Examples

The simplest blazon of parametric surfaces is accustomed by the graphs of functions of two variables:

Surfaces of anarchy accord addition important chic of surfaces that can be calmly parametrized. If the blueprint z = f(x), a ≤ x ≤ b is rotated about the z-axis again the consistent apparent has a parametrization

The beeline annular butt of ambit R about x-axis has the afterward parametric representation:

Using the all-around coordinates, the assemblage apple can be parameterized by

This parametrization break down at the arctic and south poles area the arctic bend θ is not bent uniquely.

The aforementioned apparent admits abounding altered parametrizations. For example, the alike z-plane can be parametrized as

for any constants a, b, c, d such that ad − bc ≠ 0, i.e. the cast is invertible.