/* $TOG: Region.c /main/31 1998/02/06 17:50:22 kaleb $ */

/************************************************************************

   Copyright 1987, 1988, 1998  The Open Group

   All Rights Reserved.

   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

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   CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

   Except as contained in this notice, the name of The Open Group shall not be

   used in advertising or otherwise to promote the sale, use or other dealings

   in this Software without prior written authorization from The Open Group.

   Copyright 1987, 1988 by Digital Equipment Corporation, Maynard, Massachusetts.

                        All Rights Reserved

   Permission to use, copy, modify, and distribute this software and its

   documentation for any purpose and without fee is hereby granted,

   provided that the above copyright notice appear in all copies and that

   both that copyright notice and this permission notice appear in

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   used in advertising or publicity pertaining to distribution of the

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   SOFTWARE.

************************************************************************/

/* $XFree86: xc/lib/X11/Region.c,v 1.5 1999/05/09 10:50:01 dawes Exp $ */

/*

 * The functions in this file implement the Region abstraction, similar to one

 * used in the X11 sample server. A Region is simply an area, as the name

 * implies, and is implemented as a "y-x-banded" array of rectangles. To

 * explain: Each Region is made up of a certain number of rectangles sorted

 * by y coordinate first, and then by x coordinate.

 *

 * Furthermore, the rectangles are banded such that every rectangle with a

 * given upper-left y coordinate (y1) will have the same lower-right y

 * coordinate (y2) and vice versa. If a rectangle has scanlines in a band, it

 * will span the entire vertical distance of the band. This means that some

 * areas that could be merged into a taller rectangle will be represented as

 * several shorter rectangles to account for shorter rectangles to its left

 * or right but within its "vertical scope".

 *

 * An added constraint on the rectangles is that they must cover as much

 * horizontal area as possible. E.g. no two rectangles in a band are allowed

 * to touch.

 *

 * Whenever possible, bands will be merged together to cover a greater vertical

 * distance (and thus reduce the number of rectangles). Two bands can be merged

 * only if the bottom of one touches the top of the other and they have

 * rectangles in the same places (of the same width, of course). This maintains

 * the y-x-banding that's so nice to have...

 */

#include <config.h>

#include <stdlib.h>

#include <string.h>

#include <glib.h>

#include <glib-object.h>

#include "gegl.h"

#include "gegl-region.h"

#include "gegl-region-generic.h"

typedef void (* overlapFunc)    (GeglRegion    *pReg,

                                 GeglRegionBox *r1,

                                 GeglRegionBox *r1End,

                                 GeglRegionBox *r2,

                                 GeglRegionBox *r2End,

                                 gint           y1,

                                 gint           y2);

typedef void (* nonOverlapFunc) (GeglRegion    *pReg,

                                 GeglRegionBox *r,

                                 GeglRegionBox *rEnd,

                                 gint           y1,

                                 gint           y2);

static void miRegionCopy (GeglRegion       *dstrgn,

                          const GeglRegion *rgn);

static void miRegionOp   (GeglRegion       *newReg,

                          GeglRegion       *reg1,

                          const GeglRegion *reg2,

                          overlapFunc       overlapFn,

                          nonOverlapFunc    nonOverlap1Fn,

                          nonOverlapFunc    nonOverlap2Fn);

/**

 * gegl_region_new:

 *

 * Creates a new empty #GeglRegion.

 *

 * Returns: a new empty #GeglRegion

 */

GeglRegion *

gegl_region_new (void)

{

  GeglRegion *temp;

  temp = g_slice_new (GeglRegion);

  temp->numRects   = 0;

  temp->rects      = &temp->extents;

  temp->extents.x1 = 0;

  temp->extents.y1 = 0;

  temp->extents.x2 = 0;

  temp->extents.y2 = 0;

  temp->size       = 1;

  return temp;

}

/**

 * gegl_region_rectangle:

 * @rectangle: a #GeglRectangle

 *

 * Creates a new region containing the area @rectangle.

 *

 * Return value: a new region

 **/

GeglRegion *

gegl_region_rectangle (const GeglRectangle *rectangle)

{

  GeglRegion *temp;

  g_return_val_if_fail (rectangle != NULL, NULL);

  if (rectangle->width <= 0 || rectangle->height <= 0)

    return gegl_region_new ();

  temp = g_slice_new (GeglRegion);

  temp->numRects   = 1;

  temp->rects      = &temp->extents;

  temp->extents.x1 = rectangle->x;

  temp->extents.y1 = rectangle->y;

  temp->extents.x2 = rectangle->x + rectangle->width;

  temp->extents.y2 = rectangle->y + rectangle->height;

  temp->size       = 1;

  return temp;

}

/**

 * gegl_region_copy:

 * @region: a #GeglRegion

 *

 * Copies @region, creating an identical new region.

