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Region.c

/* $XConsortium: Region.c,v 11.40 94/04/17 20:20:46 rws Exp $ */
/************************************************************************

Copyright (c) 1987, 1988  X Consortium

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,
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X CONSORTIUM 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.

Except as contained in this notice, the name of the X Consortium 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 X Consortium.


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 
supporting documentation, and that the name of Digital not be
used in advertising or publicity pertaining to distribution of the
software without specific, written prior permission.  

DIGITAL DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING
ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL
DIGITAL BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR
ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
SOFTWARE.

************************************************************************/
/*
 * 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 <stdio.h>
#include "region.h"
#include "poly.h"

#define assert(expr)

typedef void (*voidProcp)();

static void miRegionOp();
/*    Create a new empty region     */
Region
XCreateRegion()
{
    Region temp;

    if (! (temp = ( Region )Xmalloc( (unsigned) sizeof( REGION ))))
      return (Region) NULL;
    if (! (temp->rects = ( BOX * )Xmalloc( (unsigned) sizeof( BOX )))) {
      Xfree((char *) temp);
      return (Region) NULL;
    }
    temp->numRects = 0;
    temp->extents.x1 = 0;
    temp->extents.y1 = 0;
    temp->extents.x2 = 0;
    temp->extents.y2 = 0;
    temp->size = 1;
    return( temp );
}

/*-
 *-----------------------------------------------------------------------
 * 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 (pReg)
    Region        pReg;
{
    register BoxPtr     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;

    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++;
    }
    assert(pExtents->x1 < pExtents->x2);
}

XDestroyRegion( r )
    Region r;
{
    Xfree( (char *) r->rects );
    Xfree( (char *) r );
}

/*======================================================================
 *        Region Intersection
 *====================================================================*/
/*-
 *-----------------------------------------------------------------------
 * miIntersectO --
 *    Handle an overlapping band for miIntersect.
 *
 * Results:
 *    None.
 *
 * Side Effects:
 *    Rectangles may be added to the region.
 *
 *-----------------------------------------------------------------------
 */
/* static void*/
static
miIntersectO (pReg, r1, r1End, r2, r2End, y1, y2)
    register Region     pReg;
    register BoxPtr     r1;
    BoxPtr              r1End;
    register BoxPtr     r2;
    BoxPtr              r2End;
    short               y1;
    short               y2;
{
    register short      x1;
    register short      x2;
    register BoxPtr     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)
      {
          assert(y1<y2);

          MEMCHECK(pReg, pNextRect, pReg->rects);
          pNextRect->x1 = x1;
          pNextRect->y1 = y1;
          pNextRect->x2 = x2;
          pNextRect->y2 = y2;
          pReg->numRects += 1;
          pNextRect++;
          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++;
      }
    }
    return 0;     /* lint */
}

static void
miRegionCopy(dstrgn, rgn)
    register Region dstrgn;
    register Region rgn;

{
    if (dstrgn != rgn) /*  don't want to copy to itself */
    {  
        if (dstrgn->size < rgn->numRects)
        {
            if (dstrgn->rects)
            {
                if (! (dstrgn->rects = (BOX *)
                   Xrealloc((char *) dstrgn->rects,
                        (unsigned) rgn->numRects * (sizeof(BOX)))))
                return;
            }
            dstrgn->size = rgn->numRects;
      }
        dstrgn->numRects = rgn->numRects;
        dstrgn->extents.x1 = rgn->extents.x1;
        dstrgn->extents.y1 = rgn->extents.y1;
        dstrgn->extents.x2 = rgn->extents.x2;
        dstrgn->extents.y2 = rgn->extents.y2;

      memcpy((char *) dstrgn->rects, (char *) rgn->rects,
             (int) (rgn->numRects * sizeof(BOX)));
    }
}

