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波希米亚圆形[Bohemian Dome]

   ∑〖数学〗2005-1-12 12:59

A quartic surface which can be constructed as follows. Given a circle C and plane E perpendicular to the plane of C, move a second circle K of the same radius as C through space so that its center always lies on C and it remains parallel to E. Then K sweeps out the Bohemian dome. It can be given by the parametric equations
(1)

(2)

(3)

where . In the above plot, ,, and c = 1.
The Gaussian curvature and mean curvature of the surface are given by
(4)

(5)
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