% This Filename:  example-ccr.mp   [MetaPost source]
% Creation time:  Fri Dec 16 19:30:13 2011
%
% Copyright (C) 1997-2005, Fredrik Jonsson <fj@optics.kth.se>
%
% Input Filename [Stokes parameters]:  example-cc.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-cc.dat --outputfile
%     example-ccr.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) rt --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 --reverse_arrow_paths

%
% 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 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 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);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.7649,0.6428)..(-0.7409,0.6693)
    ..(-0.7159,0.6948)..(-0.6899,0.7195)..(-0.6631,0.7432)
    ..(-0.6355,0.7659)..(-0.6073,0.7876)..(-0.5786,0.8083)
    ..(-0.5494,0.8279)..(-0.5198,0.8466)..(-0.4901,0.8641)
    ..(-0.4603,0.8805)..(-0.4305,0.8958)..(-0.4009,0.9100)
    ..(-0.3716,0.9231)..(-0.3426,0.9351)..(-0.3141,0.9459)
    ..(-0.2863,0.9556)..(-0.2590,0.9641)..(-0.2327,0.9716)
    ..(-0.2072,0.9779)..(-0.1828,0.9831);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.9951,-0.0975)..(-0.9973,-0.0620)
    ..(-0.9976,-0.0264)..(-0.9960,0.0092)..(-0.9925,0.0449);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.4973,0.7490)..(-0.4659,0.7708)
    ..(-0.4346,0.7915)..(-0.4035,0.8114)..(-0.3727,0.8302)
    ..(-0.3574,0.8458)..(-0.3665,0.8568)..(-0.3737,0.8672)
    ..(-0.3790,0.8769)..(-0.3824,0.8860)..(-0.3840,0.8946)
    ..(-0.3837,0.9025)..(-0.3815,0.9099)..(-0.3774,0.9168)
    ..(-0.3716,0.9231)..(-0.3639,0.9289)..(-0.3545,0.9343)
    ..(-0.3434,0.9392);
   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);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.8250,-0.5431)..(-0.8397,-0.5132)
    ..(-0.8527,-0.4828)..(-0.8640,-0.4517)..(-0.8735,-0.4201)
    ..(-0.8812,-0.3879)..(-0.8871,-0.3554)..(-0.8912,-0.3223)
    ..(-0.8934,-0.2889)..(-0.8937,-0.2552)..(-0.8921,-0.2212)
    ..(-0.8886,-0.1870)..(-0.8832,-0.1526)..(-0.8760,-0.1181)
    ..(-0.8668,-0.0835)..(-0.8559,-0.0489)..(-0.8432,-0.0144)
    ..(-0.8286,0.0202)..(-0.8125,0.0545)..(-0.7946,0.0887)
    ..(-0.7751,0.1227)..(-0.7542,0.1564)..(-0.7318,0.1899);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.6654,0.7006)..(-0.6646,0.7137)
    ..(-0.6618,0.7263)..(-0.6573,0.7384)..(-0.6508,0.7503)
    ..(-0.6427,0.7617)..(-0.6328,0.7727)..(-0.6211,0.7835);
   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);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.6614,-0.4181)..(-0.6566,-0.3874)
    ..(-0.6499,-0.3564)..(-0.6413,-0.3251)..(-0.6308,-0.2936)
    ..(-0.6186,-0.2618)..(-0.6046,-0.2300)..(-0.5889,-0.1978)
    ..(-0.5714,-0.1657)..(-0.5523,-0.1336)..(-0.5317,-0.1014)
    ..(-0.5096,-0.0694)..(-0.4860,-0.0375)..(-0.5105,-0.0130)
    ..(-0.5413,0.0100)..(-0.5714,0.0328)..(-0.6008,0.0553)
    ..(-0.6292,0.0775)..(-0.6566,0.0993)..(-0.6829,0.1208)
    ..(-0.7080,0.1420)..(-0.7318,0.1628)..(-0.7542,0.1834);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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 0.400000 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);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.5598,-0.3888)..(-0.5906,-0.3684)
