New Loopy tiling: 'Great Great Dodecagonal'.

Officially known as the '3-4-6-12 tiling', according to, e.g.,
https://en.wikipedia.org/wiki/3-4-6-12_tiling .

Thanks to Michael Quevillon for contributing this patch (and for
choosing a less hard-to-remember name for the tiling :-).

diff --git a/grid.c b/grid.c
index 6a90c9942e3a44edff78696e9c6ffd00e554cdce..4929b5c7d3c99547183543560a9180f815c555df 100644 (file)
--- a/grid.c
+++ b/grid.c
@@ -2571,6 +2571,175 @@ static grid *grid_new_greatdodecagonal(int width, int height, const char *desc)
     return g;
 }
 
+static void grid_size_greatgreatdodecagonal(int width, int height,
+                                            int *tilesize, int *xextent, int *yextent)
+{
+    int a = DODEC_A;
+    int b = DODEC_B;
+
+    *tilesize = DODEC_TILESIZE;
+    *xextent = (4*a + 4*b) * (width-1) + 2*(2*a + b) + 2*a + 2*b;
+    *yextent = (6*a + 2*b) * (height-1) + 2*(2*a + b);
+}
+
+static grid *grid_new_greatgreatdodecagonal(int width, int height, const char *desc)
+{
+    int x, y;
+    /* Vector for side of triangle - ratio is close to sqrt(3) */
+    int a = DODEC_A;
+    int b = DODEC_B;
+
+    /* Upper bounds - don't have to be exact */
+    int max_faces = 50 * width * height;
+    int max_dots = 300 * width * height;
+
+    tree234 *points;
+
+    grid *g = grid_empty();
+    g->tilesize = DODEC_TILESIZE;
+    g->faces = snewn(max_faces, grid_face);
+    g->dots = snewn(max_dots, grid_dot);
+
+    points = newtree234(grid_point_cmp_fn);
+
+    for (y = 0; y < height; y++) {
+        for (x = 0; x < width; x++) {
+            grid_dot *d;
+            /* centre of dodecagon */
+            int px = (4*a + 4*b) * x;
+            int py = (6*a + 2*b) * y;
+            if (y % 2)
+                px += 2*a + 2*b;
+
+            /* dodecagon */
+            grid_face_add_new(g, 12);
+            d = grid_get_dot(g, points, px + (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
+            d = grid_get_dot(g, points, px + (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 1);
+            d = grid_get_dot(g, points, px + (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 2);
+            d = grid_get_dot(g, points, px + (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 3);
+            d = grid_get_dot(g, points, px + (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 4);
+            d = grid_get_dot(g, points, px + (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 5);
+            d = grid_get_dot(g, points, px - (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 6);
+            d = grid_get_dot(g, points, px - (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 7);
+            d = grid_get_dot(g, points, px - (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 8);
+            d = grid_get_dot(g, points, px - (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 9);
+            d = grid_get_dot(g, points, px - (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 10);
+            d = grid_get_dot(g, points, px - (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 11);
+
+            /* hexagon on top right of dodecagon */
+            if (y && (x < width - 1 || !(y % 2))) {
+                grid_face_add_new(g, 6);
+                d = grid_get_dot(g, points, px + (a + 2*b), py - (4*a + b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + (a + 2*b), py - (2*a + b)); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + (a +   b), py - (  a + b)); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px + (a      ), py - (2*a + b)); grid_face_set_dot(g, d, 3);
+                d = grid_get_dot(g, points, px + (a      ), py - (4*a + b)); grid_face_set_dot(g, d, 4);
+                d = grid_get_dot(g, points, px + (a +   b), py - (5*a + b)); grid_face_set_dot(g, d, 5);
+            }
+
+            /* hexagon on right of dodecagon*/
+            if (x < width - 1) {
+                grid_face_add_new(g, 6);
+                d = grid_get_dot(g, points, px + (2*a + 3*b), py -   a); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + (2*a + 3*b), py +   a); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + (2*a + 2*b), py + 2*a); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px + (2*a +   b), py +   a); grid_face_set_dot(g, d, 3);
+                d = grid_get_dot(g, points, px + (2*a +   b), py -   a); grid_face_set_dot(g, d, 4);
+                d = grid_get_dot(g, points, px + (2*a + 2*b), py - 2*a); grid_face_set_dot(g, d, 5);
+            }
+
+            /* hexagon on bottom right  of dodecagon */
+            if ((y < height - 1) && (x < width - 1 || !(y % 2))) {
+                grid_face_add_new(g, 6);
+                d = grid_get_dot(g, points, px + (a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + (a + 2*b), py + (4*a + b)); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + (a +   b), py + (5*a + b)); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px + (a      ), py + (4*a + b)); grid_face_set_dot(g, d, 3);
+                d = grid_get_dot(g, points, px + (a      ), py + (2*a + b)); grid_face_set_dot(g, d, 4);
+                d = grid_get_dot(g, points, px + (a +   b), py + (  a + b)); grid_face_set_dot(g, d, 5);
+            }
+
+            /* square on top right of dodecagon */
+            if (y && (x < width - 1 )) {
+                grid_face_add_new(g, 4);
+                d = grid_get_dot(g, points, px + (  a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + (2*a + 2*b), py - (2*a      )); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + (2*a +   b), py - (  a      )); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px + (  a +   b), py - (  a +   b)); grid_face_set_dot(g, d, 3);
+            }
+
+            /* square on bottom right of dodecagon */
+            if ((y < height - 1) && (x < width - 1 )) {
+                grid_face_add_new(g, 4);
+                d = grid_get_dot(g, points, px + (2*a + 2*b), py + (2*a      )); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + (  a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + (  a +   b), py + (  a +   b)); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px + (2*a +   b), py + (  a      )); grid_face_set_dot(g, d, 3);
+            }
+
+            /* square below dodecagon */
+            if ((y < height - 1) && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
+                grid_face_add_new(g, 4);
+                d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + a, py + (4*a + b)); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px - a, py + (4*a + b)); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 3);
+            }
+
+            /* square on bottom left of dodecagon */
+            if (x && (y < height - 1)) {
+                grid_face_add_new(g, 4);
+                d = grid_get_dot(g, points, px - (2*a +   b), py + (  a      )); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px - (  a +   b), py + (  a +   b)); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px - (  a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px - (2*a + 2*b), py + (2*a      )); grid_face_set_dot(g, d, 3);
+            }
+
+            /* square on top left of dodecagon */
+            if (x && y) {
+                grid_face_add_new(g, 4);
+                d = grid_get_dot(g, points, px - (  a +   b), py - (  a +   b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px - (2*a +   b), py - (  a      )); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px - (2*a + 2*b), py - (2*a      )); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px - (  a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 3);
+
+            }
+
+            /* square above dodecagon */
+            if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
+                grid_face_add_new(g, 4);
+                d = grid_get_dot(g, points, px + a, py - (4*a + b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 2);
+                d = grid_get_dot(g, points, px - a, py - (4*a + b)); grid_face_set_dot(g, d, 3);
+            }
+
+            /* upper triangle (v) */
+            if (y && (x < width - 1)) {
+                grid_face_add_new(g, 3);
+                d = grid_get_dot(g, points, px + (3*a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + (2*a + 2*b), py - (2*a      )); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + (  a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 2);
+            }
+
+            /* lower triangle (^) */
+            if ((y < height - 1) && (x < width - 1)) {
+                grid_face_add_new(g, 3);
+                d = grid_get_dot(g, points, px + (3*a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + (  a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + (2*a + 2*b), py + (2*a      )); grid_face_set_dot(g, d, 2);
+            }
+        }
+    }
+
+    freetree234(points);
+    assert(g->num_faces <= max_faces);
+    assert(g->num_dots <= max_dots);
+
+    grid_make_consistent(g);
+    return g;
+}
+
 typedef struct setface_ctx
 {
     int xmin, xmax, ymin, ymax;

