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+// stb_rect_pack.h - v1.01 - public domain - rectangle packing
+// Sean Barrett 2014
+//
+// Useful for e.g. packing rectangular textures into an atlas.
+// Does not do rotation.
+//
+// Before #including,
+//
+//    #define STB_RECT_PACK_IMPLEMENTATION
+//
+// in the file that you want to have the implementation.
+//
+// Not necessarily the awesomest packing method, but better than
+// the totally naive one in stb_truetype (which is primarily what
+// this is meant to replace).
+//
+// Has only had a few tests run, may have issues.
+//
+// More docs to come.
+//
+// No memory allocations; uses qsort() and assert() from stdlib.
+// Can override those by defining STBRP_SORT and STBRP_ASSERT.
+//
+// This library currently uses the Skyline Bottom-Left algorithm.
+//
+// Please note: better rectangle packers are welcome! Please
+// implement them to the same API, but with a different init
+// function.
+//
+// Credits
+//
+//  Library
+//    Sean Barrett
+//  Minor features
+//    Martins Mozeiko
+//    github:IntellectualKitty
+//
+//  Bugfixes / warning fixes
+//    Jeremy Jaussaud
+//    Fabian Giesen
+//
+// Version history:
+//
+//     1.01  (2021-07-11)  always use large rect mode, expose STBRP__MAXVAL in public section
+//     1.00  (2019-02-25)  avoid small space waste; gracefully fail too-wide rectangles
+//     0.99  (2019-02-07)  warning fixes
+//     0.11  (2017-03-03)  return packing success/fail result
+//     0.10  (2016-10-25)  remove cast-away-const to avoid warnings
+//     0.09  (2016-08-27)  fix compiler warnings
+//     0.08  (2015-09-13)  really fix bug with empty rects (w=0 or h=0)
+//     0.07  (2015-09-13)  fix bug with empty rects (w=0 or h=0)
+//     0.06  (2015-04-15)  added STBRP_SORT to allow replacing qsort
+//     0.05:  added STBRP_ASSERT to allow replacing assert
+//     0.04:  fixed minor bug in STBRP_LARGE_RECTS support
+//     0.01:  initial release
+//
+// LICENSE
+//
+//   See end of file for license information.
+
+//////////////////////////////////////////////////////////////////////////////
+//
+//       INCLUDE SECTION
+//
+
+#ifndef STB_INCLUDE_STB_RECT_PACK_H
+#define STB_INCLUDE_STB_RECT_PACK_H
+
+#define STB_RECT_PACK_VERSION  1
+
+#ifdef STBRP_STATIC
+#define STBRP_DEF static
+#else
+#define STBRP_DEF extern
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+typedef struct stbrp_context stbrp_context;
+typedef struct stbrp_node    stbrp_node;
+typedef struct stbrp_rect    stbrp_rect;
+
+typedef int            stbrp_coord;
+
+#define STBRP__MAXVAL  0x7fffffff
+// Mostly for internal use, but this is the maximum supported coordinate value.
+
+STBRP_DEF int stbrp_pack_rects (stbrp_context *context, stbrp_rect *rects, int num_rects);
+// Assign packed locations to rectangles. The rectangles are of type
+// 'stbrp_rect' defined below, stored in the array 'rects', and there
+// are 'num_rects' many of them.
+//
+// Rectangles which are successfully packed have the 'was_packed' flag
+// set to a non-zero value and 'x' and 'y' store the minimum location
+// on each axis (i.e. bottom-left in cartesian coordinates, top-left
+// if you imagine y increasing downwards). Rectangles which do not fit
+// have the 'was_packed' flag set to 0.
+//
+// You should not try to access the 'rects' array from another thread
+// while this function is running, as the function temporarily reorders
+// the array while it executes.
+//
+// To pack into another rectangle, you need to call stbrp_init_target
+// again. To continue packing into the same rectangle, you can call
+// this function again. Calling this multiple times with multiple rect
+// arrays will probably produce worse packing results than calling it
+// a single time with the full rectangle array, but the option is
+// available.
+//
+// The function returns 1 if all of the rectangles were successfully
+// packed and 0 otherwise.