    ..(-0.6211,-0.3481)..(-0.6510,-0.3279)..(-0.6803,-0.3078)
    ..(-0.7089,-0.2878)..(-0.7366,-0.2679)..(-0.7634,-0.2480)
    ..(-0.7892,-0.2283)..(-0.8138,-0.2087)..(-0.8372,-0.1892)
    ..(-0.8593,-0.1699)..(-0.8799,-0.1507)..(-0.8992,-0.1316)
    ..(-0.9168,-0.1126)..(-0.9329,-0.0937)..(-0.9472,-0.0749)
    ..(-0.9599,-0.0561)..(-0.9708,-0.0376)..(-0.9799,-0.0191)
    ..(-0.9872,-0.0006)..(-0.9925,0.0178)..(-0.9960,0.0363);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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 0.400000 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);
   drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.8092,-0.5039)..(-0.8294,-0.4879)
    ..(-0.8482,-0.4717)..(-0.8655,-0.4554)..(-0.8812,-0.4392)
    ..(-0.8953,-0.4227)..(-0.9078,-0.4062)..(-0.9185,-0.3895)
    ..(-0.9274,-0.3727);
   draw p scaled radius withcolor 0.650000 [black,white];
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   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 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   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;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (0.2451,-0.7496)..(0.2227,-0.7330)
    ..(0.1988,-0.7157)..(0.1737,-0.6976)..(0.1472,-0.6788)
    ..(0.1197,-0.6592)..(0.0911,-0.6390)..(0.0616,-0.6178)
    ..(0.0312,-0.5961)..(0.0000,-0.5736)..(-0.0318,-0.5503)
    ..(-0.0641,-0.5264)..(-0.0968,-0.5018)..(-0.1299,-0.4764)
    ..(-0.1631,-0.4504)..(-0.1965,-0.4238)..(-0.2297,-0.3966)
    ..(-0.2628,-0.3686)..(-0.2956,-0.3402)..(-0.3281,-0.3112)
    ..(-0.3600,-0.2817)..(-0.3913,-0.2517)..(-0.4220,-0.2211);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.7403,0.5162)..(-0.7329,0.5453)
    ..(-0.7238,0.5737)..(-0.7129,0.6015)..(-0.7003,0.6285)
    ..(-0.6861,0.6548)..(-0.6704,0.6801)..(-0.6532,0.7047)
    ..(-0.6345,0.7284)..(-0.6145,0.7511)..(-0.5932,0.7730)
    ..(-0.5708,0.7937)..(-0.5471,0.8136)..(-0.5227,0.8323)
    ..(-0.4973,0.8500)..(-0.4711,0.8666)..(-0.4443,0.8821)
    ..(-0.4169,0.8965)..(-0.3890,0.9097)..(-0.3608,0.9217)
    ..(-0.3324,0.9325)..(-0.3039,0.9421)..(-0.2754,0.9506);
   drawarrow reverse 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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.2648,-0.7480)..(-0.2963,-0.7268)
    ..(-0.3282,-0.7048)..(-0.3603,-0.6819)..(-0.3926,-0.6582)
    ..(-0.4249,-0.6336)..(-0.4572,-0.6082)..(-0.4893,-0.5819)
    ..(-0.5210,-0.5549)..(-0.5524,-0.5271)..(-0.5831,-0.4986)
    ..(-0.6133,-0.4694)..(-0.6427,-0.4396)..(-0.6713,-0.4090)
    ..(-0.6988,-0.3780)..(-0.7254,-0.3463)..(-0.7508,-0.3141)
    ..(-0.7750,-0.2814)..(-0.7977,-0.2483)..(-0.8191,-0.2148)
    ..(-0.8391,-0.1809)..(-0.8574,-0.1467)..(-0.8742,-0.1121);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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 (-0.1828,0.9831)..(-0.1595,0.9872);
   drawarrow reverse 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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.6736,-0.6691)..(-0.7020,-0.6429)
    ..(-0.7298,-0.6158)..(-0.7567,-0.5879)..(-0.7825,-0.5594)
    ..(-0.8073,-0.5299)..(-0.8308,-0.4999)..(-0.8532,-0.4690)
