Parametriset

Parametriset refers to objects, equations, or models that are defined by one or more parameters. A parameter is a variable whose value selects a particular member of a family of objects. Parametriset descriptions separate the description of a shape or distribution from its exact instantiation, enabling easy modification and systematic exploration of alternatives.

In mathematics, curves and surfaces are often given parametrically by functions such as x = f(t), y = g(t), and z = h(t). The parameter t ranges over an interval and maps to points in space. A circle can be described by x = r cos t and y = r sin t. Reparameterization changes the parameter without altering the geometric object itself, which can be useful for analysis or computation.

In statistics, a parametric model specifies a family of distributions characterized by a finite-dimensional parameter vector. Estimation aims to infer these parameters from data, using methods like maximum likelihood or Bayesian inference. Parametric models are efficient when the chosen form matches the data-generating process, but risk model misspecification if the form is incorrect; non-parametric approaches avoid fixed forms but require more data.

In design and engineering, parametric modelling uses parameters and constraints to define objects. Changing a parameter propagates through dependent features, enabling rapid design iterations and easy scenario testing. This approach is common in computer-aided design (CAD) and product development.

In computer graphics, parametric curves and surfaces underpin rendering and modeling. Techniques such as splines and NURBS describe shapes with control parameters, offering smooth, flexible representations.

See also: parametric equation, parameterization, parametric model.