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Contents of file 'poincare/example-d.mp':




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    1   % This Filename:  example-d.mp   [MetaPost source]
    2   % Creation time:  Thu Jan 23 20:19:33 2014
    3   %
    4   % Copyright (C) 1997-2005, Fredrik Jonsson <fj@optics.kth.se>
    5   %
    6   % Input Filename [Stokes parameters]:  example-d.dat
    7   % This MetaPost source code was automatically generated by poincare
    8   % Full set of command line options that generated this code:
    9   %     --verbose --normalize --bezier --inputfile example-d.dat --outputfile
   10   %     example-d.mp --axislengths 0.3 1.7 0.3 2.4
   11   %     0.3 1.5 --axislabels s_1(t) bot s_2(t)
   12   %     bot s_3(t) rt --rotatephi 15.0 --rotatepsi
   13   %     -60.0 --shading 0.75 0.99 --rhodivisor 50
   14   %     --phidivisor 80 --scalefactor 20.0 --paththickness 0.8
   15   %     --arrowthickness 0.4 --arrowheadangle 30.0 --draw_paths_as_arrows --arrow
   16   %     1.0 0.7 -0.58 1.0 0.7 0.15
   17   %     0 0.9 --arrow 0.28 0.9 0.52
   18   %     0.3 0.9 1.5 0 0.9
   19   %
   20   % Description:  Map of Stokes parameters, visualized as trajectories
   21   %               onto the Poincare sphere. This file contains MetaPost
   22   %               source code, to be compiled with John Hobby's MetaPost
   23   %               compiler or used with anything that understands MetaPost
   24   %               source code.
   25   %
   26   % If you want to create PostScript output, or include the resulting
   27   % output in a TeX document, this example illustrates the procedure,
   28   % assuming 'poincaremap.mp' to be the name of the file containing the
   29   % MetaPost code to be visualized: (commands run on command-line)
   30   %
   31   %       mp poincaremap.mp;
   32   %       echo "\input epsf\centerline{\epsfbox{poincaremap.1}}\bye" > tmp.tex;
   33   %       tex tmp.tex;
   34   %       dvips tmp.dvi -o poincaremap.ps;
   35   %
   36   % Here, the first command compiles the MetaPost source code, and leaves
   37   % an Encapsulated PostScript file named 'poincaremap.1', containing TeX
   38   % control codes for characters, etc. This file does not contain any
   39   % definitions for characters or TeX-specific items, and it cannot be
   40   % viewed or printed simply as is stands; it must rather be included into
   41   % TeX code in order to provide something useful.
   42   %     The second command creates a temporary minimal TeX-file 'tmp.tex',
   43   % that only includes the previously generated Encapsulated PostScript
   44   % code.
   45   %     The third command compiles the TeX-code into device-independent,
   46   % or DVI, output, stored in the file 'tmp.dvi'.
   47   %     Finally, the last command converts the DVI output into a free-
   48   % standing PostScript file 'poincaremap.ps', to be printed or viewed
   49   % with some PostScript viewer, such as GhostView.
   50   %
   51   scalefactor := 20.000000 mm;
   52   rot_psi := -60.000000;  % Rotation angle round z-axis (first rotation)
   53   rot_phi := 15.000000;  % Rotation angle round y-axis (second rotation)
   54   alpha := -24.146108;    % == arctan(sin(rot_phi)*tan(rot_psi))
   55   beta  := -8.498781;    % == arctan(sin(rot_phi)/tan(rot_psi))
   56   
   57   %
   58   % Parameters specifying the location of the light source; for Phong
   59   % shading of the sphere.
   60   %
   61   %    phi_source:  Angle (in deg.) to light source counterclockwise
   62   %                 'from three o'clock', viewed from the observer.
   63   %
   64   %  theta_source:  Angle (in deg.) between light source and observer,
   65   %                 seen from the centre of the sphere.
   66   %
   67   % Parameters specifying the shading 'intensity' in terms of maximum
   68   % (for the highlighs) and minimum (for the deep shadowed regions)
   69   % values for the Phong shading.  '0.0' <=> 'black'; '1.0' <=> 'white'
   70   %
   71   %   upper_value:  Maximum value of whiteness.
   72   %   lower_value:  Minimum value of whiteness.
