Let X(u, v) be a parametric surface.

In addition, other common parametric surfaces such as spheres and cylinders can be well approximated by relatively small numbers of cubic Bézier patches.

The second fundamental form of a general parametric surface is defined as follows.

The simplest type of parametric surfaces is given by the graphs of functions of two variables:

The local shape of a parametric surface can be analyzed by considering the Taylor expansion of the function that parametrizes it.

For a general parametric surface, the definition is more complicated, but the second fundamental form depends only on the partial derivatives of order one and two.

Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces.

The image of a continuous, injective function from R to higher-dimensional R is said to be a parametric surface.

A parametric surface need not be a topological surface.

A surface of revolution can be viewed as a special kind of parametric surface.