Parametrin

Parametrin is a noun used in some languages to denote the process or result of parameterization—the representation of an object, model, or system in terms of parameters. In English, the term is not common; the corresponding terms are parameterization or parametrization. In languages such as Swedish or Norwegian, parametrin is used to refer to either the parameter vector or the parameterization itself.

In mathematics, a parametrization is a function that assigns to each parameter value a point of a geometric object. The word parametrin may refer to either the mapping itself or to the parameters that define it. For example, a plane curve in the plane can be described by a curve r(t) = (x(t), y(t)) parametrized by a parameter t, which traces the curve as t varies.

In higher dimensions, a surface or manifold can be parameterized by two or more parameters, using a map S(u, v) → R^3. In physics, computer graphics, and statistics, parameterizations are used to express complex models in a manageable form, with the parameter values or the parameterization guiding simulations, rendering, or inference.

See also: Parameterization, Parametric equations, Parametric model, Parameter vector.