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Full Version: Conformal Mapping to the Torus

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From: bemfarmer
27 Feb 2019   [#43] In reply to [#42]
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
3 Mar 2019   [#44]
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
5 Mar 2019   [#45]
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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