rt-thread/components/rtgui/common/region.c

/*
 * File      : region.c
 * This file is part of RT-Thread RTOS
 * COPYRIGHT (C) 2006 - 2009, RT-Thread Development Team
 *
 * The license and distribution terms for this file may be
 * found in the file LICENSE in this distribution or at
 * http://www.rt-thread.org/license/LICENSE
 *
 * Change Logs:
 * Date           Author       Notes
 * 2009-10-16     Bernard      first version
 */
#include <rtgui/region.h>
#include <rtgui/rtgui_system.h>

/* #define good(reg) RT_ASSERT(rtgui_region16_valid(reg)) */
#define good(reg)

#define RTGUI_MIN(a,b) ((a) < (b) ? (a) : (b))
#define RTGUI_MAX(a,b) ((a) > (b) ? (a) : (b))

#define RTGUI_SHRT_MIN	(-32767-1)
#define RTGUI_SHRT_MAX	32767

#define PIXREGION_NIL(reg) ((reg)->data && !(reg)->data->numRects)

/* not a region */
#define PIXREGION_NAR(reg)	((reg)->data == &rtgui_brokendata)
#define PIXREGION_NUM_RECTS(reg) ((reg)->data ? (reg)->data->numRects : 1)
#define PIXREGION_SIZE(reg) ((reg)->data ? (reg)->data->size : 0)
#define PIXREGION_RECTS(reg) ((reg)->data ? (rtgui_rect_t *)((reg)->data + 1) \
			               : &(reg)->extents)
#define PIXREGION_BOXPTR(reg) ((rtgui_rect_t *)((reg)->data + 1))
#define PIXREGION_BOX(reg,i) (&PIXREGION_BOXPTR(reg)[i])
#define PIXREGION_TOP(reg) PIXREGION_BOX(reg, (reg)->data->numRects)
#define PIXREGION_END(reg) PIXREGION_BOX(reg, (reg)->data->numRects - 1)
#define PIXREGION_SZOF(n) (sizeof(rtgui_region_data_t) + ((n) * sizeof(rtgui_rect_t)))

rtgui_rect_t rtgui_empty_rect = {0, 0, 0, 0};
rtgui_point_t rtgui_empty_point = {0, 0};

static rtgui_region_data_t rtgui_region_emptydata = {0, 0};
static rtgui_region_data_t  rtgui_brokendata = {0, 0};

static rtgui_region_status_t rtgui_break(rtgui_region_t *pReg);

/*
 * 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 RTGUI_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 rtgui_region_validate in order to support several speed improvements to
 * rtgui_region_validateTree.  Bob Scheifler changed the representation to be more
 * compact when empty or a single rectangle, and did a bunch of gratuitous
 * reformatting. Carl Worth did further gratuitous reformatting while re-merging
 * the server and client region code into libpixregion.
 */

/*  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 allocData(n) rtgui_malloc(PIXREGION_SZOF(n))
#define freeData(reg) if ((reg)->data && (reg)->data->size) rtgui_free((reg)->data)

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

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

#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 (!rtgui_rect_alloc(pReg, 1))					\
	    return RTGUI_REGION_STATUS_FAILURE;						\
	pNextRect = PIXREGION_TOP(pReg);					\
    }									\
    ADDRECT(pNextRect,nx1,ny1,nx2,ny2);					\
    pReg->data->numRects++;						\
    RT_ASSERT(pReg->data->numRects<=pReg->data->size);			\
}

#define DOWNSIZE(reg,numRects)						 \
if (((numRects) < ((reg)->data->size >> 1)) && ((reg)->data->size > 50)) \
{									 \
    rtgui_region_data_t * NewData;							 \
    NewData = (rtgui_region_data_t *)rt_realloc((reg)->data, PIXREGION_SZOF(numRects));	 \
    if (NewData)							 \
    {									 \
	NewData->size = (numRects);					 \
	(reg)->data = NewData;						 \
    }									 \
}

void rtgui_region_init(rtgui_region_t *region)
{
	region->extents = rtgui_empty_rect;
	region->data = &rtgui_region_emptydata;
}

void rtgui_region_init_rect(rtgui_region_t *region,
	int x, int y, unsigned int width, unsigned int height)
{
	region->extents.x1 = x;
	region->extents.y1 = y;
	region->extents.x2 = x + width;
	region->extents.y2 = y + height;
	region->data = RT_NULL;
}

void rtgui_region_init_with_extents(rtgui_region_t *region, rtgui_rect_t *extents)
{
	region->extents = *extents;
	region->data = RT_NULL;
}

void rtgui_region_fini (rtgui_region_t *region)
{
	good (region);
	freeData (region);
}

int rtgui_region_num_rects (rtgui_region_t *region)
{
	return PIXREGION_NUM_RECTS (region);
}

rtgui_rect_t *rtgui_region_rects (rtgui_region_t *region)
{
	return PIXREGION_RECTS (region);
}

static rtgui_region_status_t rtgui_break (rtgui_region_t *region)
{
	freeData (region);
	region->extents = rtgui_empty_rect;
	region->data = &rtgui_brokendata;
	return RTGUI_REGION_STATUS_FAILURE;
}

static rtgui_region_status_t rtgui_rect_alloc(rtgui_region_t * region, int n)
{
	rtgui_region_data_t *data;

	if (!region->data)
	{
		n++;
		region->data = allocData(n);
		if (!region->data) return rtgui_break (region);
		region->data->numRects = 1;
		*PIXREGION_BOXPTR(region) = region->extents;
	}
	else if (!region->data->size)
	{
		region->data = allocData(n);
		if (!region->data) return rtgui_break (region);
		region->data->numRects = 0;
	}
	else
	{
		if (n == 1)
		{
			n = region->data->numRects;
			if (n > 500) /* XXX pick numbers out of a hat */
				n = 250;
		}
		n += region->data->numRects;
		data = (rtgui_region_data_t *)rt_realloc(region->data, PIXREGION_SZOF(n));
		if (!data) return rtgui_break (region);
		region->data = data;
	}
	region->data->size = n;
	return RTGUI_REGION_STATUS_SUCCESS;
}

rtgui_region_status_t rtgui_region_copy(rtgui_region_t *dst, rtgui_region_t *src)
{
	good(dst);
	good(src);
	if (dst == src)
		return RTGUI_REGION_STATUS_SUCCESS;
	dst->extents = src->extents;
	if (!src->data || !src->data->size)
	{
		freeData(dst);
		dst->data = src->data;
		return RTGUI_REGION_STATUS_SUCCESS;
	}
	if (!dst->data || (dst->data->size < src->data->numRects))
	{
		freeData(dst);
		dst->data = allocData(src->data->numRects);
		if (!dst->data) return rtgui_break (dst);
		dst->data->size = src->data->numRects;
	}
	dst->data->numRects = src->data->numRects;
	rt_memmove((char *)PIXREGION_BOXPTR(dst),(char *)PIXREGION_BOXPTR(src),
			dst->data->numRects * sizeof(rtgui_rect_t));
	return RTGUI_REGION_STATUS_SUCCESS;
}

