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




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    1   % This Filename:  example-cc.mp   [MetaPost source]
    2   % Creation time:  Thu Jan 23 20:19:29 2014
    3   %
    4   % Copyright (C) 1997-2005, Fredrik Jonsson <fj@optics.kth.se>
    5   %
    6   % Input Filename [Stokes parameters]:  example-cc.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-cc.dat --outputfile
   10   %     example-cc.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 20.0 --draw_paths_as_arrows
   16   %
   17   % Description:  Map of Stokes parameters, visualized as trajectories
   18   %               onto the Poincare sphere. This file contains MetaPost
   19   %               source code, to be compiled with John Hobby's MetaPost
   20   %               compiler or used with anything that understands MetaPost
   21   %               source code.
   22   %
   23   % If you want to create PostScript output, or include the resulting
   24   % output in a TeX document, this example illustrates the procedure,
   25   % assuming 'poincaremap.mp' to be the name of the file containing the
   26   % MetaPost code to be visualized: (commands run on command-line)
   27   %
   28   %       mp poincaremap.mp;
   29   %       echo "\input epsf\centerline{\epsfbox{poincaremap.1}}\bye" > tmp.tex;
   30   %       tex tmp.tex;
   31   %       dvips tmp.dvi -o poincaremap.ps;
   32   %
   33   % Here, the first command compiles the MetaPost source code, and leaves
   34   % an Encapsulated PostScript file named 'poincaremap.1', containing TeX
   35   % control codes for characters, etc. This file does not contain any
   36   % definitions for characters or TeX-specific items, and it cannot be
   37   % viewed or printed simply as is stands; it must rather be included into
   38   % TeX code in order to provide something useful.
   39   %     The second command creates a temporary minimal TeX-file 'tmp.tex',
   40   % that only includes the previously generated Encapsulated PostScript
   41   % code.
   42   %     The third command compiles the TeX-code into device-independent,
   43   % or DVI, output, stored in the file 'tmp.dvi'.
   44   %     Finally, the last command converts the DVI output into a free-
   45   % standing PostScript file 'poincaremap.ps', to be printed or viewed
   46   % with some PostScript viewer, such as GhostView.
   47   %
   48   scalefactor := 20.000000 mm;
   49   rot_psi := -60.000000;  % Rotation angle round z-axis (first rotation)
   50   rot_phi := 15.000000;  % Rotation angle round y-axis (second rotation)
   51   alpha := -24.146108;    % == arctan(sin(rot_phi)*tan(rot_psi))
   52   beta  := -8.498781;    % == arctan(sin(rot_phi)/tan(rot_psi))
   53   
   54   %
   55   % Parameters specifying the location of the light source; for Phong
   56   % shading of the sphere.
   57   %
   58   %    phi_source:  Angle (in deg.) to light source counterclockwise
   59   %                 'from three o'clock', viewed from the observer.
   60   %
   61   %  theta_source:  Angle (in deg.) between light source and observer,
   62   %                 seen from the centre of the sphere.
   63   %
   64   % Parameters specifying the shading 'intensity' in terms of maximum
   65   % (for the highlighs) and minimum (for the deep shadowed regions)
   66   % values for the Phong shading.  '0.0' <=> 'black'; '1.0' <=> 'white'
   67   %
   68   %   upper_value:  Maximum value of whiteness.
   69   %   lower_value:  Minimum value of whiteness.
   70   %
   71   phi_source := 30.000000;
   72   theta_source := 30.000000;
   73   upper_value := 0.990000;
   74   lower_value := 0.750000;
   75   radius := scalefactor;
   76   delta_rho := radius/50.000000;
   77   delta_phi := 360.0/80.000000;
   78   beginfig(1);
   79     path p;
   80     path equator;
   81     transform T;
   82     c1:=lower_value;
   83     c2:=upper_value-lower_value;
   84     nx_source := sind(theta_source)*cosd(phi_source);
   85     ny_source := sind(theta_source)*sind(phi_source);
   86     nz_source := cosd(theta_source);
   87     phistop := 360.0;
   88     rhostop := radius - delta_rho/2.0;
   89   %
   90   % Draw the shaded Poincare sphere projected on 2D screen coordinates
   91   %
   92     for rho=0.0cm step delta_rho until rhostop:
   93       for phi=0.0 step delta_phi until phistop:
   94         rhomid := rho + delta_rho/2.0;
   95         phimid := phi + delta_phi/2.0;
   96         x1 := rho*cosd(phi);
   97         y1 := rho*sind(phi);
   98         x2 := (rho+delta_rho)*cosd(phi);
   99         y2 := (rho+delta_rho)*sind(phi);
  100         x3 := (rho+delta_rho)*cosd(phi+delta_phi);
  101         y3 := (rho+delta_rho)*sind(phi+delta_phi);
  102         x4 := rho*cosd(phi+delta_phi);
  103         y4 := rho*sind(phi+delta_phi);
  104         p:=makepath makepen ((x1,y1)--(x2,y2)--(x3,y3)--(x4,y4)--(x1,y1));
  105         quot := (rhomid/radius);
  106         nx_object := quot*cosd(phimid);
  107         ny_object := quot*sind(phimid);
  108         nz_object := sqrt(1-quot*quot);
  109         prod:=nx_object*nx_source+ny_object*ny_source
  110               +nz_object*nz_source;
  111         if prod < 0.0:
  112            value := c1;
  113         else:
  114            value := c1 + c2*prod*prod;
  115         fi
  116         fill p withcolor value[black,white];
  117       endfor
  118     endfor
  119   
  120   %
  121   % Draw the 'equators' of the Poincare sphere
  122   %
  123      equator := halfcircle scaled (2.0*radius);
  124      eqcolval := .45;    % '0.0' <=> 'white';  '1.0' <=> 'black'
  125   
  126      pickup pencircle scaled 0.600000 pt;
  127   %
  128   % Draw equator $S_3=0$...
  129   %
  130      T := identity yscaled sind(rot_phi) rotated 180.0;
  131      draw equator transformed T withcolor eqcolval [white,black];
  132   
  133   %
  134   % ... then equator $S_2=0$...
  135   %
  136      T := identity yscaled (cosd(rot_phi)*sind(rot_psi))
  137                    rotated (270.0 + alpha);
  138      draw equator transformed T withcolor eqcolval [white,black];
  139   
  140   %
  141   % ... and finally equator $S_1=0$.
