% This Filename: stoke.mp [MetaPost source] % Creation time: Thu Jan 23 20:19:34 2014 % % Copyright (C) 1997-2005, Fredrik Jonsson % % Input Filename [Stokes parameters]: % This MetaPost source code was automatically generated by poincare % Full set of command line options that generated this code: % --verbose --normalize --axislengths 0.3 1.6 0.3 % 2.7 0.3 1.5 --axislabels S_1 bot % S_2 bot S_3 rt --rotatephi 15.0 % --rotatepsi -70.0 --shading 0.75 0.99 --rhodivisor % 50 --phidivisor 80 --scalefactor 25.0 --outputfile % stoke.mp --auxsource polstate.mp % % 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 := 25.000000 mm; rot_psi := -70.000000; % Rotation angle round z-axis (first rotation) rot_phi := 15.000000; % Rotation angle round y-axis (second rotation) alpha := -35.416613; % == arctan(sin(rot_phi)*tan(rot_psi)) beta := -5.381520; % == 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]; % % 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 := 1.600000; outside_distance_s2 := 2.700000; 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 $S_1$ 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 $S_2$ 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 $S_3$ etex, (outside_distance_s3*y_bis_intersect, outside_distance_s3*z_bis_intersect)); % % The following external file is included (using the --auxsource option): polstate.mp [MetaPost source] % input polstate.mp endfig; end