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quadtree: Macros with complex values should be enclosed in parenthesis
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1 #include <stdio.h>
2 #include <stdlib.h>
3
4 #include "quadtree.h"
5
6 #ifdef DEBUG
7 #define debug 1
8 #else
9 #define debug 0
10 #endif
11
12 static void _trap(int line)
13 {
14         if (debug) {
15                 printf("Trapped from line %d, use debugger to get backtrace\n",
16                         line);
17                 fflush(stdout);
18                 exit(1);
19         }
20 }
21
22 #define trap() _trap(__LINE__)
23
24 static int quadtree_compare_coord(const struct vector *a,
25                                 const struct vector *b)
26 {
27         int up, left;
28
29         up = b->y < a->y;
30         left = b->x < a->x;
31
32         if (up && left)
33                 return 0;
34         if (up && !left)
35                 return 1;
36         if (left)
37                 return 2;
38         return 3;
39 }
40
41 static int quadtree_compare(const struct quadtree *a, const struct quadtree *b)
42 {
43         return quadtree_compare_coord(&a->pos, &b->pos);
44 }
45
46 static void validate_subtree(const struct quadtree *node)
47 {
48         int i, dir;
49         long int children;
50         children = 0;
51
52         if (!node) {
53                 printf("Attempted to validate a null pointer\n");
54                 fflush(stdout);
55                 trap();
56         }
57
58         for (i = 0; i < 4; i++) {
59                 if (!node->child[i])
60                         continue;
61
62                 if (node->child[i]->parent != node) {
63                         printf("%s:%d Fatal! Tree inconsistency detected at "
64                                "child %d %p in node %p, incorrent parent %p\n",
65                                __func__, __LINE__, i, node->child[i], node,
66                                node->child[i]->parent);
67                         fflush(stdout);
68                         trap();
69                 }
70
71                 if (node->parent) {
72                         if (node->child[i] == node->parent) {
73                                 printf("%s:%d Fatal! Tree loop detected "
74                                        "at child %d in node %p\n",
75                                        __func__, __LINE__, i, node);
76                                 fflush(stdout);
77                                 trap();
78                         }
79                 }
80
81                 dir = quadtree_compare(node, node->child[i]);
82
83                 if (dir != i) {
84                         printf("%s:%d Fatal! Spatial inconsistency detected "
85                                 "at child %d in node %p\n"
86                                 "parent: (%f %f), child (%f %f), "
87                                 "dir %d != %d\n",
88                                 __func__, __LINE__, i, node,
89                                 node->pos.x, node->pos.y,
90                                 node->child[i]->pos.x, node->child[i]->pos.y,
91                                 dir, i);
92                         fflush(stdout);
93                         trap();
94                 }
95
96                 children += node->child[i]->children + 1;
97
98                 validate_subtree(node->child[i]);
99         }
100
101         if (node->depth < 0) {
102                 printf("%s:%d Tree statistics inconsistency detected! "
103                        "Negative depth: %ld\n",
104                        __func__, __LINE__, node->depth);
105         }
106
107         if (node->children != children) {
108                 printf("%s:%d Tree statistics inconsistency detected! "
109                        "child count mismatch. Expected %ld, got %ld\n",
110                        __func__, __LINE__, children, node->children);
111                 fflush(stdout);
112                 trap();
113         }
114
115         for (i = 0; i < 4 && node->children; i++) {
116                 if (!node->child[i])
117                         continue;
118
119                 if (node->depth == node->child[i]->depth + 1)
120                         break;
121
122                 if (node->child[i]->depth > node->depth) {
123                         printf("%s:%d Tree statistics inconsistency detected! "
124                                "child depth mismatch %ld > %ld\n",
125                                __func__, __LINE__, node->child[i]->depth,
126                                node->depth);
127                 }
128         }
129
130         if (i == 4) {
131                 printf("%s:%d Tree statistics inconsistency detected! "
132                        "child depth mismatch.",
133                        __func__, __LINE__);
134                 fflush(stdout);
135                 trap();
136         }
137 }
138
139 static void validate_tree(const struct quadtree *node)
140 {
141         int i;
142
143         if (!debug)
144                 return;
145
146         if (!node->parent)
147                 return validate_subtree(node);
148
149         for (i = 0; i < 4; i++)
150                 if (node->parent->child[i] == node)
151                         break;
152
153         if (i == 4) {
154                 printf("%s:%d Tree inconsistency detected! "
155                         "Wrong parent %p for node %p\n",
156                         __func__, __LINE__, node->parent, node);
157                 fflush(stdout);
158                 trap();
159         }
160
161         validate_tree(node->parent);
162 }
163
164 void _quadtree_validate_tree(const struct quadtree *node)
165 {
166         validate_tree(node);
167 }
168
169 static struct quadtree *_quadtree_add(struct quadtree *parent,
170                                 struct quadtree *new)
171 {
172         int ret, i;
173
174         ret = quadtree_compare(parent, new);
175
176         if (ret < 0 || ret >= 4) {
177                 printf("Invalid comparison result of %d\n", ret);
178                 return 0;
179         }
180
181         if (parent->child[ret])
182                 return _quadtree_add(parent->child[ret], new);
183
184         parent->child[ret] = new;
185         new->parent = parent;
186         for (i = 0; i < 4; i++)
187                 new->child[i] = 0;
188
189         return new;
190 }
191
192 static void _recalculate_node_area_stats(struct quadtree *node)
193 {
194                 /* The space covered by the parent node's corner
195                  * points needs be as wide as its widest child node's
196                  * corners.
