% This Filename:  example-cs.mp   [MetaPost source]
% Creation time:  Fri Dec 16 19:30:10 2011
%
% Copyright (C) 1997-2005, Fredrik Jonsson <fj@optics.kth.se>
%
% Input Filename [Stokes parameters]:  example-cs.dat
% This MetaPost source code was automatically generated by poincare
% Full set of command line options that generated this code:
%     --verbose --normalize --bezier --inputfile example-cs.dat --outputfile
%     example-cs.mp --axislengths 0.3 1.7 0.3 2.4
%     0.3 1.5 --axislabels s_1(t) bot s_2(t)
%     bot s_3(t) urt --rotatephi 15.0 --rotatepsi
%     -60.0 --shading 0.75 0.99 --rhodivisor 50
%     --phidivisor 80 --scalefactor 20.0 --paththickness 0.8
%     --arrowthickness 0.4 --arrowheadangle 20.0 --draw_paths_as_arrows
%
% Description:  Map of Stokes parameters, visualized as trajectories
%               onto the Poincare sphere. This file contains MetaPost
%               source code, to be compiled with John Hobby's MetaPost
%               compiler or used with anything that understands MetaPost
%               source code.
%
% If you want to create PostScript output, or include the resulting
% output in a TeX document, this example illustrates the procedure,
% assuming 'poincaremap.mp' to be the name of the file containing the
% MetaPost code to be visualized: (commands run on command-line)
%
%       mp poincaremap.mp;
%       echo "\input epsf\centerline{\epsfbox{poincaremap.1}}\bye" > tmp.tex;
%       tex tmp.tex;
%       dvips tmp.dvi -o poincaremap.ps;
%
% Here, the first command compiles the MetaPost source code, and leaves
% an Encapsulated PostScript file named 'poincaremap.1', containing TeX
% control codes for characters, etc. This file does not contain any
% definitions for characters or TeX-specific items, and it cannot be
% viewed or printed simply as is stands; it must rather be included into
% TeX code in order to provide something useful.
%     The second command creates a temporary minimal TeX-file 'tmp.tex',
% that only includes the previously generated Encapsulated PostScript
% code.
%     The third command compiles the TeX-code into device-independent,
% or DVI, output, stored in the file 'tmp.dvi'.
%     Finally, the last command converts the DVI output into a free-
% standing PostScript file 'poincaremap.ps', to be printed or viewed
% with some PostScript viewer, such as GhostView.
%
scalefactor := 20.000000 mm;
rot_psi := -60.000000;  % Rotation angle round z-axis (first rotation)
rot_phi := 15.000000;  % Rotation angle round y-axis (second rotation)
alpha := -24.146108;    % == arctan(sin(rot_phi)*tan(rot_psi))
beta  := -8.498781;    % == arctan(sin(rot_phi)/tan(rot_psi))

%
% Parameters specifying the location of the light source; for Phong
% shading of the sphere.
%
%    phi_source:  Angle (in deg.) to light source counterclockwise
%                 'from three o'clock', viewed from the observer.
%
%  theta_source:  Angle (in deg.) between light source and observer,
%                 seen from the centre of the sphere.
%
% Parameters specifying the shading 'intensity' in terms of maximum
% (for the highlighs) and minimum (for the deep shadowed regions)
% values for the Phong shading.  '0.0' <=> 'black'; '1.0' <=> 'white'
%
%   upper_value:  Maximum value of whiteness.
%   lower_value:  Minimum value of whiteness.
%
phi_source := 30.000000;
theta_source := 30.000000;
upper_value := 0.990000;
lower_value := 0.750000;
radius := scalefactor;
delta_rho := radius/50.000000;
delta_phi := 360.0/80.000000;
beginfig(1);
  path p;
  path equator;
  transform T;
  c1:=lower_value;
  c2:=upper_value-lower_value;
  nx_source := sind(theta_source)*cosd(phi_source);
  ny_source := sind(theta_source)*sind(phi_source);
  nz_source := cosd(theta_source);
  phistop := 360.0;
  rhostop := radius - delta_rho/2.0;
%
% Draw the shaded Poincare sphere projected on 2D screen coordinates
%
  for rho=0.0cm step delta_rho until rhostop:
    for phi=0.0 step delta_phi until phistop:
      rhomid := rho + delta_rho/2.0;
      phimid := phi + delta_phi/2.0;
      x1 := rho*cosd(phi);
      y1 := rho*sind(phi);
      x2 := (rho+delta_rho)*cosd(phi);
      y2 := (rho+delta_rho)*sind(phi);
      x3 := (rho+delta_rho)*cosd(phi+delta_phi);
      y3 := (rho+delta_rho)*sind(phi+delta_phi);
      x4 := rho*cosd(phi+delta_phi);
      y4 := rho*sind(phi+delta_phi);
      p:=makepath makepen ((x1,y1)--(x2,y2)--(x3,y3)--(x4,y4)--(x1,y1));
      quot := (rhomid/radius);
      nx_object := quot*cosd(phimid);
      ny_object := quot*sind(phimid);
      nz_object := sqrt(1-quot*quot);
      prod:=nx_object*nx_source+ny_object*ny_source
            +nz_object*nz_source;
      if prod < 0.0:
         value := c1;
      else:
         value := c1 + c2*prod*prod;
      fi
      fill p withcolor value[black,white];
    endfor
  endfor

%
% Draw the 'equators' of the Poincare sphere
%
   equator := halfcircle scaled (2.0*radius);
   eqcolval := .45;    % '0.0' <=> 'white';  '1.0' <=> 'black'

   pickup pencircle scaled 0.600000 pt;
%
% Draw equator $S_3=0$...
