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From: Narasimham on 11 Mar 2010 06:34
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

From: dh on 11 Mar 2010 07:27
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(a)metrohm.com>
Internet:<http://www.metrohm.com>


From: Narasimham on 12 Mar 2010 07:10
On Mar 11, 5:27 pm, dh <d...(a)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...(a)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





From: Narasimham on 12 Mar 2010 07:11
contd..

This following Do command does not work on my PC.

(* from http://mathmuse.sci.ibaraki.ac.jp/geom/param20E.html *)

Do[Plot3D[10 Sin[Sqrt[n x^2/10+n y^2/10]-Pi n/2]/(n+1),{x,-20,20},
{y,-20,20},AspectRatio=EF=82=AEAutomatic,Mesh=EF=82=AEFalse,PlotRange-
>{-10,10},PlotPoints->50,Boxed->False,Axes->None],{n,0,9}]

Here neither Do command nor avoiding original shading of (u,v)
sphere succeeded.

Do[ ParametricPlot3D[ R {Cos[ u ] Cos[v], - Cos[u] Sin[v],Sin[u]}, {u,
0, 1.5}, {v, 0, Pi},PlotStyle->White ], {R, 1, 1.4,0.1} ] does not
work.

Narasimham






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