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     bool 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;                     /* stores move count at completion */
 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 bool game_fetch_preset(int i, char **name, game_params **params)
 239 {
 240     game_params *ret = snew(game_params);
 241     const 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, bool 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].u.choices.choicenames = ":Tetrahedron:Cube:Octahedron:Icosahedron";
 493     ret[0].u.choices.selected = params->solid;
 494
 495     ret[1].name = "Width / top";
 496     ret[1].type = C_STRING;
 497     sprintf(buf, "%d", params->d1);
 498     ret[1].u.string.sval = dupstr(buf);
 499
 500     ret[2].name = "Height / bottom";
 501     ret[2].type = C_STRING;
 502     sprintf(buf, "%d", params->d2);
 503     ret[2].u.string.sval = dupstr(buf);
 504
 505     ret[3].name = NULL;
 506     ret[3].type = C_END;
 507
 508     return ret;
 509 }
 510
 511 static game_params *custom_params(const config_item *cfg)
 512 {
 513     game_params *ret = snew(game_params);
 514
 515     ret->solid = cfg[0].u.choices.selected;
 516     ret->d1 = atoi(cfg[1].u.string.sval);
 517     ret->d2 = atoi(cfg[2].u.string.sval);
 518
 519     return ret;
 520 }
 521
 522 static void count_grid_square_callback(void *ctx, struct grid_square *sq)
 523 {
 524     int *classes = (int *)ctx;
 525     int thisclass;
 526
 527     if (classes[4] == 4)
 528         thisclass = sq->tetra_class;
 529     else if (classes[4] == 2)
 530         thisclass = sq->flip;
 531     else
 532         thisclass = 0;
 533
 534     classes[thisclass]++;
 535 }
 536
 537 static const char *validate_params(const game_params *params, bool full)
 538 {
 539     int classes[5];
 540     int i;
 541
 542     if (params->solid < 0 || params->solid >= lenof(solids))
 543         return "Unrecognised solid type";
 544
 545     if (solids[params->solid]->order == 4) {
 546         if (params->d1 <= 1 || params->d2 <= 1)
 547             return "Both grid dimensions must be greater than one";
 548     } else {
 549         if (params->d1 <= 0 && params->d2 <= 0)
 550             return "At least one grid dimension must be greater than zero";
 551     }
 552
 553     for (i = 0; i < 4; i++)
 554         classes[i] = 0;
 555     if (params->solid == TETRAHEDRON)
 556         classes[4] = 4;
 557     else if (params->solid == OCTAHEDRON)
 558         classes[4] = 2;
 559     else
 560         classes[4] = 1;
 561     enum_grid_squares(params, count_grid_square_callback, classes);
 562
 563     for (i = 0; i < classes[4]; i++)
 564         if (classes[i] < solids[params->solid]->nfaces / classes[4])
 565             return "Not enough grid space to place all blue faces";
 566
 567     if (grid_area(params->d1, params->d2, solids[params->solid]->order) <
 568         solids[params->solid]->nfaces + 1)
 569         return "Not enough space to place the solid on an empty square";
 570
 571     return NULL;
 572 }
 573
 574 struct grid_data {
 575     int *gridptrs[4];
 576     int nsquares[4];
 577     int nclasses;
 578     int squareindex;
 579 };
 580
 581 static void classify_grid_square_callback(void *ctx, struct grid_square *sq)
 582 {
 583     struct grid_data *data = (struct grid_data *)ctx;
 584     int thisclass;
 585
 586     if (data->nclasses == 4)
 587         thisclass = sq->tetra_class;
 588     else if (data->nclasses == 2)
 589         thisclass = sq->flip;
 590     else
 591         thisclass = 0;
 592
 593     data->gridptrs[thisclass][data->nsquares[thisclass]++] =
 594         data->squareindex++;
 595 }
 596
 597 static char *new_game_desc(const game_params *params, random_state *rs,
 598                            char **aux, bool interactive)
 599 {
 600     struct grid_data data;
 601     int i, j, k, m, area, facesperclass;
 602     bool *flags;
 603     char *desc, *p;
 604
 605     /*
 606      * Enumerate the grid squares, dividing them into equivalence
 607      * classes as appropriate. (For the tetrahedron, there is one
 608      * equivalence class for each face; for the octahedron there
 609      * are two classes; for the other two solids there's only one.)
 610      */
 611
 612     area = grid_area(params->d1, params->d2, solids[params->solid]->order);
 613     if (params->solid == TETRAHEDRON)
 614         data.nclasses = 4;
 615     else if (params->solid == OCTAHEDRON)
 616         data.nclasses = 2;
 617     else
 618         data.nclasses = 1;
 619     data.gridptrs[0] = snewn(data.nclasses * area, int);
 620     for (i = 0; i < data.nclasses; i++) {
 621         data.gridptrs[i] = data.gridptrs[0] + i * area;
 622         data.nsquares[i] = 0;
 623     }
 624     data.squareindex = 0;
 625     enum_grid_squares(params, classify_grid_square_callback, &data);
 626
 627     facesperclass = solids[params->solid]->nfaces / data.nclasses;
 628
 629     for (i = 0; i < data.nclasses; i++)
 630         assert(data.nsquares[i] >= facesperclass);
 631     assert(data.squareindex == area);
 632
 633     /*
 634      * So now we know how many faces to allocate in each class. Get
 635      * on with it.
 636      */
 637     flags = snewn(area, bool);
 638     for (i = 0; i < area; i++)
 639         flags[i] = false;
 640
 641     for (i = 0; i < data.nclasses; i++) {
 642         for (j = 0; j < facesperclass; j++) {
 643             int n = random_upto(rs, data.nsquares[i]);
 644
 645             assert(!flags[data.gridptrs[i][n]]);
 646             flags[data.gridptrs[i][n]] = true;
 647
 648             /*
 649              * Move everything else up the array. I ought to use a
 650              * better data structure for this, but for such small
 651              * numbers it hardly seems worth the effort.
