generators included

generators/README.md

@@ -0,0 +1,14 @@
+For completeness, this directory contains various programs used for generating various tables in HyperRogue.
+
+* Quotient space tables (in `hrmap_quotient` in `cell.cpp`) have been generated with `bring.cpp`, `schmutz.cpp`, `quartic.cpp`, `macbeath.cpp`, and (for Minimal) manually.
+
+* Pattern rules (in `patterns.cpp`) have been generated with patterngen.cpp.
+
+* Precomputed windmaps (`windcodes*` in `complex.cpp`) have been generated by the disabled code in `windmap::create()`.
+
+* Embedded font (`fonttable` in `nofont.cpp`) has been generated with `-DCAP_CREATEFONT=1`.
+
+* Vector graphics (`polydata[]` in `polygons.cpp`) have been generated in the Vector Graphics Editor. Press the Shift+S to generate the data in the required format. (Replace `ID` with `NEWSHAPE, id`.)
+
+Some of these programs are standalone, while some need to be compiled with HyperRogue. These programs are not maintained (they are written once and forgotten), so (in the latter case)
+it is likely that they do no longer work; however, they are still included for reference.

generators/bring.cpp

@@ -0,0 +1,122 @@
+// Bring's Surface generator
+// Copyright (C) 2018 Zeno Rogue, see 'hyper.cpp' for details
+
+#include <stdio.h>
+#include <vector>
+#include <array>
+#include <map>
+#include <algorithm>
+
+using namespace std;
+
+int isize(const auto x) { return x.size(); }
+
+int mul(int a, int b) { 
+  int p = 0;
+  for(int i=0; i<3; i++) if((a>>i)&1)
+  for(int j=0; j<3; j++) if((b>>j)&1)
+    p ^= (1<<(i+j));
+  
+  for(int z=4; z>=0; z--)
+    if(p&(8<<z)) p ^= (11<<z);
+    
+  return p;
+  }
+
+int elements = 0;
+
+vector<array<int, 5>> s5_elements;
+
+map<array<int, 5>, int> back;
+
+int multable[504][504];
+
+int mpow(int a, int n) {
+  int z = a;
+  while(n > 1) z = multable[a][z], n--;
+  return z;
+  }
+
+int inset[504];
+
+int main() {
+  array<int, 5> ar;
+  for(int i=0; i<5; i++) ar[i] = i;
+  
+  do {
+    back[ar] = isize(s5_elements);
+    s5_elements.push_back(ar);
+    }
+  while(next_permutation(ar.begin(), ar.end()));
+  
+  for(int a=0; a<120; a++)
+    for(int b=0; b<120; b++) {
+      array<int, 5> res;
+      for(int i=0; i<5; i++)
+        res[i] = s5_elements[a] [ s5_elements[b][i] ];
+      multable[a][b] = back[res];
+      }
+          
+  int id;
+  
+  for(int a=0; a<120; a++)
+    if(multable[a][a] == a) id = a;
+  
+  printf("id = %d\n", id);
+
+  int xid = 0;
+  
+  int sols = 0;
+
+  for(int R=0; R<120; R++)
+  for(int P=0; P<120; P++) {
+    if(P == 0 && mpow(R, 5) == id) printf("deg5 R\n");
+    if(multable[P][P] != id) continue;
+    if(mpow(multable[R][P], 4) != id) continue;
+    if(mpow(R, 5) != id) continue;
+    xid++;
+    vector<int> allels = {id};
+    inset[id] = xid;
+    for(int i=0; i<isize(allels); i++) {
+      for(int m: {P, R}) {
+        int im = allels[i];
+        int a = multable[im][m];
+        // printf("%d x %d = %d\n", im, m, a);
+        if(inset[a] != xid) inset[a] = xid, allels.push_back(a);
+        }
+      }
+    if(isize(allels) != 120) continue;
+    printf("R = %d P = %d count = %d\n", R, P, isize(allels));
+    for(int a: s5_elements[R]) printf("%d ", a); printf("// ");
+    for(int a: s5_elements[P]) printf("%d ", a); printf("\n");
+    sols++;
+    
+    array<int, 120> cellid;
+    array<int, 120> bycellid;
+
+    for(int a=0; a<120; a++) cellid[a] = 0;
+
+    int ncell = 0;
+    for(int a=0; a<120; a++) if(cellid[a] == 0) {
+      int b = a;
+      for(int s=0; s<5; s++) cellid[b] = ncell + s, bycellid[ncell + s] = b, b = multable[b][R];
+      ncell += 5;
+      }
+    
+    printf("ncell = %d\n", ncell);
+
+    for(int a=0; a<24; a++) {
+      printf("/* %03d */ ", a);
+      for(int b=0; b<5; b++) {
+        printf("%d, ", cellid[multable[bycellid[5*a+b]][P]]);
+        }
+      printf("\n");
+      }
+
+    return 0;
+    }
+  
+  printf("solutions = %d\n", sols);
+
+  return 0;
+  }

