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Re: Sterographic plotting program

Roger Mason <rmason at> wrote in message news:<cjtnf7$8gv$1 at>...
> 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..


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 = 
        yst, -a, {RGBColor[1, 0, 0], Thickness[.006]}}, {th, -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,
    Boxed -> False, PlotRange -> {{-3, 3}, {-3, 3}, {-1.01, 1}}];

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