cube.c

   1 /*
   2  * cube.c: Cube game.
   3  */
   4
   5 #include <stdio.h>
   6 #include <stdlib.h>
   7 #include <string.h>
   8 #include <assert.h>
   9 #include <ctype.h>
  10 #include <math.h>
  11
  12 #include "puzzles.h"
  13
  14 #define MAXVERTICES 20
  15 #define MAXFACES 20
  16 #define MAXORDER 4
  17 struct solid {
  18     int nvertices;
  19     float vertices[MAXVERTICES * 3];   /* 3*npoints coordinates */
  20     int order;
  21     int nfaces;
  22     int faces[MAXFACES * MAXORDER];    /* order*nfaces point indices */
  23     float normals[MAXFACES * 3];       /* 3*npoints vector components */
  24     float shear;                       /* isometric shear for nice drawing */
  25     float border;                      /* border required around arena */
  26 };
  27
  28 static const struct solid s_tetrahedron = {
  29     4,
  30     {
  31         0.0F, -0.57735026919F, -0.20412414523F,
  32         -0.5F, 0.28867513459F, -0.20412414523F,
  33         0.0F, -0.0F, 0.6123724357F,
  34         0.5F, 0.28867513459F, -0.20412414523F,
  35     },
  36     3, 4,
  37     {
  38         0,2,1, 3,1,2, 2,0,3, 1,3,0
  39     },
  40     {
  41         -0.816496580928F, -0.471404520791F, 0.333333333334F,
  42         0.0F, 0.942809041583F, 0.333333333333F,
  43         0.816496580928F, -0.471404520791F, 0.333333333334F,
  44         0.0F, 0.0F, -1.0F,
  45     },
  46     0.0F, 0.3F
  47 };
  48
  49 static const struct solid s_cube = {
  50     8,
  51     {
  52         -0.5F,-0.5F,-0.5F, -0.5F,-0.5F,+0.5F,
  53         -0.5F,+0.5F,-0.5F, -0.5F,+0.5F,+0.5F,
  54         +0.5F,-0.5F,-0.5F, +0.5F,-0.5F,+0.5F,
  55         +0.5F,+0.5F,-0.5F, +0.5F,+0.5F,+0.5F,
  56     },
  57     4, 6,
  58     {
  59         0,1,3,2, 1,5,7,3, 5,4,6,7, 4,0,2,6, 0,4,5,1, 3,7,6,2
  60     },
  61     {
  62         -1.0F,0.0F,0.0F, 0.0F,0.0F,+1.0F,
  63         +1.0F,0.0F,0.0F, 0.0F,0.0F,-1.0F,
  64         0.0F,-1.0F,0.0F, 0.0F,+1.0F,0.0F
  65     },
  66     0.3F, 0.5F
  67 };
  68
  69 static const struct solid s_octahedron = {
  70     6,
  71     {
  72         -0.5F, -0.28867513459472505F, 0.4082482904638664F,
  73         0.5F, 0.28867513459472505F, -0.4082482904638664F,
  74         -0.5F, 0.28867513459472505F, -0.4082482904638664F,
  75         0.5F, -0.28867513459472505F, 0.4082482904638664F,
  76         0.0F, -0.57735026918945009F, -0.4082482904638664F,
  77         0.0F, 0.57735026918945009F, 0.4082482904638664F,
  78     },
  79     3, 8,
  80     {
  81         4,0,2, 0,5,2, 0,4,3, 5,0,3, 1,4,2, 5,1,2, 4,1,3, 1,5,3
  82     },
  83     {
  84         -0.816496580928F, -0.471404520791F, -0.333333333334F,
  85         -0.816496580928F, 0.471404520791F, 0.333333333334F,
  86         0.0F, -0.942809041583F, 0.333333333333F,
  87         0.0F, 0.0F, 1.0F,
  88         0.0F, 0.0F, -1.0F,
  89         0.0F, 0.942809041583F, -0.333333333333F,
  90         0.816496580928F, -0.471404520791F, -0.333333333334F,
  91         0.816496580928F, 0.471404520791F, 0.333333333334F,
  92     },
  93     0.0F, 0.5F
  94 };
  95
  96 static const struct solid s_icosahedron = {
  97     12,
  98     {
  99         0.0F, 0.57735026919F, 0.75576131408F,
 100         0.0F, -0.93417235896F, 0.17841104489F,
 101         0.0F, 0.93417235896F, -0.17841104489F,
 102         0.0F, -0.57735026919F, -0.75576131408F,
 103         -0.5F, -0.28867513459F, 0.75576131408F,
 104         -0.5F, 0.28867513459F, -0.75576131408F,
 105         0.5F, -0.28867513459F, 0.75576131408F,
 106         0.5F, 0.28867513459F, -0.75576131408F,
 107         -0.80901699437F, 0.46708617948F, 0.17841104489F,
 108         0.80901699437F, 0.46708617948F, 0.17841104489F,
 109         -0.80901699437F, -0.46708617948F, -0.17841104489F,
 110         0.80901699437F, -0.46708617948F, -0.17841104489F,
 111     },
 112     3, 20,
 113     {
 114         8,0,2,  0,9,2,  1,10,3, 11,1,3,  0,4,6,
 115         4,1,6,  5,2,7,  3,5,7,  4,8,10,  8,5,10,
 116         9,6,11, 7,9,11,  0,8,4,  9,0,6,  10,1,4,
 117         1,11,6, 8,2,5,  2,9,7,  3,10,5, 11,3,7,
 118     },
 119     {
 120         -0.356822089773F, 0.87267799625F, 0.333333333333F,
 121         0.356822089773F, 0.87267799625F, 0.333333333333F,
 122         -0.356822089773F, -0.87267799625F, -0.333333333333F,
 123         0.356822089773F, -0.87267799625F, -0.333333333333F,
 124         -0.0F, 0.0F, 1.0F,
 125         0.0F, -0.666666666667F, 0.745355992501F,
 126         0.0F, 0.666666666667F, -0.745355992501F,
 127         0.0F, 0.0F, -1.0F,
 128         -0.934172358963F, -0.12732200375F, 0.333333333333F,
 129         -0.934172358963F, 0.12732200375F, -0.333333333333F,
 130         0.934172358963F, -0.12732200375F, 0.333333333333F,
 131         0.934172358963F, 0.12732200375F, -0.333333333333F,
 132         -0.57735026919F, 0.333333333334F, 0.745355992501F,
 133         0.57735026919F, 0.333333333334F, 0.745355992501F,
 134         -0.57735026919F, -0.745355992501F, 0.333333333334F,
 135         0.57735026919F, -0.745355992501F, 0.333333333334F,
 136         -0.57735026919F, 0.745355992501F, -0.333333333334F,
 137         0.57735026919F, 0.745355992501F, -0.333333333334F,
 138         -0.57735026919F, -0.333333333334F, -0.745355992501F,
 139         0.57735026919F, -0.333333333334F, -0.745355992501F,
 140     },
 141     0.0F, 0.8F
 142 };
 143
 144 enum {
 145     TETRAHEDRON, CUBE, OCTAHEDRON, ICOSAHEDRON
 146 };
 147 static const struct solid *solids[] = {
 148     &s_tetrahedron, &s_cube, &s_octahedron, &s_icosahedron
 149 };
 150
 151 enum {
 152     COL_BACKGROUND,
 153     COL_BORDER,
 154     COL_BLUE,
 155     NCOLOURS
 156 };
 157
 158 enum { LEFT, RIGHT, UP, DOWN, UP_LEFT, UP_RIGHT, DOWN_LEFT, DOWN_RIGHT };
 159
 160 #define PREFERRED_GRID_SCALE 48
 161 #define GRID_SCALE (ds->gridscale)
 162 #define ROLLTIME 0.13F
 163
 164 #define SQ(x) ( (x) * (x) )
 165
 166 #define MATMUL(ra,m,a) do { \
 167     float rx, ry, rz, xx = (a)[0], yy = (a)[1], zz = (a)[2], *mat = (m); \
 168     rx = mat[0] * xx + mat[3] * yy + mat[6] * zz; \
 169     ry = mat[1] * xx + mat[4] * yy + mat[7] * zz; \
 170     rz = mat[2] * xx + mat[5] * yy + mat[8] * zz; \
 171     (ra)[0] = rx; (ra)[1] = ry; (ra)[2] = rz; \
 172 } while (0)
 173
 174 #define APPROXEQ(x,y) ( SQ(x-y) < 0.1 )
 175
 176 struct grid_square {
 177     float x, y;
 178     int npoints;
 179     float points[8];                   /* maximum */
 180     int directions[8];                 /* bit masks showing point pairs */
 181     int flip;
 182     int tetra_class;
 183 };
 184
 185 struct game_params {
 186     int solid;
 187     /*
 188      * Grid dimensions. For a square grid these are width and
 189      * height respectively; otherwise the grid is a hexagon, with
 190      * the top side and the two lower diagonals having length d1
 191      * and the remaining three sides having length d2 (so that
 192      * d1==d2 gives a regular hexagon, and d2==0 gives a triangle).
