Full Version: Dupin Cyclides

Show messages:  1-4  5-22

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

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I count about 51 or so...

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Nice number! :)

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Looks like a Toot-a-Loop.

http://tinyurl.com/n2cuhze

Steve S

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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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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

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

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

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

Attachments:
DupinCyclidesUandV-Draft2.zip

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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 ;)

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...

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

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Cool shapes!

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THANKS, happy new year to all :)

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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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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

Attachments:
_DupinCyclide2017Beta.zip

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The ellipse associated with the Ring Dupin Cyclide is easy to make with MoI's ellipse command.
The center is the origin, and the two radii are the aRadius and bRadius = sqrt(aRadius*aRadius - cRadius*cRadius).
A checkbox for this may be added. Points on the ellipse are center points for spheres caged by the scaffolding network.
These spheres correspond to circles in the Top View, xy plane.
There are rendered images of tangent caged spheres on the internet. Making the spheres/circles tangent to each other seems to be trial and error?
An offset radius for the scaffolding network would permit the network to be wires of diameter twice the offset radius.

- Brian

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https://en.wikipedia.org/wiki/Problem_of_Apollonius

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