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Rev 18517 Rev 18529
Line 19... Line 19...
19 
  h=mob_ori(a,d);\
 19 
  h=mob_ori(a,d);\
20 
  mob_mul(h,mob_mul([1,0,1],mob_inv(h)))\
 20 
  mob_mul(h,mob_mul([1,0,1],mob_inv(h)))\
21 
  };\
 21 
  };\
22 
lft_fwd(g,beta,l)=my(e=exp(I*beta/2));mob_mul(g,[e,e*l,0]);\
 22 
lft_fwd(g,beta,l)=my(e=exp(I*beta/2));mob_mul(g,[e,e*l,0]);\
23 
\
 23 
\
24 
wims_export(pavage)={\
 - 
 
25 
  my(res1,res2,res3,res4,[sommets,paves,aretes,daretes]=pavage,n=#paves[1]-1);\
 - 
 
26 
  res1=matrix(#sommets,2,i,j,if(j==1,real(sommets[i]),imag(sommets[i])));\
 - 
 
27 
  res2=matrix(#paves,n+2,i,j,if(j==1,n,if(j==n+2,paves[i][n+1][3],paves[i][j-1])));\
 - 
 
28 
  [res1,res2]\
 - 
 
29 
};\
 - 
 
30 
\
 - 
 
31 
hyp_pav(v,d,eps)={\
 24 
hyp_pav(v,d,z0,eps)={\
32 
  my(n=#v,a,b,s,s1,s2,t,t1,t2,g,gg,cd0,cd1,cdd1,cd2,r2,f1,v1,w0,z,limit);\
 25 
  my(n=#v,a,b,s,s1,s2,t,t1,t2,g,gg,cd0,cd1,cdd1,cd2,r2,f1,v1,w0,z,limit,centres);\
33 
  if(eps>=1,limit=eps;eps=0,limit=1000);\
 26 
  if(eps>=1,limit=eps;eps=0,limit=1000);\
34 
  r2=(1-eps)^2;\
 27 
  r2=(1-eps)^2;\
35 
  if(!v,return(0));\
 28 
  if(!v,return(0));\
36 
\\ Les reflexions qui engendrent W\
 29 
\\ Les reflexions qui engendrent W\
37 
  g=vector(n,i,mob_ref(v[i],v[i%n+1]));\
 30 
  g=vector(n,i,mob_ref(v[i],v[i%n+1]));\
38 
\
 31 
\
39 
\\ Creation du premier pave et de son squelette\
 32 
\\ Creation du premier pave et de son squelette\
40 
  \\ Pour chaque sommet, [arite restante, derniere arete cree, affixe, dans le disque?]\
 33 
  \\ Pour chaque sommet, [arite restante, derniere arete cree, affixe, type, dans le disque?]\
41 
  cd2=List(vector(n,s,[d[s]-2,if(s==1,n,s),v[s],norm(v[s])<r2]));\
 34 
  cd2=List(vector(n,s,[d[s]-2,if(s==1,n,s),v[s],s,norm(v[s])<r2]));\
42 
  \\ Pour chaque arete, [origine, extremite, type, premier polygone borde, active]\
 35 
  \\ Pour chaque arete, [origine, extremite, type, premier polygone borde, active?]\
43 
  cd1=List(vector(n,a,[a,a%n+1,a,1,cd2[a][4]||cd2[a%n+1][4]]));\
 36 
  cd1=List(vector(n,a,[a,a%n+1,a,1,cd2[a][4]||cd2[a%n+1][4]]));\
44 
  \\ Pour chaque arete duale [pave origine, pave extremite, arete croisee]\
 37 
  \\ Pour chaque arete duale [pave origine, pave extremite, arete croisee]\
45 
  cdd1=List();\
 38 
  cdd1=List();\
46 
  \\ Pour chaque pave, ses aretes et l'élément du groupe\
 39 
  \\ Pour chaque pave, ses aretes et l'élément du groupe\