+
+struct stbrp_rect
+{
+   // reserved for your use:
+   int            id;
+
+   // input:
+   stbrp_coord    w, h;
+
+   // output:
+   stbrp_coord    x, y;
+   int            was_packed;  // non-zero if valid packing
+
+}; // 16 bytes, nominally
+
+
+STBRP_DEF void stbrp_init_target (stbrp_context *context, int width, int height, stbrp_node *nodes, int num_nodes);
+// Initialize a rectangle packer to:
+//    pack a rectangle that is 'width' by 'height' in dimensions
+//    using temporary storage provided by the array 'nodes', which is 'num_nodes' long
+//
+// You must call this function every time you start packing into a new target.
+//
+// There is no "shutdown" function. The 'nodes' memory must stay valid for
+// the following stbrp_pack_rects() call (or calls), but can be freed after
+// the call (or calls) finish.
+//
+// Note: to guarantee best results, either:
+//       1. make sure 'num_nodes' >= 'width'
+//   or  2. call stbrp_allow_out_of_mem() defined below with 'allow_out_of_mem = 1'
+//
+// If you don't do either of the above things, widths will be quantized to multiples
+// of small integers to guarantee the algorithm doesn't run out of temporary storage.
+//
+// If you do #2, then the non-quantized algorithm will be used, but the algorithm
+// may run out of temporary storage and be unable to pack some rectangles.
+
+STBRP_DEF void stbrp_setup_allow_out_of_mem (stbrp_context *context, int allow_out_of_mem);
+// Optionally call this function after init but before doing any packing to
+// change the handling of the out-of-temp-memory scenario, described above.
+// If you call init again, this will be reset to the default (false).
+
+
+STBRP_DEF void stbrp_setup_heuristic (stbrp_context *context, int heuristic);
+// Optionally select which packing heuristic the library should use. Different
+// heuristics will produce better/worse results for different data sets.
+// If you call init again, this will be reset to the default.
+
+enum
+{
+   STBRP_HEURISTIC_Skyline_default=0,
+   STBRP_HEURISTIC_Skyline_BL_sortHeight = STBRP_HEURISTIC_Skyline_default,
+   STBRP_HEURISTIC_Skyline_BF_sortHeight
+};
+
+
+//////////////////////////////////////////////////////////////////////////////
+//
+// the details of the following structures don't matter to you, but they must
+// be visible so you can handle the memory allocations for them
+
+struct stbrp_node
+{
+   stbrp_coord  x,y;
+   stbrp_node  *next;
+};
+
+struct stbrp_context
+{
+   int width;
+   int height;
+   int align;
+   int init_mode;
+   int heuristic;
+   int num_nodes;
+   stbrp_node *active_head;
+   stbrp_node *free_head;
+   stbrp_node extra[2]; // we allocate two extra nodes so optimal user-node-count is 'width' not 'width+2'
+};
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
+
+//////////////////////////////////////////////////////////////////////////////
+//
+//     IMPLEMENTATION SECTION
+//
+
+#ifdef STB_RECT_PACK_IMPLEMENTATION
+#ifndef STBRP_SORT
+#include <stdlib.h>
+#define STBRP_SORT qsort
+#endif
+
+#ifndef STBRP_ASSERT
+#include <assert.h>
+#define STBRP_ASSERT assert
+#endif
+
+#ifdef _MSC_VER
+#define STBRP__NOTUSED(v)  (void)(v)
+#define STBRP__CDECL       __cdecl
+#else
+#define STBRP__NOTUSED(v)  (void)sizeof(v)
+#define STBRP__CDECL
+#endif
+
+enum
+{
+   STBRP__INIT_skyline = 1
+};
+
+STBRP_DEF void stbrp_setup_heuristic(stbrp_context *context, int heuristic)
+{
+   switch (context->init_mode) {
+      case STBRP__INIT_skyline:
+         STBRP_ASSERT(heuristic == STBRP_HEURISTIC_Skyline_BL_sortHeight || heuristic == STBRP_HEURISTIC_Skyline_BF_sortHeight);
+         context->heuristic = heuristic;
+         break;
+      default:
+         STBRP_ASSERT(0);
+   }
+}
+
+STBRP_DEF void stbrp_setup_allow_out_of_mem(stbrp_context *context, int allow_out_of_mem)
+{
+   if (allow_out_of_mem)
+      // if it's ok to run out of memory, then don't bother aligning them;
+      // this gives better packing, but may fail due to OOM (even though
+      // the rectangles easily fit). @TODO a smarter approach would be to only
+      // quantize once we've hit OOM, then we could get rid of this parameter.
