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torus coordinates

(coordinates for toruses)

Torus coordinates are coordinates for identifying a location relative to a torus. Various systems have been invented; a common version defines coordinates in relation to a circle that encircles the torus's hole (presumably buried within the torus) and an axis from the circle's center to a point on the circle:

Such coordinates can be used for torus-shaped magnetic fields.

For example, given two points on a regular torus that have a maximum distance between each other (which could be used to hold a doughnut with two fingers), their toroidal coordinates are as far from each other as possible, but the two points' other two coordinates are identical: their poloidal coordinate is that totally opposite of the hole, and their radial coordinate is maximal, i.e., indicating the surface of the torus.


(geometry,measure,magnetism,coordinates)
Further reading:
https://en.wikipedia.org/wiki/Toroidal_and_poloidal
http://fusionwiki.ciemat.es/wiki/Toroidal_coordinates
https://www2.warwick.ac.uk/fac/sci/physics/research/cfsa/people/hnat/present/miraw_day_2009_v3.pdf

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