#ifdef notdef

/*
 *  combinRegs(newReg, reg1, reg2)
 *    if one region is above or below the other.
*/ 

static void
combineRegs(newReg, reg1, reg2)
    register Region newReg;
    Region reg1;
    Region reg2;
{
    register Region tempReg;
    register BOX *rects;
    register BOX *rects1;
    register BOX *rects2;
    register int total;

    rects1 = reg1->rects;
    rects2 = reg2->rects;

    total = reg1->numRects + reg2->numRects;
    if (! (tempReg = XCreateRegion()))
      return;
    tempReg->size = total;
    /*  region 1 is below region 2  */
    if (reg1->extents.y1 > reg2->extents.y1)
    {
        miRegionCopy(tempReg, reg2);
        rects = &tempReg->rects[tempReg->numRects];
        total -= tempReg->numRects;
        while (total--)
            *rects++ = *rects1++;
    }
    else
    {
        miRegionCopy(tempReg, reg1);
        rects = &tempReg->rects[tempReg->numRects];
        total -= tempReg->numRects;
        while (total--)
            *rects++ = *rects2++;
    }
    tempReg->extents = reg1->extents;
    tempReg->numRects = reg1->numRects + reg2->numRects;
    EXTENTS(&reg2->extents, tempReg);  
    miRegionCopy(newReg, tempReg);
    Xfree((char *)tempReg);
}

/*
 *  QuickCheck checks to see if it does not have to go through all the
 *  the ugly code for the region call.  It returns 1 if it did all
 *  the work for Union, otherwise 0 - still work to be done.
*/ 

static int
QuickCheck(newReg, reg1, reg2)
    Region newReg, reg1, reg2;
{

    /*  if unioning with itself or no rects to union with  */
    if ( (reg1 == reg2) || (!(reg1->numRects)) )
    {
        miRegionCopy(newReg, reg2);
        return(TRUE);
    }

    /*   if nothing to union   */
    if (!(reg2->numRects))
    {
        miRegionCopy(newReg, reg1);
        return(TRUE);
    }

    /*   could put an extent check to see if add above or below */

    if ((reg1->extents.y1 >= reg2->extents.y2) ||
        (reg2->extents.y1 >= reg1->extents.y2) )
    {
        combineRegs(newReg, reg1, reg2);
        return(TRUE);
    }
    return(FALSE);
}

/*   TopRects(rects, reg1, reg2)
 * N.B. We now assume that reg1 and reg2 intersect.  Therefore we are
 * NOT checking in the two while loops for stepping off the end of the
 * region.  
 */ 

static int
TopRects(newReg, rects, reg1, reg2, FirstRect)
    register Region newReg;
    register BOX *rects;
    register Region reg1;
    register Region reg2; 
    BOX *FirstRect;
{
    register BOX *tempRects;

    /*  need to add some rects from region 1 */
    if (reg1->extents.y1 < reg2->extents.y1)
    {
        tempRects = reg1->rects;
        while(tempRects->y1 < reg2->extents.y1)
      {
          MEMCHECK(newReg, rects, FirstRect);
            ADDRECTNOX(newReg,rects, tempRects->x1, tempRects->y1, 
                   tempRects->x2, MIN(tempRects->y2, reg2->extents.y1));
            tempRects++;
      }
    }
    /*  need to add some rects from region 2 */
    if (reg2->extents.y1 < reg1->extents.y1)
    {
        tempRects = reg2->rects;
        while (tempRects->y1 < reg1->extents.y1)
        {
            MEMCHECK(newReg, rects, FirstRect);
            ADDRECTNOX(newReg, rects, tempRects->x1,tempRects->y1, 
                   tempRects->x2, MIN(tempRects->y2, reg1->extents.y1));
            tempRects++;
      }
    }
    return(1);
}
#endif

/*======================================================================
 *        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
miCoalesce (pReg, prevStart, curStart)
    register Region     pReg;       /* Region to coalesce */
    int                 prevStart;        /* Index of start of previous band */
    int                 curStart;         /* Index of start of current band */
{
    register BoxPtr     pPrevBox;         /* Current box in previous band */
    register BoxPtr     pCurBox;          /* Current box in current band */
    register BoxPtr     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(newReg, reg1, reg2, overlapFunc,  nonOverlap1Func, nonOverlap2Func)
    register Region     newReg;                 /* Place to store result */
    Region        reg1;             /* First region in operation */
    Region        reg2;             /* 2d region in operation */
    void                (*overlapFunc)();       /* Function to call for over-
                                     * lapping bands */
    void                (*nonOverlap1Func)();   /* Function to call for non-
                                     * overlapping bands in region
                                     * 1 */
    void                (*nonOverlap2Func)();   /* Function to call for non-
                                     * overlapping bands in region
                                     * 2 */
{
    register BoxPtr     r1;               /* Pointer into first region */
    register BoxPtr     r2;               /* Pointer into 2d region */
    BoxPtr              r1End;                  /* End of 1st region */
    BoxPtr              r2End;                  /* End of 2d region */
    register short      ybot;             /* Bottom of intersection */
    register short      ytop;             /* Top of intersection */
    BoxPtr              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 */
    register BoxPtr     r1BandEnd;              /* End of current band in r1 */
    register BoxPtr     r2BandEnd;              /* End of current band in r2 */
    short               top;              /* Top of non-overlapping
                                     * band */
    short               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;

