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% optica.mp
% P. J. Sebastiao
input featpost3Dplus2D;
% bash: export TEX=latex
% tcsh: setenv TEX latex
verbatimtex \documentclass{article} \usepackage{beton} \usepackage{concmath} \usepackage{ccfonts} \begin{document} etex
beginfig(1);
color orig, axxc, ayyc, azzc;
color field, nalfa, ngamma[], alfacnt, gammacnt, nazy, nax, proj, align;
path alfa, gamma;
numeric nalfad, theta, radius, gammang, xxsize, yysize, zzsize;
numeric xxpos, yypos, zzpos, fieldpos, deltarad, deltapos,angrecto;
numeric thetarad, thetapos, nalfapos, ngammapos,veccpos,betarad,betapos;
numeric etalpharad, etalphapos, alphapos, gammapos;
picture xxlabel, yylabel, zzlabel, fieldlabel, deltalabel, xxcalabel,yycalabel,aMlabel;
picture nalfalabel, ngammalabel, etalphalabel, alphalabel;
picture gammalabel, thetalabel,vecclabel,betalabel;
f := (3,4,2);
nbeta := 1.3;
beta := 12;
betarad := 0.6;
betapos := 1;
deltarad := 0.8;
deltapos := 2;
nalfad := 1.0;
theta := 15;
delta := 35;
thetarad := 0.3;
thetapos := 2;
nalfapos := 1;
gammang := 60;
ngammapos := 7;
etalpharad := 0.6;
etalphapos := 2;
alphapos := 2;
alpharad := 0.9;
gammapos := 4;
Spread := 100;
xxsize := 0.8;
xxpos := 6;
yysize := 1.3;
yypos := 6;
zzsize := 1.3;
zzpos := 4;
% angrecto := 0.2;
xxcalabel = btex $x_{\mbox{\protect \scriptsize }}$ etex;
yycalabel = btex $y_{\mbox{\protect \scriptsize }}$ etex;
xxlabel = btex $\mbox{\protect \scriptsize ligth}$ etex;
yylabel = btex $\mbox{\protect \scriptsize analyser}$ etex;
zzlabel = btex $\mbox{\protect \scriptsize polariser}$ etex;
deltalabel = btex $\Delta$ etex;
aMlabel = btex $\bar{\alpha}$ etex;
fieldlabel = btex $\mathbf{B}$ etex;
thetalabel = btex $\Delta$ etex;
betalabel = btex $\xi$ etex;
nalfalabel = btex $\mathbf{n}_a$ etex;
ngammalabel = btex $\mathbf{n}_\gamma$ etex;
etalphalabel= btex $\theta$ etex;
alphalabel = btex $\alpha$ etex;
gammalabel = btex $\gamma$ etex;
vecclabel = btex $\mathbf{c}$ etex;
veccpos = 3;
field = (0.7,0,0);
fieldpos = 2;
orig = (0,0,0);
axxc = (xxsize,0,0);
ayyc = (0,yysize,0);
azzc = (0,0,zzsize);
nalfa = (0,nbeta*cosd(beta)*sind(delta),nbeta*cosd(beta)*cosd(delta));
alfacnt = nalfa;
radius = nbeta*sind(beta);
alfa = rigorouscircle( alfacnt, (0,0,1), radius );
gammacnt = nalfa;
gamma = rigorouscircle( gammacnt, nalfa, radius );
for i=0 step 40 until 0:
nazy := radius*sind(gammang+i)*ncrossprod( nalfa, axxc );
nax := radius*cosd(gammang+i)*ncrossprod( ayyc, nalfa );
ngamma[i] := gammacnt+nax+nazy;
pickup pencircle scaled 1.5;
drawarrow rp(orig)..rp(ngamma[i]);
endfor;
pickup pencircle scaled 0.5;
% draw alfa dashed evenly;
align = 1*(0,+sind(10),cosd(10));
draw rp(orig)..rp(align);
drawarrow rp(orig)..rp(axxc);
drawarrow rp(orig)..rp(ayyc);
% draw rp(orig)..rp(-axxc);
drawarrow rp(orig)..rp(azzc);
% drawarrow rp(orig)..rp(field);
draw rp(orig)..rp(nalfa);
% draw subpath (3.05,1.05) of alfa;
% drawarrow subpath (4,3) of alfa;
% draw subpath (0,1.3) of gamma;
% draw subpath (7.5,8) of gamma;
% drawarrow subpath (1,2) of gamma;
% anglinen( field, azzc, orig, deltarad, deltalabel, deltapos );
anglinen( ngamma0, nalfa, orig, betarad, betalabel, betapos );
anglinen( azzc, align, orig, deltarad, deltalabel, deltapos );
anglinen( align, nalfa, orig, deltarad, aMlabel, deltapos );
% anglinen( ngamma0, field, orig, etalpharad, etalphalabel, etalphapos );
labeln( xxlabel, rp(axxc), xxpos );
labeln( yylabel, rp(ayyc), yypos );
labeln( zzlabel, rp(azzc), zzpos );
