src/rtree.c

   1 /* $Id$ */
   2
   3 /*
   4  *                            COPYRIGHT
   5  *
   6  *  PCB, interactive printed circuit board design
   7  *  Copyright (C) 1994,1995,1996 Thomas Nau
   8  *  Copyright (C) 1998,1999,2000,2001,2002,2003,2004 harry eaton
   9  *
  10  *  This program is free software; you can redistribute it and/or modify
  11  *  it under the terms of the GNU General Public License as published by
  12  *  the Free Software Foundation; either version 2 of the License, or
  13  *  (at your option) any later version.
  14  *
  15  *  This program is distributed in the hope that it will be useful,
  16  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  17  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  18  *  GNU General Public License for more details.
  19  *
  20  *  You should have received a copy of the GNU General Public License
  21  *  along with this program; if not, write to the Free Software
  22  *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
  23  *
  24  *  Contact addresses for paper mail and Email:
  25  *  harry eaton, 6697 Buttonhole Ct, Columbia, MD 21044 USA
  26  *  haceaton@aplcomm.jhuapl.edu
  27  *
  28  */
  29
  30 /* this file, rtree.c, was written and is
  31  * Copyright (c) 2004, harry eaton
  32  */
  33
  34 /* implements r-tree structures.
  35  * these should be much faster for the auto-router
  36  * because the recursive search is much more efficient
  37  * and that's where the auto-router spends all its time.
  38  */
  39 #ifdef HAVE_CONFIG_H
  40 #include "config.h"
  41 #endif
  42
  43 #include "global.h"
  44
  45 #include <assert.h>
  46 #include <setjmp.h>
  47
  48 /* #define DRAWBOX */
  49
  50 #ifdef DRAWBOX
  51 #include "clip.h"
  52 #include "data.h"
  53 #endif
  54 #include "mymem.h"
  55
  56 #include "rtree.h"
  57
  58 #ifdef HAVE_LIBDMALLOC
  59 #include <dmalloc.h>
  60 #endif
  61
  62 RCSID ("$Id$");
  63
  64
  65 #define SLOW_ASSERTS
  66 /* All rectangles are closed on the bottom left and open on the
  67  * top right. i.e. they contain one corner point, but not the other.
  68  */
  69
  70 /* the number of entries in each rtree node
  71  * 4 - 7 seem to be pretty good settings
  72  */
  73 #define M_SIZE 6
  74
  75 /* it seems that sorting the leaf order slows us down
  76  * but sometimes gives better routes
  77  */
  78 #undef SORT
  79 #define SORT_NONLEAF
  80
  81 #define DELETE_BY_POINTER
  82 typedef long long bigun;
  83
  84 typedef struct
  85 {
  86   const BoxType *bptr;          /* pointer to the box */
  87   BoxType bounds;               /* copy of the box for locality of reference */
  88 } Rentry;
  89
  90 struct rtree_node
  91 {
  92   BoxType box;                  /* bounds rectangle of this node */
  93   struct rtree_node *parent;    /* parent of this node, NULL = root */
  94   struct
  95   {
  96     unsigned is_leaf:1;         /* this is a leaf node */
  97     unsigned manage:31;         /* true==should free 'rect.bptr' if node is destroyed */
  98   }
  99   flags;
 100   union
 101   {
 102     struct rtree_node *kids[M_SIZE + 1];        /* when not leaf */
 103     Rentry rects[M_SIZE + 1];   /* when leaf */
 104   } u;
 105 };
 106
 107 #ifdef SLOW_ASSERTS
 108 static int
 109 __r_node_is_good (struct rtree_node *node)
 110 {
 111   int i, flag = 1;
 112   int kind = -1;
 113   Boolean last = False;
 114
 115   if (node == NULL)
 116     return 1;
 117   for (i = 0; i < M_SIZE; i++)
 118     {
 119       if (node->flags.is_leaf)
 120         {
 121           if (!node->u.rects[i].bptr)
 122             {
 123               last = True;
 124               continue;
 125             }
 126           /* check that once one entry is empty, all the rest are too */
 127           if (node->u.rects[i].bptr && last)
 128             assert (0);
 129           /* check that the box makes sense */
 130           if (node->box.X1 > node->box.X2)
 131             assert (0);
 132           if (node->box.Y1 > node->box.Y2)
 133             assert (0);
 134           /* check that bounds is the same as the pointer */
 135           if (node->u.rects[i].bounds.X1 != node->u.rects[i].bptr->X1)
 136             assert (0);
 137           if (node->u.rects[i].bounds.Y1 != node->u.rects[i].bptr->Y1)
 138             assert (0);
 139           if (node->u.rects[i].bounds.X2 != node->u.rects[i].bptr->X2)
 140             assert (0);
 141           if (node->u.rects[i].bounds.Y2 != node->u.rects[i].bptr->Y2)
 142             assert (0);
 143           /* check that entries are within node bounds */
 144           if (node->u.rects[i].bounds.X1 < node->box.X1)
 145             assert (0);
 146           if (node->u.rects[i].bounds.X2 > node->box.X2)
 147             assert (0);
 148           if (node->u.rects[i].bounds.Y1 < node->box.Y1)
 149             assert (0);
 150           if (node->u.rects[i].bounds.Y2 > node->box.Y2)
 151             assert (0);
 152         }
 153       else
 154         {
 155           if (!node->u.kids[i])
 156             {
 157               last = True;
