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RE: Re: kuen surface

• To: mathgroup at smc.vnet.net
• Subject: [mg48068] RE: [mg48055] Re: kuen surface
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Mon, 10 May 2004 06:51:25 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com
• Thread-topic: [mg48055] Re: kuen surface

>-----Original Message-----
>From: Narasimham G.L. [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net
>Sent: Sunday, May 09, 2004 9:02 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg48068] [mg48055] 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}]
>
>

Yes, a single view is not enough to look at this marvelleous thing. Perhaps you like to scan the archive for Smooth3D (http://forums.wolfram.com/mathgroup/archive/2001/May/msg00291.html) and then try

In[11]:= << Smooth3D`
In[16]:=
Smooth3D[ParametricPlot3D[{x, y, z}, {u, -3 Pi, 0}, {v, .2, 2.9}, 
    PlotPoints -> {37, 15}], Smoothing -> 5]

In[17]:= Show[%, ViewPoint -> {1.3, 2.4, 2.}]

In[18]:=
Smooth3D[ParametricPlot3D[{x, y, z}, {u, -3 Pi, Pi}, {v, .2, 2.9}, 
    PlotPoints -> {37, 15}], ViewPoint -> {1.3, 2.4, 2.}, Smoothing -> 5,
    ImageSize -> 800]

(* in case you forgot to pull it large *)


Another (simple) idea would be to display only parts from the surface patches:

In[34]:=
Block[{$DisplayFunction}, 
  ParametricPlot3D[{x, y, z, EdgeForm[]}, {u, - 4.5, 4.5}, {v, .015, 3.12}, 
      PlotPoints -> 75] /. Polygon[pts_] :> Polygon[Rest[pts]]]


or show only the wires:

In[45]:=
Block[{$DisplayFunction}, 
  Smooth3D[ParametricPlot3D[{x, y, z}, {u, - 4.5, 4.5}, {v, .015, 3.12}, 
        PlotPoints -> 75], Smoothing -> 3] /. Polygon[pts_] -> {}]


But as you see the real problem is to find a better parametrisation for calculation of the graphics.

(Possibly it is enought to draw several parts and patch them together e.g. with David Park's DrawGraphics package, see http://home.earthlink.net/~djmp/





--
Hartmut Wolf