{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 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 2 0 2 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 2 0 2 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courie r" 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 2 0 2 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 2 0 2 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 2 0 2 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 0 "" }}{PARA 18 "" 0 "" {TEXT -1 38 "SchwarzD : Esculier - 12 d\351cembre 2010" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 23 " Proc\351dures d'it\351ration" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4960 "#================================ =================================================================\nres tart:\nwith(plots):\n#******* nom_i d\351signe nom par indices et nom_ c d\351signe nom par coordonn\351es *******\n#************************ ********************************************************\npts0_c:=[[-1 /2,-1/2,1/2],[-1/2,1/2,-1/2],[-1/2,1/2,1/2],[1/2,-1/2,-1/2],[1/2,-1/2, 1/2],[1/2,1/2,-1/2],[0,0,0]]:\nfaces0_i:=[[1,3,7],[3,2,7],[2,6,7],[6,4 ,7],[4,5,7],[5,1,7]]:#--- indices dans pts0_c\nbase:=[pts0_c,faces0_i] :\n#****************************************************************** ********\n#*********** listeplex=[LS=listeSommets,LT=listeTriangles_pa r_indices_dans_LS] **********\n#************************************** ************************************\nfacesC:= proc(listeplex) # sort \+ les coordonn\351es des faces\n local i,som,F; som:=listepl ex[1]: F:=listeplex[2]:\n map(u ->[seq(som[u[i]],i=1..3)], F):\nend:\ngraphplex:=proc(listeplex) display(polygonplot3d(facesC(lis teplex))): end:\n#**************************************************** ***********************\n# methode d'it\351ration de la listeplex: \n# *** 1. faire la liste des cotes_i : L\n#*** 2. pour chaque cote_i, tro uver les faces_i adjacentes\n#*** 3. trouver le \"milieu\" et l'associ er au cot\351 \n#*** ( vrai milieu si sur contour, barycentre des s ommets compt\351s avec multiplicit\351 des 2 faces adjacentes sinon ) \n#*** 4. ajouter ces milieux \340 l'ancienne liste des sommets\n#*** \+ 4. pour chaque triangle, faire les 4 nouveaux triangles_i\n#********** ***************************************************\nitere:=proc(liste plex) # donne la listeplex d'ordre sup\351rieur\n local S_c,NS_c,F_ i,NF_i,AF_i,A_i,AetM_i,M_c,j,k, adj,arete,tp,m_i,t:\n S_c:=listeple x[1]: F_i:=listeplex[2]:\n NS_c:=op(S_c): NF_i:=NULL: AetM_i:=NULL: \n AF_i:=map( u ->[seq(\{u[i],u[(i mod 3) +1]\},i=1..3)],F_i): # li ste des aretes par faces\n A_i:=convert(convert(map(u ->op(u),AF_i ),set),list): # liste des aretes\n # calcul des milieux et liste de s nouveaux sommets\n for j to nops(A_i) do\n arete:=A_i[j]: \+ adj:=NULL:\n for k to