%
   T := identity yscaled sind(rot_phi) rotated 180.0;
   draw equator transformed T withcolor eqcolval [white,black];

%
% ... then equator $S_2=0$...
%
   T := identity yscaled (cosd(rot_phi)*sind(rot_psi))
                 rotated (270.0 + alpha);
   draw equator transformed T withcolor eqcolval [white,black];

%
% ... and finally equator $S_1=0$.
%
   T := identity yscaled (cosd(rot_phi)*cosd(rot_psi))
                 rotated (270.0 - beta);
   draw equator transformed T withcolor eqcolval [white,black];

  oldahangle:=ahangle;
  ahangle:=20.000000;
  pickup pencircle scaled 0.800000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.8195,0.5731)..(-0.7986,0.6016)
    ..(-0.7764,0.6293)..(-0.7530,0.6561)..(-0.7286,0.6821)
    ..(-0.7031,0.7072)..(-0.6767,0.7314)..(-0.6495,0.7546)
    ..(-0.6215,0.7769)..(-0.5930,0.7980)..(-0.5640,0.8182)
    ..(-0.5347,0.8373)..(-0.5050,0.8554)..(-0.4752,0.8724)
    ..(-0.4454,0.8883)..(-0.4157,0.9031)..(-0.3862,0.9167)
    ..(-0.3571,0.9292)..(-0.3283,0.9406)..(-0.3001,0.9509)
    ..(-0.2725,0.9600)..(-0.2457,0.9680)..(-0.2198,0.9749)
    ..(-0.1949,0.9806)..(-0.1710,0.9853);
   drawarrow p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.9933,-0.1153)..(-0.9965,-0.0798)
    ..(-0.9977,-0.0441)..(-0.9971,-0.0085)..(-0.9945,0.0271)
    ..(-0.9901,0.0626)..(-0.9838,0.0981)..(-0.9756,0.1334)
    ..(-0.9656,0.1685)..(-0.9538,0.2034)..(-0.9403,0.2379)
    ..(-0.9250,0.2721)..(-0.9082,0.3059)..(-0.8897,0.3393)
    ..(-0.8698,0.3721)..(-0.8484,0.4045)..(-0.8256,0.4363)
    ..(-0.8016,0.4675)..(-0.7765,0.4980)..(-0.7502,0.5278)
    ..(-0.7229,0.5569)..(-0.6947,0.5853)..(-0.6658,0.6128)
    ..(-0.6361,0.6395)..(-0.6059,0.6654)..(-0.5752,0.6904)
    ..(-0.5442,0.7145)..(-0.5130,0.7377)..(-0.4817,0.7600)
    ..(-0.4503,0.7813)..(-0.4190,0.8016)..(-0.3881,0.8209)
    ..(-0.3574,0.8393)..(-0.3621,0.8514)..(-0.3703,0.8621)
    ..(-0.3765,0.8721)..(-0.3809,0.8816)..(-0.3834,0.8904)
    ..(-0.3841,0.8986)..(-0.3828,0.9063)..(-0.3797,0.9134)
    ..(-0.3747,0.9200)..(-0.3680,0.9261)..(-0.3594,0.9317)
    ..(-0.3492,0.9368);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.2474,-0.9686)..(-0.2747,-0.9614)
    ..(-0.3027,-0.9531);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.5909,-0.8068)..(-0.6181,-0.7861)
    ..(-0.6445,-0.7644)..(-0.6700,-0.7417)..(-0.6947,-0.7180)
    ..(-0.7183,-0.6935)..(-0.7407,-0.6679)..(-0.7618,-0.6416)
    ..(-0.7818,-0.6144)..(-0.8002,-0.5864)..(-0.8172,-0.5577)
    ..(-0.8326,-0.5282)..(-0.8464,-0.4981)..(-0.8585,-0.4673)
    ..(-0.8689,-0.4360)..(-0.8776,-0.4041)..(-0.8844,-0.3717)
    ..(-0.8894,-0.3388)..(-0.8925,-0.3057)..(-0.8938,-0.2721)
    ..(-0.8931,-0.2383)..(-0.8906,-0.2042)..(-0.8862,-0.1698)
    ..(-0.8798,-0.1354)..(-0.8716,-0.1008)..(-0.8616,-0.0662)
    ..(-0.8497,-0.0317)..(-0.8361,0.0029)..(-0.8207,0.0373)
    ..(-0.8037,0.0716)..(-0.7850,0.1058)..(-0.7649,0.1396)
    ..(-0.7431,0.1732)..(-0.7200,0.2064)..(-0.6955,0.2393)
    ..(-0.6699,0.2718)..(-0.6430,0.3038)..(-0.6151,0.3353)
    ..(-0.5862,0.3663)..(-0.5565,0.3967)..(-0.5259,0.4265)
    ..(-0.4948,0.4557)..(-0.4979,0.4790)..(-0.5208,0.4987)
    ..(-0.5422,0.5178)..(-0.5621,0.5363)..(-0.5803,0.5544)
    ..(-0.5970,0.5718)..(-0.6118,0.5888)..(-0.6250,0.6053)
    ..(-0.6363,0.6213)..(-0.6458,0.6368)..(-0.6534,0.6517)
    ..(-0.6592,0.6663)..(-0.6631,0.6804)..(-0.6651,0.6940)
