cent.tex

\documentclass{article}
\usepackage{pst-solides3d,pst-eucl}
\begin{document}
\begin{pspicture}(-6,-6)(6,8)
\psset{lightsrc=viewpoint}
\psset{viewpoint=100 15 20 rtp2xyz,Decran=100}
\psSolid[object=grille,fillcolor=blue!20,
         action=draw**,grid=false,
         base=-8 8 -8 8](0,0,-2)
\psPolygonIIID(-8,-8,-2)(-8,8,-2)(8,8,-2)(8,-8,-2)
\psSolid[object=sphere,r=2,fillcolor=gray!20,
         action=draw**,grid=false,
         ngrid=30 72,linewidth=0.01,
        intersectiontype=0,
        intersectionplan={[0 0 1 0] [0 1 0 0]},
        intersectionlinewidth=2 2,
        intersectioncolor=(bleu) (rouge)]
\pscircle{2}
\pstVerb{/CoordA {2 0 -20} def
         /CoordB {2 0 20} def}
\psSolid[object=trigospherique,linestyle=dashed,linecolor=red,
         definition=geodesique_sphere,
         args=CoordA CoordB]%
\pstVerb{/CoordC {2 0 0} def
         /CoordD {2 30 0} def}
\psSolid[object=trigospherique,linestyle=dashed,linecolor=blue,
         definition=geodesique_sphere,
         args=CoordC CoordD]%
\psPoint(0,0,0){O}
\psPoint(0,0,2){N}
\psPoint(0,0,-2){S}
\psPoint(2,0,0){X1}
\psPoint(-2,0,0){X2}
\psPoint(0,-2,0){Y1}
\psPoint(0,2,0){Y2}
\psline[linestyle=dashed](X1)(X2)
\psline[linestyle=dashed](Y1)(Y2)
\uput[u](N){\color{red}{$N$}}
\uput[d](S){\color{red}{$S$}}
\pstVerb{/xP 2 40 cos mul 30 cos mul def
         /yP 2 40 sin mul 30 cos mul def
         /zP 2 30 sin mul def}
\psPoint(xP,yP,zP){P}
\uput[r](P){$P$}
\psdot(P)
\psline{->}(O)(P)
\psline[linestyle=dashed](N)(P)
% projection de P sur le plan equatorial
\psPoint(xP,yP,0){P'}
\psPoint(xP,0,0){P'x}
\psPoint(0,yP,0){P'y}
\psPoint(0,0,zP){P'z}
\pstVerb{% les coordonnées du point sur le plan P1
        /zN 2 def
        /zP1 -2 def
        /k1 zP1 zN sub zP zN sub div def
        /xP1 k1 xP mul def
        /yP1 k1 yP mul def}
%\psdot(P')
\psline[linestyle=dashed](P'x)(P')(P'y)
\psline[linestyle=dashed](P')(P)
\psline[linestyle=dashed](O)(P')
\psPoint(xP1,yP1,zP1){P1}
\psline(P)(P1)
\psdot(P1)
\uput[dr](P1){$\hat{P}$}
\psPoint(xP1,yP1,-2){P1'}
\psPoint(xP1,0,-2){P1'x}
\psPoint(0,yP1,-2){P1'y}
\psline[linestyle=dashed](P1'x)(P1')(P1'y)
\psPoint(0,0,-2){O'}
\psPoint(0,0,4){Z}
\psPoint(8,0,-2){X}
\psPoint(0,8,-2){Y}
\uput[d](X){$X$}
\uput[r](Y){$Y$}
\uput[u](Z){$Z$}
\psline{->}(O')(X)
\psline{->}(O')(Y)
\psline{->}(N)(Z)
\psline[linestyle=dashed](S)(N)
\pstMarkAngle[arrows=->,linecolor=blue,LabelSep=0.6]{P'x}{O}{P'}{\color{blue}{$\theta$}}
\pstMarkAngle[arrows=->,linecolor=red,LabelSep=0.6]{P'}{O}{P}{\color{red}{$\phi$}}
\end{pspicture}
\end{document}