    if (! (newReg->rects = (BoxPtr)
         Xmalloc ((unsigned) (sizeof(BoxRec) * newReg->size)))) {
      newReg->size = 0;
      return;
    }
    
    /*
     * 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;

      /*
       * This algorithm proceeds one source-band (as opposed to a
       * destination band, which is determined by where the two regions
       * intersect) at a time. r1BandEnd and r2BandEnd serve to mark the
       * rectangle after the last one in the current band for their
       * respective regions.
       */
      r1BandEnd = r1;
      while ((r1BandEnd != r1End) && (r1BandEnd->y1 == r1->y1))
      {
          r1BandEnd++;
      }
      
      r2BandEnd = r2;
      while ((r2BandEnd != r2End) && (r2BandEnd->y1 == r2->y1))
      {
          r2BandEnd++;
      }
      
      /*
       * First handle the band that doesn't intersect, if any.
       *
       * Note that attention is restricted to one band in the
       * non-intersecting region at once, so if a region has n
       * bands between the current position and the next place it overlaps
       * the other, this entire loop will be passed through n times.
       */
      if (r1->y1 < r2->y1)
      {
          top = max(r1->y1,ybot);
          bot = min(r1->y2,r2->y1);

          if ((top != bot) && (nonOverlap1Func != (void (*)())NULL))
          {
            (* nonOverlap1Func) (newReg, r1, r1BandEnd, top, bot);
          }

          ytop = r2->y1;
      }
      else if (r2->y1 < r1->y1)
      {
          top = max(r2->y1,ybot);
          bot = min(r2->y2,r1->y1);

          if ((top != bot) && (nonOverlap2Func != (void (*)())NULL))
          {
            (* nonOverlap2Func) (newReg, r2, r2BandEnd, top, bot);
          }

          ytop = r1->y1;
      }
      else
      {
          ytop = r1->y1;
      }

      /*
       * If any rectangles got added to the region, try and coalesce them
       * with rectangles from the previous band. Note we could just do
       * this test in miCoalesce, but some machines incur a not
       * inconsiderable cost for function calls, so...
       */
      if (newReg->numRects != curBand)
      {
          prevBand = miCoalesce (newReg, prevBand, curBand);
      }

      /*
       * Now see if we've hit an intersecting band. The two bands only
       * intersect if ybot > ytop
       */
      ybot = min(r1->y2, r2->y2);
      curBand = newReg->numRects;
      if (ybot > ytop)
      {
          (* overlapFunc) (newReg, r1, r1BandEnd, r2, r2BandEnd, ytop, ybot);

      }
      
      if (newReg->numRects != curBand)
      {
          prevBand = miCoalesce (newReg, prevBand, curBand);
      }

      /*
       * If we've finished with a band (y2 == ybot) we skip forward
       * in the region to the next band.
       */
      if (r1->y2 == ybot)
      {
          r1 = r1BandEnd;
      }
      if (r2->y2 == ybot)
      {
          r2 = r2BandEnd;
      }
    } while ((r1 != r1End) && (r2 != r2End));