    ..(-0.6652,0.7072)..(-0.6634,0.7200)..(-0.6598,0.7324)
    ..(-0.6543,0.7444)..(-0.6470,0.7560)..(-0.6379,0.7673)
    ..(-0.6272,0.7782)..(-0.6147,0.7888);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.3333,-0.9197)..(-0.3605,-0.9080)
    ..(-0.3871,-0.8951)..(-0.4130,-0.8810)..(-0.4383,-0.8658)
    ..(-0.4626,-0.8495)..(-0.4860,-0.8321)..(-0.5083,-0.8136)
    ..(-0.5294,-0.7942)..(-0.5493,-0.7737)..(-0.5678,-0.7522)
    ..(-0.5850,-0.7298)..(-0.6006,-0.7065)..(-0.6147,-0.6824)
    ..(-0.6272,-0.6574)..(-0.6379,-0.6317)..(-0.6470,-0.6052)
    ..(-0.6543,-0.5780)..(-0.6598,-0.5502)..(-0.6634,-0.5218)
    ..(-0.6652,-0.4927)..(-0.6651,-0.4632)..(-0.6631,-0.4332)
    ..(-0.6592,-0.4028)..(-0.6534,-0.3719)..(-0.6458,-0.3408)
    ..(-0.6363,-0.3094)..(-0.6250,-0.2777)..(-0.6118,-0.2459)
    ..(-0.5970,-0.2138)..(-0.5803,-0.1818)..(-0.5621,-0.1497)
    ..(-0.5422,-0.1176)..(-0.5208,-0.0855)..(-0.4979,-0.0534)
    ..(-0.4948,-0.0247)..(-0.5259,-0.0014)..(-0.5565,0.0215)
    ..(-0.5862,0.0441)..(-0.6151,0.0664)..(-0.6430,0.0884)
    ..(-0.6699,0.1101)..(-0.6955,0.1315)..(-0.7200,0.1525)
    ..(-0.7431,0.1732)..(-0.7649,0.1935)..(-0.7850,0.2136)
    ..(-0.8037,0.2333)..(-0.8207,0.2527)..(-0.8361,0.2718)
    ..(-0.8497,0.2906)..(-0.8616,0.3090)..(-0.8716,0.3271)
    ..(-0.8798,0.3451)..(-0.8862,0.3626)..(-0.8906,0.3800)
    ..(-0.8931,0.3971)..(-0.8938,0.4139)..(-0.8925,0.4305)
    ..(-0.8894,0.4469)..(-0.8844,0.4630)..(-0.8776,0.4790);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.2919,-0.8672)..(-0.3085,-0.8517)
    ..(-0.3237,-0.8353)..(-0.3372,-0.8179)..(-0.3492,-0.7996)
    ..(-0.3594,-0.7803)..(-0.3680,-0.7603)..(-0.3747,-0.7394)
    ..(-0.3797,-0.7177)..(-0.3828,-0.6953)..(-0.3841,-0.6722)
    ..(-0.3834,-0.6484)..(-0.3809,-0.6240)..(-0.3765,-0.5990)
    ..(-0.3703,-0.5736)..(-0.3621,-0.5476)..(-0.3574,-0.5219)
    ..(-0.3881,-0.5014)..(-0.4190,-0.4810)..(-0.4503,-0.4605)
    ..(-0.4817,-0.4400)..(-0.5130,-0.4194)..(-0.5442,-0.3990)
    ..(-0.5752,-0.3786)..(-0.6059,-0.3583)..(-0.6361,-0.3380)
    ..(-0.6658,-0.3179)..(-0.6947,-0.2978)..(-0.7229,-0.2778)
    ..(-0.7502,-0.2579)..(-0.7765,-0.2382)..(-0.8016,-0.2185)
    ..(-0.8256,-0.1991)..(-0.8484,-0.1796)..(-0.8698,-0.1603)
    ..(-0.8897,-0.1411)..(-0.9082,-0.1220)..(-0.9250,-0.1031)
    ..(-0.9403,-0.0843)..(-0.9538,-0.0655)..(-0.9656,-0.0469)
    ..(-0.9756,-0.0283)..(-0.9838,-0.0097)..(-0.9901,0.0087)
    ..(-0.9945,0.0271)..(-0.9971,0.0454)..(-0.9977,0.0637);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.1949,-0.8393)..(-0.2198,-0.8262)
    ..(-0.2457,-0.8129)..(-0.2725,-0.7993)..(-0.3001,-0.7855)
    ..(-0.3283,-0.7714)..(-0.3571,-0.7571)..(-0.3862,-0.7427)
    ..(-0.4157,-0.7281)..(-0.4454,-0.7133)..(-0.4752,-0.6984)
    ..(-0.5050,-0.6833)..(-0.5347,-0.6681)..(-0.5640,-0.6529)
    ..(-0.5930,-0.6375)..(-0.6215,-0.6221)..(-0.6495,-0.6066)
    ..(-0.6767,-0.5910)..(-0.7031,-0.5753)..(-0.7286,-0.5596)
    ..(-0.7530,-0.5438)..(-0.7764,-0.5279)..(-0.7986,-0.5119)
    ..(-0.8195,-0.4959)..(-0.8390,-0.4798)..(-0.8570,-0.4636)
    ..(-0.8735,-0.4473)..(-0.8885,-0.4309)..(-0.9018,-0.4144)
    ..(-0.9134,-0.3978)..(-0.9232,-0.3811)..(-0.9312,-0.3643);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.3182,-0.8824)..(-0.3467,-0.8739)
    ..(-0.3749,-0.8651)..(-0.4030,-0.8561)..(-0.4306,-0.8469)
    ..(-0.4578,-0.8375)..(-0.4842,-0.8279)..(-0.5100,-0.8181)