  142   %
  143      T := identity yscaled (cosd(rot_phi)*cosd(rot_psi))
  144                    rotated (270.0 - beta);
  145      draw equator transformed T withcolor eqcolval [white,black];
  146   
  147     oldahangle:=ahangle;
  148     ahangle:=20.000000;
  149     pickup pencircle scaled 0.800000 pt;
  150      pickup pencircle scaled 0.400000 pt;
  151      pickup pencircle scaled 0.400000 pt;
  152      pickup pencircle scaled 0.800000 pt;
  153      p := makepath makepen (0.9883,0.1506)..(0.9814,0.1857)
  154       ..(0.9727,0.2205)..(0.9622,0.2550)..(0.9499,0.2893)
  155       ..(0.9359,0.3230)..(0.9202,0.3564)..(0.9029,0.3893)
  156       ..(0.8841,0.4216)..(0.8638,0.4534)..(0.8422,0.4845)
  157       ..(0.8192,0.5150)..(0.7950,0.5447)..(0.7696,0.5738)
  158       ..(0.7433,0.6020)..(0.7160,0.6295)..(0.6879,0.6561)
  159       ..(0.6591,0.6818)..(0.6296,0.7067);
  160      drawarrow p scaled radius withcolor 0.650000 [black,white];
  161      pickup pencircle scaled 0.400000 pt;
  162      pickup pencircle scaled 0.800000 pt;
  163      p := makepath makepen (0.6147,0.7187)..(0.5845,0.7422)
  164       ..(0.5540,0.7647)..(0.5233,0.7862)..(0.4924,0.8067)
  165       ..(0.4615,0.8262)..(0.4309,0.8447)..(0.4005,0.8621)
  166       ..(0.3703,0.8785)..(0.3408,0.8939)..(0.3117,0.9082)
  167       ..(0.2833,0.9214)..(0.2556,0.9336)..(0.2291,0.9447)
  168       ..(0.2034,0.9547)..(0.1788,0.9637)..(0.1554,0.9717)
  169       ..(0.1333,0.9787)..(0.1125,0.9846)..(0.0932,0.9895)
  170       ..(0.0753,0.9934)..(0.0591,0.9964)..(0.0444,0.9984);
  171      drawarrow p scaled radius withcolor 0.650000 [black,white];
  172      pickup pencircle scaled 0.400000 pt;
  173      pickup pencircle scaled 0.400000 pt;
  174      pickup pencircle scaled 0.800000 pt;
  175      p := makepath makepen (0.8294,-0.5586)..(0.8482,-0.5290)
  176       ..(0.8655,-0.4987)..(0.8812,-0.4679)..(0.8953,-0.4363)
  177       ..(0.9078,-0.4042)..(0.9185,-0.3715)..(0.9274,-0.3385)
  178       ..(0.9346,-0.3049)..(0.9398,-0.2710)..(0.9432,-0.2368)
  179       ..(0.9447,-0.2024)..(0.9444,-0.1676)..(0.9421,-0.1327)
  180       ..(0.9379,-0.0977)..(0.9319,-0.0627)..(0.9240,-0.0275)
  181       ..(0.9142,0.0075)..(0.9026,0.0425)..(0.8893,0.0774)
  182       ..(0.8742,0.1121)..(0.8574,0.1467);
  183      drawarrow p scaled radius withcolor 0.650000 [black,white];
  184      pickup pencircle scaled 0.400000 pt;
  185      pickup pencircle scaled 0.800000 pt;
  186      p := makepath makepen (0.8485,0.1637)..(0.8293,0.1978)
  187       ..(0.8086,0.2316)..(0.7865,0.2649)..(0.7630,0.2978)
  188       ..(0.7382,0.3303)..(0.7123,0.3622)..(0.6852,0.3935)
  189       ..(0.6571,0.4244)..(0.6281,0.4545)..(0.5983,0.4841)
  190       ..(0.5678,0.5130)..(0.5367,0.5411)..(0.5052,0.5685)
  191       ..(0.4732,0.5951)..(0.4411,0.6210)..(0.4088,0.6460)
  192       ..(0.3764,0.6702)..(0.3442,0.6935)..(0.3122,0.7159)
  193       ..(0.2806,0.7375)..(0.2493,0.7582)..(0.2186,0.7780);
  194      drawarrow p scaled radius withcolor 0.650000 [black,white];
  195      pickup pencircle scaled 0.400000 pt;
  196      pickup pencircle scaled 0.800000 pt;
  197      p := makepath makepen (0.2035,0.7875)..(0.1738,0.8060)
  198       ..(0.1449,0.8234)..(0.1170,0.8400)..(0.0901,0.8557)
  199       ..(0.0644,0.8704)..(0.0398,0.8843)..(0.0166,0.8972)
  200       ..(-0.0053,0.9092)..(-0.0258,0.9204)..(-0.0447,0.9306)
  201       ..(-0.0621,0.9400)..(-0.0777,0.9485)..(-0.0917,0.9562)
  202       ..(-0.1040,0.9631)..(-0.1145,0.9692)..(-0.1231,0.9744)
  203       ..(-0.1299,0.9789)..(-0.1349,0.9827)..(-0.1379,0.9857)
  204       ..(-0.1391,0.9881)..(-0.1384,0.9897)..(-0.1359,0.9907);
  205      drawarrow p scaled radius withcolor 0.650000 [black,white];
  206      pickup pencircle scaled 0.400000 pt;
  207      pickup pencircle scaled 0.800000 pt;
  208      p := makepath makepen (0.3182,-0.9375)..(0.3467,-0.9272)
  209       ..(0.3749,-0.9158)..(0.4030,-0.9032)..(0.4306,-0.8894)
  210       ..(0.4578,-0.8745)..(0.4842,-0.8585)..(0.5100,-0.8414)
  211       ..(0.5351,-0.8231)..(0.5591,-0.8038)..(0.5821,-0.7835)
  212       ..(0.6040,-0.7622)..(0.6246,-0.7399)..(0.6440,-0.7166)
  213       ..(0.6619,-0.6925)..(0.6784,-0.6676)..(0.6935,-0.6416)
  214       ..(0.7069,-0.6150)..(0.7185,-0.5877)..(0.7286,-0.5596)
  215       ..(0.7368,-0.5308)..(0.7433,-0.5015)..(0.7479,-0.4716);
  216      drawarrow p scaled radius withcolor 0.650000 [black,white];
  217      pickup pencircle scaled 0.400000 pt;
  218      pickup pencircle scaled 0.800000 pt;
  219      p := makepath makepen (0.7495,-0.4564)..(0.7513,-0.4257)
  220       ..(0.7513,-0.3945)..(0.7494,-0.3629)..(0.7455,-0.3310)
  221       ..(0.7398,-0.2987)..(0.7321,-0.2663)..(0.7227,-0.2335)
  222       ..(0.7114,-0.2006)..(0.6983,-0.1676)..(0.6835,-0.1345)
  223       ..(0.6669,-0.1014)..(0.6487,-0.0684)..(0.6289,-0.0353)
  224       ..(0.6076,-0.0024)..(0.5848,0.0303)..(0.5606,0.0628)
  225       ..(0.5351,0.0952)..(0.5084,0.1272)..(0.4806,0.1588)
  226       ..(0.4517,0.1902)..(0.4220,0.2211)..(0.3913,0.2517);
  227      drawarrow p scaled radius withcolor 0.650000 [black,white];
  228      pickup pencircle scaled 0.400000 pt;