 193      */
 194     int d1, d2;
 195 };
 196
 197 typedef struct game_grid game_grid;
 198 struct game_grid {
 199     int refcount;
 200     struct grid_square *squares;
 201     int nsquares;
 202 };
 203
 204 #define SET_SQUARE(state, i, val) \
 205     ((state)->bluemask[(i)/32] &= ~(1 << ((i)%32)), \
 206      (state)->bluemask[(i)/32] |= ((!!val) << ((i)%32)))
 207 #define GET_SQUARE(state, i) \
 208     (((state)->bluemask[(i)/32] >> ((i)%32)) & 1)
 209
 210 struct game_state {
 211     struct game_params params;
 212     const struct solid *solid;
 213     int *facecolours;
 214     game_grid *grid;
 215     unsigned long *bluemask;
 216     int current;                       /* index of current grid square */
 217     int sgkey[2];                      /* key-point indices into grid sq */
 218     int dgkey[2];                      /* key-point indices into grid sq */
 219     int spkey[2];                      /* key-point indices into polyhedron */
 220     int dpkey[2];                      /* key-point indices into polyhedron */
 221     int previous;
 222     float angle;
 223     int completed;
 224     int movecount;
 225 };
 226
 227 static game_params *default_params(void)
 228 {
 229     game_params *ret = snew(game_params);
 230
 231     ret->solid = CUBE;
 232     ret->d1 = 4;
 233     ret->d2 = 4;
 234
 235     return ret;
 236 }
 237
 238 static int game_fetch_preset(int i, char **name, game_params **params)
 239 {
 240     game_params *ret = snew(game_params);
 241     char *str;
 242
 243     switch (i) {
 244       case 0:
 245         str = "Cube";
 246         ret->solid = CUBE;
 247         ret->d1 = 4;
 248         ret->d2 = 4;
 249         break;
 250       case 1:
 251         str = "Tetrahedron";
 252         ret->solid = TETRAHEDRON;
 253         ret->d1 = 1;
 254         ret->d2 = 2;
 255         break;
 256       case 2:
 257         str = "Octahedron";
 258         ret->solid = OCTAHEDRON;
 259         ret->d1 = 2;
 260         ret->d2 = 2;
 261         break;
 262       case 3:
 263         str = "Icosahedron";
 264         ret->solid = ICOSAHEDRON;
 265         ret->d1 = 3;
 266         ret->d2 = 3;
 267         break;
 268       default:
 269         sfree(ret);
 270         return FALSE;
 271     }
 272
 273     *name = dupstr(str);
 274     *params = ret;
 275     return TRUE;
 276 }
 277
 278 static void free_params(game_params *params)
 279 {
 280     sfree(params);
 281 }
 282
 283 static game_params *dup_params(const game_params *params)
 284 {
 285     game_params *ret = snew(game_params);
 286     *ret = *params;                    /* structure copy */
 287     return ret;
 288 }
 289
 290 static void decode_params(game_params *ret, char const *string)
 291 {
 292     switch (*string) {
 293       case 't': ret->solid = TETRAHEDRON; string++; break;
 294       case 'c': ret->solid = CUBE;        string++; break;
 295       case 'o': ret->solid = OCTAHEDRON;  string++; break;
 296       case 'i': ret->solid = ICOSAHEDRON; string++; break;
 297       default: break;
 298     }
 299     ret->d1 = ret->d2 = atoi(string);
 300     while (*string && isdigit((unsigned char)*string)) string++;
 301     if (*string == 'x') {
 302         string++;
 303         ret->d2 = atoi(string);
 304     }
 305 }
 306
 307 static char *encode_params(const game_params *params, int full)
 308 {
 309     char data[256];
 310
 311     assert(params->solid >= 0 && params->solid < 4);
 312     sprintf(data, "%c%dx%d", "tcoi"[params->solid], params->d1, params->d2);
 313
 314     return dupstr(data);
 315 }
 316 typedef void (*egc_callback)(void *, struct grid_square *);
 317
 318 static void enum_grid_squares(const game_params *params, egc_callback callback,
 319                               void *ctx)
 320 {
 321     const struct solid *solid = solids[params->solid];
 322
 323     if (solid->order == 4) {
 324         int x, y;
 325
 326         for (y = 0; y < params->d2; y++)
 327             for (x = 0; x < params->d1; x++) {
 328                 struct grid_square sq;
 329
 330                 sq.x = (float)x;
 331                 sq.y = (float)y;
 332                 sq.points[0] = x - 0.5F;
 333                 sq.points[1] = y - 0.5F;
 334                 sq.points[2] = x - 0.5F;
 335                 sq.points[3] = y + 0.5F;
 336                 sq.points[4] = x + 0.5F;
 337                 sq.points[5] = y + 0.5F;
 338                 sq.points[6] = x + 0.5F;
 339                 sq.points[7] = y - 0.5F;
 340                 sq.npoints = 4;
 341
 342                 sq.directions[LEFT]  = 0x03;   /* 0,1 */
 343                 sq.directions[RIGHT] = 0x0C;   /* 2,3 */
 344                 sq.directions[UP]    = 0x09;   /* 0,3 */
 345                 sq.directions[DOWN]  = 0x06;   /* 1,2 */
 346                 sq.directions[UP_LEFT] = 0;   /* no diagonals in a square */
 347                 sq.directions[UP_RIGHT] = 0;   /* no diagonals in a square */
 348                 sq.directions[DOWN_LEFT] = 0;   /* no diagonals in a square */
 349                 sq.directions[DOWN_RIGHT] = 0;   /* no diagonals in a square */
 350
 351                 sq.flip = FALSE;
 352
 353                 /*
 354                  * This is supremely irrelevant, but just to avoid
 355                  * having any uninitialised structure members...
 356                  */
 357                 sq.tetra_class = 0;
 358
 359                 callback(ctx, &sq);
 360             }
 361     } else {
 362         int row, rowlen, other, i, firstix = -1;
 363         float theight = (float)(sqrt(3) / 2.0);
 364
 365         for (row = 0; row < params->d1 + params->d2; row++) {
 366             if (row < params->d2) {
 367                 other = +1;
 368                 rowlen = row + params->d1;
 369             } else {
 370                 other = -1;
 371                 rowlen = 2*params->d2 + params->d1 - row;
 372             }
 373
 374             /*
 375              * There are `rowlen' down-pointing triangles.
 376              */
 377             for (i = 0; i < rowlen; i++) {
 378                 struct grid_square sq;
 379                 int ix;
 380                 float x, y;
 381
 382                 ix = (2 * i - (rowlen-1));
 383                 x = ix * 0.5F;
 384                 y = theight * row;
 385                 sq.x = x;
 386                 sq.y = y + theight / 3;
 387                 sq.points[0] = x - 0.5F;
 388                 sq.points[1] = y;
 389                 sq.points[2] = x;
 390                 sq.points[3] = y + theight;
 391                 sq.points[4] = x + 0.5F;
 392                 sq.points[5] = y;
 393                 sq.npoints = 3;
 394
 395                 sq.directions[LEFT]  = 0x03;   /* 0,1 */
 396                 sq.directions[RIGHT] = 0x06;   /* 1,2 */
 397                 sq.directions[UP]    = 0x05;   /* 0,2 */
 398                 sq.directions[DOWN]  = 0;      /* invalid move */
 399
 400                 /*
 401                  * Down-pointing triangle: both the up diagonals go
 402                  * up, and the down ones go left and right.
