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Re: kuen surface


Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote in message news:<c77tga$2pe$1 at smc.vnet.net>...
> Hi,
> http://mathworld.wolfram.com/KuenSurface.html
> Regards   Jens

> > bernazzani at mi.camcom.it wrote:
> > kindly I would want to know as the same graphics(kuen surface) is
> > constructed with Mathematica.

Some portions of Kuen surface in above Wolfram site do not show well.
Portions that ought to be negatively curved look conical, may be
improper limits of u,v parameters and/or too few PlotPoints chosen. In
http://www.zib.de/polthier/Calendar/Kalender88/February88_med.gif this
area is better depicted.
It appears even the 'classical' limits do not show the Kuen details
well enough .See detail due to extended u parameter curling it up
inside my plot:

x=2*(Cos[u]+u*Sin[u])*Sin[v]/(1+u*u*Sin[v]*Sin[v])
y=2*(Sin[u]-u*Cos[u])*Sin[v]/(1+u*u*Sin[v]*Sin[v])
z=Log[Tan[v/2]]+2*Cos[v]/(1+u*u*Sin[v]*Sin[v]) 
ParametricPlot3D[{x,y,z},{u,-3 Pi, Pi},{v,.2,2.9 },
PlotPoints->{37,15}]


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