" lines.
Dashed lines usually imply a valley fold, but not in this case. The MoI units was set to inches, and the .3dm converted and scaled to inches,
to fit standard size, thick paper.
The pdf was easy, at 1 to 1, and the 2d printout fit within an 8.5" x 11" size paper.
The scissor outline was printed on an 8.5" x 11" cut out sheet of a manila file folder, which the Brother laserjet printer
was able to print on. Glue has not yet been applied.
The V shape of the glue tabs begins at a point on the curve, but apparently due to pixel display artifact,
the visible tips of the V shape appear to extend past the curve.
that they actually meet at a point on. The pdf also shows this artifact.

(need to buy a 3d printer...)

- Brian

>> need to buy a 3d printer... <<

Till the try Shapeways. Have received my 3D print from them
last week. Nice quality, affordable price.

Something similar from Tony Wills is a D-Form shape from 2 flat sheets of paper of exactly the same edge lengths
Look at www.cutoutfoldup.com/1602-d-forms.php