Encyclopedia of Analytical Surfaces by S.N. Krivoshapko & V.N. Ivanov

Author:S.N. Krivoshapko & V.N. Ivanov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where

The generatrix circles coincide with coordinate lines v but they are not the lines of principle curvatures. In Fig. 1a, b, the surfaces with a law of changing of the radius of the generatrix circles written as R = R(u) = au are shown. The surface shown in Fig. 2 has R = R(u) = ae cu . In Fig. 3, the surface with generatrix circles R = R(u) = a(1 + c sin tu) is presented. Assuming a function of changing of the radius of generatrix circles R(u), one may construct the diversifying normal cyclic surfaces with the line of the centers in the form of a logarithmic spiral.

Fig. 2.

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