   73   %
   74   phi_source := 30.000000;
   75   theta_source := 30.000000;
   76   upper_value := 0.990000;
   77   lower_value := 0.750000;
   78   radius := scalefactor;
   79   delta_rho := radius/50.000000;
   80   delta_phi := 360.0/80.000000;
   81   beginfig(1);
   82     path p;
   83     path equator;
   84     transform T;
   85     c1:=lower_value;
   86     c2:=upper_value-lower_value;
   87     nx_source := sind(theta_source)*cosd(phi_source);
   88     ny_source := sind(theta_source)*sind(phi_source);
   89     nz_source := cosd(theta_source);
   90     phistop := 360.0;
   91     rhostop := radius - delta_rho/2.0;
   92   %
   93   % Draw the shaded Poincare sphere projected on 2D screen coordinates
   94   %
   95     for rho=0.0cm step delta_rho until rhostop:
   96       for phi=0.0 step delta_phi until phistop:
   97         rhomid := rho + delta_rho/2.0;
   98         phimid := phi + delta_phi/2.0;
   99         x1 := rho*cosd(phi);
  100         y1 := rho*sind(phi);
  101         x2 := (rho+delta_rho)*cosd(phi);
  102         y2 := (rho+delta_rho)*sind(phi);
  103         x3 := (rho+delta_rho)*cosd(phi+delta_phi);
  104         y3 := (rho+delta_rho)*sind(phi+delta_phi);
  105         x4 := rho*cosd(phi+delta_phi);
  106         y4 := rho*sind(phi+delta_phi);
  107         p:=makepath makepen ((x1,y1)--(x2,y2)--(x3,y3)--(x4,y4)--(x1,y1));
  108         quot := (rhomid/radius);
  109         nx_object := quot*cosd(phimid);
  110         ny_object := quot*sind(phimid);
  111         nz_object := sqrt(1-quot*quot);
  112         prod:=nx_object*nx_source+ny_object*ny_source
  113               +nz_object*nz_source;
  114         if prod < 0.0:
  115            value := c1;
  116         else:
  117            value := c1 + c2*prod*prod;
  118         fi
  119         fill p withcolor value[black,white];
  120       endfor
  121     endfor
  122   
  123   %
  124   % Draw the 'equators' of the Poincare sphere
  125   %
  126      equator := halfcircle scaled (2.0*radius);
  127      eqcolval := .45;    % '0.0' <=> 'white';  '1.0' <=> 'black'
  128   
  129      pickup pencircle scaled 0.600000 pt;
  130   %
  131   % Draw equator $S_3=0$...
  132   %
  133      T := identity yscaled sind(rot_phi) rotated 180.0;
  134      draw equator transformed T withcolor eqcolval [white,black];
  135   
  136   %
  137   % ... then equator $S_2=0$...
  138   %
  139      T := identity yscaled (cosd(rot_phi)*sind(rot_psi))
  140                    rotated (270.0 + alpha);
  141      draw equator transformed T withcolor eqcolval [white,black];
  142   
  143   %
  144   % ... and finally equator $S_1=0$.
  145   %
  146      T := identity yscaled (cosd(rot_phi)*cosd(rot_psi))
  147                    rotated (270.0 - beta);
  148      draw equator transformed T withcolor eqcolval [white,black];