generators/macbeath.cpp

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+// Fricke-Macbeath Surface generator
+// Copyright (C) 2018 Zeno Rogue, see 'hyper.cpp' for details
+
+#include <stdio.h>
+#include <vector>
+#include <array>
+#include <map>
+
+using namespace std;
+
+int isize(const auto x) { return x.size(); }
+
+int mul(int a, int b) { 
+  int p = 0;
+  for(int i=0; i<3; i++) if((a>>i)&1)
+  for(int j=0; j<3; j++) if((b>>j)&1)
+    p ^= (1<<(i+j));
+  
+  for(int z=4; z>=0; z--)
+    if(p&(8<<z)) p ^= (11<<z);
+    
+  return p;
+  }
+
+int multable[8][8];
+
+int elements = 0;
+
+vector<array<int, 4>> psl_elements;
+
+int multable_psl[504][504];
+
+map<array<int, 4>, int> back;
+
+int mpow(int a, int n) {
+  int z = a;
+  while(n > 1) z = multable_psl[a][z], n--;
+  return z;
+  }
+
+int inset[504];
+
+int main() {
+  for(int a=0; a<8; a++) {
+    for(int b=0; b<8; b++) printf("%d ", mul(a, b));
+    printf("\n");
+    }
+
+  for(int a=0; a<8; a++)
+    for(int b=0; b<8; b++) 
+      multable[a][b] = mul(a, b);
+
+  for(int a=0; a<8; a++)
+    for(int b=0; b<8; b++) 
+      for(int c=0; c<8; c++)
+        for(int d=0; d<8; d++) 
+          if((multable[a][d] ^ multable[b][c]) == 1) {
+            array<int, 4> arr = { a, b, c, d};
+            psl_elements.emplace_back(arr);
+            }
+          
+  printf("elements = %d\n", isize(psl_elements));
+
+  for(int a=0; a<504; a++) back[psl_elements[a]] = a;
+  
+  for(int a=0; a<504; a++)
+  for(int b=0; b<504; b++) {
+    auto pa = psl_elements[a];
+    auto pb = psl_elements[b];
+    array<int, 4> pc;
+    for(int s=0; s<4; s++) {
+      int s0 = s&2;
+      int s1 = s&1;
+      pc[s] = (multable[pa[s0]][pb[s1]] ^ multable[pa[s0^1]][pb[s1^2]]);
+      }
+    multable_psl[a][b] = back[pc];
+    }
+
+  int id;
+  
+  for(int a=0; a<504; a++)
+    if(multable_psl[a][a] == a) id = a;
+  
+  printf("id = %d\n", id);
+
+  int xid = 0;
+
+  for(int R=0; R<504; R++)
+  for(int P=0; P<504; P++) {
+    if(multable_psl[P][P] != id) continue;
+    if(mpow(multable_psl[R][P], 3) != id) continue;
+    if(mpow(R, 7) != id) continue;
+    xid++;
+    vector<int> allels = {id};
+    inset[id] = xid;
+    for(int i=0; i<isize(allels); i++) {
+      for(int m: {P, R}) {
+        int im = allels[i];
+        int a = multable_psl[im][m];
+        // printf("%d x %d = %d\n", im, m, a);
+        if(inset[a] != xid) inset[a] = xid, allels.push_back(a);
+        }
+      }
+    printf("R = %d P = %d count = %d\n", R, P, isize(allels));
+
+    array<int, 504> cellid;
+    array<int, 504> bycellid;
+
+    for(int a=0; a<504; a++) cellid[a] = 0;
+
+    int ncell = 0;
+    for(int a=0; a<504; a++) if(cellid[a] == 0) {
+      int b = a;
+      for(int s=0; s<7; s++) cellid[b] = ncell + s, bycellid[ncell + s] = b, b = multable_psl[b][R];
+      ncell += 7;
+      }
+    
+    printf("ncell = %d\n", ncell);
+
+    for(int a=0; a<72; a++) {
+      printf("/* %03d */ ", a);
+      for(int b=0; b<7; b++) {
+        printf("%d, ", cellid[multable_psl[bycellid[7*a+b]][P]]);
+        }
+      printf("\n");
+      }
+
+    return 0;
+    }
+
+  return 0;
+  }