 158               continue;
 159             }
 160           /* make sure all children are the same type */
 161           if (kind == -1)
 162             kind = node->u.kids[i]->flags.is_leaf;
 163           else if (kind != node->u.kids[i]->flags.is_leaf)
 164             assert (0);
 165           /* check that once one entry is empty, all the rest are too */
 166           if (node->u.kids[i] && last)
 167             assert (0);
 168           /* check that entries are within node bounds */
 169           if (node->u.kids[i]->box.X1 < node->box.X1)
 170             assert (0);
 171           if (node->u.kids[i]->box.X2 > node->box.X2)
 172             assert (0);
 173           if (node->u.kids[i]->box.Y1 < node->box.Y1)
 174             assert (0);
 175           if (node->u.kids[i]->box.Y2 > node->box.Y2)
 176             assert (0);
 177         }
 178       flag <<= 1;
 179     }
 180   /* check that we're completely in the parent's bounds */
 181   if (node->parent)
 182     {
 183       if (node->parent->box.X1 > node->box.X1)
 184         assert (0);
 185       if (node->parent->box.X2 < node->box.X2)
 186         assert (0);
 187       if (node->parent->box.Y1 > node->box.Y1)
 188         assert (0);
 189       if (node->parent->box.Y2 < node->box.Y2)
 190         assert (0);
 191     }
 192   /* make sure overflow is empty */
 193   if (!node->flags.is_leaf && node->u.kids[i])
 194     assert (0);
 195   if (node->flags.is_leaf && node->u.rects[i].bptr)
 196     assert (0);
 197   return 1;
 198 }
 199
 200
 201 /* check the whole tree from this node down for consistency */
 202 static Boolean
 203 __r_tree_is_good (struct rtree_node *node)
 204 {
 205   int i;
 206
 207   if (!node)
 208     return 1;
 209   if (!__r_node_is_good (node))
 210     assert (0);
 211   if (node->flags.is_leaf)
 212     return 1;
 213   for (i = 0; i < M_SIZE; i++)
 214     {
 215       if (!__r_tree_is_good (node->u.kids[i]))
 216         return 0;
 217     }
 218   return 1;
 219 }
 220 #endif
 221 #ifndef NDEBUG
 222 /* print out the tree */
 223 void
 224 __r_dump_tree (struct rtree_node *node, int depth)
 225 {
 226   int i, j;
 227   static int count;
 228   static double area;
 229
 230   if (depth == 0)
 231     {
 232       area = 0;
 233       count = 0;
 234     }
 235   area +=
 236     (node->box.X2 - node->box.X1) * (double) (node->box.Y2 - node->box.Y1);
 237   count++;
 238   for (i = 0; i < depth; i++)
 239     printf ("  ");
 240   if (!node->flags.is_leaf)
 241     {
 242       printf ("p=0x%p node X(%d, %d) Y(%d, %d)\n", (void *) node,
 243               node->box.X1, node->box.X2, node->box.Y1, node->box.Y2);
 244 #ifdef DRAWBOX
 245       gdk_gc_set_line_attributes (Output.fgGC, 4,
 246                                   GDK_LINE_SOLID, GDK_CAP_ROUND,
 247                                   GDK_JOIN_ROUND);
 248
 249       if (depth < max_layer + 1)
 250         gdk_gc_set_foreground (Output.fgGC, (LAYER_PTR (depth)->Color));
 251       else
 252         gdk_gc_set_foreground (Output.fgGC, PCB->WarnColor);
 253       XDrawCLine (Output.top_window->window, Output.fgGC,
 254                   node->box.X1, node->box.Y1, node->box.X2, node->box.Y1);
 255       XDrawCLine (Output.top_window->window, Output.fgGC,
 256                   node->box.X2, node->box.Y1, node->box.X2, node->box.Y2);
 257       XDrawCLine (Output.top_window->window, Output.fgGC,
 258                   node->box.X2, node->box.Y2, node->box.X1, node->box.Y2);
 259       XDrawCLine (Output.top_window->window, Output.fgGC,
 260                   node->box.X1, node->box.Y2, node->box.X1, node->box.Y1);
 261 #endif
 262     }
 263   else
 264     {
 265 #ifdef DRAWBOX
 266       gdk_gc_set_line_attributes (Output.fgGC, 2,
 267                                   GDK_LINE_SOLID, GDK_CAP_ROUND,
 268                                   GDK_JOIN_ROUND);
 269       gdk_gc_set_foreground (Output.fgGC, PCB->MaskColor);
 270       XDrawCLine (Output.top_window->window, Output.fgGC,
 271                   node->box.X1, node->box.Y1, node->box.X2, node->box.Y1);
 272       XDrawCLine (Output.top_window->window, Output.fgGC,
 273                   node->box.X2, node->box.Y1, node->box.X2, node->box.Y2);
 274       XDrawCLine (Output.top_window->window, Output.fgGC,
 275                   node->box.X2, node->box.Y2, node->box.X1, node->box.Y2);
 276       XDrawCLine (Output.top_window->window, Output.fgGC,
 277                   node->box.X1, node->box.Y2, node->box.X1, node->box.Y1);
 278 #endif
 279       printf ("p=0x%p leaf manage(%02x) X(%d, %d) Y(%d, %d)\n", (void *) node,
 280               node->flags.manage, node->box.X1, node->box.X2, node->box.Y1,
 281               node->box.Y2);
 282       for (j = 0; j < M_SIZE; j++)
 283         {
 284           if (!node->u.rects[j].bptr)
 285             break;
 286           area +=
 287             (node->u.rects[j].bounds.X2 -
 288              node->u.rects[j].bounds.X1) *
 289             (double) (node->u.rects[j].bounds.Y2 -
 290                       node->u.rects[j].bounds.Y1);