  149   
  150     oldahangle:=ahangle;
  151     ahangle:=30.000000;
  152     pickup pencircle scaled 0.800000 pt;
  153      pickup pencircle scaled 0.800000 pt;
  154      p := makepath makepen (0.6179,-0.7858)..(0.6468,-0.7602)
  155       ..(0.6643,-0.7405)..(0.6692,-0.7285)..(0.6612,-0.7247)
  156       ..(0.6412,-0.7283)..(0.6115,-0.7376)..(0.5749,-0.7498)
  157       ..(0.5357,-0.7622)..(0.4979,-0.7722)..(0.4651,-0.7777)
  158       ..(0.4397,-0.7771)..(0.4223,-0.7693)..(0.4119,-0.7539)
  159       ..(0.4060,-0.7310)..(0.4009,-0.7018)..(0.3933,-0.6684)
  160       ..(0.3802,-0.6339)..(0.3594,-0.6020)..(0.3306,-0.5764)
  161       ..(0.2941,-0.5603)..(0.2513,-0.5554)..(0.2044,-0.5619)
  162       ..(0.1555,-0.5785)..(0.1072,-0.6024)..(0.0615,-0.6302)
  163       ..(0.0194,-0.6579)..(-0.0185,-0.6821)..(-0.0532,-0.7003)
  164       ..(-0.0865,-0.7107)..(-0.1205,-0.7125)..(-0.1573,-0.7060)
  165       ..(-0.1986,-0.6920)..(-0.2443,-0.6723)..(-0.2939,-0.6497)
  166       ..(-0.3453,-0.6273)..(-0.3958,-0.6088)..(-0.4424,-0.5975)
  167       ..(-0.4825,-0.5958)..(-0.5138,-0.6048)..(-0.5349,-0.6241)
  168       ..(-0.5452,-0.6517)..(-0.5452,-0.6848)..(-0.5370,-0.7196)
  169       ..(-0.5237,-0.7527)..(-0.5094,-0.7814)..(-0.4980,-0.8039)
  170       ..(-0.4932,-0.8197)..(-0.4969,-0.8286)..(-0.5092,-0.8313)
  171       ..(-0.5286,-0.8287)..(-0.5519,-0.8221)..(-0.5749,-0.8131)
  172       ..(-0.5935,-0.8038);
  173      draw p scaled radius withcolor 0.650000 [black,white];
  174      pickup pencircle scaled 0.400000 pt;
  175      label.urt(btex $(\vartheta=0.6)$ etex,(0.293901,-0.913190)*radius);
  176      pickup pencircle scaled 0.800000 pt;
  177      p := makepath makepen (0.9869,-0.1557)..(0.9774,-0.1753)
  178       ..(0.9585,-0.2079)..(0.9303,-0.2473)..(0.8947,-0.2868)
  179       ..(0.8552,-0.3196)..(0.8160,-0.3403)..(0.7802,-0.3449)
  180       ..(0.7494,-0.3311)..(0.7226,-0.2984)..(0.6972,-0.2488)
  181       ..(0.6695,-0.1858)..(0.6364,-0.1155)..(0.5959,-0.0453)
  182       ..(0.5480,0.0172)..(0.4934,0.0655)..(0.4340,0.0945)
  183       ..(0.3709,0.1018)..(0.3049,0.0872)..(0.2370,0.0531)
  184       ..(0.1681,0.0040)..(0.0994,-0.0537)..(0.0325,-0.1124)
  185       ..(-0.0317,-0.1648)..(-0.0934,-0.2044)..(-0.1534,-0.2270)
  186       ..(-0.2137,-0.2303)..(-0.2760,-0.2144)..(-0.3409,-0.1818)
  187       ..(-0.4080,-0.1366)..(-0.4755,-0.0853)..(-0.5412,-0.0351)
  188       ..(-0.6033,0.0068)..(-0.6604,0.0341)..(-0.7122,0.0422)
  189       ..(-0.7584,0.0289)..(-0.7984,-0.0056)..(-0.8310,-0.0586)
  190       ..(-0.8546,-0.1251)..(-0.8688,-0.1984)..(-0.8746,-0.2708)
  191       ..(-0.8749,-0.3353)..(-0.8737,-0.3862)..(-0.8750,-0.4204)
  192       ..(-0.8815,-0.4363)..(-0.8932,-0.4343)..(-0.9079,-0.4166);
  193      draw p scaled radius withcolor 0.650000 [black,white];