+      context->align = 1;
+   else {
+      // if it's not ok to run out of memory, then quantize the widths
+      // so that num_nodes is always enough nodes.
+      //
+      // I.e. num_nodes * align >= width
+      //                  align >= width / num_nodes
+      //                  align = ceil(width/num_nodes)
+
+      context->align = (context->width + context->num_nodes-1) / context->num_nodes;
+   }
+}
+
+STBRP_DEF void stbrp_init_target(stbrp_context *context, int width, int height, stbrp_node *nodes, int num_nodes)
+{
+   int i;
+
+   for (i=0; i < num_nodes-1; ++i)
+      nodes[i].next = &nodes[i+1];
+   nodes[i].next = NULL;
+   context->init_mode = STBRP__INIT_skyline;
+   context->heuristic = STBRP_HEURISTIC_Skyline_default;
+   context->free_head = &nodes[0];
+   context->active_head = &context->extra[0];
+   context->width = width;
+   context->height = height;
+   context->num_nodes = num_nodes;
+   stbrp_setup_allow_out_of_mem(context, 0);
+
+   // node 0 is the full width, node 1 is the sentinel (lets us not store width explicitly)
+   context->extra[0].x = 0;
+   context->extra[0].y = 0;
+   context->extra[0].next = &context->extra[1];
+   context->extra[1].x = (stbrp_coord) width;
+   context->extra[1].y = (1<<30);
+   context->extra[1].next = NULL;
+}
+
+// find minimum y position if it starts at x1
+static int stbrp__skyline_find_min_y(stbrp_context *c, stbrp_node *first, int x0, int width, int *pwaste)
+{
+   stbrp_node *node = first;
+   int x1 = x0 + width;
+   int min_y, visited_width, waste_area;
+
+   STBRP__NOTUSED(c);
+
+   STBRP_ASSERT(first->x <= x0);
+
+   #if 0
+   // skip in case we're past the node
+   while (node->next->x <= x0)
+      ++node;
+   #else
+   STBRP_ASSERT(node->next->x > x0); // we ended up handling this in the caller for efficiency
+   #endif
+
+   STBRP_ASSERT(node->x <= x0);
+
+   min_y = 0;
+   waste_area = 0;
+   visited_width = 0;
+   while (node->x < x1) {
+      if (node->y > min_y) {
+         // raise min_y higher.
+         // we've accounted for all waste up to min_y,
+         // but we'll now add more waste for everything we've visted
+         waste_area += visited_width * (node->y - min_y);
+         min_y = node->y;
+         // the first time through, visited_width might be reduced
+         if (node->x < x0)
+            visited_width += node->next->x - x0;
+         else
+            visited_width += node->next->x - node->x;
+      } else {
+         // add waste area
+         int under_width = node->next->x - node->x;
+         if (under_width + visited_width > width)
+            under_width = width - visited_width;
+         waste_area += under_width * (min_y - node->y);
+         visited_width += under_width;
+      }
+      node = node->next;
+   }
+
+   *pwaste = waste_area;
+   return min_y;
+}
+
+typedef struct
+{
+   int x,y;
+   stbrp_node **prev_link;
+} stbrp__findresult;
+
+static stbrp__findresult stbrp__skyline_find_best_pos(stbrp_context *c, int width, int height)
+{
+   int best_waste = (1<<30), best_x, best_y = (1 << 30);
+   stbrp__findresult fr;
+   stbrp_node **prev, *node, *tail, **best = NULL;
+
+   // align to multiple of c->align
+   width = (width + c->align - 1);
+   width -= width % c->align;
+   STBRP_ASSERT(width % c->align == 0);
+
+   // if it can't possibly fit, bail immediately
+   if (width > c->width || height > c->height) {
+      fr.prev_link = NULL;
+      fr.x = fr.y = 0;
+      return fr;
+   }
+
+   node = c->active_head;
+   prev = &c->active_head;
+   while (node->x + width <= c->width) {
+      int y,waste;
+      y = stbrp__skyline_find_min_y(c, node, node->x, width, &waste);
+      if (c->heuristic == STBRP_HEURISTIC_Skyline_BL_sortHeight) { // actually just want to test BL
+         // bottom left
+         if (y < best_y) {
+            best_y = y;
+            best = prev;
+         }
+      } else {
+         // best-fit
