{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 Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 2 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 "Hea ding 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 "Heading 2" -1 4 1 {CSTYLE " " -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 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 "E rror" -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 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Time s" 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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 27 " Mail Ferr\351ol du28/12/2010 " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1716 "with(plots):\nmontubeplot := 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(liste[i]+t*(list e[`mod`(i, n)+1]-liste[i])), i = 1 .. nops(liste))\}, t = 0 .. 1, radi us = rc, grid = [2, 15])], style = patchnogrid, lightmodel = light2) e lse op(map(proc (u) options operator, arrow; montubeplot(u, rc, rs,cou leursommets) end proc, liste)) end if end proc:\nliste1:=[[[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:=[[[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]]]:\nA:=display(montubeplot(liste1,.02,.02,yellow),montubeplot(list e2,.02,.02,red)):\ndisplay(A,axes=boxed,tickmarks=[0,0,0],scaling=cons trained,orientation=[40,72]);\nliste1:=[[[1,0,0],[0,0,-1],[0,1,0],[-1, 0,0],[0,0,1],[0,-1,0]]]:\nliste2:=[[[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]]]:\nA2:=display(montubeplot(liste1,.02,.02,blue),montube plot(liste2,.02,.02,red)):\ndisplay(A2,axes=boxed,tickmarks=[2,2,2],sc aling=constrained,orientation=[40,72]);\n#========== modification pour SchwarzP =============\nliste11:=[[[1,0,0],[0,0,-1],[0,1,0],[-1,0,0], [0,0,1],[0,-1,0]],[[-1,0,0],[0,0,-1],[0,-1,0]],[[1,0,0],[0,0,1],[0,1,0 ]]]:\nliste22:=[[[0,0,1],[1,0,0],[0,1,0],[-1,0,0]]]:\nA1:=display(mont ubeplot(liste11,.02,.02,blue),montubeplot(liste22,.025,.025,red)):\ndi splay(A1,axes=boxed,tickmarks=[2,2,2],scaling=constrained,orientation= [40,72]);" }}{PARA 8 "" 1 "" {TEXT -1 363 "Error, (in plots:-display) \+ unexpected option: PLOT3D(MESH([[[.03, 0., 0.], [1.83697019872103e-018 , .03, 0.], [-.03, 3.67394039744206e-018, 0.], [-5.51091059616309e-018 , -.03, 0.], [.03, -7.34788079488412e-018, 0.]], [[.03, 0., 3.], [1.83 697019872103e-018, .03, 3.], [-.03, 3.67394039744206e-018, 3.], [-5.51 091059616309e-018, -.03, 3.], [.03, -7.3478807948841...\n" }}{PARA 8 " " 1 "" {TEXT -1 363 "Error, (in plots:-display) unexpected option: PLO T3D(MESH([[[.03, 0., 0.], [1.83697019872103e-018, .03, 0.], [-.03, 3.6 7394039744206e-018, 0.], [-5.51091059616309e-018, -.03, 0.], [.03, -7. 34788079488412e-018, 0.]], [[.03, 0., 3.], [1.83697019872103e-018, .03 , 3.], [-.03, 3.67394039744206e-018, 3.], [-5.51091059616309e-018, -.0 3, 3.], [.03, -7.3478807948841...\n" }}{PARA 8 "" 1 "" {TEXT -1 363 "E rror, (in plots:-display) unexpected option: PLOT3D(MESH([[[.03, 0., 0 .], [1.83697019872103e-018, .03, 0.], [-.03, 3.67394039744206e-018, 0. ], [-5.51091059616309e-018, -.03, 0.], [.03, -7.34788079488412e-018, 0 .]], [[.03, 0., 3.], [1.83697019872103e-018, .03, 3.], [-.03, 3.673940 39744206e-018, 3.], [-5.51091059616309e-018, -.03, 3.], [.03, -7.34788 07948841...\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 71 " Les transformations \351l\351men taires pour des listes de lignes polygonales" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1964 "#********* \n#restart:\nwith(plots):\nps:=proc(U ,V) #**** produit scalaire\n local u,v; u:=expand(U): v:=expand( V): add(u[i]*v[i],i=1..nops(u)):\nend:pv:=proc(u,v) #*** produit ve ctoriel\n local 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 -> e xpand(U/sqrt(ps(U,U))): #*** norm2\nrot:=proc(axe,t,point) # rotatio n\n local axe1: axe1:=norm2(axe):\n expand(expand(cos(t)*point) +exp and(sin(t)*pv(axe1,point)) +expand((1-cos(t))*ps(axe1,point)*axe1))\ne nd:\n#**************transformations de base appliqu\351es \340 une lis te******************************\nLsymXY:= Liste -> if type(evalf(Lis te[1,1]),numeric) then map( u ->[u[1],u[2],-u[3]],Liste): else map( u- >LsymXY(u),Liste): fi:\nLsymYZ:= Liste -> if type(evalf(Liste[1,1]),nu meric) then map( u ->[-u[1],u[2],u[3]],Liste): else map( u->LsymYZ(u), Liste): fi:\nLsymZX:= 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:\nLtra ns:=(V,Liste) -> if type(evalf(Liste[1,1]),numeric) then map( u ->expa nd(u+V),Liste): else map( u->Ltrans(V,u),Liste) fi:\n#*************** \+ axes(d) d=longueur *******************\naxes:=d -> display([tubeplot([ 0, 0, d*t], t = 0 .. 1, radius = 0.3e-1, color = cyan, grid = [2, 5]), tubeplot([d*t, 0, 0], t = 0 .. 1, radius = 0.3e-1, color = red, grid \+ = [2, 5]), tubeplot([0, d*t, 0], t = 0 .. 1, radius = 0.3e-1, color = \+ COLOR(RGB,0,0.6,0), grid = [2, 5])],scaling=constrained):\n#******* tu beplot 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(expand(L[i]+t*( L[ (i mod p) +1 ]-L[i])),i=1..nops(L))\},t=0..1,radius=0.04,grid=[2,10],style=patchnog rid,color=COLOR(RGB,0,0.6,0)):\n else op(map(tracelist,L)): fi;\nen d:" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 23 " Proc\351dures d'it\351ration" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 17 " initialisations " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1245 "#================================================== ===============================================\n#******* nom_i d\351s igne nom par indices et nom_c d\351signe nom par coordonn\351es ****** *\n#******* IMPERATIF DE METTRE LES POINTS DU CONTOUR DANS L'ORDRE *** ****************\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] ]:\n#[[-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:=[[1,2,7],[2,3,7],[3, 4,7],[4,5,7],[5,6,7],[6,1,7]]:#--- indices dans pts0_c\n#[[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=l isteTriangles_par_indices_dans_LS] **********\n#********************** ****************************************************\nfacesC:= proc(li steplex) # sort les coordonn\351es des faces\n local i,som ,F; som:=listeplex[1]: F:=listeplex[2]:\n map(u ->[seq(som [u[i]],i=1..3)],F):\nend:\ngraphplex:=proc(listeplex) display(polygonp lot3d(facesC(listeplex))): end:\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 22 " it\351ratio n \351l\351mentaire" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2002 "#** ********************************************************************** ***\n# methode d'it\351ration de la listeplex: \n#*** 1. faire la list e des cotes_i : L\n#*** 2. pour chaque cote_i, trouver les faces_i adj acentes\n#*** 3. trouver le \"milieu\" et l'associer au cot\351 \n#*** ( vrai milieu si sur contour, barycentre des sommets compt\351s av ec multiplicit\351 des 2 faces adjacentes sinon )\n#*** 4. ajouter ces milieux \340 l'ancienne liste des sommets\n#*** 4. pour chaque triang le, faire les 4 nouveaux triangles_i\n#******************************* ******************************\nitere:=proc(listeplex) # donne la list eplex 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:=listeplex[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): # liste des aretes par f aces\n A_i:=convert(convert(map(u ->op(u),AF_i),set),list): # liste des aretes\n # calcul des milieux et liste des nouveaux sommets\n \+ for j to nops(A_i) do\n arete:=A_i[j]: adj:=NULL:\n f or k to nops(AF_i) do #--dans adj, indices des faces ayant cette are te ------\n if member(arete,AF_i[k]) then adj:=adj,k fi:\n \+ od:\n adj:=[adj]:\n if nops(adj)=1 then M_c:=expan d((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([N S_c])]:\n od:\n AetM_i:=[AetM_i]:NS_c:=[NS_c]:\n # nouvell es faces_i\n for j to nops(AF_i) do #--- ancienne face --> 3 nouve lles ---\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] intersect 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" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 43 " it\351ratio ns r\351cursives avec ou sans lissage" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2357 "#================= iteration d'ordre n =====\n#**** *********** it\351ration simple ( il reste des d\351fauts en certains \+ points )***********************\nitereSimple:= (n,base) -> if n=1 then base else itere(itereSimple(n-1,base)) fi:\n#*************** it\351ra tion avec lissage des points introduits \340 l'it\351ration pr\351c \351dente ************\nitereN:= proc(n,base)\n local tp,soms,face s_i,diff,places,i,j,k,facesadj,NS,diff1,grafplex,somsN,ct,p,cond,v0 : \+ #ct contour initial\n if n=0 then print(\"n doit \352tre un entie r 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]: faces_i:=tp[2];\n grafplex:=itere(tp): somsN:=gr afplex[1]:\n diff1:= convert(soms,set) minus convert(itereN(n -2,base)[1],set):\n diff1:= convert(diff1,list): \n \+ diff:=NULL;\n # \351limination des \"milieux\" des bords( p lus g\351n\351ral au-dessous )\n # for i to nops(diff1) do i f not(has(diff1[i],\{1/2,-1/2\})) then diff:=diff,diff1[i]: fi: od: \n p:=nops(base[1])-1: ct:=base[1,1..p]: v0:=[0,0,0]:\n \+ for i from 1 to nops(diff1) do ## \351limination des \"milieux\" \+ sur les bords\n cond:=pv(ct[1]-ct[2],ct[1]-diff1[i])<>v0: \n for j from 2 to p do cond:=cond and pv(ct[j]-ct[(j mod p)+1],ct[j]-diff1[i])<>v0: od:\n if cond then diff:=dif f,diff1[i]: fi:\n od: diff:=[diff]:#,[0,0,0]\n \+ places:=NULL;\n for i to nops(diff) do ##--- on trouve l es indices des sommets nouveaux ----\n if member(diff[i],som s,'p') then places:=places,p: fi:\n od:\n places:=[ places]:\n for i to nops(places) do\n tp:=place s[i]: facesadj:=NULL;\n for j to nops(faces_i) do\n \+ if member(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/n ops(facesadj):\n somsN:=subsop(tp= NS,somsN):\n od : \n [somsN,grafplex[2]]:\n fi;\nend:\n#******** les bri ques \351l\351mentaires ***************************\n#display([graphpl ex(itereSimple(4,base))],title=\"avec des d\351fauts\",orientation=[-1 5,80]);\n#display([graphplex(itereN(4,base))],title=\"lissage des d \351fauts\",orientation=[-15,80]);" }{TEXT -1 0 "" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 71 " Une premi\350re construction de SchwarzD avec une cellule de base con nexe" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1047 " g4:=facesC(itereN (1,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],bo rdbase),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)),Ltrans([-1/2,1/2,3/2],Lrot([0, 0,1],-Pi/2,bordbase)) ]:\n#polygonplot3d([cell,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(seq(Ltrans([2*i,2*j,0],bordc ell),i=0..n-1),j=0..n-1)]):\n#bordcouche(3);\n#******************** la cellule de base de la constuction ***************\n#********* la surf ace s'en d\351duit par des translations successives ******\npolygonplo t3d(cell,orientation=[20,65],style=patch,scaling=constrained,color=COL OR(RGB,1,1,0.8),lightmodel=light2,title=\"La cellule de base\");" } {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT3D 745 745 745 {PLOTDATA 3 "6( -%)POLYGONSG6;7%7%$\"\"!F)F($\"\"\"F)7%F(F*F*7%$\"+++++]!#5F.F.7%F,7%F (F*F(F-7%F27%F*F*F(F-7%F47%F*F(F(F-7%F67%F*F(F*F-7%F8F'F-7%F'7%F($!\" \"F)F*7%$!+++++]F0F?F.7%F;7%F(F7%FB7%F7%FD7%F7%FF7% F7%FHF'F>7%7%F*F<$\"\"#F)7%F(F " 0 "" {MPLTEXT 1 0 402 "#******** une portion de la surface ***************************************\nn:=3;# nombre d' \351tages\ngr:=display(polygonplot3d(Ltrans([0,0,2],couche(n))),polygo nplot3d(couche(n))\n ,tracelist(bordcouche(n)),tracelist(Lt rans([0,0,2],bordcouche(n)))\n ,orientation=[20,65],style=pa tch,scaling=constrained,lightmodel=light2):#,color=COLOR(RGB,0.8,0.8,0 .6)\ngr; " }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"$" }}{PARA 13 "" 1 "" {GLPLOT3D 745 745 745 {PLOTDATA 3 "6bfl-%)POLYGONSG6dx7%7%$\"\"!F)F($\"\"$F)7%F($\"\"\"F )F*7%$\"+++++]!#5F0$\"+++++D!\"*7%F,7%F(F-$\"\"#F)F/7%F77%F-F-F8F/7%F; 7%F-F(F8F/7%F=7%F-F(F*F/7%F?F'F/7%F'7%F($!\"\"F)F*7%$!+++++]F2FFF37%FB 7%F(FCF8FE7%FI7%FCFCF8FE7%FK7%FCF(F8FE7%FM7%FCF(F*FE7%FOF'FE7%7%F-FC$ \"\"%F)7%F(FCFS7%F0FF$\"+++++NF57%FUFBFV7%FBF'FV7%F'F?FV7%F?7%F-F(FSFV 7%FgnFRFV7%7%FCF-FS7%F(F-FS7%FFF0FW7%F[oF,F\\o7%F,F'F\\o7%F'FOF\\o7%FO 7%FCF(FSF\\o7%FaoFjnF\\o7%7%F8F(F*7%F8F-F*7%F3F0F37%Feo7%F8F-F8Ffo7%Fh o7%F*F-F8Ffo7%Fjo7%F*F(F8Ffo7%F\\p7%F*F(F*Ffo7%F^pFdoFfo7%Fdo7%F8FCF*7 %$\"+++++:F5FFF37%Fap7%F8FCF8Fbp7%Ffp7%F-FCF8Fbp7%FhpF=Fbp7%F=F?Fbp7%F ?FdoFbp7%7%F*FCFS7%F8FCFS7%F3FFFW7%F^qFapF_q7%FapFdoF_q7%FdoF^pF_q7%F^ p7%F*F(FSF_q7%FdqF]qF_q7%7%F-F-FS7%F8F-FS7%FcpF0FW7%FhqFeoFiq7%FeoFdoF 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\"#lF)F." 1 2 0 1 10 0 2 1 4 1 1 1.000000 54.000000 71.000000 1 0 "Cur ve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Cur ve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14 " "Curve 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "C urve 21" "Curve 22" "Curve 23" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33 " "Curve 34" "Curve 35" "Curve 36" "Curve 37" "Curve 38" "Curve 39" "C urve 40" "Curve 41" "Curve 42" "Curve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52 " "Curve 53" "Curve 54" "Curve 55" "Curve 56" "Curve 57" "Curve 58" "C urve 59" "Curve 60" "Curve 61" "Curve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71 " "Curve 72" "Curve 73" "Curve 74" "Curve 75" "Curve 76" "Curve 77" "C urve 78" "Curve 79" "Curve 80" "Curve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90 " "Curve 91" "Curve 92" "Curve 93" "Curve 94" "Curve 95" "Curve 96" "C urve 97" "Curve 98" "Curve 99" "Curve 100" "Curve 101" "Curve 102" "Cu rve 103" "Curve 104" "Curve 105" "Curve 106" "Curve 107" "Curve 108" " Curve 109" "Curve 110" "Curve 111" "Curve 112" "Curve 113" "Curve 114 " "Curve 115" "Curve 116" "Curve 117" "Curve 118" "Curve 119" "Curve 1 20" "Curve 121" "Curve 122" "Curve 123" "Curve 124" "Curve 125" "Curve 126" "Curve 127" "Curve 128" "Curve 129" "Curve 130" "Curve 131" "Cur ve 132" "Curve 133" "Curve 134" "Curve 135" "Curve 136" "Curve 137" "C urve 138" "Curve 139" "Curve 140" "Curve 141" "Curve 142" "Curve 143" "Curve 144" "Curve 145" "Curve 146" "Curve 147" "Curve 148" "Curve 149 " "Curve 150" "Curve 151" "Curve 152" "Curve 153" "Curve 154" "Curve 1 55" "Curve 156" "Curve 157" "Curve 158" "Curve 159" "Curve 160" "Curve 161" "Curve 162" "Curve 163" "Curve 164" "Curve 165" "Curve 166" "Cur ve 167" "Curve 168" "Curve 169" "Curve 170" "Curve 171" "Curve 172" "C urve 173" "Curve 174" "Curve 175" "Curve 176" "Curve 177" "Curve 178" "Curve 179" "Curve 180" "Curve 181" "Curve 182" "Curve 183" "Curve 184 " "Curve 185" "Curve 186" "Curve 187" "Curve 188" "Curve 189" "Curve 1 90" "Curve 191" "Curve 192" "Curve 193" "Curve 194" "Curve 195" "Curve 196" "Curve 197" "Curve 198" "Curve 199" "Curve 200" "Curve 201" "Cur ve 202" "Curve 203" "Curve 204" "Curve 205" "Curve 206" "Curve 207" "C urve 208" "Curve 209" "Curve 210" "Curve 211" "Curve 212" "Curve 213" "Curve 214" "Curve 215" "Curve 216" "Curve 217" "Curve 218" "Curve 219 " "Curve 220" "Curve 221" "Curve 222" "Curve 223" "Curve 224" "Curve 2 25" "Curve 226" "Curve 227" "Curve 228" "Curve 229" "Curve 230" "Curve 231" "Curve 232" "Curve 233" "Curve 234" "Curve 235" "Curve 236" "Cur ve 237" "Curve 238" "Curve 239" "Curve 240" "Curve 241" "Curve 242" "C urve 243" "Curve 244" "Curve 245" "Curve 246" "Curve 247" "Curve 248" "Curve 249" "Curve 250" "Curve 251" "Curve 252" "Curve 253" "Curve 254 " "Curve 255" "Curve 256" "Curve 257" "Curve 258" "Curve 259" "Curve 2 60" "Curve 261" "Curve 262" "Curve 263" "Curve 264" "Curve 265" "Curve 266" "Curve 267" "Curve 268" "Curve 269" "Curve 270" "Curve 271" "Cur ve 272" "Curve 273" "Curve 274" "Curve 275" "Curve 276" "Curve 277" "C urve 278" "Curve 279" "Curve 280" "Curve 281" "Curve 282" "Curve 283" "Curve 284" "Curve 285" "Curve 286" "Curve 287" "Curve 288" "Curve 289 " "Curve 290" "Curve 291" "Curve 292" "Curve 293" "Curve 294" "Curve 2 95" "Curve 296" "Curve 297" "Curve 298" "Curve 299" "Curve 300" "Curve 301" "Curve 302" "Curve 303" "Curve 304" "Curve 305" "Curve 306" "Cur ve 307" "Curve 308" "Curve 309" "Curve 310" "Curve 311" "Curve 312" "C urve 313" "Curve 314" "Curve 315" "Curve 316" "Curve 317" "Curve 318" "Curve 319" "Curve 320" "Curve 321" "Curve 322" "Curve 323" "Curve 324 " "Curve 325" "Curve 326" "Curve 327" "Curve 328" "Curve 329" "Curve 3 30" "Curve 331" "Curve 332" "Curve 333" "Curve 334" "Curve 335" "Curve 336" "Curve 337" "Curve 338" "Curve 339" "Curve 340" "Curve 341" "Cur ve 342" "Curve 343" "Curve 344" "Curve 345" "Curve 346" "Curve 347" "C urve 348" "Curve 349" "Curve 350" "Curve 351" "Curve 352" "Curve 353" "Curve 354" "Curve 355" "Curve 356" "Curve 357" "Curve 358" "Curve 359 " "Curve 360" "Curve 361" "Curve 362" "Curve 363" "Curve 364" "Curve 3 65" "Curve 366" "Curve 367" "Curve 368" "Curve 369" "Curve 370" "Curve 371" "Curve 372" "Curve 373" "Curve 374" "Curve 375" "Curve 376" "Cur ve 377" "Curve 378" "Curve 379" "Curve 380" "Curve 381" "Curve 382" "C urve 383" "Curve 384" "Curve 385" "Curve 386" "Curve 387" "Curve 388" "Curve 389" "Curve 390" "Curve 391" "Curve 392" "Curve 393" "Curve 394 " "Curve 395" "Curve 396" "Curve 397" "Curve 398" "Curve 399" "Curve 4 00" "Curve 401" "Curve 402" "Curve 403" "Curve 404" "Curve 405" "Curve 406" "Curve 407" "Curve 408" "Curve 409" "Curve 410" "Curve 411" "Cur ve 412" "Curve 413" "Curve 414" "Curve 415" "Curve 416" "Curve 417" "C urve 418" "Curve 419" "Curve 420" "Curve 421" "Curve 422" "Curve 423" "Curve 424" "Curve 425" "Curve 426" "Curve 427" "Curve 428" "Curve 429 " "Curve 430" "Curve 431" "Curve 432" "Curve 433" "Curve 434" }}}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 77 " SchwarzD avec une cellule de bas e non connexe combin\351e selon deux m\351thodes" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 445 "g4:=facesC(itereN(1,base)):\n#************* ******* la cellule de base des constructions ***************\ncell:=Lt rans([0,0,-2],map(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(cel l,orientation=[80,65],style=patch,scaling=constrained,color=COLOR(RGB, 1,1,0.8),lightmodel=light2,title=\"La cellule de base\");" }}{PARA 13 "" 1 "" {GLPLOT3D 745 745 745 {PLOTDATA 3 "6(-%)POLYGONSG6;7%7%$\"\"!F )F($\"\"\"F)7%F(F*F*7%$\"+++++]!#5F.F.7%F,7%F(F*F(F-7%F27%F*F*F(F-7%F4 7%F*F(F(F-7%F67%F*F(F*F-7%F8F'F-7%F'7%F($!\"\"F)F*7%$!+++++]F0F?F.7%F; 7%F(F7%FB7%F7%FD7%F7%FF7%F7%FHF'F>7%7%F*F " 0 "" {MPLTEXT 1 0 563 "#*************************************************** ************************************************\n#******************* une m\351thode de construction o\371 l'on voit bien les sym\351tries \+ ******************\nnoeud:=map(op,[cell,Ltrans([1,1,-1],Lrot([0,0,1], Pi/2,cell)),Ltrans([-1,-1,-1],Lrot([0,0,1],Pi/2,cell))\n \+ ,Ltrans([+1,-1,1],Lrot([0,0,1],Pi/2,cell)),Ltrans([-1,1,1],Lrot([ 0,0,1],Pi/2,cell)) ]):\nnoeudSym:=LsymXY(noeud):\ndisplay([axes(2),pol ygonplot3d(noeud)],scaling=constrained ,orientation=[20,70],color=COLO R(RGB,1,1,0.8),lightmodel=light2);\n" }}{PARA 13 "" 1 "" {GLPLOT3D 745 745 745 {PLOTDATA 3 "6*-%%MESHG6$7$7'7%$\"0+++++++$!#;$\"\"!F-F,7% $\"0.@()>qp$=!#KF)F,7%$!0+++++++$F+$\"01UuRSRn$F1F,7%$!04jhf54^&F1F3F, 7%F)$!07%)[z!)yM(F1F,7'7%F)F,$\"\"#F-7%F/F)F?7%F3F5F?7%F8F3F?7%F)F;F?- %&COLORG6&%$RGBGF,$\"*++++\"!\")FI-F$6$7$7'7%F,F)F,7%F,F/F)7%F,F3F57%F ,F8F37%F,F)F;7'7%F?F)F,7%F?F/F)7%F?F3F57%F?F8F37%F?F)F;-FF6&FHFIF,F,-F $6$7$7'F(7%F/F,F37%F3F,$!01UuRSRn$F17%F8F,F)7%F)F,$\"07%)[z!)yM(F17'7% F)F?F,7%F/F?F37%F3F?F]o7%F8F?F)7%F)F?Fao-FF6&FHF,$\"\"'!\"\"F,-%)POLYG ONSG6dr7%7%F,F,$\"\"\"F-7%F,FcpFcp7%$\"+++++]!#5FgpFgp7%Fep7%F,FcpF,Ff p7%F[q7%FcpFcpF,Ffp7%F]q7%FcpF,F,Ffp7%F_q7%FcpF,FcpFfp7%FaqFbpFfp7%Fbp 7%F,$F]pF-Fcp7%$!+++++]FipFgqFgp7%Fdq7%F,FeqF,Ffq7%Fjq7%FeqFeqF,Ffq7%F \\r7%FeqF,F,Ffq7%F^r7%FeqF,FcpFfq7%F`rFbpFfq7%7%FcpFeqF,Fjq7%FgpFgqFgq 7%Fjq7%F,FeqFeqFdr7%Ffr7%F,F,FeqFdr7%Fhr7%FcpF,FeqFdr7%FjrF_qFdr7%F_qF crFdr7%7%FeqFcpF,F[q7%FgqFgpFgq7%F[q7%F,FcpFeqF_s7%FasFhrF_s7%Fhr7%Feq F,FeqF_s7%FdsF^rF_s7%F^rF^sF_s7%F]qF[q7%Fgp$\"+++++:!