Spiral _FGraph3D
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 From:  bemfarmer
10530.9 In reply to 10530.1 
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.

EDITED: 16 Aug 2022 by BEMFARMER

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 From:  Zooen
10530.10 
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

EDITED: 19 Dec 2021 by ZOOEN

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 From:  Zooen
10530.11 
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

EDITED: 24 Dec 2021 by ZOOEN

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 From:  Psygorn (DRILLBIT)
10530.12 In reply to 10530.9 
where can I find the biconcave script?
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 From:  Zooen
10530.13 In reply to 10530.12 
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