 403                  */
 404                 sq.directions[UP_LEFT] = sq.directions[UP_RIGHT] =
 405                     sq.directions[UP];
 406                 sq.directions[DOWN_LEFT] = sq.directions[LEFT];
 407                 sq.directions[DOWN_RIGHT] = sq.directions[RIGHT];
 408
 409                 sq.flip = TRUE;
 410
 411                 if (firstix < 0)
 412                     firstix = ix & 3;
 413                 ix -= firstix;
 414                 sq.tetra_class = ((row+(ix&1)) & 2) ^ (ix & 3);
 415
 416                 callback(ctx, &sq);
 417             }
 418
 419             /*
 420              * There are `rowlen+other' up-pointing triangles.
 421              */
 422             for (i = 0; i < rowlen+other; i++) {
 423                 struct grid_square sq;
 424                 int ix;
 425                 float x, y;
 426
 427                 ix = (2 * i - (rowlen+other-1));
 428                 x = ix * 0.5F;
 429                 y = theight * row;
 430                 sq.x = x;
 431                 sq.y = y + 2*theight / 3;
 432                 sq.points[0] = x + 0.5F;
 433                 sq.points[1] = y + theight;
 434                 sq.points[2] = x;
 435                 sq.points[3] = y;
 436                 sq.points[4] = x - 0.5F;
 437                 sq.points[5] = y + theight;
 438                 sq.npoints = 3;
 439
 440                 sq.directions[LEFT]  = 0x06;   /* 1,2 */
 441                 sq.directions[RIGHT] = 0x03;   /* 0,1 */
 442                 sq.directions[DOWN]  = 0x05;   /* 0,2 */
 443                 sq.directions[UP]    = 0;      /* invalid move */
 444
 445                 /*
 446                  * Up-pointing triangle: both the down diagonals go
 447                  * down, and the up ones go left and right.
 448                  */
 449                 sq.directions[DOWN_LEFT] = sq.directions[DOWN_RIGHT] =
 450                     sq.directions[DOWN];
 451                 sq.directions[UP_LEFT] = sq.directions[LEFT];
 452                 sq.directions[UP_RIGHT] = sq.directions[RIGHT];
 453
 454                 sq.flip = FALSE;
 455
 456                 if (firstix < 0)
 457                     firstix = (ix - 1) & 3;
 458                 ix -= firstix;
 459                 sq.tetra_class = ((row+(ix&1)) & 2) ^ (ix & 3);
 460
 461                 callback(ctx, &sq);
 462             }
 463         }
 464     }
 465 }
 466
 467 static int grid_area(int d1, int d2, int order)
 468 {
 469     /*
 470      * An NxM grid of squares has NM squares in it.
 471      *
 472      * A grid of triangles with dimensions A and B has a total of
 473      * A^2 + B^2 + 4AB triangles in it. (You can divide it up into
 474      * a side-A triangle containing A^2 subtriangles, a side-B
 475      * triangle containing B^2, and two congruent parallelograms,
 476      * each with side lengths A and B, each therefore containing AB
 477      * two-triangle rhombuses.)
 478      */
 479     if (order == 4)
 480         return d1 * d2;
 481     else
 482         return d1*d1 + d2*d2 + 4*d1*d2;
 483 }
 484
 485 static config_item *game_configure(const game_params *params)
 486 {
 487     config_item *ret = snewn(4, config_item);
 488     char buf[80];
 489
 490     ret[0].name = "Type of solid";
 491     ret[0].type = C_CHOICES;
 492     ret[0].sval = ":Tetrahedron:Cube:Octahedron:Icosahedron";
 493     ret[0].ival = params->solid;
 494
 495     ret[1].name = "Width / top";
 496     ret[1].type = C_STRING;
 497     sprintf(buf, "%d", params->d1);
 498     ret[1].sval = dupstr(buf);
 499     ret[1].ival = 0;
 500
 501     ret[2].name = "Height / bottom";
 502     ret[2].type = C_STRING;
 503     sprintf(buf, "%d", params->d2);
 504     ret[2].sval = dupstr(buf);
 505     ret[2].ival = 0;
 506
 507     ret[3].name = NULL;
 508     ret[3].type = C_END;
 509     ret[3].sval = NULL;
 510     ret[3].ival = 0;
 511
 512     return ret;
 513 }
 514
 515 static game_params *custom_params(const config_item *cfg)
 516 {
 517     game_params *ret = snew(game_params);
 518
 519     ret->solid = cfg[0].ival;
 520     ret->d1 = atoi(cfg[1].sval);
 521     ret->d2 = atoi(cfg[2].sval);
 522
 523     return ret;
 524 }
 525
 526 static void count_grid_square_callback(void *ctx, struct grid_square *sq)
 527 {
 528     int *classes = (int *)ctx;
 529     int thisclass;
 530
 531     if (classes[4] == 4)
 532         thisclass = sq->tetra_class;
 533     else if (classes[4] == 2)
 534         thisclass = sq->flip;
 535     else
 536         thisclass = 0;
 537
 538     classes[thisclass]++;
 539 }
 540
 541 static char *validate_params(const game_params *params, int full)
 542 {
 543     int classes[5];
 544     int i;
 545
 546     if (params->solid < 0 || params->solid >= lenof(solids))
 547         return "Unrecognised solid type";
 548
 549     if (solids[params->solid]->order == 4) {
 550         if (params->d1 <= 0 || params->d2 <= 0)
 551             return "Both grid dimensions must be greater than zero";
 552     } else {
 553         if (params->d1 <= 0 && params->d2 <= 0)
 554             return "At least one grid dimension must be greater than zero";
 555     }
 556
 557     for (i = 0; i < 4; i++)
 558         classes[i] = 0;
 559     if (params->solid == TETRAHEDRON)
 560         classes[4] = 4;
 561     else if (params->solid == OCTAHEDRON)
 562         classes[4] = 2;
 563     else
 564         classes[4] = 1;
 565     enum_grid_squares(params, count_grid_square_callback, classes);
 566
 567     for (i = 0; i < classes[4]; i++)
 568         if (classes[i] < solids[params->solid]->nfaces / classes[4])
 569             return "Not enough grid space to place all blue faces";
 570
 571     if (grid_area(params->d1, params->d2, solids[params->solid]->order) <
 572         solids[params->solid]->nfaces + 1)
 573         return "Not enough space to place the solid on an empty square";
 574
 575     return NULL;
 576 }
 577
 578 struct grid_data {
 579     int *gridptrs[4];
 580     int nsquares[4];
 581     int nclasses;
 582     int squareindex;
 583 };
 584
 585 static void classify_grid_square_callback(void *ctx, struct grid_square *sq)
 586 {
 587     struct grid_data *data = (struct grid_data *)ctx;
 588     int thisclass;
 589
 590     if (data->nclasses == 4)
 591         thisclass = sq->tetra_class;
 592     else if (data->nclasses == 2)
 593         thisclass = sq->flip;
 594     else
 595         thisclass = 0;
 596
 597     data->gridptrs[thisclass][data->nsquares[thisclass]++] =
 598         data->squareindex++;
 599 }
 600
 601 static char *new_game_desc(const game_params *params, random_state *rs,
 602                            char **aux, int interactive)
 603 {
 604     struct grid_data data;
 605     int i, j, k, m, area, facesperclass;
 606     int *flags;
 607     char *desc, *p;
 608
 609     /*
 610      * Enumerate the grid squares, dividing them into equivalence
 611      * classes as appropriate. (For the tetrahedron, there is one
 612      * equivalence class for each face; for the octahedron there
 613      * are two classes; for the other two solids there's only one.)