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

/*-
 *-----------------------------------------------------------------------
 * rtgui_coalesce --
 *	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 rtgui_op.
 *
 * 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.
 *	    - region->data->numRects will be decreased.
 *
 *-----------------------------------------------------------------------
 */
rt_inline int
rtgui_coalesce (
	rtgui_region_t *region,	    	/* Region to coalesce		     */
	int	    	  	prevStart,  	/* Index of start of previous band   */
	int	    	  	curStart)   	/* Index of start of current band    */
{
	rtgui_rect_t *	pPrevBox;   	/* Current box in previous band	     */
	rtgui_rect_t *	pCurBox;    	/* Current box in current band       */
	int  	numRects;	/* Number rectangles in both bands   */
	int	y2;		/* Bottom of current band	     */
	/*
	 * Figure out how many rectangles are in the band.
	 */
	numRects = curStart - prevStart;
	RT_ASSERT(numRects == region->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 = PIXREGION_BOX(region, prevStart);
	pCurBox = PIXREGION_BOX(region, 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;
	region->data->numRects -= numRects;
	do
	{
		pPrevBox--;
		pPrevBox->y2 = y2;
		numRects--;
	}
	while (numRects);
	return prevStart;
}

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

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

/*-
 *-----------------------------------------------------------------------
 * rtgui_region_appendNonO --
 *	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:
 *	region->data->numRects is incremented and the rectangles overwritten
 *	with the rectangles we're passed.
 *
 *-----------------------------------------------------------------------
 */

rt_inline rtgui_region_status_t
rtgui_region_appendNonO (
	rtgui_region_t *region,
	rtgui_rect_t *r,
	rtgui_rect_t *rEnd,
	int  	y1,
	int  	y2)
{
	rtgui_rect_t *	pNextRect;
	int	newRects;

	newRects = rEnd - r;

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

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

	return RTGUI_REGION_STATUS_SUCCESS;
}

#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 = rEnd - r;				\
    if (newRects) {							\
	RECTALLOC(newReg, newRects);			\
	rt_memmove((char *)PIXREGION_TOP(newReg),(char *)r,		\
              newRects * sizeof(rtgui_rect_t));				\
	newReg->data->numRects += newRects;		\
    }										\
}

/*-
 *-----------------------------------------------------------------------
 * rtgui_op --
 *	Apply an operation to two regions. Called by rtgui_region_union, rtgui_region_inverse,
 *	rtgui_region_subtract, rtgui_region_intersect....  Both regions MUST have at least one
 *      rectangle, and cannot be the same object.
 *
 * Results:
 *	RTGUI_REGION_STATUS_SUCCESS if successful.
 *
 * Side Effects:
 *	The new region is overwritten.
 *	pOverlap set to RTGUI_REGION_STATUS_SUCCESS if overlapFunc ever returns RTGUI_REGION_STATUS_SUCCESS.
 *
 * 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 rtgui_region_status_t (*OverlapProcPtr)(
	rtgui_region_t	 *region,
	rtgui_rect_t *r1,
	rtgui_rect_t *r1End,
	rtgui_rect_t *r2,
	rtgui_rect_t *r2End,
	short    	 y1,
	short    	 y2,
	int		 *pOverlap);

static rtgui_region_status_t
rtgui_op(
	rtgui_region_t *newReg,		    /* Place to store result	     */
	rtgui_region_t *reg1,		    /* First region in operation     */
	rtgui_region_t *reg2,		    /* 2d region in operation        */
	OverlapProcPtr  overlapFunc,	/* Function to call for over-
									 * lapping bands		     */
	int	    appendNon1,				/* Append non-overlapping bands  */
	/* in region 1 ? */
	int	    appendNon2,				/* Append non-overlapping bands  */
	/* in region 2 ? */
	int	    *pOverlap)
{
	rtgui_rect_t * r1;			    /* Pointer into first region     */
	rtgui_rect_t * r2;			    /* Pointer into 2d region	     */
	rtgui_rect_t *	    r1End;		    /* End of 1st region	     */
	rtgui_rect_t *	    r2End;		    /* End of 2d region		     */
	short	    ybot;		    /* Bottom of intersection	     */
	short	    ytop;		    /* Top of intersection	     */
	rtgui_region_data_t *	    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		     */
	rtgui_rect_t * r1BandEnd;		    /* End of current band in r1     */
	rtgui_rect_t * r2BandEnd;		    /* End of current band in r2     */
	short	    top;		    /* Top of non-overlapping band   */
	short	    bot;		    /* Bottom of non-overlapping band*/
	int    r1y1;		    /* Temps for r1->y1 and r2->y1   */
	int    r2y1;
	int		    newSize;
	int		    numRects;

	/*
	 * Break any region computed from a broken region
	 */
	if (PIXREGION_NAR (reg1) || PIXREGION_NAR(reg2))
		return rtgui_break (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 = PIXREGION_RECTS(reg1);
	newSize = PIXREGION_NUM_RECTS(reg1);
	r1End = r1 + newSize;
	numRects = PIXREGION_NUM_RECTS(reg2);
	r2 = PIXREGION_RECTS(reg2);
	r2End = r2 + numRects;
	RT_ASSERT(r1 != r1End);
	RT_ASSERT(r2 != r2End);

	oldData = (rtgui_region_data_t *)RT_NULL;
	if (((newReg == reg1) && (newSize > 1)) ||
			((newReg == reg2) && (numRects > 1)))
	{
		oldData = newReg->data;
		newReg->data = &rtgui_region_emptydata;
	}
	/* guess at new size */
	if (numRects > newSize)
		newSize = numRects;
	newSize <<= 1;
	if (!newReg->data)
		newReg->data = &rtgui_region_emptydata;
	else if (newReg->data->size)
		newReg->data->numRects = 0;
	if (newSize > newReg->data->size)
		if (!rtgui_rect_alloc(newReg, newSize))
			return RTGUI_REGION_STATUS_FAILURE;

