/utils/vnc/reflector/region.c

/* $XFree86: xc/programs/Xserver/mi/miregion.c,v 1.8 2001/12/14 20:00:26 dawes Exp $ */
/***********************************************************

Copyright 1987, 1988, 1989, 1998  The Open Group

Permission to use, copy, modify, distribute, and sell this software and its
documentation for any purpose is hereby granted without fee, provided that
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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, 1989 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
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******************************************************************/
/* $Xorg: miregion.c,v 1.4 2001/02/09 02:05:21 xorgcvs Exp $ */

/* The panoramix components contained the following notice */
/****************************************************************
*                                                               *
*    Copyright (c) Digital Equipment Corporation, 1991, 1997    *
*                                                               *
*   All Rights Reserved.  Unpublished rights  reserved  under   *
*   the copyright laws of the United States.                    *
*                                                               *
*   The software contained on this media  is  proprietary  to   *
*   and  embodies  the  confidential  technology  of  Digital   *
*   Equipment Corporation.  Possession, use,  duplication  or   *
*   dissemination of the software and media is authorized only  *
*   pursuant to a valid written license from Digital Equipment  *
*   Corporation.                                                *
*                                                               *
*   RESTRICTED RIGHTS LEGEND   Use, duplication, or disclosure  *
*   by the U.S. Government is subject to restrictions  as  set  *
*   forth in Subparagraph (c)(1)(ii)  of  DFARS  252.227-7013,  *
*   or  in  FAR 52.227-19, as applicable.                       *
*                                                               *
*****************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* Get definitions for CARD16 etc. */
#include "rfblib.h"

#include "region.h"

#if defined (__GNUC__) && !defined (NO_INLINES)
#define INLINE	__inline
#else
#define INLINE
#endif

#undef assert
#ifdef DEBUG
#define assert(expr) {if (!(expr)) \
		FatalError("Assertion failed file %s, line %d: expr\n", \
			__FILE__, __LINE__); }
#else
#define assert(expr)
#endif

#define good(reg) assert(miValidRegion(reg))

/*
 * The functions in this file implement the Region abstraction used extensively
 * throughout the X11 sample server. A Region is simply a set of disjoint
 * (non-overlapping) rectangles, plus an "extent" rectangle which is the
 * smallest single rectangle that contains all the non-overlapping rectangles.
 *
 * A Region is implemented as a "y-x-banded" array of rectangles.  This array
 * imposes two degrees of order.  First, all rectangles are sorted by top side
 * y coordinate first (y1), and then by left side x coordinate (x1).
 *
 * Furthermore, the rectangles are grouped into "bands".  Each rectangle in a
 * band has the same top y coordinate (y1), and each has the same bottom y
 * coordinate (y2).  Thus all rectangles in a band differ only in their left
 * and right side (x1 and x2).  Bands are implicit in the array of rectangles:
 * there is no separate list of band start pointers.
 *
 * The y-x band representation does not minimize rectangles.  In particular,
 * if a rectangle vertically crosses a band (the rectangle has scanlines in 
 * the y1 to y2 area spanned by the band), then the rectangle may be broken
 * down into two or more smaller rectangles stacked one atop the other. 
 *
 *  -----------				    -----------
 *  |         |				    |         |		    band 0
 *  |         |  --------		    -----------  --------
 *  |         |  |      |  in y-x banded    |         |  |      |   band 1
 *  |         |  |      |  form is	    |         |  |      |
 *  -----------  |      |		    -----------  --------
 *               |      |				 |      |   band 2
 *               --------				 --------
 *
 * An added constraint on the rectangles is that they must cover as much
 * horizontal area as possible: no two rectangles within 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).
 *
 * Adam de Boor wrote most of the original region code.  Joel McCormack
 * substantially modified or rewrote most of the core arithmetic routines,
 * and added miRegionValidate in order to support several speed improvements
 * to miValidateTree.  Bob Scheifler changed the representation to be more
 * compact when empty or a single rectangle, and did a bunch of gratuitous
 * reformatting.
 */

/*  true iff two Boxes overlap */
#define EXTENTCHECK(r1,r2) \
      (!( ((r1)->x2 <= (r2)->x1)  || \
          ((r1)->x1 >= (r2)->x2)  || \
          ((r1)->y2 <= (r2)->y1)  || \
          ((r1)->y1 >= (r2)->y2) ) )

/* true iff (x,y) is in Box */
#define INBOX(r,x,y) \
      ( ((r)->x2 >  x) && \
        ((r)->x1 <= x) && \
        ((r)->y2 >  y) && \
        ((r)->y1 <= y) )

/* true iff Box r1 contains Box r2 */
#define SUBSUMES(r1,r2) \
      ( ((r1)->x1 <= (r2)->x1) && \
        ((r1)->x2 >= (r2)->x2) && \
        ((r1)->y1 <= (r2)->y1) && \
        ((r1)->y2 >= (r2)->y2) )

#define min(a, b) (((a) < (b)) ? (a) : (b))
#define max(a, b) (((a) > (b)) ? (a) : (b))

#define xallocData(n)    (RegDataPtr)malloc(REGION_SZOF(n))
#define xfreeData(reg)   if ((reg)->data && (reg)->data->size) \
                           free((reg)->data)

#define RECTALLOC_BAIL(pReg,n,bail) \
if (!(pReg)->data || (((pReg)->data->numRects + (n)) > (pReg)->data->size)) \
    if (!miRectAlloc(pReg, n)) { goto bail; }

#define RECTALLOC(pReg,n) \
if (!(pReg)->data || (((pReg)->data->numRects + (n)) > (pReg)->data->size)) \
    if (!miRectAlloc(pReg, n)) { return FALSE; }

#define ADDRECT(pNextRect,nx1,ny1,nx2,ny2)	\
{						\
    pNextRect->x1 = nx1;			\
    pNextRect->y1 = ny1;			\
    pNextRect->x2 = nx2;			\
    pNextRect->y2 = ny2;			\
    pNextRect++;				\
}

#define NEWRECT(pReg,pNextRect,nx1,ny1,nx2,ny2)			\
{									\
    if (!(pReg)->data || ((pReg)->data->numRects == (pReg)->data->size))\
    {									\
	if (!miRectAlloc(pReg, 1))					\
	    return FALSE;						\
	pNextRect = REGION_TOP(pReg);					\
    }									\
    ADDRECT(pNextRect,nx1,ny1,nx2,ny2);					\
    pReg->data->numRects++;						\
    assert(pReg->data->numRects<=pReg->data->size);			\
}