 291           count++;
 292 #ifdef DRAWBOX
 293           gdk_gc_set_line_attributes (Output.fgGC, 1,
 294                                       GDK_LINE_SOLID, GDK_CAP_ROUND,
 295                                       GDK_JOIN_ROUND);
 296           gdk_gc_set_foreground (Output.fgGC, PCB->ViaSelectedColor);
 297           XDrawCLine (Output.top_window->window, Output.fgGC,
 298                       node->u.rects[j].bounds.X1, node->u.rects[j].bounds.Y1,
 299                       node->u.rects[j].bounds.X2, node->u.rects[j].bounds.Y1);
 300           XDrawCLine (Output.top_window->window, Output.fgGC,
 301                       node->u.rects[j].bounds.X2, node->u.rects[j].bounds.Y1,
 302                       node->u.rects[j].bounds.X2, node->u.rects[j].bounds.Y2);
 303           XDrawCLine (Output.top_window->window, Output.fgGC,
 304                       node->u.rects[j].bounds.X2, node->u.rects[j].bounds.Y2,
 305                       node->u.rects[j].bounds.X1, node->u.rects[j].bounds.Y2);
 306           XDrawCLine (Output.top_window->window, Output.fgGC,
 307                       node->u.rects[j].bounds.X1, node->u.rects[j].bounds.Y2,
 308                       node->u.rects[j].bounds.X1, node->u.rects[j].bounds.Y1);
 309 #endif
 310           for (i = 0; i < depth + 1; i++)
 311             printf ("  ");
 312           printf ("entry 0x%p X(%d, %d) Y(%d, %d)\n",
 313                   (void *) (node->u.rects[j].bptr),
 314                   node->u.rects[j].bounds.X1, node->u.rects[j].bounds.X2,
 315                   node->u.rects[j].bounds.Y1, node->u.rects[j].bounds.Y2);
 316         }
 317       return;
 318     }
 319   for (i = 0; i < M_SIZE; i++)
 320     if (node->u.kids[i])
 321       __r_dump_tree (node->u.kids[i], depth + 1);
 322   if (depth == 0)
 323     printf ("average box area is %g\n", area / count);
 324 }
 325 #endif
 326
 327 /* Sort the children or entries of a node
 328  * according to the largest side.
 329  */
 330 #ifdef SORT
 331 static int
 332 cmp_box (const BoxType * a, const BoxType * b)
 333 {
 334   /* compare two box coordinates so that the __r_search
 335    * will fail at the earliest comparison possible.
 336    * It needs to see the biggest X1 first, then the
 337    * smallest X2, the biggest Y1 and smallest Y2
 338    */
 339   if (a->X1 < b->X1)
 340     return 0;
 341   if (a->X1 > b->X1)
 342     return 1;
 343   if (a->X2 > b->X2)
 344     return 0;
 345   if (a->X2 < b->X2)
 346     return 1;
 347   if (a->Y1 < b->Y1)
 348     return 0;
 349   if (a->Y1 > b->Y1)
 350     return 1;
 351   if (a->Y2 > b->Y2)
 352     return 0;
 353   return 1;
 354 }
 355
 356 static void
 357 sort_node (struct rtree_node *node)
 358 {
 359   if (node->flags.is_leaf)
 360     {
 361       register Rentry *r, *i, temp;
 362
 363       for (r = &node->u.rects[1]; r->bptr; r++)
 364         {
 365           temp = *r;
 366           i = r - 1;
 367           while (i >= &node->u.rects[0])
 368             {
 369               if (cmp_box (&i->bounds, &r->bounds))
 370                 break;
 371               *(i + 1) = *i;
 372               i--;
 373             }
 374           *(i + 1) = temp;
 375         }
 376     }
 377 #ifdef SORT_NONLEAF
 378   else
 379     {
 380       register struct rtree_node **r, **i, *temp;
 381
 382       for (r = &node->u.kids[1]; *r; r++)
 383         {
 384           temp = *r;
 385           i = r - 1;
 386           while (i >= &node->u.kids[0])
 387             {
 388               if (cmp_box (&(*i)->box, &(*r)->box))
 389                 break;
 390               *(i + 1) = *i;
 391               i--;
 392             }
 393           *(i + 1) = temp;
 394         }
 395     }
 396 #endif
 397 }
 398 #else
 399 #define sort_node(x)
 400 #endif
 401
 402 /* set the node bounds large enough to encompass all
 403  * of the children's rectangles
 404  */
 405 static void
 406 adjust_bounds (struct rtree_node *node)
 407 {
 408   int i;
 409
 410   assert (node);
 411   assert (node->u.kids[0]);
 412   if (node->flags.is_leaf)
 413     {
 414       node->box = node->u.rects[0].bounds;
 415       for (i = 1; i < M_SIZE + 1; i++)
 416         {
 417           if (!node->u.rects[i].bptr)
 418             return;
 419           MAKEMIN (node->box.X1, node->u.rects[i].bounds.X1);
 420           MAKEMAX (node->box.X2, node->u.rects[i].bounds.X2);
 421           MAKEMIN (node->box.Y1, node->u.rects[i].bounds.Y1);
 422           MAKEMAX (node->box.Y2, node->u.rects[i].bounds.Y2);
 423         }
 424     }
 425   else
 426     {
 427       node->box = node->u.kids[0]->box;
 428       for (i = 1; i < M_SIZE + 1; i++)
 429         {
 430           if (!node->u.kids[i])
 431             return;
 432           MAKEMIN (node->box.X1, node->u.kids[i]->box.X1);
 433           MAKEMAX (node->box.X2, node->u.kids[i]->box.X2);
 434           MAKEMIN (node->box.Y1, node->u.kids[i]->box.Y1);
 435           MAKEMAX (node->box.Y2, node->u.kids[i]->box.Y2);
 436         }
 437     }
 438 }
 439
 440 /* create an r-tree from an unsorted list of boxes.