 652              */
 653             while (n < data.nsquares[i]-1) {
 654                 data.gridptrs[i][n] = data.gridptrs[i][n+1];
 655                 n++;
 656             }
 657             data.nsquares[i]--;
 658         }
 659     }
 660
 661     /*
 662      * Now we know precisely which squares are blue. Encode this
 663      * information in hex. While we're looping over this, collect
 664      * the non-blue squares into a list in the now-unused gridptrs
 665      * array.
 666      */
 667     desc = snewn(area / 4 + 40, char);
 668     p = desc;
 669     j = 0;
 670     k = 8;
 671     m = 0;
 672     for (i = 0; i < area; i++) {
 673         if (flags[i]) {
 674             j |= k;
 675         } else {
 676             data.gridptrs[0][m++] = i;
 677         }
 678         k >>= 1;
 679         if (!k) {
 680             *p++ = "0123456789ABCDEF"[j];
 681             k = 8;
 682             j = 0;
 683         }
 684     }
 685     if (k != 8)
 686         *p++ = "0123456789ABCDEF"[j];
 687
 688     /*
 689      * Choose a non-blue square for the polyhedron.
 690      */
 691     sprintf(p, ",%d", data.gridptrs[0][random_upto(rs, m)]);
 692
 693     sfree(data.gridptrs[0]);
 694     sfree(flags);
 695
 696     return desc;
 697 }
 698
 699 static void add_grid_square_callback(void *ctx, struct grid_square *sq)
 700 {
 701     game_grid *grid = (game_grid *)ctx;
 702
 703     grid->squares[grid->nsquares++] = *sq;   /* structure copy */
 704 }
 705
 706 static int lowest_face(const struct solid *solid)
 707 {
 708     int i, j, best;
 709     float zmin;
 710
 711     best = 0;
 712     zmin = 0.0;
 713     for (i = 0; i < solid->nfaces; i++) {
 714         float z = 0;
 715
 716         for (j = 0; j < solid->order; j++) {
 717             int f = solid->faces[i*solid->order + j];
 718             z += solid->vertices[f*3+2];
 719         }
 720
 721         if (i == 0 || zmin > z) {
 722             zmin = z;
 723             best = i;
 724         }
 725     }
 726
 727     return best;
 728 }
 729
 730 static bool align_poly(const struct solid *solid, struct grid_square *sq,
 731                        int *pkey)
 732 {
 733     float zmin;
 734     int i, j;
 735     int flip = (sq->flip ? -1 : +1);
 736
 737     /*
 738      * First, find the lowest z-coordinate present in the solid.
 739      */
 740     zmin = 0.0;
 741     for (i = 0; i < solid->nvertices; i++)
 742         if (zmin > solid->vertices[i*3+2])
 743             zmin = solid->vertices[i*3+2];
 744
 745     /*
 746      * Now go round the grid square. For each point in the grid
 747      * square, we're looking for a point of the polyhedron with the
 748      * same x- and y-coordinates (relative to the square's centre),
 749      * and z-coordinate equal to zmin (near enough).
 750      */
 751     for (j = 0; j < sq->npoints; j++) {
 752         int matches, index;
 753
 754         matches = 0;
 755         index = -1;
 756
 757         for (i = 0; i < solid->nvertices; i++) {
 758             float dist = 0;
 759
 760             dist += SQ(solid->vertices[i*3+0] * flip - sq->points[j*2+0] + sq->x);
 761             dist += SQ(solid->vertices[i*3+1] * flip - sq->points[j*2+1] + sq->y);
 762             dist += SQ(solid->vertices[i*3+2] - zmin);
 763
 764             if (dist < 0.1) {
 765                 matches++;
 766                 index = i;
 767             }
 768         }
 769
 770         if (matches != 1 || index < 0)
 771             return false;
 772         pkey[j] = index;
 773     }
 774
 775     return true;
 776 }
 777
 778 static void flip_poly(struct solid *solid, bool flip)
 779 {
 780     int i;
 781
 782     if (flip) {
 783         for (i = 0; i < solid->nvertices; i++) {
 784             solid->vertices[i*3+0] *= -1;
 785             solid->vertices[i*3+1] *= -1;
 786         }
 787         for (i = 0; i < solid->nfaces; i++) {
 788             solid->normals[i*3+0] *= -1;
 789             solid->normals[i*3+1] *= -1;
 790         }
 791     }
 792 }
 793
 794 static struct solid *transform_poly(const struct solid *solid, bool flip,
 795                                     int key0, int key1, float angle)
 796 {
 797     struct solid *ret = snew(struct solid);
 798     float vx, vy, ax, ay;
 799     float vmatrix[9], amatrix[9], vmatrix2[9];
 800     int i;
 801
 802     *ret = *solid;                     /* structure copy */
 803
 804     flip_poly(ret, flip);
 805
 806     /*
 807      * Now rotate the polyhedron through the given angle. We must
 808      * rotate about the Z-axis to bring the two vertices key0 and
 809      * key1 into horizontal alignment, then rotate about the
 810      * X-axis, then rotate back again.
