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3.22. Hyperbolic Helicoid


The Hyperbolic Helicoid [ 6 ] is represented by the following equations.


x = sinh(v) cos(a u)/(1+cosh(u) cosh(v))



y = sinh(v) sin(a u)/(1+cosh(u) cosh(v))



z = cosh(v) sinh(u)/(1+cosh(u) cosh(v))


The constant a determines the appearance of the figure.

To represent the area, the two parameters u and v can assume the following values ​​(domain of definition), for example.


u is an element from the set of numbers [-4, 4]


v is an element from the number set [-4, 4]


The Hyperbolic Helicoid is an open figure, so the domain of definition can be changed in the plugin.

Fig. 26

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