  229      pickup pencircle scaled 0.800000 pt;
  230      p := makepath makepen (0.3758,0.2667)..(0.3441,0.2965)
  231       ..(0.3119,0.3258)..(0.2793,0.3545)..(0.2463,0.3827)
  232       ..(0.2131,0.4103)..(0.1798,0.4372)..(0.1465,0.4635)
  233       ..(0.1133,0.4892)..(0.0805,0.5141)..(0.0479,0.5385)
  234       ..(0.0158,0.5621)..(-0.0156,0.5849)..(-0.0464,0.6071)
  235       ..(-0.0764,0.6285)..(-0.1055,0.6492)..(-0.1336,0.6691)
  236       ..(-0.1605,0.6883)..(-0.1864,0.7067)..(-0.2109,0.7244)
  237       ..(-0.2340,0.7414)..(-0.2558,0.7576)..(-0.2760,0.7731);
  238      drawarrow p scaled radius withcolor 0.650000 [black,white];
  239      pickup pencircle scaled 0.400000 pt;
  240      pickup pencircle scaled 0.800000 pt;
  241      p := makepath makepen (-0.2855,0.7806)..(-0.3033,0.7951)
  242       ..(-0.3195,0.8088)..(-0.3339,0.8218)..(-0.3465,0.8342)
  243       ..(-0.3574,0.8458)..(-0.3665,0.8568)..(-0.3737,0.8672)
  244       ..(-0.3790,0.8769)..(-0.3824,0.8860)..(-0.3840,0.8946)
  245       ..(-0.3837,0.9025)..(-0.3815,0.9099)..(-0.3774,0.9168)
  246       ..(-0.3716,0.9231)..(-0.3639,0.9289)..(-0.3545,0.9343)
  247       ..(-0.3434,0.9392);
  248      draw p scaled radius withcolor 0.650000 [black,white];
  249      pickup pencircle scaled 0.400000 pt;
  250      pickup pencircle scaled 0.800000 pt;
  251      p := makepath makepen (0.3199,-0.8838)..(0.3410,-0.8694)
  252       ..(0.3609,-0.8539)..(0.3795,-0.8374)..(0.3966,-0.8199)
  253       ..(0.4124,-0.8014)..(0.4266,-0.7819)..(0.4391,-0.7615)
  254       ..(0.4500,-0.7402)..(0.4592,-0.7182)..(0.4666,-0.6953)
  255       ..(0.4722,-0.6717)..(0.4761,-0.6473)..(0.4780,-0.6223)
  256       ..(0.4781,-0.5966)..(0.4762,-0.5704)..(0.4726,-0.5436)
  257       ..(0.4670,-0.5163)..(0.4596,-0.4886)..(0.4502,-0.4605)
  258       ..(0.4392,-0.4319)..(0.4263,-0.4031)..(0.4116,-0.3740);
  259      drawarrow p scaled radius withcolor 0.650000 [black,white];
  260      pickup pencircle scaled 0.400000 pt;
  261      pickup pencircle scaled 0.800000 pt;
  262      p := makepath makepen (0.4035,-0.3595)..(0.3863,-0.3300)
  263       ..(0.3674,-0.3005)..(0.3469,-0.2707)..(0.3251,-0.2410)
  264       ..(0.3016,-0.2112)..(0.2769,-0.1815)..(0.2509,-0.1516)
  265       ..(0.2237,-0.1220)..(0.1954,-0.0925)..(0.1661,-0.0631)
  266       ..(0.1359,-0.0339)..(0.1049,-0.0050)..(0.0732,0.0237)
  267       ..(0.0409,0.0521)..(0.0083,0.0802)..(-0.0248,0.1079)
  268       ..(-0.0582,0.1353)..(-0.0916,0.1622)..(-0.1250,0.1887)
  269       ..(-0.1584,0.2149)..(-0.1915,0.2405)..(-0.2243,0.2657);
  270      drawarrow p scaled radius withcolor 0.650000 [black,white];
  271      pickup pencircle scaled 0.400000 pt;
  272      pickup pencircle scaled 0.800000 pt;
  273      p := makepath makepen (-0.2404,0.2781)..(-0.2726,0.3025)
  274       ..(-0.3039,0.3265)..(-0.3347,0.3499)..(-0.3645,0.3728)
  275       ..(-0.3935,0.3951)..(-0.4214,0.4168)..(-0.4482,0.4381)
  276       ..(-0.4737,0.4589)..(-0.4979,0.4790)..(-0.5208,0.4987)
  277       ..(-0.5422,0.5178)..(-0.5621,0.5363)..(-0.5803,0.5544)
  278       ..(-0.5970,0.5718)..(-0.6118,0.5888)..(-0.6250,0.6053)
  279       ..(-0.6363,0.6213)..(-0.6458,0.6368)..(-0.6534,0.6517)
  280       ..(-0.6592,0.6663)..(-0.6631,0.6804)..(-0.6651,0.6940);
  281      drawarrow p scaled radius withcolor 0.650000 [black,white];
  282      pickup pencircle scaled 0.400000 pt;
  283      pickup pencircle scaled 0.800000 pt;
  284      p := makepath makepen (-0.6654,0.7006)..(-0.6646,0.7137)
  285       ..(-0.6618,0.7263)..(-0.6573,0.7384)..(-0.6508,0.7503)
  286       ..(-0.6427,0.7617)..(-0.6328,0.7727)..(-0.6211,0.7835);
  287      draw p scaled radius withcolor 0.650000 [black,white];
  288      pickup pencircle scaled 0.400000 pt;
  289      pickup pencircle scaled 0.800000 pt;
  290      p := makepath makepen (0.1994,-0.8401)..(0.2052,-0.8235)
  291       ..(0.2090,-0.8060)..(0.2110,-0.7878)..(0.2112,-0.7687)
  292       ..(0.2095,-0.7491)..(0.2058,-0.7287)..(0.2004,-0.7077)
  293       ..(0.1931,-0.6862)..(0.1839,-0.6641)..(0.1729,-0.6415)
  294       ..(0.1602,-0.6185)..(0.1456,-0.5950)..(0.1294,-0.5712)
  295       ..(0.1116,-0.5470)..(0.0921,-0.5226)..(0.0712,-0.4979)
  296       ..(0.0488,-0.4729)..(0.0251,-0.4479)..(-0.0000,-0.4226)
  297       ..(-0.0262,-0.3972)..(-0.0536,-0.3718)..(-0.0820,-0.3463);
  298      drawarrow p scaled radius withcolor 0.650000 [black,white];
  299      pickup pencircle scaled 0.400000 pt;
  300      pickup pencircle scaled 0.800000 pt;
  301      p := makepath makepen (-0.0965,-0.3337)..(-0.1262,-0.3082)
  302       ..(-0.1567,-0.2827)..(-0.1879,-0.2573)..(-0.2196,-0.2322)
  303       ..(-0.2517,-0.2070)..(-0.2841,-0.1821)..(-0.3168,-0.1572)
  304       ..(-0.3495,-0.1326)..(-0.3822,-0.1082)..(-0.4148,-0.0840)
  305       ..(-0.4471,-0.0601)..(-0.4790,-0.0364)..(-0.5105,-0.0130)
  306       ..(-0.5413,0.0100)..(-0.5714,0.0328)..(-0.6008,0.0553)
  307       ..(-0.6292,0.0775)..(-0.6566,0.0993)..(-0.6829,0.1208)
  308       ..(-0.7080,0.1420)..(-0.7318,0.1628)..(-0.7542,0.1834);
  309      drawarrow p scaled radius withcolor 0.650000 [black,white];
  310      pickup pencircle scaled 0.400000 pt;
