Hello, I recovered this (double) spiral from an AutoCAD file. But there are corner points and small deformations that bother me to use it at my convenience.
So, my question and the next one: would there be among the experts, somebody who could give me the right function to enter in "_FGraph3D", to get this kind of form, because it is beyond my competence!
There is also maybe a possibility with the "Nodeeditor" but I do not know it either.

thank you in advance
- Zooen

With the _FGraph3D
https://moiscript.weebly.com/fx-graph-3d.html
Not yet exactly your form but some tracks

Put the formula after the Tab key pressed then Enter
(of course plugin _fxgraph3D by Max Smirnov mut be installed before)

Spiral
_FxGraph3D cos(u/c)*(cos(v)+a/b)*b;sin(u/c)*(cos(v)+a/b)*b;sin(v)*b+u;0;50;0;6.283185307179586;100;20;10;3;2;UV

Spiral Conic
_FxGraph3D cos(u)*(u/(a*pi)*cos(v)+b)*c;sin(u)*(u/(a*pi)*cos(v)+b)*c;u*sin(v)/(a*pi)*c;0;9.42477796076938;0;6.283185307179586;100;20;1.5;5;1;U

(with some erased sections before the Loft)

Hi,
I've looked at all of this and do quite a bit of other research. As here: https://mathcurve.com/courbes3d/courbes3d.shtml
I haven't found a solution yet.

- Zooen

Maybe a solution will be a simple spiral "Flowed" to a wished section! ;)

And rotate a simple section ?

and Bemfarmer tools ?

http://moi3d.com/forum/index.php?webtag=MOI&msg=6697.1

Another possibility is to use the script Reconstructcurve which transform you curve and soft it.
Use same number of points and the curve will be clean.

Right or no ?

Hi Zooen, if the rest of the curve is how you want it and you just want to smooth out that one area you could try trimming away some space there and then cut the curve into 2 pieces also using Edit > Trim and then put in a blend curve using Construct > Blend.

- Michael

It's also possible to use the Transform > Deform > Twist command to "helix-ize" curves like this:





Then with the Twist command applied it will generate results like this:



If you were planning on cutting grooves or something it also could be good to construct an entire solid in a straight version first and apply twist to the solid.

- Michael

The Biconcave script was used to create left and right profile. The two profiles were joined, and revolved around the x axis.
The resulting "dumbbell" was rotated to the z-axis.
A MoI helix along the z-axis, with radius greater than that of the dumbbell, was created, from bottom of dumbbell to top of dumbbell.
The helix was rotated, (with copy on), 180 degrees, along z-axis.
A line segment was drawn between the bottom ends of the two helices.
The line segment was swept along the two helical rails, created a helicoid. The attached .3dm is at this stage. The next two steps still need to be done.
The dumbbell was trimmed with the helicoid, to create two symmetric ribbons on the dumbbell.
The top edge of each ribbon was joined to make a curve, and a second curve, along the dumbbell.

(I like Michaels method, which may give similar results.)

A superb paper, with helices and OTHER types of spirals, and their varieties of "helicoids":
Spirals on surfaces of revolution
http://elib.mi.sanu.ac.rs/files/journals/vm/57/vmn57p2-10.pdf

Another (unstudied) link:
https://scholar.google.com/scholar?hl=en&as_sdt=0%2C48&q=Accelerated+Algorithm+for+Solids+of+Revolution+Converting+into+Ribbon+by+Spiral+Coordinate+System&btnG=

The existing MoI projection command does not seem to do radial projection(?)

- Brian
The two ribbons look cool, also.

Thank you all for looking into this problem.
-phiro, I often use "Rebuild" and / or "ReconstructCurve", but, unless I'm mistaken, there will always be, even at best, a small difference between the original and the rebuild. And since my 3D spirals have to go through precise points, this is not suitable.
-Pilou, Je vais explorer le lien.
-Thank you in particular to bemfarmer for the links (funny, the last reference at the end of the super paper referring to the site that I cited here http://moi3d.com/forum/index.php?webtag=MOI&msg=10530.3). I will also be inspired by your solution.
-Thank you Michael: the method is simple and elegant (I will test it).

- Zooen

There is a peculiarity that I did not mention, in addition to the dumbbell shape with vertical symmetry: these are two identical mirrored spirals, which develop with irregular steps. So for now, and before I look into the problem, I decided to correct the spirals with "Rebuild", Refit with a tolerance of 0.01. the difference with the original is minimal! So I no longer have sharp angles.

This subject is related to this one:
http://moi3d.com/forum/index.php?webtag=MOI&msg=10536.1

Good, have a good Christmas holiday, see you later!

- Zooen

where can I find the biconcave script?

Biconcave ici : http://moi3d.com/forum/index.php?webtag=MOI&msg=6718.1