ternary tiling

binary-tiling.cpp

@@ -127,6 +127,12 @@ EX namespace binary {
       else
         h->emeraldval = ((parent->emeraldval - d1) * 7508 + 15015) % 15015;
       }
+    if(geometry == gTernary) {
+      if(d < 2)
+        h->emeraldval = (parent->emeraldval * 3 + d) % 10010;
+      else
+        h->emeraldval = ((parent->emeraldval - d1) * 3337 + 2*10010) % 10010;
+      }
     if(WDIM == 3 && h->c7) make_binary_lands(parent, h);
     #if DEBUG_BINARY_TILING
     xcode[h] = expected_xcode(parent, d);
@@ -239,6 +245,24 @@ EX namespace binary {
                 return path(h, 4, 2, {3, 4, 1});
             }
           }
+        case gTernary: {
+          switch(d) {
+            case 0: case 1: case 2:
+              return build(parent, d, 4, 6, d, 1);
+            case 4:
+              return build(parent, 4, parent->zebraval, 6, nextdir(3), -1);
+            case 3:
+              if(parent->zebraval < 2)
+                return path(h, 3, 5, {4, parent->zebraval + 1});
+              else
+                return path(h, 3, 5, {4, 3, 0});
+            case 5:
+              if(parent->zebraval > 0)
+                return path(h, 5, 3, {4, parent->zebraval - 1});
+              else
+                return path(h, 5, 3, {4, 5, 2});
+            }
+          }
         #if MAXMDIM >= 4         
         case gBinary3: {
           switch(d) {
@@ -506,6 +530,7 @@ EX namespace binary {
   
   EX int updir() {
     if(geometry == gBinary4) return 3;
+    if(geometry == gTernary) return 4;
     if(geometry == gBinaryTiling) return 5;
     if(penrose) return 0;
     if(!binarytiling) return 0;
@@ -523,6 +548,14 @@ EX namespace binary {
       direct_tmatrix[4] = parabolic(-1);
       use_direct = 1+2+4+16;
       }
+    if(geometry == gTernary) {
+      direct_tmatrix[0] = xpush(-log(3)) * parabolic(-1);
+      direct_tmatrix[1] = xpush(-log(3));
+      direct_tmatrix[2] = xpush(-log(3)) * parabolic(+1);
+      direct_tmatrix[3] = parabolic(1);
+      direct_tmatrix[5] = parabolic(-1);
+      use_direct = 1+2+4+8+32;
+      }
     if(geometry == gBinary3) {
       direct_tmatrix[0] = xpush(-log(2)) * parabolic3(-1, -1);
       direct_tmatrix[1] = xpush(-log(2)) * parabolic3(1, -1);
@@ -892,24 +925,46 @@ EX hyperpoint get_corner_horo_coordinates(cell *c, int i) {
   ld yx = log(2) / 2;
   ld yy = yx;
   ld xx = 1 / sqrt(2)/2;
-  if(geometry == gBinaryTiling) switch(gmod(i, c->type)) {
+  switch(geometry) {
-    case 0: return point2(-yy, xx);
+    case gBinaryTiling:    
-    case 1: return point2(yy, 2*xx);
+      switch(gmod(i, c->type)) {
-    case 2: return point2(yy, xx);
+        case 0: return point2(-yy, xx);
-    case 3: return point2(yy, -xx);
+        case 1: return point2(yy, 2*xx);
-    case 4: return point2(yy, -2*xx);
+        case 2: return point2(yy, xx);
-    case 5: return point2(-yy, -xx);
+        case 3: return point2(yy, -xx);
-    case 6: return point2(-yy, 0);    
+        case 4: return point2(yy, -2*xx);
-    default: return point2(0, 0);
+        case 5: return point2(-yy, -xx);
-    }
+        case 6: return point2(-yy, 0);    
-  else switch(gmod(i, c->type)) {
+        default: return point2(0, 0);
-    case 0: return point2(yy, -2*xx);
+        }
-    case 1: return point2(yy, +0*xx);
+    
-    case 2: return point2(yy, +2*xx);
+    case gBinary4:
-    case 3: return point2(-yy, xx);
+      switch(gmod(i, c->type)) {
-    case 4: return point2(-yy, -xx);
+        case 0: return point2(yy, -2*xx);
-    default: return point2(0, 0);
+        case 1: return point2(yy, +0*xx);
+        case 2: return point2(yy, +2*xx);
+        case 3: return point2(-yy, xx);
+        case 4: return point2(-yy, -xx);
+        default: return point2(0, 0);
+        }
+    
+    case gTernary:
+      yy = log(3) / 2;
+      xx = 1 / sqrt(3) / 2;
+      switch(gmod(i, c->type)) {
+        case 0: return point2(yy, -3*xx);
+        case 1: return point2(yy, -1*xx);
+        case 2: return point2(yy, +1*xx);
+        case 3: return point2(yy, +3*xx);
+        case 4: return point2(-yy, xx);
+        case 5: return point2(-yy, -xx);
+        default: return point2(0, 0);
+        }
+    
+    default:
+      return point2(0, 0);
     }
+  return point2(0, 0);
   }
 
 

classes.cpp

@@ -585,8 +585,9 @@ vector<geometryinfo> ginf = {
   {"kd2",    "none",    "kite-and-dart",                              "kd2",      4, 3, qPENROSE,  giEuclid2, 0x48000, {{7, 7}}, eVariation::pure},
   {"kd3",    "none",    "kite-and-dart on horospheres",               "kd3",     12, 3, qsBP,      giHyperb3, 0x48200, {{7, 3}}, eVariation::pure},
   {"nil",    "none",    "Nil geometry",                               "nil",      6, 3, 0,         giNil,     0x48600, {{7, 5}}, eVariation::pure},
-  {"product","none",    "product space",                              "product",  7, 3, qHYBRID,   giProduct, 0x48400, {{7, 3}}, eVariation::pure},
+  {"product","none",    "product space",                              "product",  7, 3, qHYBRID,   giProduct, 0x00000, {{7, 3}}, eVariation::pure},
-  {"twisted","none",    "rotation space",                             "twisted",  7, 3, qHYBRID,   giSL2,     0x49000, {{6, 4}}, eVariation::pure},
+  {"twisted","none",    "rotation space",                             "twisted",  7, 3, qHYBRID,   giSL2,     0x00000, {{6, 4}}, eVariation::pure},
+  {"ternary","none",    "standard ternary tiling",                    "ternary",  6, 3, qBINARY,   giHyperb2, 0x48400, {{6, 4}}, eVariation::pure},
   };
 
   // bits: 9, 10, 15, 16, (reserved for later) 17, 18

classes.h

@@ -215,6 +215,7 @@ enum eGeometry {
   gField435, gField534,
   gBinary4, gSol,
   gKiteDart2, gKiteDart3, gNil, gProduct, gRotSpace,
+  gTernary, 
   gGUARD};
 
 enum eGeometryClass { gcHyperbolic, gcEuclid, gcSphere, gcSol, gcNil, gcProduct, gcSL2 };

floorshapes.cpp

@@ -673,6 +673,17 @@ void geometry_information::generate_floorshapes() {
       }
     }
 
+  else if(geometry == gTernary) {
+    heptagon modelh;
+    cell model;
+    model.master = &modelh;
+    model.type = S7; 
+    for(int i: {0,1,2}) {
+      modelh.zebraval = i;
+      generate_floorshapes_for(i, &model, 1, 0);
+      }
+    }
+
   else if(PURE && geometry != gBinaryTiling && geosupport_football() < 2) {
     cell model;
     model.type = S7; 
@@ -793,7 +804,7 @@ EX int shvid(cell *c) {
     return c->type-6;
   else if(penrose)
     return kite::getshape(c->master);
-  else if(geometry == gBinary4)
+  else if(geometry == gBinary4 || geometry == gTernary)
     return c->master->zebraval;
   else if(PURE)
     return 0;

geometry2.cpp

@@ -554,6 +554,18 @@ EX hyperpoint nearcorner(cell *c, int i) {
     neis[4] = binary::get_horopoint(0, -1);
     return neis[i];
     }
+  if(geometry == gTernary) {
+    ld yx = log(3) / 2;
+    ld yy = yx;
+    hyperpoint neis[6];
+    neis[0] = binary::get_horopoint(2*yy, -1);
+    neis[1] = binary::get_horopoint(2*yy, +0);
+    neis[2] = binary::get_horopoint(2*yy, +1);
+    neis[3] = binary::get_horopoint(0, 1);
+    neis[4] = binary::get_horopoint(-2*yy, c->master->zebraval / 3.);
+    neis[5] = binary::get_horopoint(0, -1);
+    return neis[i];
+    }
   if(penrose) {
     if(approx_nearcorner)
       return kite::get_corner(c, i, 3) + kite::get_corner(c, i+1, 3) - C0;

graph.cpp

@@ -4619,7 +4619,7 @@ void draw_grid_at(cell *c, const transmatrix& V) {
     }
   #endif
   #if CAP_BT
-  else if(binarytiling && WDIM == 2) {
+  else if(binarytiling && WDIM == 2 && geometry != gTernary) {
     ld yx = log(2) / 2;
     ld yy = yx;
     ld xx = 1 / sqrt(2)/2;