 614      */
 615
 616     area = grid_area(params->d1, params->d2, solids[params->solid]->order);
 617     if (params->solid == TETRAHEDRON)
 618         data.nclasses = 4;
 619     else if (params->solid == OCTAHEDRON)
 620         data.nclasses = 2;
 621     else
 622         data.nclasses = 1;
 623     data.gridptrs[0] = snewn(data.nclasses * area, int);
 624     for (i = 0; i < data.nclasses; i++) {
 625         data.gridptrs[i] = data.gridptrs[0] + i * area;
 626         data.nsquares[i] = 0;
 627     }
 628     data.squareindex = 0;
 629     enum_grid_squares(params, classify_grid_square_callback, &data);
 630
 631     facesperclass = solids[params->solid]->nfaces / data.nclasses;
 632
 633     for (i = 0; i < data.nclasses; i++)
 634         assert(data.nsquares[i] >= facesperclass);
 635     assert(data.squareindex == area);
 636
 637     /*
 638      * So now we know how many faces to allocate in each class. Get
 639      * on with it.
 640      */
 641     flags = snewn(area, int);
 642     for (i = 0; i < area; i++)
 643         flags[i] = FALSE;
 644
 645     for (i = 0; i < data.nclasses; i++) {
 646         for (j = 0; j < facesperclass; j++) {
 647             int n = random_upto(rs, data.nsquares[i]);
 648
 649             assert(!flags[data.gridptrs[i][n]]);
 650             flags[data.gridptrs[i][n]] = TRUE;
 651
 652             /*
 653              * Move everything else up the array. I ought to use a
 654              * better data structure for this, but for such small
 655              * numbers it hardly seems worth the effort.
 656              */
 657             while (n < data.nsquares[i]-1) {
 658                 data.gridptrs[i][n] = data.gridptrs[i][n+1];
 659                 n++;
 660             }
 661             data.nsquares[i]--;
 662         }
 663     }
 664
 665     /*
 666      * Now we know precisely which squares are blue. Encode this
 667      * information in hex. While we're looping over this, collect
 668      * the non-blue squares into a list in the now-unused gridptrs
 669      * array.
 670      */
 671     desc = snewn(area / 4 + 40, char);
 672     p = desc;
 673     j = 0;
 674     k = 8;
 675     m = 0;
 676     for (i = 0; i < area; i++) {
 677         if (flags[i]) {
 678             j |= k;
 679         } else {
 680             data.gridptrs[0][m++] = i;
 681         }
 682         k >>= 1;
 683         if (!k) {
 684             *p++ = "0123456789ABCDEF"[j];
 685             k = 8;
 686             j = 0;
 687         }
 688     }
 689     if (k != 8)
 690         *p++ = "0123456789ABCDEF"[j];
 691
 692     /*
 693      * Choose a non-blue square for the polyhedron.
 694      */
 695     sprintf(p, ",%d", data.gridptrs[0][random_upto(rs, m)]);
 696
 697     sfree(data.gridptrs[0]);
 698     sfree(flags);
 699
 700     return desc;
 701 }
 702
 703 static void add_grid_square_callback(void *ctx, struct grid_square *sq)
 704 {
 705     game_grid *grid = (game_grid *)ctx;
 706
 707     grid->squares[grid->nsquares++] = *sq;   /* structure copy */
 708 }
 709
 710 static int lowest_face(const struct solid *solid)
 711 {
 712     int i, j, best;
 713     float zmin;
 714
 715     best = 0;
 716     zmin = 0.0;
 717     for (i = 0; i < solid->nfaces; i++) {
 718         float z = 0;
 719
 720         for (j = 0; j < solid->order; j++) {
 721             int f = solid->faces[i*solid->order + j];
 722             z += solid->vertices[f*3+2];
 723         }
 724
 725         if (i == 0 || zmin > z) {
 726             zmin = z;
 727             best = i;
 728         }
 729     }
 730
 731     return best;
 732 }
 733
 734 static int align_poly(const struct solid *solid, struct grid_square *sq,
 735                       int *pkey)
 736 {
 737     float zmin;
 738     int i, j;
 739     int flip = (sq->flip ? -1 : +1);
 740
 741     /*
 742      * First, find the lowest z-coordinate present in the solid.
 743      */
 744     zmin = 0.0;
 745     for (i = 0; i < solid->nvertices; i++)
 746         if (zmin > solid->vertices[i*3+2])
 747             zmin = solid->vertices[i*3+2];
 748
 749     /*
 750      * Now go round the grid square. For each point in the grid
 751      * square, we're looking for a point of the polyhedron with the
 752      * same x- and y-coordinates (relative to the square's centre),
 753      * and z-coordinate equal to zmin (near enough).
 754      */
 755     for (j = 0; j < sq->npoints; j++) {
 756         int matches, index;
 757
 758         matches = 0;
 759         index = -1;
 760
 761         for (i = 0; i < solid->nvertices; i++) {
 762             float dist = 0;
 763
 764             dist += SQ(solid->vertices[i*3+0] * flip - sq->points[j*2+0] + sq->x);
 765             dist += SQ(solid->vertices[i*3+1] * flip - sq->points[j*2+1] + sq->y);
 766             dist += SQ(solid->vertices[i*3+2] - zmin);
 767
 768             if (dist < 0.1) {
 769                 matches++;
 770                 index = i;
 771             }
 772         }
 773
 774         if (matches != 1 || index < 0)
 775             return FALSE;
 776         pkey[j] = index;
 777     }
 778
 779     return TRUE;
 780 }
 781
 782 static void flip_poly(struct solid *solid, int flip)
 783 {
 784     int i;
 785
 786     if (flip) {
 787         for (i = 0; i < solid->nvertices; i++) {
 788             solid->vertices[i*3+0] *= -1;
 789             solid->vertices[i*3+1] *= -1;
 790         }
 791         for (i = 0; i < solid->nfaces; i++) {
 792             solid->normals[i*3+0] *= -1;
 793             solid->normals[i*3+1] *= -1;
 794         }
 795     }
 796 }
 797
 798 static struct solid *transform_poly(const struct solid *solid, int flip,
 799                                     int key0, int key1, float angle)
 800 {
 801     struct solid *ret = snew(struct solid);
 802     float vx, vy, ax, ay;
 803     float vmatrix[9], amatrix[9], vmatrix2[9];
 804     int i;
 805
 806     *ret = *solid;                     /* structure copy */
 807
 808     flip_poly(ret, flip);
 809
 810     /*
 811      * Now rotate the polyhedron through the given angle. We must
 812      * rotate about the Z-axis to bring the two vertices key0 and
 813      * key1 into horizontal alignment, then rotate about the
 814      * X-axis, then rotate back again.