47 
  cd0=List([vector(n+1,a,if(a>n,[1,0,0],a))]);\
 40 
  cd0=List([vector(n+1,a,if(a>n,[1,0,0],a))]);\
48 
\
 41 
\
49 
  while(#cd0<limit&&f1<#cd1, f1+=1; v1=cd1[f1]; if(v1[5],\
 42 
  while(#cd0<limit&&f1<#cd1, f1+=1; v1=cd1[f1]; if(v1[5],\
50 
    s=v1[3]; \\ type de l'arete (ambigu)\
 43 
    s=v1[3]; \\ type de l'arete (ambigu)\
51 
\\  Nouveau pave et ses aretes, manquantes ou pas\
 44 
\\  Nouveau pave et ses aretes, manquantes ou pas\
52 
    w0=vector(n+1);\
 45 
    w0=vector(n+1);\
53 
    w0[n+1]=gg=mob_mul(cd0[v1[4]][n+1],g[s]);\
 46 
    w0[n+1]=gg=mob_mul(cd0[v1[4]][n+1],g[s]);\
Line 64... Line 57...
64 
      w0[t2]=a=cd2[s2][2]; cd1[a][5]=0; listput(cdd1,[cd1[a][4],#cd0+1,a]);\
 57 
      w0[t2]=a=cd2[s2][2]; cd1[a][5]=0; listput(cdd1,[cd1[a][4],#cd0+1,a]);\
65 
      s2=cd1[a][1]+cd1[a][2]-s2; t2=t2%n+1);\
 58 
      s2=cd1[a][1]+cd1[a][2]-s2; t2=t2%n+1);\
66 
    while(t1!=t2, \\ Il y a au moins deux aretes a creer\
 59 
    while(t1!=t2, \\ Il y a au moins deux aretes a creer\
67 
      if(s1<s2,\
 60 
      if(s1<s2,\
68 
        z=mob(gg,v[t1]);\
 61 
        z=mob(gg,v[t1]);\
69 
        listput(cd2,[d[t1]-1,#cd1+1,z,norm(z)<r2]);\
 62 
        listput(cd2,[d[t1]-1,#cd1+1,z,t1,norm(z)<r2]);\
70 
        listput(cd1,[s1,#cd2,t1,#cd0+1,cd2[s1][4]||cd2[#cd2][4]]); w0[t1]=#cd1;\
 63 
        listput(cd1,[s1,#cd2,t1,#cd0+1,cd2[s1][5]||cd2[#cd2][5]]); w0[t1]=#cd1;\
71 
        cd2[s1][1]-=1; cd2[s1][2]=#cd1; s1=#cd2; t1=(t1-2)%n+1,\
 64 
        cd2[s1][1]-=1; cd2[s1][2]=#cd1; s1=#cd2; t1=(t1-2)%n+1,\
72 
        z=mob(gg,v[t2%n+1]);\
 65 
        z=mob(gg,v[t2%n+1]);\
73 
        listput(cd2,[d[t2%n+1]-1,#cd1+1,z,norm(z)<r2]);\
 66 
        listput(cd2,[d[t2%n+1]-1,#cd1+1,z,t2%n+1,norm(z)<r2]);\
74 
        listput(cd1,[s2,#cd2,t2,#cd0+1,cd2[s2][4]||cd2[#cd2][4]]); w0[t2]=#cd1;\
 67 
        listput(cd1,[s2,#cd2,t2,#cd0+1,cd2[s2][5]||cd2[#cd2][5]]); w0[t2]=#cd1;\
75 
        cd2[s2][1]-=1; cd2[s2][2]=#cd1; s2=#cd2; t2=t2%n+1));\
 68 
        cd2[s2][1]-=1; cd2[s2][2]=#cd1; s2=#cd2; t2=t2%n+1));\
76 
      listput(cd1,[s1,s2,t1,#cd0+1,cd2[s1][4]||cd2[s2][4]]); w0[t1]=#cd1;\
 69 
      listput(cd1,[s1,s2,t1,#cd0+1,cd2[s1][5]||cd2[s2][5]]); w0[t1]=#cd1;\
77 
      cd2[s1][1]-=1; cd2[s1][2]=#cd1; cd2[s2][1]-=1; cd2[s2][2]=#cd1;\
 70 
      cd2[s1][1]-=1; cd2[s1][2]=#cd1; cd2[s2][1]-=1; cd2[s2][2]=#cd1;\
78 
      listput(cd0,w0)));\
 71 
      listput(cd0,w0)));\
- 
 