  311      pickup pencircle scaled 0.800000 pt;
  312      p := makepath makepen (-0.7649,0.1935)..(-0.7850,0.2136)
  313       ..(-0.8037,0.2333)..(-0.8207,0.2527)..(-0.8361,0.2718)
  314       ..(-0.8497,0.2906)..(-0.8616,0.3090)..(-0.8716,0.3271)
  315       ..(-0.8798,0.3451)..(-0.8862,0.3626)..(-0.8906,0.3800)
  316       ..(-0.8931,0.3971)..(-0.8938,0.4139)..(-0.8925,0.4305)
  317       ..(-0.8894,0.4469)..(-0.8844,0.4630)..(-0.8776,0.4790);
  318      draw p scaled radius withcolor 0.650000 [black,white];
  319      pickup pencircle scaled 0.400000 pt;
  320      pickup pencircle scaled 0.400000 pt;
  321      pickup pencircle scaled 0.800000 pt;
  322      p := makepath makepen (0.0028,-0.8231)..(-0.0091,-0.8070)
  323       ..(-0.0227,-0.7903)..(-0.0380,-0.7732)..(-0.0549,-0.7556)
  324       ..(-0.0735,-0.7376)..(-0.0934,-0.7192)..(-0.1149,-0.7005)
  325       ..(-0.1376,-0.6815)..(-0.1616,-0.6622)..(-0.1868,-0.6427)
  326       ..(-0.2131,-0.6230)..(-0.2404,-0.6030)..(-0.2686,-0.5829)
  327       ..(-0.2975,-0.5627)..(-0.3272,-0.5424)..(-0.3574,-0.5219)
  328       ..(-0.3881,-0.5014)..(-0.4190,-0.4810)..(-0.4503,-0.4605)
  329       ..(-0.4817,-0.4400)..(-0.5130,-0.4194)..(-0.5442,-0.3990);
  330      drawarrow p scaled radius withcolor 0.650000 [black,white];
  331      pickup pencircle scaled 0.400000 pt;
  332      pickup pencircle scaled 0.800000 pt;
  333      p := makepath makepen (-0.5598,-0.3888)..(-0.5906,-0.3684)
  334       ..(-0.6211,-0.3481)..(-0.6510,-0.3279)..(-0.6803,-0.3078)
  335       ..(-0.7089,-0.2878)..(-0.7366,-0.2679)..(-0.7634,-0.2480)
  336       ..(-0.7892,-0.2283)..(-0.8138,-0.2087)..(-0.8372,-0.1892)
  337       ..(-0.8593,-0.1699)..(-0.8799,-0.1507)..(-0.8992,-0.1316)
  338       ..(-0.9168,-0.1126)..(-0.9329,-0.0937)..(-0.9472,-0.0749)
  339       ..(-0.9599,-0.0561)..(-0.9708,-0.0376)..(-0.9799,-0.0191)
  340       ..(-0.9872,-0.0006)..(-0.9925,0.0178)..(-0.9960,0.0363);
  341      drawarrow p scaled radius withcolor 0.650000 [black,white];
  342      pickup pencircle scaled 0.400000 pt;
  343      pickup pencircle scaled 0.800000 pt;
  344      p := makepath makepen (-0.9971,0.0454)..(-0.9977,0.0637);
  345      draw p scaled radius withcolor 0.650000 [black,white];
  346      pickup pencircle scaled 0.400000 pt;
  347      pickup pencircle scaled 0.400000 pt;
  348      pickup pencircle scaled 0.800000 pt;
  349      p := makepath makepen (-0.1949,-0.8393)..(-0.2198,-0.8262)
  350       ..(-0.2457,-0.8129)..(-0.2725,-0.7993)..(-0.3001,-0.7855)
  351       ..(-0.3283,-0.7714)..(-0.3571,-0.7571)..(-0.3862,-0.7427)
  352       ..(-0.4157,-0.7281)..(-0.4454,-0.7133)..(-0.4752,-0.6984)
  353       ..(-0.5050,-0.6833)..(-0.5347,-0.6681)..(-0.5640,-0.6529)
  354       ..(-0.5930,-0.6375)..(-0.6215,-0.6221)..(-0.6495,-0.6066)
  355       ..(-0.6767,-0.5910)..(-0.7031,-0.5753)..(-0.7286,-0.5596)
  356       ..(-0.7530,-0.5438)..(-0.7764,-0.5279)..(-0.7986,-0.5119);
  357      drawarrow p scaled radius withcolor 0.650000 [black,white];
  358      pickup pencircle scaled 0.400000 pt;
  359      pickup pencircle scaled 0.800000 pt;
  360      p := makepath makepen (-0.8092,-0.5039)..(-0.8294,-0.4879)
  361       ..(-0.8482,-0.4717)..(-0.8655,-0.4554)..(-0.8812,-0.4392)
  362       ..(-0.8953,-0.4227)..(-0.9078,-0.4062)..(-0.9185,-0.3895)
  363       ..(-0.9274,-0.3727);
  364      draw p scaled radius withcolor 0.650000 [black,white];
  365      pickup pencircle scaled 0.400000 pt;
  366      pickup pencircle scaled 0.400000 pt;
  367      pickup pencircle scaled 0.400000 pt;
  368      pickup pencircle scaled 0.800000 pt;
  369      p := makepath makepen (-0.3182,-0.8824)..(-0.3467,-0.8739)
  370       ..(-0.3749,-0.8651)..(-0.4030,-0.8561)..(-0.4306,-0.8469)
  371       ..(-0.4578,-0.8375)..(-0.4842,-0.8279)..(-0.5100,-0.8181)
  372       ..(-0.5351,-0.8080)..(-0.5591,-0.7977)..(-0.5821,-0.7873)
  373       ..(-0.6040,-0.7766)..(-0.6246,-0.7657)..(-0.6440,-0.7545)
  374       ..(-0.6619,-0.7431)..(-0.6784,-0.7315)..(-0.6935,-0.7195)
  375       ..(-0.7069,-0.7073);
  376      draw p scaled radius withcolor 0.650000 [black,white];
  377      pickup pencircle scaled 0.400000 pt;
  378      pickup pencircle scaled 0.400000 pt;
  379      pickup pencircle scaled 0.400000 pt;
  380      pickup pencircle scaled 0.400000 pt;
  381      pickup pencircle scaled 0.800000 pt;
  382      p := makepath makepen (-0.3199,-0.9361)..(-0.3410,-0.9317)
  383       ..(-0.3609,-0.9270)..(-0.3795,-0.9219)..(-0.3966,-0.9165)
  384       ..(-0.4124,-0.9107);
  385      draw p scaled radius withcolor 0.650000 [black,white];
  386      pickup pencircle scaled 0.400000 pt;
  387      pickup pencircle scaled 0.400000 pt;
  388      pickup pencircle scaled 0.400000 pt;
  389      pickup pencircle scaled 0.400000 pt;
  390      pickup pencircle scaled 0.400000 pt;
  391      pickup pencircle scaled 0.400000 pt;
  392      pickup pencircle scaled 0.400000 pt;
  393      pickup pencircle scaled 0.800000 pt;
  394      p := makepath makepen (0.5770,0.8167)..(0.5490,0.8358)
  395       ..(0.5204,0.8538)..(0.4915,0.8707)..(0.4623,0.8865)
  396       ..(0.4330,0.9012)..(0.4038,0.9147)..(0.3745,0.9271)
