{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Cour ier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "Variables et macros" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 53 "with(linalg): with(DEtools): with(Maplets[Elem ents]):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names n orm and trace have been redefined and unprotected\n" }}{PARA 7 "" 1 " " {TEXT -1 45 "Warning, the name adjoint has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "xyz:=[x,y,z]: non,e1,e2,e3:= [0,0,0],[1,0,0],[0,1,0],[0,0,1]:" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 37 "Equation fondamentale du mouvement 3D" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "position:=;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)positionG-%'RTABLEG6%\")sSB9-%'MATRIXG6#7%7#%\"XG7#%\"YG7#%\" ZG&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "translation:=: rotation:=: torseur:=t ranslation+;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(torseurG-%'RTABLEG6%\")SR58-%'MATRIXG6#7%7#,(&%\"tG6 #%\"xG\"\"\"*&&%\"rG6#%\"yGF3%\"ZGF3F3*&&F66#%\"zGF3%\"YGF3!\"\"7#,(&F 0F7F3*&F;F3%\"XGF3F3*&&F6F1F3F9F3F?7#,(&F0FF3F3*&F5F3FDF3F? &%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "mo uv_XYZ:=\{D(X)=torseur[1],D(Y)=torseur[2],D(Z)=torseur[3]\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)mouv_XYZG<%/-%\"DG6#%\"XG,(&%\"tG6#%\"xG \"\"\"*&&%\"rG6#%\"yGF0%\"ZGF0F0*&&F36#%\"zGF0%\"YGF0!\"\"/-F(6#F;,(&F -F4F0*&F8F0F*F0F0*&&F3F.F0F6F0F " 0 "" {MPLTEXT 1 0 14 "vision:=;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'visionG-%'RTABLEG6%\")[>j8-%'MATRIXG6#7$7#%\" uG7#%\"vG&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Xu:=\{X=Z*u/f,Y=Z*v/f\}; uX:=\{u=f*X/Z,v=f*Y/Z\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#XuG<$/%\"XG*(%\"ZG\"\"\"%\"uGF*%\"fG!\"\"/% \"YG*(F)F*%\"vGF*F,F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#uXG<$/%\"u G*(%\"fG\"\"\"%\"XGF*%\"ZG!\"\"/%\"vG*(F)F*%\"YGF*F,F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Duv:=D(subs(uX,[u,v]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$DuvG7$,(*(-%\"DG6#%\"fG\"\"\"%\"XGF,%\"ZG !\"\"F,*(F+F,-F)6#F-F,F.F/F,**F+F,F-F,-F)6#F.F,F.!\"#F/,(*(F(F,%\"YGF, F.F/F,*(F+F,-F)6#F9F,F.F/F,**F+F,F9F,F4F,F.F6F/" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 63 "m:=: mouv_uv:=exp and(simplify(m));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(mouv_uvG-%'RTA BLEG6%\")SA::-%'MATRIXG6#7$7#,$*(,0*(-%\"DG6#%\"fG\"\"\"%\"uGF6%\"ZGF6 !\"\"*&&%\"tG6#%\"xGF6)F5\"\"#F6F9*(&%\"rG6#%\"yGF6F8F6F?F6F9**F5F6&FC 6#%\"zGF6F8F6%\"vGF6F6*(F7F6&F " 0 "" {MPLTEXT 1 0 79 "A:=matrix(2,3,[seq(seq(expand(Z*coe ff(mouv_uv[j],t[xyz[i]])),i=1..3),j=1..2)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7%%\"fG\"\"!,$%\"uG!\"\"7%F+F*,$%\" vGF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "B:=matrix(2,3,[seq( seq(expand(f*coeff(mouv_uv[j],r[xyz[i]])),i=1..3),j=1..2)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7$7%,$*&%\"uG\"\"\"%\"vGF- !