 441  * the r-tree will keep pointers into
 442  * it, so don't free the box list until you've called r_destroy_tree.
 443  * if you set 'manage' to true, r_destroy_tree will free your boxlist.
 444  */
 445 rtree_t *
 446 r_create_tree (const BoxType * boxlist[], int N, int manage)
 447 {
 448   rtree_t *rtree;
 449   struct rtree_node *node;
 450   int i;
 451
 452   assert (N >= 0);
 453   rtree = calloc (1, sizeof (*rtree));
 454   /* start with a single empty leaf node */
 455   node = calloc (1, sizeof (*node));
 456   node->flags.is_leaf = 1;
 457   node->parent = NULL;
 458   rtree->root = node;
 459   /* simple, just insert all of the boxes! */
 460   for (i = 0; i < N; i++)
 461     {
 462       assert (boxlist[i]);
 463       r_insert_entry (rtree, boxlist[i], manage);
 464     }
 465 #ifdef SLOW_ASSERTS
 466   assert (__r_tree_is_good (rtree->root));
 467 #endif
 468   return rtree;
 469 }
 470
 471 static void
 472 __r_destroy_tree (struct rtree_node *node)
 473 {
 474   int i, flag = 1;
 475
 476   if (node->flags.is_leaf)
 477     for (i = 0; i < M_SIZE; i++)
 478       {
 479         if (!node->u.rects[i].bptr)
 480           break;
 481         if (node->flags.manage & flag)
 482           free ((void *) node->u.rects[i].bptr);
 483         flag = flag << 1;
 484       }
 485   else
 486     for (i = 0; i < M_SIZE; i++)
 487       {
 488         if (!node->u.kids[i])
 489           break;
 490         __r_destroy_tree (node->u.kids[i]);
 491       }
 492   free (node);
 493 }
 494
 495 /* free the memory associated with an rtree. */
 496 void
 497 r_destroy_tree (rtree_t ** rtree)
 498 {
 499
 500   __r_destroy_tree ((*rtree)->root);
 501   free (*rtree);
 502   *rtree = NULL;
 503 }
 504
 505 typedef struct
 506 {
 507   int (*check_it) (const BoxType * region, void *cl);
 508   int (*found_it) (const BoxType * box, void *cl);
 509   void *closure;
 510 } r_arg;
 511
 512 /* most of the auto-routing time is spent in this routine
 513  * so some careful thought has been given to maximizing the speed
 514  *
 515  */
 516 int
 517 __r_search (struct rtree_node *node, const BoxType * query, r_arg * arg)
 518 {
 519   assert (node);
 520   /** assert that starting_region is well formed */
 521   assert (query->X1 <= query->X2 && query->Y1 <= query->Y2);
 522   assert (node->box.X1 < query->X2 && node->box.X2 > query->X1 &&
 523           node->box.Y1 < query->Y2 && node->box.Y2 > query->X1);
 524 #ifdef SLOW_ASSERTS
 525   /** assert that node is well formed */
 526   assert (__r_node_is_good (node));
 527 #endif
 528   /* the check for bounds is done before entry. This saves the overhead
 529    * of building/destroying the stack frame for each bounds that fails
 530    * to intersect, which is the most common condition.
 531    */
 532   if (node->flags.is_leaf)
 533     {
 534       register int i;
 535       if (arg->found_it)        /* test this once outside of loop */
 536         {
 537           register int seen = 0;
 538           for (i = 0; node->u.rects[i].bptr; i++)
 539             {
 540               if ((node->u.rects[i].bounds.X1 < query->X2) &&
 541                   (node->u.rects[i].bounds.X2 > query->X1) &&
 542                   (node->u.rects[i].bounds.Y1 < query->Y2) &&
 543                   (node->u.rects[i].bounds.Y2 > query->Y1) &&
 544                   arg->found_it (node->u.rects[i].bptr, arg->closure))
 545                 seen++;
 546             }
 547           return seen;
 548         }
 549       else
 550         {
 551           register int seen = 0;
 552           for (i = 0; node->u.rects[i].bptr; i++)
 553             {
 554               if ((node->u.rects[i].bounds.X1 < query->X2) &&
 555                   (node->u.rects[i].bounds.X2 > query->X1) &&
 556                   (node->u.rects[i].bounds.Y1 < query->Y2) &&
 557                   (node->u.rects[i].bounds.Y2 > query->Y1))
 558                 seen++;
 559             }
 560           return seen;
 561         }
 562     }
 563
 564   /* not a leaf, recurse on lower nodes */
 565   if (arg->check_it)
 566     {
 567       int seen = 0;
 568       struct rtree_node **n;
 569       for (n = &node->u.kids[0]; *n; n++)
 570         {
 571           if ((*n)->box.X1 >= query->X2 ||
 572               (*n)->box.X2 <= query->X1 ||
 573               (*n)->box.Y1 >= query->Y2 || (*n)->box.Y2 <= query->Y1 ||
 574               !arg->check_it (&(*n)->box, arg->closure))
 575             continue;
 576           seen += __r_search (*n, query, arg);
 577         }
 578       return seen;
 579     }
 580   else
 581     {
 582       int seen = 0;
 583       struct rtree_node **n;
 584       for (n = &node->u.kids[0]; *n; n++)
 585         {
 586           if ((*n)->box.X1 >= query->X2 ||
 587               (*n)->box.X2 <= query->X1 ||
 588               (*n)->box.Y1 >= query->Y2 || (*n)->box.Y2 <= query->Y1)
 589             continue;
 590           seen += __r_search (*n, query, arg);
 591         }
 592       return seen;
 593     }
 594 }
 595
 596 /* Parameterized search in the rtree.