 811      */
 812     vx = ret->vertices[key1*3+0] - ret->vertices[key0*3+0];
 813     vy = ret->vertices[key1*3+1] - ret->vertices[key0*3+1];
 814     assert(APPROXEQ(vx*vx + vy*vy, 1.0));
 815
 816     vmatrix[0] =  vx; vmatrix[3] = vy; vmatrix[6] = 0;
 817     vmatrix[1] = -vy; vmatrix[4] = vx; vmatrix[7] = 0;
 818     vmatrix[2] =   0; vmatrix[5] =  0; vmatrix[8] = 1;
 819
 820     ax = (float)cos(angle);
 821     ay = (float)sin(angle);
 822
 823     amatrix[0] = 1; amatrix[3] =   0; amatrix[6] =  0;
 824     amatrix[1] = 0; amatrix[4] =  ax; amatrix[7] = ay;
 825     amatrix[2] = 0; amatrix[5] = -ay; amatrix[8] = ax;
 826
 827     memcpy(vmatrix2, vmatrix, sizeof(vmatrix));
 828     vmatrix2[1] = vy;
 829     vmatrix2[3] = -vy;
 830
 831     for (i = 0; i < ret->nvertices; i++) {
 832         MATMUL(ret->vertices + 3*i, vmatrix, ret->vertices + 3*i);
 833         MATMUL(ret->vertices + 3*i, amatrix, ret->vertices + 3*i);
 834         MATMUL(ret->vertices + 3*i, vmatrix2, ret->vertices + 3*i);
 835     }
 836     for (i = 0; i < ret->nfaces; i++) {
 837         MATMUL(ret->normals + 3*i, vmatrix, ret->normals + 3*i);
 838         MATMUL(ret->normals + 3*i, amatrix, ret->normals + 3*i);
 839         MATMUL(ret->normals + 3*i, vmatrix2, ret->normals + 3*i);
 840     }
 841
 842     return ret;
 843 }
 844
 845 static const char *validate_desc(const game_params *params, const char *desc)
 846 {
 847     int area = grid_area(params->d1, params->d2, solids[params->solid]->order);
 848     int i, j;
 849
 850     i = (area + 3) / 4;
 851     for (j = 0; j < i; j++) {
 852         int c = desc[j];
 853         if (c >= '0' && c <= '9') continue;
 854         if (c >= 'A' && c <= 'F') continue;
 855         if (c >= 'a' && c <= 'f') continue;
 856         return "Not enough hex digits at start of string";
 857         /* NB if desc[j]=='\0' that will also be caught here, so we're safe */
 858     }
 859
 860     if (desc[i] != ',')
 861         return "Expected ',' after hex digits";
 862
 863     i++;
 864     do {
 865         if (desc[i] < '0' || desc[i] > '9')
 866             return "Expected decimal integer after ','";
 867         i++;
 868     } while (desc[i]);
 869
 870     return NULL;
 871 }
 872
 873 static game_state *new_game(midend *me, const game_params *params,
 874                             const char *desc)
 875 {
 876     game_grid *grid = snew(game_grid);
 877     game_state *state = snew(game_state);
 878     int area;
 879
 880     state->params = *params;           /* structure copy */
 881     state->solid = solids[params->solid];
 882
 883     area = grid_area(params->d1, params->d2, state->solid->order);
 884     grid->squares = snewn(area, struct grid_square);
 885     grid->nsquares = 0;
 886     enum_grid_squares(params, add_grid_square_callback, grid);
 887     assert(grid->nsquares == area);
 888     state->grid = grid;
 889     grid->refcount = 1;
 890
 891     state->facecolours = snewn(state->solid->nfaces, int);
 892     memset(state->facecolours, 0, state->solid->nfaces * sizeof(int));
 893
 894     state->bluemask = snewn((state->grid->nsquares + 31) / 32, unsigned long);
 895     memset(state->bluemask, 0, (state->grid->nsquares + 31) / 32 *
 896            sizeof(unsigned long));
 897
 898     /*
 899      * Set up the blue squares and polyhedron position according to
 900      * the game description.
 901      */
 902     {
 903         const char *p = desc;
 904         int i, j, v;
 905
 906         j = 8;
 907         v = 0;
 908         for (i = 0; i < state->grid->nsquares; i++) {
 909             if (j == 8) {
 910                 v = *p++;
 911                 if (v >= '0' && v <= '9')
 912                     v -= '0';
 913                 else if (v >= 'A' && v <= 'F')
 914                     v -= 'A' - 10;
 915                 else if (v >= 'a' && v <= 'f')
 916                     v -= 'a' - 10;
 917                 else
 918                     break;
 919             }
 920             if (v & j)
 921                 SET_SQUARE(state, i, true);
 922             j >>= 1;
 923             if (j == 0)
 924                 j = 8;
 925         }
 926
 927         if (*p == ',')
 928             p++;
 929
 930         state->current = atoi(p);
 931         if (state->current < 0 || state->current >= state->grid->nsquares)
 932             state->current = 0;        /* got to do _something_ */
 933     }
 934
 935     /*
 936      * Align the polyhedron with its grid square and determine
 937      * initial key points.