nops(AF_i) do #--dans adj, indices des \+ faces ayant cette arete ------\n if member(arete,AF_i[k]) th en adj:=adj,k fi:\n od:\n adj:=[adj]:\n if nops(a dj)=1 then M_c:=expand((S_c[arete[1]]+S_c[arete[2]])/2):\n \+ else\n M_c:=expand( add( S_c[ F_i[adj[1],t]]+S_c[F_i [adj[2],t]],t=1..3)/6):\n fi;\n NS_c:=NS_c,M_c: AetM_i:= AetM_i,[arete,nops([NS_c])]:\n od:\n AetM_i:=[AetM_i]:NS_c:=[N S_c]:\n # nouvelles faces_i\n for j to nops(AF_i) do #--- anci enne face --> 3 nouvelles ---\n for k to 3 do #--- milieu de chaque arete -----\n for t while AetM_i[t,1]<> AF_i[j,k ] to nops(AetM_i) do od:\n m_i[k]:= AetM_i[t]:\n od: \n tp:=seq([m_i[k][2],m_i[(k mod 3)+1][2],op( m_i[k][1] interse ct m_i[(k mod 3)+1][1])],k=1..3):\n NF_i:=NF_i,[seq(m_i[k][2],k =1..3)],tp : \n od: \n[NS_c,[NF_i]]: \nend:\n#================ = iteration d'ordre n =====\n#*************** it\351ration simple ( il reste des d\351fauts en certains points )***********************\nite reSimple:= n -> if n=1 then base else itere(itereSimple(n-1)) fi:\n#** ************* it\351ration avec lissage des points introduits \340 l' it\351ration pr\351c\351dente ************\nitereN:= proc(n,base)\n \+ local tp,soms,faces_i,diff,places,i,j,k,facesadj,NS,diff1,grafplex,s omsN:\n if n=0 then print(\"n doit \352tre un entier strictement \+ positif\"):\n elif n=1 then base:\n elif n=2 then itere( base): \n else\n tp:=itereN(n-1,base); soms:=tp[1]: f aces_i:=tp[2];\n grafplex:=itere(tp): somsN:=grafplex[1]:\n \+ diff1:= convert(soms,set) minus convert(itereN(n-2,base)[1],se t):\n diff1:= convert(diff1,list): \n diff:=NULL; \n for i to nops(diff1) do ## \351limination des \"milieux\" \+ sur les bords( voir plus g\351n\351ral dans SchwarzH )\n i f not(has(diff1[i],\{1/2,-1/2\})) then diff:=diff,diff1[i]: fi:\n \+ od:\n diff:=[diff,[0,0,0]]:\n places:=NULL;\n \+ for i to nops(diff) do ##--- on trouve les indices des sommet s nouveaux ----\n if member(diff[i],soms,'p') then places:= places,p: fi:\n od:\n places:=[places]:\n f or i to nops(places) do\n tp:=places[i]: facesadj:=NULL; \n for j to nops(faces_i) do\n if memb er(tp,faces_i[j]) then facesadj:=facesadj,faces_i[j]: fi;\n \+ od:\n facesadj:=[facesadj]:\n NS:=add(add(soms [ facesadj[k,t]],t=1..3),k=1..nops(facesadj))/3/nops(facesadj):\n \+ somsN:=subsop(tp= NS,somsN):\n od: \n [somsN ,grafplex[2]]:\n fi;\nend:\n#******** les briques \351l\351mentair es ***************************\ndisplay([graphplex(itereSimple(3))],ti tle=\"avec des d\351fauts\",orientation=[-15,80]);\ndisplay([graphplex (itereN(3,base))],title=\"lissage des d\351fauts\",orientation=[-15,80 ]);" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT3D 547 547 547 {PLOTDATA 3 "6%-%)POLYGONSG6\\q7%7%$!+*)))))))Q!#5$\"+66666F*$\"+6666O F*7%$!+++++DF*$\"\"!F3$\"+++++DF*7%$!+6666OF*$!+66666F*$\"+*)))))))QF* 7%F'F/7%$!