  397       ..(0.3455,0.9384);
  398      draw p scaled radius withcolor 0.650000 [black,white];
  399      pickup pencircle scaled 0.400000 pt;
  400     ahangle:=oldahangle;
  401     oldahangle:=ahangle;
  402     ahangle:=20.000000;
  403     pickup pencircle scaled 0.800000 pt;
  404      pickup pencircle scaled 0.800000 pt;
  405      p := makepath makepen (-0.0028,-0.9968)..(0.0091,-0.9941)
  406       ..(0.0227,-0.9906)..(0.0380,-0.9861)..(0.0549,-0.9807)
  407       ..(0.0735,-0.9744)..(0.0934,-0.9671)..(0.1149,-0.9588)
  408       ..(0.1376,-0.9496)..(0.1616,-0.9393)..(0.1868,-0.9281)
  409       ..(0.2131,-0.9158)..(0.2404,-0.9025)..(0.2686,-0.8882)
  410       ..(0.2975,-0.8729)..(0.3272,-0.8566)..(0.3574,-0.8393)
  411       ..(0.3881,-0.8209)..(0.4190,-0.8016)..(0.4503,-0.7813)
  412       ..(0.4817,-0.7600)..(0.5130,-0.7377)..(0.5442,-0.7145);
  413      drawarrow p scaled radius withcolor black;
  414      pickup pencircle scaled 0.400000 pt;
  415      pickup pencircle scaled 0.800000 pt;
  416      p := makepath makepen (0.5598,-0.7026)..(0.5906,-0.6780)
  417       ..(0.6211,-0.6526)..(0.6510,-0.6262)..(0.6803,-0.5991)
  418       ..(0.7089,-0.5712)..(0.7366,-0.5425)..(0.7634,-0.5130)
  419       ..(0.7892,-0.4828)..(0.8138,-0.4520)..(0.8372,-0.4205)
  420       ..(0.8593,-0.3884)..(0.8799,-0.3558)..(0.8992,-0.3226)
  421       ..(0.9168,-0.2891)..(0.9329,-0.2550)..(0.9472,-0.2207)
  422       ..(0.9599,-0.1859)..(0.9708,-0.1510)..(0.9799,-0.1158)
  423       ..(0.9872,-0.0804)..(0.9925,-0.0449)..(0.9960,-0.0092);
  424      drawarrow p scaled radius withcolor black;
  425      pickup pencircle scaled 0.400000 pt;
  426      pickup pencircle scaled 0.800000 pt;
  427      p := makepath makepen (0.9971,0.0085)..(0.9977,0.0441)
  428       ..(0.9965,0.0798)..(0.9933,0.1153)..(0.9883,0.1506);
  429      draw p scaled radius withcolor black;
  430      pickup pencircle scaled 0.400000 pt;
  431      pickup pencircle scaled 0.400000 pt;
  432      pickup pencircle scaled 0.800000 pt;
  433      p := makepath makepen (0.1949,-0.9806)..(0.2198,-0.9749)
  434       ..(0.2457,-0.9680)..(0.2725,-0.9600)..(0.3001,-0.9509)
  435       ..(0.3283,-0.9406)..(0.3571,-0.9292)..(0.3862,-0.9167)
  436       ..(0.4157,-0.9031)..(0.4454,-0.8883)..(0.4752,-0.8724)
  437       ..(0.5050,-0.8554)..(0.5347,-0.8373)..(0.5640,-0.8182)
  438       ..(0.5930,-0.7980)..(0.6215,-0.7769)..(0.6495,-0.7546)
  439       ..(0.6767,-0.7314)..(0.7031,-0.7072)..(0.7286,-0.6821)
  440       ..(0.7530,-0.6561)..(0.7764,-0.6293)..(0.7986,-0.6016);
  441      drawarrow p scaled radius withcolor black;
  442      pickup pencircle scaled 0.400000 pt;
  443      pickup pencircle scaled 0.800000 pt;
  444      p := makepath makepen (0.8092,-0.5875)..(0.8294,-0.5586);
  445      draw p scaled radius withcolor black;
  446      pickup pencircle scaled 0.400000 pt;
  447      pickup pencircle scaled 0.400000 pt;
  448      pickup pencircle scaled 0.400000 pt;
  449      pickup pencircle scaled 0.400000 pt;
  450      pickup pencircle scaled 0.400000 pt;
  451      pickup pencircle scaled 0.400000 pt;
  452      pickup pencircle scaled 0.800000 pt;
  453      p := makepath makepen (-0.3434,0.9392)..(-0.3306,0.9436)
  454       ..(-0.3163,0.9475)..(-0.3004,0.9511)..(-0.2831,0.9543)
  455       ..(-0.2643,0.9570);
  456      drawarrow p scaled radius withcolor black;
  457      pickup pencircle scaled 0.400000 pt;
  458      pickup pencircle scaled 0.400000 pt;
  459      pickup pencircle scaled 0.400000 pt;
  460      pickup pencircle scaled 0.400000 pt;
  461      pickup pencircle scaled 0.800000 pt;
  462      p := makepath makepen (-0.6211,0.7835)..(-0.6079,0.7939)
  463       ..(-0.5930,0.8040)..(-0.5766,0.8138)..(-0.5587,0.8233)
  464       ..(-0.5395,0.8325)..(-0.5190,0.8414)..(-0.4973,0.8500)
  465       ..(-0.4744,0.8584)..(-0.4506,0.8666)..(-0.4257,0.8745)
  466       ..(-0.4001,0.8821)..(-0.3738,0.8895)..(-0.3469,0.8967)
  467       ..(-0.3195,0.9036)..(-0.2917,0.9103);
  468      drawarrow p scaled radius withcolor black;
  469      pickup pencircle scaled 0.400000 pt;
  470      pickup pencircle scaled 0.400000 pt;
  471      pickup pencircle scaled 0.400000 pt;
  472      pickup pencircle scaled 0.800000 pt;
  473      p := makepath makepen (-0.8776,0.4790)..(-0.8689,0.4947)
  474       ..(-0.8585,0.5102)..(-0.8464,0.5256)..(-0.8326,0.5409)
  475       ..(-0.8172,0.5559)..(-0.8002,0.5708);
  476      drawarrow p scaled radius withcolor black;
  477      pickup pencircle scaled 0.400000 pt;
  478      pickup pencircle scaled 0.800000 pt;
  479      p := makepath makepen (-0.7911,0.5782)..(-0.7720,0.5928)
  480       ..(-0.7514,0.6074)..(-0.7296,0.6218)..(-0.7066,0.6361)
  481       ..(-0.6825,0.6503)..(-0.6574,0.6643)..(-0.6314,0.6782)
  482       ..(-0.6046,0.6919)..(-0.5770,0.7056)..(-0.5490,0.7191)
  483       ..(-0.5204,0.7325)..(-0.4915,0.7458)..(-0.4623,0.7589)
  484       ..(-0.4330,0.7718)..(-0.4038,0.7846)..(-0.3745,0.7972)
  485       ..(-0.3455,0.8096)..(-0.3169,0.8218)..(-0.2887,0.8338)
  486       ..(-0.2610,0.8455)..(-0.2340,0.8571)..(-0.2078,0.8683);
  487      drawarrow p scaled radius withcolor black;