	/*
	 * Initialize ybot.
	 * In the upcoRTGUI_MINg 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 = RTGUI_MIN(r1->y1, r2->y1);

	/*
	 * prevBand serves to mark the start of the previous band so rectangles
	 * can be coalesced into larger rectangles. qv. rtgui_coalesce, 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 deterRTGUI_MINed 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.
		 */
		RT_ASSERT(r1 != r1End);
		RT_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 = RTGUI_MAX(r1y1, ybot);
				bot = RTGUI_MIN(r1->y2, r2y1);
				if (top != bot)
				{
					curBand = newReg->data->numRects;
					rtgui_region_appendNonO(newReg, r1, r1BandEnd, top, bot);
					Coalesce(newReg, prevBand, curBand);
				}
			}
			ytop = r2y1;
		}
		else if (r2y1 < r1y1)
		{
			if (appendNon2)
			{
				top = RTGUI_MAX(r2y1, ybot);
				bot = RTGUI_MIN(r2->y2, r1y1);
				if (top != bot)
				{
					curBand = newReg->data->numRects;
					rtgui_region_appendNonO(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 = RTGUI_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;
		rtgui_region_appendNonO(newReg, r1, r1BandEnd, RTGUI_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;
		rtgui_region_appendNonO(newReg, r2, r2BandEnd, RTGUI_MAX(r2y1, ybot), r2->y2);
		Coalesce(newReg, prevBand, curBand);
		/* Append rest of boxes */
		AppendRegions(newReg, r2BandEnd, r2End);
	}

	if (oldData)
		rtgui_free(oldData);

	numRects = newReg->data->numRects;
	if (!numRects)
	{
		freeData(newReg);
		newReg->data = &rtgui_region_emptydata;
	}
	else if (numRects == 1)
	{
		newReg->extents = *PIXREGION_BOXPTR(newReg);
		freeData(newReg);
		newReg->data = (rtgui_region_data_t *)RT_NULL;
	}
	else
	{
		DOWNSIZE(newReg, numRects);
	}

	return RTGUI_REGION_STATUS_SUCCESS;
}

/*-
 *-----------------------------------------------------------------------
 * rtgui_set_extents --
 *	Reset the extents of a region to what they should be. Called by
 *	rtgui_region_subtract and rtgui_region_intersect as they can't figure it out along the
 *	way or do so easily, as rtgui_region_union can.
 *
 * Results:
 *	None.
 *
 * Side Effects:
 *	The region's 'extents' structure is overwritten.
 *
 *-----------------------------------------------------------------------
 */
static void
rtgui_set_extents (rtgui_region_t *region)
{
	rtgui_rect_t *box, *boxEnd;

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

	box = PIXREGION_BOXPTR(region);
	boxEnd = PIXREGION_END(region);

	/*
	 * Since box is the first rectangle in the region, it must have the
	 * smallest y1 and since boxEnd is the last rectangle in the region,
	 * it must have the largest y2, because of banding. Initialize x1 and
	 * x2 from  box and boxEnd, resp., as good things to initialize them
	 * to...
	 */
	region->extents.x1 = box->x1;
	region->extents.y1 = box->y1;
	region->extents.x2 = boxEnd->x2;
	region->extents.y2 = boxEnd->y2;

	RT_ASSERT(region->extents.y1 < region->extents.y2);
	while (box <= boxEnd)
	{
		if (box->x1 < region->extents.x1)
			region->extents.x1 = box->x1;
		if (box->x2 > region->extents.x2)
			region->extents.x2 = box->x2;
		box++;
	};

	RT_ASSERT(region->extents.x1 < region->extents.x2);
}

/*======================================================================
 *	    Region Intersection
 *====================================================================*/
/*-
 *-----------------------------------------------------------------------
 * rtgui_region_intersectO --
 *	Handle an overlapping band for rtgui_region_intersect.
 *
 * Results:
 *	RTGUI_REGION_STATUS_SUCCESS if successful.
 *
 * Side Effects:
 *	Rectangles may be added to the region.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/
static rtgui_region_status_t
rtgui_region_intersectO (
	rtgui_region_t *region,
	rtgui_rect_t *r1,
	rtgui_rect_t *r1End,
	rtgui_rect_t *r2,
	rtgui_rect_t *r2End,
	short		y1,
	short		y2,
	int			*pOverlap)
{
	int  	x1;
	int  	x2;
	rtgui_rect_t *	pNextRect;

	pNextRect = PIXREGION_TOP(region);

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

	do
	{
		x1 = RTGUI_MAX(r1->x1, r2->x1);
		x2 = RTGUI_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(region, 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 RTGUI_REGION_STATUS_SUCCESS;
}

rtgui_region_status_t
rtgui_region_intersect(rtgui_region_t *newReg,
						rtgui_region_t *reg1,
						rtgui_region_t *reg2)
{
	good(reg1);
	good(reg2);
	good(newReg);
	/* check for trivial reject */
	if (PIXREGION_NIL(reg1)  || PIXREGION_NIL(reg2) ||
			!EXTENTCHECK(&reg1->extents, &reg2->extents))
	{
		/* Covers about 20% of all cases */
		freeData(newReg);
		newReg->extents.x2 = newReg->extents.x1;
		newReg->extents.y2 = newReg->extents.y1;
		if (PIXREGION_NAR(reg1) || PIXREGION_NAR(reg2))
		{
			newReg->data = &rtgui_brokendata;
			return RTGUI_REGION_STATUS_FAILURE;
		}
		else
			newReg->data = &rtgui_region_emptydata;
	}
	else if (!reg1->data && !reg2->data)
	{
		/* Covers about 80% of cases that aren't trivially rejected */
		newReg->extents.x1 = RTGUI_MAX(reg1->extents.x1, reg2->extents.x1);
		newReg->extents.y1 = RTGUI_MAX(reg1->extents.y1, reg2->extents.y1);
		newReg->extents.x2 = RTGUI_MIN(reg1->extents.x2, reg2->extents.x2);
		newReg->extents.y2 = RTGUI_MIN(reg1->extents.y2, reg2->extents.y2);
		freeData(newReg);
		newReg->data = (rtgui_region_data_t *)RT_NULL;
	}
	else if (!reg2->data && SUBSUMES(&reg2->extents, &reg1->extents))
	{
		return rtgui_region_copy(newReg, reg1);
	}
	else if (!reg1->data && SUBSUMES(&reg1->extents, &reg2->extents))
	{
		return rtgui_region_copy(newReg, reg2);
	}
	else if (reg1 == reg2)
	{
		return rtgui_region_copy(newReg, reg1);
	}
	else
	{
		/* General purpose intersection */
		int overlap; /* result ignored */
		if (!rtgui_op(newReg, reg1, reg2, rtgui_region_intersectO, RTGUI_REGION_STATUS_FAILURE, RTGUI_REGION_STATUS_FAILURE,
					   &overlap))
			return RTGUI_REGION_STATUS_FAILURE;
		rtgui_set_extents(newReg);
	}