    ..(-0.8741,-0.4376)..(-0.8937,-0.4055)..(-0.9118,-0.3729)
    ..(-0.9282,-0.3398)..(-0.9431,-0.3062)..(-0.9562,-0.2722)
    ..(-0.9677,-0.2378)..(-0.9773,-0.2031)..(-0.9851,-0.1681)
    ..(-0.9911,-0.1328)..(-0.9951,-0.0975);
   draw p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.3434,0.9392)..(-0.3306,0.9436)
    ..(-0.3163,0.9475)..(-0.3004,0.9511)..(-0.2831,0.9543)
    ..(-0.2643,0.9570);
   drawarrow reverse 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 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.6211,0.7835)..(-0.6079,0.7939)
    ..(-0.5930,0.8040)..(-0.5766,0.8138)..(-0.5587,0.8233)
    ..(-0.5395,0.8325)..(-0.5190,0.8414)..(-0.4973,0.8500)
    ..(-0.4744,0.8584)..(-0.4506,0.8666)..(-0.4257,0.8745)
    ..(-0.4001,0.8821)..(-0.3738,0.8895)..(-0.3469,0.8967)
    ..(-0.3195,0.9036)..(-0.2917,0.9103);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.7911,0.5782)..(-0.7720,0.5928)
    ..(-0.7514,0.6074)..(-0.7296,0.6218)..(-0.7066,0.6361)
    ..(-0.6825,0.6503)..(-0.6574,0.6643)..(-0.6314,0.6782)
    ..(-0.6046,0.6919)..(-0.5770,0.7056)..(-0.5490,0.7191)
    ..(-0.5204,0.7325)..(-0.4915,0.7458)..(-0.4623,0.7589)
    ..(-0.4330,0.7718)..(-0.4038,0.7846)..(-0.3745,0.7972)
    ..(-0.3455,0.8096)..(-0.3169,0.8218)..(-0.2887,0.8338)
    ..(-0.2610,0.8455)..(-0.2340,0.8571)..(-0.2078,0.8683);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.6147,0.4599)..(-0.5845,0.4788)
    ..(-0.5540,0.4976)..(-0.5233,0.5165)..(-0.4924,0.5353)
    ..(-0.4615,0.5541)..(-0.4309,0.5728)..(-0.4005,0.5914)
    ..(-0.3703,0.6100)..(-0.3408,0.6284)..(-0.3117,0.6468)
    ..(-0.2833,0.6649)..(-0.2556,0.6830)..(-0.2291,0.7007)
    ..(-0.2034,0.7183)..(-0.1788,0.7356)..(-0.1554,0.7526)
    ..(-0.1333,0.7693)..(-0.1125,0.7857)..(-0.0932,0.8017)
    ..(-0.0753,0.8173)..(-0.0591,0.8324)..(-0.0444,0.8471);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.9274,-0.3727)..(-0.9346,-0.3558)
    ..(-0.9398,-0.3387)..(-0.9432,-0.3215)..(-0.9447,-0.3042)
    ..(-0.9444,-0.2866)..(-0.9421,-0.2689)..(-0.9379,-0.2510)
    ..(-0.9319,-0.2329)..(-0.9240,-0.2146)..(-0.9142,-0.1961)
    ..(-0.9026,-0.1773)..(-0.8893,-0.1584)..(-0.8742,-0.1391)
    ..(-0.8574,-0.1196);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.2035,0.3911)..(-0.1738,0.4150)
    ..(-0.1449,0.4388)..(-0.1170,0.4626)..(-0.0901,0.4863)
    ..(-0.0644,0.5098)..(-0.0398,0.5332)..(-0.0166,0.5563)
    ..(0.0053,0.5793)..(0.0258,0.6020)..(0.0447,0.6243)
    ..(0.0621,0.6463)..(0.0777,0.6680)..(0.0917,0.6892)
    ..(0.1040,0.7099)..(0.1145,0.7302)..(0.1231,0.7499)
    ..(0.1299,0.7690)..(0.1349,0.7876)..(0.1379,0.8054)
    ..(0.1391,0.8227)..(0.1384,0.8391)..(0.1359,0.8548);
   drawarrow reverse 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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.7495,-0.6351)..(-0.7513,-0.6208)
    ..(-0.7513,-0.6062)..(-0.7494,-0.5912)..(-0.7455,-0.5759)
    ..(-0.7398,-0.5602)..(-0.7321,-0.5441)..(-0.7227,-0.5275)
    ..(-0.7114,-0.5105)..(-0.6983,-0.4931)..(-0.6835,-0.4752)
    ..(-0.6669,-0.4569)..(-0.6487,-0.4382)..(-0.6289,-0.4189)
    ..(-0.6076,-0.3992)..(-0.5848,-0.3790)..(-0.5606,-0.3584)