 *

 * Return value: a new region identical to @region

 **/

GeglRegion *

gegl_region_copy (const GeglRegion *region)

{

  GeglRegion *temp;

  g_return_val_if_fail (region != NULL, NULL);

  temp = gegl_region_new ();

  miRegionCopy (temp, region);

  return temp;

}

/**

 * gegl_region_get_clipbox:

 * @region: a #GeglRegion

 * @rectangle: return location for the clipbox

 *

 * Obtains the smallest rectangle which includes the entire #GeglRegion.

 *

 */

void

gegl_region_get_clipbox (GeglRegion    *region,

                         GeglRectangle *rectangle)

{

  g_return_if_fail (region != NULL);

  g_return_if_fail (rectangle != NULL);

  rectangle->x      = region->extents.x1;

  rectangle->y      = region->extents.y1;

  rectangle->width  = region->extents.x2 - region->extents.x1;

  rectangle->height = region->extents.y2 - region->extents.y1;

}

/**

 * gegl_region_get_rectangles:

 * @region: a #GeglRegion

 * @rectangles: return location for an array of rectangles

 * @n_rectangles: length of returned array

 *

 * Obtains the area covered by the region as a list of rectangles.

 * The array returned in @rectangles must be freed with g_free().

 **/

void

gegl_region_get_rectangles (GeglRegion     *region,

                            GeglRectangle **rectangles,

                            gint           *n_rectangles)

{

  gint i;

  g_return_if_fail (region != NULL);

  g_return_if_fail (rectangles != NULL);

  g_return_if_fail (n_rectangles != NULL);

  *n_rectangles = region->numRects;

  *rectangles   = g_new (GeglRectangle, region->numRects);

  for (i = 0; i < region->numRects; i++)

    {

      GeglRegionBox rect;

      rect                    = region->rects[i];

      (*rectangles)[i].x      = rect.x1;

      (*rectangles)[i].y      = rect.y1;

      (*rectangles)[i].width  = rect.x2 - rect.x1;

      (*rectangles)[i].height = rect.y2 - rect.y1;

    }

}

/**

 * gegl_region_union_with_rect:

 * @region: a #GeglRegion.

 * @rect: a #GeglRectangle.

 *

 * Sets the area of @region to the union of the areas of @region and

 * @rect. The resulting area is the set of pixels contained in

 * either @region or @rect.

 **/

void

gegl_region_union_with_rect (GeglRegion          *region,

                             const GeglRectangle *rect)

{

  GeglRegion tmp_region;

  g_return_if_fail (region != NULL);

  g_return_if_fail (rect != NULL);

  if (rect->width <= 0 || rect->height <= 0)

    return;

  tmp_region.rects      = &tmp_region.extents;

  tmp_region.numRects   = 1;

  tmp_region.extents.x1 = rect->x;

  tmp_region.extents.y1 = rect->y;

  tmp_region.extents.x2 = rect->x + rect->width;

  tmp_region.extents.y2 = rect->y + rect->height;

  tmp_region.size       = 1;

  gegl_region_union (region, &tmp_region);

}

/*-

 *-----------------------------------------------------------------------

 * miSetExtents --

 *	Reset the extents of a region to what they should be. Called by

 *	miSubtract and miIntersect b/c they can't figure it out along the

 *	way or do so easily, as miUnion can.

 *

 * Results:

 *	None.

 *

 * Side Effects:

 *	The region's 'extents' structure is overwritten.

 *

 *-----------------------------------------------------------------------

 */

static void

miSetExtents (GeglRegion *pReg)

{

  GeglRegionBox *pBox, *pBoxEnd, *pExtents;

  if (pReg->numRects == 0)

    {

      pReg->extents.x1 = 0;

      pReg->extents.y1 = 0;

      pReg->extents.x2 = 0;

      pReg->extents.y2 = 0;

      return;

    }

  pExtents = &pReg->extents;

  pBox     = pReg->rects;

  pBoxEnd  = &pBox[pReg->numRects - 1];

  /*

   * Since pBox is the first rectangle in the region, it must have the

   * smallest y1 and since pBoxEnd is the last rectangle in the region,

   * it must have the largest y2, because of banding. Initialize x1 and

   * x2 from  pBox and pBoxEnd, resp., as good things to initialize them

   * to...