	good(newReg);
	return(RTGUI_REGION_STATUS_SUCCESS);
}

rtgui_region_status_t
rtgui_region_intersect_rect(rtgui_region_t *newReg,
						rtgui_region_t *reg1,
						rtgui_rect_t *rect)
{
	rtgui_region_t region;

	region.data = RT_NULL;
	region.extents.x1 = rect->x1;
	region.extents.y1 = rect->y1;
	region.extents.x2 = rect->x2;
	region.extents.y2 = rect->y2;

	return rtgui_region_intersect(newReg, reg1, &region);
}

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

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

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

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

	pNextRect = PIXREGION_TOP(region);

	/* 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(region, pNextRect, x1, y1, x2, y2);

	return RTGUI_REGION_STATUS_SUCCESS;
}

/* Convenience function for perforRTGUI_MINg union of region with a single rectangle */
rtgui_region_status_t
rtgui_region_union_rect(rtgui_region_t *dest, rtgui_region_t *source, rtgui_rect_t* rect)
{
	rtgui_region_t region;

	region.data = RT_NULL;
	region.extents.x1 = rect->x1;
	region.extents.y1 = rect->y1;
	region.extents.x2 = rect->x2;
	region.extents.y2 = rect->y2;

	return rtgui_region_union (dest, source, &region);
}

rtgui_region_status_t
rtgui_region_union(rtgui_region_t *newReg, rtgui_region_t *reg1, rtgui_region_t *reg2)
{
	int overlap; /* result ignored */

	/* Return RTGUI_REGION_STATUS_SUCCESS 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 rtgui_region_copy(newReg, reg1);
	}

	/*
	 * Region 1 is empty
	 */
	if (PIXREGION_NIL(reg1))
	{
		if (PIXREGION_NAR(reg1)) return rtgui_break (newReg);
		if (newReg != reg2)
			return rtgui_region_copy(newReg, reg2);
		return RTGUI_REGION_STATUS_SUCCESS;
	}

	/*
	 * Region 2 is empty
	 */
	if (PIXREGION_NIL(reg2))
	{
		if (PIXREGION_NAR(reg2)) return rtgui_break (newReg);
		if (newReg != reg1)
			return rtgui_region_copy(newReg, reg1);
		return RTGUI_REGION_STATUS_SUCCESS;
	}

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

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

	if (!rtgui_op(newReg, reg1, reg2, rtgui_region_unionO, RTGUI_REGION_STATUS_SUCCESS, RTGUI_REGION_STATUS_SUCCESS, &overlap))
		return RTGUI_REGION_STATUS_FAILURE;

	newReg->extents.x1 = RTGUI_MIN(reg1->extents.x1, reg2->extents.x1);
	newReg->extents.y1 = RTGUI_MIN(reg1->extents.y1, reg2->extents.y1);
	newReg->extents.x2 = RTGUI_MAX(reg1->extents.x2, reg2->extents.x2);
	newReg->extents.y2 = RTGUI_MAX(reg1->extents.y2, reg2->extents.y2);
	good(newReg);
	return RTGUI_REGION_STATUS_SUCCESS;
}

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

/*-
 *-----------------------------------------------------------------------
 * rtgui_region_append --
 *
 *      "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 rtgui_region_validate to ensure that a valid region is constructed.
 *
 * Results:
 *	RTGUI_REGION_STATUS_SUCCESS if successful.
 *
 * Side Effects:
 *      dstrgn is modified if rgn has rectangles.
 *
 */
rtgui_region_status_t
rtgui_region_append(rtgui_region_t *dstrgn,
					 rtgui_region_t *rgn)
{
	int numRects, dnumRects, size;
	rtgui_rect_t *new, *old;
	int prepend;

	if (PIXREGION_NAR(rgn)) return rtgui_break (dstrgn);

	if (!rgn->data && (dstrgn->data == &rtgui_region_emptydata))
	{
		dstrgn->extents = rgn->extents;
		dstrgn->data = (rtgui_region_data_t *)RT_NULL;
		return RTGUI_REGION_STATUS_SUCCESS;
	}

	numRects = PIXREGION_NUM_RECTS(rgn);
	if (!numRects)
		return RTGUI_REGION_STATUS_SUCCESS;
	prepend = RTGUI_REGION_STATUS_FAILURE;
	size = numRects;
	dnumRects = PIXREGION_NUM_RECTS(dstrgn);
	if (!dnumRects && (size < 200))
		size = 200; /* XXX pick numbers out of a hat */
	RECTALLOC(dstrgn, size);
	old = PIXREGION_RECTS(rgn);
	if (!dnumRects)
		dstrgn->extents = rgn->extents;
	else if (dstrgn->extents.x2 > dstrgn->extents.x1)
	{
		rtgui_rect_t *first, *last;

		first = old;
		last = PIXREGION_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 = PIXREGION_BOXPTR(dstrgn);
			last = old + (numRects - 1);
			if ((first->y1 > last->y2) ||
					((first->y1 == last->y1) && (first->y2 == last->y2) &&
					 (first->x1 > last->x2)))
			{
				prepend = RTGUI_REGION_STATUS_SUCCESS;
				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 = PIXREGION_BOX(dstrgn, numRects);
		if (dnumRects == 1)
			*new = *PIXREGION_BOXPTR(dstrgn);
		else
			rt_memmove((char *)new,(char *)PIXREGION_BOXPTR(dstrgn),
					dnumRects * sizeof(rtgui_rect_t));
		new = PIXREGION_BOXPTR(dstrgn);
	}
	else
		new = PIXREGION_BOXPTR(dstrgn) + dnumRects;
	if (numRects == 1)
		*new = *old;
	else
		rt_memmove((char *)new, (char *)old, numRects * sizeof(rtgui_rect_t));
	dstrgn->data->numRects += numRects;
	return RTGUI_REGION_STATUS_SUCCESS;
}

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

static void QuickSortRects(rtgui_rect_t rects[], int numRects)
{
	int	y1;
	int	x1;
	int        i, j;
	rtgui_rect_t *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);
}