#define DOWNSIZE(reg,numRects)						 \
if (((numRects) < ((reg)->data->size >> 1)) && ((reg)->data->size > 50)) \
{									 \
    RegDataPtr NewData;							 \
    NewData = (RegDataPtr)xrealloc((reg)->data, REGION_SZOF(numRects));	 \
    if (NewData)							 \
    {									 \
	NewData->size = (numRects);					 \
	(reg)->data = NewData;						 \
    }									 \
}


BoxRec miEmptyBox = {0, 0, 0, 0};
RegDataRec miEmptyData = {0, 0};

RegDataRec  miBrokenData = {0, 0};
RegionRec   miBrokenRegion = { { 0, 0, 0, 0 }, &miBrokenData };

#ifdef DEBUG
int
miPrintRegion(rgn)
    RegionPtr rgn;
{
    int num, size;
    register int i;
    BoxPtr rects;

    num = REGION_NUM_RECTS(rgn);
    size = REGION_SIZE(rgn);
    rects = REGION_RECTS(rgn);
    ErrorF("num: %d size: %d\n", num, size);
    ErrorF("extents: %d %d %d %d\n",
	   rgn->extents.x1, rgn->extents.y1, rgn->extents.x2, rgn->extents.y2);
    for (i = 0; i < num; i++)
      ErrorF("%d %d %d %d \n",
	     rects[i].x1, rects[i].y1, rects[i].x2, rects[i].y2);
    ErrorF("\n");
    return(num);
}

Bool
miRegionsEqual(reg1, reg2)
    RegionPtr reg1;
    RegionPtr reg2;
{
    int i;
    BoxPtr rects1, rects2;

    if (reg1->extents.x1 != reg2->extents.x1) return FALSE;
    if (reg1->extents.x2 != reg2->extents.x2) return FALSE;
    if (reg1->extents.y1 != reg2->extents.y1) return FALSE;
    if (reg1->extents.y2 != reg2->extents.y2) return FALSE;
    if (REGION_NUM_RECTS(reg1) != REGION_NUM_RECTS(reg2)) return FALSE;
    
    rects1 = REGION_RECTS(reg1);
    rects2 = REGION_RECTS(reg2);
    for (i = 0; i != REGION_NUM_RECTS(reg1); i++) {
	if (rects1[i].x1 != rects2[i].x1) return FALSE;
	if (rects1[i].x2 != rects2[i].x2) return FALSE;
	if (rects1[i].y1 != rects2[i].y1) return FALSE;
	if (rects1[i].y2 != rects2[i].y2) return FALSE;
    }
    return TRUE;
}

Bool
miValidRegion(reg)
    RegionPtr reg;
{
    register int i, numRects;

    if ((reg->extents.x1 > reg->extents.x2) ||
	(reg->extents.y1 > reg->extents.y2))
	return FALSE;
    numRects = REGION_NUM_RECTS(reg);
    if (!numRects)
	return ((reg->extents.x1 == reg->extents.x2) &&
		(reg->extents.y1 == reg->extents.y2) &&
		(reg->data->size || (reg->data == &miEmptyData)));
    else if (numRects == 1)
	return (!reg->data);
    else
    {
	register BoxPtr pboxP, pboxN;
	BoxRec box;

	pboxP = REGION_RECTS(reg);
	box = *pboxP;
	box.y2 = pboxP[numRects-1].y2;
	pboxN = pboxP + 1;
	for (i = numRects; --i > 0; pboxP++, pboxN++)
	{
	    if ((pboxN->x1 >= pboxN->x2) ||
		(pboxN->y1 >= pboxN->y2))
		return FALSE;
	    if (pboxN->x1 < box.x1)
	        box.x1 = pboxN->x1;
	    if (pboxN->x2 > box.x2)
		box.x2 = pboxN->x2;
	    if ((pboxN->y1 < pboxP->y1) ||
		((pboxN->y1 == pboxP->y1) &&
		 ((pboxN->x1 < pboxP->x2) || (pboxN->y2 != pboxP->y2))))
		return FALSE;
	}
	return ((box.x1 == reg->extents.x1) &&
		(box.x2 == reg->extents.x2) &&
		(box.y1 == reg->extents.y1) &&
		(box.y2 == reg->extents.y2));
    }
}

#endif /* DEBUG */


/*****************************************************************
 *   RegionCreate(rect, size)
 *     This routine does a simple malloc to make a structure of
 *     REGION of "size" number of rectangles.
 *****************************************************************/

RegionPtr
miRegionCreate(rect, size)
    BoxPtr rect;
    int size;
{
    register RegionPtr pReg;
   
    pReg = (RegionPtr)xalloc(sizeof(RegionRec));
    if (!pReg)
	return &miBrokenRegion;
    if (rect)
    {
	pReg->extents = *rect;
	pReg->data = (RegDataPtr)NULL;
    }
    else
    {
	pReg->extents = miEmptyBox;
	if ((size > 1) && (pReg->data = xallocData(size)))
	{
	    pReg->data->size = size;
	    pReg->data->numRects = 0;
	}
	else
	    pReg->data = &miEmptyData;
    }
    return(pReg);
}

/*****************************************************************
 *   RegionInit(pReg, rect, size)
 *     Outer region rect is statically allocated.
 *****************************************************************/

void
miRegionInit(pReg, rect, size)
    RegionPtr pReg;
    BoxPtr rect;
    int size;
{
    if (rect)
    {
	pReg->extents = *rect;
	pReg->data = (RegDataPtr)NULL;
    }
    else
    {
	pReg->extents = miEmptyBox;
	if ((size > 1) && (pReg->data = xallocData(size)))
	{
	    pReg->data->size = size;
	    pReg->data->numRects = 0;
	}
	else
	    pReg->data = &miEmptyData;
    }
}

void
miRegionDestroy(pReg)
    RegionPtr pReg;
{
    good(pReg);
    xfreeData(pReg);
    if (pReg != &miBrokenRegion)
	xfree(pReg);
}

void
miRegionUninit(pReg)
    RegionPtr pReg;
{
    good(pReg);
    xfreeData(pReg);
}

