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From: bemfarmer
Here is a slight update to the Hopf torus .nod.
The three spherical curve versions are switchable. A 3+ input switch would be nice... Also a double throw, triple pole switch...
The trig and sinusoid formulas make the same, or nearly the same Hopf torus, if their inputs are the same.
One lobe is calculated, lofted, circular arrayed, and joined, to a solid.
The number of total lobes can be 1, 2, 3, 4, ...
The shape factor can be adjusted.
The number of circles generated can be adjusted by numpoints.
A second set of 20 or so network curves has not been done yet.
- Brian
Attachments:
ParametricHopfTorus_3Versions01.zip
From: bemfarmer
For one lobe, without loft, with just the many circles, LINEWEB, curve version, can be applied to the circles.
Then, by selecting all of the circles and lineweb curves, NETWORK will produce a surface, but had slight wrinkles in the center area.
Circular array works, but join does not. Boolean union of the 3 circular array lobes, will make the 3 lobe solid, but with the slight wrinkles still present.
The loft version looks better.
- Brian
From: bemfarmer
The ElasticaSpherical3 script can be used to create a closed curve on the sphere.
For 4 lobes, the correct one quarter of this curve will make one lobe, but is must be oriented correctly.
The one that I used is similar to a portion of the tennis ball curve, which was used to orient the elastica curve portion correctly.
The curve was colored "coral", and the node "Get by style" (set to color coral), will select it, and then Karsten's mPath_array will yield points, for input into the previously posted spherically projected Hopf generator, including loft, circular array, and manual boolean union to a solid.
A nice looking 4lobe R3 Hopf solid resulted.
The correct orientation may be that the north pole of the 3 sphere is in the correct orientation for the spherical projection.
- Brian
(The beginning coral colored qtr spherical elastica, oriented, is inside the emerald Hopf solid.)
Attachments:
SphereElastic_Hopf4lobeOriented.zip
From: bemfarmer
MathPts node is not drawing single lobes the same as one lobe of multiple lobes, so something must be corrected...
Also the angle of the lobe must be determined. Looks line 30 degrees rotation around y towards z (?)
- Brian
The problem is using only 21 points for the full curve, and only 21 points for the partial curve.
From: bemfarmer
Network of numerous circle curves, and numerous lineweb curves, perhaps 100+ each, makes a smooth looking lobe, without the "wrinkles".
So a .nod of lineweb will be helpful, so as to maintain ordering of the input circle curves. Reconstruct curve should be a good model(?) It may take a few days...
- Brian
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