+LLLLLF*$\"+nmmm;F*FA7%F/F67%$!+nmmm;F*FE$\"+LLLLLF*7%F6F'7% $!+++++]F*F2$\"+++++]F*7%F'7%$!+WWWWWF*$\"+cbbbIF*FS7%FKF4FM7%F'FPF>7% FPFU7%FKFMFM7%FUF'FJ7%F/7%$!+LLLL$)!#6FfnFA7%FE$\"+LLLL$)FhnFjn7%F/Fen FD7%FenFin7%F2F2F27%FinF/F>7%F67%FKF0FM7%$!+cbbbIF*Fco$\"+WWWWWF*7%F6F aoFJ7%FaoFbo7%FKFKFM7%FboF6FD7%7%F7F;F97%F0F4F27%F(F-F+7%F\\pF]p7%FEFG FE7%F]pF^pF>7%F^pF\\p7%FKFMF27%F\\p7%FcoFeoFco7%FKFMF07%F\\pFepF`p7%Fe pFfp7%FKFMFK7%FfpF\\pFcp7%F]pFin7%FfnFAFfn7%F]pFinF>7%FinF\\qF^o7%F\\q F]pF`p7%F^p7%FKFMF4FP7%F^pFaqFcp7%FaqFPFX7%FPF^pF>7%7%F+F-F(7%F2F4F07% F9F;F77%FfqFgq7%FAFAF?7%FgqFhqF`p7%FhqFfq7%F2FMFK7%Ffq7%FSFSFQ7%F4FMFK 7%FfqF_rFjq7%F_rF`r7%FMFMFK7%F`rFfqF]r7%FgqF\\q7%FjnFjnFE7%FgqF\\qF`p7 %F\\qFfrF^o7%FfrFgqFjq7%Fhq7%F0FMFKFep7%FhqF[sF]r7%F[sFepFip7%FepFhqF` p7%7%F;F9F77%F4F2F07%F-F+F(7%F`sFas7%FGFEFE7%FasFbsFjq7%FbsF`s7%FMF2FK 7%F`s7%FeoFcoFco7%FMF0FK7%F`sFisFds7%FisFjs7%FMFKFK7%FjsF`sFgs7%FasFfr 7%FAFfnFfn7%FasFfrFjq7%FfrF`tF^o7%F`tFasFds7%Fbs7%FMF4FKF_r7%FbsFetFgs 7%FetF_rFcr7%F_rFbsFjq7%7%F-F(F+7%F4F0F27%F;F7F97%FjtF[u7%FAF?FA7%F[uF \\uFds7%F\\uFjt7%FMFKF27%Fjt7%FSFQFS7%FMFKF47%FjtFcuF^u7%FcuFdu7%FMFKF M7%FduFjtFau7%F[uF`t7%FjnFEFjn7%F[uF`tFds7%F`tFjuF^o7%FjuF[uF^u7%F\\u7 %FMFKF0Fis7%F\\uF_vFau7%F_vFisF]t7%FisF\\uFds7%7%F9F7F;7%F2F0F47%F+F(F -7%FdvFevFD7%FevFfvF^u7%FfvFdv7%F2FKFM7%FdvFbo7%F0FKFM7%FdvFboFD7%FboF \\wFio7%F\\wFdvFjv7%FevFjuFen7%FevFjuF^u7%FjuFenF^o7%FenFevFD7%Ffv7%F4 FKFMFcu7%FfvFewFjv7%FewFcuFgu7%FcuFfvF^u-%&TITLEG6#Q1avec~des~d|dyfaut s6\"-%+PROJECTIONG6%$!#:F3$\"#!)F3\"\"\"" 1 2 0 1 10 0 2 1 1 1 2 1.000000 80.000000 -15.000000 1 0 "Curve 1" }}}{PARA 13 "" 1 "" {GLPLOT3D 547 547 547 {PLOTDATA 3 "6%-%)POLYGONSG6\\q7%7%$!+*)))))))Q! #5$\"+66666F*$\"+6666OF*7%$!+++++DF*$\"\"!F3$\"+++++DF*7%$!+6666OF*$!+ 66666F*$\"+*)))))))QF*7%F'F/7%$!+[\"[\"[JF*$\"+_=&=&=F*FA7%F/F67%$!+_= &=&=F*FE$\"+[\"[\"[JF*7%F6F'7%$!+++++]F*F2$\"+++++]F*7%F'7%$!+WWWWWF*$ \"+cbbbIF*FS7%FKF4FM7%F'FPF>7%FPFU7%FKFMFM7%FUF'FJ7%F/7%$!+LLLL$)!#6Ff n$\"+nmmm;F*7%$!+nmmm;F*$\"+LLLL$)FhnF^o7%F/FenFD7%FenF[o7%F2F2F27%F[o F/F>7%F67%FKF0FM7%$!+cbbbIF*Fgo$\"+WWWWWF*7%F6FeoFJ7%FeoFfo7%FKFKFM7%F foF6FD7%7%F7F;F97%F0F4F27%F(F-F+7%F`pFap7%FEFGFE7%FapFbpF>7%FbpF`p7%FK FMF27%F`p7%FgoFioFgo7%FKFMF07%F`pFipFdp7%FipFjp7%FKFMFK7%FjpF`pFgp7%Fa pF[o7%FfnFinFfn7%FapF[oF>7%F[oF`qFbo7%F`qFapFdp7%Fbp7%FKFMF4FP7%FbpFeq Fgp7%FeqFPFX7%FPFbpF>7%7%F+F-F(7%F2F4F07%F9F;F77%FjqF[r7%FAFAF?7%F[rF \\rFdp7%F\\rFjq7%F2FMFK7%Fjq7%FSFSFQ7%F4FMFK7%FjqFcrF^r7%FcrFdr7%FMFMF K7%FdrFjqFar7%F[rF`q7%F^oF^oF\\o7%F[rF`qFdp7%F`qFjrFbo7%FjrF[rF^r7%F\\ r7%F0FMFKFip7%F\\rF_sFar7%F_sFipF]q7%FipF\\rFdp7%7%F;F9F77%F4F2F07%F-F +F(7%FdsFes7%FGFEFE7%FesFfsF^r7%FfsFds7%FMF2FK7%Fds7%FioFgoFgo7%FMF0FK 7%FdsF]tFhs7%F]tF^t7%FMFKFK7%F^tFdsF[t7%FesFjr7%FinFfnFfn7%FesFjrF^r7% FjrFdtFbo7%FdtFesFhs7%Ffs7%FMF4FKFcr7%FfsFitF[t7%FitFcrFgr7%FcrFfsF^r7 %7%F-F(F+7%F4F0F27%F;F7F97%F^uF_u7%FAF?FA7%F_uF`uFhs7%F`uF^u7%FMFKF27% F^u7%FSFQFS7%FMFKF47%F^uFguFbu7%FguFhu7%FMFKFM7%FhuF^uFeu7%F_uFdt7%F^o F\\oF^o7%F_uFdtFhs7%FdtF^vFbo7%F^vF_uFbu7%F`u7%FMFKF0F]t7%F`uFcvFeu7%F cvF]tFat7%F]tF`uFhs7%7%F9F7F;7%F2F0F47%F+F(F-7%FhvFivFD7%FivFjvFbu7%Fj vFhv7%F2FKFM7%FhvFfo7%F0FKFM7%FhvFfoFD7%FfoF`wF]p7%F`wFhvF^w7%FivF^vFe n7%FivF^vFbu7%F^vFenFbo7%FenFivFD7%Fjv7%F4FKFMFgu7%FjvFiwF^w7%FiwFguF[ v7%FguFjvFbu-%&TITLEG6#Q4lissage~des~d|dyfauts6\"-%+PROJECTIONG6%$!#:F 3$\"#!)F3\"\"\"" 1 2 0 1 10 0 2 1 1 4 2 1.000000 78.000000 63.000000 1 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots ):" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 564 "montubeplot := proc (liste, rc, rs, couleursommets) local n; if type(evalf(liste[1, 1]), \+ float) then n := nops(liste); display([plot3d(\{seq(expand(liste[i]+rs *[cos(u)*sin(v), sin(u)*sin(v), cos(v)]), i = 1 .. nops(liste))\}, u = 0 .. 2*Pi, v = 0 .. Pi, grid = [20, 10]), \ntubeplot(\{seq(expand(lis te[i]+t*(liste[`mod`(i, n)+1]-liste[i])), i = 1 .. nops(liste))\}, t = 0 .. 1, radius = rc, grid = [2, 15])], style = patchnogrid, lightmode l = light2) else op(map(proc (u) options operator, arrow; montubeplot( u, rc, rs,couleursommets) end proc, liste)) end if end proc:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 237 "liste1:=[[[0.5,0.5,-0.5],[0.5,-0.5,-0.5],[0.5,-0.5 ,0.5],[-0.5,-0.5,0.5],[-0.5,0.5,0.5],[-0.5,0.5,-0.5]]]:\nliste2:=[\n[[ 0.5,-0.5,0],[-0.5,0.5,0]],[[0,0.5,-0.5],[0,0,0]],[[0,0,0],[0,-0.5,0.5] ],[[0.5,0,-0.5],[0,0,0]],[[0,0,0],[-0.5,0,0.5]]]:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 159 "A:=display(montubeplot(liste1,.02,.02,yellow),mont ubeplot(liste2,.02,.02,red)):display(A,axes=boxed,tickmarks=[0,0,0],sc aling=constrained,orientation=[40,72]);" }}{PARA 13 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT3D 440 430 430 {PLOTDATA 3 "6G-%%MESHG6 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"Curve 12" "Curve 13" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 71 " Les transformations \351 l\351mentaires pour des listes de lignes polygonales" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1832 "#********* \nps:=proc(U,V) #**** pr oduit scalaire\n local u,v; u:=expand(U): v:=expand(V): add(u[i]*v [i],i=1..nops(u)):\nend:\npv:=proc(u,v) #*** produit vectoriel\n lo cal U,V; U:=expand(u): V:=expand(v): [U[2]*V[3]-U[3]*V[2],U[3]*V[1]-U[ 1]*V[3],U[1]*V[2]-U[2]*V[1]]:\nend proc:\nnorm2:= U -> expand(U/sqrt(p s(U,U))): #*** norm2\nrot:=proc(axe,t,point) # rotation\n local axe 1: axe1:=norm2(axe):\n expand(expand(cos(t)*point) +expand(sin(t)*pv( axe1,point)) +expand((1-cos(t))*ps(axe1,point)*axe1))\nend:\n#******** ******transformations de base appliqu\351es \340 une liste************ ******************\nLsymXY:= Liste -> if type(evalf(Liste[1,1]),numer ic) then map( u ->[u[1],u[2],-u[3]],Liste): else