Conformal Mapping to the Torus

 From:  bemfarmer
9223.7 In reply to 9223.6 
Hi Al,

I'll do some more work on the ConformalMapT node.
Add point mapping.
Add poloidal circle of radius r, with center at (r,0). associated with angle theta.
Add toroidal circle of radius R, with center at (0,0). associated with angle phi.

The two circle outputs could then be swept, to yield the torus surface.

T is associated with circumference of T units, and r and v and theta. (2PI*r = T) (edit, this statement is FALSE)
S is associated with circumference of S units, and R and u and theta. (2PI*R = S) (FALSE statement)
(The div divider in the conformal mapping reduces the size of the Torus...)

Note that input of integer 2 to the Columns input of the FlatHexGrid macro, will map only two columns.
The rest of the columns can then be created by circular array.


I've attempted to write (by equation change) a NonConformalMapT, but after several corrections, have only created an ellipsoid (M&M candy),
not a Torus :-( , which shows some incorrect thinking...
OK, fixed. It helps to put the parenthesis in the correct locations.

Your .nod is crashing my computer. I'll try some examination and earlier outputs...

Rebuild with tolerance of .001 may be helpful...

- Brian

( I see that you are making some smaller/offset hexagons. Probably the goal is to make the hex curves into 3D bars, with square cross section.)
(I have not had much luck sweeping circles along the curves.)

EDITED: 27 Jan 2019 by BEMFARMER