Barycentres

3 Barycentres

\begin{pspicture}(5,5)%\psgrid
  \psset{dotscale=0.1, PointSymbol=+}
  \newpsstyle{Fig}{CodeFig=true, CodeFigColor=black}
  
  % isobarycentre de 2 points
  \pstGeonode[PosAngle=160](1,4.2){A}
  \pstGeonode[PosAngle=-30](4,4.6){B}
  \ncline{|-|}{A}{B}
  \pstMiddleAB[dotscale=1, style=Fig, PosAngle=-90]{A}{B}{I}

  % isobarycentre de 3 points
  \pstTriangle[PosAngleA=90, PosAngleC=-70](3,3.5){A}(4.5,.5){B}(.5,.8){C}
  \psset{dotscale=1}
  \pstMiddleAB[style=Fig, PosAngle=130]{A}{C}{J}
  \pstMiddleAB[style=Fig, PosAngle=-80, SegmentSymbol=pstslash]{B}{C}{I}
  \pstMiddleAB[style=Fig,PosAngle=10,SegmentSymbol=pstslashslashslash]{A}{B}{K}
  \psset{linestyle=dashed}
  \psline(A)(I)\psline(B)(J)\psline(C)(K)
  \pstCGravABC{A}{B}{C}{G}
\end{pspicture}

\begin{pspicture}(0,0)(18,3)%\psgrid
  \psset{PointSymbol=+}

  % barycentre G1 de {(A,3);(B,2)}
  \pstGeonode[PosAngle=180](3,2){A}
  \pstGeonode(6.5,2){B}
  \pstLineAB{A}{B}
  \pstHomO[PosAngle=90, HomCoef=.4]{A}{B}{G_1}
  \rput{-30}(A){
    \pstGeonode[PosAngle=-120](2.5;0){B'}
    \pstGeonode[PosAngle=-120](1;0){G'}
    \multips{0}(A)(.5,0){5}{\psline(0,0)(0,.1)}
  }
  \pstLineABd[nodesepB=-.5]{A}{B'}{(\Delta)}
  {\psset{linestyle=dashed}
    \ncline{G'}{G_1}\ncline{B'}{B}}

  % barycentre G2 de {(A,5);(B,-2)}
  \pstGeonode[PosAngle=90](12,2){A}
  \pstGeonode(14,2){B}
  \pstHomO[PosAngle=-90, HomCoef=-.666]{A}{B}{G_2}
  \rput(A){\pstGeonode(1;140){G''}}
  \ncline{|-|}{G_2}{B}
  \rput{-40}(G''){
    \pstGeonode[PosAngle=-120](2.5;0){B''}
    \multips{0}(.5,0){5}{\psline(0,0)(0,.1)}
  }
  \pstLineABd[nodesep=-.5]{G''}{B''}{(\Delta)}
  \psset{linestyle=dashed}
  \psline(G_2)(G'')\psline(B'')(B)
\end{pspicture}

\begin{pspicture}(6,8)
  \psset{dotscale=0.1}
  \newcommand{\tick}{\psline(0,0)(0,.1)}
  \newcommand{\commun}{
    \pstTriangle[PosAngleA=80, PosAngleB=-100, PosAngleC=-10]
                (4,3){A}(2,1){B}(6,1){C}
    \rput{-150}(A){
      \multips{0}(.6,0){5}{\tick}
      \psline(0,0)(3.2;0)
      \pnode(1.8;0){kk}\pnode(3;0){bb}
    }
    \pstHomO[HomCoef=.6, PosAngle=-80]{A}{B}{K_3}
    \pstMiddleAB[dotscale=1, PosAngle=70]{C}{K_3}{G}
    \psline(K_3)(C)
    \psset{linestyle=dashed, dash=3pt 2pt}
    \psline(bb)(B)\psline(kk)(K_3)
  }
                                % 1er dessin
  \rput(0,4){\commun}
                                % 2ème dessin
  \commun
  \rput{-15}(B){  \multips{0}(.4,0){8}{\tick}          % 8 ticks de .4
                  \psline(0,0)(3.8,0)                  % 8*.t + .2
                  \pnode(2.0,0){kb}\pnode(3.2;0){cb}   % 5*.t, 8*t
  }
  \rput{95}(C){   \multips{0}(.3,0){7}{\tick}          % 7 ticks de .3
                  \psline(0,0)(2.3;0)                  % 7*t + .2
                  \pnode(.6;0){kc}\pnode(2.1;0){cc}    % 2*t, 7*t
  }
  \pstHomO[HomCoef=0.625, PosAngle=-60]{B}{C}{K_1}  % 5/8
  \pstHomO[HomCoef=0.286, PosAngle=80]{C}{A}{K_2}   % 2/7
  \psline(A)(K_1)\psline(B)(K_2)
  \psset{linestyle=dashed, dash=3pt 2pt}
  \psline(kb)(K_1)\psline(cb)(C)
  \psline(kc)(K_2)\psline(cc)(A)
\end{pspicture}