  194      pickup pencircle scaled 0.400000 pt;
  195      label.urt(btex $(\vartheta=1.3)$ etex,(0.475533,-0.511636)*radius);
  196      pickup pencircle scaled 0.800000 pt;
  197      p := makepath makepen (0.9217,0.3867)..(0.9303,0.3496)
  198       ..(0.9304,0.3118)..(0.9207,0.2797)..(0.9016,0.2596)
  199       ..(0.8742,0.2561)..(0.8396,0.2716)..(0.7984,0.3059)
  200       ..(0.7506,0.3560)..(0.6962,0.4168)..(0.6364,0.4814)
  201       ..(0.5730,0.5430)..(0.5089,0.5955)..(0.4466,0.6345)
  202       ..(0.3874,0.6578)..(0.3310,0.6643)..(0.2760,0.6541)
  203       ..(0.2202,0.6288)..(0.1616,0.5904)..(0.0994,0.5433)
  204       ..(0.0338,0.4931)..(-0.0342,0.4464)..(-0.1032,0.4097)
  205       ..(-0.1720,0.3882)..(-0.2395,0.3844)..(-0.3050,0.3986)
  206       ..(-0.3670,0.4281)..(-0.4243,0.4679)..(-0.4755,0.5116)
  207       ..(-0.5205,0.5529)..(-0.5604,0.5858)..(-0.5977,0.6061)
  208       ..(-0.6357,0.6111)..(-0.6769,0.5993)..(-0.7226,0.5702)
  209       ..(-0.7719,0.5250)..(-0.8218,0.4663)..(-0.8688,0.3986)
  210       ..(-0.9095,0.3284)..(-0.9419,0.2629)..(-0.9653,0.2088)
  211       ..(-0.9804,0.1715)..(-0.9877,0.1537);
  212      draw p scaled radius withcolor 0.650000 [black,white];
  213      pickup pencircle scaled 0.400000 pt;
  214      label.urt(btex $(\vartheta=1.9)$ etex,(0.475533,0.085285)*radius);
  215      pickup pencircle scaled 0.800000 pt;
  216      p := makepath makepen (0.6040,0.7968)..(0.6040,0.7942)
  217       ..(0.5923,0.7979)..(0.5689,0.8084)..(0.5349,0.8252)
  218       ..(0.4924,0.8469)..(0.4441,0.8708)..(0.3933,0.8945)
  219       ..(0.3431,0.9157)..(0.2963,0.9329)..(0.2546,0.9455)
  220       ..(0.2183,0.9535)..(0.1866,0.9571)..(0.1573,0.9567)
  221       ..(0.1282,0.9522)..(0.0968,0.9441)..(0.0615,0.9327)
  222       ..(0.0216,0.9195)..(-0.0224,0.9062)..(-0.0691,0.8949)
  223       ..(-0.1165,0.8874)..(-0.1623,0.8848)..(-0.2043,0.8874)
  224       ..(-0.2408,0.8942)..(-0.2706,0.9035)..(-0.2939,0.9132)
  225       ..(-0.3117,0.9216)..(-0.3262,0.9272)..(-0.3407,0.9293)
  226       ..(-0.3583,0.9271)..(-0.3815,0.9205)..(-0.4119,0.9088)
  227       ..(-0.4494,0.8918)..(-0.4920,0.8697)..(-0.5370,0.8433)
  228       ..(-0.5802,0.8145);
  229      draw p scaled radius withcolor 0.650000 [black,white];
  230      pickup pencircle scaled 0.400000 pt;
  231      label.urt(btex $(\vartheta=2.5)$ etex,(0.293901,0.649686)*radius);
  232     ahangle:=oldahangle;
  233     oldahangle:=ahangle;
  234     ahangle:=30.000000;
  235     pickup pencircle scaled 0.800000 pt;
  236      pickup pencircle scaled 0.800000 pt;
  237      p := makepath makepen (0.2939,-0.9132)..(0.3117,-0.9216)
  238       ..(0.3262,-0.9272)..(0.3407,-0.9293)..(0.3583,-0.9271)
  239       ..(0.3815,-0.9205)..(0.4119,-0.9088)..(0.4494,-0.8918)