    /*
     * Deal with whichever region still has rectangles left.
     */
    curBand = newReg->numRects;
    if (r1 != r1End)
    {
      if (nonOverlap1Func != (void (*)())NULL)
      {
          do
          {
            r1BandEnd = r1;
            while ((r1BandEnd < r1End) && (r1BandEnd->y1 == r1->y1))
            {
                r1BandEnd++;
            }
            (* nonOverlap1Func) (newReg, r1, r1BandEnd,
                             max(r1->y1,ybot), r1->y2);
            r1 = r1BandEnd;
          } while (r1 != r1End);
      }
    }
    else if ((r2 != r2End) && (nonOverlap2Func != (void (*)())NULL))
    {
      do
      {
          r2BandEnd = r2;
          while ((r2BandEnd < r2End) && (r2BandEnd->y1 == r2->y1))
          {
             r2BandEnd++;
          }
          (* nonOverlap2Func) (newReg, r2, r2BandEnd,
                        max(r2->y1,ybot), r2->y2);
          r2 = r2BandEnd;
      } while (r2 != r2End);
    }

    if (newReg->numRects != curBand)
    {
      (void) miCoalesce (newReg, prevBand, curBand);
    }

    /*
     * A bit of cleanup. To keep regions from growing without bound,
     * we shrink the array of rectangles to match the new number of
     * rectangles in the region. This never goes to 0, however...
     *
     * Only do this stuff if the number of rectangles allocated is more than
     * twice the number of rectangles in the region (a simple optimization...).
     */
    if (newReg->numRects < (newReg->size >> 1))
    {
      if (REGION_NOT_EMPTY(newReg))
      {
          BoxPtr prev_rects = newReg->rects;
          newReg->size = newReg->numRects;
          newReg->rects = (BoxPtr) Xrealloc ((char *) newReg->rects,
                           (unsigned) (sizeof(BoxRec) * newReg->size));
          if (! newReg->rects)
            newReg->rects = prev_rects;
      }
      else
      {
          /*
           * No point in doing the extra work involved in an Xrealloc if
           * the region is empty
           */
          newReg->size = 1;
          Xfree((char *) newReg->rects);
          newReg->rects = (BoxPtr) Xmalloc(sizeof(BoxRec));
      }
    }
    Xfree ((char *) oldRects);
    return;
}


/*======================================================================
 *        Region Union
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * miUnionNonO --
 *    Handle a non-overlapping band for the union operation. Just
 *    Adds the rectangles into the region. Doesn't have to check for
 *    subsumption or anything.
 *
 * Results:
 *    None.
 *
 * Side Effects:
 *    pReg->numRects is incremented and the final rectangles overwritten
 *    with the rectangles we're passed.
 *
 *-----------------------------------------------------------------------
 */
/* static void*/
static
miUnionNonO (pReg, r, rEnd, y1, y2)
    register Region     pReg;
    register BoxPtr     r;
    BoxPtr              rEnd;
    register short      y1;
    register short      y2;
{
    register BoxPtr     pNextRect;

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

    assert(y1 < y2);

    while (r != rEnd)
    {
      assert(r->x1 < r->x2);
      MEMCHECK(pReg, pNextRect, pReg->rects);
      pNextRect->x1 = r->x1;
      pNextRect->y1 = y1;
      pNextRect->x2 = r->x2;
      pNextRect->y2 = y2;
      pReg->numRects += 1;
      pNextRect++;

      assert(pReg->numRects<=pReg->size);
      r++;
    }
    return 0;     /* lint */
}


/*-
 *-----------------------------------------------------------------------
 * miUnionO --
 *    Handle an overlapping band for the union operation. Picks the
 *    left-most rectangle each time and merges it into the region.
 *
 * Results:
 *    None.
 *
 * Side Effects:
 *    Rectangles are overwritten in pReg->rects and pReg->numRects will
 *    be changed.
 *
 *-----------------------------------------------------------------------
 */

/* static void*/
static
miUnionO (pReg, r1, r1End, r2, r2End, y1, y2)
    register Region     pReg;
    register BoxPtr     r1;
    BoxPtr              r1End;
    register BoxPtr     r2;
    BoxPtr              r2End;
    register short      y1;
    register short      y2;
{
    register BoxPtr     pNextRect;
    
    pNextRect = &pReg->rects[pReg->numRects];