\"\",&*$)%\"fG\"\"#F-F-*$)F,F4F-F-,$*&F.F-F3F-F/7%,&F1F/*$)F.F4F-F/F+ *&F,F-F3F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "mouv_transla tion:=a/Z,multiply(A,translation))>; mouv_rotation:=b/ f,multiply(B,rotation))>;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%1mouv_t ranslationG-%'RTABLEG6%\")_Zf:-%'MATRIXG6#7$7#*&,&*&&%\"tG6#%\"xG\"\" \"%\"fGF5F5*&%\"uGF5&F26#%\"zGF5!\"\"F5%\"ZGF<7#*&,&*&&F26#%\"yGF5F6F5 F5*&%\"vGF5F9F5F%.mouv_rotationG-%'RTABLEG6%\")_\\f:-%'MATRIXG6#7$7#*& ,(*(%\"uG\"\"\"%\"vGF2&%\"rG6#%\"xGF2!\"\"*&,&*$)%\"fG\"\"#F2F2*$)F1F> F2F2F2&F56#%\"yGF2F2*(F3F2F=F2&F56#%\"zGF2F8F2F=F87#*&,(*&,&F;F8*$)F3F >F2F8F2F4F2F2*(F1F2F3F2FAF2F2*(F1F2F=F2FEF2F2F2F=F8&%'VectorG6#%'colum nG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "zoom:=simplify(mouv_u v-(mouv_translation+mouv_rotation));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%%zoomG-%'RTABLEG6%\")!=KO\"-%'MATRIXG6#7$7#*(-%\"DG6#%\"fG\"\"\"% \"uGF3F2!\"\"7#*(F/F3%\"vGF3F2F5&%'VectorG6#%'columnG" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 14 "Visualisations" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 470 "_m:=subs(D(f)=g,m): visualiser:=proc(tr,rot) globa l _m,t,r,f,g,u,v,Z; local i,test,tors,T,U,V; test:=u=U(T),v=V(T),f=1,Z =1; for i to 3 do test:=test,t[xyz[i]]=tr[i],r[xyz[i]]=rot[i]; end do; if nargs=3 then tors:=subs([test,g=args[3]],_m) else tors:=subs([test ,g=0],_m) end if; ; dfieldplot([D(U)(T)=tors[1],D(V)(T)=tors[2]],[U(T) ,V(T)],T=0..1,U=-10..10,V=-10..10, arrows=LARGE,color=(tors[1]^2+tors[ 2]^2)*(1+.000000000001*U*V),axes=NONE, scaling=CONSTRAINED); end proc: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 275 "# visualiser(e1,non): \+ visualiser(e2,non): visualiser(e1+e2,non): visualiser(e3,non): visuali ser(non,non,1): visualiser(5*e1+e3,non): visualiser(5*e2-e3,non): visu aliser(non,e1): visualiser(e1,e1): visualiser(e2,e1): visualiser(non,e 3): visualiser(e3,e3): visualiser(e3,e3,1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 520 "viz := Maplet([ [\"Translation :\", [ListBox['TX' ]('value'=1,[-1,0,1]), ListBox['TY']('value'=0,[-1,0,1]), ListBox['TZ' ]('value'=0,[-1,0,1])], \"Rotation :\", [ListBox['RX']('value'=0,[-1,0 ,1]), ListBox['RY']('value'=0,[-1,0,1]), ListBox['RZ']('value'=0,[-1,0 ,1])], \"Zoom :\", ListBox['ZOOM']('value'=0,[0,1])], Plotter['VIZ'](p lot(undefined, U=-10..10, V=-10..10, axes=NONE, scaling=CONSTRAINED)), [Button(\"Visualiser\", Evaluate('VIZ' ='visualiser([TX,TY,TZ],[RX,RY ,RZ],ZOOM)')), Button(\"Passer \340 la suite\", Shutdown())] ]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Maplets[Display](viz):" }} {PARA 6 "" 1 "" {TEXT -1 38 "Initializing Java runtime environment." } }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 57 "Equation fondamentale du mouve ment \340 travers une lentille" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot([1/(1+1/z),1],z=-5..5,-5..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 474 254 254 {PLOTDATA 2 "6&-%'CURVESG6$7bp7$$!