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3.51. Kuen's Surface

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The Kuen's Surface [ 2,7,11 ] is represented by the following equations. To keep the formulas a little clearer, we use the constant h.

 

h = 1 + u 2 sin(v) sin(v)

3-168

 

x = (2 (cos(u) + u sin(u)) sin(v))/h

3-169

 

y = (2 (-u cos(u) + sin(u)) sin(v))/h

3-170

 

z = log(tan(v/2)) + 2 cos(v)/h

3-171

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 [-4.3, 4.3]

 
 

v is an element of the number set [0.03, 3.11]

 

The Kuen's Surface is an open figure, so the definition range can be changed with the plugin.


Fig. 55


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