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A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters :. Parametric representation is a very general way to specify a surface, as well as implicit representation .
In mathematics, and more specifically in geometry, 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. [1] "
In the case of two parameters, the point describes a surface, called a parametric surface. In all cases, the equations are collectively called a parametric representation , [ 2 ] or parametric system , [ 3 ] or parameterization (also spelled parametrization , parametrisation ) of the object.
The parameter domain is the surface that the mesh is mapped onto. Parameterization was mainly used for mapping textures to surfaces. Recently, it has become a powerful tool for many applications in mesh processing. [citation needed] Various techniques are developed for different types of parameter domains with different parameterization properties.
Parametrization (geometry), the process of finding parametric equations of a curve, surface, etc. Parametrization by arc length, a natural parametrization of a curve; Parameterization theorem or s mn theorem, a result in computability theory; Parametrization (atmospheric modeling), a method of approximating complex processes
The 3-dimensional surface volume of a 3-sphere of radius r is ... As a 3-dimensional manifold one should be able to parameterize S 3 by three coordinates, ...
Assume that f is a scalar, vector, or tensor field defined on a surface S.To find an explicit formula for the surface integral of f over S, we need to parameterize S by defining a system of curvilinear coordinates on S, like the latitude and longitude on a sphere.
The top of a car hood is an example of a surface open in both directions. Surfaces closed in one direction include a cylinder, cone, and hemisphere. Depending on the direction of travel, an observer on the surface may hit a boundary on such a surface or travel forever. Surfaces closed in both directions include a sphere and a torus.