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 ?
The only spacelike or timelike surfaces of revolution in R3 whose Gauss map G: M [right arrow] [M.sup.2]([epsilon]) satisfies (2) are locally the following spaces:
The main purpose of this note is to complete classification of surfaces of revolution in [R.sup.3.sub.1] whose Gauss map satisfies the condition [[DELTA].sup.h]G = [LAMBDA]G.
From this we obtain four kinds of surfaces of revolution in [R.sup.3.sub.1].
Generally, it may be concluded that for the Herschel-Bulkley ERF flows in the clearance between two surfaces of revolution the pressure values
Walicka, "Pressure distribution in a squeeze film of a Shulman fluid between surfaces of revolution," International Journal of Engineering Science, vol.
17 and 16 depict the minimal axes of revolution and minimum surfaces of revolution for the values m = -1, m = 0, and m =1.
We should point out that depending on the complexity of the function or parametric curve and the length of the interval [a, b], it may not be feasible to determine the minimum surfaces of revolution due to the rather demanding computational requirements; but it is feasible to do so for many problems of interest.
Then we classify rational rotation hypersurfaces of [L.sup.n+1] with pointwise 1-type Gauss map which extend the results given in [13] on rational surfaces of revolution in [L.sup.3] to the hypersurfaces of [L.sup.n+1].
On classification of some surfaces of revolution of finite type.
Surfaces of revolution with pointwise 1-type Gauss map.
The new design methodology BladeCAD was motivated by the need to define and modify blade sections within general surfaces of revolution while it provides intuitive interactivity Direct definition and modification of a three-dimensional space curve, which characterizes both the shape of the blade section and the stream surface, would be extremely difficult.
The 3-D capability will allow the analysis to handle the contact of deformable bodies idealized as curved shells and brick elements, and of rigid bodies modeled as flat patches, ruled surfaces, surfaces of revolution, or Bezier surfaces.