  240       ..(0.4920,-0.8697)..(0.5370,-0.8433)..(0.5802,-0.8145)
  241       ..(0.6179,-0.7858);
  242      draw p scaled radius withcolor black;
  243      pickup pencircle scaled 0.800000 pt;
  244      p := makepath makepen (-0.5935,-0.8038)..(-0.6040,-0.7968)
  245       ..(-0.6040,-0.7942)..(-0.5923,-0.7979)..(-0.5689,-0.8084)
  246       ..(-0.5349,-0.8252)..(-0.4924,-0.8469)..(-0.4441,-0.8708)
  247       ..(-0.3933,-0.8945)..(-0.3431,-0.9157)..(-0.2963,-0.9329)
  248       ..(-0.2546,-0.9455)..(-0.2183,-0.9535)..(-0.1866,-0.9571)
  249       ..(-0.1573,-0.9567)..(-0.1282,-0.9522)..(-0.0968,-0.9441)
  250       ..(-0.0615,-0.9327)..(-0.0216,-0.9195)..(0.0224,-0.9062)
  251       ..(0.0691,-0.8949)..(0.1165,-0.8874)..(0.1623,-0.8848)
  252       ..(0.2043,-0.8874)..(0.2408,-0.8942)..(0.2706,-0.9035)
  253       ..(0.2939,-0.9132);
  254      drawarrow p scaled radius withcolor black;
  255      pickup pencircle scaled 0.400000 pt;
  256      label.urt(btex $(\vartheta=0.6)$ etex,(0.293901,-0.913190)*radius);
  257      pickup pencircle scaled 0.800000 pt;
  258      p := makepath makepen (0.4755,-0.5116)..(0.5205,-0.5529)
  259       ..(0.5604,-0.5858)..(0.5977,-0.6061)..(0.6357,-0.6111)
  260       ..(0.6769,-0.5993)..(0.7226,-0.5702)..(0.7719,-0.5250)
  261       ..(0.8218,-0.4663)..(0.8688,-0.3986)..(0.9095,-0.3284)
  262       ..(0.9419,-0.2629)..(0.9653,-0.2088)..(0.9804,-0.1715)
  263       ..(0.9877,-0.1537)..(0.9869,-0.1557);
  264      draw p scaled radius withcolor black;
  265      pickup pencircle scaled 0.800000 pt;
  266      p := makepath makepen (-0.9079,-0.4166)..(-0.9217,-0.3867)
  267       ..(-0.9303,-0.3496)..(-0.9304,-0.3118)..(-0.9207,-0.2797)
  268       ..(-0.9016,-0.2596)..(-0.8742,-0.2561)..(-0.8396,-0.2716)
  269       ..(-0.7984,-0.3059)..(-0.7506,-0.3560)..(-0.6962,-0.4168)
  270       ..(-0.6364,-0.4814)..(-0.5730,-0.5430)..(-0.5089,-0.5955)
  271       ..(-0.4466,-0.6345)..(-0.3874,-0.6578)..(-0.3310,-0.6643)
  272       ..(-0.2760,-0.6541)..(-0.2202,-0.6288)..(-0.1616,-0.5904)
  273       ..(-0.0994,-0.5433)..(-0.0338,-0.4931)..(0.0342,-0.4464)
  274       ..(0.1032,-0.4097)..(0.1720,-0.3882)..(0.2395,-0.3844)
  275       ..(0.3050,-0.3986)..(0.3670,-0.4281)..(0.4243,-0.4679)
  276       ..(0.4755,-0.5116);
  277      drawarrow p scaled radius withcolor black;
  278      pickup pencircle scaled 0.400000 pt;
  279      label.urt(btex $(\vartheta=1.3)$ etex,(0.475533,-0.511636)*radius);
  280      pickup pencircle scaled 0.800000 pt;
  281      p := makepath makepen (0.4755,0.0853)..(0.5412,0.0351)
  282       ..(0.6033,-0.0068)..(0.6604,-0.0341)..(0.7122,-0.0422)
  283       ..(0.7584,-0.0289)..(0.7984,0.0056)..(0.8310,0.0586)
  284       ..(0.8546,0.1251)..(0.8688,0.1984)..(0.8746,0.2708)
  285       ..(0.8749,0.3353)..(0.8737,0.3862)..(0.8750,0.4204)
