parameteriserade

Parameteriserade is a Swedish term meaning expressed or defined in terms of parameters. The word derives from parameterisera and its past participle parameteriserad, and it is used to describe objects, models or equations that are specified by one or more parameters rather than fixed constants. In practice, a parameteriserad form can be manipulated by adjusting the parameter values.

In mathematics and geometry, a parameteriserad object is described by functions of one or more parameters. A parameteriserad curve, for example, is given by x = x(t), y = y(t), possibly z = z(t); a parameteriserad surface uses two parameters (u, v). This representation enables smooth variation, sampling, and easy deformation of the object as parameters change.

In statistics and modeling, a parameteriserad model expresses the data-generating process in terms of unknown quantities called parameters. Estimation, inference, and prediction focus on determining parameter values from data, assessing model fit, and exploring how changes in parameters affect outcomes.

In computer-aided design and computer graphics, parameteriserad geometry is controlled by parameters. Changing a small set of parameters can alter size, shape, or topology without re-creating the object, enabling design exploration, automation, and generative modeling. Common schemes include splines, polynomials, and NURBS-based parameterizations.

While many objects can be parameteriserad, others are defined explicitly or discretely. The choice of parameterization influences ease of analysis, numerical stability, and interpretability, and different parameterizations may be more suitable for different tasks or optimizations.