   */

  pExtents->x1 = pBox->x1;

  pExtents->y1 = pBox->y1;

  pExtents->x2 = pBoxEnd->x2;

  pExtents->y2 = pBoxEnd->y2;

  g_assert (pExtents->y1 < pExtents->y2);

  while (pBox <= pBoxEnd)

    {

      if (pBox->x1 < pExtents->x1)

        {

          pExtents->x1 = pBox->x1;

        }

      if (pBox->x2 > pExtents->x2)

        {

          pExtents->x2 = pBox->x2;

        }

      pBox++;

    }

  g_assert (pExtents->x1 < pExtents->x2);

}

/**

 * gegl_region_destroy:

 * @region: a #GeglRegion

 *

 * Destroys a #GeglRegion.

 */

void

gegl_region_destroy (GeglRegion *region)

{

  g_return_if_fail (region != NULL);

  if (region->rects != &region->extents)

    g_free (region->rects);

  g_slice_free (GeglRegion, region);

}

/**

 * gegl_region_offset:

 * @region: a #GeglRegion

 * @dx: the distance to move the region horizontally

 * @dy: the distance to move the region vertically

 *

 * Moves a region the specified distance.

 */

void

gegl_region_offset (GeglRegion *region,

                    gint        x,

                    gint        y)

{

  int            nbox;

  GeglRegionBox *pbox;

  g_return_if_fail (region != NULL);

  pbox = region->rects;

  nbox = region->numRects;

  while (nbox--)

    {

      pbox->x1 += x;

      pbox->x2 += x;

      pbox->y1 += y;

      pbox->y2 += y;

      pbox++;

    }

  if (region->rects != &region->extents)

    {

      region->extents.x1 += x;

      region->extents.x2 += x;

      region->extents.y1 += y;

      region->extents.y2 += y;

    }

}

/*

   Utility procedure Compress:

   Replace r by the region r', where

     p in r' iff (Quantifer m <= dx) (p + m in r), and

     Quantifier is Exists if grow is TRUE, For all if grow is FALSE, and

     (x,y) + m = (x+m,y) if xdir is TRUE; (x,y+m) if xdir is FALSE.

   Thus, if xdir is TRUE and grow is FALSE, r is replaced by the region

   of all points p such that p and the next dx points on the same

   horizontal scan line are all in r.  We do this using by noting

   that p is the head of a run of length 2^i + k iff p is the head

   of a run of length 2^i and p+2^i is the head of a run of length

   k. Thus, the loop invariant: s contains the region corresponding

   to the runs of length shift.  r contains the region corresponding

   to the runs of length 1 + dxo & (shift-1), where dxo is the original

   value of dx.  dx = dxo & ~(shift-1).  As parameters, s and t are

   scratch regions, so that we don't have to allocate them on every

   call.

 */

#define ZOpRegion(a, b)       if (grow) gegl_region_union (a, b);\

  else gegl_region_intersect (a, b)

#define ZShiftRegion(a, b)    if (xdir) gegl_region_offset (a, b, 0);\

  else gegl_region_offset (a, 0, b)

static void

Compress (GeglRegion *r,

          GeglRegion *s,

          GeglRegion *t,

          guint       dx,

          int         xdir,

          int         grow)

{

  guint shift = 1;

  miRegionCopy (s, r);

  while (dx)

    {

      if (dx & shift)

        {

          ZShiftRegion (r, -(int) shift);

          ZOpRegion (r, s);

          dx -= shift;

          if (!dx) break;

        }

      miRegionCopy (t, s);

      ZShiftRegion (s, -(int) shift);

      ZOpRegion (s, t);

      shift <<= 1;

    }

}

#undef ZOpRegion

#undef ZShiftRegion

#undef ZCopyRegion

/**

 * gegl_region_shrink:

 * @region: a #GeglRegion

 * @dx: the number of pixels to shrink the region horizontally

 * @dy: the number of pixels to shrink the region vertically

 *

 * Resizes a region by the specified amount.

 * Positive values shrink the region. Negative values expand it.