map( u->LsymXY(u),Lis te): fi:\nLsymYZ:= Liste -> if type(evalf(Liste[1,1]),numeric) then ma p( u ->[-u[1],u[2],u[3]],Liste): else map( u->LsymYZ(u),Liste): fi:\nL symZX:= Liste -> if type(evalf(Liste[1,1]),numeric) then map( u ->[u[1 ],-u[2],u[3]],Liste): else map( u->LsymZX(u),Liste): fi:\nLrot:=(axe,t ,Liste) -> if type(evalf(Liste[1,1]),numeric) then map( u ->rot(axe,t ,u),Liste): else map( u->Lrot(axe,t,u),Liste): fi:\nLtrans:=(V,Liste) \+ -> if type(evalf(Liste[1,1]),numeric) then map( u ->expand(u+V),Liste) : else map( u->Ltrans(V,u),Liste) fi: \naxes:=display([tubeplot([0,0,3 *t],t=0..1,radius=0.03,color=cyan,grid=[2,5]),\n tubeplo t([3*t,0,0],t=0..1,radius=0.03,color=red,grid=[2,5]),\n \+ tubeplot([0,3*t,0],t=0..1,radius=0.03,color=green,grid=[2,5])], style= patchnogrid):\n#******* tubeplot g\351n\351ralis\351 \340 une suite de lignes polygonale ********** \ntracelist:=proc(L) local p; \n if \+ type(L[1,1],numeric) then p:=nops(L):\n tubeplot(\{seq(expan d(L[i]+t*( L[ (i mod p) +1]-L[i])),i=1..nops(L))\},t=0..1,radius=0.04, grid=[2,8],style=patchnogrid,color=white):\n else display(map(trace list,L)): fi;\nend:" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{SECT 0 {PARA 3 "" 0 "" {TEXT -1 59 " Une premi\350re construction av ec une cellule de base connexe" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1047 " g4:=facesC(itereN(3,base)):\ncell:=map(op,[Ltrans([1/2,1/2,1/ 2],g4),Ltrans([-1/2,-1/2,1/2],Lrot([0,0,1],Pi,g4)),Ltrans([+1/2,-1/2,3 /2],Lrot([0,0,1],Pi/2,g4)),Ltrans([-1/2,1/2,3/2],Lrot([0,0,1],-Pi/2,g4 )) ]):\nbordbase:=[[-1/2, -1/2, 1/2], [-1/2, 1/2, 1/2], [-1/2, 1/2, -1 /2], [1/2, 1/2, -1/2], [1/2, -1/2, -1/2], [1/2, -1/2, 1/2]]:\nbordcell :=[Ltrans([1/2,1/2,1/2],bordbase),Ltrans([-1/2,-1/2,1/2],Lrot([0,0,1], Pi,bordbase)),Ltrans([+1/2,-1/2,3/2],Lrot([0,0,1],Pi/2,bordbase)),Ltra ns([-1/2,1/2,3/2],Lrot([0,0,1],-Pi/2,bordbase)) ]:\n#polygonplot3d([ce ll,Ltrans([0,0,2],cell)]);#\ncouche:= n -> map(op,[seq(seq(Ltrans([2*i ,2*j,0],cell),i=0..n-1),j=0..n-1)]):\nbordcouche:= n -> map(op,[seq(se q(Ltrans([2*i,2*j,0],bordcell),i=0..n-1),j=0..n-1)]):\n#bordcouche(3); \n#******************** la cellule de base de la constuction ********* ******\n#********* la surface s'en d\351duit par des translations succ essives ******\npolygonplot3d(cell,orientation=[20,65],style=patch,sca ling=constrained,color=COLOR(RGB,1,1,0.8),lightmodel=light2,title=\"La cellule de base\");" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT3D 664 498 498 {PLOTDATA 3 "6(-%)POLYGONSG6]cl7%7%$\"+66666!