197                  */
198 #define CHILD_CORNER_SAFE(node, ch_idx, cor_idx, axis)          \
199         ((node)->child[ch_idx] ?                                \
200                 (node)->child[ch_idx]->corner[cor_idx].axis :   \
201                 (node)->pos.axis)
202
203                 node->corner[0].x = MIN(CHILD_CORNER_SAFE(node, 0, 0, x),
204                                         CHILD_CORNER_SAFE(node, 2, 0, x));
205                 node->corner[0].y = MIN(CHILD_CORNER_SAFE(node, 0, 0, y),
206                                         CHILD_CORNER_SAFE(node, 1, 0, y));
207                 node->corner[1].x = MAX(CHILD_CORNER_SAFE(node, 1, 1, x),
208                                         CHILD_CORNER_SAFE(node, 3, 1, x));
209                 node->corner[1].y = MAX(CHILD_CORNER_SAFE(node, 2, 1, y),
210                                         CHILD_CORNER_SAFE(node, 3, 1, y));
211 #undef CHILD_CORNER_SAFE
212 }
213
214 static void recalculate_parent_area_stats(struct quadtree *node)
215 {
216         while (node) {
217                 _recalculate_node_area_stats(node);
218
219                 node = node->parent;
220         }
221 }
222
223 /*
224  * Recursively walk through the tree and propagate changes made to the
225  * given node up until the highest parent.
226  */
227 static void quadtree_recalculate_parent_stats(struct quadtree *node,
228                                                      struct quadtree_ops *ops)
229 {
230         int i;
231
232         while (node) {
233                 node->depth = 0;
234                 node->children = 0;
235
236                 for (i = 0; i < 4; i++) {
237                         if (!node->child[i])
238                                 continue;
239
240                         node->depth = MAX(node->depth,
241                                           node->child[i]->depth + 1);
242                         node->children += node->child[i]->children + 1;
243                 }
244
245                 _recalculate_node_area_stats(node);
246
247                 if (ops->recalculate_stats)
248                         ops->recalculate_stats(node);
249
250                 node = node->parent;
251         }
252 }
253
254 /**
255  * quadtree_add - add a node to a quadtree
256  * @parent: parent node
257  * @new: the new node to be added
258  *
259  * Add a node to a quadtree. The tree is kept in order, the new node
260  * is placed in the end of appropriate branch.
261  *
262  * The case of nodes sharing identical coordinates is not taken into
263  * account at all.
