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
