Parametrization, also spelled parameterization, parametrisation or parameterisation, is the process of defining or choosing parameters.

Why do we use parametrization?

This procedure is particularly effective for vector-valued functions of a single variable. We pick an interval in their domain, and these functions will map that interval into a curve. If the function is two or three-dimensional, we can easily plot these curves to visualize the behavior of the function.

What is parametrization of a curve?

A parametrization of a curve is a map r(t) = <x(t), y(t)> from a parameter interval R = [a, b] to the plane. The functions x(t), y(t) are called coordinate functions. ... As t varies, the end point of this vector moves along the curve. The parametrization contains more information about the curve then the curve alone.