/*-
 *-----------------------------------------------------------------------
 * rtgui_region_validate --
 *
 *      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:
 *	RTGUI_REGION_STATUS_SUCCESS if successful.
 *
 * Side Effects:
 *      The passed-in ``region'' may be modified.
 *	pOverlap set to RTGUI_REGION_STATUS_SUCCESS if any retangles overlapped, else RTGUI_REGION_STATUS_FAILURE;
 *
 * Strategy:
 *      Step 1. Sort the rectangles into ascending order with primary key y1
 *		and secondary key x1.
 *
 *      Step 2. Split the rectangles into the RTGUI_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 transformation (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
 *		rtgui_region_union.  Maximize the work each rtgui_region_union call does by using
 *		a binary merge.
 *
 *-----------------------------------------------------------------------
 */
rtgui_region_status_t rtgui_region_validate(rtgui_region_t * badreg,
	int *pOverlap)
{
	/* Descriptor for regions under construction  in Step 2. */
	typedef struct
	{
		rtgui_region_t   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			    */
	int	j;	    /* Index into ri			    */
	RegionInfo *rit;       /* &ri[j]				    */
	rtgui_region_t *  reg;        /* ri[j].reg			    */
	rtgui_rect_t *	box;	    /* Current box in rects		    */
	rtgui_rect_t *	riBox;      /* Last box in ri[j].reg		    */
	rtgui_region_t *  hreg;       /* ri[j_half].reg			    */
	rtgui_region_status_t ret = RTGUI_REGION_STATUS_SUCCESS;

	*pOverlap = RTGUI_REGION_STATUS_FAILURE;
	if (!badreg->data)
	{
		good(badreg);
		return RTGUI_REGION_STATUS_SUCCESS;
	}
	numRects = badreg->data->numRects;
	if (!numRects)
	{
		if (PIXREGION_NAR(badreg))
			return RTGUI_REGION_STATUS_FAILURE;
		good(badreg);
		return RTGUI_REGION_STATUS_SUCCESS;
	}
	if (badreg->extents.x1 < badreg->extents.x2)
	{
		if ((numRects) == 1)
		{
			freeData(badreg);
			badreg->data = (rtgui_region_data_t *) RT_NULL;
		}
		else
		{
			DOWNSIZE(badreg, numRects);
		}
		good(badreg);
		return RTGUI_REGION_STATUS_SUCCESS;
	}

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

	/* Step 2: Scatter the sorted array into the RTGUI_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 *) rtgui_malloc(4 * sizeof(RegionInfo));
	if (!ri) return rtgui_break (badreg);
	sizeRI = 4;
	numRI = 1;
	ri[0].prevBand = 0;
	ri[0].curBand = 0;
	ri[0].reg = *badreg;
	box = PIXREGION_BOXPTR(&ri[0].reg);
	ri[0].reg.extents = *box;
	ri[0].reg.data->numRects = 1;

	/* Now scatter rectangles into the RTGUI_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 = PIXREGION_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 = RTGUI_REGION_STATUS_SUCCESS;
					if (box->x2 > riBox->x2) riBox->x2 = box->x2;
				}
				else
				{
					RECTALLOC_BAIL(reg, 1, bail);
					*PIXREGION_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);
				*PIXREGION_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 *) rt_realloc(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 = (rtgui_region_data_t *)RT_NULL;
		if (!rtgui_rect_alloc(&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 = PIXREGION_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 */
		{
			freeData(reg);
			reg->data = (rtgui_region_data_t *)RT_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 (!rtgui_op(reg, reg, hreg, rtgui_region_unionO, RTGUI_REGION_STATUS_SUCCESS, RTGUI_REGION_STATUS_SUCCESS, pOverlap))
				ret = RTGUI_REGION_STATUS_FAILURE;
			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;
			freeData(hreg);
		}
		numRI -= half;
	}
	*badreg = ri[0].reg;
	rtgui_free(ri);
	good(badreg);
	return ret;

bail:
	for (i = 0; i < numRI; i++)
		freeData(&ri[i].reg);
	rtgui_free (ri);

	return rtgui_break (badreg);
}

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

/*-
 *-----------------------------------------------------------------------
 * rtgui_region_subtractO --
 *	Overlapping band subtraction. x1 is the left-most point not yet
 *	checked.
 *
 * Results:
 *	RTGUI_REGION_STATUS_SUCCESS if successful.
 *
 * Side Effects:
 *	region may have rectangles added to it.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/
static rtgui_region_status_t
rtgui_region_subtractO (
	rtgui_region_t *region,
	rtgui_rect_t *r1,
	rtgui_rect_t *r1End,
	rtgui_rect_t *r2,
	rtgui_rect_t *r2End,
	short  	y1,
	short  	y2,
	int		*pOverlap)
{
	rtgui_rect_t *	pNextRect;
	int  	x1;

	x1 = r1->x1;

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

	pNextRect = PIXREGION_TOP(region);

	do
	{
		if (r2->x2 <= x1)
		{
			/*
			 * Subtrahend entirely to left of minuend: go to next subtrahend.
			 */
			r2++;
		}
		else if (r2->x1 <= x1)
		{
			/*
			 * Subtrahend preceeds RTGUI_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 RTGUI_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.
			 */
			RT_ASSERT(x1<r2->x1);
			NEWRECT(region, pNextRect, x1, y1, r2->x1, y2);

			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)
				NEWRECT(region, pNextRect, x1, y1, r1->x2, y2);
			r1++;
			if (r1 != r1End)
				x1 = r1->x1;
		}
	}
	while ((r1 != r1End) && (r2 != r2End));

	/*
	 * Add remaining minuend rectangles to region.
	 */
	while (r1 != r1End)
	{
		RT_ASSERT(x1<r1->x2);
		NEWRECT(region, pNextRect, x1, y1, r1->x2, y2);
		r1++;
		if (r1 != r1End)
			x1 = r1->x1;
	}
	return RTGUI_REGION_STATUS_SUCCESS;
}

/*-
 *-----------------------------------------------------------------------
 * rtgui_region_subtract --
 *	Subtract regS from regM and leave the result in regD.
 *	S stands for subtrahend, M for minuend and D for difference.
 *
 * Results:
 *	RTGUI_REGION_STATUS_SUCCESS if successful.
 *
 * Side Effects:
 *	regD is overwritten.
 *
 *-----------------------------------------------------------------------
 */
rtgui_region_status_t
rtgui_region_subtract(rtgui_region_t *regD,
					   rtgui_region_t *regM,
					   rtgui_region_t *regS)
{
	int overlap; /* result ignored */

	good(regM);
	good(regS);
	good(regD);
	/* check for trivial rejects */
	if (PIXREGION_NIL(regM) || PIXREGION_NIL(regS) ||
			!EXTENTCHECK(&regM->extents, &regS->extents))
	{
		if (PIXREGION_NAR (regS)) return rtgui_break (regD);
		return rtgui_region_copy(regD, regM);
	}
	else if (regM == regS)
	{
		freeData(regD);
		regD->extents.x2 = regD->extents.x1;
		regD->extents.y2 = regD->extents.y1;
		regD->data = &rtgui_region_emptydata;
		return RTGUI_REGION_STATUS_SUCCESS;
	}