264  */
265
266 struct quadtree *quadtree_add(struct quadtree *parent, struct quadtree *new,
267                               struct quadtree_ops *ops)
268 {
269         if (parent == new)
270                 trap();
271
272         validate_tree(parent);
273
274         _quadtree_add(parent, new);
275
276         if (debug) {
277                 printf("adding node %p to parent %p\n", new, parent);
278                 fflush(stdout);
279         }
280
281         quadtree_recalculate_parent_stats(new, ops);
282
283         validate_tree(new);
284
285         return new;
286 }
287
288 static int is_within(struct vector *pos, struct vector *corner)
289 {
290         if ((pos->x >= corner[1].x) && (pos->x <= corner[0].x) &&
291             (pos->y >= corner[1].y) && (pos->y <= corner[0].y))
292                 return 1;
293         return 0;
294 }
295
296 static int quadrants_to_search(struct quadtree *node, struct vector *corner)
297 {
298         int direction = 0, i;
299         int up = 0, left = 0, right = 0, down = 0;
300
301         for (i = 0; i < 2; i++) {
302                 if (corner[i].x <= node->pos.x)
303                         left = 1;
304                 else if (corner[i].x >= node->pos.x)
305                         right = 1;
306                 if (corner[i].y <= node->pos.y)
307                         up = 1;
308                 else if (corner[i].y >= node->pos.y)
309                         down = 1;
310         }
311
312         if (left || up)
313                 direction |= QUADTREE_UPLEFT;
314         if (right || up)
315                 direction |= QUADTREE_UPRIGHT;
316         if (left || down)
317                 direction |= QUADTREE_DOWNLEFT;
318         if (right || down)
319                 direction |= QUADTREE_DOWNRIGHT;
320
321         return direction;
322 }
323
324 static struct quadtree *quadtree_find_nearest(struct quadtree *tree,
325                                         struct vector *pos,
326                                         struct vector *corner)
327 {
328         struct vector tmp;
329         struct quadtree *nearest, *node;
330         double distance = 0, dist;
331         int i, directions;
332
333         if (!is_within(pos, corner)) {
334                 if (debug) {
335                         printf("No nearest to be found from (%f %f) (%f %f) "
336                                 "pos (%f %f)\n",
337                                 corner[0].x, corner[0].y,
338                                 corner[1].x, corner[1].y,
339                                 pos->x, pos->y);
340                         fflush(stdout);
341                 }
342                 return NULL;
343         }
344
345         if (is_within(&tree->pos, corner)) {
346                 vector_sub(pos, &tree->pos, &tmp);
347                 distance = vector_abs(&tmp);
348                 nearest = tree;
349         } else {
350                 nearest = NULL;
351         }
352
353         directions = quadrants_to_search(tree, corner);
354
355         for (i = 0; i < 4; i++) {
356                 if (!tree->child[i])
357                         continue;
358
359 /*
360                 if (!(directions & (1 << i)))
361                         continue;
362 */
363                 node = quadtree_find_nearest(tree->child[i], pos, corner);
364
365                 if (!node)
366                         continue;
367
368                 vector_sub(pos, &node->pos, &tmp);
369                 dist = vector_abs(&tmp);
370
371                 if (!nearest || dist < distance) {
372                         nearest = node;
373                         distance = dist;
374
375                 }
376         }
377
378         if (nearest && !is_within(&nearest->pos, corner)) {
379                 if (debug)
380                         printf("Node %p (%f %f) is not within "
381                                 "search window (%f %f) (%f %f)\n",
382                                 nearest, nearest->pos.x, nearest->pos.y,
383                                 corner[0].x, corner[0].y,
384                                 corner[1].x, corner[1].y);
385                 return NULL;
386         }
387
388         return nearest;
389 }
390
391 static struct quadtree *quadtree_find_nearest_noparent(struct quadtree *tree,
392                                                 struct vector *pos,
393                                                 struct vector *corner)
394 {
395         struct quadtree *nearest;
396         struct vector sub;
397         struct quadtree *node;
398         double dist = 0, dist2;
399         int i;
400
401         nearest = quadtree_find_nearest(tree, pos, corner);
402
403         if (nearest != tree)
404                 goto out;
405
406         if (debug)
407                 printf("Avoiding parent or NULL node %p\n", nearest);
408
409         /*
410          * oops, we don't want to pick the parent node, let's choose
411          * another one
412          */
413         nearest = NULL;
414         for (i = 0; i < 4; i++) {
415                 if (!tree->child[i])