  286       ..(0.8815,0.4363)..(0.8932,0.4343)..(0.9079,0.4166)
  287       ..(0.9217,0.3867);
  288      draw p scaled radius withcolor black;
  289      pickup pencircle scaled 0.800000 pt;
  290      p := makepath makepen (-0.9877,0.1537)..(-0.9869,0.1557)
  291       ..(-0.9774,0.1753)..(-0.9585,0.2079)..(-0.9303,0.2473)
  292       ..(-0.8947,0.2868)..(-0.8552,0.3196)..(-0.8160,0.3403)
  293       ..(-0.7802,0.3449)..(-0.7494,0.3311)..(-0.7226,0.2984)
  294       ..(-0.6972,0.2488)..(-0.6695,0.1858)..(-0.6364,0.1155)
  295       ..(-0.5959,0.0453)..(-0.5480,-0.0172)..(-0.4934,-0.0655)
  296       ..(-0.4340,-0.0945)..(-0.3709,-0.1018)..(-0.3049,-0.0872)
  297       ..(-0.2370,-0.0531)..(-0.1681,-0.0040)..(-0.0994,0.0537)
  298       ..(-0.0325,0.1124)..(0.0317,0.1648)..(0.0934,0.2044)
  299       ..(0.1534,0.2270)..(0.2137,0.2303)..(0.2760,0.2144)
  300       ..(0.3409,0.1818)..(0.4080,0.1366)..(0.4755,0.0853);
  301      drawarrow p scaled radius withcolor black;
  302      pickup pencircle scaled 0.400000 pt;
  303      label.urt(btex $(\vartheta=1.9)$ etex,(0.475533,0.085285)*radius);
  304      pickup pencircle scaled 0.800000 pt;
  305      p := makepath makepen (0.2939,0.6497)..(0.3453,0.6273)
  306       ..(0.3958,0.6088)..(0.4424,0.5975)..(0.4825,0.5958)
  307       ..(0.5138,0.6048)..(0.5349,0.6241)..(0.5452,0.6517)
  308       ..(0.5452,0.6848)..(0.5370,0.7196)..(0.5237,0.7527)
  309       ..(0.5094,0.7814)..(0.4980,0.8039)..(0.4932,0.8197)
  310       ..(0.4969,0.8286)..(0.5092,0.8313)..(0.5286,0.8287)
  311       ..(0.5519,0.8221)..(0.5749,0.8131)..(0.5935,0.8038)
  312       ..(0.6040,0.7968);
  313      draw p scaled radius withcolor black;
  314      pickup pencircle scaled 0.800000 pt;
  315      p := makepath makepen (-0.5802,0.8145)..(-0.6179,0.7858)
  316       ..(-0.6468,0.7602)..(-0.6643,0.7405)..(-0.6692,0.7285)
  317       ..(-0.6612,0.7247)..(-0.6412,0.7283)..(-0.6115,0.7376)
  318       ..(-0.5749,0.7498)..(-0.5357,0.7622)..(-0.4979,0.7722)
  319       ..(-0.4651,0.7777)..(-0.4397,0.7771)..(-0.4223,0.7693)
  320       ..(-0.4119,0.7539)..(-0.4060,0.7310)..(-0.4009,0.7018)
  321       ..(-0.3933,0.6684)..(-0.3802,0.6339)..(-0.3594,0.6020)
  322       ..(-0.3306,0.5764)..(-0.2941,0.5603)..(-0.2513,0.5554)
  323       ..(-0.2044,0.5619)..(-0.1555,0.5785)..(-0.1072,0.6024)
  324       ..(-0.0615,0.6302)..(-0.0194,0.6579)..(0.0185,0.6821)
  325       ..(0.0532,0.7003)..(0.0865,0.7107)..(0.1205,0.7125)
  326       ..(0.1573,0.7060)..(0.1986,0.6920)..(0.2443,0.6723)
  327       ..(0.2939,0.6497);
  328      drawarrow p scaled radius withcolor black;
  329      pickup pencircle scaled 0.400000 pt;
  330      label.urt(btex $(\vartheta=2.5)$ etex,(0.293901,0.649686)*radius);
  331     ahangle:=oldahangle;
  332   %
  333   % Draw the paths of the arrows specified by the user.
