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Re: ParametricPlot3D with three parameters

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108249] Re: ParametricPlot3D with three parameters
  • From: dh <dh at metrohm.com>
  • Date: Thu, 11 Mar 2010 07:27:24 -0500 (EST)
  • References: <hnakg8$5o2$1@smc.vnet.net>

Hi Narasimham,
what you want to plot is not a hypersurface but a region in 3D space. 
You could plot the enlosing surfaces, but this is laborious . The 
easiest way to do this is: "RegionPlot3D"  like e.g.:

RegionPlot3D[1 < x^2 + y^2 + z^2 < 2, {x, 0, 2}, {y, 0, 2}, {z, 0, 2}]

Daniel


On 11.03.2010 12:34, Narasimham wrote:
> Clear[t,ph];
> R=1; ph = Pi/8 ;
> line=R{Cos[ph]Cos[t], Cos[ph]Sin[t] ,Sin[ph]};
> Lati=ParametricPlot3D[line,{t,0,Pi}]
> surf=Table[R{Cos[ph]Cos[t], Cos[ph]Sin[t] ,Sin[ph]}, {ph,0,1.3,.12},{t,
> 0,Pi,Pi/16.}];
> Needs["Graphics`Graphics3D`"];
> sph=ListSurfacePlot3D[surf]
> Show[{Lati,sph},PlotRange->All]
> hypsurf=Table[R{ Cos[ph]Cos[t], Cos[ph]Sin[t] ,Sin[ph]}, {ph,
> 0,1.3,.12},{t,0,Pi,Pi/16.},{R,1,1.15,0.05}] ;
> hy=ListSurfacePlot3D[hypsurf]
> Show[{Lati,sph,hy},PlotRange->All]
> " The ParametricPlot3D accepts  coords in 3 D by one set of
> independent parameters to form lines in space,
> two sets of independent parameters for surfaces in space, but not
> three  sets of parameters for hypersurfaces in space.How to form
> concentric spherical surfaces here, like onion layers? I am attempting
> to form coordinate sets from _three_  parameters.
> ListSurfacePlot3D is reverted to here as there is at present  no
> command like
> ParameterPlot3D[ f{u,v,w},g{u,v,w},h{u,v,w},{u,u1,u2},{v,v1,v2},
> {w,w1,w2}] in Mathematica. I feel or would like to suggest that this
> last command if made available in Mathematica would be great for solid
> modelling  and hyperspaces, no matter large volume of layered data. "
> Table[R{ Cos[ph]Cos[t], Cos[ph]Sin[t] ,Sin[ph]}, {ph,0,1.3,.12},{t,
> 0,Pi,Pi/16.},{R,1,1.15,0.05}];
> ListSurfacePlot3D[%, PlotLabel->" How to Remove curly brackets?"]
>
> Best Regards
> Narasimham
>


-- 

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>



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