#5$\"+6666hF*$\"+ 6666')F*7%$\"+++++DF*$\"+++++]F*$\"+++++vF*7%$\"+*))))))Q\"F*$\"+*)))) )))QF*$\"+*)))))))))F*7%F'F/7%$\"+_=&=&=F*$\"+_=&=&oF*FA7%F/F67%$\"+[ \"[\"[JF*FE$\"+[\"[\"[\")F*7%F6F'7%$\"\"!FLF2$\"\"\"FL7%F'7%$\"+cbbbb! #6$\"+cbbb!)F*FT7%FKF4FM7%F'FPF>7%FPFV7%FKFMFM7%FVF'FJ7%F/7%$\"+nmmmTF *Fgn$\"+nmmmmF*7%$\"+LLLLLF*$\"+LLLLeF*F^o7%F/FfnFD7%FfnF[o7%F2F2F27%F [oF/F>7%F67%FKF0FM7%$\"+WWWW>F*Fgo$\"+WWWW%*F*7%F6FeoFJ7%FeoFfo7%FKFKF M7%FfoF6FD7%7%F7F;F97%F0F4F27%F(F-F+7%F`pFap7%FEFGFE7%FapFbpF>7%FbpF`p 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documents/Schwarz4-light2-cyan.bmp\",p lotoptions=\"width=1400,height=1000\");\n#gr; plotsetup(inline);" } {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"$" }}{PARA 8 "" 1 "" {TEXT -1 72 "Error, (in plots:-polygonplot3d) incorrect spec ification of points data\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#grG" } }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 77 " SchwarzD avec une cellule de base non connexe combin \351e selon deux m\351thodes" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 519 "g4:=facesC(itereN(3,base)):\n#********************************* ***************************************\n#******************** la cell ule de base des constructions ***************\ncell:=Ltrans([0,0,-2],m ap(op,[Ltrans([1/2,1/2,1/2+2],g4),Ltrans([-1/2,-1/2,1/2+2],Lrot([0,0,1 ],Pi,g4)),Ltrans([+1/2,-1/2,3/2],Lrot([0,0,1],Pi/2,g4)),Ltrans([-1/2,1 /2,3/2],Lrot([0,0,1],-Pi/2,g4)) ])):\npolygonplot3d(cell,orientation=[ 80,65],style=patch,scaling=constrained,color=COLOR(RGB,1,1,0.8),lightm odel=light2,title=\"La cellule de base\");" }}{PARA 13 "" 1 "" {GLPLOT3D 547 547 547 {PLOTDATA 3 "6(-%)POLYGONSG6]cl7%7%$\"+66666!#5$ \"+6666hF*$\"+6666')F*7%$\"+++++DF*$\"+++++]F*$\"+++++vF*7%$\"+*)))))) Q\"F*$\"+*)))))))QF*$\"+*)))))))))F*7%F'F/7%$\"+_=&=&=F*$\"+_=&=&oF*FA 7%F/F67%$\"+[\"[\"[JF*FE$\"+[\"[\"[\")F*7%F6F'7%$\"\"!FLF2$\"\"\"FL7%F '7%$\"+cbbbb!#6$\"+cbbb!)F*FT7%FKF4FM7%F'FPF>7%FPFV7%FKFMFM7%FVF'FJ7%F /7%$\"+nmmmTF*Fgn$\"+nmmmmF*7%$\"+LLLLLF*$\"+LLLLeF*F^o7%F/FfnFD7%FfnF [o7%F2F2F27%F[oF/F>7%F67%FKF0FM7%$\"+WWWW>F*Fgo$\"+WWWW%*F*7%F6FeoFJ7% FeoFfo7%FKFKFM7%FfoF6FD7%7%F7F;F97%F0F4F27%F(F-F+7%F`pFap7%FEFGFE7%Fap FbpF>7%FbpF`p7%FKFMF27%F`p7%FgoFioFgo7%FKFMF07%F`pFipFdp7%FipFjp7%FKFM FK7%FjpF`pFgp7%FapF[o7%FgnFinFgn7%FapF[oF>7%F[oF`qFbo7%F`qFapFdp7%Fbp7 %FKFMF4FP7%FbpFeqFgp7%FeqFPFY7%FPFbpF>7%7%F+F-F(7%F2F4F07%F9F;F77%FjqF [r7%FAFAF?7%F[rF\\rFdp7%F\\rFjq7%F2FMFK7%Fjq7%FTFTFQ7%F4FMFK7%FjqFcrF^ 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***********\n#********************* Construction par translations de l a cellule \351l\351mentaire **********************\ncoucouchestype1:=( p,q,r)-> map(op,[seq(seq(seq(Ltrans([-2*i,-2*j,2*k],cell),i=0..p),j=0. .q),k=0..r)]):\ndisplay([#axes,\n polygonplot3d(coucouchestype 1(1,2,1))]\n ,scaling=constrained ,orientation=[20,65],lightmode l=light2);#color=COLOR(RGB,1,1,0.8)," }}{PARA 13 "" 1 "" {GLPLOT3D 744 589 589 {PLOTDATA 3 "6&-%)POLYGONSG6\\[]l7%7%$\"+66666!