Bool
miRegionBreak (pReg)
    RegionPtr pReg;
{
    xfreeData (pReg);
    pReg->extents = miEmptyBox;
    pReg->data = &miBrokenData;
    return FALSE;
}

Bool
miRectAlloc(
    register RegionPtr pRgn,
    int n)
{
    RegDataPtr	data;
    
    if (!pRgn->data)
    {
	n++;
	pRgn->data = xallocData(n);
	if (!pRgn->data)
	    return miRegionBreak (pRgn);
	pRgn->data->numRects = 1;
	*REGION_BOXPTR(pRgn) = pRgn->extents;
    }
    else if (!pRgn->data->size)
    {
	pRgn->data = xallocData(n);
	if (!pRgn->data)
	    return miRegionBreak (pRgn);
	pRgn->data->numRects = 0;
    }
    else
    {
	if (n == 1)
	{
	    n = pRgn->data->numRects;
	    if (n > 500) /* XXX pick numbers out of a hat */
		n = 250;
	}
	n += pRgn->data->numRects;
	data = (RegDataPtr)xrealloc(pRgn->data, REGION_SZOF(n));
	if (!data)
	    return miRegionBreak (pRgn);
	pRgn->data = data;
    }
    pRgn->data->size = n;
    return TRUE;
}

Bool
miRegionCopy(dst, src)
    register RegionPtr dst;
    register RegionPtr src;
{
    good(dst);
    good(src);
    if (dst == src)
	return TRUE;
    dst->extents = src->extents;
    if (!src->data || !src->data->size)
    {
	xfreeData(dst);
	dst->data = src->data;
	return TRUE;
    }
    if (!dst->data || (dst->data->size < src->data->numRects))
    {
	xfreeData(dst);
	dst->data = xallocData(src->data->numRects);
	if (!dst->data)
	    return miRegionBreak (dst);
	dst->data->size = src->data->numRects;
    }
    dst->data->numRects = src->data->numRects;
    memmove((char *)REGION_BOXPTR(dst),(char *)REGION_BOXPTR(src), 
	  dst->data->numRects * sizeof(BoxRec));
    return TRUE;
}


/*======================================================================
 *	    Generic Region Operator
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * miCoalesce --
 *	Attempt to merge the boxes in the current band with those in the
 *	previous one.  We are guaranteed that the current band extends to
 *      the end of the rects array.  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->data->numRects will be decreased.
 *
 *-----------------------------------------------------------------------
 */
INLINE static int
miCoalesce (
    register RegionPtr	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 int  	numRects;	/* Number rectangles in both bands   */
    register int	y2;		/* Bottom of current band	     */
    /*
     * Figure out how many rectangles are in the band.
     */
    numRects = curStart - prevStart;
    assert(numRects == pReg->data->numRects - curStart);

    if (!numRects) return curStart;

    /*
     * The bands may only be coalesced if the bottom of the previous
     * matches the top scanline of the current.
     */
    pPrevBox = REGION_BOX(pReg, prevStart);
    pCurBox = REGION_BOX(pReg, curStart);
    if (pPrevBox->y2 != pCurBox->y1) return curStart;

    /*
     * 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.
     */
    y2 = pCurBox->y2;

    do {
	if ((pPrevBox->x1 != pCurBox->x1) || (pPrevBox->x2 != pCurBox->x2)) {
	    return (curStart);
	}
	pPrevBox++;
	pCurBox++;
	numRects--;
    } while (numRects);

    /*
     * The bands may be merged, so set the bottom y of each box
     * in the previous band to the bottom y of the current band.
     */
    numRects = curStart - prevStart;
    pReg->data->numRects -= numRects;
    do {
	pPrevBox--;
	pPrevBox->y2 = y2;
	numRects--;
    } while (numRects);
    return prevStart;
}


/* Quicky macro to avoid trivial reject procedure calls to miCoalesce */

#define Coalesce(newReg, prevBand, curBand)				\
    if (curBand - prevBand == newReg->data->numRects - curBand) {	\
	prevBand = miCoalesce(newReg, prevBand, curBand);		\
    } else {								\
	prevBand = curBand;						\
    }

/*-
 *-----------------------------------------------------------------------
 * miAppendNonO --
 *	Handle a non-overlapping band for the union and subtract operations.
 *      Just adds the (top/bottom-clipped) rectangles into the region.
 *      Doesn't have to check for subsumption or anything.
 *
 * Results:
 *	None.
 *
 * Side Effects:
 *	pReg->data->numRects is incremented and the rectangles overwritten
 *	with the rectangles we're passed.
 *
 *-----------------------------------------------------------------------
 */

INLINE static Bool
miAppendNonO (
    register RegionPtr	pReg,
    register BoxPtr	r,
    BoxPtr  	  	rEnd,
    register int  	y1,
    register int  	y2)
{
    register BoxPtr	pNextRect;
    register int	newRects;

    newRects = rEnd - r;

    assert(y1 < y2);
    assert(newRects != 0);

    /* Make sure we have enough space for all rectangles to be added */
    RECTALLOC(pReg, newRects);
    pNextRect = REGION_TOP(pReg);
    pReg->data->numRects += newRects;
    do {
	assert(r->x1 < r->x2);
	ADDRECT(pNextRect, r->x1, y1, r->x2, y2);
	r++;
    } while (r != rEnd);

    return TRUE;
}

#define FindBand(r, rBandEnd, rEnd, ry1)		    \
{							    \
    ry1 = r->y1;					    \
    rBandEnd = r+1;					    \
    while ((rBandEnd != rEnd) && (rBandEnd->y1 == ry1)) {   \
	rBandEnd++;					    \
    }							    \
}

#define	AppendRegions(newReg, r, rEnd)					\
{									\
    int newRects;							\
    if ((newRects = rEnd - r)) {					\
	RECTALLOC(newReg, newRects);					\
	memmove((char *)REGION_TOP(newReg),(char *)r, 			\
              newRects * sizeof(BoxRec));				\
	newReg->data->numRects += newRects;				\
    }									\
}

