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parameterize

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Definitions of parameterize in various dictionaries:

PARAMETERIZE - Parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, o...

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Possible Dictionary Clues
To describe in terms of parameters.

Parameterize might refer to
Parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. "To parameterize" by itself means "to express in terms of parameters".Parametrization is a mathematical process consisting of expressing the state of a system, process or model as a function of some independent quantities called parameters. The state of the system is generally determined by a finite set of coordinates, and the parametrisation consists thus of one function of several real variables for each coordinate. The number of parameters is the number of degrees of freedom of the system. * For example, the position of a point that moves on a curve in the three-dimensional space is determined by the time needed to reach the point when starting from a fixed origin. If x, y, z are the coordinates of the point, the movement is thus described by a parametric equation * * * * * * * * x * * * * = * f * ( * t * ) * * * * * y * * * * = * g * ( * t * ) * * * * * z * * * * = * h * ( * t * ) * , * * * * * * * {\displaystyle {\begin{aligned}x&=f(t)\\y&=g(t)\\z&=h(t),\end{aligned}}} * where t denotes the time. Such a parametric equation determines completely the curve, without the need of any interpretation of t as a time, and is thus called a parametric equation of the curve (this is sometimes abbreviated by saying that one has a parametric curve). One gets similarly the parametric equation of a surface by considering functions of two parameters t and u.

Parameterize might refer to

Parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. "To parameterize" by itself means "to express in terms of parameters".Parametrization is a mathematical process consisting of expressing the state of a system, process or model as a function of some independent quantities called parameters. The state of the system is generally determined by a finite set of coordinates, and the parametrisation consists thus of one function of several real variables for each coordinate. The number of parameters is the number of degrees of freedom of the system.
* For example, the position of a point that moves on a curve in the three-dimensional space is determined by the time needed to reach the point when starting from a fixed origin. If x, y, z are the coordinates of the point, the movement is thus described by a parametric equation *
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* {\displaystyle {\begin{aligned}x&=f(t)\\y&=g(t)\\z&=h(t),\end{aligned}}}
* where t denotes the time. Such a parametric equation determines completely the curve, without the need of any interpretation of t as a time, and is thus called a parametric equation of the curve (this is sometimes abbreviated by saying that one has a parametric curve). One gets similarly the parametric equation of a surface by considering functions of two parameters t and u.

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