 938      */
 939     {
 940         int pkey[4];
 941         bool ret;
 942
 943         ret = align_poly(state->solid, &state->grid->squares[state->current], pkey);
 944         assert(ret);
 945
 946         state->dpkey[0] = state->spkey[0] = pkey[0];
 947         state->dpkey[1] = state->spkey[0] = pkey[1];
 948         state->dgkey[0] = state->sgkey[0] = 0;
 949         state->dgkey[1] = state->sgkey[0] = 1;
 950     }
 951
 952     state->previous = state->current;
 953     state->angle = 0.0;
 954     state->completed = 0;
 955     state->movecount = 0;
 956
 957     return state;
 958 }
 959
 960 static game_state *dup_game(const game_state *state)
 961 {
 962     game_state *ret = snew(game_state);
 963
 964     ret->params = state->params;           /* structure copy */
 965     ret->solid = state->solid;
 966     ret->facecolours = snewn(ret->solid->nfaces, int);
 967     memcpy(ret->facecolours, state->facecolours,
 968            ret->solid->nfaces * sizeof(int));
 969     ret->current = state->current;
 970     ret->grid = state->grid;
 971     ret->grid->refcount++;
 972     ret->bluemask = snewn((ret->grid->nsquares + 31) / 32, unsigned long);
 973     memcpy(ret->bluemask, state->bluemask, (ret->grid->nsquares + 31) / 32 *
 974            sizeof(unsigned long));
 975     ret->dpkey[0] = state->dpkey[0];
 976     ret->dpkey[1] = state->dpkey[1];
 977     ret->dgkey[0] = state->dgkey[0];
 978     ret->dgkey[1] = state->dgkey[1];
 979     ret->spkey[0] = state->spkey[0];
 980     ret->spkey[1] = state->spkey[1];
 981     ret->sgkey[0] = state->sgkey[0];
 982     ret->sgkey[1] = state->sgkey[1];
 983     ret->previous = state->previous;
 984     ret->angle = state->angle;
 985     ret->completed = state->completed;
 986     ret->movecount = state->movecount;
 987
 988     return ret;
 989 }
 990
 991 static void free_game(game_state *state)
 992 {
 993     if (--state->grid->refcount <= 0) {
 994         sfree(state->grid->squares);
 995         sfree(state->grid);
 996     }
 997     sfree(state->bluemask);
 998     sfree(state->facecolours);
 999     sfree(state);
1000 }
1001
1002 static char *solve_game(const game_state *state, const game_state *currstate,
1003                         const char *aux, const char **error)
1004 {
1005     return NULL;
1006 }
1007
1008 static bool game_can_format_as_text_now(const game_params *params)
1009 {
1010     return true;
1011 }
1012
1013 static char *game_text_format(const game_state *state)
1014 {
1015     return NULL;
1016 }
1017
1018 static game_ui *new_ui(const game_state *state)
1019 {
1020     return NULL;
1021 }
1022
1023 static void free_ui(game_ui *ui)
1024 {
1025 }
1026
1027 static char *encode_ui(const game_ui *ui)
1028 {
1029     return NULL;
1030 }
1031
1032 static void decode_ui(game_ui *ui, const char *encoding)
1033 {
1034 }
1035
1036 static void game_changed_state(game_ui *ui, const game_state *oldstate,
1037                                const game_state *newstate)
1038 {
1039 }
1040
1041 struct game_drawstate {
1042     float gridscale;
1043     int ox, oy;                        /* pixel position of float origin */
1044 };
1045
1046 /*
1047  * Code shared between interpret_move() and execute_move().
1048  */
1049 static int find_move_dest(const game_state *from, int direction,
1050                           int *skey, int *dkey)
1051 {
1052     int mask, dest, i, j;
1053     float points[4];
1054
1055     /*
1056      * Find the two points in the current grid square which
1057      * correspond to this move.
1058      */
1059     mask = from->grid->squares[from->current].directions[direction];
1060     if (mask == 0)
1061         return -1;
1062     for (i = j = 0; i < from->grid->squares[from->current].npoints; i++)
1063         if (mask & (1 << i)) {
1064             points[j*2] = from->grid->squares[from->current].points[i*2];
1065             points[j*2+1] = from->grid->squares[from->current].points[i*2+1];
1066             skey[j] = i;
1067             j++;
1068         }
1069     assert(j == 2);
1070
1071     /*
1072      * Now find the other grid square which shares those points.
1073      * This is our move destination.
1074      */
1075     dest = -1;
1076     for (i = 0; i < from->grid->nsquares; i++)
1077         if (i != from->current) {
1078             int match = 0;
1079             float dist;
1080
1081             for (j = 0; j < from->grid->squares[i].npoints; j++) {
1082                 dist = (SQ(from->grid->squares[i].points[j*2] - points[0]) +
1083                         SQ(from->grid->squares[i].points[j*2+1] - points[1]));
1084                 if (dist < 0.1)
1085                     dkey[match++] = j;
1086                 dist = (SQ(from->grid->squares[i].points[j*2] - points[2]) +
1087                         SQ(from->grid->squares[i].points[j*2+1] - points[3]));
1088                 if (dist < 0.1)
1089                     dkey[match++] = j;
1090             }
1091
1092             if (match == 2) {
1093                 dest = i;
1094                 break;
1095             }
1096         }
1097
1098     return dest;
1099 }
1100
1101 static char *interpret_move(const game_state *state, game_ui *ui,
1102                             const game_drawstate *ds,
1103                             int x, int y, int button)
1104 {
1105     int direction, mask, i;
1106     int skey[2], dkey[2];
1107
1108     button = button & (~MOD_MASK | MOD_NUM_KEYPAD);
1109
1110     /*
1111      * Moves can be made with the cursor keys or numeric keypad, or
1112      * alternatively you can left-click and the polyhedron will
1113      * move in the general direction of the mouse pointer.
1114      */
1115     if (button == CURSOR_UP || button == (MOD_NUM_KEYPAD | '8'))
1116         direction = UP;
1117     else if (button == CURSOR_DOWN || button == (MOD_NUM_KEYPAD | '2'))
1118         direction = DOWN;
1119     else if (button == CURSOR_LEFT || button == (MOD_NUM_KEYPAD | '4'))
1120         direction = LEFT;
1121     else if (button == CURSOR_RIGHT || button == (MOD_NUM_KEYPAD | '6'))
1122         direction = RIGHT;
1123     else if (button == (MOD_NUM_KEYPAD | '7'))
1124         direction = UP_LEFT;
1125     else if (button == (MOD_NUM_KEYPAD | '1'))
1126         direction = DOWN_LEFT;
1127     else if (button == (MOD_NUM_KEYPAD | '9'))
1128         direction = UP_RIGHT;
1129     else if (button == (MOD_NUM_KEYPAD | '3'))
1130         direction = DOWN_RIGHT;
1131     else if (button == LEFT_BUTTON) {
1132         /*
1133          * Find the bearing of the click point from the current
1134          * square's centre.
