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. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem and the divergence theorem, are frequently given in a parametric form. The curvature and arc length of curves on the surface, surface area, differential geometric invariants such as the first and second fundamental forms, Gaussian, mean, and principal curvatures can all be computed from a given parametrization.
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A parametricsurface is a surface in the Euclidean space R 3 {\displaystyle \mathbb {R} ^{3}} which is defined by a parametric equation with two parameters...
curve or surface, called a parametric curve and parametricsurface, respectively. In such cases, the equations are collectively called a parametric representation...
whose parameters oscillate in time Parametricsurface, a particular type of surface in the Euclidean space R3 Parametric family, a family of objects whose...
Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametricsurfaces. This definition of surface area is based...
offers an increased surface area for analytes to bind to the inner lining of the fiber optic. Hydrogen sensor Multi-parametricsurface plasmon resonance...
2D orthographic views, finite element analysis, parametric modeling, sub-divisional and NURBS surface modeling, Drafting, and NC and tooling functionality...
used for checking optically the smoothness of surface connections. For a surface (implicit or parametric), which is differentiable enough, the normal vector...
second fundamental form of a parametricsurface S in R3 was introduced and studied by Gauss. First suppose that the surface is the graph of a twice continuously...
can be seen in the Figure. The formation is measured using multi-parametricsurface plasmon resonance to determine adsorption kinetics, layer thickness...
Parametric design is a design method in which features, such as building elements and engineering components, are shaped based on algorithmic processes...
transmission Free electron model Gap surface plasmon Heat-assisted magnetic recording Multi-parametricsurface plasmon resonance Plasma oscillation Plasmonic...
represented in two ways as the envelope of a one parametric pencil of spheres, i.e. it is a canal surface with two directrices. The pair of directrices are...
solid–liquid, and liquid–gas surfaces. Multi-parametricsurface plasmon resonance works in solid–gas, solid–liquid, liquid–gas surfaces and can detect even sub-nanometer...
(1950–2016). Parametricism has its origin in parametric design, which is based on the constraints in a parametric equation. Parametricism relies on programs...
investigations of curved surfaces) considered a surfaceparametrically, with the Cartesian coordinates x, y, and z of points on the surface depending on two auxiliary...
OpenVSP, also known as Open Vehicle Sketch Pad, is an open source parametric aircraft geometry tool originally developed by NASA. It can be used to create...
dy.} An even more general formula for the area of the graph of a parametricsurface in the vector form r = r ( u , v ) , {\displaystyle \mathbf {r} =\mathbf...
binding to receptors (i.e. a substrate binding to an enzyme). Multi-parametricsurface plasmon resonance can be used not only to measure molecular interactions...
instruments here are parametric curves and parametricsurfaces, such as Bézier curves, spline curves and surfaces. An important non-parametric approach is the...
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