merc.tex

\documentclass{article}
\usepackage{pst-solides3d,pst-eucl}
\begin{document}
\begin{pspicture}(-6,-6)(6,8)
\psset{lightsrc=viewpoint}
\psset{solidmemory}
\psset{viewpoint=100 5 15 rtp2xyz,Decran=100}
\psSolid[object=sphere,r=4,fillcolor=gray!20,
         action=draw**,grid=false,
         ngrid=30 72,linewidth=0.01,
        intersectiontype=0,
        intersectionplan={[-40 sin 40 cos 0 0] [-55 sin 55 cos 0 0] [0 0 1 0] [0 0 1 -2] [0 1 0 0]},
        intersectionlinewidth=2 2 2 2 2,
        intersectioncolor=(bleu) (rouge) (Green) (Green) (Black)]
\psSolid[object=cylindre,r=4,h=8,
         action=draw,
         ngrid=1 36,linewidth=0.01](0,0,-4)
\defFunction[algebraic]{CERCLE}(t){4*cos(t)}{4*sin(t)}{4}
\psSolid[object=courbe,
        r=0,
        range=0 6.28,
        resolution=360,
        function=CERCLE]%
\pscircle{4}
\pstVerb{/CoordA {4 40 -80} def
         /CoordB {4 40 91} def}
\psSolid[object=trigospherique,linestyle=dashed,linecolor=blue,
         definition=geodesique_sphere,
         args=CoordA CoordB]
\psSolid[object=trigospherique,linecolor=blue,
         definition=arcspherique,linewidth=2\pslinewidth,
         args=CoordA CoordB]%
\pstVerb{/CoordC {4 55 -80} def
         /CoordD {4 55 91} def}
\psSolid[object=trigospherique,linestyle=dashed,linecolor=red,
         definition=geodesique_sphere,
         args=CoordC CoordD]
\psSolid[object=trigospherique,linecolor=red,
         definition=arcspherique,linewidth=2\pslinewidth,
         args=CoordC CoordD]%
\pstVerb{/CoordE {4 0 0} def
         /CoordF {4 30 0} def}
\psSolid[object=trigospherique,linestyle=dashed,linecolor=green,
         definition=geodesique_sphere,
         args=CoordE CoordF]
\pstVerb{/CoordG {4 0 30} def
         /CoordH {4 0 -30} def}
\psSolid[object=trigospherique,linestyle=dashed,
         definition=geodesique_sphere,
         args=CoordG CoordH]
\psSolid[object=vecteur,
         args=0 0 2](0,0,4)%
\pstVerb{/xE1 4 40 cos mul def
         /yE1 4 40 sin mul def
         /xE2 4 55 cos mul def
         /yE2 4 55 sin mul def}
\psPoint(0,0,0){O}
\psPoint(0,0,4){N}
\psPoint(0,0,-4){S}
\psPoint(4,0,0){X1}
\psPoint(-4,0,0){X2}
\psPoint(0,-4,0){Y1}
\psPoint(0,4,0){Y2}
\psPoint(xE1,yE1,0){E1}
\psPoint(xE2,yE2,0){E2}
\psline(O)(E1)
\psline(O)(E2)
\psline(S)(N)
\psdots[linecolor=red](N)(S)
\psline[linestyle=dashed](X1)(X2)
\uput[u](N){\color{red}{$N$}}
\uput[d](S){\color{red}{$S$}}
\pstVerb{/xP 4 40 cos mul 30 cos mul def
         /yP 4 40 sin mul 30 cos mul def
         /zP 4 30 sin mul def}
\psPoint(xP,yP,zP){P}
\psSolid[object=vecteur,
         linecolor=red,
         args=xP yP zP](0,0,0)%
\psset{arrowsize=0.2}
\pstMarkAngle[arrows=->,MarkAngleRadius=0.4,LabelSep=0.6]{X1}{O}{E1}{$\phi_1$}
\pstMarkAngle[arrows=->,MarkAngleRadius=0.8,LabelSep=1]{X1}{O}{E2}{$\phi_2$}
\pstMarkAngle[arrows=->,MarkAngleRadius=1,LabelSep=1.2,linecolor=blue]{E1}{O}{P}{\color{blue}{$\beta$}}
\end{pspicture}
\end{document}