1135          */
1136         int cx, cy;
1137         double angle;
1138
1139         cx = (int)(state->grid->squares[state->current].x * GRID_SCALE) + ds->ox;
1140         cy = (int)(state->grid->squares[state->current].y * GRID_SCALE) + ds->oy;
1141
1142         if (x == cx && y == cy)
1143             return NULL;               /* clicked in exact centre!  */
1144         angle = atan2(y - cy, x - cx);
1145
1146         /*
1147          * There are three possibilities.
1148          *
1149          *  - This square is a square, so we choose between UP,
1150          *    DOWN, LEFT and RIGHT by dividing the available angle
1151          *    at the 45-degree points.
1152          *
1153          *  - This square is an up-pointing triangle, so we choose
1154          *    between DOWN, LEFT and RIGHT by dividing into
1155          *    120-degree arcs.
1156          *
1157          *  - This square is a down-pointing triangle, so we choose
1158          *    between UP, LEFT and RIGHT in the inverse manner.
1159          *
1160          * Don't forget that since our y-coordinates increase
1161          * downwards, `angle' is measured _clockwise_ from the
1162          * x-axis, not anticlockwise as most mathematicians would
1163          * instinctively assume.
1164          */
1165         if (state->grid->squares[state->current].npoints == 4) {
1166             /* Square. */
1167             if (fabs(angle) > 3*PI/4)
1168                 direction = LEFT;
1169             else if (fabs(angle) < PI/4)
1170                 direction = RIGHT;
1171             else if (angle > 0)
1172                 direction = DOWN;
1173             else
1174                 direction = UP;
1175         } else if (state->grid->squares[state->current].directions[UP] == 0) {
1176             /* Up-pointing triangle. */
1177             if (angle < -PI/2 || angle > 5*PI/6)
1178                 direction = LEFT;
1179             else if (angle > PI/6)
1180                 direction = DOWN;
1181             else
1182                 direction = RIGHT;
1183         } else {
1184             /* Down-pointing triangle. */
1185             assert(state->grid->squares[state->current].directions[DOWN] == 0);
1186             if (angle > PI/2 || angle < -5*PI/6)
1187                 direction = LEFT;
1188             else if (angle < -PI/6)
1189                 direction = UP;
1190             else
1191                 direction = RIGHT;
1192         }
1193     } else
1194         return NULL;
1195
1196     mask = state->grid->squares[state->current].directions[direction];
1197     if (mask == 0)
1198         return NULL;
1199
1200     /*
1201      * Translate diagonal directions into orthogonal ones.
1202      */
1203     if (direction > DOWN) {
1204         for (i = LEFT; i <= DOWN; i++)
1205             if (state->grid->squares[state->current].directions[i] == mask) {
1206                 direction = i;
1207                 break;
1208             }
1209         assert(direction <= DOWN);
1210     }
1211
1212     if (find_move_dest(state, direction, skey, dkey) < 0)
1213         return NULL;
1214
1215     if (direction == LEFT)  return dupstr("L");
1216     if (direction == RIGHT) return dupstr("R");
1217     if (direction == UP)    return dupstr("U");
1218     if (direction == DOWN)  return dupstr("D");
1219
1220     return NULL;                       /* should never happen */
1221 }
1222
1223 static game_state *execute_move(const game_state *from, const char *move)
1224 {
1225     game_state *ret;
1226     float angle;
1227     struct solid *poly;
1228     int pkey[2];
1229     int skey[2], dkey[2];
1230     int i, j, dest;
1231     int direction;
1232
1233     switch (*move) {
1234       case 'L': direction = LEFT; break;
1235       case 'R': direction = RIGHT; break;
1236       case 'U': direction = UP; break;
1237       case 'D': direction = DOWN; break;
1238       default: return NULL;
1239     }
1240
1241     dest = find_move_dest(from, direction, skey, dkey);
1242     if (dest < 0)
1243         return NULL;
1244
1245     ret = dup_game(from);
1246     ret->current = dest;
1247
1248     /*
1249      * So we know what grid square we're aiming for, and we also
1250      * know the two key points (as indices in both the source and
1251      * destination grid squares) which are invariant between source
1252      * and destination.
1253      *
1254      * Next we must roll the polyhedron on to that square. So we
1255      * find the indices of the key points within the polyhedron's
1256      * vertex array, then use those in a call to transform_poly,
1257      * and align the result on the new grid square.
1258      */
1259     {
1260         int all_pkey[4];
1261         align_poly(from->solid, &from->grid->squares[from->current], all_pkey);
1262         pkey[0] = all_pkey[skey[0]];
1263         pkey[1] = all_pkey[skey[1]];
1264         /*
1265          * Now pkey[0] corresponds to skey[0] and dkey[0], and
1266          * likewise [1].
1267          */
1268     }
1269
1270     /*
1271      * Now find the angle through which to rotate the polyhedron.
1272      * Do this by finding the two faces that share the two vertices
1273      * we've found, and taking the dot product of their normals.
1274      */
1275     {
1276         int f[2], nf = 0;
1277         float dp;
1278
1279         for (i = 0; i < from->solid->nfaces; i++) {
1280             int match = 0;
1281             for (j = 0; j < from->solid->order; j++)
1282                 if (from->solid->faces[i*from->solid->order + j] == pkey[0] ||
1283                     from->solid->faces[i*from->solid->order + j] == pkey[1])
1284                     match++;
1285             if (match == 2) {
1286                 assert(nf < 2);
1287                 f[nf++] = i;
1288             }
1289         }
1290
1291         assert(nf == 2);
1292
1293         dp = 0;
1294         for (i = 0; i < 3; i++)
1295             dp += (from->solid->normals[f[0]*3+i] *
1296                    from->solid->normals[f[1]*3+i]);
1297         angle = (float)acos(dp);
1298     }
1299
1300     /*
1301      * Now transform the polyhedron. We aren't entirely sure
1302      * whether we need to rotate through angle or -angle, and the
1303      * simplest way round this is to try both and see which one
1304      * aligns successfully!