generators/quartic.cpp

@@ -0,0 +1,105 @@
+// this generates data for Klein's Quartic (-geo 0 -quartic) and Bolza surface (in -geo 7 -quartic) and 2x Bolza (-geo7 -quartic2)
+// Copyright (C) 2018 Zeno Rogue, see 'hyper.cpp' for details
+
+#include "../init.cpp"
+
+using namespace hr;
+
+int qty;
+
+namespace hr {
+cellwalker& operator += (cellwalker& cw, int spin);
+cellwalker& operator += (cellwalker& cw, wstep_t);
+}
+
+void recursive(cell *c, int col, int dir, int dbl) {
+  c->landparam = col;
+  c->mondir = dir;
+  c->monst = moButterfly;
+  if(S7 == 7) {
+    for(int i=0; i<7; i++) {
+      for(int j=3; j<5; j++) {
+        cellwalker cw(c, dir + i);
+        for(int u=0; u<4; u++) {
+          cw += wstep;
+          cw += j;
+          }
+        cw += -dir;
+        if(cw.c->landparam == -1) recursive(cw.c, col^dbl, dir, dbl);
+        }
+      }
+    }
+  if(S7 == 8) {
+    for(int i=0; i<8; i++) {
+      cellwalker cw(c, dir);
+      cw += i;
+      cw += wstep;
+      cw += 4;
+      cw += wstep;
+      cw += (4-i);
+//    if(cw.c->landparam == -1) recursive(cw.c, (col ^ 1));
+      if(cw.c->landparam == -1) recursive(cw.c, col ^ dbl, cw.spin, dbl);
+      }
+    }
+  }
+
+void generate_quartic(bool dbl) {
+  celllister clgen(cwt.c, S7==7?10:8, 1000000, NULL);
+  int d;
+  for(cell *c1: clgen.lst) { c1->landparam = -1; d = celldist(c1); }
+  for(cell *c1: clgen.lst) if(c1->landparam == -1) {
+    recursive(c1, qty, 0, dbl);
+    qty++;
+    if(dbl) qty++;
+    }
+  vector<unsigned> colors;
+  for(cell *c1: clgen.lst) {
+    if(celldist(c1) >= d-1) continue;
+    if(c1->mov[c1->mondir]->landparam > c1->mov[c1->mondir ^ 4]->landparam)
+      c1->mondir ^= 4;
+    }
+
+  if(0) for(cell *c1: clgen.lst) {
+    if(celldist(c1) >= d-2) continue;
+    vector<int> connections;
+    cellwalker cw(c1, c1->mondir);
+    for(int i=0; i<S7; i++) {
+      cellwalker cwx = cw; cwx += wstep;
+      connections.push_back(cwx.c->landparam * S7 + (cwx.spin - cwx.c->mondir + MODFIXER) % S7);
+      cw += 1;
+      }
+    printf("/* %03d */", c1->landparam);
+    for(int i=0; i<S7; i++) printf(" %d,", connections[i]);
+    printf("\n");
+    }
+  printf("qty = %d\n", qty);
+  for(int i=0; i<qty; i++) colors.push_back(hrand(0x1000000));
+  for(cell *c1: clgen.lst) {
+    c1->landparam = colors[c1->landparam % qty];
+    }
+  }
+
+int readArgs() {
+  using namespace arg;
+           
+  if(0) ;
+  else if(argis("-quartic")) {
+    PHASE(3);
+    start_game();
+    generate_quartic(0);
+    }
+  else if(argis("-quartic2")) {
+    PHASE(3);
+    start_game();
+    generate_quartic(1);
+    }
+  else return 1;
+  return 0;
+  }
+
+auto hook = addHook(hooks_args, 100, readArgs);
+ 
+// Bolza:: genus 2 => Euler characteristic -2
+// octagon: -2/6
+// ~> 6 octagons
+