 815      */
 816     vx = ret->vertices[key1*3+0] - ret->vertices[key0*3+0];
 817     vy = ret->vertices[key1*3+1] - ret->vertices[key0*3+1];
 818     assert(APPROXEQ(vx*vx + vy*vy, 1.0));
 819
 820     vmatrix[0] =  vx; vmatrix[3] = vy; vmatrix[6] = 0;
 821     vmatrix[1] = -vy; vmatrix[4] = vx; vmatrix[7] = 0;
 822     vmatrix[2] =   0; vmatrix[5] =  0; vmatrix[8] = 1;
 823
 824     ax = (float)cos(angle);
 825     ay = (float)sin(angle);
 826
 827     amatrix[0] = 1; amatrix[3] =   0; amatrix[6] =  0;
 828     amatrix[1] = 0; amatrix[4] =  ax; amatrix[7] = ay;
 829     amatrix[2] = 0; amatrix[5] = -ay; amatrix[8] = ax;
 830
 831     memcpy(vmatrix2, vmatrix, sizeof(vmatrix));
 832     vmatrix2[1] = vy;
 833     vmatrix2[3] = -vy;
 834
 835     for (i = 0; i < ret->nvertices; i++) {
 836         MATMUL(ret->vertices + 3*i, vmatrix, ret->vertices + 3*i);
 837         MATMUL(ret->vertices + 3*i, amatrix, ret->vertices + 3*i);
 838         MATMUL(ret->vertices + 3*i, vmatrix2, ret->vertices + 3*i);
 839     }
 840     for (i = 0; i < ret->nfaces; i++) {
 841         MATMUL(ret->normals + 3*i, vmatrix, ret->normals + 3*i);
 842         MATMUL(ret->normals + 3*i, amatrix, ret->normals + 3*i);
 843         MATMUL(ret->normals + 3*i, vmatrix2, ret->normals + 3*i);
 844     }
 845
 846     return ret;
 847 }
 848
 849 static char *validate_desc(const game_params *params, const char *desc)
 850 {
 851     int area = grid_area(params->d1, params->d2, solids[params->solid]->order);
 852     int i, j;
 853
 854     i = (area + 3) / 4;
 855     for (j = 0; j < i; j++) {
 856         int c = desc[j];
 857         if (c >= '0' && c <= '9') continue;
 858         if (c >= 'A' && c <= 'F') continue;
 859         if (c >= 'a' && c <= 'f') continue;
 860         return "Not enough hex digits at start of string";
 861         /* NB if desc[j]=='\0' that will also be caught here, so we're safe */
 862     }
 863
 864     if (desc[i] != ',')
 865         return "Expected ',' after hex digits";
 866
 867     i++;
 868     do {
 869         if (desc[i] < '0' || desc[i] > '9')
 870             return "Expected decimal integer after ','";
 871         i++;
 872     } while (desc[i]);
 873
 874     return NULL;
 875 }
 876
 877 static game_state *new_game(midend *me, const game_params *params,
 878                             const char *desc)
 879 {
 880     game_grid *grid = snew(game_grid);
 881     game_state *state = snew(game_state);
 882     int area;
 883
 884     state->params = *params;           /* structure copy */
 885     state->solid = solids[params->solid];
 886
 887     area = grid_area(params->d1, params->d2, state->solid->order);
 888     grid->squares = snewn(area, struct grid_square);
 889     grid->nsquares = 0;
 890     enum_grid_squares(params, add_grid_square_callback, grid);
 891     assert(grid->nsquares == area);
 892     state->grid = grid;
 893     grid->refcount = 1;
 894
 895     state->facecolours = snewn(state->solid->nfaces, int);
 896     memset(state->facecolours, 0, state->solid->nfaces * sizeof(int));
 897
 898     state->bluemask = snewn((state->grid->nsquares + 31) / 32, unsigned long);
 899     memset(state->bluemask, 0, (state->grid->nsquares + 31) / 32 *
 900            sizeof(unsigned long));
 901
 902     /*
 903      * Set up the blue squares and polyhedron position according to
 904      * the game description.
 905      */
 906     {
 907         const char *p = desc;
 908         int i, j, v;
 909
 910         j = 8;
 911         v = 0;
 912         for (i = 0; i < state->grid->nsquares; i++) {
 913             if (j == 8) {
 914                 v = *p++;
 915                 if (v >= '0' && v <= '9')
 916                     v -= '0';
 917                 else if (v >= 'A' && v <= 'F')
 918                     v -= 'A' - 10;
 919                 else if (v >= 'a' && v <= 'f')
 920                     v -= 'a' - 10;
 921                 else
 922                     break;
 923             }
 924             if (v & j)
 925                 SET_SQUARE(state, i, TRUE);
 926             j >>= 1;
 927             if (j == 0)
 928                 j = 8;
 929         }
 930
 931         if (*p == ',')
 932             p++;
 933
 934         state->current = atoi(p);
 935         if (state->current < 0 || state->current >= state->grid->nsquares)
 936             state->current = 0;        /* got to do _something_ */
 937     }
 938
 939     /*
 940      * Align the polyhedron with its grid square and determine
 941      * initial key points.
 942      */
 943     {
 944         int pkey[4];
 945         int ret;
 946
 947         ret = align_poly(state->solid, &state->grid->squares[state->current], pkey);
 948         assert(ret);
 949
 950         state->dpkey[0] = state->spkey[0] = pkey[0];
 951         state->dpkey[1] = state->spkey[0] = pkey[1];
 952         state->dgkey[0] = state->sgkey[0] = 0;
 953         state->dgkey[1] = state->sgkey[0] = 1;
 954     }
 955
 956     state->previous = state->current;
 957     state->angle = 0.0;
 958     state->completed = 0;
 959     state->movecount = 0;
 960
 961     return state;
 962 }
 963
 964 static game_state *dup_game(const game_state *state)
 965 {
 966     game_state *ret = snew(game_state);
 967
 968     ret->params = state->params;           /* structure copy */
 969     ret->solid = state->solid;
 970     ret->facecolours = snewn(ret->solid->nfaces, int);
 971     memcpy(ret->facecolours, state->facecolours,
 972            ret->solid->nfaces * sizeof(int));
 973     ret->current = state->current;
 974     ret->grid = state->grid;
 975     ret->grid->refcount++;
 976     ret->bluemask = snewn((ret->grid->nsquares + 31) / 32, unsigned long);
 977     memcpy(ret->bluemask, state->bluemask, (ret->grid->nsquares + 31) / 32 *
 978            sizeof(unsigned long));
 979     ret->dpkey[0] = state->dpkey[0];
 980     ret->dpkey[1] = state->dpkey[1];
 981     ret->dgkey[0] = state->dgkey[0];
 982     ret->dgkey[1] = state->dgkey[1];
 983     ret->spkey[0] = state->spkey[0];
 984     ret->spkey[1] = state->spkey[1];
 985     ret->sgkey[0] = state->sgkey[0];
 986     ret->sgkey[1] = state->sgkey[1];
 987     ret->previous = state->previous;
 988     ret->angle = state->angle;
 989     ret->completed = state->completed;
 990     ret->movecount = state->movecount;
 991
 992     return ret;
 993 }
 994
 995 static void free_game(game_state *state)
 996 {
 997     if (--state->grid->refcount <= 0) {
 998         sfree(state->grid->squares);
 999         sfree(state->grid);
1000     }
1001     sfree(state->bluemask);
1002     sfree(state->facecolours);
1003     sfree(state);
1004 }
1005
1006 static char *solve_game(const game_state *state, const game_state *currstate,
1007                         const char *aux, char **error)
1008 {
1009     return NULL;
1010 }
1011
1012 static int game_can_format_as_text_now(const game_params *params)
1013 {
1014     return TRUE;
1015 }
1016
1017 static char *game_text_format(const game_state *state)
1018 {
1019     return NULL;
1020 }
1021
1022 static game_ui *new_ui(const game_state *state)
1023 {
1024     return NULL;
1025 }
1026
1027 static void free_ui(game_ui *ui)
1028 {
1029 }
1030
1031 static char *encode_ui(const game_ui *ui)
1032 {
1033     return NULL;
1034 }
1035
1036 static void decode_ui(game_ui *ui, const char *encoding)
1037 {
1038 }
1039
1040 static void game_changed_state(game_ui *ui, const game_state *oldstate,
1041                                const game_state *newstate)
1042 {
1043 }
1044
1045 struct game_drawstate {
1046     float gridscale;
1047     int ox, oy;                        /* pixel position of float origin */
1048 };
1049
1050 /*
1051  * Code shared between interpret_move() and execute_move().
1052  */
1053 static int find_move_dest(const game_state *from, int direction,
1054                           int *skey, int *dkey)
1055 {
1056     int mask, dest, i, j;
1057     float points[4];
1058
1059     /*
1060      * Find the two points in the current grid square which
1061      * correspond to this move.
1062      */
1063     mask = from->grid->squares[from->current].directions[direction];
1064     if (mask == 0)
1065         return -1;
1066     for (i = j = 0; i < from->grid->squares[from->current].npoints; i++)
1067         if (mask & (1 << i)) {
1068             points[j*2] = from->grid->squares[from->current].points[i*2];
1069             points[j*2+1] = from->grid->squares[from->current].points[i*2+1];
1070             skey[j] = i;
1071             j++;
1072         }
1073     assert(j == 2);
1074
1075     /*
1076      * Now find the other grid square which shares those points.
1077      * This is our move destination.
1078      */
1079     dest = -1;
1080     for (i = 0; i < from->grid->nsquares; i++)
1081         if (i != from->current) {
1082             int match = 0;
1083             float dist;
1084
1085             for (j = 0; j < from->grid->squares[i].npoints; j++) {
1086                 dist = (SQ(from->grid->squares[i].points[j*2] - points[0]) +
1087                         SQ(from->grid->squares[i].points[j*2+1] - points[1]));
1088                 if (dist < 0.1)
1089                     dkey[match++] = j;
1090                 dist = (SQ(from->grid->squares[i].points[j*2] - points[2]) +
1091                         SQ(from->grid->squares[i].points[j*2+1] - points[3]));
1092                 if (dist < 0.1)
1093                     dkey[match++] = j;
1094             }
1095
1096             if (match == 2) {
1097                 dest = i;
1098                 break;
1099             }
1100         }
1101
1102     return dest;
1103 }
1104
1105 static char *interpret_move(const game_state *state, game_ui *ui,
1106                             const game_drawstate *ds,
1107                             int x, int y, int button)
1108 {
1109     int direction, mask, i;
1110     int skey[2], dkey[2];
1111
1112     button = button & (~MOD_MASK | MOD_NUM_KEYPAD);
1113
1114     /*
1115      * Moves can be made with the cursor keys or numeric keypad, or
1116      * alternatively you can left-click and the polyhedron will
1117      * move in the general direction of the mouse pointer.
1118      */
1119     if (button == CURSOR_UP || button == (MOD_NUM_KEYPAD | '8'))
1120         direction = UP;
1121     else if (button == CURSOR_DOWN || button == (MOD_NUM_KEYPAD | '2'))
1122         direction = DOWN;
1123     else if (button == CURSOR_LEFT || button == (MOD_NUM_KEYPAD | '4'))
1124         direction = LEFT;
1125     else if (button == CURSOR_RIGHT || button == (MOD_NUM_KEYPAD | '6'))
1126         direction = RIGHT;
1127     else if (button == (MOD_NUM_KEYPAD | '7'))
1128         direction = UP_LEFT;
1129     else if (button == (MOD_NUM_KEYPAD | '1'))
1130         direction = DOWN_LEFT;
1131     else if (button == (MOD_NUM_KEYPAD | '9'))
1132         direction = UP_RIGHT;
1133     else if (button == (MOD_NUM_KEYPAD | '3'))
1134         direction = DOWN_RIGHT;
1135     else if (button == LEFT_BUTTON) {
1136         /*
1137          * Find the bearing of the click point from the current
1138          * square's centre.
1139          */
1140         int cx, cy;
1141         double angle;
1142
1143         cx = (int)(state->grid->squares[state->current].x * GRID_SCALE) + ds->ox;
1144         cy = (int)(state->grid->squares[state->current].y * GRID_SCALE) + ds->oy;
1145
1146         if (x == cx && y == cy)
1147             return NULL;               /* clicked in exact centre!  */
1148         angle = atan2(y - cy, x - cx);
1149
1150         /*
1151          * There are three possibilities.
1152          *
1153          *  - This square is a square, so we choose between UP,
1154          *    DOWN, LEFT and RIGHT by dividing the available angle
1155          *    at the 45-degree points.
1156          *
1157          *  - This square is an up-pointing triangle, so we choose
1158          *    between DOWN, LEFT and RIGHT by dividing into
1159          *    120-degree arcs.
1160          *
1161          *  - This square is a down-pointing triangle, so we choose
1162          *    between UP, LEFT and RIGHT in the inverse manner.
1163          *
1164          * Don't forget that since our y-coordinates increase
1165          * downwards, `angle' is measured _clockwise_ from the
1166          * x-axis, not anticlockwise as most mathematicians would
1167          * instinctively assume.
1168          */
1169         if (state->grid->squares[state->current].npoints == 4) {
1170             /* Square. */
1171             if (fabs(angle) > 3*PI/4)
1172                 direction = LEFT;
1173             else if (fabs(angle) < PI/4)
1174                 direction = RIGHT;
1175             else if (angle > 0)
1176                 direction = DOWN;
1177             else
1178                 direction = UP;
1179         } else if (state->grid->squares[state->current].directions[UP] == 0) {
1180             /* Up-pointing triangle. */
1181             if (angle < -PI/2 || angle > 5*PI/6)
1182                 direction = LEFT;
1183             else if (angle > PI/6)
1184                 direction = DOWN;
1185             else
1186                 direction = RIGHT;
1187         } else {
1188             /* Down-pointing triangle. */
1189             assert(state->grid->squares[state->current].directions[DOWN] == 0);
1190             if (angle > PI/2 || angle < -5*PI/6)
1191                 direction = LEFT;
1192             else if (angle < -PI/6)
1193                 direction = UP;
1194             else
1195                 direction = RIGHT;
1196         }
1197     } else
1198         return NULL;
1199
1200     mask = state->grid->squares[state->current].directions[direction];
1201     if (mask == 0)
1202         return NULL;
1203
1204     /*
1205      * Translate diagonal directions into orthogonal ones.
1206      */
1207     if (direction > DOWN) {
1208         for (i = LEFT; i <= DOWN; i++)
1209             if (state->grid->squares[state->current].directions[i] == mask) {
1210                 direction = i;
1211                 break;
1212             }
1213         assert(direction <= DOWN);
1214     }
1215
1216     if (find_move_dest(state, direction, skey, dkey) < 0)
1217         return NULL;
1218
1219     if (direction == LEFT)  return dupstr("L");
1220     if (direction == RIGHT) return dupstr("R");
1221     if (direction == UP)    return dupstr("U");
1222     if (direction == DOWN)  return dupstr("D");
1223
1224     return NULL;                       /* should never happen */
1225 }
1226
1227 static game_state *execute_move(const game_state *from, const char *move)
1228 {
1229     game_state *ret;
1230     float angle;
1231     struct solid *poly;
1232     int pkey[2];
1233     int skey[2], dkey[2];
1234     int i, j, dest;
1235     int direction;
1236
1237     switch (*move) {
1238       case 'L': direction = LEFT; break;
1239       case 'R': direction = RIGHT; break;
1240       case 'U': direction = UP; break;
1241       case 'D': direction = DOWN; break;
1242       default: return NULL;
1243     }
1244
1245     dest = find_move_dest(from, direction, skey, dkey);
1246     if (dest < 0)
1247         return NULL;
1248
1249     ret = dup_game(from);
1250     ret->current = dest;
1251
1252     /*
1253      * So we know what grid square we're aiming for, and we also
1254      * know the two key points (as indices in both the source and
1255      * destination grid squares) which are invariant between source
1256      * and destination.
1257      *
1258      * Next we must roll the polyhedron on to that square. So we
1259      * find the indices of the key points within the polyhedron's
1260      * vertex array, then use those in a call to transform_poly,
1261      * and align the result on the new grid square.
1262      */
1263     {
1264         int all_pkey[4];
1265         align_poly(from->solid, &from->grid->squares[from->current], all_pkey);
1266         pkey[0] = all_pkey[skey[0]];
1267         pkey[1] = all_pkey[skey[1]];
1268         /*
1269          * Now pkey[0] corresponds to skey[0] and dkey[0], and
1270          * likewise [1].
1271          */
1272     }
1273
1274     /*
1275      * Now find the angle through which to rotate the polyhedron.
1276      * Do this by finding the two faces that share the two vertices
1277      * we've found, and taking the dot product of their normals.
1278      */
1279     {
1280         int f[2], nf = 0;
1281         float dp;
1282
1283         for (i = 0; i < from->solid->nfaces; i++) {
1284             int match = 0;
1285             for (j = 0; j < from->solid->order; j++)
1286                 if (from->solid->faces[i*from->solid->order + j] == pkey[0] ||
1287                     from->solid->faces[i*from->solid->order + j] == pkey[1])
1288                     match++;
1289             if (match == 2) {
1290                 assert(nf < 2);
1291                 f[nf++] = i;
1292             }
1293         }
1294
1295         assert(nf == 2);
1296
1297         dp = 0;
1298         for (i = 0; i < 3; i++)
1299             dp += (from->solid->normals[f[0]*3+i] *
1300                    from->solid->normals[f[1]*3+i]);
1301         angle = (float)acos(dp);
1302     }
1303
1304     /*
1305      * Now transform the polyhedron. We aren't entirely sure
1306      * whether we need to rotate through angle or -angle, and the
1307      * simplest way round this is to try both and see which one
1308      * aligns successfully!
