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Parametrization (or parameterization; also parameterisation, parametrisation) is the process of deciding and defining the parameters necessary for a complete or relevant specification of a model or geometric object. Parametrization is also 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. Sometimes, this may only involve identifying certain parameters or variables. If, for example, the model is of a wind turbine with a particular interest in the efficiency of power generation, then the parameters of interest will probably include the number, length and pitch of the blades. Most often, parametrization is a mathematical process involving the identification of a complete set of effective coordinates or degrees of freedom of the system, process or model, without regard to their utility in some design. Parametrization of a line, surface or volume, for example, implies identification of a set of coordinates that allows one to uniquely identify any point (on the line, surface, or volume) with an ordered list of numbers. Each of the coordinates can be defined parametrically in the form of a parametric curve (one-dimensional) or a parametric equation (2+ dimensions). == Non-uniqueness == Parametrizations are not generally unique. The ordinary three-dimensional object can be parametrized (or 'coordinatized') equally efficiently with Cartesian coordinates (x,y,z), cylindrical polar coordinates (ρ, φ, z), spherical coordinates (r,φ,θ) or other coordinate systems. Similarly, the color space of human trichromatic color vision can be parametrized in terms of the three colors red, green and blue, RGB, or with cyan, magenta, yellow and black, CMYK. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「parametrization」の詳細全文を読む スポンサード リンク
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