Search:

Return to previous page

Contents of file 'poincare/stoke.mp':




Deprecated: Function split() is deprecated in /storage/content/45/2011745/jonsson.eu/public_html/php/htmlicise.php on line 46
    1   % This Filename:  stoke.mp   [MetaPost source]
    2   % Creation time:  Thu Jan 23 20:19:34 2014
    3   %
    4   % Copyright (C) 1997-2005, Fredrik Jonsson <fj@optics.kth.se>
    5   %
    6   % Input Filename [Stokes parameters]:  
    7   % This MetaPost source code was automatically generated by poincare
    8   % Full set of command line options that generated this code:
    9   %     --verbose --normalize --axislengths 0.3 1.6 0.3
   10   %     2.7 0.3 1.5 --axislabels S_1 bot
   11   %     S_2 bot S_3 rt --rotatephi 15.0
   12   %     --rotatepsi -70.0 --shading 0.75 0.99 --rhodivisor
   13   %     50 --phidivisor 80 --scalefactor 25.0 --outputfile
   14   %     stoke.mp --auxsource polstate.mp
   15   %
   16   % Description:  Map of Stokes parameters, visualized as trajectories
   17   %               onto the Poincare sphere. This file contains MetaPost
   18   %               source code, to be compiled with John Hobby's MetaPost
   19   %               compiler or used with anything that understands MetaPost
   20   %               source code.
   21   %
   22   % If you want to create PostScript output, or include the resulting
   23   % output in a TeX document, this example illustrates the procedure,
   24   % assuming 'poincaremap.mp' to be the name of the file containing the
   25   % MetaPost code to be visualized: (commands run on command-line)
   26   %
   27   %       mp poincaremap.mp;
   28   %       echo "\input epsf\centerline{\epsfbox{poincaremap.1}}\bye" > tmp.tex;
   29   %       tex tmp.tex;
   30   %       dvips tmp.dvi -o poincaremap.ps;
   31   %
   32   % Here, the first command compiles the MetaPost source code, and leaves
   33   % an Encapsulated PostScript file named 'poincaremap.1', containing TeX
   34   % control codes for characters, etc. This file does not contain any
   35   % definitions for characters or TeX-specific items, and it cannot be
   36   % viewed or printed simply as is stands; it must rather be included into
   37   % TeX code in order to provide something useful.
   38   %     The second command creates a temporary minimal TeX-file 'tmp.tex',
   39   % that only includes the previously generated Encapsulated PostScript
   40   % code.
   41   %     The third command compiles the TeX-code into device-independent,
   42   % or DVI, output, stored in the file 'tmp.dvi'.
   43   %     Finally, the last command converts the DVI output into a free-
   44   % standing PostScript file 'poincaremap.ps', to be printed or viewed
   45   % with some PostScript viewer, such as GhostView.
   46   %
   47   scalefactor := 25.000000 mm;
   48   rot_psi := -70.000000;  % Rotation angle round z-axis (first rotation)
   49   rot_phi := 15.000000;  % Rotation angle round y-axis (second rotation)
   50   alpha := -35.416613;    % == arctan(sin(rot_phi)*tan(rot_psi))
   51   beta  := -5.381520;    % == arctan(sin(rot_phi)/tan(rot_psi))
   52   
   53   %
   54   % Parameters specifying the location of the light source; for Phong
   55   % shading of the sphere.
   56   %
   57   %    phi_source:  Angle (in deg.) to light source counterclockwise
   58   %                 'from three o'clock', viewed from the observer.
   59   %
   60   %  theta_source:  Angle (in deg.) between light source and observer,
   61   %                 seen from the centre of the sphere.
   62   %
   63   % Parameters specifying the shading 'intensity' in terms of maximum
   64   % (for the highlighs) and minimum (for the deep shadowed regions)
   65   % values for the Phong shading.  '0.0' <=> 'black'; '1.0' <=> 'white'