  488      pickup pencircle scaled 0.400000 pt;
  489      pickup pencircle scaled 0.400000 pt;
  490      pickup pencircle scaled 0.400000 pt;
  491      pickup pencircle scaled 0.800000 pt;
  492      p := makepath makepen (-0.9977,0.0637)..(-0.9965,0.0819)
  493       ..(-0.9933,0.1002)..(-0.9883,0.1184)..(-0.9814,0.1366)
  494       ..(-0.9727,0.1547)..(-0.9622,0.1729)..(-0.9499,0.1912)
  495       ..(-0.9359,0.2094)..(-0.9202,0.2278)..(-0.9029,0.2461)
  496       ..(-0.8841,0.2644)..(-0.8638,0.2828)..(-0.8422,0.3012)
  497       ..(-0.8192,0.3198)..(-0.7950,0.3383)..(-0.7696,0.3570)
  498       ..(-0.7433,0.3755)..(-0.7160,0.3942)..(-0.6879,0.4130)
  499       ..(-0.6591,0.4317)..(-0.6296,0.4505);
  500      drawarrow p scaled radius withcolor black;
  501      pickup pencircle scaled 0.400000 pt;
  502      pickup pencircle scaled 0.800000 pt;
  503      p := makepath makepen (-0.6147,0.4599)..(-0.5845,0.4788)
  504       ..(-0.5540,0.4976)..(-0.5233,0.5165)..(-0.4924,0.5353)
  505       ..(-0.4615,0.5541)..(-0.4309,0.5728)..(-0.4005,0.5914)
  506       ..(-0.3703,0.6100)..(-0.3408,0.6284)..(-0.3117,0.6468)
  507       ..(-0.2833,0.6649)..(-0.2556,0.6830)..(-0.2291,0.7007)
  508       ..(-0.2034,0.7183)..(-0.1788,0.7356)..(-0.1554,0.7526)
  509       ..(-0.1333,0.7693)..(-0.1125,0.7857)..(-0.0932,0.8017)
  510       ..(-0.0753,0.8173)..(-0.0591,0.8324)..(-0.0444,0.8471);
  511      drawarrow p scaled radius withcolor black;
  512      pickup pencircle scaled 0.400000 pt;
  513      pickup pencircle scaled 0.400000 pt;
  514      pickup pencircle scaled 0.800000 pt;
  515      p := makepath makepen (-0.9274,-0.3727)..(-0.9346,-0.3558)
  516       ..(-0.9398,-0.3387)..(-0.9432,-0.3215)..(-0.9447,-0.3042)
  517       ..(-0.9444,-0.2866)..(-0.9421,-0.2689)..(-0.9379,-0.2510)
  518       ..(-0.9319,-0.2329)..(-0.9240,-0.2146)..(-0.9142,-0.1961)
  519       ..(-0.9026,-0.1773)..(-0.8893,-0.1584)..(-0.8742,-0.1391)
  520       ..(-0.8574,-0.1196);
  521      drawarrow p scaled radius withcolor black;
  522      pickup pencircle scaled 0.400000 pt;
  523      pickup pencircle scaled 0.800000 pt;
  524      p := makepath makepen (-0.8485,-0.1098)..(-0.8293,-0.0900)
  525       ..(-0.8086,-0.0699)..(-0.7865,-0.0495)..(-0.7630,-0.0289)
  526       ..(-0.7382,-0.0080)..(-0.7123,0.0130)..(-0.6852,0.0344)
  527       ..(-0.6571,0.0560)..(-0.6281,0.0779)..(-0.5983,0.1000)
  528       ..(-0.5678,0.1224)..(-0.5367,0.1449)..(-0.5052,0.1677)
  529       ..(-0.4732,0.1906)..(-0.4411,0.2138)..(-0.4088,0.2371)
  530       ..(-0.3764,0.2606)..(-0.3442,0.2841)..(-0.3122,0.3078)
  531       ..(-0.2806,0.3316)..(-0.2493,0.3553)..(-0.2186,0.3793);
  532      drawarrow p scaled radius withcolor black;
  533      pickup pencircle scaled 0.400000 pt;
  534      pickup pencircle scaled 0.800000 pt;
  535      p := makepath makepen (-0.2035,0.3911)..(-0.1738,0.4150)
  536       ..(-0.1449,0.4388)..(-0.1170,0.4626)..(-0.0901,0.4863)
  537       ..(-0.0644,0.5098)..(-0.0398,0.5332)..(-0.0166,0.5563)
  538       ..(0.0053,0.5793)..(0.0258,0.6020)..(0.0447,0.6243)
  539       ..(0.0621,0.6463)..(0.0777,0.6680)..(0.0917,0.6892)
  540       ..(0.1040,0.7099)..(0.1145,0.7302)..(0.1231,0.7499)
  541       ..(0.1299,0.7690)..(0.1349,0.7876)..(0.1379,0.8054)
  542       ..(0.1391,0.8227)..(0.1384,0.8391)..(0.1359,0.8548);
  543      drawarrow p scaled radius withcolor black;
  544      pickup pencircle scaled 0.400000 pt;
  545      pickup pencircle scaled 0.800000 pt;
  546      p := makepath makepen (-0.7069,-0.7073)..(-0.7185,-0.6949)
  547       ..(-0.7286,-0.6822)..(-0.7368,-0.6691)..(-0.7433,-0.6557)
  548       ..(-0.7479,-0.6420);
  549      drawarrow p scaled radius withcolor black;
  550      pickup pencircle scaled 0.400000 pt;
  551      pickup pencircle scaled 0.800000 pt;
  552      p := makepath makepen (-0.7495,-0.6351)..(-0.7513,-0.6208)
  553       ..(-0.7513,-0.6062)..(-0.7494,-0.5912)..(-0.7455,-0.5759)
  554       ..(-0.7398,-0.5602)..(-0.7321,-0.5441)..(-0.7227,-0.5275)
  555       ..(-0.7114,-0.5105)..(-0.6983,-0.4931)..(-0.6835,-0.4752)
  556       ..(-0.6669,-0.4569)..(-0.6487,-0.4382)..(-0.6289,-0.4189)
  557       ..(-0.6076,-0.3992)..(-0.5848,-0.3790)..(-0.5606,-0.3584)
  558       ..(-0.5351,-0.3373)..(-0.5084,-0.3157)..(-0.4806,-0.2937)
  559       ..(-0.4517,-0.2711)..(-0.4220,-0.2481)..(-0.3913,-0.2246);
  560      drawarrow p scaled radius withcolor black;
  561      pickup pencircle scaled 0.400000 pt;
  562      pickup pencircle scaled 0.800000 pt;
  563      p := makepath makepen (-0.3758,-0.2128)..(-0.3441,-0.1887)
  564       ..(-0.3119,-0.1641)..(-0.2793,-0.1391)..(-0.2463,-0.1138)
  565       ..(-0.2131,-0.0881)..(-0.1798,-0.0620)..(-0.1465,-0.0356)
  566       ..(-0.1133,-0.0087)..(-0.0805,0.0183)..(-0.0479,0.0457)
  567       ..(-0.0158,0.0733)..(0.0156,0.1011)..(0.0464,0.1291)
  568       ..(0.0764,0.1572)..(0.1055,0.1856)..(0.1336,0.2140)
  569       ..(0.1605,0.2424)..(0.1864,0.2708)..(0.2109,0.2992)
  570       ..(0.2340,0.3276)..(0.2558,0.3559)..(0.2760,0.3840);
  571      drawarrow p scaled radius withcolor black;
  572      pickup pencircle scaled 0.400000 pt;
  573      pickup pencircle scaled 0.800000 pt;