generators/schmutz.cpp

@@ -0,0 +1,112 @@
+// Schmutz's Surface generator
+// Copyright (C) 2018 Zeno Rogue, see 'hyper.cpp' for details
+
+#include <stdio.h>
+#include <vector>
+#include <array>
+#include <map>
+#include <algorithm>
+
+using namespace std;
+
+void dualize(vector<int>& t) {
+  int N = t.size();
+  /*
+  printf("N = %d\n", N);
+
+  printf("pre dual:\n");
+  for(int a=0; a<N; a++) {
+    printf("%3d, ", t[a]);
+    if(a % 12 == 11) printf("\n");    
+    }
+  
+  printf("post dual:\n");
+  */
+
+  vector<int> tmap(N, -1);
+  vector<int> trmap(N, -1);
+  int s = 0;
+  for(int i=0; i<N; i++) if(tmap[i] == -1) {
+    int j = i;
+    for(int k=0; k<12; k++) {
+      tmap[j] = s;
+      trmap[s] = j;
+      s++;
+      int oj = j;
+      j = t[j];
+      j = (j % 3 == 2) ? (j-2) : (j+1);
+      // printf("%d -> %d\n", oj, j);
+      }
+    if(j != i) printf("not equal\n"), exit(1);
+    // printf("OK\n");
+    }
+  // for(int a: tmap) printf("%d ", a); printf("\n");
+  // for(int a: trmap) printf("%d ", a); printf("\n");
+  vector<int> res(N, -1);
+  for(int i=0; i<N; i++) {
+    // printf("i=%d\n", i);
+    res[i] = tmap[t[trmap[i]]];
+    }
+  // for(int a: res) printf("%d ", a); printf("\n");
+  t = res;
+
+  for(int i=0; i<N; i++) {
+    int a = i;
+    for(int s=0; s<3; s++) {
+      a = res[a];
+      a++;
+      if(a % 12 == 0) a -= 12;
+      }
+    if(a != i) { printf("bug\n"); exit(1); }
+    }
+  }
+
+int main() {
+
+  vector<int> triangles;
+  
+  for(int a=0; a<12; a++) {
+    triangles.emplace_back(3 * ((a+1) % 12) + 1);
+    triangles.emplace_back(3 * ((a+11) % 12));
+    triangles.emplace_back(36 + (a%4) * 3 + 2 - (a/4));
+    }
+  
+  for(int a=0; a<12; a++)
+    triangles.emplace_back(0);
+
+  for(int a=0; a<36; a++) if(triangles[a] >= 36) triangles[triangles[a]] = a;
+  
+  dualize(triangles);
+  
+  for(int a=0; a<48; a++) {
+    if(a % 12 == 0) printf("\n");
+    printf("%3d, ", triangles[a]);
+    }
+  
+  printf("\n");
+  
+  triangles.clear();
+
+  for(int a=0; a<12; a++) {
+    triangles.emplace_back(3 * ((a+1) % 12) + 1);
+    triangles.emplace_back(3 * ((a+11) % 12));
+    triangles.emplace_back(36 + 3 * a);
+    }
+
+  for(int a=0; a<12; a++) {
+    triangles.emplace_back(3 * a + 2);
+    triangles.emplace_back(36 + (3 * a + 36 - 15 + 2) % 36);
+    triangles.emplace_back(36 + (3 * a + 36 + 15 + 1) % 36);
+    }
+  
+  dualize(triangles);
+
+  for(int a=0; a<12*2*3; a++) {
+    if(a % 12 == 0) printf("\n");
+    printf("%3d, ", triangles[a]);
+    }
+  
+  printf("\n");
+  
+  return 0;
+  }