 */

void

gegl_region_shrink (GeglRegion *region,

                    int         dx,

                    int         dy)

{

  GeglRegion *s, *t;

  int         grow;

  g_return_if_fail (region != NULL);

  if (!dx && !dy)

    return;

  s = gegl_region_new ();

  t = gegl_region_new ();

  grow = (dx < 0);

  if (grow)

    dx = -dx;

  if (dx)

    Compress (region, s, t, (unsigned) 2 * dx, TRUE, grow);

  grow = (dy < 0);

  if (grow)

    dy = -dy;

  if (dy)

    Compress (region, s, t, (unsigned) 2 * dy, FALSE, grow);

  gegl_region_offset (region, dx, dy);

  gegl_region_destroy (s);

  gegl_region_destroy (t);

}

/*======================================================================

 *	    Region Intersection

 *====================================================================*/

/*-

 *-----------------------------------------------------------------------

 * miIntersectO --

 *	Handle an overlapping band for miIntersect.

 *

 * Results:

 *	None.

 *

 * Side Effects:

 *	Rectangles may be added to the region.

 *

 *-----------------------------------------------------------------------

 */

/* static void*/

static void

miIntersectO (GeglRegion    *pReg,

              GeglRegionBox *r1,

              GeglRegionBox *r1End,

              GeglRegionBox *r2,

              GeglRegionBox *r2End,

              gint           y1,

              gint           y2)

{

  int            x1;

  int            x2;

  GeglRegionBox *pNextRect;

  pNextRect = &pReg->rects[pReg->numRects];

  while ((r1 != r1End) && (r2 != r2End))

    {

      x1 = MAX (r1->x1, r2->x1);

      x2 = MIN (r1->x2, r2->x2);

      /*

       * If there's any overlap between the two rectangles, add that

       * overlap to the new region.

       * There's no need to check for subsumption because the only way

       * such a need could arise is if some region has two rectangles

       * right next to each other. Since that should never happen...

       */

      if (x1 < x2)

        {

          g_assert (y1 < y2);

          MEMCHECK (pReg, pNextRect, pReg->rects);

          pNextRect->x1   = x1;

          pNextRect->y1   = y1;

          pNextRect->x2   = x2;

          pNextRect->y2   = y2;

          pReg->numRects += 1;

          pNextRect++;

          g_assert (pReg->numRects <= pReg->size);

        }

      /*

       * Need to advance the pointers. Shift the one that extends

       * to the right the least, since the other still has a chance to

       * overlap with that region's next rectangle, if you see what I mean.

       */

      if (r1->x2 < r2->x2)

        {

          r1++;

        }

      else if (r2->x2 < r1->x2)

        {

          r2++;

        }

      else

        {

          r1++;

          r2++;

        }

    }

}

/**

 * gegl_region_intersect:

 * @source1: a #GeglRegion

 * @source2: another #GeglRegion

 *

 * Sets the area of @source1 to the intersection of the areas of @source1

 * and @source2. The resulting area is the set of pixels contained in

 * both @source1 and @source2.

 **/

void

gegl_region_intersect (GeglRegion       *source1,

                       const GeglRegion *source2)

{

  g_return_if_fail (source1 != NULL);

  g_return_if_fail (source2 != NULL);

  /* check for trivial reject */

  if ((!(source1->numRects)) || (!(source2->numRects)) ||

      (!EXTENTCHECK (&source1->extents, &source2->extents)))

    source1->numRects = 0;

  else

    miRegionOp (source1, source1, source2,

                miIntersectO, (nonOverlapFunc) NULL, (nonOverlapFunc) NULL);

  /*

   * Can't alter source1's extents before miRegionOp depends on the

   * extents of the regions being unchanged. Besides, this way there's

   * no checking against rectangles that will be nuked due to

   * coalescing, so we have to examine fewer rectangles.

   */

  miSetExtents (source1);

}

static void

miRegionCopy (GeglRegion       *dstrgn,

              const GeglRegion *rgn)

{

  if (dstrgn != rgn) /*  don't want to copy to itself */

    {

      if (dstrgn->size < rgn->numRects)

        {

          if (dstrgn->rects != &dstrgn->extents)

            g_free (dstrgn->rects);

          dstrgn->rects = g_new (GeglRegionBox, rgn->numRects);

          dstrgn->size  = rgn->numRects;

        }

      dstrgn->numRects = rgn->numRects;

      dstrgn->extents  = rgn->extents;

      memcpy (dstrgn->rects, rgn->rects, rgn->numRects * sizeof (GeglRegionBox));

    }

}

/*======================================================================

 *	    Generic Region Operator

 *====================================================================*/

/*-

 *-----------------------------------------------------------------------

 * miCoalesce --

 *	Attempt to merge the boxes in the current band with those in the

 *	previous one. Used only by miRegionOp.

