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New Loopy tiling: 'Great Great Dodecagonal'.

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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 :-).
This commit is contained in:
Simon Tatham
2017-04-23 07:41:46 +01:00
parent eedea41320
commit e37d915f44
3 changed files with 173 additions and 0 deletions
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169
grid.c
View File

@ -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;

1
grid.h
View File

@ -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)

3
loopy.c
View File

@ -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