    ..(-0.5351,-0.8080)..(-0.5591,-0.7977)..(-0.5821,-0.7873)
    ..(-0.6040,-0.7766)..(-0.6246,-0.7657)..(-0.6440,-0.7545)
    ..(-0.6619,-0.7431)..(-0.6784,-0.7315)..(-0.6935,-0.7195)
    ..(-0.7069,-0.7073);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.3199,-0.9361)..(-0.3410,-0.9317)
    ..(-0.3609,-0.9270)..(-0.3795,-0.9219)..(-0.3966,-0.9165)
    ..(-0.4124,-0.9107);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
  ahangle:=oldahangle;
  oldahangle:=ahangle;
  ahangle:=20.000000;
  pickup pencircle scaled 0.800000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.0028,-0.9968)..(0.0091,-0.9941)
    ..(0.0227,-0.9906)..(0.0380,-0.9861)..(0.0549,-0.9807)
    ..(0.0735,-0.9744)..(0.0934,-0.9671)..(0.1149,-0.9588)
    ..(0.1376,-0.9496)..(0.1616,-0.9393)..(0.1868,-0.9281)
    ..(0.2131,-0.9158)..(0.2404,-0.9025)..(0.2686,-0.8882)
    ..(0.2975,-0.8729)..(0.3272,-0.8566)..(0.3522,-0.8400)
    ..(0.3404,-0.8280)..(0.3269,-0.8154)..(0.3115,-0.8020)
    ..(0.2946,-0.7879)..(0.2760,-0.7731)..(0.2558,-0.7576)
    ..(0.2340,-0.7414)..(0.2109,-0.7244)..(0.1864,-0.7067)
    ..(0.1605,-0.6883)..(0.1336,-0.6691)..(0.1055,-0.6492)
    ..(0.0764,-0.6285)..(0.0464,-0.6071)..(0.0156,-0.5849)
    ..(-0.0158,-0.5621)..(-0.0479,-0.5385)..(-0.0805,-0.5141)
    ..(-0.1133,-0.4892)..(-0.1465,-0.4635)..(-0.1798,-0.4372)
    ..(-0.2131,-0.4103)..(-0.2463,-0.3827)..(-0.2793,-0.3545)
    ..(-0.3119,-0.3258)..(-0.3441,-0.2965)..(-0.3758,-0.2667)
    ..(-0.4067,-0.2364)..(-0.4370,-0.2057)..(-0.4662,-0.1746)
    ..(-0.4946,-0.1431)..(-0.5219,-0.1112)..(-0.5480,-0.0790)
    ..(-0.5728,-0.0466)..(-0.5964,-0.0140)..(-0.6185,0.0188)
    ..(-0.6390,0.0518)..(-0.6581,0.0849)..(-0.6754,0.1180)
    ..(-0.6911,0.1511)..(-0.7051,0.1842)..(-0.7173,0.2171)
    ..(-0.7277,0.2499)..(-0.7362,0.2826)..(-0.7429,0.3149)
    ..(-0.7476,0.3471)..(-0.7505,0.3788)..(-0.7515,0.4102)
    ..(-0.7506,0.4411)..(-0.7479,0.4716)..(-0.7433,0.5015)
    ..(-0.7368,0.5308)..(-0.7286,0.5596)..(-0.7185,0.5877)
    ..(-0.7069,0.6150)..(-0.6935,0.6416)..(-0.6784,0.6676)
    ..(-0.6619,0.6925)..(-0.6440,0.7166)..(-0.6246,0.7399)
    ..(-0.6040,0.7622)..(-0.5821,0.7835)..(-0.5591,0.8038)
    ..(-0.5351,0.8231)..(-0.5100,0.8414)..(-0.4842,0.8585)
    ..(-0.4578,0.8745)..(-0.4306,0.8894)..(-0.4030,0.9032)
    ..(-0.3749,0.9158)..(-0.3467,0.9272)..(-0.3182,0.9375)
    ..(-0.2896,0.9465);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (0.1390,-0.9890)..(0.1388,-0.9870)
    ..(0.1366,-0.9843)..(0.1326,-0.9809)..(0.1267,-0.9768)
    ..(0.1190,-0.9719)..(0.1094,-0.9662)..(0.0980,-0.9598)
    ..(0.0849,-0.9525)..(0.0701,-0.9444)..(0.0536,-0.9354)
    ..(0.0354,-0.9256)..(0.0157,-0.9149)..(-0.0054,-0.9033)
    ..(-0.0280,-0.8908)..(-0.0519,-0.8775)..(-0.0771,-0.8632)
    ..(-0.1035,-0.8480)..(-0.1309,-0.8318)..(-0.1593,-0.8148)
    ..(-0.1885,-0.7968)..(-0.2186,-0.7780)..(-0.2493,-0.7582)
    ..(-0.2806,-0.7375)..(-0.3122,-0.7159)..(-0.3442,-0.6935)
    ..(-0.3764,-0.6702)..(-0.4088,-0.6460)..(-0.4411,-0.6210)
    ..(-0.4732,-0.5951)..(-0.5052,-0.5685)..(-0.5367,-0.5411)
    ..(-0.5678,-0.5130)..(-0.5983,-0.4841)..(-0.6281,-0.4545)
    ..(-0.6571,-0.4244)..(-0.6852,-0.3935)..(-0.7123,-0.3622)
    ..(-0.7382,-0.3303)..(-0.7630,-0.2978)..(-0.7865,-0.2649)
    ..(-0.8086,-0.2316)..(-0.8293,-0.1978)..(-0.8485,-0.1637)
    ..(-0.8660,-0.1294)..(-0.8820,-0.0948)..(-0.8962,-0.0600)
