torus coordinates

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:

• toroidal coordinate: an angle "around the circle", between the axis and a plane normal to the circle's plane that includes both the location/point and the center of the circle.
• poloidal coordinate: angle between two lines that meet at the circle's point that has same toroidal coordinate as the location, specifically the line through the location itself and the line through the center of the circle.
• radial coordinate: distance between the location and the circle's point that has the same toroidal coordinate as the location.

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.