Plane in 3D

What this variable type does is to define a two dimensional coordinate system in a plane. To do that you need an origin O and two orthonormal vectors u and v.  Any point in the plane can be written as O + a· u + b· v, and corresponds to the coordinate (a,b).

Instead of viewing the plane in terms of u and v, it is viewed in terms of the normal and the up vector.  The up vector is the same as the v vector since that vector corresponds to the coordinate (0,1), but the normal is a more natural way to view a plane and the u vector can be computed by the normal and v by the cross product of v and n.