Generally any point P( x ; y ; z ) of an area A (in space) can be defined by functions fx, fy and fz in the manner
x = fx(u,v) y = fy(u,v) z = fz(u,v) (1)
with parameters u and v within a determined domain. We call (1) parameter representation of the area A.
The lines (curves) onto the area A, which arise from u = const. (v variable) resp. v = const. (u variable), in planar theory are generally called parameter lines or especially v-lines resp. u-lines. The v-linies resp. u-linies span a parameter grid onto the area. We can say that the u- and v-linies correspond to the axes x = const. and y = const. of a Cartesian system of co-ordinates.
Example:
The parameter representation of an area is given with the example of the surface of the Earth (illustration from [3] under literature).
A point onto the Earth sphere can be determined by two parameters, the so called geographic longitude u and the geographic latitude v (see figure above). The equator is discribed by the u-line v = 0, the North Pole by v = / 2 and the South Pole by v = -
/ 2 .
Here we have to consider a kind of handicap of the parameter method: There is no unique geographic longitude u for the poles. Thus the poles are special points in the parameter grid. This is not caused by geometry because onto the sphere all points are equitable.