 597  * Returns the number of rectangles found.
 598  * calls found_rectangle for each intersection seen
 599  * and calls check_region with the current sub-region
 600  * to see whether deeper searching is desired
 601  */
 602 int
 603 r_search (rtree_t * rtree, const BoxType * query,
 604           int (*check_region) (const BoxType * region, void *cl),
 605           int (*found_rectangle) (const BoxType * box, void *cl), void *cl)
 606 {
 607   r_arg arg;
 608
 609   if (!rtree || rtree->size < 1)
 610     return 0;
 611   if (query)
 612     {
 613 #if DEBUG
 614       if (query->X2 < query->X1 || query->Y2 < query->Y1)
 615         return 0;
 616 #endif
 617       /* check this box. If it's not touched we're done here */
 618       if (rtree->root->box.X1 >= query->X2 ||
 619           rtree->root->box.X2 <= query->X1 ||
 620           rtree->root->box.Y1 >= query->Y2
 621           || rtree->root->box.Y2 <= query->Y1)
 622         return 0;
 623       arg.check_it = check_region;
 624       arg.found_it = found_rectangle;
 625       arg.closure = cl;
 626       return __r_search (rtree->root, query, &arg);
 627     }
 628   else
 629     {
 630       arg.check_it = check_region;
 631       arg.found_it = found_rectangle;
 632       arg.closure = cl;
 633       return __r_search (rtree->root, &rtree->root->box, &arg);
 634     }
 635 }
 636
 637 /*------ r_region_is_empty ------*/
 638 static int
 639 __r_region_is_empty_rect_in_reg (const BoxType * box, void *cl)
 640 {
 641   jmp_buf *envp = (jmp_buf *) cl;
 642   longjmp (*envp, 1);           /* found one! */
 643 }
 644
 645 /* return 0 if there are any rectangles in the given region. */
 646 int
 647 r_region_is_empty (rtree_t * rtree, const BoxType * region)
 648 {
 649   jmp_buf env;
 650   int r;
 651
 652   if (setjmp (env))
 653     return 0;
 654   r = r_search (rtree, region, NULL, __r_region_is_empty_rect_in_reg, &env);
 655   assert (r == 0);              /* otherwise longjmp would have been called */
 656   return 1;                     /* no rectangles found */
 657 }
 658
 659 struct centroid
 660 {
 661   float x, y, area;
 662 };
 663
 664 /* split the node into two nodes putting clusters in each
 665  * use the k-means clustering algorithm
 666  */
 667 struct rtree_node *
 668 find_clusters (struct rtree_node *node)
 669 {
 670   float total_a, total_b;
 671   float a_X, a_Y, b_X, b_Y;
 672   Boolean belong[M_SIZE + 1];
 673   struct centroid center[M_SIZE + 1];
 674   int clust_a, clust_b, tries;
 675   int a_manage = 0, b_manage = 0;
 676   int i, old_ax, old_ay, old_bx, old_by;
 677   struct rtree_node *new_node;
 678   BoxType *b;
 679
 680   for (i = 0; i < M_SIZE + 1; i++)
 681     {
 682       if (node->flags.is_leaf)
 683         b = &(node->u.rects[i].bounds);
 684       else
 685         b = &(node->u.kids[i]->box);
 686       center[i].x = 0.5 * (b->X1 + b->X2);
 687       center[i].y = 0.5 * (b->Y1 + b->Y2);
 688       /* adding 1 prevents zero area */
 689       center[i].area = 1. + (float) (b->X2 - b->X1) * (float) (b->Y2 - b->Y1);
 690     }
 691   /* starting 'A' cluster center */
 692   a_X = center[0].x;
 693   a_Y = center[0].y;
 694   /* starting 'B' cluster center */
 695   b_X = center[M_SIZE].x;
 696   b_Y = center[M_SIZE].y;
 697   /* don't allow the same cluster centers */
 698   if (b_X == a_X && b_Y == a_Y)
 699     {
 700       b_X += 10000;
 701       a_Y -= 10000;
 702     }
 703   for (tries = 0; tries < M_SIZE; tries++)
 704     {
 705       old_ax = (int) a_X;
 706       old_ay = (int) a_Y;
 707       old_bx = (int) b_X;
 708       old_by = (int) b_Y;
 709       clust_a = clust_b = 0;
 710       for (i = 0; i < M_SIZE + 1; i++)
 711         {
 712           float dist1, dist2;
 713
 714           dist1 = SQUARE (a_X - center[i].x) + SQUARE (a_Y - center[i].y);
 715           dist2 = SQUARE (b_X - center[i].x) + SQUARE (b_Y - center[i].y);
 716           if (dist1 * (clust_a + M_SIZE / 2) < dist2 * (clust_b + M_SIZE / 2))
 717             {
 718               belong[i] = True;
 719               clust_a++;
 720             }
 721           else
 722             {
 723               belong[i] = False;
 724               clust_b++;
 725             }
 726         }
 727       /* kludge to fix degenerate cases */
 728       if (clust_a == M_SIZE + 1)
 729         belong[M_SIZE / 2] = False;
 730       else if (clust_b == M_SIZE + 1)
 731         belong[M_SIZE / 2] = True;
 732       /* compute new center of gravity of clusters */
 733       total_a = total_b = 0;
 734       a_X = a_Y = b_X = b_Y = 0;
 735       for (i = 0; i < M_SIZE + 1; i++)
 736         {
 737           if (belong[i])