\"*Fgq7%F[qFasFhs 7%Fas7%F,F?FeqFhs7%F^t7%FcpF?FeqFhs7%F`t7%FcpF?F,Fhs7%FbtF]qFhs7%F]q7% F?FcpF,7%FisFgpFgq7%Fet7%F?FcpFeqFft7%Fht7%F?F,FeqFft7%FjtFjrFft7%FjrF _qFft7%F_qF]qFft7%7%F?F?FeqFht7%FisFis$!+++++:F[t7%Fht7%F?Fcp$!\"#F-F` u7%Fdu7%FcpFcpFeuF`u7%Fhu7%FcpF?FeuF`u7%FjuF`tF`u7%F`tF_uF`u7%FhrFas7% FgpFgpFau7%Fas7%F,FcpFeuF^v7%F`vFhuF^v7%Fhu7%FcpF,FeuF^v7%FcvFjrF^v7%F jrFhrF^v7%F\\r7%FeuFeqF,7%FauFgqFgq7%Fgv7%FeuFeqFeqFhv7%Fjv7%FeuF,FeqF hv7%F\\wFdsFhv7%FdsF^rFhv7%F^rF\\rFhv7%F\\rFjq7%FgqFauFgq7%FjqFfrFaw7% Ffr7%F,FeuFeqFaw7%Fdw7%FeqFeuFeqFaw7%Ffw7%FeqFeuF,Faw7%FhwF\\rFaw7%Fhr Ffr7%FgqFgqFau7%Ffr7%F,FeqFeuF[x7%F]x7%FeqFeqFeuF[x7%F_x7%FeqF,FeuF[x7 %FaxFdsF[x7%FdsFhrF[x7%7%FeuFeuFeqFjv7%FauFauFau7%Fjv7%FeuFeqFeuFfx7%F hxF_xFfx7%F_x7%FeqFeuFeuFfx7%F[yFfwFfx7%FfwFexFfx7%7%FcpFeqF?7%F,FeqF? 7%FgpFgqFis7%F`yFdqFay7%FdqFbpFay7%FbpFaqFay7%Faq7%FcpF,F?Fay7%FfyF_yF ay7%F_y7%F?FeqF?7%FisFauFis7%Fiy7%F?FeqFcpFjy7%F\\z7%F?FeuFcpFjy7%F^z7 %FcpFeuFcpFjy7%F`z7%FcpFeuF?Fjy7%FbzF_yFjy7%7%F?F,FcpF\\z7%FisFgqFgp7% F\\z7%F?FeqF,Ffz7%FhzFcrFfz7%FcrF_qFfz7%F_qFaqFfz7%FaqFezFfz7%7%F,FeuF cpFdq7%FgpFauFgp7%FdqFjqF_[l7%FjqFcrF_[l7%Fcr7%FcpFeuF,F_[l7%Fc[lF`zF_ [l7%F`zF^[lF_[l7%7%FeqFcpF?7%FeuFcpF?7%FauFisFis7%Fh[l7%FeuFcpFcpFi[l7 %F[\\l7%FeuF?FcpFi[l7%F]\\l7%FeqF?FcpFi[l7%F_\\l7%FeqF?F?Fi[l7%Fa\\lFg [lFi[l7%Fg[l7%F,FcpF?7%FgqFgpFis7%Fd\\lFepFe\\l7%FepFbpFe\\l7%FbpF`rFe \\l7%F`r7%FeqF,F?Fe\\l7%Fj\\lFg[lFe\\l7%7%F,F?FcpFep7%FgqFisFgp7%FepF[ qF^]l7%F[qF^sF^]l7%F^s7%FeqF?F,F^]l7%Fb]lF_\\lF^]l7%F_\\lF]]lF^]l7%7%F euF,FcpF[\\l7%FauFgpFgp7%F[\\l7%FeuFcpF,Fg]l7%Fi]lF^sFg]l7%F^sF^rFg]l7 %F^rF`rFg]l7%F`rFf]lFg]l-FF6&FHFcpFcp$\"\")F]p-%+LIGHTMODELG6#%(LIGHT_ 2G-%(SCALINGG6#%,CONSTRAINEDG-%+PROJECTIONG6%$\"#?F-$\"#qF-Fdp" 1 2 0 1 10 0 2 6 4 1 1 1.000000 52.000000 99.000000 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 " # pour co mpl\351ter un peu la surface \n#noeud,Ltrans([+1,1,3],noeudSym),Ltrans ([-1,-1,3],noeudSym);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 328 " \ntype2:= (p,r) -> map(op,[seq(seq(op([Ltrans([2*i,2*i,4*k],noeud ),\n Ltrans([2*i+1,2*i+1,4*k+3],n oeudSym )\n ]),i=0..p),k=0..r)\n]):\ndisplay( \{axes(4),polygonplot3d(type2(1,0))\},scaling=constrained ,orientation =[-30,70],lightmodel=light2);#,color=COLOR(RGB,1,1,0.8)" }{TEXT -1 0 " " }}{PARA 13 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 13 "" 1 "" {GLPLOT3D 745 745 745 {PLOTDATA 3 "6)-%)POLYGONSG6\\i l7%7%$\"\"!F)F($\"\"\"F)7%F(F*F*7%$\"+++++]!#5F.F.7%F,7%F(F*F(F-7%F27% F*F*F(F-7%F47%F*F(F(F-7%F67%F*F(F*F-7%F8F'F-7%F'7%F($!\"\"F)F*7%$!++++ +]F0F?F.7%F;7%F(F7%FB7%F7%FD7%F7%FF7%F7%FHF' F>7%7%F*Fqp$=!#KF^imF(7%$!0+++++++$F`im$\"01 UuRSRn$FdimF(7%$!04jhf54^&FdimFfimF(7%F^im$!07%)[z!)yM(FdimF(7'7%F^imF (Fd[l7%FbimF^imFd[l7%FfimFhimFd[l7%F[jmFfimFd[l7%F^imF^jmFd[l-%&COLORG 6&%$RGBGF($\"*++++\"!\")Fjjm-Fihm6$7$7'7%F(F^imF(7%F(FbimF^im7%F(FfimF him7%F(F[jmFfim7%F(F^imF^jm7'7%Fd[lF^imF(7%Fd[lFbimF^im7%Fd[lFfimFhim7 %Fd[lF[jmFfim7%Fd[lF^imF^jm-Fgjm6&FijmFjjmF(F(-Fihm6$7$7'F]im7%FbimF(F fim7%FfimF($!01UuRSRn$Fdim7%F[jmF(F^im7%F^imF($\"07%)[z!)yM(Fdim7'7%F^ imFd[lF(7%FbimFd[lFfim7%FfimFd[lFd\\n7%F[jmFd[lF^im7%F^imFd[lFh\\n-Fgj m6&FijmF($\"\"'F=F(-%+LIGHTMODELG6#%(LIGHT_2G-%(SCALINGG6#%,CONSTRAINE DG-%+PROJECTIONG6%$!#IF)$\"#qF)F+" 1 2 0 1 10 0 2 1 4 1 1 1.000000 61.000000 102.000000 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 467 "#************************** ********************************************************************** ***\n#********************* Construction par translations de la cellul e \351l\351mentaire **********************\ncoucouchestype1:=(p,q,r)-> map(op,[seq(seq(seq(Ltrans([-2*i,-2*j,2*k],cell),i=0..p),j=0..q),k=0. .r)]):\ndisplay([#axes(2),\n polygonplot3d(coucouchestype1(1,1 ,1))]\n ,scaling=constrained ,orientation=[20,65],lightmodel=lig ht2);#color=COLOR(RGB,1,1,0.8)," }}{PARA 13 "" 1 "" {GLPLOT3D 745 745 745 {PLOTDATA 3 "6&-%)POLYGONSG6\\w7%7%$\"\"!F)F($\"\"\"F)7%F(F*F*7%$ \"+++++]!#5F.F.7%F,7%F(F*F(F-7%F27%F*F*F(F-7%F47%F*F(F(F-7%F67%F*F(F*F -7%F8F'F-7%F'7%F($!\"\"F)F*7%$!+++++]F0F?F.7%F;7%F(F7%FB7%F7%FD7%F7%FF7%F7%FHF'F>7%7%F*F " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 54 " Une su rface obtenue avec base1 combin\351e diff\351remment." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 975 "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 ]], [[1,2,7],[2,3,7],[3,4,7],[4,5,7],[5,6,7],[6,1,7]]]:\n#polygonplot3 d(facesC(base1));\n#polygonplot3d(facesC(itereN(4,base1)),orientation= [10,70]);\n\ng:=facesC(itereN(4,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)),Ltra ns([-1,-1,0],Lrot([0,0,1],+Pi,g))]):\ncouchepaire:= (n,h) -> map(op,[ \+ seq(seq(op([Ltrans([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([Ltra ns([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:=polygonplot3d([\ncouchepaire(0,1),coucheimpaire(0,-1)\n,co ucheimpaire(0,1)\n],scaling=constrained,style=patch,orientation=[60,40 ],color=COLOR(RGB,1,1,0.8),lightmodel=light2):\ngr;\n#plotsetup(bmp,pl otoutput=\"D:/Mes documents/surf-base1_2.bmp\",plotoptions=\"width=140 0,height=1000\");\n#gr; plotsetup(inline);\n" }}{PARA 8 "" 1 "" {TEXT -1 72 "Error, (in plots:-polygonplot3d) incorrect specification of poi nts data\n" }}{PARA 13 "" 1 "" {GLPLOT3D 614 614 614 {PLOTDATA 3 "6bfl -%)POLYGONSG6dx7%7%$\"\"!F)F($\"\"$F)7%F($\"\"\"F)F*7%$\"+++++]!#5F0$ \"+++++D!\"*7%F,7%F(F-$\"\"#F)F/7%F77%F-F-F8F/7%F;7%F-F(F8F/7%F=7%F-F( F*F/7%F?F'F/7%F'7%F($!\"\"F)F*7%$!+++++]F2FFF37%FB7%F(FCF8FE7%FI7%FCFC F8FE7%FK7%FCF(F8FE7%FM7%FCF(F*FE7%FOF'FE7%7%F-FC$\"\"%F)7%F(FCFS7%F0FF $\"+++++NF57%FUFBFV7%FBF'FV7%F'F?FV7%F?7%F-F(FSFV7%FgnFRFV7%7%FCF-FS7% F(F-FS7%FFF0FW7%F[oF,F\\o7%F,F'F\\o7%F'FOF\\o7%FO7%FCF(FSF\\o7%FaoFjnF \\o7%7%F8F(F*7%F8F-F*7%F3F0F37%Feo7%F8F-F8Ffo7%Fho7%F*F-F8Ffo7%Fjo7%F* 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"Curve 147" "Curve 148" "Curve 149" "Curve 150" "C urve 151" "Curve 152" "Curve 153" "Curve 154" "Curve 155" "Curve 156" "Curve 157" "Curve 158" "Curve 159" "Curve 160" "Curve 161" "Curve 162 " "Curve 163" "Curve 164" "Curve 165" "Curve 166" "Curve 167" "Curve 1 68" "Curve 169" "Curve 170" "Curve 171" "Curve 172" "Curve 173" "Curve 174" "Curve 175" "Curve 176" "Curve 177" "Curve 178" "Curve 179" "Cur ve 180" "Curve 181" "Curve 182" "Curve 183" "Curve 184" "Curve 185" "C urve 186" "Curve 187" "Curve 188" "Curve 189" "Curve 190" "Curve 191" "Curve 192" "Curve 193" "Curve 194" "Curve 195" "Curve 196" "Curve 197 " "Curve 198" "Curve 199" "Curve 200" "Curve 201" "Curve 202" "Curve 2 03" "Curve 204" "Curve 205" "Curve 206" "Curve 207" "Curve 208" "Curve 209" "Curve 210" "Curve 211" "Curve 212" "Curve 213" "Curve 214" "Cur ve 215" "Curve 216" "Curve 217" "Curve 218" "Curve 219" "Curve 220" "C urve 221" "Curve 