	/* Add those rectangles in region 1 that aren't in region 2,
	   do yucky substraction for overlaps, and
	   just throw away rectangles in region 2 that aren't in region 1 */
	if (!rtgui_op(regD, regM, regS, rtgui_region_subtractO, RTGUI_REGION_STATUS_SUCCESS, RTGUI_REGION_STATUS_FAILURE, &overlap))
		return RTGUI_REGION_STATUS_FAILURE;

	/*
	 * Can't alter RegD's extents before we call rtgui_op because
	 * it might be one of the source regions and rtgui_op depends
	 * on the extents of those regions being unaltered. Besides, this
	 * way there's no checking against rectangles that will be nuked
	 * due to coalescing, so we have to exaRTGUI_MINe fewer rectangles.
	 */
	rtgui_set_extents(regD);
	good(regD);
	return RTGUI_REGION_STATUS_SUCCESS;
}

rtgui_region_status_t
rtgui_region_subtract_rect (rtgui_region_t *regD, rtgui_region_t *regM, rtgui_rect_t* rect)
{
	rtgui_region_t region;

	region.data = RT_NULL;
	region.extents.x1 = rect->x1;
	region.extents.y1 = rect->y1;
	region.extents.x2 = rect->x2;
	region.extents.y2 = rect->y2;

	return rtgui_region_subtract(regD, regM, &region);
}

/*======================================================================
 *	    Region Inversion
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * rtgui_region_inverse --
 *	Take a region and a box and return a region that is everything
 *	in the box but not in the region. The careful reader will note
 *	that this is the same as subtracting the region from the box...
 *
 * Results:
 *	RTGUI_REGION_STATUS_SUCCESS.
 *
 * Side Effects:
 *	newReg is overwritten.
 *
 *-----------------------------------------------------------------------
 */
rtgui_region_status_t
rtgui_region_inverse(rtgui_region_t *newReg,       /* Destination region */
					  rtgui_region_t *reg1,         /* Region to invert */
					  rtgui_rect_t *invRect) 		/* Bounding box for inversion */
{
	rtgui_region_t	  invReg;   	/* Quick and dirty region made from the
					 * bounding box */
	int	  overlap;	/* result ignored */

	good(reg1);
	good(newReg);
	/* check for trivial rejects */
	if (PIXREGION_NIL(reg1) || !EXTENTCHECK(invRect, &reg1->extents))
	{
		if (PIXREGION_NAR(reg1)) return rtgui_break (newReg);
		newReg->extents = *invRect;
		freeData(newReg);
		newReg->data = (rtgui_region_data_t *)RT_NULL;
		return RTGUI_REGION_STATUS_SUCCESS;
	}

	/* Add those rectangles in region 1 that aren't in region 2,
	   do yucky substraction for overlaps, and
	   just throw away rectangles in region 2 that aren't in region 1 */
	invReg.extents = *invRect;
	invReg.data = (rtgui_region_data_t *)RT_NULL;
	if (!rtgui_op(newReg, &invReg, reg1, rtgui_region_subtractO, RTGUI_REGION_STATUS_SUCCESS, RTGUI_REGION_STATUS_FAILURE, &overlap))
		return RTGUI_REGION_STATUS_FAILURE;

	/*
	 * Can't alter newReg's extents before we call rtgui_op because
	 * it might be one of the source regions and rtgui_op depends
	 * on the extents of those regions being unaltered. Besides, this
	 * way there's no checking against rectangles that will be nuked
	 * due to coalescing, so we have to exaRTGUI_MINe fewer rectangles.
	 */
	rtgui_set_extents(newReg);
	good(newReg);
	return RTGUI_REGION_STATUS_SUCCESS;
}

/*
 *   RectIn(region, rect)
 *   This routine takes a pointer to a region and a pointer to a box
 *   and deterRTGUI_MINes if the box is outside/inside/partly inside the region.
 *
 *   The idea is to travel through the list of rectangles trying to cover the
 *   passed box with them. Anytime a piece of the rectangle isn't covered
 *   by a band of rectangles, partOut is set RTGUI_REGION_STATUS_SUCCESS. Any time a rectangle in
 *   the region covers part of the box, partIn is set RTGUI_REGION_STATUS_SUCCESS. The process ends
 *   when either the box has been completely covered (we reached a band that
 *   doesn't overlap the box, partIn is RTGUI_REGION_STATUS_SUCCESS and partOut is false), the
 *   box has been partially covered (partIn == partOut == RTGUI_REGION_STATUS_SUCCESS -- because of
 *   the banding, the first time this is true we know the box is only
 *   partially in the region) or is outside the region (we reached a band
 *   that doesn't overlap the box at all and partIn is false)
 */

int rtgui_region_contains_rectangle(rtgui_region_t *region, rtgui_rect_t *prect)
{
	int	x;
	int	y;
	rtgui_rect_t *     pbox;
	rtgui_rect_t *     pboxEnd;
	int			partIn, partOut;
	int			numRects;

	good(region);
	numRects = PIXREGION_NUM_RECTS(region);
	/* useful optimization */
	if (!numRects || !EXTENTCHECK(&region->extents, prect))
		return(RTGUI_REGION_OUT);

	if (numRects == 1)
	{
		/* We know that it must be rgnIN or rgnPART */
		if (SUBSUMES(&region->extents, prect))
			return(RTGUI_REGION_IN);
		else
			return(RTGUI_REGION_PART);
	}

	partOut = RTGUI_REGION_STATUS_FAILURE;
	partIn = RTGUI_REGION_STATUS_FAILURE;

	/* (x,y) starts at upper left of rect, moving to the right and down */
	x = prect->x1;
	y = prect->y1;