    ..(-0.9086,-0.0250)..(-0.9193,0.0100)..(-0.9281,0.0451)
    ..(-0.9351,0.0802)..(-0.9403,0.1152)..(-0.9435,0.1502)
    ..(-0.9448,0.1850)..(-0.9442,0.2196)..(-0.9418,0.2540)
    ..(-0.9374,0.2881)..(-0.9312,0.3218)..(-0.9232,0.3551)
    ..(-0.9134,0.3879)..(-0.9018,0.4203)..(-0.8885,0.4521)
    ..(-0.8735,0.4834)..(-0.8570,0.5140)..(-0.8390,0.5439)
    ..(-0.8195,0.5731);
   draw p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.0670,-0.9950)..(-0.0841,-0.9916)
    ..(-0.1026,-0.9872)..(-0.1227,-0.9817)..(-0.1442,-0.9753)
    ..(-0.1670,-0.9679)..(-0.1909,-0.9594)..(-0.2160,-0.9499)
    ..(-0.2423,-0.9392)..(-0.2694,-0.9276)..(-0.2974,-0.9149)
    ..(-0.3261,-0.9011)..(-0.3554,-0.8863)..(-0.3854,-0.8704)
    ..(-0.4156,-0.8535)..(-0.4462,-0.8356)..(-0.4771,-0.8166)
    ..(-0.5079,-0.7966)..(-0.5386,-0.7756)..(-0.5693,-0.7536)
    ..(-0.5996,-0.7306)..(-0.6296,-0.7067)..(-0.6591,-0.6818)
    ..(-0.6879,-0.6561)..(-0.7160,-0.6295)..(-0.7433,-0.6020)
    ..(-0.7696,-0.5738)..(-0.7950,-0.5447)..(-0.8192,-0.5150)
    ..(-0.8422,-0.4845)..(-0.8638,-0.4534)..(-0.8841,-0.4216)
    ..(-0.9029,-0.3893)..(-0.9202,-0.3564)..(-0.9359,-0.3230)
    ..(-0.9499,-0.2893)..(-0.9622,-0.2550)..(-0.9727,-0.2205)
    ..(-0.9814,-0.1857)..(-0.9883,-0.1506)..(-0.9933,-0.1153);
   draw p scaled radius withcolor black;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.3492,0.9368)..(-0.3372,0.9414)
    ..(-0.3237,0.9456)..(-0.3085,0.9494)..(-0.2919,0.9527)
    ..(-0.2739,0.9557);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.3027,-0.9531)..(-0.3312,-0.9436)
    ..(-0.3599,-0.9329)..(-0.3891,-0.9211)..(-0.4184,-0.9081)
    ..(-0.4477,-0.8940)..(-0.4769,-0.8788)..(-0.5060,-0.8624)
    ..(-0.5347,-0.8450)..(-0.5631,-0.8264)..(-0.5909,-0.8068);
   draw p scaled radius withcolor black;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.6147,0.7888)..(-0.6006,0.7990)
    ..(-0.5850,0.8089)..(-0.5678,0.8186)..(-0.5493,0.8279)
    ..(-0.5294,0.8370)..(-0.5083,0.8457)..(-0.4860,0.8543)
    ..(-0.4626,0.8625)..(-0.4383,0.8705)..(-0.4130,0.8783)
    ..(-0.3871,0.8858)..(-0.3605,0.8931)..(-0.3333,0.9002)
    ..(-0.3057,0.9070);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.8776,0.4790)..(-0.8689,0.4947)
    ..(-0.8585,0.5102)..(-0.8464,0.5256)..(-0.8326,0.5409)
    ..(-0.8172,0.5559)..(-0.8002,0.5708)..(-0.7818,0.5855)
    ..(-0.7618,0.6002)..(-0.7407,0.6146)..(-0.7183,0.6290)
    ..(-0.6947,0.6432)..(-0.6700,0.6573)..(-0.6445,0.6712)
    ..(-0.6181,0.6851)..(-0.5909,0.6988)..(-0.5631,0.7124)
    ..(-0.5347,0.7259)..(-0.5060,0.7392)..(-0.4769,0.7523)
    ..(-0.4477,0.7654)..(-0.4184,0.7782)..(-0.3891,0.7909)
    ..(-0.3599,0.8034)..(-0.3312,0.8157)..(-0.3027,0.8278)
    ..(-0.2747,0.8397)..(-0.2474,0.8513)..(-0.2208,0.8627);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.9977,0.0637)..(-0.9965,0.0819)
    ..(-0.9933,0.1002)..(-0.9883,0.1184)..(-0.9814,0.1366)
    ..(-0.9727,0.1547)..(-0.9622,0.1729)..(-0.9499,0.1912)
    ..(-0.9359,0.2094)..(-0.9202,0.2278)..(-0.9029,0.2461)
    ..(-0.8841,0.2644)..(-0.8638,0.2828)..(-0.8422,0.3012)
    ..(-0.8192,0.3198)..(-0.7950,0.3383)..(-0.7696,0.3570)
    ..(-0.7433,0.3755)..(-0.7160,0.3942)..(-0.6879,0.4130)
    ..(-0.6591,0.4317)..(-0.6296,0.4505)..(-0.5996,0.4693)
    ..(-0.5693,0.4882)..(-0.5386,0.5071)..(-0.5079,0.5258)
    ..(-0.4771,0.5446)..(-0.4462,0.5635)..(-0.4156,0.5821)