222" "Curve 223" "Curve 224" "Curve 225" "Curve 226" "Curve 227" "Curve 228" "Curve 229" "Curve 230" "Curve 231" "Curve 232 " "Curve 233" "Curve 234" "Curve 235" "Curve 236" "Curve 237" "Curve 2 38" "Curve 239" "Curve 240" "Curve 241" "Curve 242" "Curve 243" "Curve 244" "Curve 245" "Curve 246" "Curve 247" "Curve 248" "Curve 249" "Cur ve 250" "Curve 251" "Curve 252" "Curve 253" "Curve 254" "Curve 255" "C urve 256" "Curve 257" "Curve 258" "Curve 259" "Curve 260" "Curve 261" "Curve 262" "Curve 263" "Curve 264" "Curve 265" "Curve 266" "Curve 267 " "Curve 268" "Curve 269" "Curve 270" "Curve 271" "Curve 272" "Curve 2 73" "Curve 274" "Curve 275" "Curve 276" "Curve 277" "Curve 278" "Curve 279" "Curve 280" "Curve 281" "Curve 282" "Curve 283" "Curve 284" "Cur ve 285" "Curve 286" "Curve 287" "Curve 288" "Curve 289" "Curve 290" "C urve 291" "Curve 292" "Curve 293" "Curve 294" "Curve 295" "Curve 296" "Curve 297" "Curve 298" "Curve 299" "Curve 300" "Curve 301" "Curve 302 " "Curve 303" "Curve 304" "Curve 305" "Curve 306" "Curve 307" "Curve 3 08" "Curve 309" "Curve 310" "Curve 311" "Curve 312" "Curve 313" "Curve 314" "Curve 315" "Curve 316" "Curve 317" "Curve 318" "Curve 319" "Cur ve 320" "Curve 321" "Curve 322" "Curve 323" "Curve 324" "Curve 325" "C urve 326" "Curve 327" "Curve 328" "Curve 329" "Curve 330" "Curve 331" "Curve 332" "Curve 333" "Curve 334" "Curve 335" "Curve 336" "Curve 337 " "Curve 338" "Curve 339" "Curve 340" "Curve 341" "Curve 342" "Curve 3 43" "Curve 344" "Curve 345" "Curve 346" "Curve 347" "Curve 348" "Curve 349" "Curve 350" "Curve 351" "Curve 352" "Curve 353" "Curve 354" "Cur ve 355" "Curve 356" "Curve 357" "Curve 358" "Curve 359" "Curve 360" "C urve 361" "Curve 362" "Curve 363" "Curve 364" "Curve 365" "Curve 366" "Curve 367" "Curve 368" "Curve 369" "Curve 370" "Curve 371" "Curve 372 " "Curve 373" "Curve 374" "Curve 375" "Curve 376" "Curve 377" "Curve 3 78" "Curve 379" "Curve 380" "Curve 381" "Curve 382" "Curve 383" "Curve 384" "Curve 385" "Curve 386" "Curve 387" "Curve 388" "Curve 389" "Cur ve 390" "Curve 391" "Curve 392" "Curve 393" "Curve 394" "Curve 395" "C urve 396" "Curve 397" "Curve 398" "Curve 399" "Curve 400" "Curve 401" "Curve 402" "Curve 403" "Curve 404" "Curve 405" "Curve 406" "Curve 407 " "Curve 408" "Curve 409" "Curve 410" "Curve 411" "Curve 412" "Curve 4 13" "Curve 414" "Curve 415" "Curve 416" "Curve 417" "Curve 418" "Curve 419" "Curve 420" "Curve 421" "Curve 422" "Curve 423" "Curve 424" "Cur ve 425" "Curve 426" "Curve 427" "Curve 428" "Curve 429" "Curve 430" "C urve 431" "Curve 432" "Curve 433" "Curve 434" }}}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 40 " Schw arzD avec base quadrilat\350re gauche " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 337 "base0: =[[[-1/2,-1/2,1/2],[-1/2,0,1/2],[0,0,0],[0,-1/2,1/2],[-1/4,-1/4,3/8]], [[1,2,5],[2,3,5],[3,4,5],[4,1,5]]]:\nbe:=facesC(itereN(3,base0)): #--- la brique la plus \351l\351mentaire --------\ndisplay(A,polygonplot3d (be,orientation=[80,65],style=patch,scaling=constrained,color=COLOR(RG B,1,1,0.8),lightmodel=light2,title=\"La cellule de base\"));\n" }} {PARA 8 "" 1 "" {TEXT -1 68 "Error, (in plots:-display) expecting plot structure but received: A\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 317 "be1:=Lrot([1,-1,0],Pi,be):\ng4:=[op(be),op(be1),op(Lrot([1,1,1] ,2*Pi/3,be)),op(Lrot([1,1,1],-2*Pi/3,be)),op(Lrot([1,1,1],2*Pi/3,be1)) ,op(Lrot([1,1,1],-2*Pi/3,be1))]:\ndisplay(A,polygonplot3d(g4,orientati on=[80,65],style=patch,scaling=constrained,color=COLOR(RGB,1,1,0.8),li ghtmodel=light2,title=\"La cellule de base\"));\n" }}{PARA 13 "" 1 "" {GLPLOT3D 498 540 540 {PLOTDATA 3 "6G-%%MESHG6$XR%)anythingG6\"6\"[gl' !%\"!!$c`m\"5\"+\"$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!BFE000000000000 0BFE00000000000003FE0A3D70A3D70A4BFDF8FED45596629BFE00000000000003FE09 9F590AFB939BFDF2D5F1130CBEBBFE00000000000003FE07D823B93819BBFDEE438861 0F2B2BFE00000000000003FE051EB851EB852BFDEBD4C568A3214BFE00000000000003 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"Curve 32" "Curve 33" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 476 "uu:=0.5:liste1:=[[[0.5+uu,0.5+uu,-0.5+uu],[0.5+uu,-0.5+uu,-0.5+uu ],[0.5+uu,-0.5+uu,0.5+uu],[-0.5+uu,-0.5+uu,0.5+uu],[-0.5+uu,0.5+uu,0.5 +uu],[-0.5+uu,0.5+uu,-0.5+uu]]]:\nliste2:=[[[0.5+uu,-0.5+uu,0+uu],[-0. 5+uu,0.5+uu,0+uu]],[[0+uu,0.5+uu,-0.5+uu],[0+uu,0+uu,0+uu]],[[0+uu,0+u u,0+uu],[0+uu,-0.5+uu,0.5+uu]],[[0.5+uu,0+uu,-0.5+uu],[0+uu,0+uu,0+uu] ],[[0+uu,0+uu,0+uu],[-0.5+uu,0+uu,0.5+uu]]]:\nA:=display(montubeplot(l iste1,.02,.02,red),montubeplot(liste2,.02,.02,red),color=red):\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 429 "\n#******************** la \+ cellule de base des constructions ***************\ncell:=Ltrans([0,0,- 2],map(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)) ])):\ndisplay(A,polygonplot3d(cell ,orientation=[80,65],style=patch,scaling=constrained,color=COLOR(RGB,1 ,1,0.8),lightmodel=light2,title=\"La cellule de base\"));" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 581 "#****************************************** *********************************************************\n#********** ********* une m\351thode de construction o\371 l'on voit bien les sym \351tries ******************\nnoeud:=map(op,[cell,Ltrans([1,1,-1],Lro t([0,0,1],Pi/2,cell)),Ltrans([-1,-1,-1],Lrot([0,0,1],Pi/2,cell))\n \+ ,Ltrans([+1,-1,1],Lrot([0,0,1],Pi/2,cell)),Ltrans([-1,1 ,1],Lrot([0,0,1],Pi/2,cell)) ]):\nnoeudSym:=LsymXY(noeud):\ndisplay(A, [polygonplot3d(noeud,style=patch)],scaling=constrained ,orientation=[2 0,70],color=COLOR(RGB,1,1,0.8),lightmodel=light2);# axes,nogrid" } {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT3D 614 614 614 {PLOTDATA 3 "6G -%%MESHG6%XR%)anythingG6\"6\"[gl'!%\"!!$c`m\"5\"+\"$!