   66   %
   67   %   upper_value:  Maximum value of whiteness.
   68   %   lower_value:  Minimum value of whiteness.
   69   %
   70   phi_source := 30.000000;
   71   theta_source := 30.000000;
   72   upper_value := 0.990000;
   73   lower_value := 0.750000;
   74   radius := scalefactor;
   75   delta_rho := radius/50.000000;
   76   delta_phi := 360.0/80.000000;
   77   beginfig(1);
   78     path p;
   79     path equator;
   80     transform T;
   81     c1:=lower_value;
   82     c2:=upper_value-lower_value;
   83     nx_source := sind(theta_source)*cosd(phi_source);
   84     ny_source := sind(theta_source)*sind(phi_source);
   85     nz_source := cosd(theta_source);
   86     phistop := 360.0;
   87     rhostop := radius - delta_rho/2.0;
   88   %
   89   % Draw the shaded Poincare sphere projected on 2D screen coordinates
   90   %
   91     for rho=0.0cm step delta_rho until rhostop:
   92       for phi=0.0 step delta_phi until phistop:
   93         rhomid := rho + delta_rho/2.0;
   94         phimid := phi + delta_phi/2.0;
   95         x1 := rho*cosd(phi);
   96         y1 := rho*sind(phi);
   97         x2 := (rho+delta_rho)*cosd(phi);
   98         y2 := (rho+delta_rho)*sind(phi);
   99         x3 := (rho+delta_rho)*cosd(phi+delta_phi);
  100         y3 := (rho+delta_rho)*sind(phi+delta_phi);
  101         x4 := rho*cosd(phi+delta_phi);
  102         y4 := rho*sind(phi+delta_phi);
  103         p:=makepath makepen ((x1,y1)--(x2,y2)--(x3,y3)--(x4,y4)--(x1,y1));
  104         quot := (rhomid/radius);
  105         nx_object := quot*cosd(phimid);
  106         ny_object := quot*sind(phimid);
  107         nz_object := sqrt(1-quot*quot);
  108         prod:=nx_object*nx_source+ny_object*ny_source
  109               +nz_object*nz_source;
  110         if prod < 0.0:
  111            value := c1;
  112         else:
  113            value := c1 + c2*prod*prod;
  114         fi
  115         fill p withcolor value[black,white];
  116       endfor
  117     endfor
  118   
  119   %
  120   % Draw the 'equators' of the Poincare sphere
  121   %
  122      equator := halfcircle scaled (2.0*radius);
  123      eqcolval := .45;    % '0.0' <=> 'white';  '1.0' <=> 'black'
  124   
  125      pickup pencircle scaled 0.600000 pt;
  126   %
  127   % Draw equator $S_3=0$...
  128   %
  129      T := identity yscaled sind(rot_phi) rotated 180.0;
  130      draw equator transformed T withcolor eqcolval [white,black];
  131   
  132   %
  133   % ... then equator $S_2=0$...
  134   %
  135      T := identity yscaled (cosd(rot_phi)*sind(rot_psi))
  136                    rotated (270.0 + alpha);
  137      draw equator transformed T withcolor eqcolval [white,black];
  138   
  139   %
  140   % ... and finally equator $S_1=0$.
  141   %
  142      T := identity yscaled (cosd(rot_phi)*cosd(rot_psi))
  143                    rotated (270.0 - beta);
  144      draw equator transformed T withcolor eqcolval [white,black];
  145   
  146   %
  147   % Draw the $S_1$-, $S_2$- and $S_3$-axis of the Poincare sphere.
  148   % First of all, calculate the transformations of the intersections
  149   % for the unity sphere.
  150   %
  151   % Used variables:
  152   %
  153   %    behind_distance : Specifies the relative distance of the coordi-
  154   %                      axes to be plotted behind origo (in negative di-
  155   %                      rection of respective axis.
  156   %
  157   %   outside_distance_s1 : The relative distance from origo to the point
  158   %                         of the arrow head of the coordinate axis S1.
  159   %                         If this is set to 1.0, the arrow head will
  160   %                         point directly at the Poincare sphere.
  161   %