diff --git a/grid.h b/grid.h
index 17d0aa196157c3e14d5e7838c79631833ea09f02..fb8ac48790ac34b16e41d13e325875bad8513ac4 100644 (file)
--- a/grid.h
+++ b/grid.h
@@ -105,6 +105,7 @@ typedef struct grid {
   A(FLORET,floret) \
   A(DODECAGONAL,dodecagonal) \
   A(GREATDODECAGONAL,greatdodecagonal) \
+  A(GREATGREATDODECAGONAL,greatgreatdodecagonal) \
   A(PENROSE_P2,penrose_p2_kite) \
   A(PENROSE_P3,penrose_p3_thick)
 

diff --git a/loopy.c b/loopy.c
index 44d51eeacaf42f58bdd47335e3e3ba585943e8ce..15623eeb367605e458d5292892fc63b6d4dafbae 100644 (file)
--- a/loopy.c
+++ b/loopy.c
@@ -258,6 +258,7 @@ static void check_caches(const solver_state* sstate);
     A(Great-Dodecagonal,GRID_GREATDODECAGONAL,2,2) \
     A(Penrose (kite/dart),GRID_PENROSE_P2,3,3) \
     A(Penrose (rhombs),GRID_PENROSE_P3,3,3)
+    A(Great-Great-Dodecagonal,GRID_GREATGREATDODECAGONAL,2,2) \
 
 #define GRID_NAME(title,type,amin,omin) #title,
 #define GRID_CONFIG(title,type,amin,omin) ":" #title
@@ -505,6 +506,7 @@ static const game_params presets[] = {
     {  3,  3, DIFF_HARD, 8 },
     {  3,  3, DIFF_HARD, 9 },
     {  3,  3, DIFF_HARD, 10 },
+    {  3,  2, DIFF_HARD, 13 },
     {  6,  6, DIFF_HARD, 11 },
     {  6,  6, DIFF_HARD, 12 },
 #else
@@ -524,6 +526,7 @@ static const game_params presets[] = {
     {  5,  5, DIFF_HARD, 8 },
     {  5,  4, DIFF_HARD, 9 },
     {  5,  4, DIFF_HARD, 10 },
+    {  5,  3, DIFF_HARD, 13 },
     {  10, 10, DIFF_HARD, 11 },
     {  10, 10, DIFF_HARD, 12 }
 #endif