 72 
  centres=vector(#cd0);\
79 
  for(f=1,#cd0,\
 73 
  for(f=1,#cd0,\
- 
 
 74 
    w=cd0[f]; g=w[#w]; centres[f]=mob(g,z0); w[#w]=g[3];\
80 
    w=cd0[f];a=cd1[w[1]];b=cd1[w[n]];\
 75 
    a=cd1[w[1]];b=cd1[w[n]];\
81 
    s=a[1];if(s!=b[1]&&s!=b[2],s=a[2]);\
 76 
    s=a[1];if(s!=b[1]&&s!=b[2],s=a[2]);\
82 
    for(i=1,n,a=cd1[w[i]];w[i]=s;s=a[1]+a[2]-s);\
 77 
    for(i=1,n,a=cd1[w[i]];w[i]=s;s=a[1]+a[2]-s);\
83 
    cd0[f]=w);\
 78 
    cd0[f]=w);\
84 
  [vector(#cd2,i,cd2[i][3]),Vec(cd0),Vec(cd1),Vec(cdd1)]\
 79 
  [vector(#cd2,i,cd2[i][3..4]),Vec(cd0),Vec(cd1),centres,Vec(cdd1)]\
85 
};\
 80 
};\
86 
abc(A,B,C)={\
 81 
abc(A,B,C)={\
87 
  if (A+B+C >= Pi, return(0));\
 82 
  if (A+B+C >= Pi, return(0));\
88 
  my(cha=(cos(A)+cos(B)*cos(C))/(sin(B)*sin(C)),\
 83 
  my(cha=(cos(A)+cos(B)*cos(C))/(sin(B)*sin(C)),\
89 
    chb=(cos(B)+cos(A)*cos(C))/(sin(A)*sin(C)),\
 84 
    chb=(cos(B)+cos(A)*cos(C))/(sin(A)*sin(C)),\
90 
    chc=(cos(C)+cos(B)*cos(A))/(sin(B)*sin(A)));\
 85 
    chc=(cos(C)+cos(B)*cos(A))/(sin(B)*sin(A)));\
91 
  [sqrt((cha-1)/(cha+1)),sqrt((chb-1)/(chb+1)),sqrt((chc-1)/(chc+1))]\
 86 
  [sqrt((cha-1)/(cha+1)),sqrt((chb-1)/(chb+1)),sqrt((chc-1)/(chc+1))]\
92 
};\
 87 
};\
93 
tangentiel(a,centre)={\
 88 
tangentiel(a,auCentre)={\
94 
  my(l,cs=apply(x->cos(x/2),a),\
 89 
  my(l,cs=apply(x->cos(x/2),a),rays=vector(1+#a),\
95 
    k=solve(t=0,1,vecsum(apply(x->asin(t*x),cs))-Pi),\
 90 
    k=solve(t=0,1,vecsum(apply(x->asin(t*x),cs))-Pi),\
96 
    R=sqrt(2/(1+k)-1), g=[1,0,0], h, res=vector(#a));\
 91 
    R=sqrt(2/(1+k)-1), g=[1,0,0], h, res=vector(#a));\
97 
  if(centre,g=lft_fwd(lft_fwd([1,0,0],-asin(k*cs[1]),R),Pi/2,0));\
 92 
  if(auCentre,g=lft_fwd(lft_fwd([1,0,0],-asin(k*cs[1]),R),Pi/2,0));\
98 
  for(i=1,#a,\
 93 
  for(i=1,#a,\
99 
    l=abc(Pi/2,a[i]/2,asin(k*cs[i]))[3];\
 94 
    rays[i]=l=abc(Pi/2,a[i]/2,asin(k*cs[i]))[3];\
100 
    g=lft_fwd(g,0,l);\
 95 
    g=lft_fwd(g,0,l);\
101 
    res[i]=mob(g,0);\
 96 
    res[i]=mob(g,0);\
102 
    g=lft_fwd(g,Pi-a[i],l));\
 97 
    g=lft_fwd(g,Pi-a[i],l));\
- 
 
 98 
  rays[#rays]=R;\
103 
  [res,R]\
 99 
  [res,rays]\
104 
};\
 100 
};\
105 
\
 101 
\
106 
catalan(d,limite,centre)={\
 102 
catalan(d,limite,auCentre)={\
107 
  my([h,R]=tangentiel(apply(x->2*Pi/x,d),centre));\
 103 
  my([h,rays]=tangentiel(apply(x->2*Pi/x,d),auCentre));\
- 
 
 104 
  [hyp_pav(h,d,if(auCentre,0,rays[#rays]*I),limite),rays];\
- 
 
 105 
};\
- 
 
 106 
\
108 
  [hyp_pav(h,d,limite),R,if(centre,0,R*I)]\
 107 
wims_catalan(d,limite,auCentre,option)={\
- 
 
 108 
  my([pavage,rays]=catalan(d,limite,auCentre));\
- 
 
 109 
  my([sommets,paves,aretes,centres,daretes]=pavage,R,z,p1,p2);\
- 
 
 110 
  my(res0,res1,res2,res3,res4,n=#paves[1]-1,temp);\
- 
 
 111 
  if(option==1 || option==3 ,\
- 
 
 112 
    res1=matrix(#sommets,2,i,j,if(j==1,real(sommets[i][1]),imag(sommets[i][1])));\
- 
 
 113 
    res0=matrix(#paves,n+2,i,j,if(j==1,n,paves[i][j-1]));\
- 
 
 114 
    res2=List(); for(i=1,#paves,listput(res2,Vec(res0[i,])));\
- 
 
 115 
  );\
- 
 
 116 
  if(option==2 || option==3,\
- 
 
 117 
    res3=matrix(#paves,2,i,j,if(j==1,real(centres[i]),imag(centres[i])));\
- 
 
 118 
    temp=vector(#paves,i,List());\
- 
 
 119 
    foreach(daretes,x,listput(temp[x[1]],x[2]));\
- 
 
 120 
    res4=List();\
- 
 
 121 
    for(i=1,#paves,if(#temp[i],listinsert(temp[i],i,1);listput(res4,Vec(temp[i])))));\
- 
 
 122 
  [res1,Vec(res2),res3,Vec(res4)];\
109 
}\
 123 
};\