\"&\"\"!$\"3++ +++++]7!#<7$$!3YLLLe%G?y%F-$\"3]R$)Hv$3WE\"F-7$$!3OmmT&esBf%F-$\"35CfW 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gl7$F_clFagl7$FdclFagl7$FiclFagl7$F^dlFagl7$FcdlFagl7$FhdlFagl7$F]elFa gl7$FbelFagl7$FgelFagl7$F\\flFagl7$FaflFagl-Fffl6&FhflF\\glFiflF\\gl-% +AXESLABELSG6$Q\"z6\"Q!Fijl-%%VIEWG6$;F(FaflF^[m" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "fF:=\{f=1/(1/F+1/Z)\}: XuF:=simplif y(subs(fF,Xu)); uXF:=simplify(subs(fF,uX));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$XuFG<$/%\"XG*(%\"uG\"\"\",&%\"ZGF*%\"FGF*F*F-!\"\"/% \"YG*(%\"vGF*F+F*F-F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$uXFG<$/%\" vG*(%\"FG\"\"\"%\"YGF*,&%\"ZGF*F)F*!\"\"/%\"uG*(F)F*%\"XGF*F,F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "DuvF:=subs(D(F)=0,D(subs(uXF ,[u,v])));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%DuvFG7$,&*(%\"FG\"\" \"-%\"DG6#%\"XGF),&%\"ZGF)F(F)!\"\"F)**F(F)F-F)-F+6#F/F)F.!\"#F0,&*(F( F)-F+6#%\"YGF)F.F0F)**F(F)F9F)F2F)F.F4F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "mF:=: mouv_uvF:=expand (simplify(mF));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)mouv_uvFG-%'RTAB LEG6%\");'R1\"-%'MATRIXG6#7$7#,$*(,4*&&%\"tG6#%\"xG\"\"\")%\"FG\"\"#F6 !\"\"*(&%\"rG6#%\"yGF6%\"ZGF6F7F6F:**F8F6&F=6#%\"zGF6%\"vGF6F@F6F6*(FB F6FEF6F7F6F6*(%\"uGF6&F3FCF6F8F6F6**FHF6&F=F4F6F@F6FEF6F6**FHF6FKF6FEF 6F8F6F6*(FF6F7F6F:**F8F6FBF6FHF6F@F6F:*(FBF6FHF6F7F6F:*(FKF6F@F6F7F6F6*(F EF6FIF6F8F6F6*(FKF6F@F6)FEF9F6F6*(FKF6FfnF6F8F6F6**FEF6F " 0 "" {MPLTEXT 1 0 81 "AF:=matrix(2,3,[seq(seq(expa nd(Z*coeff(mouv_uvF[j],t[xyz[i]])),i=1..3),j=1..2)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AFG-%'matrixG6#7$7%*(%\"ZG\"\"\"%\"FGF,,&F+F,F- F,!\"\"\"\"!,$*(F+F,%\"uGF,F.F/F/7%F0F*,$*(F+F,%\"vGF,F.F/F/" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "BF:=matrix(2,3,[seq(seq(exp and(collect(simplify(F*coeff(mouv_uvF[j],r[xyz[i]])),[u,v])),i=1..3),j =1..2)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BFG-%'matrixG6#7$7%,$* &%\"uG\"\"\"%\"vGF-!\"\",&*$)F,\"\"#F-F-*(%\"ZGF-%\"FGF3,&F5F-F6F-F/F- ,$*&F.F-F6F-F/7%,&*$)F.F3F-F/F4F/F+*&F,F-F6F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "mouv_translationF:=simplify(a/Z,multipl y(AF,translation))>); mouv_rotationF:=b/F,multiply(BF,rotation ))>;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%2mouv_translationFG-%'RTABLE G6%\")cW(H\"-%'MATRIXG6#7$7#,$*&,&*&&%\"tG6#%\"xG\"\"\"%\"FGF6!\"\"*&% \"uGF6&F36#%\"zGF6F6F6,&%\"ZGF6F7F6F8F87#,$*&,&*&&F36#%\"yGF6F7F6F8*&% \"vGF6F;F6F6F6F>F8F8&%'VectorG6#%'columnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/mouv_rotationFG-%'RTABLEG6%\")'\\uH\"-%'MATRIXG6#7$7 #*&,(*(%\"uG\"\"\"%\"vGF2&%\"rG6#%\"xGF2!