 738             {
 739               a_X += center[i].x * center[i].area;
 740               a_Y += center[i].y * center[i].area;
 741               total_a += center[i].area;
 742             }
 743           else
 744             {
 745               b_X += center[i].x * center[i].area;
 746               b_Y += center[i].y * center[i].area;
 747               total_b += center[i].area;
 748             }
 749         }
 750       a_X /= total_a;
 751       a_Y /= total_a;
 752       b_X /= total_b;
 753       b_Y /= total_b;
 754       if (old_ax == (int) a_X && old_ay == (int) a_Y &&
 755           old_bx == (int) b_X && old_by == (int) b_Y)
 756         break;
 757     }
 758   /* Now 'belong' has the partition map */
 759   new_node = calloc (1, sizeof (*new_node));
 760   new_node->parent = node->parent;
 761   new_node->flags.is_leaf = node->flags.is_leaf;
 762   clust_a = clust_b = 0;
 763   if (node->flags.is_leaf)
 764     {
 765       int flag, a_flag, b_flag;
 766       flag = a_flag = b_flag = 1;
 767       for (i = 0; i < M_SIZE + 1; i++)
 768         {
 769           if (belong[i])
 770             {
 771               node->u.rects[clust_a++] = node->u.rects[i];
 772               if (node->flags.manage & flag)
 773                 a_manage |= a_flag;
 774               a_flag <<= 1;
 775             }
 776           else
 777             {
 778               new_node->u.rects[clust_b++] = node->u.rects[i];
 779               if (node->flags.manage & flag)
 780                 b_manage |= b_flag;
 781               b_flag <<= 1;
 782             }
 783           flag <<= 1;
 784         }
 785     }
 786   else
 787     {
 788       for (i = 0; i < M_SIZE + 1; i++)
 789         {
 790           if (belong[i])
 791             node->u.kids[clust_a++] = node->u.kids[i];
 792           else
 793             {
 794               node->u.kids[i]->parent = new_node;
 795               new_node->u.kids[clust_b++] = node->u.kids[i];
 796             }
 797         }
 798     }
 799   node->flags.manage = a_manage;
 800   new_node->flags.manage = b_manage;
 801   assert (clust_a != 0);
 802   assert (clust_b != 0);
 803   if (node->flags.is_leaf)
 804     for (; clust_a < M_SIZE + 1; clust_a++)
 805       node->u.rects[clust_a].bptr = NULL;
 806   else
 807     for (; clust_a < M_SIZE + 1; clust_a++)
 808       node->u.kids[clust_a] = NULL;
 809   adjust_bounds (node);
 810   sort_node (node);
 811   adjust_bounds (new_node);
 812   sort_node (new_node);
 813   return (new_node);
 814 }
 815
 816 /* split a node according to clusters
 817  */
 818 static void
 819 split_node (struct rtree_node *node)
 820 {
 821   int i;
 822   struct rtree_node *new_node;
 823
 824   assert (node);
 825   assert (node->flags.is_leaf ? (void *) node->u.rects[M_SIZE].
 826           bptr : (void *) node->u.kids[M_SIZE]);
 827   new_node = find_clusters (node);
 828   if (node->parent == NULL)     /* split root node */
 829     {
 830       struct rtree_node *second;
 831
 832       second = calloc (1, sizeof (*second));
 833       *second = *node;
 834       if (!second->flags.is_leaf)
 835         for (i = 0; i < M_SIZE; i++)
 836           if (second->u.kids[i])
 837             second->u.kids[i]->parent = second;
 838       node->flags.is_leaf = 0;
 839       node->flags.manage = 0;
 840       second->parent = new_node->parent = node;
 841       node->u.kids[0] = new_node;
 842       node->u.kids[1] = second;
 843       for (i = 2; i < M_SIZE + 1; i++)
 844         node->u.kids[i] = NULL;
 845       adjust_bounds (node);
 846       sort_node (node);
 847 #ifdef SLOW_ASSERTS
 848       assert (__r_tree_is_good (node));
 849 #endif
 850       return;
 851     }
 852   for (i = 0; i < M_SIZE; i++)
 853     if (!node->parent->u.kids[i])
 854       break;
 855   node->parent->u.kids[i] = new_node;
 856 #ifdef SLOW_ASSERTS
 857   assert (__r_node_is_good (node));
 858   assert (__r_node_is_good (new_node));
 859 #endif
 860   if (i < M_SIZE)
 861     {
 862 #ifdef SLOW_ASSERTS
 863       assert (__r_node_is_good (node->parent));
 864 #endif
 865       sort_node (node->parent);
 866       return;
 867     }
 868   split_node (node->parent);
 869 }
 870
 871 static inline int
 872 contained (struct rtree_node *node, const BoxType * query)
 873 {
 874   if (node->box.X1 > query->X1 || node->box.X2 < query->X2 ||
 875       node->box.Y1 > query->Y1 || node->box.Y2 < query->Y2)
 876     return 0;
 877   return 1;
 878 }
 879
 880
 881 static inline bigun
 882 penalty (struct rtree_node *node, const BoxType * query)
 883 {
 884   long long score;
 885
 886   /* Compute the area penalty for inserting here and return.