    ..(-0.5351,-0.3373)..(-0.5084,-0.3157)..(-0.4806,-0.2937)
    ..(-0.4517,-0.2711)..(-0.4220,-0.2481)..(-0.3913,-0.2246);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (0.2855,0.3980)..(0.3033,0.4259)
    ..(0.3195,0.4535)..(0.3339,0.4808)..(0.3465,0.5078)
    ..(0.3422,0.5322)..(0.3123,0.5525)..(0.2829,0.5728)
    ..(0.2544,0.5930)..(0.2267,0.6130)..(0.1998,0.6329)
    ..(0.1741,0.6525)..(0.1494,0.6719)..(0.1261,0.6911)
    ..(0.1040,0.7099)..(0.0833,0.7285)..(0.0640,0.7467)
    ..(0.0463,0.7644)..(0.0301,0.7818)..(0.0157,0.7987)
    ..(0.0029,0.8151)..(-0.0081,0.8310)..(-0.0173,0.8463);
   drawarrow reverse 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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.4035,-0.7320)..(-0.3863,-0.7165)
    ..(-0.3674,-0.7003)..(-0.3469,-0.6834)..(-0.3251,-0.6660)
    ..(-0.3016,-0.6478)..(-0.2769,-0.6289)..(-0.2509,-0.6093)
    ..(-0.2237,-0.5892)..(-0.1954,-0.5682)..(-0.1661,-0.5467)
    ..(-0.1359,-0.5244)..(-0.1049,-0.5016)..(-0.0732,-0.4779)
    ..(-0.0409,-0.4538)..(-0.0083,-0.4289)..(0.0248,-0.4035)
    ..(0.0582,-0.3774)..(0.0916,-0.3508)..(0.1250,-0.3236)
    ..(0.1584,-0.2958)..(0.1915,-0.2675)..(0.2243,-0.2387);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (0.0398,0.3845)..(0.0130,0.4099)
    ..(-0.0127,0.4353)..(-0.0371,0.4604)..(-0.0602,0.4855)
    ..(-0.0819,0.5103)..(-0.1021,0.5348)..(-0.1207,0.5592)
    ..(-0.1378,0.5832)..(-0.1531,0.6068)..(-0.1668,0.6301)
    ..(-0.1786,0.6529)..(-0.1887,0.6752)..(-0.1970,0.6970)
    ..(-0.2034,0.7183)..(-0.2079,0.7390)..(-0.2106,0.7590)
    ..(-0.2113,0.7784)..(-0.2102,0.7970)..(-0.2072,0.8148)
    ..(-0.2025,0.8319)..(-0.1959,0.8482)..(-0.1875,0.8636);
   drawarrow reverse 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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (0.0965,-0.7578)..(0.1262,-0.7383)
    ..(0.1567,-0.7180)..(0.1879,-0.6968)..(0.2196,-0.6748)
    ..(0.2517,-0.6519)..(0.2841,-0.6283)..(0.3168,-0.6038)
    ..(0.3495,-0.5786)..(0.3822,-0.5525)..(0.4148,-0.5257)
    ..(0.4471,-0.4983)..(0.4790,-0.4701)..(0.4611,-0.4486)
    ..(0.4349,-0.4276)..(0.4076,-0.4060)..(0.3791,-0.3840)
    ..(0.3497,-0.3613)..(0.3194,-0.3382)..(0.2883,-0.3146)
    ..(0.2566,-0.2904)..(0.2243,-0.2657)..(0.1915,-0.2405);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (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);
   drawarrow reverse p scaled radius withcolor black;
   pickup pencircle scaled 0.400000 pt;
   pickup pencircle scaled 0.800000 pt;
   p := makepath makepen (-0.4329,0.4176)..(-0.4450,0.4462)
    ..(-0.4551,0.4746)..(-0.4635,0.5025)..(-0.4700,0.5301)
    ..(-0.4747,0.5571)..(-0.4774,0.5836)..(-0.4783,0.6095)
    ..(-0.4773,0.6349)..(-0.4743,0.6596)..(-0.4697,0.6836)
    ..(-0.4631,0.7068)..(-0.4548,0.7294)..(-0.4447,0.7510)
    ..(-0.4330,0.7718)..(-0.4197,0.7917)..(-0.4047,0.8107)
    ..(-0.3882,0.8288)..(-0.3704,0.8458)..(-0.3511,0.8618)
    ..(-0.3306,0.8767)..(-0.3089,0.8906)..(-0.2861,0.9034);
   drawarrow reverse 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.rt(btex $s_3(t)$ etex,
             (outside_distance_s3*y_bis_intersect,
              outside_distance_s3*z_bis_intersect));

   endfig;
end