Dupin Cyclides  1-20  21-22

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 From:  bemfarmer
6390.1 
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.


EDITED: 21 Dec 2013 by BEMFARMER


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 From:  bemfarmer
6390.2 
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

EDITED: 24 Jun 2016 by BEMFARMER


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 From:  bemfarmer
6390.3 
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
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 From:  BurrMan
6390.4 In reply to 6390.3 
"The man" of parametric NURBS functions!

Thanks Bem....
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 From:  Frenchy Pilou (PILOU)
6390.5 
Next year I will make an index of all your crazzy scripts!
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Pilou
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 From:  bemfarmer
6390.6 In reply to 6390.5 
I count about 51 or so...
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 From:  Frenchy Pilou (PILOU)
6390.7 In reply to 6390.6 
Nice number! :)
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 From:  SteveS
6390.8 In reply to 6390.1 
Looks like a Toot-a-Loop.

http://tinyurl.com/n2cuhze

Steve S
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 From:  futagoza (STEFAN)
6390.9 
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
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 From:  bemfarmer
6390.10 In reply to 6390.9 
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

EDITED: 31 Dec 2013 by BEMFARMER

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 From:  bemfarmer
6390.11 In reply to 6390.10 
One start point determines one curve, which may be of one color.
Will start another discussion.
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 From:  futagoza (STEFAN)
6390.12 In reply to 6390.10 
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
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 From:  Frenchy Pilou (PILOU)
6390.13 
Can you repost the Draft2 U & V.zip in normal zip format?
Seems there is something wrong on the compression!
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 From:  bemfarmer
6390.14 In reply to 6390.13 
The previous 7z file unzips with 7zip program ok.
Attached is a .zip version, made with 7zip, with the zip option.
- Brian

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 From:  Frenchy Pilou (PILOU)
6390.15 In reply to 6390.14 
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 ;)

EDITED: 6 Jan 2014 by PILOU

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 From:  Frenchy Pilou (PILOU)
6390.16 
---
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 From:  bemfarmer
6390.17 In reply to 6390.16 
Cool shapes!
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 From:  KaĆ«l (KAEL)
6390.18 
THANKS, happy new year to all :)
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 From:  bemfarmer
6390.19 
The DupinCyclides script can be used to make a torus, by setting c = 0.

Sweep can be used, instead of Loft or Network, to make a Dupin cyclide, or torus,
by setting the uDensity# to an odd number, say 101 or 201, and the vDensity# to 3.
Then along the x axis, select the largest circle and the smallest circle, to be swept,
with the rails the inner v circle around the hole, and the outer v perimeter circle.

- Brian

A help window checkbox may be added,
as well as a checkbox for Villarceau circles.
The "a" "c" and "mu" values should be clarified, in relation to the 4 circles mentioned in the above paragraph.
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 From:  bemfarmer
6390.20 In reply to 6390.19 
DupinCyclide2017beta script uses 3 point MoI NURBS circles, instead of interpcurve pseudo circles.
Beta version, because there are numerous permutations of the 3 main parameters, which might cause exceptions.
Trying to make a circle out of a singularity is avoided by having a minimum 3 point circle size.

Network works well on the scaffold of the 7 types of (elliptical related) Dupin Cyclides.

For best network results, the scaffold of the 3 types of horn cyclides should be trimmed into two parts, across the singularity point(s),
and Networked separately. The old script did not make clean solids at the singularity point(s).

There is much more documentation in the script. Note that uDensity and vDensity should be even numbers, preferably.

Next will be the addition of Inversion and creation of Villarceau circles on the Ring Dupin cyclides.

- Brian

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