416                         continue;
417
418                 if (!nearest) {
419                         nearest = quadtree_find_nearest(tree->child[i], pos,
420                                                         corner);
421
422                         if (nearest == NULL)
423                                 continue;
424
425                         vector_sub(pos, &nearest->pos, &sub);
426                         dist = vector_abs(&sub);
427                         continue;
428                 }
429                 node = quadtree_find_nearest(tree->child[i],
430                                         pos, corner);
431
432                 if (node == NULL)
433                         continue;
434
435                 vector_sub(pos, &node->pos, &sub);
436                 dist2 = vector_abs(&sub);
437
438                 if (dist2 < dist) {
439                         nearest = node;
440                         dist = dist2;
441                 }
442         }
443
444 out:
445         return nearest;
446 }
447
448 static void get_middle_point(struct vector *corner, struct vector *middle)
449 {
450         middle->x = (corner[0].x + corner[1].x) / (double)2;
451         middle->y = (corner[0].y + corner[1].y) / (double)2;
452 }
453
454 static int quadtree_split_by_node(struct quadtree *node,
455                                 struct vector *corner, int dir)
456 {
457         if (!is_within(&node->pos, corner)) {
458                 if (debug)
459                         printf("Not within search rectangle\n");
460                 return 0;
461         }
462
463         switch (dir) {
464         case QUADTREE_UPLEFT:
465                 corner[0] = node->pos;
466                 break;
467         case QUADTREE_UPRIGHT:
468                 corner[0].y = node->pos.y;
469                 corner[1].x = node->pos.x;
470                 break;
471         case QUADTREE_DOWNRIGHT:
472                 corner[1] = node->pos;
473                 break;
474         case QUADTREE_DOWNLEFT:
475                 corner[0].x = node->pos.x;
476                 corner[1].y = node->pos.y;
477                 break;
478         default:
479                 trap();
480         }
481
482         if (debug)
483                 printf("Search rectangle is now (%f %f) (%f %f), (%f %f)\n",
484                         corner[0].x, corner[0].y,
485                         corner[1].x, corner[1].y,
486                         node->pos.x, node->pos.y);
487
488         if ((corner[0].x < corner[1].x) ||
489             (corner[0].y < corner[1].y))
490                 trap();
491
492         return 1;
493 }
494
495 /*
496  * Quickly detach a node from a tree. Move all child nodes under
497  * @parent node.
498  */
499 static int _quadtree_del(struct quadtree *node, struct quadtree *parent)
500 {
501         struct quadtree *n;
502         int i;
503
504         /* Detach from the tree */
505         if (node->parent)
506                 for (i = 0; i < 4; i++) {
507                         if (node->parent->child[i] == node) {
508                                 node->parent->child[i] = 0;
509                                 break;
510                         }
511                 }
512
513         if (i == 4)
514                 trap();
515
516
517         for (i = 0; i < 4; i++) {
518                 if (!node->child[i])
519                         continue;
520
521                 n = node->child[i];
522                 _quadtree_del(n, parent);
523                 _quadtree_add(parent, n);
524         }
525
526         return 0;
527 }
528
529 /**
530  * Move everything under @tree node to @parent node, everything
531  * else except the @tree node itself
532  */
533 static int optimally_move_tree(struct quadtree *tree, struct quadtree *parent,
534                         struct vector *corner_orig,
535                         struct quadtree_ops *ops)
536 {
537         struct vector corner[2], mid;
538         struct quadtree *t, *tmp;
539         int moved = 0;
540
541         get_middle_point(corner_orig, &mid);
542         t = quadtree_find_nearest_noparent(tree, &mid, corner_orig);
543
544         if (!t) {
545                 if (debug)
546                         printf("Cannot find nearest node\n");
547
548                 goto out;
549         }
550
551         /*
552          * Now we have the t node which contains the object of the
553          * spatial middle coordinates of the tree.
554          */
555
556         if (debug) {
557                 printf("Relocating node %p (%f %f) under parent %p\n", t,
558                         t->pos.x, t->pos.y, parent);
559                 printf("There are %ld child nodes left\n", tree->children);
560                 fflush(stdout);
561         }
562         _quadtree_del(t, tree);
563         quadtree_add(parent, t, ops);
564
565         moved++;
566         tree->children--;
567         if (!tree->children)
568                 goto out;
569
570         /*
571          * Now split the search rectangle in quadtres and do the same
572          * with all of the quarters.
