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3.22. Hyperbolic Helicoid

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

 

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

3-80

 

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

3-81

 

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

3-82

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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