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!000000000000000000000000000000003FF051EB851EB8523F7C 04AEA9A675AD00000000000000003FF04CFAC857DC9C3F8A541DD9E682AE0000000000 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nF_]]n7%Fc^]nFa^]n7%F\\[]lF5FN7%Fa^]nF`[]n7%F\\i\\lF5FN7%Fa^]nF`[]nFaj \\n7%F`[]nFi^]nFfhr7%Fi^]nFa^]nFg^]n7%Fb^]nFh]]nFij\\n7%Fb^]nFh]]nF_]] n7%Fh]]nFij\\nF][]n7%Fij\\nFb^]nFaj\\n7%Fc^]n7%Fb[]lF5FNFc]]n7%Fc^]nFb _]nFg^]n7%Fb_]nFc]]nFf_[n7%Fc]]nFc^]nF_]]n-F+6#%&PATCHG-%&COLORG6&F1FN FN$\"\")F\\[q-%+LIGHTMODELG6#%(LIGHT_2G-%(SCALINGG6#%,CONSTRAINEDG-%+P ROJECTIONG6%$\"#?F6$\"#qF6FO" 1 2 0 1 10 0 2 6 4 1 1 1.000000 70.000000 20.000000 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Cur ve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 1 8" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" " Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curv e 31" "Curve 32" "Curve 33" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 40 " SchwarzP avec base qua drilat\350re gauche " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "bas e0:=[[[0,0,1],[-1,0,0],[0,1,0],[1,0,0], [0,1/4,1/4]],[[1,2,5],[2,3,5] ,[3,4,5],[4,1,5]]]:\n#base1:=[[[-1,0,0],[0,0,1],[-1,0,2],[-1,-1,1], [ -3/4,-1/4,1]],[[1,2,5],[2,3,5],[3,4,5],[4,1,5]]]:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 956 "#=================\nliste1:=[[[1,0,0],[0,0, -1],[0,1,0],[-1,0,0],[0,0,1],[0,-1,0]]]:\nbe:=Ltrans([0,1,1],facesC(it ereN(n,base0))): #--- la brique la plus \351l\351mentaire ------- -\nliste2:=[[[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]]]:\nA2:=d isplay(montubeplot(liste1,.02,.02,blue),montubeplot(liste2,.02,.02,red )):\nLhomo:=proc(k,Liste) :if type(evalf(Liste[1,1]),numeric) then map ( u ->expand(u*k),Liste): else map( u->Lhomo(k,u),Liste) fi:end:\nbe2: =Ltrans([-1/2,0,0],Lhomo(1/2,facesC(itereN(4,base0)))):\ndisplay([axes (1), polygonplot3d(be)]);\ndisplay(A2,[#axes(1),\n polygonp lot3d([seq(op(Lrot([1,1,1],2*i*Pi/3,be2)),i=0..2),\n \+ seq(op(Lrot([1,1,1],2*i*Pi/3,Lrot([0,-1,1],Pi,be2))), i=0..2)],color=COLOR(RGB,1,1,0.8))\n ],orientation=[10,65],sty le=patch,scaling=constrained,lightmodel=light2,orientation=[80,65]);\n #====================" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 8 "" 1 "" {TEXT -1 168 "Error, (in plots:-display) expecting plot stru cture but received: montubeplot([[[1, 0, 0], [0, 0, -1], [0, 1, 0], [- 1, 0, 0], [0, 0, 1], [0, -1, 0]]],.2e-1,.2e-1,blue)\n" }}{PARA 13 "" 1 "" {GLPLOT3D 614 614 614 {PLOTDATA 3 "6'-%%MESHG6$7$7'7%$\"0+++++++$ !#;$\"\"!F-F,7%$\"0.@()>qp$=!#KF)F,7%$!0+++++++$F+$\"01UuRSRn$F1F,7%$! 04jhf54^&F1F3F,7%F)$!07%)[z!)yM(F1F,7'7%F)F,$\"\"\"F-7%F/F)F?7%F3F5F?7 %F8F3F?7%F)F;F?-%&COLORG6&%$RGBGF,$\"*++++\"!\")FI-F$6$7$7'7%F,F)F,7%F ,F/F)7%F,F3F57%F,F8F37%F,F)F;7'7%F?F)F,7%F?F/F)7%F?F3F57%F?F8F37%F?F)F ;-FF6&FHFIF,F,-F$6$7$7'F(7%F/F,F37%F3F,$!01UuRSRn$F17%F8F,F)7%F)F,$\"0 7%)[z!)yM(F17'7%F)F?F,7%F/F?F37%F3F?F]o7%F8F?F)7%F)F?Fao-FF6&FHF,$\"\" '!\"\"F,-%)POLYGONSG6\\o7%7%$!+WWWWW!#5$\"+AAA(4\"!\"*$\"+WWW>8Fhp7%$! +WWWW>Fep$\"+yxx_6Fhp$\"+AAAZ8Fhp7%$!+AAAAAFep$\"+WWWp5Fhp$\"+*))))Q^ \"Fhp7%FbpF[q7%$!+LLLLLFep$\"+AAAA7FhpF]r7%F[qFbq7%F,$\"+66666Fhp$\"+W WWW9Fhp7%FbqFbp7%$!+++++]FepF?$\"+++++:Fhp7%Fbp7%$!+6666hFep$\"+nmmm6F hpF_s7%$!+++++vFepF?$\"++++]7Fhp7%FbpF\\sFjq7%F\\sFas7%$F]pF-F?F?7%Fas FbpFfr7%F[q7%F,$\"+WWW%>\"Fhp$\"+cbb08Fhp7%$!+66666FepFdsFds7%F[qF\\tF `r7%F\\tFat7%F,FdsFds7%FatF[qFjq7%Fbq7%$!+++++DFepF?$\"++++]FepF`qF^q7%$\"+AAAAAFepFgqFeq7%FdwFgw7%$\"+LLLLLFepF]rF]r7 %FgwFjwF^v7%FjwFdw7%$\"+++++]FepFirF?7%Fdw7%$\"+6666hFepF_sF_s7%$\"+++ ++vFepFdsF?7%FdwFgxF^x7%FgxFjx7%F?F?F?7%FjxFdwFcx7%FgwFjv7%$FbrFepFdsF ds7%FgwFjvF^v7%FjvFbyFft7%FbyFgwF^x7%Fjw7%$\"+++++DFepF\\uF?Fcv7%FjwFh yFcx7%FhyFcvFgv7%FcvFjwF^v7%7%F[xFeqFgq7%FhwF^qF`q7%FewFfpFip7%F_zF`zF `r7%F`zFazF^x7%FazF_z7%FdxF?Fir7%F_zF^u7%FiyF?F\\u7%F_zF^uF`r7%F^uFgzF eu7%FgzF_zFez7%F`zFbyF\\t7%F`zFbyF^x7%FbyF\\tFft7%F\\tF`zF`r7%Faz7%F[y F?FdsFgx7%FazF`[lFez7%F`[lFgxF_y7%FgxFazF^x-%(SCALINGG6#%,CONSTRAINEDG " 1 2 0 1 10 0 2 1 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "C urve 2" "Curve 3" "Curve 4" }}}{PARA 8 "" 1 "" {TEXT -1 69 "Error, (in plots:-display) expecting plot structure but received: A2\n" }}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 40 " construction avec une cellule \" cubique\"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "n:=3;\nbe:=Ltr ans([0,1,1],facesC(itereN(n,base0))): #--- la brique la plus \351 l\351mentaire --------\ndisplay(A2,[axes(1),polygonplot3d(be)],orienta tion=[50,65],style=patch,scaling=constrained,color=COLOR(RGB,1,1,0.8), lightmodel=light2);\nbe1:=Ltrans([-1,1,2],Lrot([0,0,1],-Pi/2,Lrot([0,1 ,0],Pi/2,facesC(itereN(n,base0))))):\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"$" }}{PARA 8 "" 1 "" {TEXT -1 69 "Error, (in plots:-di splay) expecting plot structure but received: A2\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 836 "\nbe1:=Ltrans([0,1,1],facesC(itereN(n,base 1))):\npolygonplot3d(map(op,[be,be1])):\nbords:=[Ltrans([0,1,1],base0[ 1,1..4]), Ltrans([-1,1,2],Lrot([0,0,1],-Pi/2,Lrot([0,1,0],Pi/2,base0[1 ,1..4])))]:\ncouronne:=[seq(op(Lrot([0,0,1],i*Pi/2,[be1,be])),i=0..3), seq(Ltrans([0,0,4],Lrot([0,0,1],i*Pi/2,LsymXY(be))),i=0..3)]:\nbords_c ouronne:=[seq(op(Lrot([0,0,1],i*Pi/2,bords)),i=0..3),seq(Ltrans([0,0,4 ],Lrot([0,0,1],i*Pi/2,LsymXY(Ltrans([0,1,1],base0[1,1..4])))),i=0..3)] :\ncouches_p:=(p,q)-> seq(seq(Ltrans([-4+4*i,4*j,0],couronne),i=0..p), j=0..q):\ncouches_i:=(p,q,h)-> seq(seq(Ltrans([-2+4*i,2+4*j,2*h],couro nne),i=0..p),j=0..q):\nbords_couches_p:=(p,q) -> seq(seq(Ltrans([-4+4* i,4*j,0],bords_couronne),i=0..p),j=0..q):\nbords_couches_i:=(p,q,h)-> \+ seq(seq(Ltrans([-2+4*i,2+4*j,2*h],bords_couronne),i=0..p),j=0..q):\n# \+ ===== la surface =================" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 393 "p,q,r:=0,0,1; #1,1,1;\ngr:=display([#axes(4),\n polygonpl ot3d(map(op,[couches_p(1,1),couches_i(p,q,r), couches_i(p,q,-r)\n \+ ]),\n style=patch,scalin g=constrained,color=COLOR(RGB,1,1,0.8))\n ,op(map(tracelist,[b ords_couches_p(1,1),bords_couches_i(p,q,r),bords_couches_i(p,q,-r)])) \n ],orientation=[-70,78],lightmodel=light2):gr;\n\011" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6%%\"pG%\"qG%\"rG6%\"\"!F)\"\"\"" }}{PARA 8 "" 1 "" {TEXT -1 72 "Error, (in plots:-polygonplot3d) incorrect spec ification of points data\n" }}{PARA 13 "" 1 "" {GLPLOT3D 735 735 735 {PLOTDATA 3 "6bfl-%)POLYGONSG6dx7%7%$\"\"!F)F($\"\"$F)7%F($\"\"\"F)F*7 %$\"+++++]!#5F0$\"+++++D!\"*7%F,7%F(F-$\"\"#F)F/7%F77%F-F-F8F/7%F;7%F- F(F8F/7%F=7%F-F(F*F/7%F?F'F/7%F'7%F($!\"\"F)F*7%$!