#define MERGERECT(r) \
    if ((pReg->numRects != 0) &&  \
      (pNextRect[-1].y1 == y1) &&  \
      (pNextRect[-1].y2 == y2) &&  \
      (pNextRect[-1].x2 >= r->x1))  \
    {  \
      if (pNextRect[-1].x2 < r->x2)  \
      {  \
          pNextRect[-1].x2 = r->x2;  \
          assert(pNextRect[-1].x1<pNextRect[-1].x2); \
      }  \
    }  \
    else  \
    {  \
      MEMCHECK(pReg, pNextRect, pReg->rects);  \
      pNextRect->y1 = y1;  \
      pNextRect->y2 = y2;  \
      pNextRect->x1 = r->x1;  \
      pNextRect->x2 = r->x2;  \
      pReg->numRects += 1;  \
        pNextRect += 1;  \
    }  \
    assert(pReg->numRects<=pReg->size);\
    r++;
    
    assert (y1<y2);
    while ((r1 != r1End) && (r2 != r2End))
    {
      if (r1->x1 < r2->x1)
      {
          MERGERECT(r1);
      }
      else
      {
          MERGERECT(r2);
      }
    }
    
    if (r1 != r1End)
    {
      do
      {
          MERGERECT(r1);
      } while (r1 != r1End);
    }
    else while (r2 != r2End)
    {
      MERGERECT(r2);
    }
    return 0;     /* lint */
}

XUnionRegion(reg1, reg2, newReg)
    Region    reg1;
    Region    reg2;             /* source regions     */
    Region    newReg;                  /* destination Region */
{
    /*  checks all the simple cases */

    /*
     * Region 1 and 2 are the same or region 1 is empty
     */
    if ( (reg1 == reg2) || (!(reg1->numRects)) )
    {
        if (newReg != reg2)
            miRegionCopy(newReg, reg2);
        return(TRUE);
    }

    /*
     * if nothing to union (region 2 empty)
     */
    if (!(reg2->numRects))
    {
        if (newReg != reg1)
            miRegionCopy(newReg, reg1);
        return(TRUE);
    }

    /*
     * Region 1 completely subsumes region 2
     */
    if ((reg1->numRects == 1) && 
      (reg1->extents.x1 <= reg2->extents.x1) &&
      (reg1->extents.y1 <= reg2->extents.y1) &&
      (reg1->extents.x2 >= reg2->extents.x2) &&
      (reg1->extents.y2 >= reg2->extents.y2))
    {
        if (newReg != reg1)
            miRegionCopy(newReg, reg1);
        return(TRUE);
    }

    /*
     * Region 2 completely subsumes region 1
     */
    if ((reg2->numRects == 1) && 
      (reg2->extents.x1 <= reg1->extents.x1) &&
      (reg2->extents.y1 <= reg1->extents.y1) &&
      (reg2->extents.x2 >= reg1->extents.x2) &&
      (reg2->extents.y2 >= reg1->extents.y2))
    {
        if (newReg != reg2)
            miRegionCopy(newReg, reg2);
        return(TRUE);
    }

    miRegionOp (newReg, reg1, reg2, (voidProcp) miUnionO, 
            (voidProcp) miUnionNonO, (voidProcp) miUnionNonO);

    newReg->extents.x1 = min(reg1->extents.x1, reg2->extents.x1);
    newReg->extents.y1 = min(reg1->extents.y1, reg2->extents.y1);
    newReg->extents.x2 = max(reg1->extents.x2, reg2->extents.x2);
    newReg->extents.y2 = max(reg1->extents.y2, reg2->extents.y2);

    return(1);
}


/*======================================================================
 *            Region Subtraction
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * miSubtractNonO --
 *    Deal with non-overlapping band for subtraction. Any parts from
 *    region 2 we discard. Anything from region 1 we add to the region.
 *
 * Results:
 *    None.
 *
 * Side Effects:
 *    pReg may be affected.
 *
 *-----------------------------------------------------------------------
 */
/* static void*/
static
miSubtractNonO1 (pReg, r, rEnd, y1, y2)
    register Region     pReg;
    register BoxPtr     r;
    BoxPtr              rEnd;
    register short      y1;
    register short      y2;
{
    register BoxPtr     pNextRect;
      
    pNextRect = &pReg->rects[pReg->numRects];
      
    assert(y1<y2);

    while (r != rEnd)
    {
      assert(r->x1<r->x2);
      MEMCHECK(pReg, pNextRect, pReg->rects);
      pNextRect->x1 = r->x1;
      pNextRect->y1 = y1;
      pNextRect->x2 = r->x2;
      pNextRect->y2 = y2;
      pReg->numRects += 1;
      pNextRect++;

