Torus coordinates are coordinates for identifying a location
relative to a torus.
Such coordinates, for example, can be used by models
of a torus-shaped magnetic fields.
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 center of the circle and the point being specified.
poloidal coordinate: angle between two lines that meet at the circle's point that has same toroidal coordinate as the point being specified, specifically the line through the point being specified and the line through the center of the circle.
radial coordinate: distance between the point being specified and the circle's point that has the same toroidal coordinate as the point being specified.
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 (180 degrees apart), but the two points'
other two coordinates are identical: their poloidal coordinate is
that totally opposite of the hole (also 180 degrees), and their
radial coordinate is maximal, i.e., indicating the surface of the
torus.