New grid type: the trihexagonal tiling, or 'kagome lattice'.

Regular hexagons and equilateral triangles in strict alternation, with
two of each interleaved around each vertex.
https://en.wikipedia.org/wiki/Trihexagonal_tiling

Thanks to Michael Quevillon for the patch.

1 files changed, 96 insertions, 0 deletions

diff --git a/grid.c b/grid.c
index 52648e5..b5e6bb0 100644
--- a/grid.c
+++ b/grid.c
@@ -2060,6 +2060,102 @@ static grid *grid_new_greathexagonal(int width, int height, const char *desc)
     return g;
 }
 
+#define KAGOME_TILESIZE 18
+/* Vector for side of triangle - ratio is close to sqrt(3) */
+#define KAGOME_A 15
+#define KAGOME_B 26
+
+static void grid_size_kagome(int width, int height,
+                             int *tilesize, int *xextent, int *yextent)
+{
+    int a = KAGOME_A;
+    int b = KAGOME_B;
+
+    *tilesize = KAGOME_TILESIZE;
+    *xextent = (4*a) * (width-1) + 6*a;
+    *yextent = (2*b) * (height-1) + 2*b;
+}
+
+static grid *grid_new_kagome(int width, int height, const char *desc)
+{
+    int x, y;
+    int a = KAGOME_A;
+    int b = KAGOME_B;
+
+    /* Upper bounds - don't have to be exact */
+    int max_faces = 6 * (width + 1) * (height + 1);
+    int max_dots = 6 * width * height;
+
+    tree234 *points;
+
+    grid *g = grid_empty();
+    g->tilesize = KAGOME_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 hexagon */
+            int px = (4*a) * x;
+            int py = (2*b) * y;
+            if (y % 2)
+                px += 2*a;
+
+            /* hexagon */
+            grid_face_add_new(g, 6);
+            d = grid_get_dot(g, points, px +   a, py -   b); grid_face_set_dot(g, d, 0);
+            d = grid_get_dot(g, points, px + 2*a, py      ); grid_face_set_dot(g, d, 1);
+            d = grid_get_dot(g, points, px +   a, py +   b); grid_face_set_dot(g, d, 2);
+            d = grid_get_dot(g, points, px -   a, py +   b); grid_face_set_dot(g, d, 3);
+            d = grid_get_dot(g, points, px - 2*a, py      ); grid_face_set_dot(g, d, 4);
+            d = grid_get_dot(g, points, px -   a, py -   b); grid_face_set_dot(g, d, 5);
+
+            /* Triangle above right */
+            if ((x < width - 1) || (!(y % 2) && y)) {
+                grid_face_add_new(g, 3);
+                d = grid_get_dot(g, points, px + 3*a, py - b); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px + 2*a, py    ); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px +   a, py - b); grid_face_set_dot(g, d, 2);
+            }
+
+            /* Triangle below right */
+            if ((x < width - 1) || (!(y % 2) && (y < height - 1))) {
+                grid_face_add_new(g, 3);
+                d = grid_get_dot(g, points, px + 3*a, py + b); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px +   a, py + b); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px + 2*a, py    ); grid_face_set_dot(g, d, 2);
+            }
+
+            /* Left triangles */
+            if (!x && (y % 2)) {
+                /* Triangle above left */
+                grid_face_add_new(g, 3);
+                d = grid_get_dot(g, points, px -   a, py - b); grid_face_set_dot(g, d, 0);
+                d = grid_get_dot(g, points, px - 2*a, py    ); grid_face_set_dot(g, d, 1);
+                d = grid_get_dot(g, points, px - 3*a, py - b); grid_face_set_dot(g, d, 2);
+
+                /* Triangle below left */
+                if (y < height - 1) {
+                    grid_face_add_new(g, 3);
+                    d = grid_get_dot(g, points, px -   a, py + b); grid_face_set_dot(g, d, 0);
+                    d = grid_get_dot(g, points, px - 3*a, py + b); grid_face_set_dot(g, d, 1);
+                    d = grid_get_dot(g, points, px - 2*a, py    ); 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;
+}
+
 #define OCTAGONAL_TILESIZE 40
 /* b/a approx sqrt(2) */
 #define OCTAGONAL_A 29