R6.6 is the Xorg base-lineXORG-MAIN

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+/***********************************************************
+
+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
+the above copyright notice appear in all copies and that both that
+copyright notice and this permission notice appear in supporting
+documentation.
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL THE
+OPEN GROUP BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
+AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+Except as contained in this notice, the name of The 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
+ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL
+DIGITAL BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR
+ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
+WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
+ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
+SOFTWARE.
+
+******************************************************************/
+/* $Xorg: miregion.c,v 1.4 2001/02/09 02:05:21 xorgcvs Exp $ */
+
+#include <stdio.h>
+#include "miscstruct.h"
+#include "regionstr.h"
+#include "Xprotostr.h"
+#include "gc.h"
+
+#if defined (__GNUC__) && !defined (NO_INLINES)
+#define INLINE	__inline
+#else
+#define INLINE
+#endif
+
+/*
+ * hack until callers of these functions can deal with out-of-memory
+ */
+
+extern Bool Must_have_memory;
+
+#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 xallocData(n) (RegDataPtr)xalloc(REGION_SZOF(n))
+#define xfreeData(reg) if ((reg)->data && (reg)->data->size) xfree((reg)->data)
+
+#define RECTALLOC(pReg,n) \
+if (!(pReg)->data || (((pReg)->data->numRects + (n)) > (pReg)->data->size)) \
+    miRectAlloc(pReg, n)
+
+#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))\
+    {									\
+	miRectAlloc(pReg, 1);						\
+	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};
+
+#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;
+   
+    Must_have_memory = TRUE; /* XXX */
+    pReg = (RegionPtr)xalloc(sizeof(RegionRec));
+    Must_have_memory = FALSE; /* XXX */
+    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);
+    xfree(pReg);
+}
+
+void
+miRegionUninit(pReg)
+    RegionPtr pReg;
+{
+    good(pReg);
+    xfreeData(pReg);
+}
+
+Bool
+miRectAlloc(pRgn, n)
+    register RegionPtr pRgn;
+    int n;
+{
+    Must_have_memory = TRUE; /* XXX */
+    if (!pRgn->data)
+    {
+	n++;
+	pRgn->data = xallocData(n);
+	pRgn->data->numRects = 1;
+	*REGION_BOXPTR(pRgn) = pRgn->extents;
+    }
+    else if (!pRgn->data->size)
+    {
+	pRgn->data = xallocData(n);
+	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;
+	pRgn->data = (RegDataPtr)xrealloc(pRgn->data, REGION_SZOF(n));
+    }
+    Must_have_memory = FALSE; /* XXX */
+    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);
+	Must_have_memory = TRUE; /* XXX */
+	dst->data = xallocData(src->data->numRects);
+	Must_have_memory = FALSE; /* XXX */
+	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 (pReg, prevStart, curStart)
+    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 (pReg, r, rEnd, y1, y2)
+    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.
+ *
+ *-----------------------------------------------------------------------
+ */
+static Bool
+miRegionOp(newReg, reg1, reg2, overlapFunc, appendNon1, appendNon2, pOverlap)
+    RegionPtr       newReg;		    /* Place to store result	     */
+    RegionPtr       reg1;		    /* First region in operation     */
+    RegionPtr       reg2;		    /* 2d region in operation        */
+    Bool	    (*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;
+
+    /*
+     * 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)
+	miRectAlloc(newReg, newSize);
+
+    /*
+     * 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 (pReg, r1, r1End, r2, r2End, y1, y2, pOverlap)
+    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;
+	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 (pReg, r1, r1End, r2, r2End, y1, y2, pOverlap)
+    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 (newReg != reg2)
+	    return miRegionCopy(newReg, reg2);
+        return TRUE;
+    }
+
+    /*
+     * Region 2 is empty
+     */
+    if (REGION_NIL(reg2))
+    {
+        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 (!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(rects, numRects)