  574      p := makepath makepen (0.2855,0.3980)..(0.3033,0.4259)
  575       ..(0.3195,0.4535)..(0.3339,0.4808)..(0.3465,0.5078)
  576       ..(0.3574,0.5345)..(0.3665,0.5606)..(0.3737,0.5864)
  577       ..(0.3790,0.6116)..(0.3824,0.6362)..(0.3840,0.6604)
  578       ..(0.3837,0.6838)..(0.3815,0.7066)..(0.3774,0.7286)
  579       ..(0.3716,0.7499)..(0.3639,0.7704)..(0.3545,0.7901)
  580       ..(0.3434,0.8088)..(0.3306,0.8267)..(0.3163,0.8436)
  581       ..(0.3004,0.8596)..(0.2831,0.8745)..(0.2643,0.8884);
  582      drawarrow p scaled radius withcolor black;
  583      pickup pencircle scaled 0.400000 pt;
  584      pickup pencircle scaled 0.800000 pt;
  585      p := makepath makepen (-0.4124,-0.9107)..(-0.4266,-0.9045)
  586       ..(-0.4391,-0.8979)..(-0.4500,-0.8908)..(-0.4592,-0.8834)
  587       ..(-0.4666,-0.8755)..(-0.4722,-0.8671)..(-0.4761,-0.8582)
  588       ..(-0.4780,-0.8489)..(-0.4781,-0.8390)..(-0.4762,-0.8286)
  589       ..(-0.4726,-0.8176)..(-0.4670,-0.8061)..(-0.4596,-0.7940)
  590       ..(-0.4502,-0.7813)..(-0.4392,-0.7679)..(-0.4263,-0.7540)
  591       ..(-0.4116,-0.7395);
  592      drawarrow p scaled radius withcolor black;
  593      pickup pencircle scaled 0.400000 pt;
  594      pickup pencircle scaled 0.800000 pt;
  595      p := makepath makepen (-0.4035,-0.7320)..(-0.3863,-0.7165)
  596       ..(-0.3674,-0.7003)..(-0.3469,-0.6834)..(-0.3251,-0.6660)
  597       ..(-0.3016,-0.6478)..(-0.2769,-0.6289)..(-0.2509,-0.6093)
  598       ..(-0.2237,-0.5892)..(-0.1954,-0.5682)..(-0.1661,-0.5467)
  599       ..(-0.1359,-0.5244)..(-0.1049,-0.5016)..(-0.0732,-0.4779)
  600       ..(-0.0409,-0.4538)..(-0.0083,-0.4289)..(0.0248,-0.4035)
  601       ..(0.0582,-0.3774)..(0.0916,-0.3508)..(0.1250,-0.3236)
  602       ..(0.1584,-0.2958)..(0.1915,-0.2675)..(0.2243,-0.2387);
  603      drawarrow p scaled radius withcolor black;
  604      pickup pencircle scaled 0.400000 pt;
  605      pickup pencircle scaled 0.800000 pt;
  606      p := makepath makepen (0.2404,-0.2242)..(0.2726,-0.1947)
  607       ..(0.3039,-0.1648)..(0.3347,-0.1345)..(0.3645,-0.1038)
  608       ..(0.3935,-0.0729)..(0.4214,-0.0417)..(0.4482,-0.0102)
  609       ..(0.4737,0.0216)..(0.4979,0.0534)..(0.5208,0.0855)
  610       ..(0.5422,0.1176)..(0.5621,0.1497)..(0.5803,0.1818)
  611       ..(0.5970,0.2138)..(0.6118,0.2459)..(0.6250,0.2777)
  612       ..(0.6363,0.3094)..(0.6458,0.3408)..(0.6534,0.3719)
  613       ..(0.6592,0.4028)..(0.6631,0.4332)..(0.6651,0.4632);
  614      drawarrow p scaled radius withcolor black;
  615      pickup pencircle scaled 0.400000 pt;
  616      pickup pencircle scaled 0.800000 pt;
  617      p := makepath makepen (0.6654,0.4780)..(0.6646,0.5073)
  618       ..(0.6618,0.5361)..(0.6573,0.5642)..(0.6508,0.5917)
  619       ..(0.6427,0.6186)..(0.6328,0.6447)..(0.6211,0.6700)
  620       ..(0.6079,0.6946)..(0.5930,0.7183)..(0.5766,0.7412)
  621       ..(0.5587,0.7631)..(0.5395,0.7840)..(0.5190,0.8040)
  622       ..(0.4973,0.8230)..(0.4744,0.8409)..(0.4506,0.8578)
  623       ..(0.4257,0.8736)..(0.4001,0.8882)..(0.3738,0.9017)
  624       ..(0.3469,0.9140)..(0.3195,0.9252)..(0.2917,0.9352);
  625      drawarrow p scaled radius withcolor black;
  626      pickup pencircle scaled 0.400000 pt;
  627      pickup pencircle scaled 0.800000 pt;
  628      p := makepath makepen (-0.1994,-0.9798)..(-0.2052,-0.9776)
  629       ..(-0.2090,-0.9749)..(-0.2110,-0.9716)..(-0.2112,-0.9676)
  630       ..(-0.2095,-0.9630)..(-0.2058,-0.9577)..(-0.2004,-0.9516)
  631       ..(-0.1931,-0.9449)..(-0.1839,-0.9375)..(-0.1729,-0.9293)
  632       ..(-0.1602,-0.9203)..(-0.1456,-0.9105)..(-0.1294,-0.8999)
  633       ..(-0.1116,-0.8886)..(-0.0921,-0.8764)..(-0.0712,-0.8633)
  634       ..(-0.0488,-0.8495)..(-0.0251,-0.8347)..(0.0000,-0.8192)
  635       ..(0.0262,-0.8027)..(0.0536,-0.7854)..(0.0820,-0.7672);
  636      drawarrow p scaled radius withcolor black;
  637      pickup pencircle scaled 0.400000 pt;
  638      pickup pencircle scaled 0.800000 pt;
  639      p := makepath makepen (0.0965,-0.7578)..(0.1262,-0.7383)
  640       ..(0.1567,-0.7180)..(0.1879,-0.6968)..(0.2196,-0.6748)
  641       ..(0.2517,-0.6519)..(0.2841,-0.6283)..(0.3168,-0.6038)
  642       ..(0.3495,-0.5786)..(0.3822,-0.5525)..(0.4148,-0.5257)
  643       ..(0.4471,-0.4983)..(0.4790,-0.4701)..(0.5105,-0.4412)
  644       ..(0.5413,-0.4117)..(0.5714,-0.3815)..(0.6008,-0.3509)
  645       ..(0.6292,-0.3196)..(0.6566,-0.2878)..(0.6829,-0.2556)
  646       ..(0.7080,-0.2229)..(0.7318,-0.1899)..(0.7542,-0.1564);
  647      drawarrow p scaled radius withcolor black;
  648      pickup pencircle scaled 0.400000 pt;
  649      pickup pencircle scaled 0.800000 pt;
  650      p := makepath makepen (0.7649,-0.1396)..(0.7850,-0.1058)
  651       ..(0.8037,-0.0716)..(0.8207,-0.0373)..(0.8361,-0.0029)
  652       ..(0.8497,0.0317)..(0.8616,0.0662)..(0.8716,0.1008)
  653       ..(0.8798,0.1354)..(0.8862,0.1698)..(0.8906,0.2042)
  654       ..(0.8931,0.2383)..(0.8938,0.2721)..(0.8925,0.3057)
  655       ..(0.8894,0.3388)..(0.8844,0.3717)..(0.8776,0.4041)
  656       ..(0.8689,0.4360)..(0.8585,0.4673)..(0.8464,0.4981)
  657       ..(0.8326,0.5282)..(0.8172,0.5577)..(0.8002,0.5864);