573          */
574
575         corner[0] = corner_orig[0];
576         corner[1] = corner_orig[1];
577         if (quadtree_split_by_node(t, corner, QUADTREE_UPLEFT))
578                 moved += optimally_move_tree(tree, parent, corner, ops);
579
580         corner[0] = corner_orig[0];
581         corner[1] = corner_orig[1];
582         if (quadtree_split_by_node(t, corner, QUADTREE_UPRIGHT))
583                 moved += optimally_move_tree(tree, parent, corner, ops);
584
585         corner[0] = corner_orig[0];
586         corner[1] = corner_orig[1];
587         if (quadtree_split_by_node(t, corner, QUADTREE_DOWNLEFT))
588                 moved += optimally_move_tree(tree, parent, corner, ops);
589
590         corner[0] = corner_orig[0];
591         corner[1] = corner_orig[1];
592         if (quadtree_split_by_node(t, corner, QUADTREE_DOWNRIGHT))
593                 moved += optimally_move_tree(tree, parent, corner, ops);
594
595         get_middle_point(corner_orig, &mid);
596         tmp = quadtree_find_nearest(tree, &mid, corner_orig);
597         if (tmp && tmp != tree)
598                 trap();
599
600 out:
601         if (debug)
602                 printf("Now moved %d nodes, %ld left\n", moved, tree->children);
603
604         return moved;
605 }
606
607 /*
608  * quadtree_del - Detach a node from the tree
609  *
610  * Return value: The new root node of the tree. If we are detaching
611  * anything but the root node of the entire tree, the returned root
612  * value will be the original root of the tree.
613  */
614 struct quadtree *quadtree_del(struct quadtree *node,
615                               struct quadtree_ops *ops)
616 {
617         struct quadtree *parent = NULL;
618         struct vector corner[2];
619         int i, children = node->children, moved;
620
621         validate_tree(node);
622
623         if (debug) {
624                 printf("Deleting node %p under parent %p\n",
625                                node, node->parent);
626                 printf("Relocating %ld children\n", node->children);
627                 fflush(stdout);
628         }
629
630         if (!node->parent) {
631                 /*
632                  * We are deleting the root node. This means we have
633                  * to select a new root node and reconstruct the
634                  * entire tree under it again.
635                  */
636                 if (debug) {
637                         printf("Deleting root node\n");
638                         fflush(stdout);
639                 }
640                 for (i = 0; i < 4; i++) {
641                         if (!node->child[i])
642                                 continue;
643
644                         parent = node->child[i];
645                         _quadtree_del(parent, node);
646                         parent->parent = 0;
647                         quadtree_recalculate_parent_stats(parent, ops);
648                         break;
649                 }
650         } else {
651                 /*
652                  * The node has a parent. Detach the node from it and
653                  * relocate the children.
654                  */
655
656                 for (i = 0; i < 4; i++) {
657                         if (node->parent->child[i] == node) {
658                                 node->parent->child[i] = 0;
659                                 break;
660                         }
661                 }
662                 if (i == 4)
663                         trap();
664
665                 parent = node->parent;
666
667                 /*
668                  * The sub branch is now detached from the main
669                  * tree. Fix the stats.
670                  */
671                 quadtree_recalculate_parent_stats(node->parent, ops);
672         }
673
674         validate_tree(parent);
675
676         if (!node->children)
677                 goto out;
678         /*
679          * Now we are ready to prepare for relocating the nodes under
680          * the parent.
