Re: ParametricPlot3D with three parameters
- To: mathgroup at smc.vnet.net
- Subject: [mg108272] Re: ParametricPlot3D with three parameters
- From: Narasimham <mathma18 at hotmail.com>
- Date: Fri, 12 Mar 2010 07:10:47 -0500 (EST)
- References: <hnakg8$5o2$1@smc.vnet.net> <hnankc$977$1@smc.vnet.net>
On Mar 11, 5:27 pm, dh <d... at metrohm.com> wrote:
> 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:d... at metrohm.com>
> Internet:<http://www.metrohm.com>
Thanks.. I want to see the projecting out surfaces rather than the
enveloping space. If u = const and v = constant are latitude and
longitude lines on the globe, we get a finned cage or curved grill
over the globe consisting of two Gitter sets, one rib surface running
for u = const and w = constant as longitudes, where ribs stick
normally out of the spherical surface and another surface as v = const
and w = constant providing latitude fins/ribs.
I expected that may be only a couple of lines only need to be added in
the central part (without Options) in the Mathematica code for
ParametricPlot3D.
I see no reason why if ListPlot3D etc. can give the points in a Table
for three parameter surface embeddings in 3-space, then they cannot be
plotted in a proper desired sequence.
Erroneous usage of 'hyper space ' was partly deliberate, as I do not
know of the proper conceptually continuing word in mathematics for
Line, Surface, ... Next ??
Regards,
Narasimham