/*-
 *-----------------------------------------------------------------------
 * miRegionOp --
 *	Apply an operation to two regions. Called by miUnion, miInverse,
 *	miSubtract, miIntersect....  Both regions MUST have at least one
 *      rectangle, and cannot be the same object.
 *
 * Results:
 *	TRUE if successful.
 *
 * Side Effects:
 *	The new region is overwritten.
 *	pOverlap set to TRUE if overlapFunc ever returns TRUE.
 *
 * 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.
 *
 *-----------------------------------------------------------------------
 */

typedef Bool (*OverlapProcPtr)(
    RegionPtr	pReg,
    BoxPtr	r1,
    BoxPtr   	r1End,
    BoxPtr	r2,
    BoxPtr   	r2End,
    short    	y1,
    short    	y2,
    Bool	*pOverlap);

static Bool
miRegionOp(
    RegionPtr       newReg,		    /* Place to store result	     */
    RegionPtr       reg1,		    /* First region in operation     */
    RegionPtr       reg2,		    /* 2d region in operation        */
    OverlapProcPtr  overlapFunc,            /* Function to call for over-
					     * lapping bands		     */
    Bool	    appendNon1,		    /* Append non-overlapping bands  */
					    /* in region 1 ? */
    Bool	    appendNon2,		    /* Append non-overlapping bands  */
					    /* in region 2 ? */
    Bool	    *pOverlap)
{
    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		     */
    short	    ybot;		    /* Bottom of intersection	     */
    short	    ytop;		    /* Top of intersection	     */
    RegDataPtr	    oldData;		    /* Old data 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*/
    register int    r1y1;		    /* Temps for r1->y1 and r2->y1   */
    register int    r2y1;
    int		    newSize;
    int		    numRects;

    /*
     * Break any region computed from a broken region
     */
    if (REGION_NAR (reg1) || REGION_NAR(reg2))
	return miRegionBreak (newReg);
    
    /*
     * Initialization:
     *	set r1, r2, r1End and r2End appropriately, save the rectangles
     * 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 = REGION_RECTS(reg1);
    newSize = REGION_NUM_RECTS(reg1);
    r1End = r1 + newSize;
    numRects = REGION_NUM_RECTS(reg2);
    r2 = REGION_RECTS(reg2);
    r2End = r2 + numRects;
    assert(r1 != r1End);
    assert(r2 != r2End);

    oldData = (RegDataPtr)NULL;
    if (((newReg == reg1) && (newSize > 1)) ||
	((newReg == reg2) && (numRects > 1)))
    {
	oldData = newReg->data;
	newReg->data = &miEmptyData;
    }
    /* guess at new size */
    if (numRects > newSize)
	newSize = numRects;
    newSize <<= 1;
    if (!newReg->data)
	newReg->data = &miEmptyData;
    else if (newReg->data->size)
	newReg->data->numRects = 0;
    if (newSize > newReg->data->size)
	if (!miRectAlloc(newReg, newSize))
	    return FALSE;

    /*
     * Initialize ybot.
     * 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.
     */

    ybot = min(r1->y1, r2->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 {
	/*
	 * 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.
	 */
	assert(r1 != r1End);
	assert(r2 != r2End);
    
	FindBand(r1, r1BandEnd, r1End, r1y1);
	FindBand(r2, r2BandEnd, r2End, r2y1);

	/*
	 * 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 (r1y1 < r2y1) {
	    if (appendNon1) {
		top = max(r1y1, ybot);
		bot = min(r1->y2, r2y1);
		if (top != bot)	{
		    curBand = newReg->data->numRects;
		    miAppendNonO(newReg, r1, r1BandEnd, top, bot);
		    Coalesce(newReg, prevBand, curBand);
		}
	    }
	    ytop = r2y1;
	} else if (r2y1 < r1y1) {
	    if (appendNon2) {
		top = max(r2y1, ybot);
		bot = min(r2->y2, r1y1);
		if (top != bot) {
		    curBand = newReg->data->numRects;
		    miAppendNonO(newReg, r2, r2BandEnd, top, bot);
		    Coalesce(newReg, prevBand, curBand);
		}
	    }
	    ytop = r1y1;
	} else {
	    ytop = r1y1;
	}

	/*
	 * Now see if we've hit an intersecting band. The two bands only
	 * intersect if ybot > ytop
	 */
	ybot = min(r1->y2, r2->y2);
	if (ybot > ytop) {
	    curBand = newReg->data->numRects;
	    (* overlapFunc)(newReg, r1, r1BandEnd, r2, r2BandEnd, ytop, ybot,
			    pOverlap);
	    Coalesce(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 (if any) still has rectangles left.
     *
     * We only need to worry about banding and coalescing for the very first
     * band left.  After that, we can just group all remaining boxes,
     * regardless of how many bands, into one final append to the list.
     */

    if ((r1 != r1End) && appendNon1) {
	/* Do first nonOverlap1Func call, which may be able to coalesce */
	FindBand(r1, r1BandEnd, r1End, r1y1);
	curBand = newReg->data->numRects;
	miAppendNonO(newReg, r1, r1BandEnd, max(r1y1, ybot), r1->y2);
	Coalesce(newReg, prevBand, curBand);
	/* Just append the rest of the boxes  */
	AppendRegions(newReg, r1BandEnd, r1End);

    } else if ((r2 != r2End) && appendNon2) {
	/* Do first nonOverlap2Func call, which may be able to coalesce */
	FindBand(r2, r2BandEnd, r2End, r2y1);
	curBand = newReg->data->numRects;
	miAppendNonO(newReg, r2, r2BandEnd, max(r2y1, ybot), r2->y2);
	Coalesce(newReg, prevBand, curBand);
	/* Append rest of boxes */
	AppendRegions(newReg, r2BandEnd, r2End);
    }

    if (oldData)
	xfree(oldData);

    if (!(numRects = newReg->data->numRects))
    {
	xfreeData(newReg);
	newReg->data = &miEmptyData;
    }
    else if (numRects == 1)
    {
	newReg->extents = *REGION_BOXPTR(newReg);
	xfreeData(newReg);
	newReg->data = (RegDataPtr)NULL;
    }
    else
    {
	DOWNSIZE(newReg, numRects);
    }

    return TRUE;
}

/*-
 *-----------------------------------------------------------------------
 * miSetExtents --
 *	Reset the extents of a region to what they should be. Called by
 *	miSubtract and miIntersect as 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.
 *
 *-----------------------------------------------------------------------
 */
void
miSetExtents (pReg)
    register RegionPtr pReg;
{
    register BoxPtr pBox, pBoxEnd;

    if (!pReg->data)
	return;
    if (!pReg->data->size)
    {
	pReg->extents.x2 = pReg->extents.x1;
	pReg->extents.y2 = pReg->extents.y1;
	return;
    }

    pBox = REGION_BOXPTR(pReg);
    pBoxEnd = REGION_END(pReg);