681          */
682
683         corner[0] = node->corner[1];
684         corner[1] = node->corner[0];
685         moved = optimally_move_tree(node, parent, corner, ops);
686
687         if (debug) {
688                 if (moved != children) {
689                         printf("Got %d children but %d were moved\n",
690                                 children, moved);
691                         printf("nearest children left:\n");
692                         for (i = 0 ; i < 4; i++)
693                                 if (node->child[i])
694                                         printf("   node %d %p, (%f %f)\n",
695                                                 i, node->child[i],
696                                                 node->child[i]->pos.x,
697                                                 node->child[i]->pos.y);
698                         fflush(stdout);
699                         trap();
700                 }
701                 printf("Delete done, returning parent %p\n", parent);
702                 fflush(stdout);
703         }
704
705 out:
706         validate_tree(parent);
707         return quadtree_find_parent(parent);
708 }
709
710 static void check_for_crossed_subnodes(struct quadtree *node,
711                                 struct vector *limit, struct quadtree_ops *ops)
712 {
713         int direction = 0, i;
714         int up = 0, left = 0, right = 0, down = 0;
715
716         for (i = 0; i < 2; i++) {
717                 if (limit[i].x < node->pos.x)
718                         left = 1;
719                 else
720                         right = 1;
721                 if (limit[i].y < node->pos.y)
722                         up = 1;
723                 else
724                         down = 1;
725         }
726
727         if (left || up)
728                 direction |= QUADTREE_UPLEFT;
729         if (right || up)
730                 direction |= QUADTREE_UPRIGHT;
731         if (left || down)
732                 direction |= QUADTREE_DOWNLEFT;
733         if (right || down)
734                 direction |= QUADTREE_DOWNRIGHT;
735         if ((left && right) || (up && down))
736                 direction |= QUADTREE_SELF;
737
738         if ((direction & QUADTREE_UPLEFT) && node->child[0])
739                 check_for_crossed_subnodes(node->child[0], limit, ops);
740
741         if ((direction & QUADTREE_UPRIGHT) && node->child[1])
742                 check_for_crossed_subnodes(node->child[0], limit, ops);
743
744         if ((direction & QUADTREE_DOWNLEFT) && node->child[2])
745                 check_for_crossed_subnodes(node->child[0], limit, ops);
746
747         if ((direction & QUADTREE_DOWNRIGHT) && node->child[3])
748                 check_for_crossed_subnodes(node->child[0], limit, ops);
749
750         if (direction & QUADTREE_SELF) {
751                 struct quadtree *parent;
752
753                 parent = quadtree_del(node, ops);
754                 quadtree_add(parent, node, ops);
755         }
756 }
757
758 struct quadtree *quadtree_move(struct quadtree *node, struct vector new_pos,
759                         struct quadtree_ops *ops)
760 {
761         struct quadtree *parent, *tree_parent;
762         int modify;
763
764         /* Check if we have crossed any of the parents */
765         parent = node->parent;
766         while (parent) {
767                 if (node->pos.x < parent->pos.x && new_pos.x > parent->pos.x)
768                         modify = 1;
769                 if (node->pos.x > parent->pos.x && new_pos.x < parent->pos.x)
770                         modify = 1;
771                 if (node->pos.y < parent->pos.y && new_pos.y > parent->pos.y)
772                         modify = 1;
773                 if (node->pos.y > parent->pos.y && new_pos.y < parent->pos.y)
774                         modify = 1;
775
776                 if (!modify) {
777                         parent = parent->parent;
778                         continue;
779                 }
780
781                 /*
782                  * If the node has crossed the boundaries, remove it
783                  * from the tree and add it again to it. It is then
784                  * guaranteed to be in the correct position of the
785                  * tree.
786                  */
787                 tree_parent = quadtree_del(node, ops);
788                 node->pos = new_pos;
789                 quadtree_add(tree_parent, node, ops);
790                 quadtree_recalculate_parent_stats(node, ops);
791                 return tree_parent;
792         }
793
794         /* Move the node into its new location */
795         node->pos = new_pos;
796
797         if(node->children) {
798                 /*
799                  * Now, search the subtree for any children that are
800                  * located in wrong place and move them into correct
801                  * place within the tree.
802                  */
803                 struct vector limit[2];
804
805                 limit[0] = node->pos;
806                 limit[1] = new_pos;
807                 check_for_crossed_subnodes(node, limit, ops);
808         }
809
810         quadtree_recalculate_parent_stats(node, ops);
811         return quadtree_find_parent(node);
812
813 }
814
815 static int _walk_tree(struct quadtree *head, const struct quadtree_iterator *it)
816 {
817         int direction, count = 0;
818
819         direction = it->direction(head, (struct quadtree_iterator *)it);
820
821         if ((direction & QUADTREE_UPLEFT) && head->child[0])
822                 count += _walk_tree(head->child[0], it);
823
824         if ((direction & QUADTREE_UPRIGHT) && head->child[1])
825                 count += _walk_tree(head->child[1], it);
826
827         if ((direction & QUADTREE_DOWNLEFT) && head->child[2])
828                 count += _walk_tree(head->child[2], it);
829
830         if ((direction & QUADTREE_DOWNRIGHT) && head->child[3])
831                 count += _walk_tree(head->child[3], it);
832
833         if ((direction & QUADTREE_SELF) && it->callback) {
834                 it->callback(head, (struct quadtree_iterator *)it);
835                 count++;
836         }
837
838         return count;
839 }
840
841 int walk_quadtree(const struct quadtree_iterator *it)
842 {
843         return _walk_tree(it->head, it);
844 }