A parametric surface is a 3-dimensional surface defined by a set of
parametric equations with two parameters. These equations map points
in some 2-dimensional space (the domain) to the
position vectors of the points on the 3-dimensional surface . This
parametric representation can be written:
The vectors , and are the basis
vectors
of the 3-dimensional space that the surface is embedded in. For
Cartesian coordinates in the normal Euclidean space these are the familiar X, Y and Z axes.
For example, the parametric representation of a cone is:
So the parametric equations are:
And the domain is:
And here it is (with limited to the interval -2 to +2):