    /*
     * 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...
     */
    pReg->extents.x1 = pBox->x1;
    pReg->extents.y1 = pBox->y1;
    pReg->extents.x2 = pBoxEnd->x2;
    pReg->extents.y2 = pBoxEnd->y2;

    assert(pReg->extents.y1 < pReg->extents.y2);
    while (pBox <= pBoxEnd) {
	if (pBox->x1 < pReg->extents.x1)
	    pReg->extents.x1 = pBox->x1;
	if (pBox->x2 > pReg->extents.x2)
	    pReg->extents.x2 = pBox->x2;
	pBox++;
    };

    assert(pReg->extents.x1 < pReg->extents.x2);
}

/*======================================================================
 *	    Region Intersection
 *====================================================================*/
/*-
 *-----------------------------------------------------------------------
 * miIntersectO --
 *	Handle an overlapping band for miIntersect.
 *
 * Results:
 *	TRUE if successful.
 *
 * Side Effects:
 *	Rectangles may be added to the region.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/
static Bool
miIntersectO (
    register RegionPtr	pReg,
    register BoxPtr	r1,
    BoxPtr  	  	r1End,
    register BoxPtr	r2,
    BoxPtr  	  	r2End,
    short    	  	y1,
    short    	  	y2,
    Bool		*pOverlap)
{
    register int  	x1;
    register int  	x2;
    register BoxPtr	pNextRect;

    pNextRect = REGION_TOP(pReg);

    assert(y1 < y2);
    assert(r1 != r1End && r2 != r2End);

    do {
	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.
	 */
	if (x1 < x2)
	    NEWRECT(pReg, pNextRect, x1, y1, x2, y2);

	/*
	 * Advance the pointer(s) with the leftmost right side, since the next
	 * rectangle on that list may still overlap the other region's
	 * current rectangle.
	 */
	if (r1->x2 == x2) {
	    r1++;
	}
	if (r2->x2 == x2) {
	    r2++;
	}
    } while ((r1 != r1End) && (r2 != r2End));

    return TRUE;
}


Bool
miIntersect(newReg, reg1, reg2)
    register RegionPtr 	newReg;     /* destination Region */
    register RegionPtr 	reg1;
    register RegionPtr	reg2;       /* source regions     */
{
    good(reg1);
    good(reg2);
    good(newReg);
   /* check for trivial reject */
    if (REGION_NIL(reg1)  || REGION_NIL(reg2) ||
	!EXTENTCHECK(&reg1->extents, &reg2->extents))
    {
	/* Covers about 20% of all cases */
	xfreeData(newReg);
	newReg->extents.x2 = newReg->extents.x1;
	newReg->extents.y2 = newReg->extents.y1;
	if (REGION_NAR(reg1) || REGION_NAR(reg2))
	{
	    newReg->data = &miBrokenData;
	    return FALSE;
	}
	else
	    newReg->data = &miEmptyData;
    }
    else if (!reg1->data && !reg2->data)
    {
	/* Covers about 80% of cases that aren't trivially rejected */
	newReg->extents.x1 = max(reg1->extents.x1, reg2->extents.x1);
	newReg->extents.y1 = max(reg1->extents.y1, reg2->extents.y1);
	newReg->extents.x2 = min(reg1->extents.x2, reg2->extents.x2);
	newReg->extents.y2 = min(reg1->extents.y2, reg2->extents.y2);
	xfreeData(newReg);
	newReg->data = (RegDataPtr)NULL;
    }
    else if (!reg2->data && SUBSUMES(&reg2->extents, &reg1->extents))
    {
	return miRegionCopy(newReg, reg1);
    }
    else if (!reg1->data && SUBSUMES(&reg1->extents, &reg2->extents))
    {
	return miRegionCopy(newReg, reg2);
    }
    else if (reg1 == reg2)
    {
	return miRegionCopy(newReg, reg1);
    }
    else
    {
	/* General purpose intersection */
	Bool overlap; /* result ignored */
	if (!miRegionOp(newReg, reg1, reg2, miIntersectO, FALSE, FALSE,
			&overlap))
	    return FALSE;
	miSetExtents(newReg);
    }

    good(newReg);
    return(TRUE);
}

#define MERGERECT(r)						\
{								\
    if (r->x1 <= x2) {						\
	/* Merge with current rectangle */			\
	if (r->x1 < x2) *pOverlap = TRUE;				\
	if (x2 < r->x2) x2 = r->x2;				\
    } else {							\
	/* Add current rectangle, start new one */		\
	NEWRECT(pReg, pNextRect, x1, y1, x2, y2);		\
	x1 = r->x1;						\
	x2 = r->x2;						\
    }								\
    r++;							\
}

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

/*-
 *-----------------------------------------------------------------------
 * miUnionO --
 *	Handle an overlapping band for the union operation. Picks the
 *	left-most rectangle each time and merges it into the region.
 *
 * Results:
 *	TRUE if successful.
 *
 * Side Effects:
 *	pReg is overwritten.
 *	pOverlap is set to TRUE if any boxes overlap.
 *
 *-----------------------------------------------------------------------
 */
static Bool
miUnionO (
    register RegionPtr	pReg,
    register BoxPtr	r1,
	     BoxPtr  	r1End,
    register BoxPtr	r2,
	     BoxPtr  	r2End,
	     short	y1,
	     short	y2,
	     Bool	*pOverlap)
{
    register BoxPtr     pNextRect;
    register int        x1;     /* left and right side of current union */
    register int        x2;

    assert (y1 < y2);
    assert(r1 != r1End && r2 != r2End);

    pNextRect = REGION_TOP(pReg);

    /* Start off current rectangle */
    if (r1->x1 < r2->x1)
    {
	x1 = r1->x1;
	x2 = r1->x2;
	r1++;
    }
    else
    {
	x1 = r2->x1;
	x2 = r2->x2;
	r2++;
    }
    while (r1 != r1End && r2 != r2End)
    {
	if (r1->x1 < r2->x1) MERGERECT(r1) else MERGERECT(r2);
    }