  334   %
  335      pickup pencircle scaled 0.5pt;
  336      p := makepath makepen
  337         (-0.381833,-0.626402)..(-0.383762,-0.618065)
  338                     ..(-0.385658,-0.609605)
  339                     ..(-0.387520,-0.601024)
  340                     ..(-0.389346,-0.592324)
  341                     ..(-0.391134,-0.583505)
  342                     ..(-0.392884,-0.574569)
  343                     ..(-0.394594,-0.565519)
  344                     ..(-0.396263,-0.556356)
  345                     ..(-0.397890,-0.547082)
  346                     ..(-0.399473,-0.537701)
  347                     ..(-0.401012,-0.528214)
  348                     ..(-0.402505,-0.518624)
  349                     ..(-0.403950,-0.508934)
  350                     ..(-0.405348,-0.499146)
  351                     ..(-0.406697,-0.489265)
  352                     ..(-0.407995,-0.479292)
  353                     ..(-0.409243,-0.469232)
  354                     ..(-0.410439,-0.459088)
  355                     ..(-0.411582,-0.448864)
  356                     ..(-0.412672,-0.438562)
  357                     ..(-0.413708,-0.428189)
  358                     ..(-0.414690,-0.417746)
  359                     ..(-0.415616,-0.407238)
  360                     ..(-0.416486,-0.396670)
  361                     ..(-0.417301,-0.386045);
  362      drawarrow p scaled radius withcolor 0.900000 [white,black];
  363      p := makepath makepen
  364         (-0.417301,-0.386045)..(-0.418059,-0.375368)
  365                     ..(-0.418760,-0.364643)
  366                     ..(-0.419405,-0.353874)
  367                     ..(-0.419992,-0.343067)
  368                     ..(-0.420523,-0.332225)
  369                     ..(-0.420996,-0.321353)
  370                     ..(-0.421412,-0.310456)
  371                     ..(-0.421771,-0.299538)
  372                     ..(-0.422073,-0.288603)
  373                     ..(-0.422319,-0.277657)
  374                     ..(-0.422508,-0.266703)
  375                     ..(-0.422642,-0.255747)
  376                     ..(-0.422721,-0.244792)
  377                     ..(-0.422744,-0.233843)
  378                     ..(-0.422714,-0.222904)
  379                     ..(-0.422630,-0.211980)
  380                     ..(-0.422493,-0.201075)
  381                     ..(-0.422303,-0.190193)
  382                     ..(-0.422063,-0.179338)
  383                     ..(-0.421771,-0.168514)
  384                     ..(-0.421430,-0.157725)
  385                     ..(-0.421041,-0.146974)
  386                     ..(-0.420603,-0.136266)
  387                     ..(-0.420119,-0.125604)
  388                     ..(-0.419588,-0.114992);
  389      draw p scaled radius withcolor 0.900000 [white,black];
  390      p := makepath makepen
  391         (0.192771,0.245539)..(0.191524,0.254864)
  392                     ..(0.190253,0.264210)
  393                     ..(0.188958,0.273573)
  394                     ..(0.187640,0.282952)
  395                     ..(0.186297,0.292344)
  396                     ..(0.184931,0.301745)
  397                     ..(0.183542,0.311152)
  398                     ..(0.182130,0.320564)
  399                     ..(0.180694,0.329977)
  400                     ..(0.179235,0.339387)
  401                     ..(0.177754,0.348792)
  402                     ..(0.176251,0.358190)
  403                     ..(0.174725,0.367576)
  404                     ..(0.173178,0.376948)
  405                     ..(0.171609,0.386302)
  406                     ..(0.170020,0.395636)
  407                     ..(0.168409,0.404947)
  408                     ..(0.166779,0.414231)
  409                     ..(0.165128,0.423485)
  410                     ..(0.163459,0.432707)
  411                     ..(0.161770,0.441893)
  412                     ..(0.160063,0.451040)
  413                     ..(0.158337,0.460145)
  414                     ..(0.156595,0.469206)
  415                     ..(0.154835,0.478219);
  416      drawarrow p scaled radius withcolor 0.900000 [white,black];
  417      p := makepath makepen
  418         (0.154835,0.478219)..(0.153059,0.487182)
  419                     ..(0.151268,0.496091)
  420                     ..(0.149461,0.504944)
  421                     ..(0.147639,0.513738)
  422                     ..(0.145804,0.522471)
  423                     ..(0.143955,0.531140)
  424                     ..(0.142094,0.539743)
  425                     ..(0.140220,0.548276)
  426                     ..(0.138335,0.556738)
  427                     ..(0.136439,0.565126)
  428                     ..(0.134533,0.573439)
  429                     ..(0.132617,0.581673)
  430                     ..(0.130693,0.589827)
  431                     ..(0.128761,0.597900)
  432                     ..(0.126821,0.605888)
  433                     ..(0.124874,0.613791)
  434                     ..(0.122922,0.621607)
  435                     ..(0.120963,0.629334)
  436                     ..(0.119001,0.636970)
  437                     ..(0.117034,0.644515)
  438                     ..(0.115063,0.651966)
  439                     ..(0.113090,0.659324)
  440                     ..(0.111115,0.666586)
  441                     ..(0.109139,0.673752)
  442                     ..(0.107161,0.680820);
  443      draw p scaled radius withcolor 0.900000 [white,black];
  444   %
  445   % Draw the $S_1$-, $S_2$- and $S_3$-axis of the Poincare sphere.
  446   % First of all, calculate the transformations of the intersections
  447   % for the unity sphere.