+    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			    */
+
+    *pOverlap = FALSE;
+    if (!badreg->data)
+    {
+	good(badreg);
+	return TRUE;
+    }
+    numRects = badreg->data->numRects;
+    if (!numRects)
+    {
+	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 */
+    Must_have_memory = TRUE; /* XXX */
+    ri = (RegionInfo *) xalloc(4 * sizeof(RegionInfo));
+    Must_have_memory = FALSE; /* XXX */
+    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(reg, 1);
+		    *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(reg, 1);
+		*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;
+	    Must_have_memory = TRUE; /* XXX */
+	    ri = (RegionInfo *) xrealloc(ri, sizeRI * sizeof(RegionInfo));
+	    Must_have_memory = FALSE; /* XXX */
+	    rit = &ri[numRI];
+	}
+	numRI++;
+	rit->prevBand = 0;
+	rit->curBand = 0;
+	rit->reg.extents = *box;
+	rit->reg.data = (RegDataPtr)NULL;
+	miRectAlloc(&rit->reg, (i+numRI) / numRI); /* MUST force allocation */
+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;
+	    miRegionOp(reg, reg, hreg, miUnionO, TRUE, TRUE, pOverlap);
+	    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 TRUE;
+}
+
+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 (!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;
+    }
+    Must_have_memory = TRUE; /* XXX */
+    pData = xallocData(nrects);
+    pBox = (BoxPtr) (pData + 1);
+    Must_have_memory = FALSE; /* XXX */
+    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 (pReg, r1, r1End, r2, r2End, y1, y2, pOverlap)
+    register RegionPtr	pReg;
+    register BoxPtr	r1;
+    BoxPtr  	  	r1End;
+    register BoxPtr	r2;
+    BoxPtr  	  	r2End;
+    register int  	y1;
+             int  	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;
+	    if (x1 >= r1->x2)
+	    {
+		/*
+		 * Minuend completely covered: advance to next minuend and
+		 * reset left fence to edge of new minuend.
+		 */
+		r1++;
+		if (r1 != r1End)
+		    x1 = r1->x1;
+	    }
+	    else
+	    {
+		/*
+		 * Subtrahend now used up since it doesn't extend beyond
+		 * minuend
+		 */
+		r2++;
+	    }
+	}
+	else if (r2->x1 < r1->x2)
+	{
+	    /*
+	     * Left part of subtrahend covers part of minuend: add uncovered
+	     * part of minuend to region and skip to next subtrahend.
+	     */
+	    assert(x1<r2->x1);
+	    NEWRECT(pReg, 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(pReg, 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)
+    {
+	assert(x1<r1->x2);
+	NEWRECT(pReg, pNextRect, x1, y1, r1->x2, y2);
+	r1++;
+	if (r1 != r1End)
+	    x1 = r1->x1;
+    }
+    return TRUE;
+}
+	
+/*-
+ *-----------------------------------------------------------------------
+ * miSubtract --
+ *	Subtract regS from regM and leave the result in regD.
+ *	S stands for subtrahend, M for minuend and D for difference.
+ *
+ * Results:
+ *	TRUE if successful.
+ *
+ * Side Effects:
+ *	regD is overwritten.
+ *
+ *-----------------------------------------------------------------------
+ */
+Bool
+miSubtract(regD, regM, regS)
+    register RegionPtr	regD;               
+    register RegionPtr 	regM;
+    register RegionPtr	regS;          
+{
+    Bool overlap; /* result ignored */
+
+    good(regM);
+    good(regS);
+    good(regD);
+   /* check for trivial rejects */
+    if (REGION_NIL(regM) || REGION_NIL(regS) ||
+	!EXTENTCHECK(&regM->extents, &regS->extents))
+    {
+	return miRegionCopy(regD, regM);
+    }
+    else if (regM == regS)
+    {
+	xfreeData(regD);
+	regD->extents.x2 = regD->extents.x1;
+	regD->extents.y2 = regD->extents.y1;
+	regD->data = &miEmptyData;
+	return TRUE;
+    }
+ 
+    /* 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 (!miRegionOp(regD, regM, regS, miSubtractO, TRUE, FALSE, &overlap))
+	return FALSE;
+
+    /*
+     * Can't alter RegD's extents before we call miRegionOp because
+     * it might be one of the source regions and miRegionOp 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 examine fewer rectangles.
+     */
+    miSetExtents(regD);
+    good(regD);
+    return TRUE;
+}
+
+/*======================================================================
+ *	    Region Inversion
+ *====================================================================*/
+
+/*-
+ *-----------------------------------------------------------------------
+ * miInverse --
+ *	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:
+ *	TRUE.