+++++]F2FFF37%FB7%F( FCF8FE7%FI7%FCFCF8FE7%FK7%FCF(F8FE7%FM7%FCF(F*FE7%FOF'FE7%7%F-FC$\"\"% F)7%F(FCFS7%F0FF$\"+++++NF57%FUFBFV7%FBF'FV7%F'F?FV7%F?7%F-F(FSFV7%Fgn FRFV7%7%FCF-FS7%F(F-FS7%FFF0FW7%F[oF,F\\o7%F,F'F\\o7%F'FOF\\o7%FO7%FCF (FSF\\o7%FaoFjnF\\o7%7%F8F(F*7%F8F-F*7%F3F0F37%Feo7%F8F-F8Ffo7%Fho7%F* F-F8Ffo7%Fjo7%F*F(F8Ffo7%F\\p7%F*F(F*Ffo7%F^pFdoFfo7%Fdo7%F8FCF*7%$\"+ 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"Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74" "Curve 75" "Curve 76" "Curve 77" "Curve 78 " "Curve 79" "Curve 80" "Curve 81" "Curve 82" "Curve 83" "Curve 84" "C urve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93" "Curve 94" "Curve 95" "Curve 96" "Curve 97 " "Curve 98" "Curve 99" "Curve 100" "Curve 101" "Curve 102" "Curve 103 " "Curve 104" "Curve 105" "Curve 106" "Curve 107" "Curve 108" "Curve 1 09" "Curve 110" "Curve 111" "Curve 112" "Curve 113" "Curve 114" "Curve 115" "Curve 116" "Curve 117" "Curve 118" "Curve 119" "Curve 120" "Cur ve 121" "Curve 122" "Curve 123" "Curve 124" "Curve 125" "Curve 126" "C urve 127" "Curve 128" "Curve 129" "Curve 130" "Curve 131" "Curve 132" "Curve 133" "Curve 134" "Curve 135" "Curve 136" "Curve 137" "Curve 138 " "Curve 139" "Curve 140" "Curve 141" "Curve 142" "Curve 143" "Curve 1 44" "Curve 145" "Curve 146" "Curve 147" "Curve 148" "Curve 149" "Curve 150" "Curve 151" "Curve 152" "Curve 153" "Curve 154" "Curve 155" "Cur ve 156" "Curve 157" "Curve 158" "Curve 159" "Curve 160" "Curve 161" "C urve 162" "Curve 163" "Curve 164" "Curve 165" "Curve 166" "Curve 167" "Curve 168" "Curve 169" "Curve 170" "Curve 171" "Curve 172" "Curve 173 " "Curve 174" "Curve 175" "Curve 176" "Curve 177" "Curve 178" "Curve 1 79" "Curve 180" "Curve 181" "Curve 182" "Curve 183" "Curve 184" "Curve 185" "Curve 186" "Curve 187" "Curve 188" "Curve 189" "Curve 190" "Cur ve 191" "Curve 192" "Curve 193" "Curve 194" "Curve 195" "Curve 196" "C urve 197" "Curve 198" "Curve 199" "Curve 200" "Curve 201" "Curve 202" "Curve 203" "Curve 204" "Curve 205" "Curve 206" "Curve 207" "Curve 208 " "Curve 209" "Curve 210" "Curve 211" "Curve 212" "Curve 213" "Curve 2 14" "Curve 215" "Curve 216" "Curve 217" "Curve 218" "Curve 219" "Curve 220" "Curve 221" "Curve 222" "Curve 223" "Curve 224" "Curve 225" "Cur ve 226" "Curve 227" "Curve 228" "Curve 229" "Curve 230" "Curve 231" "C urve 232" "Curve 233" "Curve 234" "Curve 235" "Curve 236" "Curve 237" "Curve 238" "Curve 239" "Curve 240" "Curve 241" "Curve 242" "Curve 243 " "Curve 244" "Curve 245" "Curve 246" "Curve 247" "Curve 248" "Curve 2 49" "Curve 250" "Curve 251" "Curve 252" "Curve 253" "Curve 254" "Curve 255" "Curve 256" "Curve 257" "Curve 258" "Curve 259" "Curve 260" "Cur ve 261" "Curve 262" "Curve 263" "Curve 264" "Curve 265" "Curve 266" "C urve 267" "Curve 268" "Curve 269" "Curve 270" "Curve 271" "Curve 272" "Curve 273" "Curve 274" "Curve 275" "Curve 276" "Curve 277" "Curve 278 " "Curve 279" "Curve 280" "Curve 281" "Curve 282" "Curve 283" "Curve 2 84" "Curve 285" "Curve 286" "Curve 287" "Curve 288" "Curve 289" "Curve 290" "Curve 291" "Curve 292" "Curve 293" "Curve 294" "Curve 295" "Cur ve 296" "Curve 297" "Curve 298" "Curve 299" "Curve 300" "Curve 301" "C urve 302" "Curve 303" "Curve 304" "Curve 305" "Curve 306" "Curve 307" "Curve 308" "Curve 309" "Curve 310" "Curve 311" "Curve 312" "Curve 313 " "Curve 314" "Curve 315" "Curve 316" "Curve 317" "Curve 318" "Curve 3 19" "Curve 320" "Curve 321" "Curve 322" "Curve 323" "Curve 324" "Curve 325" "Curve 326" "Curve 327" "Curve 328" "Curve 329" "Curve 330" "Cur ve 331" "Curve 332" "Curve 333" "Curve 334" "Curve 335" "Curve 336" "C urve 337" "Curve 338" "Curve 339" "Curve 340" "Curve 341" "Curve 342" "Curve 343" "Curve 344" "Curve 345" "Curve 346" "Curve 347" "Curve 348 " "Curve 349" "Curve 350" "Curve 351" "Curve 352" "Curve 353" "Curve 3 54" "Curve 355" "Curve 356" "Curve 357" "Curve 358" "Curve 359" "Curve 360" "Curve 361" "Curve 362" "Curve 363" "Curve 364" "Curve 365" "Cur ve 366" "Curve 367" "Curve 368" "Curve 369" "Curve 370" "Curve 371" "C urve 372" "Curve 373" "Curve 374" "Curve 375" "Curve 376" "Curve 377" "Curve 378" "Curve 379" "Curve 380" "Curve 381" "Curve 382" "Curve 383 " "Curve 384" "Curve 385" "Curve 386" "Curve 387" "Curve 388" "Curve 3 89" "Curve 390" "Curve 391" "Curve 392" "Curve 393" "Curve 394" "Curve 395" "Curve 396" "Curve 397" "Curve 398" "Curve 399" "Curve 400" "Cur ve 401" "Curve 402" "Curve 403" "Curve 404" "Curve 405" "Curve 406" "C urve 407" "Curve 408" "Curve 409" "Curve 410" "Curve 411" "Curve 412" "Curve 413" "Curve 414" "Curve 415" "Curve 416" "Curve 417" "Curve 418 " "Curve 419" "Curve 420" "Curve 421" "Curve 422" "Curve 423" "Curve 4 24" "Curve 425" "Curve 426" "Curve 427" "Curve 428" "Curve 429" "Curve 430" "Curve 431" "Curve 432" "Curve 433" "Curve 434" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "polygonplot3d(evalf(couches_p(1,1)),style=patch,scal ing=constrained,color=COLOR(RGB,1,1,0.8),\n orientation=[-70,7 8],lightmodel=light2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 8 "" 1 "" {TEXT -1 85 "Error, (in plots:-polygonplot3d) points cannot \+ be converted to floating-point values\n" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 39 " construction avec une cellule \"ronde\"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 936 "n:=3:\nprintf(\"Nombre d'it\351rat ions =%a\",n);\nbe:=Ltrans([0,1,1],facesC(itereN(n,base0))):\nbe1:=Ltr ans([-2,2,2],Lrot([0,0,1],-Pi/2,Lrot([0,1,0],Pi/2,be))):\nbe2:=Ltrans( [-2,2,2],LsymXY(Lrot([0,0,1],-Pi/2,be))):\nbords_be:=Ltrans([0,1,1],ba se0[1,1..4]):\nbords_be1:=Ltrans([-2,2,2],Lrot([0,0,1],-Pi/2,Lrot([0,1 ,0],Pi/2,bords_be))):\nbords_be2:=Ltrans([-2,2,2],LsymXY(Lrot([0,0,1], -Pi/2,bords_be))):\ncou_be:=[seq(op(Lrot([0,0,1],i*Pi/2,be)),i=0..3)]: \ncou_be1:=[seq(op(Lrot([0,0,1],i*Pi/2,be1)),i=0..3)]:\ncouronne1:=map (op,[cou_be,cou_be1]):\ncouronne2:=[seq(op(Lrot([0,1,0],i*Pi/2,be2)),i =0..3),seq(op(Lrot([0,1,0],i*Pi/2,be)),i=1..3)]:\nbords_cou_be:=[seq(L rot([0,0,1],i*Pi/2,bords_be),i=0..3)]:\nbords_cou_be1:=[seq(Lrot([0,0, 1],i*Pi/2,bords_be1),i=0..3)]:\nbords_couronne1:=[bords_cou_be,bords_c ou_be1]:\nbords_couronne2:=[seq(Lrot([0,1,0],i*Pi/2,bords_be2),i=0..3) ,seq(Lrot([0,1,0],i*Pi/2,bords_be),i=1..3)]:\n#polygonplot3d(map(op,[b e,be1,be2]));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 790 "bords:=display(ma p(tracelist, [bords_couronne1,bords_couronne2,LsymZX(bords_couronne2), Ltrans([0,0,-4],bords_cou_be1)\n ,[seq(Lr ot([0,1,0],i*Pi+Pi/2,bords_cou_be1),i=0..1)]\n \+ ,[seq(Lrot([0,0,1],i*Pi-Pi/2,Lrot([1,0,0],-Pi/2,bords_be)),i=0.. 1)] \n ] )):\n#display(map(tracelist,[bords_cou ronne1,bords_couronne2]));\ndisplay(A2,[axes(4),\n polygonplot 3d(map(op,[couronne1,couronne2,LsymZX(couronne2),Ltrans([0,0,-4],cou_b e1)\n ,seq(Lrot([0,1,0],i*Pi+Pi/2,cou_be1 ),i=0..1)\n ,seq(Lrot([0,0,1],i*Pi-Pi/2,L rot([1,0,0],-Pi/2,be)),i=0..1) \n ])) \n , bords \n ],orientation=[58,80],lightmodel=light2,scaling =constrained);" }}{PARA 6 "" 1 "" {TEXT -1 22 "Nombre d'it\351rations \+ =3" }}{PARA 8 "" 1 "" {TEXT -1 69 "Error, (in plots:-display) expectin g plot structure but received: A2\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 650 "#### = ========== pa de raccordments possibles =============\ncubo:=[seq(op(L rot([1,0,0],i*Pi/2,couronne1)),i=0..3),\n seq(op(Lrot([0,1,0],i* Pi/2,Ltrans([-4,0,0],Lrot([0,1,0],Pi/2,couronne1)))),i=0..2),\n \+ seq(op(Lrot([1,0,0],i*Pi/2,Lrot([0,1,0],Pi/2,Ltrans([-4,0,0],Lrot([0,1 ,0],Pi/2,couronne1))))),i=1..3) ]:\n\n#******************** la cellule de base des constructions ***************\ndisplay([axes(4),polygonpl ot3d(map(op,[cubo #,Ltrans([6,2,2],cubo),Ltrans([6,-2,2]*1.1,cubo)\n \+ ]),orientation=[75,75],style=patch,scaling=co nstrained,color=COLOR(RGB,1,1,0.8))\n#,op(map(tracelist,bords_cubo)) \+ \n],lightmodel=light2);" }}{PARA 13 "" 1 "" {GLPLOT3D 591 591 591 {PLOTDATA 3 "6)-%%MESHG6$7$7'7%$\"0+++++++$!