 887    * The penalty is the increase in area necessary
 888    * to include the query->
 889    */
 890   score = (MAX (node->box.X2, query->X2) - MIN (node->box.X1, query->X1));
 891   score *=
 892     (MAX (node->box.Y2, query->Y2) - MIN (node->box.Y1, query->Y1));
 893   score -=
 894     ((long long) node->box.X2 -
 895      node->box.X1) * ((long long) node->box.Y2 - node->box.Y1);
 896   return score;
 897 }
 898
 899 static void
 900 __r_insert_node (struct rtree_node *node, const BoxType * query,
 901                  int manage, Boolean force)
 902 {
 903
 904 #ifdef SLOW_ASSERTS
 905   assert (__r_node_is_good (node));
 906 #endif
 907   /* Ok, at this point we must already enclose the query or we're forcing
 908    * this node to expand to enclose it, so if we're a leaf, simply store
 909    * the query here
 910    */
 911
 912   if (node->flags.is_leaf)
 913     {
 914       register int i;
 915
 916       if (manage)
 917         {
 918           register int flag = 1;
 919
 920           for (i = 0; i < M_SIZE; i++)
 921             {
 922               if (!node->u.rects[i].bptr)
 923                 break;
 924               flag <<= 1;
 925             }
 926           node->flags.manage |= flag;
 927         }
 928       else
 929         {
 930           for (i = 0; i < M_SIZE; i++)
 931             if (!node->u.rects[i].bptr)
 932               break;
 933         }
 934       /* the node always has an extra space available */
 935       node->u.rects[i].bptr = query;
 936       node->u.rects[i].bounds = *query;
 937       /* first entry in node determines initial bounding box */
 938       if (i == 0)
 939         node->box = *query;
 940       else if (force)
 941         {
 942           MAKEMIN (node->box.X1, query->X1);
 943           MAKEMAX (node->box.X2, query->X2);
 944           MAKEMIN (node->box.Y1, query->Y1);
 945           MAKEMAX (node->box.Y2, query->Y2);
 946         }
 947       if (i < M_SIZE)
 948         {
 949           sort_node (node);
 950           return;
 951         }
 952       /* we must split the node */
 953       split_node (node);
 954       return;
 955     }
 956   else
 957     {
 958       int i;
 959       struct rtree_node *best_node;
 960       long long score, best_score;
 961
 962       if (force)
 963         {
 964           MAKEMIN (node->box.X1, query->X1);
 965           MAKEMAX (node->box.X2, query->X2);
 966           MAKEMIN (node->box.Y1, query->Y1);
 967           MAKEMAX (node->box.Y2, query->Y2);
 968         }
 969
 970       /* this node encloses it, but it's not a leaf, so descend the tree */
 971
 972       /* First check if any children actually encloses it */
 973       assert (node->u.kids[0]);
 974       for (i = 0; i < M_SIZE; i++)
 975         {
 976           if (!node->u.kids[i])
 977             break;
 978           if (contained (node->u.kids[i], query))
 979             {
 980               __r_insert_node (node->u.kids[i], query, manage, False);
 981               sort_node (node);
 982               return;
 983             }
 984         }
 985
 986       /* see if there is room for a new leaf node */
 987       if (node->u.kids[0]->flags.is_leaf && i < M_SIZE)
 988         {
 989           struct rtree_node *new_node;
 990           new_node = calloc (1, sizeof (*new_node));
 991           new_node->parent = node;
 992           new_node->flags.is_leaf = True;
 993           node->u.kids[i] = new_node;
 994           new_node->u.rects[0].bptr = query;
 995           new_node->u.rects[0].bounds = *query;
 996           new_node->box = *query;
 997           if (manage)
 998             new_node->flags.manage = 1;
 999           sort_node (node);
1000           return;
1001         }
1002
1003       /* Ok, so we're still here - look for the best child to push it into */
1004       best_score = penalty (node->u.kids[0], query);
1005       best_node = node->u.kids[0];
1006       for (i = 1; i < M_SIZE; i++)
1007         {
1008           if (!node->u.kids[i])
1009             break;
1010           score = penalty (node->u.kids[i], query);
1011           if (score < best_score)
1012             {
1013               best_score = score;
1014               best_node = node->u.kids[i];
1015             }
1016         }
1017       __r_insert_node (best_node, query, manage, True);
1018       sort_node (node);
1019       return;
1020     }
1021 }
1022
1023 void
1024 r_insert_entry (rtree_t * rtree, const BoxType * which, int man)
1025 {
1026   assert (which);
1027   assert (which->X1 <= which->X2);
1028   assert (which->Y1 <= which->Y2);
1029   /* recursively search the tree for the best leaf node */
1030   assert (rtree->root);
1031   __r_insert_node (rtree->root, which, man,
1032                    rtree->root->box.X1 > which->X1
1033                    || rtree->root->box.X2 < which->X2
1034                    || rtree->root->box.Y1 > which->Y1
1035                    || rtree->root->box.Y2 < which->Y2);
1036   rtree->size++;
1037 }
1038
1039 Boolean