    /* Finish off whoever (if any) is left */
    if (r1 != r1End)
    {
	do
	{
	    MERGERECT(r1);
	} while (r1 != r1End);
    }
    else if (r2 != r2End)
    {
	do
	{
	    MERGERECT(r2);
	} while (r2 != r2End);
    }
    
    /* Add current rectangle */
    NEWRECT(pReg, pNextRect, x1, y1, x2, y2);

    return TRUE;
}

Bool 
miUnion(newReg, reg1, reg2)
    RegionPtr		newReg;                  /* destination Region */
    register RegionPtr 	reg1;
    register RegionPtr	reg2;             /* source regions     */
{
    Bool overlap; /* result ignored */

    /* Return TRUE if some overlap between reg1, reg2 */
    good(reg1);
    good(reg2);
    good(newReg);
    /*  checks all the simple cases */

    /*
     * Region 1 and 2 are the same
     */
    if (reg1 == reg2)
    {
	return miRegionCopy(newReg, reg1);
    }

    /*
     * Region 1 is empty
     */
    if (REGION_NIL(reg1))
    {
	if (REGION_NAR(reg1))
	    return miRegionBreak (newReg);
        if (newReg != reg2)
	    return miRegionCopy(newReg, reg2);
        return TRUE;
    }

    /*
     * Region 2 is empty
     */
    if (REGION_NIL(reg2))
    {
	if (REGION_NAR(reg2))
	    return miRegionBreak (newReg);
        if (newReg != reg1)
	    return miRegionCopy(newReg, reg1);
        return TRUE;
    }

    /*
     * Region 1 completely subsumes region 2
     */
    if (!reg1->data && SUBSUMES(&reg1->extents, &reg2->extents))
    {
        if (newReg != reg1)
	    return miRegionCopy(newReg, reg1);
        return TRUE;
    }

    /*
     * Region 2 completely subsumes region 1
     */
    if (!reg2->data && SUBSUMES(&reg2->extents, &reg1->extents))
    {
        if (newReg != reg2)
	    return miRegionCopy(newReg, reg2);
        return TRUE;
    }

    if (!miRegionOp(newReg, reg1, reg2, miUnionO, TRUE, TRUE, &overlap))
	return FALSE;

    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);
    good(newReg);
    return TRUE;
}


/*======================================================================
 *	    Batch Rectangle Union
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * miRegionAppend --
 * 
 *      "Append" the rgn rectangles onto the end of dstrgn, maintaining
 *      knowledge of YX-banding when it's easy.  Otherwise, dstrgn just
 *      becomes a non-y-x-banded random collection of rectangles, and not
 *      yet a true region.  After a sequence of appends, the caller must
 *      call miRegionValidate to ensure that a valid region is constructed.
 *
 * Results:
 *	TRUE if successful.
 *
 * Side Effects:
 *      dstrgn is modified if rgn has rectangles.
 *
 */
Bool
miRegionAppend(dstrgn, rgn)
    register RegionPtr dstrgn;
    register RegionPtr rgn;
{
    int numRects, dnumRects, size;
    BoxPtr new, old;
    Bool prepend;

    if (REGION_NAR(rgn))
	return miRegionBreak (dstrgn);
    
    if (!rgn->data && (dstrgn->data == &miEmptyData))
    {
	dstrgn->extents = rgn->extents;
	dstrgn->data = (RegDataPtr)NULL;
	return TRUE;
    }

    numRects = REGION_NUM_RECTS(rgn);
    if (!numRects)
	return TRUE;
    prepend = FALSE;
    size = numRects;
    dnumRects = REGION_NUM_RECTS(dstrgn);
    if (!dnumRects && (size < 200))
	size = 200; /* XXX pick numbers out of a hat */
    RECTALLOC(dstrgn, size);
    old = REGION_RECTS(rgn);
    if (!dnumRects)
	dstrgn->extents = rgn->extents;
    else if (dstrgn->extents.x2 > dstrgn->extents.x1)
    {
	register BoxPtr first, last;

	first = old;
	last = REGION_BOXPTR(dstrgn) + (dnumRects - 1);
	if ((first->y1 > last->y2) ||
	    ((first->y1 == last->y1) && (first->y2 == last->y2) &&
	     (first->x1 > last->x2)))
	{
	    if (rgn->extents.x1 < dstrgn->extents.x1)
		dstrgn->extents.x1 = rgn->extents.x1;
	    if (rgn->extents.x2 > dstrgn->extents.x2)
		dstrgn->extents.x2 = rgn->extents.x2;
	    dstrgn->extents.y2 = rgn->extents.y2;
	}
	else
	{
	    first = REGION_BOXPTR(dstrgn);
	    last = old + (numRects - 1);
	    if ((first->y1 > last->y2) ||
		((first->y1 == last->y1) && (first->y2 == last->y2) &&
		 (first->x1 > last->x2)))
	    {
		prepend = TRUE;
		if (rgn->extents.x1 < dstrgn->extents.x1)
		    dstrgn->extents.x1 = rgn->extents.x1;
		if (rgn->extents.x2 > dstrgn->extents.x2)
		    dstrgn->extents.x2 = rgn->extents.x2;
		dstrgn->extents.y1 = rgn->extents.y1;
	    }
	    else
		dstrgn->extents.x2 = dstrgn->extents.x1;
	}
    }
    if (prepend)
    {
	new = REGION_BOX(dstrgn, numRects);
	if (dnumRects == 1)
	    *new = *REGION_BOXPTR(dstrgn);
	else
	    memmove((char *)new,(char *)REGION_BOXPTR(dstrgn), 
		  dnumRects * sizeof(BoxRec));
	new = REGION_BOXPTR(dstrgn);
    }
    else
	new = REGION_BOXPTR(dstrgn) + dnumRects;
    if (numRects == 1)
	*new = *old;
    else
	memmove((char *)new, (char *)old, numRects * sizeof(BoxRec));
    dstrgn->data->numRects += numRects;
    return TRUE;
}

   
#define ExchangeRects(a, b) \
{			    \
    BoxRec     t;	    \
    t = rects[a];	    \
    rects[a] = rects[b];    \
    rects[b] = t;	    \
}

static void
QuickSortRects(
    register BoxRec     rects[],
    register int        numRects)
{
    register int	y1;
    register int	x1;
    register int        i, j;
    register BoxPtr     r;

    /* Always called with numRects > 1 */

    do
    {
	if (numRects == 2)
	{
	    if (rects[0].y1 > rects[1].y1 ||
		    (rects[0].y1 == rects[1].y1 && rects[0].x1 > rects[1].x1))
		ExchangeRects(0, 1);
	    return;
	}

	/* Choose partition element, stick in location 0 */
        ExchangeRects(0, numRects >> 1);
	y1 = rects[0].y1;
	x1 = rects[0].x1;

        /* Partition array */
        i = 0;
        j = numRects;
        do
	{
	    r = &(rects[i]);
	    do
	    {
		r++;
		i++;
            } while (i != numRects &&
		     (r->y1 < y1 || (r->y1 == y1 && r->x1 < x1)));
	    r = &(rects[j]);
	    do
	    {
		r--;
		j--;
            } while (y1 < r->y1 || (y1 == r->y1 && x1 < r->x1));
            if (i < j)
		ExchangeRects(i, j);
        } while (i < j);

        /* Move partition element back to middle */
        ExchangeRects(0, j);

	/* Recurse */
        if (numRects-j-1 > 1)
	    QuickSortRects(&rects[j+1], numRects-j-1);
        numRects = j;
    } while (numRects > 1);
}

/*-
 *-----------------------------------------------------------------------
 * miRegionValidate --
 * 
 *      Take a ``region'' which is a non-y-x-banded random collection of
 *      rectangles, and compute a nice region which is the union of all the
 *      rectangles.
 *
 * Results:
 *	TRUE if successful.
 *
 * Side Effects:
 *      The passed-in ``region'' may be modified.
 *	pOverlap set to TRUE if any retangles overlapped, else FALSE;
 *
 * Strategy:
 *      Step 1. Sort the rectangles into ascending order with primary key y1
 *		and secondary key x1.
 *
 *      Step 2. Split the rectangles into the minimum number of proper y-x
 *		banded regions.  This may require horizontally merging
 *		rectangles, and vertically coalescing bands.  With any luck,
 *		this step in an identity tranformation (ala the Box widget),
 *		or a coalescing into 1 box (ala Menus).
 *
 *	Step 3. Merge the separate regions down to a single region by calling
 *		miUnion.  Maximize the work each miUnion call does by using
 *		a binary merge.
 *
 *-----------------------------------------------------------------------
 */

Bool
miRegionValidate(badreg, pOverlap)
    RegionPtr badreg;
    Bool *pOverlap;
{
    /* Descriptor for regions under construction  in Step 2. */
    typedef struct {
	RegionRec   reg;
	int	    prevBand;
	int	    curBand;
    } RegionInfo;

	     int	numRects;   /* Original numRects for badreg	    */
	     RegionInfo *ri;	    /* Array of current regions		    */
    	     int	numRI;      /* Number of entries used in ri	    */
	     int	sizeRI;	    /* Number of entries available in ri    */
	     int	i;	    /* Index into rects			    */
    register int	j;	    /* Index into ri			    */
    register RegionInfo *rit;       /* &ri[j]				    */
    register RegionPtr  reg;        /* ri[j].reg			    */
    register BoxPtr	box;	    /* Current box in rects		    */
    register BoxPtr	riBox;      /* Last box in ri[j].reg		    */
    register RegionPtr  hreg;       /* ri[j_half].reg			    */
    Bool		ret = TRUE;

    *pOverlap = FALSE;
    if (!badreg->data)
    {
	good(badreg);
	return TRUE;
    }
    numRects = badreg->data->numRects;
    if (!numRects)
    {
	if (REGION_NAR(badreg))
	    return FALSE;
	good(badreg);
	return TRUE;
    }
    if (badreg->extents.x1 < badreg->extents.x2)
    {
	if ((numRects) == 1)
	{
	    xfreeData(badreg);
	    badreg->data = (RegDataPtr) NULL;
	}
	else
	{
	    DOWNSIZE(badreg, numRects);
	}
	good(badreg);
	return TRUE;
    }

    /* Step 1: Sort the rects array into ascending (y1, x1) order */
    QuickSortRects(REGION_BOXPTR(badreg), numRects);

    /* Step 2: Scatter the sorted array into the minimum number of regions */

    /* Set up the first region to be the first rectangle in badreg */
    /* Note that step 2 code will never overflow the ri[0].reg rects array */
    ri = (RegionInfo *) xalloc(4 * sizeof(RegionInfo));
    if (!ri)
	return miRegionBreak (badreg);
    sizeRI = 4;
    numRI = 1;
    ri[0].prevBand = 0;
    ri[0].curBand = 0;
    ri[0].reg = *badreg;
    box = REGION_BOXPTR(&ri[0].reg);
    ri[0].reg.extents = *box;
    ri[0].reg.data->numRects = 1;

    /* Now scatter rectangles into the minimum set of valid regions.  If the
       next rectangle to be added to a region would force an existing rectangle
       in the region to be split up in order to maintain y-x banding, just
       forget it.  Try the next region.  If it doesn't fit cleanly into any
       region, make a new one. */

    for (i = numRects; --i > 0;)
    {
	box++;
	/* Look for a region to append box to */
	for (j = numRI, rit = ri; --j >= 0; rit++)
	{
	    reg = &rit->reg;
	    riBox = REGION_END(reg);

	    if (box->y1 == riBox->y1 && box->y2 == riBox->y2)
	    {
		/* box is in same band as riBox.  Merge or append it */
		if (box->x1 <= riBox->x2)
		{
		    /* Merge it with riBox */
		    if (box->x1 < riBox->x2) *pOverlap = TRUE;
		    if (box->x2 > riBox->x2) riBox->x2 = box->x2;
		}
		else
		{
		    RECTALLOC_BAIL(reg, 1, bail);
		    *REGION_TOP(reg) = *box;
		    reg->data->numRects++;
		}
		goto NextRect;   /* So sue me */
	    }
	    else if (box->y1 >= riBox->y2)
	    {
		/* Put box into new band */
		if (reg->extents.x2 < riBox->x2) reg->extents.x2 = riBox->x2;
		if (reg->extents.x1 > box->x1)   reg->extents.x1 = box->x1;
		Coalesce(reg, rit->prevBand, rit->curBand);
		rit->curBand = reg->data->numRects;
		RECTALLOC_BAIL(reg, 1, bail);
		*REGION_TOP(reg) = *box;
		reg->data->numRects++;
		goto NextRect;
	    }
	    /* Well, this region was inappropriate.  Try the next one. */
	} /* for j */