	/* can stop when both partOut and partIn are RTGUI_REGION_STATUS_SUCCESS, or we reach prect->y2 */
	for (pbox = PIXREGION_BOXPTR(region), pboxEnd = pbox + numRects;
			pbox != pboxEnd;
			pbox++)
	{

		if (pbox->y2 <= y)
			continue;    /* getting up to speed or skipping remainder of band */

		if (pbox->y1 > y)
		{
			partOut = RTGUI_REGION_STATUS_SUCCESS;      /* missed part of rectangle above */
			if (partIn || (pbox->y1 >= prect->y2))
				break;
			y = pbox->y1;        /* x guaranteed to be == prect->x1 */
		}

		if (pbox->x2 <= x)
			continue;            /* not far enough over yet */

		if (pbox->x1 > x)
		{
			partOut = RTGUI_REGION_STATUS_SUCCESS;      /* missed part of rectangle to left */
			if (partIn)
				break;
		}

		if (pbox->x1 < prect->x2)
		{
			partIn = RTGUI_REGION_STATUS_SUCCESS;      /* definitely overlap */
			if (partOut)
				break;
		}

		if (pbox->x2 >= prect->x2)
		{
			y = pbox->y2;        /* finished with this band */
			if (y >= prect->y2)
				break;
			x = prect->x1;       /* reset x out to left again */
		}
		else
		{
			/*
			 * Because boxes in a band are maximal width, if the first box
			 * to overlap the rectangle doesn't completely cover it in that
			 * band, the rectangle must be partially out, since some of it
			 * will be uncovered in that band. partIn will have been set true
			 * by now...
			 */
			partOut = RTGUI_REGION_STATUS_SUCCESS;
			break;
		}
	}

	return(partIn ? ((y < prect->y2) ? RTGUI_REGION_PART : RTGUI_REGION_IN) : RTGUI_REGION_OUT);
}

/* rtgui_region_translate (region, x, y)
   translates in place
*/
void rtgui_region_translate (rtgui_region_t *region, int x, int y)
{
	int x1, x2, y1, y2;
	int nbox;
	rtgui_rect_t * pbox;

	good(region);
	region->extents.x1 = x1 = region->extents.x1 + x;
	region->extents.y1 = y1 = region->extents.y1 + y;
	region->extents.x2 = x2 = region->extents.x2 + x;
	region->extents.y2 = y2 = region->extents.y2 + y;
	if (((x1 - RTGUI_SHRT_MIN)|(y1 - RTGUI_SHRT_MIN)|(RTGUI_SHRT_MAX - x2)|(RTGUI_SHRT_MAX - y2)) >= 0)
	{
		nbox = region->data->numRects;
		if (region->data && nbox)
		{
			for (pbox = PIXREGION_BOXPTR(region); nbox--; pbox++)
			{
				pbox->x1 += x;
				pbox->y1 += y;
				pbox->x2 += x;
				pbox->y2 += y;
			}
		}
		return;
	}
	if (((x2 - RTGUI_SHRT_MIN)|(y2 - RTGUI_SHRT_MIN)|(RTGUI_SHRT_MAX - x1)|(RTGUI_SHRT_MAX - y1)) <= 0)
	{
		region->extents.x2 = region->extents.x1;
		region->extents.y2 = region->extents.y1;
		freeData(region);
		region->data = &rtgui_region_emptydata;
		return;
	}
	if (x1 < RTGUI_SHRT_MIN)
		region->extents.x1 = RTGUI_SHRT_MIN;
	else if (x2 > RTGUI_SHRT_MAX)
		region->extents.x2 = RTGUI_SHRT_MAX;
	if (y1 < RTGUI_SHRT_MIN)
		region->extents.y1 = RTGUI_SHRT_MIN;
	else if (y2 > RTGUI_SHRT_MAX)
		region->extents.y2 = RTGUI_SHRT_MAX;

	nbox = region->data->numRects;
	if (region->data && nbox)
	{
		rtgui_rect_t * pboxout;

		for (pboxout = pbox = PIXREGION_BOXPTR(region); nbox--; pbox++)
		{
			pboxout->x1 = x1 = pbox->x1 + x;
			pboxout->y1 = y1 = pbox->y1 + y;
			pboxout->x2 = x2 = pbox->x2 + x;
			pboxout->y2 = y2 = pbox->y2 + y;
			if (((x2 - RTGUI_SHRT_MIN)|(y2 - RTGUI_SHRT_MIN)|
					(RTGUI_SHRT_MAX - x1)|(RTGUI_SHRT_MAX - y1)) <= 0)
			{
				region->data->numRects--;
				continue;
			}
			if (x1 < RTGUI_SHRT_MIN)
				pboxout->x1 = RTGUI_SHRT_MIN;
			else if (x2 > RTGUI_SHRT_MAX)
				pboxout->x2 = RTGUI_SHRT_MAX;
			if (y1 < RTGUI_SHRT_MIN)
				pboxout->y1 = RTGUI_SHRT_MIN;
			else if (y2 > RTGUI_SHRT_MAX)
				pboxout->y2 = RTGUI_SHRT_MAX;
			pboxout++;
		}
		if (pboxout != pbox)
		{
			if (region->data->numRects == 1)
			{
				region->extents = *PIXREGION_BOXPTR(region);
				freeData(region);
				region->data = (rtgui_region_data_t *)RT_NULL;
			}
			else
				rtgui_set_extents(region);
		}
	}
}

void rtgui_region_reset(rtgui_region_t *region, rtgui_rect_t* rect)
{
	good(region);
	freeData(region);

	rtgui_region_init_with_extents(region, rect);
}

/* box is "return" value */
int rtgui_region_contains_point(rtgui_region_t * region,
							 int x, int y,
							 rtgui_rect_t * box)
{
	rtgui_rect_t *pbox, *pboxEnd;
	int numRects;

	good(region);
	numRects = PIXREGION_NUM_RECTS(region);
	if (!numRects || !INBOX(&region->extents, x, y))
		return -RT_ERROR;

	if (numRects == 1)
	{
		*box = region->extents;
		return RT_EOK;
	}

	for (pbox = PIXREGION_BOXPTR(region), pboxEnd = pbox + numRects;
			pbox != pboxEnd;
			pbox++)
	{
		if (y >= pbox->y2)
			continue;		/* not there yet */
		if ((y < pbox->y1) || (x < pbox->x1))
			break;		/* missed it */
		if (x >= pbox->x2)
			continue;		/* not there yet */
		*box = *pbox;
		return RT_EOK;
	}

	return -RT_ERROR;
}

int rtgui_region_not_empty(rtgui_region_t * region)
{
	good(region);

	return(!PIXREGION_NIL(region));
}

void rtgui_region_empty(rtgui_region_t * region)
{
	good(region);
	freeData(region);

	region->extents = rtgui_empty_rect;
	region->data = &rtgui_region_emptydata;
}

rtgui_rect_t *rtgui_region_extents(rtgui_region_t * region)
{
	good(region);
	return(&region->extents);
}