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

      r++;
    }
    return 0;     /* lint */
}

/*-
 *-----------------------------------------------------------------------
 * miSubtractO --
 *    Overlapping band subtraction. x1 is the left-most point not yet
 *    checked.
 *
 * Results:
 *    None.
 *
 * Side Effects:
 *    pReg may have rectangles added to it.
 *
 *-----------------------------------------------------------------------
 */
/* static void*/
static
miSubtractO (pReg, r1, r1End, r2, r2End, y1, y2)
    register Region     pReg;
    register BoxPtr     r1;
    BoxPtr              r1End;
    register BoxPtr     r2;
    BoxPtr              r2End;
    register short      y1;
    register short      y2;
{
    register BoxPtr     pNextRect;
    register int        x1;
    
    x1 = r1->x1;
    
    assert(y1<y2);
    pNextRect = &pReg->rects[pReg->numRects];

    while ((r1 != r1End) && (r2 != r2End))
    {
      if (r2->x2 <= x1)
      {
          /*
           * Subtrahend missed the boat: go to next subtrahend.
           */
          r2++;
      }
      else if (r2->x1 <= x1)
      {
          /*
           * Subtrahend preceeds minuend: nuke left edge of minuend.
           */
          x1 = r2->x2;
          if (x1 >= r1->x2)
          {
            /*
             * Minuend completely covered: advance to next minuend and
             * reset left fence to edge of new minuend.
             */
            r1++;
            if (r1 != r1End)
                x1 = r1->x1;
          }
          else
          {
            /*
             * Subtrahend now used up since it doesn't extend beyond
             * minuend
             */
            r2++;
          }
      }
      else if (r2->x1 < r1->x2)
      {
          /*
           * Left part of subtrahend covers part of minuend: add uncovered
           * part of minuend to region and skip to next subtrahend.
           */
          assert(x1<r2->x1);
          MEMCHECK(pReg, pNextRect, pReg->rects);
          pNextRect->x1 = x1;
          pNextRect->y1 = y1;
          pNextRect->x2 = r2->x1;
          pNextRect->y2 = y2;
          pReg->numRects += 1;
          pNextRect++;

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

          x1 = r2->x2;
          if (x1 >= r1->x2)
          {
            /*
             * Minuend used up: advance to new...
             */
            r1++;
            if (r1 != r1End)
                x1 = r1->x1;
          }
          else
          {
            /*
             * Subtrahend used up
             */
            r2++;
          }
      }
      else
      {
          /*
           * Minuend used up: add any remaining piece before advancing.
           */
          if (r1->x2 > x1)
          {
            MEMCHECK(pReg, pNextRect, pReg->rects);
            pNextRect->x1 = x1;
            pNextRect->y1 = y1;
            pNextRect->x2 = r1->x2;
            pNextRect->y2 = y2;
            pReg->numRects += 1;
            pNextRect++;
            assert(pReg->numRects<=pReg->size);
          }
          r1++;
          x1 = r1->x1;
      }
    }

    /*
     * Add remaining minuend rectangles to region.
     */
    while (r1 != r1End)
    {
      assert(x1<r1->x2);
      MEMCHECK(pReg, pNextRect, pReg->rects);
      pNextRect->x1 = x1;
      pNextRect->y1 = y1;
      pNextRect->x2 = r1->x2;
      pNextRect->y2 = y2;
      pReg->numRects += 1;
      pNextRect++;

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

      r1++;
      if (r1 != r1End)
      {
          x1 = r1->x1;
      }
    }
    return 0;     /* lint */
}
      
int 
XPointInRegion( pRegion, x, y )
    Region pRegion;
    int x, y;
{
    int i;

    if (pRegion->numRects == 0)
        return(FALSE);
    if (!INBOX(pRegion->extents, x, y))
        return(FALSE);
    for (i=0; i<pRegion->numRects; i++)
    {
        if (INBOX (pRegion->rects[i], x, y))
          return(TRUE);
    }
    return(FALSE);
}

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