+         if (y + height <= c->height) {
+            // can only use it if it first vertically
+            if (y < best_y || (y == best_y && waste < best_waste)) {
+               best_y = y;
+               best_waste = waste;
+               best = prev;
+            }
+         }
+      }
+      prev = &node->next;
+      node = node->next;
+   }
+
+   best_x = (best == NULL) ? 0 : (*best)->x;
+
+   // if doing best-fit (BF), we also have to try aligning right edge to each node position
+   //
+   // e.g, if fitting
+   //
+   //     ____________________
+   //    |____________________|
+   //
+   //            into
+   //
+   //   |                         |
+   //   |             ____________|
+   //   |____________|
+   //
+   // then right-aligned reduces waste, but bottom-left BL is always chooses left-aligned
+   //
+   // This makes BF take about 2x the time
+
+   if (c->heuristic == STBRP_HEURISTIC_Skyline_BF_sortHeight) {
+      tail = c->active_head;
+      node = c->active_head;
+      prev = &c->active_head;
+      // find first node that's admissible
+      while (tail->x < width)
+         tail = tail->next;
+      while (tail) {
+         int xpos = tail->x - width;
+         int y,waste;
+         STBRP_ASSERT(xpos >= 0);
+         // find the left position that matches this
+         while (node->next->x <= xpos) {
+            prev = &node->next;
+            node = node->next;
+         }
+         STBRP_ASSERT(node->next->x > xpos && node->x <= xpos);
+         y = stbrp__skyline_find_min_y(c, node, xpos, width, &waste);
+         if (y + height <= c->height) {
+            if (y <= best_y) {
+               if (y < best_y || waste < best_waste || (waste==best_waste && xpos < best_x)) {
+                  best_x = xpos;
+                  STBRP_ASSERT(y <= best_y);
+                  best_y = y;
+                  best_waste = waste;
+                  best = prev;
+               }
+            }
+         }
+         tail = tail->next;
+      }
+   }
+
+   fr.prev_link = best;
+   fr.x = best_x;
+   fr.y = best_y;
+   return fr;
+}
+
+static stbrp__findresult stbrp__skyline_pack_rectangle(stbrp_context *context, int width, int height)
+{
+   // find best position according to heuristic
+   stbrp__findresult res = stbrp__skyline_find_best_pos(context, width, height);
+   stbrp_node *node, *cur;
+
+   // bail if:
+   //    1. it failed
+   //    2. the best node doesn't fit (we don't always check this)
+   //    3. we're out of memory
+   if (res.prev_link == NULL || res.y + height > context->height || context->free_head == NULL) {
+      res.prev_link = NULL;
+      return res;
+   }
+
+   // on success, create new node
+   node = context->free_head;
+   node->x = (stbrp_coord) res.x;
+   node->y = (stbrp_coord) (res.y + height);
+
+   context->free_head = node->next;
+
+   // insert the new node into the right starting point, and
+   // let 'cur' point to the remaining nodes needing to be
+   // stiched back in
+
+   cur = *res.prev_link;
+   if (cur->x < res.x) {
+      // preserve the existing one, so start testing with the next one
+      stbrp_node *next = cur->next;
+      cur->next = node;
+      cur = next;
+   } else {
+      *res.prev_link = node;
+   }
+
+   // from here, traverse cur and free the nodes, until we get to one
+   // that shouldn't be freed
+   while (cur->next && cur->next->x <= res.x + width) {
+      stbrp_node *next = cur->next;
+      // move the current node to the free list
+      cur->next = context->free_head;
+      context->free_head = cur;
+      cur = next;
+   }
+
+   // stitch the list back in
+   node->next = cur;
+
+   if (cur->x < res.x + width)
+      cur->x = (stbrp_coord) (res.x + width);
+
+#ifdef _DEBUG
+   cur = context->active_head;
+   while (cur->x < context->width) {
+      STBRP_ASSERT(cur->x < cur->next->x);
+      cur = cur->next;
+   }
+   STBRP_ASSERT(cur->next == NULL);
+
+   {
+      int count=0;