+ *
+ * Side Effects:
+ *	newReg is overwritten.
+ *
+ *-----------------------------------------------------------------------
+ */
+Bool
+miInverse(newReg, reg1, invRect)
+    RegionPtr 	  newReg;       /* Destination region */
+    RegionPtr 	  reg1;         /* Region to invert */
+    BoxPtr     	  invRect; 	/* Bounding box for inversion */
+{
+    RegionRec	  invReg;   	/* Quick and dirty region made from the
+				 * bounding box */
+    Bool	  overlap;	/* result ignored */
+
+    good(reg1);
+    good(newReg);
+   /* check for trivial rejects */
+    if (REGION_NIL(reg1) || !EXTENTCHECK(invRect, &reg1->extents))
+    {
+	newReg->extents = *invRect;
+	xfreeData(newReg);
+	newReg->data = (RegDataPtr)NULL;
+        return TRUE;
+    }
+
+    /* 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 = (RegDataPtr)NULL;
+    if (!miRegionOp(newReg, &invReg, reg1, miSubtractO, TRUE, FALSE, &overlap))
+	return FALSE;
+
+    /*
+     * Can't alter newReg's extents before we call miRegionOp because
+     * it might be one of the source regions and miRegionOp 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 examine fewer rectangles.
+     */
+    miSetExtents(newReg);
+    good(newReg);
+    return TRUE;
+}
+
+/*
+ *   RectIn(region, rect)
+ *   This routine takes a pointer to a region and a pointer to a box
+ *   and determines 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 TRUE. Any time a rectangle in
+ *   the region covers part of the box, partIn is set TRUE. The process ends
+ *   when either the box has been completely covered (we reached a band that
+ *   doesn't overlap the box, partIn is TRUE and partOut is false), the
+ *   box has been partially covered (partIn == partOut == TRUE -- 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
+miRectIn(region, prect)
+    register RegionPtr  region;
+    register BoxPtr     prect;
+{
+    register int	x;
+    register int	y;
+    register BoxPtr     pbox;
+    register BoxPtr     pboxEnd;
+    int			partIn, partOut;
+    int			numRects;
+
+    good(region);
+    numRects = REGION_NUM_RECTS(region);
+    /* useful optimization */
+    if (!numRects || !EXTENTCHECK(&region->extents, prect))
+        return(rgnOUT);
+
+    if (numRects == 1)
+    {
+	/* We know that it must be rgnIN or rgnPART */
+	if (SUBSUMES(&region->extents, prect))
+	    return(rgnIN);
+	else
+	    return(rgnPART);
+    }
+
+    partOut = FALSE;
+    partIn = FALSE;
+
+    /* (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 TRUE, or we reach prect->y2 */
+    for (pbox = REGION_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 = TRUE;      /* 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 = TRUE;      /* missed part of rectangle to left */
+           if (partIn)
+              break;
+        }
+
+        if (pbox->x1 < prect->x2)
+        {
+            partIn = TRUE;      /* 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 = TRUE;
+	    break;
+	}
+    }
+
+    return(partIn ? ((y < prect->y2) ? rgnPART : rgnIN) : rgnOUT);
+}
+
+/* TranslateRegion(pReg, x, y)
+   translates in place
+*/
+
+void
+miTranslateRegion(pReg, x, y)
+    register RegionPtr pReg;
+    register int x;
+    register int y;
+{
+    int x1, x2, y1, y2;
+    register int nbox;
+    register BoxPtr pbox;
+
+    good(pReg);
+    pReg->extents.x1 = x1 = pReg->extents.x1 + x;