  162   %   outside_distance_s2 : Same as above, except that this one controls
  163   %                         the S2 coordinate axis instead.
  164   %
  165   %   outside_distance_s3 : Same as above, except that this one controls
  166   %                         the S3 coordinate axis instead.
  167   %
  168   %    insidecolval :    Specifies the shade of gray to use for the parts
  169   %                      of the coordinate axes that are inside the Poin-
  170   %                      care sphere. Values must be between 0 and 1,
  171   %                      where:  '0.0' <=> 'white';  '1.0' <=> 'black'
  172   %
  173      behind_distance_s1  := -0.300000;
  174      behind_distance_s2  := -0.300000;
  175      behind_distance_s3  := -0.300000;
  176      outside_distance_s1 :=  1.600000;
  177      outside_distance_s2 :=  2.700000;
  178      outside_distance_s3 :=  1.500000;
  179      insidecolval := .85;    % '0.0' <=> 'white';  '1.0' <=> 'black'
  180   
  181      pickup pencircle scaled 0.600000 pt;
  182   %
  183   % Start with drawing the x-axis...
  184   %
  185      x_bis_start :=  radius*behind_distance_s1*cosd(rot_psi)*cosd(rot_phi);
  186      y_bis_start :=  radius*behind_distance_s1*sind(rot_psi);
  187      z_bis_start := -radius*behind_distance_s1*cosd(rot_psi)*sind(rot_phi);
  188      x_bis_intersect :=  radius*cosd(rot_psi)*cosd(rot_phi);
  189      y_bis_intersect :=  radius*sind(rot_psi);
  190      z_bis_intersect := -radius*cosd(rot_psi)*sind(rot_phi);
  191      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  192                (outside_distance_s1*y_bis_intersect,
  193                 outside_distance_s1*z_bis_intersect);
  194      drawarrow p;
  195      label.bot(btex $S_1$ etex,
  196                (outside_distance_s1*y_bis_intersect,
  197                 outside_distance_s1*z_bis_intersect));
  198   
  199   %
  200   % ... then draw the y-axis ...
  201   %
  202      x_bis_start := -radius*behind_distance_s2*sind(rot_psi)*cosd(rot_phi);
  203      y_bis_start :=  radius*behind_distance_s2*cosd(rot_psi);
  204      z_bis_start :=  radius*behind_distance_s2*sind(rot_psi)*sind(rot_phi);
  205      x_bis_intersect := -radius*sind(rot_psi)*cosd(rot_phi);
  206      y_bis_intersect :=  radius*cosd(rot_psi);
  207      z_bis_intersect :=  radius*sind(rot_psi)*sind(rot_phi);
  208      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  209                (outside_distance_s2*y_bis_intersect,
  210                 outside_distance_s2*z_bis_intersect);
  211      drawarrow p;
  212      label.bot(btex $S_2$ etex,
  213                (outside_distance_s2*y_bis_intersect,
  214                 outside_distance_s2*z_bis_intersect));
  215   
  216   %
  217   % ... then, finally, draw the z-axis.
  218   %
  219      x_bis_start := radius*behind_distance_s3*sind(rot_phi);
  220      y_bis_start := 0.0;
  221      z_bis_start := radius*behind_distance_s3*cosd(rot_phi);
  222      x_bis_intersect := radius*sind(rot_phi);
  223      y_bis_intersect := 0.0;
  224      z_bis_intersect := radius*cosd(rot_phi);
  225      p := makepath makepen (y_bis_intersect,z_bis_intersect)--
  226                (outside_distance_s3*y_bis_intersect,
  227                 outside_distance_s3*z_bis_intersect);
  228      drawarrow p;
  229      label.rt(btex $S_3$ etex,
  230                (outside_distance_s3*y_bis_intersect,
  231                 outside_distance_s3*z_bis_intersect));
  232   
  233   %
  234   % The following external file is included (using the --auxsource option): polstate.mp  [MetaPost source]
  235   %
  236      input polstate.mp
  237      endfig;
  238   end
  239   

Return to previous page

Generated by ::viewsrc::

Last modified Thursday 23 Jan 2014