Parameterization

Parametrization (or parameterization; also parameterisation, parametrisation) is the process of deciding and defining the parameters necessary for a complete or relevant specification of a model or geometric object.

Parametrization is also the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization.

Sometimes, this may only involve identifying certain parameters or variables. If, for example, the model is of a wind turbine with a particular interest in the efficiency of power generation, then the parameters of interest will probably include the number, length and pitch of the blades.

Most often, parametrization is a mathematical process involving the identification of a complete set of effective coordinates or degrees of freedom of the system, process or model, deemed to be relevant to some design goal. Parametrization of a line, surface or volume, for example, implies identification of a set of coordinates that allows one to uniquely identify any point (on the line, surface, or volume) with an ordered list of numbers. Each of the coordinates can be defined parametrically in the form of a parametric curve (one-dimensional) or a parametric equation (2+ dimensions).

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