Spent some time reading about these. They can be represented in Nurbs and Beziers, somehow.
They are also used in some Blending...

An approximation can be made by sweeping correctly placed circles. In the attached .3dm, the two circles in the xz plane can be profiles which are
swept, using the two circles in the xy plane as rails. Maintain Height Checkbox gives two versions.

Created a simple script to draw a bunch of (approximate) circles. They can then be lofted to get the Cyclide.

A better way might be to create actual NURBS circles.

Draft2 removes the duplicate little circle.
c>a is not permitted or sqrt of negative number occurs. I'd better add a check for this. Also for negativity...

Here is another version with both "U" and "V". (I think uValue= MoI V, and vice versa).

Did a small circle sweep.

- Brian

To both of the preceeding scripts:
Added aValue = Math.abs(aValue); make aValue positive.

Added if (cValue >= aValue)
cValue = aValue - 0.1;
to make cValue less than aValue.
Negative cValue and bValue seem to reverse the object.

- Brian

"The man" of parametric NURBS functions!

Thanks Bem....

Next year I will make an index of all your crazzy scripts!

I count about 51 or so...

Nice number! :)

Looks like a Toot-a-Loop.

http://tinyurl.com/n2cuhze

Steve S

Always interesting scripts you do!

have you also considered to try out "Strange Attractor" splines, like the Lorenz Attractor etc. they look imho pretty cool and interesting when swept with a profile. There are also Rhino (C4D and 3dsMax) scripts available, to show how they can be programmed. Well, just a thought. ;-)

Best regards
Stefan

The Paul Bourke C code is only about 23 lines.
It looks really simple to program in javascript, to form say 10,000 points or less, then add a curve factory...

http://paulbourke.net/fractals/lorenz/

Do not know how or when they change color...
Somehow change the color when "near" the "attractor."

- Brian

One start point determines one curve, which may be of one color.
Will start another discussion.

Well, i think color is not mandatory, like in those beautiful C4D examples, which also seem to use lesser points and still look really nice.

http://www.behance.net/gallery/MathRules-Strange-Attractors/7618879

Regards
Stefan

Can you repost the Draft2 U & V.zip in normal zip format?
Seems there is something wrong on the compression!

The previous 7z file unzips with 7zip program ok.
Attached is a .zip version, made with 7zip, with the zip option.
- Brian

I have 7z but there is a problem with the uncompression "7" for mysterious reason! Maybe version number ...

No problem with your last post! Zip option is better for most users!

I will ask you each time i will have a problem! :)

Here th UV ;)

...

http://moiscript.weebly.com/geacuteomeacutetries-par-bemfarmer.html

Cool shapes!