 *

 * Results:

 *	The new index for the previous band.

 *

 * Side Effects:

 *	If coalescing takes place:

 *	    - rectangles in the previous band will have their y2 fields

 *	      altered.

 *	    - pReg->numRects will be decreased.

 *

 *-----------------------------------------------------------------------

 */

/* static int*/

static int

miCoalesce (GeglRegion *pReg,         /* Region to coalesce */

            gint        prevStart,   /* Index of start of previous band */

            gint        curStart)    /* Index of start of current band */

{

  GeglRegionBox *pPrevBox;      /* Current box in previous band */

  GeglRegionBox *pCurBox;       /* Current box in current band */

  GeglRegionBox *pRegEnd;       /* End of region */

  int            curNumRects;   /* Number of rectangles in current

                                 * band */

  int            prevNumRects;  /* Number of rectangles in previous

                                 * band */

  int            bandY1;        /* Y1 coordinate for current band */

  pRegEnd = &pReg->rects[pReg->numRects];

  pPrevBox     = &pReg->rects[prevStart];

  prevNumRects = curStart - prevStart;

  /*

   * Figure out how many rectangles are in the current band. Have to do

   * this because multiple bands could have been added in miRegionOp

   * at the end when one region has been exhausted.

   */

  pCurBox = &pReg->rects[curStart];

  bandY1  = pCurBox->y1;

  for (curNumRects = 0;

       (pCurBox != pRegEnd) && (pCurBox->y1 == bandY1);

       curNumRects++)

    {

      pCurBox++;

    }

  if (pCurBox != pRegEnd)

    {

      /*

       * If more than one band was added, we have to find the start

       * of the last band added so the next coalescing job can start

       * at the right place... (given when multiple bands are added,

       * this may be pointless -- see above).

       */

      pRegEnd--;

      while (pRegEnd[-1].y1 == pRegEnd->y1)

        {

          pRegEnd--;

        }

      curStart = pRegEnd - pReg->rects;

      pRegEnd  = pReg->rects + pReg->numRects;

    }

  if ((curNumRects == prevNumRects) && (curNumRects != 0))

    {

      pCurBox -= curNumRects;

      /*

       * The bands may only be coalesced if the bottom of the previous

       * matches the top scanline of the current.

       */

      if (pPrevBox->y2 == pCurBox->y1)

        {

          /*

           * Make sure the bands have boxes in the same places. This

           * assumes that boxes have been added in such a way that they

           * cover the most area possible. I.e. two boxes in a band must

           * have some horizontal space between them.

           */

          do

            {

              if ((pPrevBox->x1 != pCurBox->x1) ||

                  (pPrevBox->x2 != pCurBox->x2))

                {

                  /*

                   * The bands don't line up so they can't be coalesced.

                   */

                  return (curStart);

                }

              pPrevBox++;

              pCurBox++;

              prevNumRects -= 1;

            } while (prevNumRects != 0);

          pReg->numRects -= curNumRects;

          pCurBox        -= curNumRects;

          pPrevBox       -= curNumRects;

          /*

           * The bands may be merged, so set the bottom y of each box

           * in the previous band to that of the corresponding box in

           * the current band.

           */

          do

            {

              pPrevBox->y2 = pCurBox->y2;

              pPrevBox++;

              pCurBox++;

              curNumRects -= 1;

            } while (curNumRects != 0);

          /*

           * If only one band was added to the region, we have to backup

           * curStart to the start of the previous band.

           *

           * If more than one band was added to the region, copy the

           * other bands down. The assumption here is that the other bands

           * came from the same region as the current one and no further

           * coalescing can be done on them since it's all been done

           * already... curStart is already in the right place.

           */

          if (pCurBox == pRegEnd)

            {

              curStart = prevStart;

            }

          else

            {

              do

                {

                  *pPrevBox++ = *pCurBox++;

                } while (pCurBox != pRegEnd);

            }

        }

    }

  return curStart;

}

/*-

 *-----------------------------------------------------------------------

 * miRegionOp --

 *	Apply an operation to two regions. Called by miUnion, miInverse,

 *	miSubtract, miIntersect...