1040 __r_delete (rtree_t * seed, struct rtree_node *node, const BoxType * query)
1041 {
1042   int i, flag, mask, a;
1043
1044   /* the tree might be inconsistent during delete */
1045   if (query->X1 < node->box.X1 || query->Y1 < node->box.Y1
1046       || query->X2 > node->box.X2 || query->Y2 > node->box.Y2)
1047     return False;
1048   if (!node->flags.is_leaf)
1049     {
1050       for (i = 0; i < M_SIZE; i++)
1051         {
1052           /* if this is us being removed, free and copy over */
1053           if (node->u.kids[i] == (struct rtree_node *) query)
1054             {
1055               free ((void *) query);
1056               for (; i < M_SIZE; i++)
1057                 {
1058                   node->u.kids[i] = node->u.kids[i + 1];
1059                   if (!node->u.kids[i])
1060                     break;
1061                 }
1062               /* nobody home here now ? */
1063               if (!node->u.kids[0])
1064                 {
1065                   if (!node->parent)
1066                     {
1067                       /* wow, the root is empty! */
1068                       node->flags.is_leaf = 1;
1069                       /* changing type of node, be sure it's all zero */
1070                       for (i = 1; i < M_SIZE + 1; i++)
1071                         node->u.rects[i].bptr = NULL;
1072                       return True;
1073                     }
1074                   return (__r_delete (seed, node->parent, &node->box));
1075                 }
1076               else
1077                 /* propegate boundary adjust upward */
1078                 while (node)
1079                   {
1080                     adjust_bounds (node);
1081                     node = node->parent;
1082                   }
1083               return True;
1084             }
1085           if (node->u.kids[i])
1086             {
1087               if (__r_delete (seed, node->u.kids[i], query))
1088                 return True;
1089             }
1090           else
1091             break;
1092         }
1093       return False;
1094     }
1095   /* leaf node here */
1096   mask = 0;
1097   a = 1;
1098   for (i = 0; i < M_SIZE; i++)
1099     {
1100 #ifdef DELETE_BY_POINTER
1101       if (!node->u.rects[i].bptr || node->u.rects[i].bptr == query)
1102 #else
1103       if (node->u.rects[i].bounds.X1 == query->X1 &&
1104           node->u.rects[i].bounds.X2 == query->X2 &&
1105           node->u.rects[i].bounds.Y1 == query->Y1 &&
1106           node->u.rects[i].bounds.Y2 == query->Y2)
1107 #endif
1108         break;
1109       mask |= a;
1110       a <<= 1;
1111     }
1112   if (!node->u.rects[i].bptr)
1113     return False;               /* not at this leaf */
1114   if (node->flags.manage & a)
1115     {
1116       free ((void *) node->u.rects[i].bptr);
1117       node->u.rects[i].bptr = NULL;
1118     }
1119   /* squeeze the manage flags together */
1120   flag = node->flags.manage & mask;
1121   mask = (~mask) << 1;
1122   node->flags.manage = flag | ((node->flags.manage & mask) >> 1);
1123   /* remove the entry */
1124   for (; i < M_SIZE; i++)
1125     {
1126       node->u.rects[i] = node->u.rects[i + 1];
1127       if (!node->u.rects[i].bptr)
1128         break;
1129     }
1130   if (!node->u.rects[0].bptr)
1131     {
1132       if (node->parent)
1133         __r_delete (seed, node->parent, &node->box);
1134       return True;
1135     }
1136   else
1137     /* propagate boundary adjustment upward */
1138     while (node)
1139       {
1140         adjust_bounds (node);
1141         node = node->parent;
1142       }
1143   return True;
1144 }
1145
1146 Boolean
1147 r_delete_entry (rtree_t * rtree, const BoxType * box)
1148 {
1149   Boolean r;
1150
1151   assert (box);
1152   assert (rtree);
1153   r = __r_delete (rtree, rtree->root, box);
1154   if (r)
1155     rtree->size--;
1156 #ifdef SLOW_ASSERTS
1157   assert (__r_tree_is_good (rtree->root));
1158 #endif
1159   return r;
1160 }
1161
1162 int
1163 __r_sub (struct rtree_node *node, const BoxType * b, const BoxType * a,
1164          jmp_buf * e)
1165 {
1166   int i;
1167
1168   if (node->flags.is_leaf)
1169     {
1170       for (i = 0; i < M_SIZE; i++)
1171         if (node->u.rects[i].bptr == b)
1172           {
1173             node->u.rects[i].bptr = a;
1174             assert (a->X1 == node->u.rects[i].bounds.X1);
1175             assert (a->X2 == node->u.rects[i].bounds.X2);
1176             assert (a->Y1 == node->u.rects[i].bounds.Y1);
1177             assert (a->Y2 == node->u.rects[i].bounds.Y2);
1178             longjmp (*e, 1);
1179           }
1180       return 0;
1181     }
1182   for (i = 0; i < M_SIZE; i++)
1183     if (node->u.kids[i] && __r_sub (node->u.kids[i], b, a, e))
1184       return 1;
1185   return 0;
1186 }
1187
1188
1189 void
1190 r_substitute (rtree_t * rtree, const BoxType * before, const BoxType * after)
1191 {
1192   jmp_buf env;
1193
1194   if (before == after)
1195     return;
1196   if (setjmp (env) == 0)
1197     __r_sub (rtree->root, before, after, &env);
1198 }