1305      *
1306      * Unfortunately, _both_ will align successfully if this is a
1307      * cube, which won't tell us anything much. So for that
1308      * particular case, I resort to gross hackery: I simply negate
1309      * the angle before trying the alignment, depending on the
1310      * direction. Which directions work which way is determined by
1311      * pure trial and error. I said it was gross :-/
1312      */
1313     {
1314         int all_pkey[4];
1315         bool success;
1316
1317         if (from->solid->order == 4 && direction == UP)
1318             angle = -angle;            /* HACK */
1319
1320         poly = transform_poly(from->solid,
1321                               from->grid->squares[from->current].flip,
1322                               pkey[0], pkey[1], angle);
1323         flip_poly(poly, from->grid->squares[ret->current].flip);
1324         success = align_poly(poly, &from->grid->squares[ret->current], all_pkey);
1325
1326         if (!success) {
1327             sfree(poly);
1328             angle = -angle;
1329             poly = transform_poly(from->solid,
1330                                   from->grid->squares[from->current].flip,
1331                                   pkey[0], pkey[1], angle);
1332             flip_poly(poly, from->grid->squares[ret->current].flip);
1333             success = align_poly(poly, &from->grid->squares[ret->current], all_pkey);
1334         }
1335
1336         assert(success);
1337     }
1338
1339     /*
1340      * Now we have our rotated polyhedron, which we expect to be
1341      * exactly congruent to the one we started with - but with the
1342      * faces permuted. So we map that congruence and thereby figure
1343      * out how to permute the faces as a result of the polyhedron
1344      * having rolled.
1345      */
1346     {
1347         int *newcolours = snewn(from->solid->nfaces, int);
1348
1349         for (i = 0; i < from->solid->nfaces; i++)
1350             newcolours[i] = -1;
1351
1352         for (i = 0; i < from->solid->nfaces; i++) {
1353             int nmatch = 0;
1354
1355             /*
1356              * Now go through the transformed polyhedron's faces
1357              * and figure out which one's normal is approximately
1358              * equal to this one.
1359              */
1360             for (j = 0; j < poly->nfaces; j++) {
1361                 float dist;
1362                 int k;
1363
1364                 dist = 0;
1365
1366                 for (k = 0; k < 3; k++)
1367                     dist += SQ(poly->normals[j*3+k] -
1368                                from->solid->normals[i*3+k]);
1369
1370                 if (APPROXEQ(dist, 0)) {
1371                     nmatch++;
1372                     newcolours[i] = ret->facecolours[j];
1373                 }
1374             }
1375
1376             assert(nmatch == 1);
1377         }
1378
1379         for (i = 0; i < from->solid->nfaces; i++)
1380             assert(newcolours[i] != -1);
1381
1382         sfree(ret->facecolours);
1383         ret->facecolours = newcolours;
1384     }
1385
1386     ret->movecount++;
1387
1388     /*
1389      * And finally, swap the colour between the bottom face of the
1390      * polyhedron and the face we've just landed on.
1391      *
1392      * We don't do this if the game is already complete, since we
1393      * allow the user to roll the fully blue polyhedron around the
1394      * grid as a feeble reward.
1395      */
1396     if (!ret->completed) {
1397         i = lowest_face(from->solid);
1398         j = ret->facecolours[i];
1399         ret->facecolours[i] = GET_SQUARE(ret, ret->current);
1400         SET_SQUARE(ret, ret->current, j);
1401
1402         /*
1403          * Detect game completion.
1404          */
1405         j = 0;
1406         for (i = 0; i < ret->solid->nfaces; i++)
1407             if (ret->facecolours[i])
1408                 j++;
1409         if (j == ret->solid->nfaces)
1410             ret->completed = ret->movecount;
1411     }
1412
1413     sfree(poly);
1414
1415     /*
1416      * Align the normal polyhedron with its grid square, to get key
1417      * points for non-animated display.
1418      */
1419     {
1420         int pkey[4];
1421         bool success;
1422
1423         success = align_poly(ret->solid, &ret->grid->squares[ret->current], pkey);
1424         assert(success);
1425
1426         ret->dpkey[0] = pkey[0];
1427         ret->dpkey[1] = pkey[1];
1428         ret->dgkey[0] = 0;
1429         ret->dgkey[1] = 1;
1430     }
1431
1432
1433     ret->spkey[0] = pkey[0];
1434     ret->spkey[1] = pkey[1];
1435     ret->sgkey[0] = skey[0];
1436     ret->sgkey[1] = skey[1];
1437     ret->previous = from->current;
1438     ret->angle = angle;
1439
1440     return ret;
1441 }
1442
1443 /* ----------------------------------------------------------------------
1444  * Drawing routines.
1445  */
1446
1447 struct bbox {
1448     float l, r, u, d;
1449 };
1450
1451 static void find_bbox_callback(void *ctx, struct grid_square *sq)
1452 {
1453     struct bbox *bb = (struct bbox *)ctx;
1454     int i;
1455
1456     for (i = 0; i < sq->npoints; i++) {
1457         if (bb->l > sq->points[i*2]) bb->l = sq->points[i*2];
1458         if (bb->r < sq->points[i*2]) bb->r = sq->points[i*2];
1459         if (bb->u > sq->points[i*2+1]) bb->u = sq->points[i*2+1];
1460         if (bb->d < sq->points[i*2+1]) bb->d = sq->points[i*2+1];
1461     }
1462 }
1463
1464 static struct bbox find_bbox(const game_params *params)
1465 {
1466     struct bbox bb;
1467
1468     /*
1469      * These should be hugely more than the real bounding box will
1470      * be.
