Parametrisierter

Parametrisierter is a German adjective describing something that has been described or defined through a parameterization. It is used mainly in technical contexts such as mathematics, computer graphics, CAD, and modeling, where a shape, curve, or system is expressed by parameters rather than fixed coordinates alone.

In mathematics and geometry, a parametrisierter curve, surface or solid is given by a parameterization function X of one or more parameters. For example, a planar curve can be written as x = x(t), y = y(t) with t in an interval, while a surface may be described by X(u,v) = (x(u,v), y(u,v), z(u,v)) for (u,v) in a parameter domain. The parameterization provides a compact representation and facilitates differentiation, integration, and transformations.

In computer graphics and CAD, parametrisierte Modelle rely on design parameters such as dimensions, angles, or control points. Adjusting these parameters yields a family of related shapes, enabling parametric modeling, constraints, and procedural generation. Parametrisierte Baugruppen allow coordinated changes across components when a shared parameter is modified.

In statistics and mathematical modelling, a parametrisertes Modell uses a parameter vector θ to specify its behavior. Fitting such a model involves estimating θ from data.

Etymology and usage notes: parametrisierter derives from parameterisieren (to parameterize) and Parameterisierung (parameterization). The term emphasizes the state of being defined by parameters, in contrast to a non-parameterized or purely fixed representation.