#5$\"+6666h F*$\"+6666')F*7%$\"+++++DF*$\"+++++]F*$\"+++++vF*7%$\"+*))))))Q\"F*$\" +*)))))))QF*$\"+*)))))))))F*7%F'F/7%$\"+_=&=&=F*$\"+_=&=&oF*FA7%F/F67% $\"+[\"[\"[JF*FE$\"+[\"[\"[\")F*7%F6F'7%$\"\"!FLF2$\"\"\"FL7%F'7%$\"+c bbbb!#6$\"+cbbb!)F*FT7%FKF4FM7%F'FPF>7%FPFV7%FKFMFM7%FVF'FJ7%F/7%$\"+n mmmTF*Fgn$\"+nmmmmF*7%$\"+LLLLLF*$\"+LLLLeF*F^o7%F/FfnFD7%FfnF[o7%F2F2 F27%F[oF/F>7%F67%FKF0FM7%$\"+WWWW>F*Fgo$\"+WWWW%*F*7%F6FeoFJ7%FeoFfo7% FKFKFM7%FfoF6FD7%7%F7F;F97%F0F4F27%F(F-F+7%F`pFap7%FEFGFE7%FapFbpF>7%F 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F^^uF^d[l7%Fe]hlFf]hlFffgl7%Ff]hlFg]hlF`\\hl7%Fg]hlFe]hl7%F\\jnF[^uFcb z7%Fe]hlFeggl7%F\\jnF__uFcbz7%Fe]hlFegglFffgl7%FegglF]^hlFc_bl7%F]^hlF e]hlF[^hl7%Ff]hlF[]hlF^ggl7%Ff]hlF[]hlF`\\hl7%F[]hlF^gglFbggl7%F^gglFf ]hlFffgl7%Fg]hl7%F\\jnFa`uFcbzFe\\hl7%Fg]hlFf^hlF[^hl7%Ff^hlFe\\hlFhif l7%Fe\\hlFg]hlF`\\hl-%(SCALINGG6#%,CONSTRAINEDG-%+LIGHTMODELG6#%(LIGHT _2G-%+PROJECTIONG6%$\"#?FL$\"#lFLFN" 1 2 0 1 10 0 2 1 4 1 1 1.000000 62.000000 17.000000 1 0 "Curve 1" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Avec base1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 998 "base1:=[[[1/ 2, 1/2, 1/2], [-1/2, 1/2, -1/2], [-1/2, 1/2, 1/2], [1/2, -1/2, -1/2], \+ [1/2, -1/2, 1/2], [1/2, 1/2, -1/2], [1/6, 1/6, 0]], [[1, 3, 7], [3, 2, 7], [2, 6, 7], [6, 4, 7], [4, 5, 7], [5, 1, 7]]]:\n#polygonplot3d(fac esC(base1));\npolygonplot3d(facesC(base1),orientation=[10,70]);\n\ng:= facesC(itereN(3,base1)):\ncell:=map(op,[g,Ltrans([0,-1,0],Lrot([0,0,1] ,-Pi/2,g)),Ltrans([-1,0,0],Lrot([0,0,1],+Pi/2,g)),Ltrans([-1,-1,0],Lro t([0,0,1],+Pi,g))]):\ncouchepaire:= (n,h) -> map(op,[ seq(seq(op([Ltra ns([4*i,4*j-1,h],cell),Ltrans([4*i+2,4*j+1,h],cell)]),i=0..n),j=0..n)] ):\ncoucheimpaire:= (n,h) -> map(op,[ seq(seq(op([Ltrans([4*i+2,4*j-1, h+1],cell),Ltrans([4*i,4*j+1,h+1],cell)]),i=0..n),j=0..n)]):\ngr:=poly gonplot3d([\ncouchepaire(1,0),couchepaire(1,0)\n,coucheimpaire(1,0)\n] ,scaling=constrained,style=patch,orientation=[60,40],color=COLOR(RGB,1 ,1,0.8),lightmodel=light2):\ngr;\n#plotsetup(bmp,plotoutput=\"D:/Mes d ocuments/surf-base1_2.bmp\",plotoptions=\"width=1400,height=1000\");\n #gr; plotsetup(inline);\n" }}{PARA 13 "" 1 "" {GLPLOT3D 614 614 614 {PLOTDATA 3 "6$-%)POLYGONSG6(7%7%$\"+++++]!#5F(F(7%$!+++++]F*F(F(7%$\" +nmmm;F*F/$\"\"!F27%F+7%F,F(F,F.7%F47%F(F(F,F.7%F67%F(F,F,F.7%F87%F(F, F(F.7%F:F'F.-%+PROJECTIONG6%$\"#5F2$\"#qF2\"\"\"" 1 2 0 1 10 0 2 1 1 1 2 1.000000 55.000000 6.000000 1 0 "Curve 1" }}}{PARA 8 "" 1 "" {TEXT -1 72 "Error, (in plots:-polygonplot3d) incorrect specification \+ of points data\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#grG" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 " Comparaison avec r\351sultats Mathematica" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1834 "#=== donn\351es math\351matica 2 et 3 it \351rations====\nS1_mathematica:=[[-1/2,-1/2,1/2],[-1/2,1/2,-1/2],[-1/ 