    ..(-0.3854,0.6007)..(-0.3554,0.6192)..(-0.3261,0.6376)
    ..(-0.2974,0.6559)..(-0.2694,0.6739)..(-0.2423,0.6918)
    ..(-0.2160,0.7096)..(-0.1909,0.7270)..(-0.1670,0.7441)
    ..(-0.1442,0.7611)..(-0.1227,0.7775)..(-0.1026,0.7938)
    ..(-0.0841,0.8095)..(-0.0670,0.8249)..(-0.0516,0.8398);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.9312,-0.3643)..(-0.9374,-0.3473)
    ..(-0.9418,-0.3302)..(-0.9442,-0.3128)..(-0.9448,-0.2954)
    ..(-0.9435,-0.2777)..(-0.9403,-0.2599)..(-0.9351,-0.2420)
    ..(-0.9281,-0.2238)..(-0.9193,-0.2054)..(-0.9086,-0.1867)
    ..(-0.8962,-0.1678)..(-0.8820,-0.1487)..(-0.8660,-0.1294)
    ..(-0.8485,-0.1098)..(-0.8293,-0.0900)..(-0.8086,-0.0699)
    ..(-0.7865,-0.0495)..(-0.7630,-0.0289)..(-0.7382,-0.0080)
    ..(-0.7123,0.0130)..(-0.6852,0.0344)..(-0.6571,0.0560)
    ..(-0.6281,0.0779)..(-0.5983,0.1000)..(-0.5678,0.1224)
    ..(-0.5367,0.1449)..(-0.5052,0.1677)..(-0.4732,0.1906)
    ..(-0.4411,0.2138)..(-0.4088,0.2371)..(-0.3764,0.2606)
    ..(-0.3442,0.2841)..(-0.3122,0.3078)..(-0.2806,0.3316)
    ..(-0.2493,0.3553)..(-0.2186,0.3793)..(-0.1885,0.4031)
    ..(-0.1593,0.4269)..(-0.1309,0.4507)..(-0.1035,0.4744)
    ..(-0.0771,0.4980)..(-0.0519,0.5215)..(-0.0280,0.5448)
    ..(-0.0054,0.5678)..(0.0157,0.5906)..(0.0354,0.6132)
    ..(0.0536,0.6354)..(0.0701,0.6572)..(0.0849,0.6786)
    ..(0.0980,0.6996)..(0.1094,0.7201)..(0.1190,0.7401)
    ..(0.1267,0.7595)..(0.1326,0.7784)..(0.1366,0.7966)
    ..(0.1388,0.8141)..(0.1390,0.8309)..(0.1374,0.8470);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.7069,-0.7073)..(-0.7185,-0.6949)
    ..(-0.7286,-0.6822)..(-0.7368,-0.6691)..(-0.7433,-0.6557)
    ..(-0.7479,-0.6420)..(-0.7506,-0.6280)..(-0.7515,-0.6135)
    ..(-0.7505,-0.5988)..(-0.7476,-0.5837)..(-0.7429,-0.5681)
    ..(-0.7362,-0.5522)..(-0.7277,-0.5358)..(-0.7173,-0.5191)
    ..(-0.7051,-0.5019)..(-0.6911,-0.4843)..(-0.6754,-0.4662)
    ..(-0.6581,-0.4476)..(-0.6390,-0.4286)..(-0.6185,-0.4091)
    ..(-0.5964,-0.3892)..(-0.5728,-0.3688)..(-0.5480,-0.3479)
    ..(-0.5219,-0.3266)..(-0.4946,-0.3047)..(-0.4662,-0.2824)
    ..(-0.4370,-0.2596)..(-0.4067,-0.2364)..(-0.3758,-0.2128)
    ..(-0.3441,-0.1887)..(-0.3119,-0.1641)..(-0.2793,-0.1391)
    ..(-0.2463,-0.1138)..(-0.2131,-0.0881)..(-0.1798,-0.0620)
    ..(-0.1465,-0.0356)..(-0.1133,-0.0087)..(-0.0805,0.0183)
    ..(-0.0479,0.0457)..(-0.0158,0.0733)..(0.0156,0.1011)
    ..(0.0464,0.1291)..(0.0764,0.1572)..(0.1055,0.1856)
    ..(0.1336,0.2140)..(0.1605,0.2424)..(0.1864,0.2708)
    ..(0.2109,0.2992)..(0.2340,0.3276)..(0.2558,0.3559)
    ..(0.2760,0.3840)..(0.2946,0.4120)..(0.3115,0.4398)
    ..(0.3269,0.4672)..(0.3404,0.4943)..(0.3522,0.5212)
    ..(0.3272,0.5424)..(0.2975,0.5627)..(0.2686,0.5829)
    ..(0.2404,0.6030)..(0.2131,0.6230)..(0.1868,0.6427)
    ..(0.1616,0.6622)..(0.1376,0.6815)..(0.1149,0.7005)
    ..(0.0934,0.7192)..(0.0735,0.7376)..(0.0549,0.7556)
    ..(0.0380,0.7732)..(0.0227,0.7903)..(0.0091,0.8070)
    ..(-0.0028,0.8231)..(-0.0130,0.8387);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.4124,-0.9107)..(-0.4266,-0.9045)
    ..(-0.4391,-0.8979)..(-0.4500,-0.8908)..(-0.4592,-0.8834)
    ..(-0.4666,-0.8755)..(-0.4722,-0.8671)..(-0.4761,-0.8582)
    ..(-0.4780,-0.8489)..(-0.4781,-0.8390)..(-0.4762,-0.8286)
    ..(-0.4726,-0.8176)..(-0.4670,-0.8061)..(-0.4596,-0.7940)