	/* Uh-oh.  No regions were appropriate.  Create a new one. */
	if (sizeRI == numRI)
	{
	    /* Oops, allocate space for new region information */
	    sizeRI <<= 1;
	    rit = (RegionInfo *) xrealloc(ri, sizeRI * sizeof(RegionInfo));
	    if (!rit)
		goto bail;
	    ri = rit;
	    rit = &ri[numRI];
	}
	numRI++;
	rit->prevBand = 0;
	rit->curBand = 0;
	rit->reg.extents = *box;
	rit->reg.data = (RegDataPtr)NULL;
	if (!miRectAlloc(&rit->reg, (i+numRI) / numRI)) /* MUST force allocation */
	    goto bail;
NextRect: ;
    } /* for i */

    /* Make a final pass over each region in order to Coalesce and set
       extents.x2 and extents.y2 */

    for (j = numRI, rit = ri; --j >= 0; rit++)
    {
	reg = &rit->reg;
	riBox = REGION_END(reg);
	reg->extents.y2 = riBox->y2;
	if (reg->extents.x2 < riBox->x2) reg->extents.x2 = riBox->x2;
	Coalesce(reg, rit->prevBand, rit->curBand);
	if (reg->data->numRects == 1) /* keep unions happy below */
	{
	    xfreeData(reg);
	    reg->data = (RegDataPtr)NULL;
	}
    }

    /* Step 3: Union all regions into a single region */
    while (numRI > 1)
    {
	int half = numRI/2;
	for (j = numRI & 1; j < (half + (numRI & 1)); j++)
	{
	    reg = &ri[j].reg;
	    hreg = &ri[j+half].reg;
	    if (!miRegionOp(reg, reg, hreg, miUnionO, TRUE, TRUE, pOverlap))
		ret = FALSE;
	    if (hreg->extents.x1 < reg->extents.x1)
		reg->extents.x1 = hreg->extents.x1;
	    if (hreg->extents.y1 < reg->extents.y1)
		reg->extents.y1 = hreg->extents.y1;
	    if (hreg->extents.x2 > reg->extents.x2)
		reg->extents.x2 = hreg->extents.x2;
	    if (hreg->extents.y2 > reg->extents.y2)
		reg->extents.y2 = hreg->extents.y2;
	    xfreeData(hreg);
	}
	numRI -= half;
    }
    *badreg = ri[0].reg;
    xfree(ri);
    good(badreg);
    return ret;
bail:
    for (i = 0; i < numRI; i++)
	xfreeData(&ri[i].reg);
    xfree (ri);
    return miRegionBreak (badreg);
}

RegionPtr
miRectsToRegion(nrects, prect, ctype)
    int			nrects;
    register xRectangle	*prect;
    int			ctype;
{
    register RegionPtr	pRgn;
    register RegDataPtr	pData;
    register BoxPtr	pBox;
    register int        i;
    int			x1, y1, x2, y2;

    pRgn = miRegionCreate(NullBox, 0);
    if (REGION_NAR (pRgn))
	return pRgn;
    if (!nrects)
	return pRgn;
    if (nrects == 1)
    {
	x1 = prect->x;
	y1 = prect->y;
	if ((x2 = x1 + (int) prect->width) > MAXSHORT)
	    x2 = MAXSHORT;
	if ((y2 = y1 + (int) prect->height) > MAXSHORT)
	    y2 = MAXSHORT;
	if (x1 != x2 && y1 != y2)
	{
	    pRgn->extents.x1 = x1;
	    pRgn->extents.y1 = y1;
	    pRgn->extents.x2 = x2;
	    pRgn->extents.y2 = y2;
	    pRgn->data = (RegDataPtr)NULL;
	}
	return pRgn;
    }
    pData = xallocData(nrects);
    if (!pData)
    {
	miRegionBreak (pRgn);
	return pRgn;
    }
    pBox = (BoxPtr) (pData + 1);
    for (i = nrects; --i >= 0; prect++)
    {
	x1 = prect->x;
	y1 = prect->y;
	if ((x2 = x1 + (int) prect->width) > MAXSHORT)
	    x2 = MAXSHORT;
	if ((y2 = y1 + (int) prect->height) > MAXSHORT)
	    y2 = MAXSHORT;
	if (x1 != x2 && y1 != y2)
	{
	    pBox->x1 = x1;
	    pBox->y1 = y1;
	    pBox->x2 = x2;
	    pBox->y2 = y2;
	    pBox++;
	}
    }
    if (pBox != (BoxPtr) (pData + 1))
    {
	pData->size = nrects;
	pData->numRects = pBox - (BoxPtr) (pData + 1);
    	pRgn->data = pData;
    	if (ctype != CT_YXBANDED)
    	{
	    Bool overlap; /* result ignored */
	    pRgn->extents.x1 = pRgn->extents.x2 = 0;
	    miRegionValidate(pRgn, &overlap);
    	}
    	else
	    miSetExtents(pRgn);
    	good(pRgn);
    }
    else
    {
	xfree (pData);
    }
    return pRgn;
}

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


/*-
 *-----------------------------------------------------------------------
 * miSubtractO --
 *	Overlapping band subtraction. x1 is the left-most point not yet
 *	checked.
 *
 * Results:
 *	TRUE if successful.
 *
 * Side Effects:
 *	pReg may have rectangles added to it.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/
static Bool
miSubtractO (
    register RegionPtr	pReg,
    register BoxPtr	r1,
    BoxPtr  	  	r1End,
    register BoxPtr	r2,
    BoxPtr  	  	r2End,
    register short  	y1,
             short  	y2,
    Bool		*pOverlap)
{
    register BoxPtr	pNextRect;
    register int  	x1;

    x1 = r1->x1;
    
    assert(y1<y2);
    assert(r1 != r1End && r2 != r2End);

    pNextRect = REGION_TOP(pReg);

    do
    {
	if (r2->x2 <= x1)
	{
	    /*
	     * Subtrahend entirely to left of minuend: go to next subtrahend.
	     */
	    r2++;
	}
	else if (r2->x1 <= x1)
	{
	    /*
	     * Subtrahend preceeds minuend: nuke left edge of minuend.
	     */
	    x1 = r2->x2;