2,1/2,1/2],[1/2,-1/2,-1/2],[1/2,-1/2,1/2],[1/2,1/2,-1/2],[0,0,0],[-1/2 ,0,1/2],[0,-1/2,1/2],[-1/6,-1/6,1/3],[-1/2,1/2,0],[0,1/2,-1/2],[-1/6,1 /3,-1/6],[-1/3,1/6,1/6],[1/2,-1/2,0],[1/2,0,-1/2],[1/3,-1/6,-1/6],[1/6 ,-1/3,1/6],[1/6,1/6,-1/3]]:\nS1_Esculier:=itereN(2,base)[1]:\nprintf( \" \351galit\351 \340 la premi\350re it\351ration = %a\\n\",evalb(conv ert(S1_mathematica,set)=convert(S1_Esculier,set)));\nS2_mathematica:=[ [-1/2,-1/2,1/2],[-1/2,1/2,-1/2],[-1/2,1/2,1/2],[1/2,-1/2,-1/2],[1/2,-1 /2,1/2],[1/2,1/2,-1/2],[0,0,0],[-1/2,0,1/2],[0,-1/2,1/2],[-13/72,-13/7 2,23/72],[-1/2,1/2,0],[0,1/2,-1/2],[-13/72,23/72,-13/72],[-23/72,13/72 ,13/72],[1/2,-1/2,0],[1/2,0,-1/2],[23/72,-13/72,-13/72],[13/72,-23/72, 13/72],[13/72,13/72,-23/72],[-1/2,-1/4,1/2],[-1/4,-1/2,1/2],[-11/36,-1 1/36,4/9],[-1/2,1/2,-1/4],[-1/4,1/2,-1/2],[-11/36,4/9,-11/36],[-1/2,1/ 4,1/2],[-1/2,1/2,1/4],[-4/9,11/36,11/36],[1/2,-1/2,-1/4],[1/2,-1/4,-1/ 2],[4/9,-11/36,-11/36],[1/4,-1/2,1/2],[1/2,-1/2,1/4],[11/36,-4/9,11/36 ],[1/4,1/2,-1/2],[1/2,1/4,-1/2],[11/36,11/36,-4/9],[-1/12,-1/12,1/6],[ -1/12,1/6,-1/12],[-1/6,1/12,1/12],[1/6,-1/12,-1/12],[1/12,-1/6,1/12],[ 1/12,1/12,-1/6],[-13/36,-1/9,7/18],[-7/18,1/9,13/36],[-1/9,-13/36,7/18 ],[1/9,-7/18,13/36],[-1/4,0,1/4],[0,-1/4,1/4],[-13/36,7/18,-1/9],[-7/1 8,13/36,1/9],[-1/9,7/18,-13/36],[1/9,13/36,-7/18],[-1/4,1/4,0],[0,1/4, -1/4],[7/18,-13/36,-1/9],[13/36,-7/18,1/9],[7/18,-1/9,-13/36],[13/36,1 /9,-7/18],[1/4,-1/4,0],[1/4,0,-1/4]]:\nS2_Esculier:=itereN(3,base)[1]: \ndelta:=convert(S2_mathematica,set) intersect convert(S2_Esculier,set ); \nprintf( \"A COMPARER LES %a DIFFERENCES SUIVANTES :\",nops(S2_Esc ulier)-nops(delta));\ndiff_mathematica:=evalf(convert(S2_mathematica,s et) minus delta,4);\ndiff_Esculier:=evalf(convert(S2_Esculier,set) min us delta,4);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 211 " #r\351ordonn \351 \340 la main ! ... diff\351rences de l'ordre de 5.10e-3\ndiff_mat hematica:=\{[.3194,-.1806,-.1806],[.1806,.1806,-.3194],[.1806,-.3194,. 1806],[-.1806,.3194,-.1806],[-.1806,-.1806,.3194],[-.3194,.1806,.1806] \};" }}{PARA 0 "" 0 "" {TEXT -1 148 "diff_Esculier:=\{[.3148,-.1852,-. 1852],[.1852,.1852,-.3148],[.1852,-.3148,.1852],[-.1852,.3148,-.1852], [-.1852,-.1852,.3148],[-.3148,.1852,.1852]\}; " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 " res tes inutilis\351s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 408 "cotesC := proc(listeplex) # sort les coordonn\351es des cot\351s des faces\n \+ local i,som,F,tp; som:=listeplex[1]: F:=listeplex[2]:\n \+ tp:=map(u ->[seq(som[u[i]],i=1..3)],F):\n map( u ->[seq(\{u[i],u[(i mod 3) +1]\},i=1..3)],tp)\nend:\ncotesI:= proc(lis teplex) # sort les indices dans LS des cot\351s des faces\n \+ map( u ->[seq(\{u[i],u[(i mod 3) +1]\},i=1..3)],listeplex[2])\nend: \n\n" }}}}}{MARK "1 2 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }