{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 " " 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 18 "Cyclo\357de sph\351rique " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 " Programme \+ original" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart:\nwith(l inalg):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "xx:=time():\nMM:=omega- >matrix(3,3,[1,0,0,0,cos(omega),-sin(omega),0,sin(omega),cos(omega)]): \nomega:=Pi/4:\nR:=4:r:=1:\np:=1: # pour pr\351ciser le nombr e de tours \340 effectuer\nn:=25: # le nombre de positions du \+ cercle mobile" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 378 "# Je fabrique la matrice de la rotation vectoriel le d'axe la tangente au cercle fixe\nP:=t->matrix(3,3,[-sin(t),-cos(t) ,0,cos(t),-sin(t),0,0,0,1]):\nM:=t->evalm(P(t)&*MM(omega)&*inverse(P(t ))):\n# On conna\356t l'image de O dans la rotation affine\nrota:=(x,y ,z)->op(convert((evalm(M(t)&*vector([x,y,z])+vector([R*(1-cos(omega))* cos(t),R*(1-cos(omega))*sin(t),R*sin(omega)]))),list)):\n" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 386 "\n#cercles:=seq(tubeplot([rota((R-r)*cos(t) +r*cos(t-u),(R-r)*sin(t)+r*sin(t-u),0),u=0..2*Pi,radius=#0.05],color=b lack),t=seq(k*p*2*Pi/n,k=0..n-1)):\ncercles:=seq(polygonplot3d([seq([r ota((R-r)*cos(t)+r*cos(t-u),(R-r)*sin(t)+r*sin(t-u),0)],u=seq(k*2*Pi/n ,k=0..n-1))],color=white),t=seq(k*p*2*Pi/n,k=0..n-1)):\ncerclefixe:=sp acecurve([R*cos(v),R*sin(v),0,v=0..2*Pi],color=blue,thickness=2):\n" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "\ncyclosph:=spacecurve([rota((R-r )*cos(t)+r*cos(t-R/r*t),(R-r)*sin(t)+r*sin(t-R/r*t),0),t=0..2*p*Pi],nu mpoints=400,color=red):\n\nh:=(r-R*cos(omega))/sin(omega):\nRho:=sqrt( R**2+h**2):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 176 "h:=(r-R*cos(omega ))/sin(omega):\nRho:=sqrt(R**2+h**2):\nsphere:=plot3d([Rho*cos(a)*cos( b),Rho*cos(a)*sin(b),Rho*sin(a)+h],a=-Pi/2..Pi/2+arctan(R/h),b=0..2*Pi ,style=patchnogrid):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "segments:=seq( spacecurve([[rota((R-r)*c os(t),(R-r)*sin(t),0)],\n [rota((R-r)*cos(t)+r*cos(t-R/r *t),(R-r)*sin(t)+r*sin(t-R/r*t),0)]],\n color=black, thickness=2),t=seq(k*2*p*Pi/n,k=0..n-1)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 329 "with(plots):\n#plotsetup(gif,plotoutput=\"c:/aaa/cyc losph.gif\",plotoptions=\"height=150 width=200\" );\n# enlever \"scali ng=constrained\" ci-dessous pour obtenir le gif anim\351\ndisplay([cer clefixe,sphere,cyclosph,display([cercles],insequence=true),display([se gments],insequence=true)],orientation=[-60,82],scaling=constrained);\n time()-xx;" }{TEXT -1 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 34 " Programme tr\350s l\351g\350rement modifi\351" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart:\nwith(linalg):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plotsetup(default);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 237 "xx:=time():\nMM:=omega->matrix(3,3,[1,0,0,0,cos(omeg a),-sin(omega),0,sin(omega),cos(omega)]):\nomega:=Pi/3:\nR:=4:r:=R/3: \np:=1: # pour pr\351ciser le nombre de tours \340 effectuer \nn:=25: # le nombre de positions du cercle mobile" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 378 "# Je fabrique la matrice de la rotation ve ctorielle d'axe la tangente au cercle fixe\nP:=t->matrix(3,3,[-sin(t), -cos(t),0,cos(t),-sin(t),0,0,0,1]):\nM:=t->evalm(P(t)&*MM(omega)&*inve rse(P(t))):\n# On conna\356t l'image de O dans la rotation affine\nrot a:=(x,y,z)->op(convert((evalm(M(t)&*vector([x,y,z])+vector([R*(1-cos(o mega))*cos(t),R*(1-cos(omega))*sin(t),R*sin(omega)]))),list)):\n" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 225 "#cercles:=seq(tubeplot([rota((R-r) *cos(t)+r*cos(t-u),(R-r)*sin(t)+r*sin(t-u),0),u=0..2*Pi,radius=#0.05], color=black),t=seq(k*p*2*Pi/n,k=0..n-1)):\nxx:=time():\n#sorti:=[rota( (R-r)*cos(t)+r*cos(t-u),(R-r)*sin(t)+r*sin(t-u),0)] :" }{TEXT -1 1 "\n " }{MPLTEXT 1 0 269 "#cercles:=seq(polygonplot3d([seq(sorti,u=seq(k*2* Pi/n,k=0..n-1))],\n# color=white),t=seq(k*p*2*Pi/n,k=0..n-1)):\n# \+ ( ne change pas beaucoup avec la r\351daction suivante )\ncalcul1:=sub s(u=u*2*Pi/n,t=t*p*2*Pi/n,[rota((R-r)*cos(t)+r*cos(t-u),(R-r)*sin(t)+r *sin(t-u),0)]):\n" }{TEXT -1 86 " # On a int\351r\352t \340 sort ir la ligne ci-dessus de la s\351quence de la ligne suivante" } {MPLTEXT 1 0 157 " \ncercles:=seq(polygonplot3d([seq(calcul1,u=0..n-1) ],color=white),t=0..n-1):\ncerclefixe:=spacecurve([R*cos(v),R*sin(v),0 ,v=0..2*Pi],color=blue,thickness=2):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 180 "cyclosph:=spacecurve([rota((R-r)*cos(t)+r*cos(t-R/r*t),(R-r)* sin(t)+r*sin(t-R/r*t),0),t=0..2*p*Pi],numpoints=400,color=red):\n\nh:= (r-R*cos(omega))/sin(omega):\nRho:=sqrt(R**2+h**2):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 192 "h:=(r-R*cos(omega))/sin(omega):\nRho:=sqrt(R**2 +h**2):\nsphere:=plot3d([Rho*cos(a)*cos(b),Rho*cos(a)*sin(b),Rho*sin(a )+h],\n a=-Pi/2..Pi/2+arctan(R/h),b=0..2*Pi,style=patchn ogrid):\n" }{TEXT -1 96 "# Le trac\351 du reste de la sph\350re en mod e \"transparent\" montre que tout se passe sur la sph\350re ??" } {MPLTEXT 1 0 172 "\nsphere1:=plot3d([Rho*cos(a)*cos(b),Rho*cos(a)*sin( b),Rho*sin(a)+h],\n a=Pi/2..Pi/2+arctan(R/h),b=0..2*Pi,s tyle=WIREFRAME,color=COLOR(RGB,1,1,0),grid=[6,20]):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "sorti1:=[ rota((R-r)*cos(t),(R-r)*sin(t),0)],\n [rota((R-r)*cos(t)+r*cos( t-R/r*t),(R-r)*sin(t)+r*sin(t-R/r*t),0)]:\n" }{TEXT -1 87 " # O n a int\351r\352t \340 sortir la ligne ci-dessus de la s\351quence de \+ la ligne suivante" }{MPLTEXT 1 0 88 "\nsegments:=seq(spacecurve([sort i1],color=black,thickness=2),t=seq(k*2*p*Pi/n,k=0..n-1)):" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "plotsetup(gif,plotoutput=\"d:/cyclosph.gif\",plotoptions=\"he ight=150 width=200\" );\ndisplay([cerclefixe,sphere,sphere1,cyclosph,d isplay([cercles],insequence=true),display([segments],insequence=true)] ,orientation=[-60,82]);" }{TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "time()-xx;" }}{PARA 11 "" 1 "" {XPPMATH 20 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