Full Version: Dupin Cyclides

Show messages:  1-17  18-22

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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Show messages:  1-17  18-22