1309      *
1310      * Unfortunately, _both_ will align successfully if this is a
1311      * cube, which won't tell us anything much. So for that
1312      * particular case, I resort to gross hackery: I simply negate
1313      * the angle before trying the alignment, depending on the
1314      * direction. Which directions work which way is determined by
1315      * pure trial and error. I said it was gross :-/
1316      */
1317     {
1318         int all_pkey[4];
1319         int success;
1320
1321         if (from->solid->order == 4 && direction == UP)
1322             angle = -angle;            /* HACK */
1323
1324         poly = transform_poly(from->solid,
1325                               from->grid->squares[from->current].flip,
1326                               pkey[0], pkey[1], angle);
1327         flip_poly(poly, from->grid->squares[ret->current].flip);
1328         success = align_poly(poly, &from->grid->squares[ret->current], all_pkey);
1329
1330         if (!success) {
1331             sfree(poly);
1332             angle = -angle;
1333             poly = transform_poly(from->solid,
1334                                   from->grid->squares[from->current].flip,
1335                                   pkey[0], pkey[1], angle);
1336             flip_poly(poly, from->grid->squares[ret->current].flip);
1337             success = align_poly(poly, &from->grid->squares[ret->current], all_pkey);
1338         }
1339
1340         assert(success);
1341     }
1342
1343     /*
1344      * Now we have our rotated polyhedron, which we expect to be
1345      * exactly congruent to the one we started with - but with the
1346      * faces permuted. So we map that congruence and thereby figure
1347      * out how to permute the faces as a result of the polyhedron
1348      * having rolled.
1349      */
1350     {
1351         int *newcolours = snewn(from->solid->nfaces, int);
1352
1353         for (i = 0; i < from->solid->nfaces; i++)
1354             newcolours[i] = -1;
1355
1356         for (i = 0; i < from->solid->nfaces; i++) {
1357             int nmatch = 0;
1358
1359             /*
1360              * Now go through the transformed polyhedron's faces
1361              * and figure out which one's normal is approximately
1362              * equal to this one.
1363              */
1364             for (j = 0; j < poly->nfaces; j++) {
1365                 float dist;
1366                 int k;
1367
1368                 dist = 0;
1369
1370                 for (k = 0; k < 3; k++)
1371                     dist += SQ(poly->normals[j*3+k] -
1372                                from->solid->normals[i*3+k]);
1373
1374                 if (APPROXEQ(dist, 0)) {
1375                     nmatch++;
1376                     newcolours[i] = ret->facecolours[j];
1377                 }
1378             }
1379
1380             assert(nmatch == 1);
1381         }
1382
1383         for (i = 0; i < from->solid->nfaces; i++)
1384             assert(newcolours[i] != -1);
1385
1386         sfree(ret->facecolours);
1387         ret->facecolours = newcolours;
1388     }
1389
1390     ret->movecount++;
1391
1392     /*
1393      * And finally, swap the colour between the bottom face of the
1394      * polyhedron and the face we've just landed on.
1395      *
1396      * We don't do this if the game is already complete, since we
1397      * allow the user to roll the fully blue polyhedron around the
1398      * grid as a feeble reward.
1399      */
1400     if (!ret->completed) {
1401         i = lowest_face(from->solid);
1402         j = ret->facecolours[i];
1403         ret->facecolours[i] = GET_SQUARE(ret, ret->current);
1404         SET_SQUARE(ret, ret->current, j);
1405
1406         /*
1407          * Detect game completion.
1408          */
1409         j = 0;
1410         for (i = 0; i < ret->solid->nfaces; i++)
1411             if (ret->facecolours[i])
1412                 j++;
1413         if (j == ret->solid->nfaces)
1414             ret->completed = ret->movecount;
1415     }
1416
1417     sfree(poly);
1418
1419     /*
1420      * Align the normal polyhedron with its grid square, to get key
1421      * points for non-animated display.
1422      */
1423     {
1424         int pkey[4];
1425         int success;
1426
1427         success = align_poly(ret->solid, &ret->grid->squares[ret->current], pkey);
1428         assert(success);
1429
1430         ret->dpkey[0] = pkey[0];
1431         ret->dpkey[1] = pkey[1];
1432         ret->dgkey[0] = 0;
1433         ret->dgkey[1] = 1;
1434     }
1435
1436
1437     ret->spkey[0] = pkey[0];
1438     ret->spkey[1] = pkey[1];
1439     ret->sgkey[0] = skey[0];
1440     ret->sgkey[1] = skey[1];
1441     ret->previous = from->current;
1442     ret->angle = angle;
1443
1444     return ret;
1445 }
1446
1447 /* ----------------------------------------------------------------------
1448  * Drawing routines.
1449  */
1450
1451 struct bbox {
1452     float l, r, u, d;
1453 };
1454
1455 static void find_bbox_callback(void *ctx, struct grid_square *sq)
1456 {
1457     struct bbox *bb = (struct bbox *)ctx;
1458     int i;
1459
1460     for (i = 0; i < sq->npoints; i++) {
1461         if (bb->l > sq->points[i*2]) bb->l = sq->points[i*2];
1462         if (bb->r < sq->points[i*2]) bb->r = sq->points[i*2];
1463         if (bb->u > sq->points[i*2+1]) bb->u = sq->points[i*2+1];
1464         if (bb->d < sq->points[i*2+1]) bb->d = sq->points[i*2+1];
1465     }
1466 }
1467
1468 static struct bbox find_bbox(const game_params *params)
1469 {
1470     struct bbox bb;
1471
1472     /*
1473      * These should be hugely more than the real bounding box will
1474      * be.
1475      */
1476     bb.l = 2.0F * (params->d1 + params->d2);
1477     bb.r = -2.0F * (params->d1 + params->d2);
1478     bb.u = 2.0F * (params->d1 + params->d2);
1479     bb.d = -2.0F * (params->d1 + params->d2);
1480     enum_grid_squares(params, find_bbox_callback, &bb);
1481
1482     return bb;
1483 }
1484
1485 #define XSIZE(gs, bb, solid) \
1486     ((int)(((bb).r - (bb).l + 2*(solid)->border) * gs))
1487 #define YSIZE(gs, bb, solid) \
1488     ((int)(((bb).d - (bb).u + 2*(solid)->border) * gs))
1489
1490 static void game_compute_size(const game_params *params, int tilesize,
1491                               int *x, int *y)
1492 {
1493     struct bbox bb = find_bbox(params);
1494
1495     *x = XSIZE(tilesize, bb, solids[params->solid]);
1496     *y = YSIZE(tilesize, bb, solids[params->solid]);
1497 }
1498
1499 static void game_set_size(drawing *dr, game_drawstate *ds,
1500                           const game_params *params, int tilesize)
1501 {
1502     struct bbox bb = find_bbox(params);
1503
1504     ds->gridscale = (float)tilesize;
1505     ds->ox = (int)(-(bb.l - solids[params->solid]->border) * ds->gridscale);
1506     ds->oy = (int)(-(bb.u - solids[params->solid]->border) * ds->gridscale);
1507 }
1508
1509 static float *game_colours(frontend *fe, int *ncolours)
1510 {
1511     float *ret = snewn(3 * NCOLOURS, float);
1512
1513     frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
1514
1515     ret[COL_BORDER * 3 + 0] = 0.0;
1516     ret[COL_BORDER * 3 + 1] = 0.0;
1517     ret[COL_BORDER * 3 + 2] = 0.0;
1518
1519     ret[COL_BLUE * 3 + 0] = 0.0;
1520     ret[COL_BLUE * 3 + 1] = 0.0;
1521     ret[COL_BLUE * 3 + 2] = 1.0;
1522
1523     *ncolours = NCOLOURS;
1524     return ret;
1525 }
1526
1527 static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
1528 {
1529     struct game_drawstate *ds = snew(struct game_drawstate);
1530
1531     ds->ox = ds->oy = 0;
1532     ds->gridscale = 0.0F; /* not decided yet */
1533
1534     return ds;
1535 }
1536
1537 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
1538 {
1539     sfree(ds);
1540 }
1541
1542 static void game_redraw(drawing *dr, game_drawstate *ds,
1543                         const game_state *oldstate, const game_state *state,
1544                         int dir, const game_ui *ui,
1545                         float animtime, float flashtime)
1546 {
1547     int i, j;
1548     struct bbox bb = find_bbox(&state->params);
1549     struct solid *poly;
1550     const int *pkey, *gkey;
1551     float t[3];
1552     float angle;
1553     int square;
1554
1555     draw_rect(dr, 0, 0, XSIZE(GRID_SCALE, bb, state->solid),
1556               YSIZE(GRID_SCALE, bb, state->solid), COL_BACKGROUND);
1557
1558     if (dir < 0) {
1559         const game_state *t;
1560
1561         /*
1562          * This is an Undo. So reverse the order of the states, and
1563          * run the roll timer backwards.
