Tangent Plane


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tangent plane

[′tan·jənt ′plān]
(mathematics)
The tangent plane to a surface at a point is the plane having every line in it tangent to some curve on the surface at that point.

Tangent Plane

 

The tangent plane to a surface S at a point M is the plane that passes through the point M and that is characterized by the property that the distance from this plane to the variable point M’ on the surface S is infinitesimal in comparison with the distance MM’ as M ’ approaches M. If a surface S has the equation z = f(x, y), then the equation of the tangent plane at the point (x0, y0, z0), where z0 = f(x0, y0), has the form

z − z0 = A(x - x0) + B(y - y0)

if and only if the function f(x, y) has a total differential at thepoint (x0, y0). In this case, A and B are the values of the partialderivatives ∂f/∂x and ∂f/∂x at the point (x0y0) (seeDIFFER-ENTIAL CALCULUS).

References in periodicals archive ?
The tangent plane at any point in the equatorial plane is parallel to the x-axis so the d[p.
epsilon]] in the local tangent plane to the surface.
As shown in Figure 9, the local Cartesian coordinate systems are different since they are established in different tangent planes to the curved element surface.
3] is a surface whose tangent planes make a constant angle with a fixed constant vector field of the ambient space [1, 9].
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Using a reflectance model based on the distribution of normals to local tangent planes on the surface, a BRDF was constructed from surface topographical measurements.
The tangent plane at a point P [member of] M on a curve is denoted by [T.
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2], there are other points where the tangent plane is horizontal, for example the origin in the saddle-shaped graph of f(x,y) = [x.
For a differentiable function there is a well-defined tangent plane at each point of the graph and an upward-pointing normal perpendicular to that plane.
If z'(s) = 0, the tangent vector [delta]X/[delta]s is horizontal, and geometrically, it says that the tangent plane to S at [alpha](s) is horizontal.
4 Parabolic surfaces with a horizontal tangent plane