 *

 * Results:

 *	None.

 *

 * Side Effects:

 *	The new region is overwritten.

 *

 * Notes:

 *	The idea behind this function is to view the two regions as sets.

 *	Together they cover a rectangle of area that this function divides

 *	into horizontal bands where points are covered only by one region

 *	or by both. For the first case, the nonOverlapFunc is called with

 *	each the band and the band's upper and lower extents. For the

 *	second, the overlapFunc is called to process the entire band. It

 *	is responsible for clipping the rectangles in the band, though

 *	this function provides the boundaries.

 *	At the end of each band, the new region is coalesced, if possible,

 *	to reduce the number of rectangles in the region.

 *

 *-----------------------------------------------------------------------

 */

/* static void*/

static void

miRegionOp (GeglRegion       *newReg,

            GeglRegion       *reg1,

            const GeglRegion *reg2,

            overlapFunc       overlapFn,        /* Function to call for over-

                                                 * lapping bands */

            nonOverlapFunc    nonOverlap1Fn,    /* Function to call for non-

                                                 * overlapping bands in region

                                                 * 1 */

            nonOverlapFunc    nonOverlap2Fn)    /* Function to call for non-

                                                 * overlapping bands in region

                                                 * 2 */

{

  GeglRegionBox *r1;                    /* Pointer into first region */

  GeglRegionBox *r2;                    /* Pointer into 2d region */

  GeglRegionBox *r1End;                 /* End of 1st region */

  GeglRegionBox *r2End;                 /* End of 2d region */

  int            ybot;                  /* Bottom of intersection */

  int            ytop;                  /* Top of intersection */

  GeglRegionBox *oldRects;              /* Old rects for newReg */

  int            prevBand;              /* Index of start of

                                         * previous band in newReg */

  int            curBand;               /* Index of start of current

                                         * band in newReg */

  GeglRegionBox *r1BandEnd;             /* End of current band in r1 */

  GeglRegionBox *r2BandEnd;             /* End of current band in r2 */

  int            top;                   /* Top of non-overlapping

                                         * band */

  int            bot;                   /* Bottom of non-overlapping

                                         * band */

  /*

   * Initialization:

   *	set r1, r2, r1End and r2End appropriately, preserve the important

   * parts of the destination region until the end in case it's one of

   * the two source regions, then mark the "new" region empty, allocating

   * another array of rectangles for it to use.

   */

  r1    = reg1->rects;

  r2    = reg2->rects;

  r1End = r1 + reg1->numRects;

  r2End = r2 + reg2->numRects;

  oldRects = newReg->rects;

  EMPTY_REGION (newReg);

  /*

   * Allocate a reasonable number of rectangles for the new region. The idea

   * is to allocate enough so the individual functions don't need to

   * reallocate and copy the array, which is time consuming, yet we don't

   * have to worry about using too much memory. I hope to be able to

   * nuke the Xrealloc() at the end of this function eventually.

   */

  newReg->size  = MAX (reg1->numRects, reg2->numRects) * 2;

  newReg->rects = g_new (GeglRegionBox, newReg->size);

  /*

   * Initialize ybot and ytop.

   * In the upcoming loop, ybot and ytop serve different functions depending

   * on whether the band being handled is an overlapping or non-overlapping

   * band.

   * 	In the case of a non-overlapping band (only one of the regions

   * has points in the band), ybot is the bottom of the most recent

   * intersection and thus clips the top of the rectangles in that band.

   * ytop is the top of the next intersection between the two regions and

   * serves to clip the bottom of the rectangles in the current band.

   *	For an overlapping band (where the two regions intersect), ytop clips

   * the top of the rectangles of both regions and ybot clips the bottoms.

   */

  if (reg1->extents.y1 < reg2->extents.y1)

    ybot = reg1->extents.y1;

  else

    ybot = reg2->extents.y1;

  /*

   * prevBand serves to mark the start of the previous band so rectangles

   * can be coalesced into larger rectangles. qv. miCoalesce, above.

   * In the beginning, there is no previous band, so prevBand == curBand

   * (curBand is set later on, of course, but the first band will always

   * start at index 0). prevBand and curBand must be indices because of

   * the possible expansion, and resultant moving, of the new region's

   * array of rectangles.

   */

  prevBand = 0;

  do

    {

      curBand = newReg->numRects;