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}}];