#;$\"\"!F-F,7%$\"0.@()>qp$ =!#KF)F,7%$!0+++++++$F+$\"01UuRSRn$F1F,7%$!04jhf54^&F1F3F,7%F)$!07%)[z !)yM(F1F,7'7%F)F,$\"\"%F-7%F/F)F?7%F3F5F?7%F8F3F?7%F)F;F?-%&COLORG6&%$ RGBGF,$\"*++++\"!\")FI-F$6$7$7'7%F,F)F,7%F,F/F)7%F,F3F57%F,F8F37%F,F)F ;7'7%F?F)F,7%F?F/F)7%F?F3F57%F?F8F37%F?F)F;-FF6&FHFIF,F,-F$6$7$7'F(7%F /F,F37%F3F,$!01UuRSRn$F17%F8F,F)7%F)F,$\"07%)[z!)yM(F17'7%F)F?F,7%F/F? 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!++++]AFhpF[z7%FiemFc`lF[fm7%FdbpFfdpF]cp7%FfdpFidpFc`o7%FidpFdbpF[cp7 %7%FbfmFebpFdfm7%FgfmFbbpFifm7%F\\gmF_bpF^gm7%F^epF_ep7%FbgmFc`lFdgm7% F_epF`epFgbp7%F`epF^ep7%FgrF^cpFir7%F^ep7%F[hmFc`lF]hm7%F\\uFgdpFir7%F ^epFgepFbep7%FgepFhepF^gl7%FhepF^epFeep7%F_epF^dp7%FehmFc`lFghm7%F_epF ^dpFgbp7%F^dpF]fpFcdp7%F]fpF_epFbep7%F`ep7%FdsFdcpFirF`cp7%F`epFbfpFee p7%FbfpF`cpFhcp7%F`cpF`epFgbp7%7%F\\gm$!+cbbb:FhpF^gm7%Fgfm$!+cbb0=Fhp Fifm7%Fbfm$!+yxxx " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 26 "SchwarzP ave c parabolo\357des" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "with(p lots):\npbase0:=[[[0,0,1],[-1,0,0],[0,1,0],[1,0,0], [0,1/4,1/4]],[[1, 2,5],[2,3,5],[3,4,5],[4,1,5]]]:\na,b,c,d:=[0,0,1],[-1,0,0],[0,1,0],[1, 0,0]:\n#a,b,c,d:=[-1,0,2],[0,0,1],[-1,0,0],[-1,-1,1]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1367 "m1:=uu -> a+uu*(b-a): m2:= uu->d+uu*(c-d):\nm: =(uu,vv) -> expand(m1(uu)+vv*(m2(uu)-m1(uu))):\n#eliminate(convert(m(u u,vv)-[x,y,z],set),\{uu,vv\});\n#--- \351quation du parabolo\357de : - 2*y+z^2-2*z-2*z*y+1-x^2+y^2 -------------\n#display(tracelist([a,b,c,d ]),tracelist([m(0.2,0),m(0.2,1)]),tracelist([m(0,0.3),m(1,0.3)]));\nn: =5:\nhyper:=[seq(seq(op([[m(i/n,j/n),m((i+1)/n,j/n),m(i/n,(j+1)/n)],\n [m(i/n,(j+1)/n),m((i+1)/n,(j+1)/n),m((i+1)/n,j/n)] ]),i=0..n-1),j=0..n-1)]:\npbe:=Ltrans([0,1,1],hyper):\npbe1:=Ltrans([- 1,1,2],Lrot([0,0,1],-Pi/2,Lrot([0,1,0],Pi/2,hyper))):\npbords:=[Ltrans ([0,1,1],pbase0[1,1..4]), Ltrans([-1,1,2],Lrot([0,0,1],-Pi/2,Lrot([0,1 ,0],Pi/2,pbase0[1,1..4])))]:\npcouronne:=[seq(op(Lrot([0,0,1],i*Pi/2,[ pbe1,pbe])),i=0..3),seq(Ltrans([0,0,4],Lrot([0,0,1],i*Pi/2,LsymXY(pbe) )),i=0..3)]:\npbords_couronne:=[seq(op(Lrot([0,0,1],i*Pi/2,pbords)),i= 0..3),seq(Ltrans([0,0,4],Lrot([0,0,1],i*Pi/2,LsymXY(Ltrans([0,1,1],pba se0[1,1..4])))),i=0..3)]:\npcouches_p:=(p,q)-> seq(seq(Ltrans([-4+4*i, 4*j,0],pcouronne),i=0..p),j=0..q):\npcouches_i:=(p,q,h)-> seq(seq(Ltra ns([-2+4*i,2+4*j,2*h],pcouronne),i=0..p),j=0..q):\npbords_couches_p:=( p,q) -> seq(seq(Ltrans([-4+4*i,4*j,0],pbords_couronne),i=0..p),j=0..q) :\npbords_couches_i:=(p,q,h)-> seq(seq(Ltrans([-2+4*i,2+4*j,2*h],pbord s_couronne),i=0..p),j=0..q):\n#polygonplot3d(map(op,[be,be1]));\n#poly gonplot3d(hyper);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 547 "p,q,r:=0,0,1;\nprintf(\" nombre de barres = %a\",n); \ngr:=display([#axes,\n polygonplot3d(map(op,[pcouches_p(1 ,1),pcouches_i(p,q,r), pcouches_i(p,q,-r)\n \+ ]), style=patch,color=COLOR(RGB,1,1,0.8))\n ,op(map(trac elist,[pbords_couches_p(1,1),pbords_couches_i(p,q,r),pbords_couches_i( p,q,-r)]))\n ],scaling=constrained,orientation=[-70,78],li ghtmodel=light2):\n#plotsetup(bmp,plotoutput=\"D:/Mes documents/surf-S chwarzP_parabole_D.bmp\",plotoptions=\"width=1400,height=1000\");\ngr; plotsetup(inline);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >6%%\"pG%\"qG%\"rG6%\"\"!F)\"\"\"" }}{PARA 6 "" 1 "" {TEXT -1 21 " nom bre de barres = 5" }}{PARA 8 "" 1 "" {TEXT -1 72 "Error, (in plots:-po lygonplot3d) 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"Curve 408" "Cur ve 409" "Curve 410" "Curve 411" "Curve 412" "Curve 413" "Curve 414" "C urve 415" "Curve 416" "Curve 417" "Curve 418" "Curve 419" "Curve 420" "Curve 421" "Curve 422" "Curve 423" "Curve 424" "Curve 425" "Curve 426 " "Curve 427" "Curve 428" "Curve 429" "Curve 430" "Curve 431" "Curve 4 32" "Curve 433" "Curve 434" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 76 " Comparaison des brique s \351l\351mentaires paraboloide et avec it\351ration de base0" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "display(polygonplot3d(Ltran s([0,1,+1],facesC(itereN(6,base0))),color=red),polygonplot3d(pbe,color =blue));" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 " Essai " } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "with(plots):base2:=[[[0,0, 1],[1,0,0],[0,1,0],[-1,0,0],[0,1/4,1/4]], [[1,2,5],[2,3,5],[3,4,5],[1, 4,5]]]:\ndisplay(axes(1),polygonplot3d(facesC(base2)));" }{TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 345 "g0:=facesC(itereN(3,ba se2)):\ng:=Ltrans([-1,1,0],Lrot([1,1,0],Pi,g0)):\ng1:=Ltrans([1,0,1],L rot([1,0,-1],Pi,g0)):\n\ng2:=[g0,g,g1]:\ncell:= seq(Lrot([0,0,1],i*Pi/ 2,g1),i=0..3):\ndisplay([axes(2),\n polygonplot3d(map(op,[g2,L trans([-2,2,-2],g2)]))],scaling=constrained,style=patch,orientation=[6 0,40],color=COLOR(RGB,1,1,0.8),lightmodel=light2);" }}{PARA 13 "" 1 " " {TEXT -1 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 39 " Comparaison avec r\351sultats Ma thematica" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1834 "#=== donn\351 es 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:=i tereN(2,base)[1]:\nprintf(\" \351galit\351 \340 la premi\350re it\351r ation = %a\\n\",evalb(convert(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,-13/72,23/72],[-1/2,1/2,0],[0,1/2,-1/2],[-13/72,2 3/72,-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,-11/36,4/9],[-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],[-7/18,13/36,1/9],[-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_Es culier:=itereN(3,base)[1]:\ndelta:=convert(S2_mathematica,set) interse ct convert(S2_Esculier,set); \nprintf( \"A COMPARER LES %a DIFFERENCES SUIVANTES :\",nops(S2_Esculier)-nops(delta));\ndiff_mathematica:=eval f(convert(S2_mathematica,set) minus delta,4);\ndiff_Esculier:=evalf(co nvert(S2_Esculier,set) minus 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_mathematica:=\{[.3194,-.1806,-.1806],[.1806,.1 806,-.3194],[.1806,-.3194,.1806],[-.1806,.3194,-.1806],[-.1806,-.1806, .3194],[-.3194,.1806,.1806]\};" }}{PARA 0 "" 0 "" {TEXT -1 148 "diff_E sculier:=\{[.3148,-.1852,-.1852],[.1852,.1852,-.3148],[.1852,-.3148,.1 852],[-.1852,.3148,-.1852],[-.1852,-.1852,.3148],[-.3148,.1852,.1852] \}; " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "15 6 0 0" 569 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }