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From James Harvey (via a period of collaborative polishing), a patch
to add two kinds of Penrose tiling to the grid types supported by Loopy. This has involved a certain amount of infrastructure work, because of course the whole point of Penrose tilings is that they don't have to be the same every time: so now grid.c has grown the capacity to describe its grids as strings, and reconstitute them from those string descriptions. Hence a Penrose Loopy game description consists of a string identifying a particular piece of Penrose tiling, followed by the normal Loopy clue encoding. All the existing grid types decline to provide a grid description string, so their Loopy game descriptions have not changed encoding. [originally from svn r9159]
This commit is contained in:
Simon Tatham
43
grid.h
43
grid.h
@ -9,6 +9,8 @@
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#ifndef PUZZLES_GRID_H
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#define PUZZLES_GRID_H
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#include "puzzles.h" /* for random_state */
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/* Useful macros */
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#define SQ(x) ( (x) * (x) )
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@ -89,22 +91,41 @@ typedef struct grid {
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int refcount;
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} grid;
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grid *grid_new_square(int width, int height);
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grid *grid_new_honeycomb(int width, int height);
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grid *grid_new_triangular(int width, int height);
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grid *grid_new_snubsquare(int width, int height);
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grid *grid_new_cairo(int width, int height);
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grid *grid_new_greathexagonal(int width, int height);
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grid *grid_new_octagonal(int width, int height);
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grid *grid_new_kites(int width, int height);
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grid *grid_new_floret(int width, int height);
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grid *grid_new_dodecagonal(int width, int height);
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grid *grid_new_greatdodecagonal(int width, int height);
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/* Grids are specified by type: GRID_SQUARE, GRID_KITE, etc. */
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#define GRIDGEN_LIST(A) \
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A(SQUARE,square) \
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A(HONEYCOMB,honeycomb) \
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A(TRIANGULAR,triangular) \
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A(SNUBSQUARE,snubsquare) \
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A(CAIRO,cairo) \
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A(GREATHEXAGONAL,greathexagonal) \
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A(OCTAGONAL,octagonal) \
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A(KITE,kites) \
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A(FLORET,floret) \
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A(DODECAGONAL,dodecagonal) \
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A(GREATDODECAGONAL,greatdodecagonal) \
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A(PENROSE_P2,penrose_p2_kite) \
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A(PENROSE_P3,penrose_p3_thick)
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#define ENUM(upper,lower) GRID_ ## upper,
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typedef enum grid_type { GRIDGEN_LIST(ENUM) GRID_TYPE_MAX } grid_type;
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#undef ENUM
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/* Free directly after use if non-NULL. Will never contain an underscore
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* (so clients can safely use that as a separator). */
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char *grid_new_desc(grid_type type, int width, int height, random_state *rs);
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char *grid_validate_desc(grid_type type, int width, int height, char *desc);
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grid *grid_new(grid_type type, int width, int height, char *desc);
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void grid_free(grid *g);
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grid_edge *grid_nearest_edge(grid *g, int x, int y);
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void grid_compute_size(grid_type type, int width, int height,
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int *tilesize, int *xextent, int *yextent);
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void grid_find_incentre(grid_face *f);
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#endif /* PUZZLES_GRID_H */
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9
loopy.R
9
loopy.R
@ -1,6 +1,6 @@
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# -*- makefile -*-
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LOOPY_EXTRA = tree234 dsf grid
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LOOPY_EXTRA = tree234 dsf grid penrose
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loopy : [X] GTK COMMON loopy LOOPY_EXTRA loopy-icon|no-icon
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@ -9,6 +9,13 @@ loopy : [G] WINDOWS COMMON loopy LOOPY_EXTRA loopy.res|noicon.res
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loopysolver : [U] loopy[STANDALONE_SOLVER] LOOPY_EXTRA STANDALONE m.lib
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loopysolver : [C] loopy[STANDALONE_SOLVER] LOOPY_EXTRA STANDALONE
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#penrose : [U] penrose[TEST_PENROSE] STANDALONE m.lib
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#penrose : [C] penrose[TEST_PENROSE] STANDALONE
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#test-basis : [U] penrose[TEST_VECTORS] tree234 STANDALONE m.lib
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#test-basis : [C] penrose[TEST_VECTORS] tree234 STANDALONE
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ALL += loopy[COMBINED] LOOPY_EXTRA
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!begin gtk
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209
loopy.c
209
loopy.c
@ -107,7 +107,7 @@ enum {
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};
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struct game_state {
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grid *game_grid;
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grid *game_grid; /* ref-counted (internally) */
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/* Put -1 in a face that doesn't get a clue */
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signed char *clues;
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@ -207,10 +207,6 @@ struct game_params {
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int w, h;
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int diff;
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int type;
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/* Grid generation is expensive, so keep a (ref-counted) reference to the
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* grid for these parameters, and only generate when required. */
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grid *game_grid;
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};
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/* line_drawstate is the same as line_state, but with the extra ERROR
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@ -247,29 +243,31 @@ static void check_caches(const solver_state* sstate);
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/* ------- List of grid generators ------- */
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#define GRIDLIST(A) \
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A(Squares,grid_new_square,3,3) \
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A(Triangular,grid_new_triangular,3,3) \
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A(Honeycomb,grid_new_honeycomb,3,3) \
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A(Snub-Square,grid_new_snubsquare,3,3) \
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A(Cairo,grid_new_cairo,3,4) \
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A(Great-Hexagonal,grid_new_greathexagonal,3,3) \
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A(Octagonal,grid_new_octagonal,3,3) \
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A(Kites,grid_new_kites,3,3) \
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A(Floret,grid_new_floret,1,2) \
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A(Dodecagonal,grid_new_dodecagonal,2,2) \
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A(Great-Dodecagonal,grid_new_greatdodecagonal,2,2)
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A(Squares,GRID_SQUARE,3,3) \
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A(Triangular,GRID_TRIANGULAR,3,3) \
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A(Honeycomb,GRID_HONEYCOMB,3,3) \
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A(Snub-Square,GRID_SNUBSQUARE,3,3) \
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A(Cairo,GRID_CAIRO,3,4) \
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A(Great-Hexagonal,GRID_GREATHEXAGONAL,3,3) \
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A(Octagonal,GRID_OCTAGONAL,3,3) \
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A(Kites,GRID_KITE,3,3) \
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A(Floret,GRID_FLORET,1,2) \
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A(Dodecagonal,GRID_DODECAGONAL,2,2) \
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A(Great-Dodecagonal,GRID_GREATDODECAGONAL,2,2) \
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A(Penrose (kite/dart),GRID_PENROSE_P2,3,3) \
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A(Penrose (rhombs),GRID_PENROSE_P3,3,3)
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#define GRID_NAME(title,fn,amin,omin) #title,
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#define GRID_CONFIG(title,fn,amin,omin) ":" #title
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#define GRID_FN(title,fn,amin,omin) &fn,
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#define GRID_SIZES(title,fn,amin,omin) \
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#define GRID_NAME(title,type,amin,omin) #title,
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#define GRID_CONFIG(title,type,amin,omin) ":" #title
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#define GRID_TYPE(title,type,amin,omin) type,
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#define GRID_SIZES(title,type,amin,omin) \
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{amin, omin, \
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"Width and height for this grid type must both be at least " #amin, \
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"At least one of width and height for this grid type must be at least " #omin,},
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static char const *const gridnames[] = { GRIDLIST(GRID_NAME) };
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#define GRID_CONFIGS GRIDLIST(GRID_CONFIG)
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static grid * (*(grid_fns[]))(int w, int h) = { GRIDLIST(GRID_FN) };
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#define NUM_GRID_TYPES (sizeof(grid_fns) / sizeof(grid_fns[0]))
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static grid_type grid_types[] = { GRIDLIST(GRID_TYPE) };
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#define NUM_GRID_TYPES (sizeof(grid_types) / sizeof(grid_types[0]))
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static const struct {
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int amin, omin;
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char *aerr, *oerr;
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@ -277,13 +275,10 @@ static const struct {
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/* Generates a (dynamically allocated) new grid, according to the
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* type and size requested in params. Does nothing if the grid is already
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* generated. The allocated grid is owned by the params object, and will be
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* freed in free_params(). */
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static void params_generate_grid(game_params *params)
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* generated. */
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static grid *loopy_generate_grid(game_params *params, char *grid_desc)
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{
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if (!params->game_grid) {
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params->game_grid = grid_fns[params->type](params->w, params->h);
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}
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return grid_new(grid_types[params->type], params->w, params->h, grid_desc);
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}
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/* ----------------------------------------------------------------------
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@ -480,8 +475,6 @@ static game_params *default_params(void)
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ret->diff = DIFF_EASY;
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ret->type = 0;
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ret->game_grid = NULL;
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return ret;
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}
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@ -490,44 +483,45 @@ static game_params *dup_params(game_params *params)
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game_params *ret = snew(game_params);
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*ret = *params; /* structure copy */
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if (ret->game_grid) {
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ret->game_grid->refcount++;
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}
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return ret;
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}
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static const game_params presets[] = {
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#ifdef SMALL_SCREEN
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{ 7, 7, DIFF_EASY, 0, NULL },
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{ 7, 7, DIFF_NORMAL, 0, NULL },
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{ 7, 7, DIFF_HARD, 0, NULL },
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{ 7, 7, DIFF_HARD, 1, NULL },
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{ 7, 7, DIFF_HARD, 2, NULL },
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{ 5, 5, DIFF_HARD, 3, NULL },
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{ 7, 7, DIFF_HARD, 4, NULL },
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{ 5, 4, DIFF_HARD, 5, NULL },
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{ 5, 5, DIFF_HARD, 6, NULL },
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{ 5, 5, DIFF_HARD, 7, NULL },
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{ 3, 3, DIFF_HARD, 8, NULL },
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{ 3, 3, DIFF_HARD, 9, NULL },
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{ 3, 3, DIFF_HARD, 10, NULL },
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{ 7, 7, DIFF_EASY, 0 },
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{ 7, 7, DIFF_NORMAL, 0 },
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{ 7, 7, DIFF_HARD, 0 },
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{ 7, 7, DIFF_HARD, 1 },
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{ 7, 7, DIFF_HARD, 2 },
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{ 5, 5, DIFF_HARD, 3 },
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{ 7, 7, DIFF_HARD, 4 },
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{ 5, 4, DIFF_HARD, 5 },
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{ 5, 5, DIFF_HARD, 6 },
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{ 5, 5, DIFF_HARD, 7 },
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{ 3, 3, DIFF_HARD, 8 },
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{ 3, 3, DIFF_HARD, 9 },
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{ 3, 3, DIFF_HARD, 10 },
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{ 6, 6, DIFF_HARD, 11 },
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{ 6, 6, DIFF_HARD, 12 },
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#else
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{ 7, 7, DIFF_EASY, 0, NULL },
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{ 10, 10, DIFF_EASY, 0, NULL },
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{ 7, 7, DIFF_NORMAL, 0, NULL },
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{ 10, 10, DIFF_NORMAL, 0, NULL },
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{ 7, 7, DIFF_HARD, 0, NULL },
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{ 10, 10, DIFF_HARD, 0, NULL },
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{ 10, 10, DIFF_HARD, 1, NULL },
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{ 12, 10, DIFF_HARD, 2, NULL },
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{ 7, 7, DIFF_HARD, 3, NULL },
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{ 9, 9, DIFF_HARD, 4, NULL },
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{ 5, 4, DIFF_HARD, 5, NULL },
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{ 7, 7, DIFF_HARD, 6, NULL },
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{ 5, 5, DIFF_HARD, 7, NULL },
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{ 5, 5, DIFF_HARD, 8, NULL },
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{ 5, 4, DIFF_HARD, 9, NULL },
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{ 5, 4, DIFF_HARD, 10, NULL },
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{ 7, 7, DIFF_EASY, 0 },
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{ 10, 10, DIFF_EASY, 0 },
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{ 7, 7, DIFF_NORMAL, 0 },
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{ 10, 10, DIFF_NORMAL, 0 },
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{ 7, 7, DIFF_HARD, 0 },
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{ 10, 10, DIFF_HARD, 0 },
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{ 10, 10, DIFF_HARD, 1 },
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{ 12, 10, DIFF_HARD, 2 },
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{ 7, 7, DIFF_HARD, 3 },
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{ 9, 9, DIFF_HARD, 4 },
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{ 5, 4, DIFF_HARD, 5 },
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{ 7, 7, DIFF_HARD, 6 },
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{ 5, 5, DIFF_HARD, 7 },
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{ 5, 5, DIFF_HARD, 8 },
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{ 5, 4, DIFF_HARD, 9 },
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{ 5, 4, DIFF_HARD, 10 },
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{ 10, 10, DIFF_HARD, 11 },
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{ 10, 10, DIFF_HARD, 12 }
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#endif
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};
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@ -551,18 +545,11 @@ static int game_fetch_preset(int i, char **name, game_params **params)
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static void free_params(game_params *params)
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{
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if (params->game_grid) {
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grid_free(params->game_grid);
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}
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sfree(params);
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}
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static void decode_params(game_params *params, char const *string)
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{
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if (params->game_grid) {
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grid_free(params->game_grid);
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params->game_grid = NULL;
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}
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params->h = params->w = atoi(string);
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params->diff = DIFF_EASY;
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while (*string && isdigit((unsigned char)*string)) string++;
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@ -641,7 +628,6 @@ static game_params *custom_params(config_item *cfg)
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ret->type = cfg[2].ival;
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ret->diff = cfg[3].ival;
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ret->game_grid = NULL;
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return ret;
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}
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@ -702,14 +688,44 @@ static char *state_to_text(const game_state *state)
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return retval;
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}
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#define GRID_DESC_SEP '_'
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/* Splits up a (optional) grid_desc from the game desc. Returns the
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* grid_desc (which needs freeing) and updates the desc pointer to
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* start of real desc, or returns NULL if no desc. */
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static char *extract_grid_desc(char **desc)
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{
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char *sep = strchr(*desc, GRID_DESC_SEP), *gd;
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int gd_len;
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if (!sep) return NULL;
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gd_len = sep - (*desc);
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gd = snewn(gd_len+1, char);
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memcpy(gd, *desc, gd_len);
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gd[gd_len] = '\0';
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*desc = sep+1;
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return gd;
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}
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/* We require that the params pass the test in validate_params and that the
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* description fills the entire game area */
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static char *validate_desc(game_params *params, char *desc)
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{
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int count = 0;
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grid *g;
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params_generate_grid(params);
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g = params->game_grid;
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char *grid_desc, *ret;
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/* It's pretty inefficient to do this just for validation. All we need to
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* know is the precise number of faces. */
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grid_desc = extract_grid_desc(&desc);
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ret = grid_validate_desc(grid_types[params->type], params->w, params->h, grid_desc);
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if (ret) return ret;
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g = loopy_generate_grid(params, grid_desc);
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if (grid_desc) sfree(grid_desc);
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for (; *desc; ++desc) {
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if ((*desc >= '0' && *desc <= '9') || (*desc >= 'A' && *desc <= 'Z')) {
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@ -728,6 +744,8 @@ static char *validate_desc(game_params *params, char *desc)
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if (count > g->num_faces)
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return "Description too long for board size";
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grid_free(g);
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return NULL;
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}
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@ -809,16 +827,15 @@ static void game_changed_state(game_ui *ui, game_state *oldstate,
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static void game_compute_size(game_params *params, int tilesize,
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int *x, int *y)
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{
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grid *g;
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int grid_width, grid_height, rendered_width, rendered_height;
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int g_tilesize;
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grid_compute_size(grid_types[params->type], params->w, params->h,
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&g_tilesize, &grid_width, &grid_height);
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|
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params_generate_grid(params);
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g = params->game_grid;
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grid_width = g->highest_x - g->lowest_x;
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grid_height = g->highest_y - g->lowest_y;
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/* multiply first to minimise rounding error on integer division */
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rendered_width = grid_width * tilesize / g->tilesize;
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rendered_height = grid_height * tilesize / g->tilesize;
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rendered_width = grid_width * tilesize / g_tilesize;
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rendered_height = grid_height * tilesize / g_tilesize;
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*x = rendered_width + 2 * BORDER(tilesize) + 1;
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*y = rendered_height + 2 * BORDER(tilesize) + 1;
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}
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@ -1836,13 +1853,14 @@ static char *new_game_desc(game_params *params, random_state *rs,
|
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char **aux, int interactive)
|
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{
|
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/* solution and description both use run-length encoding in obvious ways */
|
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char *retval;
|
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char *retval, *game_desc, *grid_desc;
|
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grid *g;
|
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game_state *state = snew(game_state);
|
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game_state *state_new;
|
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params_generate_grid(params);
|
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state->game_grid = g = params->game_grid;
|
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g->refcount++;
|
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grid_desc = grid_new_desc(grid_types[params->type], params->w, params->h, rs);
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state->game_grid = g = loopy_generate_grid(params, grid_desc);
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state->clues = snewn(g->num_faces, signed char);
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state->lines = snewn(g->num_edges, char);
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state->line_errors = snewn(g->num_edges, unsigned char);
|
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@ -1875,10 +1893,19 @@ static char *new_game_desc(game_params *params, random_state *rs,
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goto newboard_please;
|
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}
|
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|
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retval = state_to_text(state);
|
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game_desc = state_to_text(state);
|
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|
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free_game(state);
|
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if (grid_desc) {
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retval = snewn(strlen(grid_desc) + 1 + strlen(game_desc) + 1, char);
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sprintf(retval, "%s%c%s", grid_desc, GRID_DESC_SEP, game_desc);
|
||||
sfree(grid_desc);
|
||||
sfree(game_desc);
|
||||
} else {
|
||||
retval = game_desc;
|
||||
}
|
||||
|
||||
assert(!validate_desc(params, retval));
|
||||
|
||||
return retval;
|
||||
@ -1890,13 +1917,17 @@ static game_state *new_game(midend *me, game_params *params, char *desc)
|
||||
game_state *state = snew(game_state);
|
||||
int empties_to_make = 0;
|
||||
int n,n2;
|
||||
const char *dp = desc;
|
||||
const char *dp;
|
||||
char *grid_desc;
|
||||
grid *g;
|
||||
int num_faces, num_edges;
|
||||
|
||||
params_generate_grid(params);
|
||||
state->game_grid = g = params->game_grid;
|
||||
g->refcount++;
|
||||
grid_desc = extract_grid_desc(&desc);
|
||||
state->game_grid = g = loopy_generate_grid(params, grid_desc);
|
||||
if (grid_desc) sfree(grid_desc);
|
||||
|
||||
dp = desc;
|
||||
|
||||
num_faces = g->num_faces;
|
||||
num_edges = g->num_edges;
|
||||
|
||||
@ -4017,3 +4048,5 @@ int main(int argc, char **argv)
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
/* vim: set shiftwidth=4 tabstop=8: */
|
||||
|
||||
626
penrose.c
Normal file
626
penrose.c
Normal file
@ -0,0 +1,626 @@
|
||||
/* penrose.c
|
||||
*
|
||||
* Penrose tile generator.
|
||||
*
|
||||
* Uses half-tile technique outlined on:
|
||||
*
|
||||
* http://tartarus.org/simon/20110412-penrose/penrose.xhtml
|
||||
*/
|
||||
|
||||
#include <assert.h>
|
||||
#include <string.h>
|
||||
#include <math.h>
|
||||
#include <stdio.h>
|
||||
|
||||
#include "puzzles.h" /* for malloc routines, and PI */
|
||||
#include "penrose.h"
|
||||
|
||||
/* -------------------------------------------------------
|
||||
* 36-degree basis vector arithmetic routines.
|
||||
*/
|
||||
|
||||
/* Imagine drawing a
|
||||
* ten-point 'clock face' like this:
|
||||
*
|
||||
* -E
|
||||
* -D | A
|
||||
* \ | /
|
||||
* -C. \ | / ,B
|
||||
* `-._\|/_,-'
|
||||
* ,-' /|\ `-.
|
||||
* -B' / | \ `C
|
||||
* / | \
|
||||
* -A | D
|
||||
* E
|
||||
*
|
||||
* In case the ASCII art isn't clear, those are supposed to be ten
|
||||
* vectors of length 1, all sticking out from the origin at equal
|
||||
* angular spacing (hence 36 degrees). Our basis vectors are A,B,C,D (I
|
||||
* choose them to be symmetric about the x-axis so that the final
|
||||
* translation into 2d coordinates will also be symmetric, which I
|
||||
* think will avoid minor rounding uglinesses), so our vector
|
||||
* representation sets
|
||||
*
|
||||
* A = (1,0,0,0)
|
||||
* B = (0,1,0,0)
|
||||
* C = (0,0,1,0)
|
||||
* D = (0,0,0,1)
|
||||
*
|
||||
* The fifth vector E looks at first glance as if it needs to be
|
||||
* another basis vector, but in fact it doesn't, because it can be
|
||||
* represented in terms of the other four. Imagine starting from the
|
||||
* origin and following the path -A, +B, -C, +D: you'll find you've
|
||||
* traced four sides of a pentagram, and ended up one E-vector away
|
||||
* from the origin. So we have
|
||||
*
|
||||
* E = (-1,1,-1,1)
|
||||
*
|
||||
* This tells us that we can rotate any vector in this system by 36
|
||||
* degrees: if we start with a*A + b*B + c*C + d*D, we want to end up
|
||||
* with a*B + b*C + c*D + d*E, and we substitute our identity for E to
|
||||
* turn that into a*B + b*C + c*D + d*(-A+B-C+D). In other words,
|
||||
*
|
||||
* rotate_one_notch_clockwise(a,b,c,d) = (-d, d+a, -d+b, d+c)
|
||||
*
|
||||
* and you can verify for yourself that applying that operation
|
||||
* repeatedly starting with (1,0,0,0) cycles round ten vectors and
|
||||
* comes back to where it started.
|
||||
*
|
||||
* The other operation that may be required is to construct vectors
|
||||
* with lengths that are multiples of phi. That can be done by
|
||||
* observing that the vector C-B is parallel to E and has length 1/phi,
|
||||
* and the vector D-A is parallel to E and has length phi. So this
|
||||
* tells us that given any vector, we can construct one which points in
|
||||
* the same direction and is 1/phi or phi times its length, like this:
|
||||
*
|
||||
* divide_by_phi(vector) = rotate(vector, 2) - rotate(vector, 3)
|
||||
* multiply_by_phi(vector) = rotate(vector, 1) - rotate(vector, 4)
|
||||
*
|
||||
* where rotate(vector, n) means applying the above
|
||||
* rotate_one_notch_clockwise primitive n times. Expanding out the
|
||||
* applications of rotate gives the following direct representation in
|
||||
* terms of the vector coordinates:
|
||||
*
|
||||
* divide_by_phi(a,b,c,d) = (b-d, c+d-b, a+b-c, c-a)
|
||||
* multiply_by_phi(a,b,c,d) = (a+b-d, c+d, a+b, c+d-a)
|
||||
*
|
||||
* and you can verify for yourself that those two operations are
|
||||
* inverses of each other (as you'd hope!).
|
||||
*
|
||||
* Having done all of this, testing for equality between two vectors is
|
||||
* a trivial matter of comparing the four integer coordinates. (Which
|
||||
* it _wouldn't_ have been if we'd kept E as a fifth basis vector,
|
||||
* because then (-1,1,-1,1,0) and (0,0,0,0,1) would have had to be
|
||||
* considered identical. So leaving E out is vital.)
|
||||
*/
|
||||
|
||||
struct vector { int a, b, c, d; };
|
||||
|
||||
static vector v_origin()
|
||||
{
|
||||
vector v;
|
||||
v.a = v.b = v.c = v.d = 0;
|
||||
return v;
|
||||
}
|
||||
|
||||
/* We start with a unit vector of B: this means we can easily
|
||||
* draw an isoceles triangle centred on the X axis. */
|
||||
#ifdef TEST_VECTORS
|
||||
|
||||
static vector v_unit()
|
||||
{
|
||||
vector v;
|
||||
|
||||
v.b = 1;
|
||||
v.a = v.c = v.d = 0;
|
||||
return v;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
#define COS54 0.5877852
|
||||
#define SIN54 0.8090169
|
||||
#define COS18 0.9510565
|
||||
#define SIN18 0.3090169
|
||||
|
||||
/* These two are a bit rough-and-ready for now. Note that B/C are
|
||||
* 18 degrees from the x-axis, and A/D are 54 degrees. */
|
||||
double v_x(vector *vs, int i)
|
||||
{
|
||||
return (vs[i].a + vs[i].d) * COS54 +
|
||||
(vs[i].b + vs[i].c) * COS18;
|
||||
}
|
||||
|
||||
double v_y(vector *vs, int i)
|
||||
{
|
||||
return (vs[i].a - vs[i].d) * SIN54 +
|
||||
(vs[i].b - vs[i].c) * SIN18;
|
||||
|
||||
}
|
||||
|
||||
static vector v_trans(vector v, vector trans)
|
||||
{
|
||||
v.a += trans.a;
|
||||
v.b += trans.b;
|
||||
v.c += trans.c;
|
||||
v.d += trans.d;
|
||||
return v;
|
||||
}
|
||||
|
||||
static vector v_rotate_36(vector v)
|
||||
{
|
||||
vector vv;
|
||||
vv.a = -v.d;
|
||||
vv.b = v.d + v.a;
|
||||
vv.c = -v.d + v.b;
|
||||
vv.d = v.d + v.c;
|
||||
return vv;
|
||||
}
|
||||
|
||||
static vector v_rotate(vector v, int ang)
|
||||
{
|
||||
int i;
|
||||
|
||||
assert((ang % 36) == 0);
|
||||
while (ang < 0) ang += 360;
|
||||
ang = 360-ang;
|
||||
for (i = 0; i < (ang/36); i++)
|
||||
v = v_rotate_36(v);
|
||||
return v;
|
||||
}
|
||||
|
||||
#ifdef TEST_VECTORS
|
||||
|
||||
static vector v_scale(vector v, int sc)
|
||||
{
|
||||
v.a *= sc;
|
||||
v.b *= sc;
|
||||
v.c *= sc;
|
||||
v.d *= sc;
|
||||
return v;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
static vector v_growphi(vector v)
|
||||
{
|
||||
vector vv;
|
||||
vv.a = v.a + v.b - v.d;
|
||||
vv.b = v.c + v.d;
|
||||
vv.c = v.a + v.b;
|
||||
vv.d = v.c + v.d - v.a;
|
||||
return vv;
|
||||
}
|
||||
|
||||
static vector v_shrinkphi(vector v)
|
||||
{
|
||||
vector vv;
|
||||
vv.a = v.b - v.d;
|
||||
vv.b = v.c + v.d - v.b;
|
||||
vv.c = v.a + v.b - v.c;
|
||||
vv.d = v.c - v.a;
|
||||
return vv;
|
||||
}
|
||||
|
||||
#ifdef TEST_VECTORS
|
||||
|
||||
static const char *v_debug(vector v)
|
||||
{
|
||||
static char buf[255];
|
||||
sprintf(buf,
|
||||
"(%d,%d,%d,%d)[%2.2f,%2.2f]",
|
||||
v.a, v.b, v.c, v.d, v_x(&v,0), v_y(&v,0));
|
||||
return buf;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
/* -------------------------------------------------------
|
||||
* Tiling routines.
|
||||
*/
|
||||
|
||||
vector xform_coord(vector vo, int shrink, vector vtrans, int ang)
|
||||
{
|
||||
if (shrink < 0)
|
||||
vo = v_shrinkphi(vo);
|
||||
else if (shrink > 0)
|
||||
vo = v_growphi(vo);
|
||||
|
||||
vo = v_rotate(vo, ang);
|
||||
vo = v_trans(vo, vtrans);
|
||||
|
||||
return vo;
|
||||
}
|
||||
|
||||
|
||||
#define XFORM(n,o,s,a) vs[(n)] = xform_coord(v_edge, (s), vs[(o)], (a))
|
||||
|
||||
static int penrose_p2_small(penrose_state *state, int depth, int flip,
|
||||
vector v_orig, vector v_edge);
|
||||
|
||||
static int penrose_p2_large(penrose_state *state, int depth, int flip,
|
||||
vector v_orig, vector v_edge)
|
||||
{
|
||||
vector vv_orig, vv_edge;
|
||||
|
||||
#ifdef DEBUG_PENROSE
|
||||
{
|
||||
vector vs[3];
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 0, 0);
|
||||
XFORM(2, 0, 0, -36*flip);
|
||||
|
||||
state->new_tile(state, vs, 3, depth);
|
||||
}
|
||||
#endif
|
||||
|
||||
if (flip > 0) {
|
||||
vector vs[4];
|
||||
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 0, -36);
|
||||
XFORM(2, 0, 0, 0);
|
||||
XFORM(3, 0, 0, 36);
|
||||
|
||||
state->new_tile(state, vs, 4, depth);
|
||||
}
|
||||
if (depth >= state->max_depth) return 0;
|
||||
|
||||
vv_orig = v_trans(v_orig, v_rotate(v_edge, -36*flip));
|
||||
vv_edge = v_rotate(v_edge, 108*flip);
|
||||
|
||||
penrose_p2_small(state, depth+1, flip,
|
||||
v_orig, v_shrinkphi(v_edge));
|
||||
|
||||
penrose_p2_large(state, depth+1, flip,
|
||||
vv_orig, v_shrinkphi(vv_edge));
|
||||
penrose_p2_large(state, depth+1, -flip,
|
||||
vv_orig, v_shrinkphi(vv_edge));
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
static int penrose_p2_small(penrose_state *state, int depth, int flip,
|
||||
vector v_orig, vector v_edge)
|
||||
{
|
||||
vector vv_orig;
|
||||
|
||||
#ifdef DEBUG_PENROSE
|
||||
{
|
||||
vector vs[3];
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 0, 0);
|
||||
XFORM(2, 0, -1, -36*flip);
|
||||
|
||||
state->new_tile(state, vs, 3, depth);
|
||||
}
|
||||
#endif
|
||||
|
||||
if (flip > 0) {
|
||||
vector vs[4];
|
||||
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 0, -72);
|
||||
XFORM(2, 0, -1, -36);
|
||||
XFORM(3, 0, 0, 0);
|
||||
|
||||
state->new_tile(state, vs, 4, depth);
|
||||
}
|
||||
|
||||
if (depth >= state->max_depth) return 0;
|
||||
|
||||
vv_orig = v_trans(v_orig, v_edge);
|
||||
|
||||
penrose_p2_large(state, depth+1, -flip,
|
||||
v_orig, v_shrinkphi(v_rotate(v_edge, -36*flip)));
|
||||
|
||||
penrose_p2_small(state, depth+1, flip,
|
||||
vv_orig, v_shrinkphi(v_rotate(v_edge, -144*flip)));
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
static int penrose_p3_small(penrose_state *state, int depth, int flip,
|
||||
vector v_orig, vector v_edge);
|
||||
|
||||
static int penrose_p3_large(penrose_state *state, int depth, int flip,
|
||||
vector v_orig, vector v_edge)
|
||||
{
|
||||
vector vv_orig;
|
||||
|
||||
#ifdef DEBUG_PENROSE
|
||||
{
|
||||
vector vs[3];
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 1, 0);
|
||||
XFORM(2, 0, 0, -36*flip);
|
||||
|
||||
state->new_tile(state, vs, 3, depth);
|
||||
}
|
||||
#endif
|
||||
|
||||
if (flip > 0) {
|
||||
vector vs[4];
|
||||
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 0, -36);
|
||||
XFORM(2, 0, 1, 0);
|
||||
XFORM(3, 0, 0, 36);
|
||||
|
||||
state->new_tile(state, vs, 4, depth);
|
||||
}
|
||||
if (depth >= state->max_depth) return 0;
|
||||
|
||||
vv_orig = v_trans(v_orig, v_edge);
|
||||
|
||||
penrose_p3_large(state, depth+1, -flip,
|
||||
vv_orig, v_shrinkphi(v_rotate(v_edge, 180)));
|
||||
|
||||
penrose_p3_small(state, depth+1, flip,
|
||||
vv_orig, v_shrinkphi(v_rotate(v_edge, -108*flip)));
|
||||
|
||||
vv_orig = v_trans(v_orig, v_growphi(v_edge));
|
||||
|
||||
penrose_p3_large(state, depth+1, flip,
|
||||
vv_orig, v_shrinkphi(v_rotate(v_edge, -144*flip)));
|
||||
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
static int penrose_p3_small(penrose_state *state, int depth, int flip,
|
||||
vector v_orig, vector v_edge)
|
||||
{
|
||||
vector vv_orig;
|
||||
|
||||
#ifdef DEBUG_PENROSE
|
||||
{
|
||||
vector vs[3];
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 0, 0);
|
||||
XFORM(2, 0, 0, -36*flip);
|
||||
|
||||
state->new_tile(state, vs, 3, depth);
|
||||
}
|
||||
#endif
|
||||
|
||||
if (flip > 0) {
|
||||
vector vs[4];
|
||||
|
||||
vs[0] = v_orig;
|
||||
XFORM(1, 0, 0, -36);
|
||||
XFORM(3, 0, 0, 0);
|
||||
XFORM(2, 3, 0, -36);
|
||||
|
||||
state->new_tile(state, vs, 4, depth);
|
||||
}
|
||||
if (depth >= state->max_depth) return 0;
|
||||
|
||||
/* NB these two are identical to the first two of p3_large. */
|
||||
vv_orig = v_trans(v_orig, v_edge);
|
||||
|
||||
penrose_p3_large(state, depth+1, -flip,
|
||||
vv_orig, v_shrinkphi(v_rotate(v_edge, 180)));
|
||||
|
||||
penrose_p3_small(state, depth+1, flip,
|
||||
vv_orig, v_shrinkphi(v_rotate(v_edge, -108*flip)));
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* -------------------------------------------------------
|
||||
* Utility routines.
|
||||
*/
|
||||
|
||||
double penrose_side_length(double start_size, int depth)
|
||||
{
|
||||
return start_size / pow(PHI, depth);
|
||||
}
|
||||
|
||||
void penrose_count_tiles(int depth, int *nlarge, int *nsmall)
|
||||
{
|
||||
/* Steal sgt's fibonacci thingummy. */
|
||||
}
|
||||
|
||||
/*
|
||||
* It turns out that an acute isosceles triangle with sides in ratio 1:phi:phi
|
||||
* has an incentre which is conveniently 2*phi^-2 of the way from the apex to
|
||||
* the base. Why's that convenient? Because: if we situate the incentre of the
|
||||
* triangle at the origin, then we can place the apex at phi^-2 * (B+C), and
|
||||
* the other two vertices at apex-B and apex-C respectively. So that's an acute
|
||||
* triangle with its long sides of unit length, covering a circle about the
|
||||
* origin of radius 1-(2*phi^-2), which is conveniently enough phi^-3.
|
||||
*
|
||||
* (later mail: this is an overestimate by about 5%)
|
||||
*/
|
||||
|
||||
int penrose(penrose_state *state, int which)
|
||||
{
|
||||
vector vo = v_origin();
|
||||
vector vb = v_origin();
|
||||
|
||||
vo.b = vo.c = -state->start_size;
|
||||
vo = v_shrinkphi(v_shrinkphi(vo));
|
||||
|
||||
vb.b = state->start_size;
|
||||
|
||||
if (which == PENROSE_P2)
|
||||
return penrose_p2_large(state, 0, 1, vo, vb);
|
||||
else
|
||||
return penrose_p3_small(state, 0, 1, vo, vb);
|
||||
}
|
||||
|
||||
/*
|
||||
* We're asked for a MxN grid, which just means a tiling fitting into roughly
|
||||
* an MxN space in some kind of reasonable unit - say, the side length of the
|
||||
* two-arrow edges of the tiles. By some reasoning in a previous email, that
|
||||
* means we want to pick some subarea of a circle of radius 3.11*sqrt(M^2+N^2).
|
||||
* To cover that circle, we need to subdivide a triangle large enough that it
|
||||
* contains a circle of that radius.
|
||||
*
|
||||
* Hence: start with those three vectors marking triangle vertices, scale them
|
||||
* all up by phi repeatedly until the radius of the inscribed circle gets
|
||||
* bigger than the target, and then recurse into that triangle with the same
|
||||
* recursion depth as the number of times you scaled up. That will give you
|
||||
* tiles of unit side length, covering a circle big enough that if you randomly
|
||||
* choose an orientation and coordinates within the circle, you'll be able to
|
||||
* get any valid piece of Penrose tiling of size MxN.
|
||||
*/
|
||||
#define INCIRCLE_RADIUS 0.22426 /* phi^-3 less 5%: see above */
|
||||
|
||||
void penrose_calculate_size(int which, int tilesize, int w, int h,
|
||||
double *required_radius, int *start_size, int *depth)
|
||||
{
|
||||
double rradius, size;
|
||||
int n = 0;
|
||||
|
||||
/*
|
||||
* Fudge factor to scale P2 and P3 tilings differently. This
|
||||
* doesn't seem to have much relevance to questions like the
|
||||
* average number of tiles per unit area; it's just aesthetic.
|
||||
*/
|
||||
if (which == PENROSE_P2)
|
||||
tilesize = tilesize * 3 / 2;
|
||||
else
|
||||
tilesize = tilesize * 5 / 4;
|
||||
|
||||
rradius = tilesize * 3.11 * sqrt((double)(w*w + h*h));
|
||||
size = tilesize;
|
||||
|
||||
while ((size * INCIRCLE_RADIUS) < rradius) {
|
||||
n++;
|
||||
size = size * PHI;
|
||||
}
|
||||
|
||||
*start_size = (int)size;
|
||||
*depth = n;
|
||||
*required_radius = rradius;
|
||||
}
|
||||
|
||||
/* -------------------------------------------------------
|
||||
* Test code.
|
||||
*/
|
||||
|
||||
#ifdef TEST_PENROSE
|
||||
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
|
||||
int show_recursion = 0;
|
||||
int ntiles, nfinal;
|
||||
|
||||
int test_cb(penrose_state *state, vector *vs, int n, int depth)
|
||||
{
|
||||
int i, xoff = 0, yoff = 0;
|
||||
double l = penrose_side_length(state->start_size, depth);
|
||||
double rball = l / 10.0;
|
||||
const char *col;
|
||||
|
||||
ntiles++;
|
||||
if (state->max_depth == depth) {
|
||||
col = n == 4 ? "black" : "green";
|
||||
nfinal++;
|
||||
} else {
|
||||
if (!show_recursion)
|
||||
return 0;
|
||||
col = n == 4 ? "red" : "blue";
|
||||
}
|
||||
if (n != 4) yoff = state->start_size;
|
||||
|
||||
printf("<polygon points=\"");
|
||||
for (i = 0; i < n; i++) {
|
||||
printf("%s%f,%f", (i == 0) ? "" : " ",
|
||||
v_x(vs, i) + xoff, v_y(vs, i) + yoff);
|
||||
}
|
||||
printf("\" style=\"fill: %s; fill-opacity: 0.2; stroke: %s\" />\n", col, col);
|
||||
printf("<ellipse cx=\"%f\" cy=\"%f\" rx=\"%f\" ry=\"%f\" fill=\"%s\" />",
|
||||
v_x(vs, 0) + xoff, v_y(vs, 0) + yoff, rball, rball, col);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
void usage_exit()
|
||||
{
|
||||
fprintf(stderr, "Usage: penrose-test [--recursion] P2|P3 SIZE DEPTH\n");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
penrose_state ps;
|
||||
int which = 0;
|
||||
|
||||
while (--argc > 0) {
|
||||
char *p = *++argv;
|
||||
if (!strcmp(p, "-h") || !strcmp(p, "--help")) {
|
||||
usage_exit();
|
||||
} else if (!strcmp(p, "--recursion")) {
|
||||
show_recursion = 1;
|
||||
} else if (*p == '-') {
|
||||
fprintf(stderr, "Unrecognised option '%s'\n", p);
|
||||
exit(1);
|
||||
} else {
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
if (argc < 3) usage_exit();
|
||||
|
||||
if (strcmp(argv[0], "P2") == 0) which = PENROSE_P2;
|
||||
else if (strcmp(argv[0], "P3") == 0) which = PENROSE_P3;
|
||||
else usage_exit();
|
||||
|
||||
ps.start_size = atoi(argv[1]);
|
||||
ps.max_depth = atoi(argv[2]);
|
||||
ps.new_tile = test_cb;
|
||||
|
||||
ntiles = nfinal = 0;
|
||||
|
||||
printf("\
|
||||
<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n\
|
||||
<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 20010904//EN\"\n\
|
||||
\"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd\">\n\
|
||||
\n\
|
||||
<svg xmlns=\"http://www.w3.org/2000/svg\"\n\
|
||||
xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n\n");
|
||||
|
||||
printf("<g>\n");
|
||||
penrose(&ps, which);
|
||||
printf("</g>\n");
|
||||
|
||||
printf("<!-- %d tiles and %d leaf tiles total -->\n",
|
||||
ntiles, nfinal);
|
||||
|
||||
printf("</svg>");
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
#ifdef TEST_VECTORS
|
||||
|
||||
static void dbgv(const char *msg, vector v)
|
||||
{
|
||||
printf("%s: %s\n", msg, v_debug(v));
|
||||
}
|
||||
|
||||
int main(int argc, const char *argv[])
|
||||
{
|
||||
vector v = v_unit();
|
||||
|
||||
dbgv("unit vector", v);
|
||||
v = v_rotate(v, 36);
|
||||
dbgv("rotated 36", v);
|
||||
v = v_scale(v, 2);
|
||||
dbgv("scaled x2", v);
|
||||
v = v_shrinkphi(v);
|
||||
dbgv("shrunk phi", v);
|
||||
v = v_rotate(v, -36);
|
||||
dbgv("rotated -36", v);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
#endif
|
||||
/* vim: set shiftwidth=4 tabstop=8: */
|
||||
59
penrose.h
Normal file
59
penrose.h
Normal file
@ -0,0 +1,59 @@
|
||||
/* penrose.h
|
||||
*
|
||||
* Penrose tiling functions.
|
||||
*
|
||||
* Provides an interface with which to generate Penrose tilings
|
||||
* by recursive subdivision of an initial tile of choice (one of the
|
||||
* four sets of two pairs kite/dart, or thin/thick rhombus).
|
||||
*
|
||||
* You supply a callback function and a context pointer, which is
|
||||
* called with each tile in turn: you choose how many times to recurse.
|
||||
*/
|
||||
|
||||
#ifndef _PENROSE_H
|
||||
#define _PENROSE_H
|
||||
|
||||
#ifndef PHI
|
||||
#define PHI 1.6180339887
|
||||
#endif
|
||||
|
||||
typedef struct vector vector;
|
||||
|
||||
double v_x(vector *vs, int i);
|
||||
double v_y(vector *vs, int i);
|
||||
|
||||
typedef struct penrose_state penrose_state;
|
||||
|
||||
/* Return non-zero to clip the tree here (i.e. not recurse
|
||||
* below this tile).
|
||||
*
|
||||
* Parameters are state, vector array, npoints, depth.
|
||||
* ctx is inside state.
|
||||
*/
|
||||
typedef int (*tile_callback)(penrose_state *, vector *, int, int);
|
||||
|
||||
struct penrose_state {
|
||||
int start_size; /* initial side length */
|
||||
int max_depth; /* Recursion depth */
|
||||
|
||||
tile_callback new_tile;
|
||||
void *ctx; /* for callback */
|
||||
};
|
||||
|
||||
enum { PENROSE_P2, PENROSE_P3 };
|
||||
|
||||
extern int penrose(penrose_state *state, int which);
|
||||
|
||||
/* Returns the side-length of a penrose tile at recursion level
|
||||
* gen, given a starting side length. */
|
||||
extern double penrose_side_length(double start_size, int depth);
|
||||
|
||||
/* Returns the count of each type of tile at a given recursion depth. */
|
||||
extern void penrose_count_tiles(int gen, int *nlarge, int *nsmall);
|
||||
|
||||
/* Calculate start size and recursion depth required to produce a
|
||||
* width-by-height sized patch of penrose tiles with the given tilesize */
|
||||
extern void penrose_calculate_size(int which, int tilesize, int w, int h,
|
||||
double *required_radius, int *start_size, int *depth);
|
||||
|
||||
#endif
|
||||
Reference in New Issue
Block a user