    ..(-0.4502,-0.7813)..(-0.4392,-0.7679)..(-0.4263,-0.7540)
    ..(-0.4116,-0.7395)..(-0.3951,-0.7243)..(-0.3771,-0.7084)
    ..(-0.3574,-0.6919)..(-0.3362,-0.6748)..(-0.3135,-0.6569)
    ..(-0.2894,-0.6384)..(-0.2640,-0.6192)..(-0.2374,-0.5994)
    ..(-0.2097,-0.5788)..(-0.1809,-0.5576)..(-0.1511,-0.5357)
    ..(-0.1205,-0.5130)..(-0.0891,-0.4899)..(-0.0571,-0.4659)
    ..(-0.0247,-0.4414)..(0.0083,-0.4163)..(0.0415,-0.3905)
    ..(0.0749,-0.3642)..(0.1083,-0.3372)..(0.1418,-0.3097)
    ..(0.1749,-0.2817)..(0.2079,-0.2532)..(0.2404,-0.2242)
    ..(0.2726,-0.1947)..(0.3039,-0.1648)..(0.3347,-0.1345)
    ..(0.3645,-0.1038)..(0.3935,-0.0729)..(0.4214,-0.0417)
    ..(0.4482,-0.0102)..(0.4737,0.0216)..(0.4631,0.0482)
    ..(0.4309,0.0720)..(0.3985,0.0961)..(0.3658,0.1204)
    ..(0.3332,0.1449)..(0.3004,0.1695)..(0.2679,0.1945)
    ..(0.2356,0.2196)..(0.2037,0.2448)..(0.1722,0.2700)
    ..(0.1415,0.2954)..(0.1113,0.3209)..(0.0820,0.3463)
    ..(0.0536,0.3718)..(0.0262,0.3972)..(0.0000,0.4226)
    ..(-0.0251,0.4479)..(-0.0488,0.4729)..(-0.0712,0.4979)
    ..(-0.0921,0.5226)..(-0.1116,0.5470)..(-0.1294,0.5712)
    ..(-0.1456,0.5950)..(-0.1602,0.6185)..(-0.1729,0.6415)
    ..(-0.1839,0.6641)..(-0.1931,0.6862)..(-0.2004,0.7077)
    ..(-0.2058,0.7287)..(-0.2095,0.7491)..(-0.2112,0.7687)
    ..(-0.2110,0.7878)..(-0.2090,0.8060)..(-0.2052,0.8235)
    ..(-0.1994,0.8401)..(-0.1919,0.8560);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.1994,-0.9798)..(-0.2052,-0.9776)
    ..(-0.2090,-0.9749)..(-0.2110,-0.9716)..(-0.2112,-0.9676)
    ..(-0.2095,-0.9630)..(-0.2058,-0.9577)..(-0.2004,-0.9516)
    ..(-0.1931,-0.9449)..(-0.1839,-0.9375)..(-0.1729,-0.9293)
    ..(-0.1602,-0.9203)..(-0.1456,-0.9105)..(-0.1294,-0.8999)
    ..(-0.1116,-0.8886)..(-0.0921,-0.8764)..(-0.0712,-0.8633)
    ..(-0.0488,-0.8495)..(-0.0251,-0.8347)..(0.0000,-0.8192)
    ..(0.0262,-0.8027)..(0.0536,-0.7854)..(0.0820,-0.7672)
    ..(0.1113,-0.7482)..(0.1415,-0.7283)..(0.1722,-0.7075)
    ..(0.2037,-0.6859)..(0.2356,-0.6635)..(0.2679,-0.6402)
    ..(0.3004,-0.6161)..(0.3332,-0.5913)..(0.3658,-0.5657)
    ..(0.3985,-0.5393)..(0.4309,-0.5121)..(0.4631,-0.4842)
    ..(0.4737,-0.4589)..(0.4482,-0.4381)..(0.4214,-0.4168)
    ..(0.3935,-0.3951)..(0.3645,-0.3728)..(0.3347,-0.3499)
    ..(0.3039,-0.3265)..(0.2726,-0.3025)..(0.2404,-0.2781)
    ..(0.2079,-0.2532)..(0.1749,-0.2278)..(0.1418,-0.2019)
    ..(0.1083,-0.1755)..(0.0749,-0.1488)..(0.0415,-0.1216)
    ..(0.0083,-0.0941)..(-0.0247,-0.0662)..(-0.0571,-0.0380)
    ..(-0.0891,-0.0094)..(-0.1205,0.0194)..(-0.1511,0.0485)
    ..(-0.1809,0.0778)..(-0.2097,0.1072)..(-0.2374,0.1368)
    ..(-0.2640,0.1665)..(-0.2894,0.1963)..(-0.3135,0.2261)
    ..(-0.3362,0.2559)..(-0.3574,0.2856)..(-0.3771,0.3152)
    ..(-0.3951,0.3448)..(-0.4116,0.3740)..(-0.4263,0.4031)
    ..(-0.4392,0.4319)..(-0.4502,0.4605)..(-0.4596,0.4886)
    ..(-0.4670,0.5163)..(-0.4726,0.5436)..(-0.4762,0.5704)
    ..(-0.4781,0.5966)..(-0.4780,0.6223)..(-0.4761,0.6473)
    ..(-0.4722,0.6717)..(-0.4666,0.6953)..(-0.4592,0.7182)
    ..(-0.4500,0.7402)..(-0.4391,0.7615)..(-0.4266,0.7819)
    ..(-0.4124,0.8014)..(-0.3966,0.8199)..(-0.3795,0.8374)
    ..(-0.3609,0.8539)..(-0.3410,0.8694)..(-0.3199,0.8838)
    ..(-0.2976,0.8971);
   drawarrow p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
  ahangle:=oldahangle;
%
% Draw the $S_1$-, $S_2$- and $S_3$-axis of the Poincare sphere.
