Surface of Revolution


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surface of revolution

[¦sər·fəs əv ‚rev·ə′lü·shən]
(mathematics)
A surface realized by rotating a planar curve about some axis in its plane.

Surface of Revolution

 

a surface that can be generated by revolving a plane curve about a straight line, called the axis of the surface of revolution, lying in the plane of the curve. An example of such a surface is the sphere, which may be considered as the surface generated when a semicircle is revolved about its diameter. The curves formed by the intersection of a surface of revolution with planes passing through the axis are called meridians, and the curves of intersection of a surface of revolution with planes perpendicular to the axis are called parallels. If the z-axis of a rectangular system of coordinates x, y, and z is directed along the axis of a surface of revolution, then the parametric equations of the surface of revolution can be written

x = f(u] cos v y = f {u} sin v z = u

where f(u) is a function that determines the shape of the meridian and v is the angle of rotation of the plane of the meridian.

References in periodicals archive ?
Since a circle may be exactly represented by T-B-spline curve, we may find an exact representation of a surface of revolution provided we can represent r(v), z(v) in T-B-spline curve form.
The most convenient way to define a surface of revolution is to prescribe the (planar) generating curve, or generatrix, given by g(v) = [(r(v), 0, z(v)).
Let S be the surface of revolution in the Euclidean space [E.
Therefore all the parallels of the surface of revolution S are geodesies and so x is constant, and S is a cylinder.
1] and does represent the area of the surface of revolution in question.
Typical applications include 2- and 3-D contours, ruled, swept and lofted surface, surface of revolution, projections of arbitrary surfaces and intersections of surfaces.