% labeln( fieldlabel, rp(field), fieldpos );
% labeln( nalfalabel, rp(nalfa), nalfapos );
labeln( ngammalabel, rp(ngamma0), ngammapos );
% labeln( alphalabel, point 1.8 of alfa, alphapos );
labeln( gammalabel, point 2.1 of gamma, gammapos );
% labeln( xxcalabel, rp(gammacnt+1.3*radius*(1,0,0)), 1);
% labeln( yycalabel, rp(gammacnt+1.3*radius*(0,1,-sind(theta))), 2);
pickup pencircle scaled 0.5;
draw rp((0,0,0))..rp(alfacnt);
draw rp(gammacnt);
pickup pencircle scaled 0.5;
path arco, recta_um, recta_quatro, recta_dois, recta_ylayer, recta_xlayer, path_ngamma, recta_tres;
color tmp, tmpo;
pickup pencircle scaled 0.5;
tmp = gammacnt+radius*(0,-cosd(delta),sind(delta));
tmpo = gammacnt+radius*(0,cosd(delta),-sind(delta));
recta_um = rp(tmpo)--rp(gammacnt)--rp(tmp)--rp((0,0,Z(tmp)));
draw recta_um;
% align = (0,Z(tmp)*sind(10),Z(tmp));
drawarrow rp(orig)--rp((0,Z(tmp)*sind(10),Z(tmp)));
labeln( btex $\mbox{\protect \scriptsize rubbing}$ etex, rp((0,Z(tmp)*sind(10),Z(tmp))), 1 );
angrecto=nbeta*cosd(beta);
recta_quatro = rp((0,angrecto*sind(delta),angrecto*cosd(delta)))--rp((0,angrecto*sind(delta),0));
% recta_tres = rp((0,angrecto*sind(delta)+radius*sind(gammang)*cosd(delta),angrecto*cosd(delta)))--rp((0,angrecto*sind(delta)+radius*sind(gammang)*cosd(delta),0));
recta_tres = rp((0,angrecto*sind(delta)+radius*sind(gammang)*cosd(delta),angrecto*cosd(delta)-radius*sind(gammang)*sind(delta)))--rp((0,angrecto*sind(delta)+radius*sind(gammang)*cosd(delta),0));
% recta_dois = rp(angrecto*cosd(delta)*(0,0,1))--rp((0,angrecto*sind(delta)+radius*sind(gammang)*cosd(delta),angrecto*cosd(delta)));
% recta_dois = rp(gammacnt)--rp((0,angrecto*sind(delta)+radius*sind(gammang)*cosd(delta),angrecto*cosd(delta)));
recta_dois = rp(gammacnt)--rp((0,nbeta*cosd(beta)*sind(delta),0));
% draw recta_dois;
draw recta_tres;
% draw recta_quatro;
pickup pencircle scaled 1;
arco = (alfa cutbefore recta_dois) cutafter recta_um;
% draw arco;
pickup pencircle scaled 0.5;
drawarrow rp(gammacnt)--rp(gammacnt+1.3*radius*(1,0,0));
% path_ngamma = rp(gammacnt)--rp(ngamma0);
path_ngamma = rp(gammacnt)--rp(ngamma0)--rp((0,0,0));
draw path_ngamma;
%%% c vector
% drawarrow rp(gammacnt)--rp(ngamma0);
recta_xlayer = rp(gammacnt)--rp(gammacnt+1.3*radius*(1,0,0));
% recta_xlayer = rp(gammacnt)--rp(gammacnt+1.3*radius*(0,1,-sind(theta)));
drawarrow recta_xlayer;
% recta_ylayer = rp(gammacnt)--rp(gammacnt+1.3*radius*(0,1,-sind(theta)));
% drawarrow recta_ylayer;
proj = gammacnt+radius*sind(gammang)*(0,cosd(delta),-sind(delta));
recta_ylayer = rp(gammacnt)--rp(proj);
draw recta_ylayer;
draw rp(ngamma0)..rp(proj);
draw rp(orig)..rp(proj);
draw rp(ngamma0)..rp(1.1*etalpharad*(1,0,0)+proj);
draw rp(1.1*etalpharad*(1,0,0)+proj)..rp(1.1*etalpharad*(1,0,0));
% draw rp(radius*cosd(gammang)*(1,0,0))..rp(ngamma0);
anglinen( proj, nalfa, orig, alpharad, alphalabel, alphapos );
pickup pencircle scaled 1;
arco := (gamma cutbefore recta_xlayer) cutafter path_ngamma;
draw gamma;
% draw arco;
undraw arco;
arco := (gamma cutbefore recta_ylayer) cutafter path_ngamma;
% draw gamma;
% draw arco;
undraw arco;
pickup pencircle scaled 0.5;
draw gamma dashed evenly;
% draw subpath (0,0.9) of gamma;
% draw subpath (7.6,8) of gamma;
% draw subpath (1.5,8) of gamma;
% draw subpath (3.2,1.2) of alfa;
% labeln( vecclabel, rp(ngamma0), veccpos);
anglinen( ngamma0, field, orig, etalpharad, etalphalabel, etalphapos );
endfig;
verbatimtex \end{document} etex
end;
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