  658      drawarrow p scaled radius withcolor black;
  659      pickup pencircle scaled 0.400000 pt;
  660      pickup pencircle scaled 0.800000 pt;
  661      p := makepath makepen (0.7911,0.6005)..(0.7720,0.6281)
  662       ..(0.7514,0.6549)..(0.7296,0.6808)..(0.7066,0.7059)
  663       ..(0.6825,0.7300)..(0.6574,0.7531)..(0.6314,0.7753)
  664       ..(0.6046,0.7965)..(0.5770,0.8167);
  665      draw p scaled radius withcolor black;
  666      pickup pencircle scaled 0.800000 pt;
  667      p := makepath makepen (0.3455,0.9384)..(0.3169,0.9485)
  668       ..(0.2887,0.9574)..(0.2610,0.9651)..(0.2340,0.9717)
  669       ..(0.2078,0.9772);
  670      drawarrow p scaled radius withcolor black;
  671      pickup pencircle scaled 0.400000 pt;
  672     ahangle:=oldahangle;
  673   %
  674   % Draw the $S_1$-, $S_2$- and $S_3$-axis of the Poincare sphere.
  675   % First of all, calculate the transformations of the intersections
  676   % for the unity sphere.
  677   %
  678   % Used variables:
  679   %
  680   %    behind_distance : Specifies the relative distance of the coordi-
  681   %                      axes to be plotted behind origo (in negative di-
  682   %                      rection of respective axis.
  683   %
  684   %   outside_distance_s1 : The relative distance from origo to the point
  685   %                         of the arrow head of the coordinate axis S1.
  686   %                         If this is set to 1.0, the arrow head will
  687   %                         point directly at the Poincare sphere.
  688   %
  689   %   outside_distance_s2 : Same as above, except that this one controls
  690   %                         the S2 coordinate axis instead.
  691   %
  692   %   outside_distance_s3 : Same as above, except that this one controls
  693   %                         the S3 coordinate axis instead.
  694   %
  695   %    insidecolval :    Specifies the shade of gray to use for the parts
  696   %                      of the coordinate axes that are inside the Poin-
  697   %                      care sphere. Values must be between 0 and 1,
  698   %                      where:  '0.0' <=> 'white';  '1.0' <=> 'black'
  699   %
  700      behind_distance_s1  := -0.300000;
  701      behind_distance_s2  := -0.300000;
  702      behind_distance_s3  := -0.300000;
  703      outside_distance_s1 :=  1.700000;
  704      outside_distance_s2 :=  2.400000;
  705      outside_distance_s3 :=  1.500000;
  706      insidecolval := .85;    % '0.0' <=> 'white';  '1.0' <=> 'black'
  707   
  708      pickup pencircle scaled 0.600000 pt;
  709   %
  710   % Start with drawing the x-axis...
  711   %
  712      x_bis_start :=  radius*behind_distance_s1*cosd(rot_psi)*cosd(rot_phi);
  713      y_bis_start :=  radius*behind_distance_s1*sind(rot_psi);
  714      z_bis_start := -radius*behind_distance_s1*cosd(rot_psi)*sind(rot_phi);
  715      x_bis_intersect :=  radius*cosd(rot_psi)*cosd(rot_phi);
  716      y_bis_intersect :=  radius*sind(rot_psi);
  717      z_bis_intersect := -radius*cosd(rot_psi)*sind(rot_phi);
  718      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  719                (outside_distance_s1*y_bis_intersect,
  720                 outside_distance_s1*z_bis_intersect);
  721      drawarrow p;
  722      label.bot(btex $s_1(t)$ etex,
  723                (outside_distance_s1*y_bis_intersect,
  724                 outside_distance_s1*z_bis_intersect));
  725   
  726   %
  727   % ... then draw the y-axis ...
  728   %
  729      x_bis_start := -radius*behind_distance_s2*sind(rot_psi)*cosd(rot_phi);
  730      y_bis_start :=  radius*behind_distance_s2*cosd(rot_psi);
  731      z_bis_start :=  radius*behind_distance_s2*sind(rot_psi)*sind(rot_phi);
  732      x_bis_intersect := -radius*sind(rot_psi)*cosd(rot_phi);
  733      y_bis_intersect :=  radius*cosd(rot_psi);
  734      z_bis_intersect :=  radius*sind(rot_psi)*sind(rot_phi);
  735      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  736                (outside_distance_s2*y_bis_intersect,
  737                 outside_distance_s2*z_bis_intersect);
  738      drawarrow p;
  739      label.bot(btex $s_2(t)$ etex,
  740                (outside_distance_s2*y_bis_intersect,
  741                 outside_distance_s2*z_bis_intersect));
  742   
  743   %
  744   % ... then, finally, draw the z-axis.
  745   %
  746      x_bis_start := radius*behind_distance_s3*sind(rot_phi);
  747      y_bis_start := 0.0;
  748      z_bis_start := radius*behind_distance_s3*cosd(rot_phi);
  749      x_bis_intersect := radius*sind(rot_phi);
  750      y_bis_intersect := 0.0;
  751      z_bis_intersect := radius*cosd(rot_phi);
  752      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  753                (outside_distance_s3*y_bis_intersect,
  754                 outside_distance_s3*z_bis_intersect);
  755      drawarrow p;
  756      label.rt(btex $s_3(t)$ etex,
  757                (outside_distance_s3*y_bis_intersect,
  758                 outside_distance_s3*z_bis_intersect));
  759   
  760      endfig;
  761   end
  762   

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Last modified Thursday 23 Jan 2014