Grasshopper

algorithmic modeling for Rhino

Umbilic Torus

Trying to learn a bit about mathematical surfaces and how to build them in GH using the expression editor. This was a pretty interesting one I came across on the Internet of a form called an Umbilic Torus. It's like a Moebius Strip in that it only has one edge, but it is a 3D form.

This definition also puts to good use a method for creating tree data from a single list, a problem I had that I got some assistance on over on the old Google Group from David Rutten and others.




Umbilic_Torus.ghx

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Comment by Torolf Sauermann on June 11, 2009 at 9:29am
interesting! there are so many possibilities with
Grasshopper:)


something back to the world
---------------------------------------------------------------
X(): sin((v/1)-(13*v)) +- 3*sin((u/.25)+v)
Y(): cos(u)*((11+cos((v/1)-(13*v))+(2*cos((u/.25)+v))-v)-v)
Z(): sin(u)*((11+cos((v/1)-(13*v))+(2*cos((u/.25)+v))-v)-v)
[u]:-pi, pi
[v]:-pi, pi
------------------------------------------------------------

Cordially
Torolf
Comment by Tuan N. Tran on June 7, 2009 at 12:52am
thanks for sharing

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