% First of all, calculate the transformations of the intersections
% for the unity sphere.
%
% Used variables:
%
%    behind_distance : Specifies the relative distance of the coordi-
%                      axes to be plotted behind origo (in negative di-
%                      rection of respective axis.
%
%   outside_distance_s1 : The relative distance from origo to the point
%                         of the arrow head of the coordinate axis S1.
%                         If this is set to 1.0, the arrow head will
%                         point directly at the Poincare sphere.
%
%   outside_distance_s2 : Same as above, except that this one controls
%                         the S2 coordinate axis instead.
%
%   outside_distance_s3 : Same as above, except that this one controls
%                         the S3 coordinate axis instead.
%
%    insidecolval :    Specifies the shade of gray to use for the parts
%                      of the coordinate axes that are inside the Poin-
%                      care sphere. Values must be between 0 and 1,
%                      where:  '0.0' <=> 'white';  '1.0' <=> 'black'
%
   behind_distance_s1  := -0.300000;
   behind_distance_s2  := -0.300000;
   behind_distance_s3  := -0.300000;
   outside_distance_s1 :=  1.700000;
   outside_distance_s2 :=  2.400000;
   outside_distance_s3 :=  1.500000;
   insidecolval := .85;    % '0.0' <=> 'white';  '1.0' <=> 'black'

   pickup pencircle scaled 0.600000 pt;
%
% Start with drawing the x-axis...
%
   x_bis_start :=  radius*behind_distance_s1*cosd(rot_psi)*cosd(rot_phi);
   y_bis_start :=  radius*behind_distance_s1*sind(rot_psi);
   z_bis_start := -radius*behind_distance_s1*cosd(rot_psi)*sind(rot_phi);
   x_bis_intersect :=  radius*cosd(rot_psi)*cosd(rot_phi);
   y_bis_intersect :=  radius*sind(rot_psi);
   z_bis_intersect := -radius*cosd(rot_psi)*sind(rot_phi);
   p := makepath makepen (y_bis_intersect,z_bis_intersect)--
             (outside_distance_s1*y_bis_intersect,
              outside_distance_s1*z_bis_intersect);
   drawarrow p;
   label.bot(btex $s_1(t)$ etex,
             (outside_distance_s1*y_bis_intersect,
              outside_distance_s1*z_bis_intersect));

%
% ... then draw the y-axis ...
%
   x_bis_start := -radius*behind_distance_s2*sind(rot_psi)*cosd(rot_phi);
   y_bis_start :=  radius*behind_distance_s2*cosd(rot_psi);
   z_bis_start :=  radius*behind_distance_s2*sind(rot_psi)*sind(rot_phi);
   x_bis_intersect := -radius*sind(rot_psi)*cosd(rot_phi);
   y_bis_intersect :=  radius*cosd(rot_psi);
   z_bis_intersect :=  radius*sind(rot_psi)*sind(rot_phi);
   p := makepath makepen (y_bis_intersect,z_bis_intersect)--
             (outside_distance_s2*y_bis_intersect,
              outside_distance_s2*z_bis_intersect);
   drawarrow p;
   label.bot(btex $s_2(t)$ etex,
             (outside_distance_s2*y_bis_intersect,
              outside_distance_s2*z_bis_intersect));

%
% ... then, finally, draw the z-axis.
%
   x_bis_start := radius*behind_distance_s3*sind(rot_phi);
   y_bis_start := 0.0;
   z_bis_start := radius*behind_distance_s3*cosd(rot_phi);
   x_bis_intersect := radius*sind(rot_phi);
   y_bis_intersect := 0.0;
   z_bis_intersect := radius*cosd(rot_phi);
   p := makepath makepen (y_bis_intersect,z_bis_intersect)--
             (outside_distance_s3*y_bis_intersect,
              outside_distance_s3*z_bis_intersect);
   drawarrow p;
   label.urt(btex $s_3(t)$ etex,
             (outside_distance_s3*y_bis_intersect,
              outside_distance_s3*z_bis_intersect));

   endfig;
end