3.51. Kuen's Surface


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)



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



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



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


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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