Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Sterographic plotting program

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51250] Re: Sterographic plotting program
  • From: mathma18 at hotmail.com (Narasimham G.L.)
  • Date: Sun, 10 Oct 2004 01:57:24 -0400 (EDT)
  • References: <cjtnf7$8gv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Roger Mason <rmason at esd.mun.ca> wrote in message news:<cjtnf7$8gv$1 at smc.vnet.net>...
> Has anyone implemented a program to plot stereograms in Mathematica?
> Stereograms are used in crystallography to plot the positions of faces
> (and other planes) on crystals.[1]

In the following, Loxodromes making +/- 30 Degree to any meridian are
stereographically projected onto plane tangential to South Pole as
equi-angular/Logarithmic spirals. Please add 4 or 6 Loxos around polar
axis to get a full pattern. (Avoided it, as it may clutter up the
graphic). I remember a beautiful picturization similar to this in
'Mathographics' by Dixon Robert. A.,
New York, Dover, 1991.

Hope you get stereographic projections of icosa & dodecahedrons to
show, as precursors to crystallography..

Cheers,
Narasimham

a = 1; al = Pi/6; z = a*Tanh[Cot[al]*th]; r = a*Sech[Cot[al]*th];
x = r*Cos[th]; y = r*Sin[th];
loxo1 = ParametricPlot3D[{x, y, 
        z, {RGBColor[1, 0, 0], Thickness[.005]}}, {th, -Pi, Pi}];
loxo2 = ParametricPlot3D[{x, -y, 
        z, {RGBColor[0, 0, 1], Thickness[.005]}}, {th, -Pi, Pi}];
sphere = ParametricPlot3D[{a  Cos[u] Cos[v], a Cos[u]Sin[v], 
        a Sin[u]}, {u, -1.5, 1.5}, {v, -Pi, Pi}, Shading -> False];
rst = 2 a r/(a - z); xst = rst*Cos[th]; yst = rst*Sin[th];
stereo1 = 
    ParametricPlot3D[{xst,  
        yst, -a, {RGBColor[1, 0, 0], Thickness[.006]}}, {th, -Pi,
Pi}];
stereo2 = 
    ParametricPlot3D[{xst, -yst, -a, {RGBColor[0, 0, 1], 
          Thickness[.005]}}, {th, -Pi, Pi}];
Show[{sphere, loxo1, loxo2, stereo1, stereo2}, ViewPoint -> {1.5, -1,
1},
    Boxed -> False, PlotRange -> {{-3, 3}, {-3, 3}, {-1.01, 1}}];


  • Prev by Date: Re: Need Help: 1st order nonlinear differential equation
  • Next by Date: Re: Re: Constraints to parameters in FindFit?
  • Previous by thread: Sterographic plotting program
  • Next by thread: Re: Sterographic plotting program