+      cur = context->active_head;
+      while (cur) {
+         cur = cur->next;
+         ++count;
+      }
+      cur = context->free_head;
+      while (cur) {
+         cur = cur->next;
+         ++count;
+      }
+      STBRP_ASSERT(count == context->num_nodes+2);
+   }
+#endif
+
+   return res;
+}
+
+static int STBRP__CDECL rect_height_compare(const void *a, const void *b)
+{
+   const stbrp_rect *p = (const stbrp_rect *) a;
+   const stbrp_rect *q = (const stbrp_rect *) b;
+   if (p->h > q->h)
+      return -1;
+   if (p->h < q->h)
+      return  1;
+   return (p->w > q->w) ? -1 : (p->w < q->w);
+}
+
+static int STBRP__CDECL rect_original_order(const void *a, const void *b)
+{
+   const stbrp_rect *p = (const stbrp_rect *) a;
+   const stbrp_rect *q = (const stbrp_rect *) b;
+   return (p->was_packed < q->was_packed) ? -1 : (p->was_packed > q->was_packed);
+}
+
+STBRP_DEF int stbrp_pack_rects(stbrp_context *context, stbrp_rect *rects, int num_rects)
+{
+   int i, all_rects_packed = 1;
+
+   // we use the 'was_packed' field internally to allow sorting/unsorting
+   for (i=0; i < num_rects; ++i) {
+      rects[i].was_packed = i;
+   }
+
+   // sort according to heuristic
+   STBRP_SORT(rects, num_rects, sizeof(rects[0]), rect_height_compare);
+
+   for (i=0; i < num_rects; ++i) {
+      if (rects[i].w == 0 || rects[i].h == 0) {
+         rects[i].x = rects[i].y = 0;  // empty rect needs no space
+      } else {
+         stbrp__findresult fr = stbrp__skyline_pack_rectangle(context, rects[i].w, rects[i].h);
+         if (fr.prev_link) {
+            rects[i].x = (stbrp_coord) fr.x;
+            rects[i].y = (stbrp_coord) fr.y;
+         } else {
+            rects[i].x = rects[i].y = STBRP__MAXVAL;
+         }
+      }
+   }
+
+   // unsort
+   STBRP_SORT(rects, num_rects, sizeof(rects[0]), rect_original_order);
+
+   // set was_packed flags and all_rects_packed status
+   for (i=0; i < num_rects; ++i) {
+      rects[i].was_packed = !(rects[i].x == STBRP__MAXVAL && rects[i].y == STBRP__MAXVAL);
+      if (!rects[i].was_packed)
+         all_rects_packed = 0;
+   }
+
+   // return the all_rects_packed status
+   return all_rects_packed;
+}
+#endif
+
+/*
+------------------------------------------------------------------------------
+This software is available under 2 licenses -- choose whichever you prefer.
+------------------------------------------------------------------------------
+ALTERNATIVE A - MIT License
+Copyright (c) 2017 Sean Barrett
+Permission is hereby granted, free of charge, to any person obtaining a copy of
+this software and associated documentation files (the "Software"), to deal in
+the Software without restriction, including without limitation the rights to
+use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
+of the Software, and to permit persons to whom the Software is furnished to do
+so, subject to the following conditions:
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+------------------------------------------------------------------------------
+ALTERNATIVE B - Public Domain (www.unlicense.org)
+This is free and unencumbered software released into the public domain.
+Anyone is free to copy, modify, publish, use, compile, sell, or distribute this
+software, either in source code form or as a compiled binary, for any purpose,
+commercial or non-commercial, and by any means.
+In jurisdictions that recognize copyright laws, the author or authors of this
+software dedicate any and all copyright interest in the software to the public
+domain. We make this dedication for the benefit of the public at large and to
+the detriment of our heirs and successors. We intend this dedication to be an
+overt act of relinquishment in perpetuity of all present and future rights to
+this software under copyright law.
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+------------------------------------------------------------------------------
+*/