Parameterise

Parameterise is a verb used in mathematics, science, and computing to describe expressing something in terms of parameters, or to introduce parameters into a model, equation, or description. The common aim is to replace fixed constants with variables that can vary to describe a family of objects or behaviors.

In mathematics, to parameterise a geometric object means to describe its points as functions of one or more parameters. A curve, for example, can be written as x(t), y(t) for a parameter t. As t traverses an interval, the corresponding (x(t), y(t)) traces the curve. The circle, x = cos t and y = sin t with t in [0, 2π), is a classic parameterisation. Parameterisation also extends to surfaces and higher-dimensional manifolds, using two or more parameters.

In computing and data analysis, parameterising refers to replacing fixed values with input parameters to increase flexibility and reuse. Programs, functions, and models become adaptable to different data or conditions. Parameterised tests run the same test logic with multiple input sets. In statistics and machine learning, reparameterisation or parameterisation can improve identifiability, numerical stability, or sampling efficiency by transforming parameters into a more convenient space.

Applications span physics, engineering, computer graphics, and optimization, where parameterisations enable interpolation, animation, curve fitting, and scalable modeling. Care is needed to ensure the parameter domain covers the intended objects and that the parameterisation is appropriate for analysis or computation.

See also: parametric, parameterization, parametric equation, parametric curve.