1564          */
1565         assert(oldstate);
1566
1567         t = oldstate;
1568         oldstate = state;
1569         state = t;
1570
1571         animtime = ROLLTIME - animtime;
1572     }
1573
1574     if (!oldstate) {
1575         oldstate = state;
1576         angle = 0.0;
1577         square = state->current;
1578         pkey = state->dpkey;
1579         gkey = state->dgkey;
1580     } else {
1581         angle = state->angle * animtime / ROLLTIME;
1582         square = state->previous;
1583         pkey = state->spkey;
1584         gkey = state->sgkey;
1585     }
1586     state = oldstate;
1587
1588     for (i = 0; i < state->grid->nsquares; i++) {
1589         int coords[8];
1590
1591         for (j = 0; j < state->grid->squares[i].npoints; j++) {
1592             coords[2*j] = ((int)(state->grid->squares[i].points[2*j] * GRID_SCALE)
1593                            + ds->ox);
1594             coords[2*j+1] = ((int)(state->grid->squares[i].points[2*j+1]*GRID_SCALE)
1595                              + ds->oy);
1596         }
1597
1598         draw_polygon(dr, coords, state->grid->squares[i].npoints,
1599                      GET_SQUARE(state, i) ? COL_BLUE : COL_BACKGROUND,
1600                      COL_BORDER);
1601     }
1602
1603     /*
1604      * Now compute and draw the polyhedron.
1605      */
1606     poly = transform_poly(state->solid, state->grid->squares[square].flip,
1607                           pkey[0], pkey[1], angle);
1608
1609     /*
1610      * Compute the translation required to align the two key points
1611      * on the polyhedron with the same key points on the current
1612      * face.
1613      */
1614     for (i = 0; i < 3; i++) {
1615         float tc = 0.0;
1616
1617         for (j = 0; j < 2; j++) {
1618             float grid_coord;
1619
1620             if (i < 2) {
1621                 grid_coord =
1622                     state->grid->squares[square].points[gkey[j]*2+i];
1623             } else {
1624                 grid_coord = 0.0;
1625             }
1626
1627             tc += (grid_coord - poly->vertices[pkey[j]*3+i]);
1628         }
1629
1630         t[i] = tc / 2;
1631     }
1632     for (i = 0; i < poly->nvertices; i++)
1633         for (j = 0; j < 3; j++)
1634             poly->vertices[i*3+j] += t[j];
1635
1636     /*
1637      * Now actually draw each face.
1638      */
1639     for (i = 0; i < poly->nfaces; i++) {
1640         float points[8];
1641         int coords[8];
1642
1643         for (j = 0; j < poly->order; j++) {
1644             int f = poly->faces[i*poly->order + j];
1645             points[j*2] = (poly->vertices[f*3+0] -
1646                            poly->vertices[f*3+2] * poly->shear);
1647             points[j*2+1] = (poly->vertices[f*3+1] -
1648                              poly->vertices[f*3+2] * poly->shear);
1649         }
1650
1651         for (j = 0; j < poly->order; j++) {
1652             coords[j*2] = (int)floor(points[j*2] * GRID_SCALE) + ds->ox;
1653             coords[j*2+1] = (int)floor(points[j*2+1] * GRID_SCALE) + ds->oy;
1654         }
1655
1656         /*
1657          * Find out whether these points are in a clockwise or
1658          * anticlockwise arrangement. If the latter, discard the
1659          * face because it's facing away from the viewer.
1660          *
1661          * This would involve fiddly winding-number stuff for a
1662          * general polygon, but for the simple parallelograms we'll
1663          * be seeing here, all we have to do is check whether the
1664          * corners turn right or left. So we'll take the vector
1665          * from point 0 to point 1, turn it right 90 degrees,
1666          * and check the sign of the dot product with that and the
1667          * next vector (point 1 to point 2).
1668          */
1669         {
1670             float v1x = points[2]-points[0];
1671             float v1y = points[3]-points[1];
1672             float v2x = points[4]-points[2];
1673             float v2y = points[5]-points[3];
1674             float dp = v1x * v2y - v1y * v2x;
1675
1676             if (dp <= 0)
1677                 continue;
1678         }
1679
1680         draw_polygon(dr, coords, poly->order,
1681                      state->facecolours[i] ? COL_BLUE : COL_BACKGROUND,
1682                      COL_BORDER);
1683     }
1684     sfree(poly);
1685
1686     draw_update(dr, 0, 0, XSIZE(GRID_SCALE, bb, state->solid),
1687                 YSIZE(GRID_SCALE, bb, state->solid));
1688
1689     /*
1690      * Update the status bar.
1691      */
1692     {
1693         char statusbuf[256];
1694
1695         sprintf(statusbuf, "%sMoves: %d",
1696                 (state->completed ? "COMPLETED! " : ""),
1697                 (state->completed ? state->completed : state->movecount));
1698
1699         status_bar(dr, statusbuf);
1700     }
1701 }
1702
1703 static float game_anim_length(const game_state *oldstate,
1704                               const game_state *newstate, int dir, game_ui *ui)
1705 {
1706     return ROLLTIME;
1707 }
1708
1709 static float game_flash_length(const game_state *oldstate,
1710                                const game_state *newstate, int dir, game_ui *ui)
1711 {
1712     return 0.0F;
1713 }
1714
1715 static int game_status(const game_state *state)
1716 {
1717     return state->completed ? +1 : 0;
1718 }
1719
1720 static int game_timing_state(const game_state *state, game_ui *ui)
1721 {
1722     return TRUE;
1723 }
1724
1725 static void game_print_size(const game_params *params, float *x, float *y)
1726 {
1727 }
1728
1729 static void game_print(drawing *dr, const game_state *state, int tilesize)
1730 {
1731 }
1732
1733 #ifdef COMBINED
1734 #define thegame cube
1735 #endif
1736
1737 const struct game thegame = {
1738     "Cube", "games.cube", "cube",
1739     default_params,
1740     game_fetch_preset,
1741     decode_params,
1742     encode_params,
1743     free_params,
1744     dup_params,
1745     TRUE, game_configure, custom_params,
1746     validate_params,
1747     new_game_desc,
1748     validate_desc,
1749     new_game,
1750     dup_game,
1751     free_game,
1752     FALSE, solve_game,
1753     FALSE, game_can_format_as_text_now, game_text_format,
1754     new_ui,
1755     free_ui,
1756     encode_ui,
1757     decode_ui,
1758     game_changed_state,
1759     interpret_move,
1760     execute_move,
1761     PREFERRED_GRID_SCALE, game_compute_size, game_set_size,
1762     game_colours,
1763     game_new_drawstate,
1764     game_free_drawstate,
1765     game_redraw,
1766     game_anim_length,
1767     game_flash_length,
1768     game_status,
1769     FALSE, FALSE, game_print_size, game_print,
1770     TRUE,                              /* wants_statusbar */
1771     FALSE, game_timing_state,
1772     0,                                 /* flags */
1773 };