1471      */
1472     bb.l = 2.0F * (params->d1 + params->d2);
1473     bb.r = -2.0F * (params->d1 + params->d2);
1474     bb.u = 2.0F * (params->d1 + params->d2);
1475     bb.d = -2.0F * (params->d1 + params->d2);
1476     enum_grid_squares(params, find_bbox_callback, &bb);
1477
1478     return bb;
1479 }
1480
1481 #define XSIZE(gs, bb, solid) \
1482     ((int)(((bb).r - (bb).l + 2*(solid)->border) * gs))
1483 #define YSIZE(gs, bb, solid) \
1484     ((int)(((bb).d - (bb).u + 2*(solid)->border) * gs))
1485
1486 static void game_compute_size(const game_params *params, int tilesize,
1487                               int *x, int *y)
1488 {
1489     struct bbox bb = find_bbox(params);
1490
1491     *x = XSIZE(tilesize, bb, solids[params->solid]);
1492     *y = YSIZE(tilesize, bb, solids[params->solid]);
1493 }
1494
1495 static void game_set_size(drawing *dr, game_drawstate *ds,
1496                           const game_params *params, int tilesize)
1497 {
1498     struct bbox bb = find_bbox(params);
1499
1500     ds->gridscale = (float)tilesize;
1501     ds->ox = (int)(-(bb.l - solids[params->solid]->border) * ds->gridscale);
1502     ds->oy = (int)(-(bb.u - solids[params->solid]->border) * ds->gridscale);
1503 }
1504
1505 static float *game_colours(frontend *fe, int *ncolours)
1506 {
1507     float *ret = snewn(3 * NCOLOURS, float);
1508
1509     frontend_default_colour(fe, &ret[COL_BACKGROUND * 3]);
1510
1511     ret[COL_BORDER * 3 + 0] = 0.0;
1512     ret[COL_BORDER * 3 + 1] = 0.0;
1513     ret[COL_BORDER * 3 + 2] = 0.0;
1514
1515     ret[COL_BLUE * 3 + 0] = 0.0;
1516     ret[COL_BLUE * 3 + 1] = 0.0;
1517     ret[COL_BLUE * 3 + 2] = 1.0;
1518
1519     *ncolours = NCOLOURS;
1520     return ret;
1521 }
1522
1523 static game_drawstate *game_new_drawstate(drawing *dr, const game_state *state)
1524 {
1525     struct game_drawstate *ds = snew(struct game_drawstate);
1526
1527     ds->ox = ds->oy = 0;
1528     ds->gridscale = 0.0F; /* not decided yet */
1529
1530     return ds;
1531 }
1532
1533 static void game_free_drawstate(drawing *dr, game_drawstate *ds)
1534 {
1535     sfree(ds);
1536 }
1537
1538 static void game_get_cursor_location(const game_ui *ui,
1539                                      const game_drawstate *ds,
1540                                      const game_state *state,
1541                                      const game_params *params,
1542                                      int *x, int *y, int *w, int *h)
1543 {
1544     struct bbox bb;
1545
1546     bb.l = 2.0F * (params->d1 + params->d2);
1547     bb.r = -2.0F * (params->d1 + params->d2);
1548     bb.u = 2.0F * (params->d1 + params->d2);
1549     bb.d = -2.0F * (params->d1 + params->d2);
1550
1551     find_bbox_callback(&bb, state->grid->squares + state->current);
1552
1553     *x = ((int)(bb.l * GRID_SCALE) + ds->ox);
1554     *y = ((int)(bb.u * GRID_SCALE) + ds->oy);
1555     *w = (bb.r - bb.l) * GRID_SCALE;
1556     *h = (bb.d - bb.u) * GRID_SCALE;
1557 }
1558
1559 static void game_redraw(drawing *dr, game_drawstate *ds,
1560                         const game_state *oldstate, const game_state *state,
1561                         int dir, const game_ui *ui,
1562                         float animtime, float flashtime)
1563 {
1564     int i, j;
1565     struct bbox bb = find_bbox(&state->params);
1566     struct solid *poly;
1567     const int *pkey, *gkey;
1568     float t[3];
1569     float angle;
1570     int square;
1571
1572     draw_rect(dr, 0, 0, XSIZE(GRID_SCALE, bb, state->solid),
1573               YSIZE(GRID_SCALE, bb, state->solid), COL_BACKGROUND);
1574
1575     if (dir < 0) {
1576         const game_state *t;
1577
1578         /*
1579          * This is an Undo. So reverse the order of the states, and
1580          * run the roll timer backwards.
1581          */
1582         assert(oldstate);
1583
1584         t = oldstate;
1585         oldstate = state;
1586         state = t;
1587
1588         animtime = ROLLTIME - animtime;
1589     }
1590
1591     if (!oldstate) {
1592         oldstate = state;
1593         angle = 0.0;
1594         square = state->current;
1595         pkey = state->dpkey;
1596         gkey = state->dgkey;
1597     } else {
1598         angle = state->angle * animtime / ROLLTIME;
1599         square = state->previous;
1600         pkey = state->spkey;
1601         gkey = state->sgkey;
1602     }
1603     state = oldstate;
1604
1605     for (i = 0; i < state->grid->nsquares; i++) {
1606         int coords[8];
1607
1608         for (j = 0; j < state->grid->squares[i].npoints; j++) {
1609             coords[2*j] = ((int)(state->grid->squares[i].points[2*j] * GRID_SCALE)
1610                            + ds->ox);
1611             coords[2*j+1] = ((int)(state->grid->squares[i].points[2*j+1]*GRID_SCALE)
1612                              + ds->oy);
1613         }
1614
1615         draw_polygon(dr, coords, state->grid->squares[i].npoints,
1616                      GET_SQUARE(state, i) ? COL_BLUE : COL_BACKGROUND,
1617                      COL_BORDER);
1618     }
1619
1620     /*
1621      * Now compute and draw the polyhedron.