#define ExchangeSpans(a, b)		\
{								\
    rtgui_point_t tpt;			\
    int    tw;					\
							    \
    tpt = spans[a]; spans[a] = spans[b]; spans[b] = tpt;    \
    tw = widths[a]; widths[a] = widths[b]; widths[b] = tw;  \
}

/* ||| I should apply the merge sort code to rectangle sorting above, and see
   if mapping time can be improved.  But right now I've been at work 12 hours,
   so forget it.
*/

static void QuickSortSpans(
	rtgui_point_t spans[],
	int	    widths[],
	int	    numSpans)
{
	int	    y;
	int	    i, j, m;
	rtgui_point_t *r;

	/* Always called with numSpans > 1 */
	/* Sorts only by y, doesn't bother to sort by x */

	do
	{
		if (numSpans < 9)
		{
			/* Do insertion sort */
			int yprev;

			yprev = spans[0].y;
			i = 1;
			do
			{ /* while i != numSpans */
				y = spans[i].y;
				if (yprev > y)
				{
					/* spans[i] is out of order.  Move into proper location. */
					rtgui_point_t tpt;
					int	    tw, k;

					for (j = 0; y >= spans[j].y; j++)
					{}
					tpt = spans[i];
					tw  = widths[i];
					for (k = i; k != j; k--)
					{
						spans[k] = spans[k-1];
						widths[k] = widths[k-1];
					}
					spans[j] = tpt;
					widths[j] = tw;
					y = spans[i].y;
				} /* if out of order */
				yprev = y;
				i++;
			}
			while (i != numSpans);
			return;
		}

		/* Choose partition element, stick in location 0 */
		m = numSpans / 2;
		if (spans[m].y > spans[0].y)		ExchangeSpans(m, 0);
		if (spans[m].y > spans[numSpans-1].y)   ExchangeSpans(m, numSpans-1);
		if (spans[m].y > spans[0].y)		ExchangeSpans(m, 0);
		y = spans[0].y;

		/* Partition array */
		i = 0;
		j = numSpans;
		do
		{
			r = &(spans[i]);
			do
			{
				r++;
				i++;
			}
			while (i != numSpans && r->y < y);
			r = &(spans[j]);
			do
			{
				r--;
				j--;
			}
			while (y < r->y);
			if (i < j)
				ExchangeSpans(i, j);
		}
		while (i < j);

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

		/* Recurse */
		if (numSpans-j-1 > 1)
			QuickSortSpans(&spans[j+1], &widths[j+1], numSpans-j-1);
		numSpans = j;
	}
	while (numSpans > 1);
}

void rtgui_region_dump(rtgui_region_t* region)
{
	int num;
	int i;
	rtgui_rect_t * rects;

	num = PIXREGION_NUM_RECTS(region);
	rects = PIXREGION_RECTS(region);
	rt_kprintf("extents: (%d,%d) (%d,%d)\n",
		region->extents.x1, region->extents.y1,
		region->extents.x2, region->extents.y2);

	for (i = 0; i < num; i++)
	{
		rt_kprintf("box[%d]: (%d,%d) (%d,%d)\n", i,
			rects[i].x1, rects[i].y1,
			rects[i].x2, rects[i].y2);
	}
}

void rtgui_rect_moveto(rtgui_rect_t *rect, int x, int y)
{
	rect->x1 += x;
	rect->x2 += x;

	rect->y1 += y;
	rect->y2 += y;
}

void rtgui_rect_moveto_align(rtgui_rect_t *rect, rtgui_rect_t *to, int align)
{
	int dw, dh;
	dw = 0;
	dh = 0;

	/* get delta width and height */
	dw = rtgui_rect_width(*rect) - rtgui_rect_width(*to);
	dh = rtgui_rect_height(*rect) - rtgui_rect_height(*to);
	if (dw < 0) dw = 0;
	if (dh < 0) dh = 0;

	/* move to insider of rect */
	rtgui_rect_moveto(to, rect->x1, rect->y1);

	/* limited the destination rect to source rect */
	if (dw == 0) to->x2 = rect->x2;
	if (dh == 0) to->y2 = rect->y2;

	/* align to right */
	if (align & RTGUI_ALIGN_RIGHT)
	{
		to->x1 += dw;
		to->x2 += dw;
	}

	/* align to bottom */
	if (align & RTGUI_ALIGN_BOTTOM)
	{
		to->y1 += dh;
		to->y2 += dh;
	}

	/* align to center horizontal */
	if (align & RTGUI_ALIGN_CENTER_HORIZONTAL)
	{
		to->x1 += dw >> 1;
		to->x2 += dw >> 1;
	}

	/* align to center vertical */
	if (align & RTGUI_ALIGN_CENTER_VERTICAL)
	{
		to->y1 += dh >> 1;
		to->y2 += dh >> 1;
	}
}

void rtgui_rect_inflate(rtgui_rect_t *rect, int d)
{
	rect->x1 -= d;
	rect->x2 += d;
	rect->y1 -= d;
	rect->y2 += d;
}

/* put the intersect of src rect and dest rect to dest */
void rtgui_rect_intersect(rtgui_rect_t *src, rtgui_rect_t *dest)
{
	if (dest->x1 < src->x1) dest->x1 = src->x1;
	if (dest->y1 < src->y1) dest->y1 = src->y1;
	if (dest->x2 > src->x2) dest->x2 = src->x2;
	if (dest->y2 > src->y2) dest->y2 = src->y2;
}

int rtgui_rect_contains_point(const rtgui_rect_t *rect, int x, int y)
{
	if (INBOX(rect, x, y)) return RT_EOK;

	return -RT_ERROR;
}

int rtgui_rect_is_intersect(const rtgui_rect_t *rect1, const rtgui_rect_t *rect2)
{
	if (INBOX(rect1, rect2->x1, rect2->y1) ||
		INBOX(rect1, rect2->x1, rect2->y2) ||
		INBOX(rect1, rect2->x2, rect2->y1) ||
		INBOX(rect1, rect2->x2, rect2->y2))
	{
		return RT_EOK;
	}
	else if (INBOX(rect2, rect1->x1, rect1->y1) ||
		INBOX(rect2, rect1->x1, rect1->y2) ||
		INBOX(rect2, rect1->x2, rect1->y1) ||
		INBOX(rect2, rect1->x2, rect1->y2))
	{
		return RT_EOK;
	}

	return -RT_ERROR;
}