\"\"*&,&*$)F1\"\"#F2F2*(%\"ZG F2%\"FGF=,&F?F2F@F2F8F2F2&F56#%\"yGF2F2*(&F56#%\"zGF2F3F2F@F2F8F2F@F87 #*&,(*&,&*$)F3F=F2F8F>F8F2F4F2F2*(F1F2F3F2FBF2F2*(FFF2F1F2F@F2F2F2F@F8 &%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "si mplify(mouv_uvF-(mouv_translationF+mouv_rotationF));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")wX(H\"-%'MATRIXG6#7$7#\"\"!F+&%'Vecto rG6#%'columnG" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 14 "Visualisations " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 399 "visualiserF:=proc(tr,ro t,foc) global mouv_uvF,t,r,F,u,v,Z; local i,test,tors,T,U,V; test:=u=U (T),v=V(T),F=foc,Z=1; for i to 3 do test:=test,t[xyz[i]]=tr[i],r[xyz[i ]]=rot[i]; end do; tors:=subs(test,mouv_uvF); dfieldplot([D(U)(T)=tors [1],D(V)(T)=tors[2]],[U(T),V(T)],T=0..1,U=-10..10,V=-10..10, arrows=LA RGE,color=(tors[1]^2+tors[2]^2)*(1+.000000000001*U*V),axes=NONE, scali ng=CONSTRAINED); end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 535 "vizF := Maplet([ [\"Translation :\", [ListBox['TX']('value'=1,[-1 ,0,1]), ListBox['TY']('value'=0,[-1,0,1]), ListBox['TZ']('value'=0,[-1 ,0,1])], \"Rotation :\", [ListBox['RX']('value'=0,[-1,0,1]), ListBox[' RY']('value'=0,[-1,0,1]), ListBox['RZ']('value'=0,[-1,0,1])], \"Focale :\", ListBox['FOCALE']('value'=1,[0.1,1,10])], Plotter['VIZF'](plot(u ndefined, U=-10..10, V=-10..10, axes=NONE, scaling=CONSTRAINED)), [But ton(\"Visualiser\", Evaluate('VIZF' ='visualiserF([TX,TY,TZ],[RX,RY,RZ ],FOCALE)')), Button(\"Passer \340 la suite\", Shutdown())] ]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Maplets[Display](vizF):" }}} }{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Comparaisons" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 809 "comparer:=Maplet([ [\"Translation :\", [ Li stBox['TX']('value'=1,[-1,0,1]), ListBox['TY']('value'=0,[-1,0,1]), Li stBox['TZ']('value'=0,[-1,0,1]) ], \"Rotation : \", [ ListBox['RX']('value'=0,[-1,0,1]), ListBox['RY']('value'=0,[-1,0 ,1]), ListBox['RZ']('value'=0,[-1,0,1]) ], \"Zoom :\", ListBox['ZOOM'] ('value'=0,[0,1]), \"Foca le :\", ListBox['FOCALE']('value'=1,[0.1,1,10]) ], [ Plotter['VIZ'](pl ot(undefined, U=-10..10, V=-10..10, axes=NONE, scaling=CONSTRAINED)), \+ Plotter['VIZF'](plot(undefined, U=-10..10, V=-10..10, axes=NONE, scali ng=CONSTRAINED)) ], [ Button(\"Comparer\", Action(Evaluate('VIZ'='visu aliser([TX,TY,TZ],[RX,RY,RZ],ZOOM)'), Evaluate( 'VIZF'='visualiserF([T X,TY,TZ],[RX,RY,RZ],FOCALE)'))), Button(\"Passer \340 la suite\", Shut down())] ]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Maplets[Dis play](comparer);" }}{PARA 8 "" 1 "" {TEXT -1 119 "Error, invalid input : Maplets:-Display expects its 1st argument, maplet, to be of type fun ction, but received comparer\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "5 4 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 14234072 13103940 13631948 15152240 15594752 15594952 13632180 }{RTABLE M7R0 I5RTABLE_SAVE/14234072X*%)anythingG6"6"[gl!#%!!!"$"$%"XG%"YG%"ZGF& } {RTABLE M7R0 I5RTABLE_SAVE/13103940X*%)anythingG6"6"[gl!#%!!!"$"$,(&%"tG6#%"xG"""*&&%"rG6#%" yGF,%"ZGF,F,*&&F/6#%"zGF,%"YGF,!"",(&F)F0F,*&F4F,%"XGF,F,*&&F/F*F,F2F,F8,(&F)F5 F,*&F>F,F7F,F,*&F.F,F