  448   %
  449   % Used variables:
  450   %
  451   %    behind_distance : Specifies the relative distance of the coordi-
  452   %                      axes to be plotted behind origo (in negative di-
  453   %                      rection of respective axis.
  454   %
  455   %   outside_distance_s1 : The relative distance from origo to the point
  456   %                         of the arrow head of the coordinate axis S1.
  457   %                         If this is set to 1.0, the arrow head will
  458   %                         point directly at the Poincare sphere.
  459   %
  460   %   outside_distance_s2 : Same as above, except that this one controls
  461   %                         the S2 coordinate axis instead.
  462   %
  463   %   outside_distance_s3 : Same as above, except that this one controls
  464   %                         the S3 coordinate axis instead.
  465   %
  466   %    insidecolval :    Specifies the shade of gray to use for the parts
  467   %                      of the coordinate axes that are inside the Poin-
  468   %                      care sphere. Values must be between 0 and 1,
  469   %                      where:  '0.0' <=> 'white';  '1.0' <=> 'black'
  470   %
  471      behind_distance_s1  := -0.300000;
  472      behind_distance_s2  := -0.300000;
  473      behind_distance_s3  := -0.300000;
  474      outside_distance_s1 :=  1.700000;
  475      outside_distance_s2 :=  2.400000;
  476      outside_distance_s3 :=  1.500000;
  477      insidecolval := .85;    % '0.0' <=> 'white';  '1.0' <=> 'black'
  478   
  479      pickup pencircle scaled 0.600000 pt;
  480   %
  481   % Start with drawing the x-axis...
  482   %
  483      x_bis_start :=  radius*behind_distance_s1*cosd(rot_psi)*cosd(rot_phi);
  484      y_bis_start :=  radius*behind_distance_s1*sind(rot_psi);
  485      z_bis_start := -radius*behind_distance_s1*cosd(rot_psi)*sind(rot_phi);
  486      x_bis_intersect :=  radius*cosd(rot_psi)*cosd(rot_phi);
  487      y_bis_intersect :=  radius*sind(rot_psi);
  488      z_bis_intersect := -radius*cosd(rot_psi)*sind(rot_phi);
  489      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  490                (outside_distance_s1*y_bis_intersect,
  491                 outside_distance_s1*z_bis_intersect);
  492      drawarrow p;
  493      label.bot(btex $s_1(t)$ etex,
  494                (outside_distance_s1*y_bis_intersect,
  495                 outside_distance_s1*z_bis_intersect));
  496   
  497   %
  498   % ... then draw the y-axis ...
  499   %
  500      x_bis_start := -radius*behind_distance_s2*sind(rot_psi)*cosd(rot_phi);
  501      y_bis_start :=  radius*behind_distance_s2*cosd(rot_psi);
  502      z_bis_start :=  radius*behind_distance_s2*sind(rot_psi)*sind(rot_phi);
  503      x_bis_intersect := -radius*sind(rot_psi)*cosd(rot_phi);
  504      y_bis_intersect :=  radius*cosd(rot_psi);
  505      z_bis_intersect :=  radius*sind(rot_psi)*sind(rot_phi);
  506      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  507                (outside_distance_s2*y_bis_intersect,
  508                 outside_distance_s2*z_bis_intersect);
  509      drawarrow p;
  510      label.bot(btex $s_2(t)$ etex,
  511                (outside_distance_s2*y_bis_intersect,
  512                 outside_distance_s2*z_bis_intersect));
  513   
  514   %
  515   % ... then, finally, draw the z-axis.
  516   %
  517      x_bis_start := radius*behind_distance_s3*sind(rot_phi);
  518      y_bis_start := 0.0;
  519      z_bis_start := radius*behind_distance_s3*cosd(rot_phi);
  520      x_bis_intersect := radius*sind(rot_phi);
  521      y_bis_intersect := 0.0;
  522      z_bis_intersect := radius*cosd(rot_phi);
  523      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  524                (outside_distance_s3*y_bis_intersect,
  525                 outside_distance_s3*z_bis_intersect);
  526      drawarrow p;
  527      label.rt(btex $s_3(t)$ etex,
  528                (outside_distance_s3*y_bis_intersect,
  529                 outside_distance_s3*z_bis_intersect));
  530   
  531      endfig;
  532   end
  533   

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Last modified Thursday 23 Jan 2014