1622      */
1623     poly = transform_poly(state->solid, state->grid->squares[square].flip,
1624                           pkey[0], pkey[1], angle);
1625
1626     /*
1627      * Compute the translation required to align the two key points
1628      * on the polyhedron with the same key points on the current
1629      * face.
1630      */
1631     for (i = 0; i < 3; i++) {
1632         float tc = 0.0;
1633
1634         for (j = 0; j < 2; j++) {
1635             float grid_coord;
1636
1637             if (i < 2) {
1638                 grid_coord =
1639                     state->grid->squares[square].points[gkey[j]*2+i];
1640             } else {
1641                 grid_coord = 0.0;
1642             }
1643
1644             tc += (grid_coord - poly->vertices[pkey[j]*3+i]);
1645         }
1646
1647         t[i] = tc / 2;
1648     }
1649     for (i = 0; i < poly->nvertices; i++)
1650         for (j = 0; j < 3; j++)
1651             poly->vertices[i*3+j] += t[j];
1652
1653     /*
1654      * Now actually draw each face.
1655      */
1656     for (i = 0; i < poly->nfaces; i++) {
1657         float points[8];
1658         int coords[8];
1659
1660         for (j = 0; j < poly->order; j++) {
1661             int f = poly->faces[i*poly->order + j];
1662             points[j*2] = (poly->vertices[f*3+0] -
1663                            poly->vertices[f*3+2] * poly->shear);
1664             points[j*2+1] = (poly->vertices[f*3+1] -
1665                              poly->vertices[f*3+2] * poly->shear);
1666         }
1667
1668         for (j = 0; j < poly->order; j++) {
1669             coords[j*2] = (int)floor(points[j*2] * GRID_SCALE) + ds->ox;
1670             coords[j*2+1] = (int)floor(points[j*2+1] * GRID_SCALE) + ds->oy;
1671         }
1672
1673         /*
1674          * Find out whether these points are in a clockwise or
1675          * anticlockwise arrangement. If the latter, discard the
1676          * face because it's facing away from the viewer.
1677          *
1678          * This would involve fiddly winding-number stuff for a
1679          * general polygon, but for the simple parallelograms we'll
1680          * be seeing here, all we have to do is check whether the
1681          * corners turn right or left. So we'll take the vector
1682          * from point 0 to point 1, turn it right 90 degrees,
1683          * and check the sign of the dot product with that and the
1684          * next vector (point 1 to point 2).
1685          */
1686         {
1687             float v1x = points[2]-points[0];
1688             float v1y = points[3]-points[1];
1689             float v2x = points[4]-points[2];
1690             float v2y = points[5]-points[3];
1691             float dp = v1x * v2y - v1y * v2x;
1692
1693             if (dp <= 0)
1694                 continue;
1695         }
1696
1697         draw_polygon(dr, coords, poly->order,
1698                      state->facecolours[i] ? COL_BLUE : COL_BACKGROUND,
1699                      COL_BORDER);
1700     }
1701     sfree(poly);
1702
1703     draw_update(dr, 0, 0, XSIZE(GRID_SCALE, bb, state->solid),
1704                 YSIZE(GRID_SCALE, bb, state->solid));
1705
1706     /*
1707      * Update the status bar.
1708      */
1709     {
1710         char statusbuf[256];
1711
1712         sprintf(statusbuf, "%sMoves: %d",
1713                 (state->completed ? "COMPLETED! " : ""),
1714                 (state->completed ? state->completed : state->movecount));
1715
1716         status_bar(dr, statusbuf);
1717     }
1718 }
1719
1720 static float game_anim_length(const game_state *oldstate,
1721                               const game_state *newstate, int dir, game_ui *ui)
1722 {
1723     return ROLLTIME;
1724 }
1725
1726 static float game_flash_length(const game_state *oldstate,
1727                                const game_state *newstate, int dir, game_ui *ui)
1728 {
1729     return 0.0F;
1730 }
1731
1732 static int game_status(const game_state *state)
1733 {
1734     return state->completed ? +1 : 0;
1735 }
1736
1737 static bool game_timing_state(const game_state *state, game_ui *ui)
1738 {
1739     return true;
1740 }
1741
1742 static void game_print_size(const game_params *params, float *x, float *y)
1743 {
1744 }
1745
1746 static void game_print(drawing *dr, const game_state *state, int tilesize)
1747 {
1748 }
1749
1750 #ifdef COMBINED
1751 #define thegame cube
1752 #endif
1753
1754 const struct game thegame = {
1755     "Cube", "games.cube", "cube",
1756     default_params,
1757     game_fetch_preset, NULL,
1758     decode_params,
1759     encode_params,
1760     free_params,
1761     dup_params,
1762     true, game_configure, custom_params,
1763     validate_params,
1764     new_game_desc,
1765     validate_desc,
1766     new_game,
1767     dup_game,
1768     free_game,
1769     false, solve_game,
1770     false, game_can_format_as_text_now, game_text_format,
1771     new_ui,
1772     free_ui,
1773     encode_ui,
1774     decode_ui,
1775     NULL, /* game_request_keys */
1776     game_changed_state,
1777     interpret_move,
1778     execute_move,
1779     PREFERRED_GRID_SCALE, game_compute_size, game_set_size,
1780     game_colours,
1781     game_new_drawstate,
1782     game_free_drawstate,
1783     game_redraw,
1784     game_anim_length,
1785     game_flash_length,
1786     game_get_cursor_location,
1787     game_status,
1788     false, false, game_print_size, game_print,
1789     true,                              /* wants_statusbar */
1790     false, game_timing_state,
1791     0,                                 /* flags */
1792 };