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3.28. Henneberg's Surface

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The Henneberg's surface [ 3,8,11 ] is represented by the following equations.

 

x = 2 cos(v) sinh(u) - 0.667 cos(3 v) sinh(3 u)

3-99

 

y = 2 sin(v) sinh(u) + 0.667 sin(3 v) sinh(3 u)

3-100

 

z = 2 cos(2v) cosh(2u)

3-101

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 [-1, 1]

 
 

v is an element from the number set [-pi/2, pi/2]

 

Henneberg's surface is a half-open figure, so the definition range of u can be changed with the plugin.


Fig. 32


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