+    pReg->extents.y1 = y1 = pReg->extents.y1 + y;
+    pReg->extents.x2 = x2 = pReg->extents.x2 + x;
+    pReg->extents.y2 = y2 = pReg->extents.y2 + y;
+    if (((x1 - MINSHORT)|(y1 - MINSHORT)|(MAXSHORT - x2)|(MAXSHORT - y2)) >= 0)
+    {
+	if (pReg->data && (nbox = pReg->data->numRects))
+	{
+	    for (pbox = REGION_BOXPTR(pReg); nbox--; pbox++)
+	    {
+		pbox->x1 += x;
+		pbox->y1 += y;
+		pbox->x2 += x;
+		pbox->y2 += y;
+	    }
+	}
+	return;
+    }
+    if (((x2 - MINSHORT)|(y2 - MINSHORT)|(MAXSHORT - x1)|(MAXSHORT - y1)) <= 0)
+    {
+	pReg->extents.x2 = pReg->extents.x1;
+	pReg->extents.y2 = pReg->extents.y1;
+	xfreeData(pReg);
+	pReg->data = &miEmptyData;
+	return;
+    }
+    if (x1 < MINSHORT)
+	pReg->extents.x1 = MINSHORT;
+    else if (x2 > MAXSHORT)
+	pReg->extents.x2 = MAXSHORT;
+    if (y1 < MINSHORT)
+	pReg->extents.y1 = MINSHORT;
+    else if (y2 > MAXSHORT)
+	pReg->extents.y2 = MAXSHORT;
+    if (pReg->data && (nbox = pReg->data->numRects))
+    {
+	register BoxPtr pboxout;
+
+	for (pboxout = pbox = REGION_BOXPTR(pReg); 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 - MINSHORT)|(y2 - MINSHORT)|
+		 (MAXSHORT - x1)|(MAXSHORT - y1)) <= 0)
+	    {
+		pReg->data->numRects--;
+		continue;
+	    }
+	    if (x1 < MINSHORT)
+		pboxout->x1 = MINSHORT;
+	    else if (x2 > MAXSHORT)
+		pboxout->x2 = MAXSHORT;
+	    if (y1 < MINSHORT)
+		pboxout->y1 = MINSHORT;
+	    else if (y2 > MAXSHORT)
+		pboxout->y2 = MAXSHORT;
+	    pboxout++;
+	}
+	if (pboxout != pbox)
+	{
+	    if (pReg->data->numRects == 1)
+	    {
+		pReg->extents = *REGION_BOXPTR(pReg);
+		xfreeData(pReg);
+		pReg->data = (RegDataPtr)NULL;
+	    }
+	    else
+		miSetExtents(pReg);
+	}
+    }
+}
+
+void
+miRegionReset(pReg, pBox)
+    RegionPtr pReg;
+    BoxPtr pBox;
+{
+    good(pReg);
+    assert(pBox->x1<=pBox->x2);
+    assert(pBox->y1<=pBox->y2);
+    pReg->extents = *pBox;
+    xfreeData(pReg);
+    pReg->data = (RegDataPtr)NULL;
+}
+
+Bool
+miPointInRegion(pReg, x, y, box)
+    register RegionPtr pReg;
+    register int x, y;
+    BoxPtr box;     /* "return" value */
+{
+    register BoxPtr pbox, pboxEnd;
+    int numRects;
+
+    good(pReg);
+    numRects = REGION_NUM_RECTS(pReg);
+    if (!numRects || !INBOX(&pReg->extents, x, y))
+        return(FALSE);
+    if (numRects == 1)
+    {
+	*box = pReg->extents;
+	return(TRUE);
+    }
+    for (pbox = REGION_BOXPTR(pReg), 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(TRUE);
+    }
+    return(FALSE);
+}
+
+Bool
+miRegionNotEmpty(pReg)
+    RegionPtr pReg;
+{
+    good(pReg);
+    return(!REGION_NIL(pReg));
+}
+
+
+void
+miRegionEmpty(pReg)
+    RegionPtr pReg;
+{
+    good(pReg);
+    xfreeData(pReg);
+    pReg->extents.x2 = pReg->extents.x1;
+    pReg->extents.y2 = pReg->extents.y1;
+    pReg->data = &miEmptyData;
+}
+
+BoxPtr
+miRegionExtents(pReg)
+    RegionPtr pReg;
+{
+    good(pReg);
+    return(&pReg->extents);
+}
+
+#define ExchangeSpans(a, b)				    \
+{							    \
+    DDXPointRec     tpt;				    \
+    register 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(spans, widths, numSpans)
+    register DDXPointRec    spans[];
+    register int	    widths[];
+    register int	    numSpans;
+{
+    register int	    y;
+    register int	    i, j, m;
+    register DDXPointPtr    r;
+
+    /* Always called with numSpans > 1 */
+    /* Sorts only by y, doesn't bother to sort by x */
+
+    do
+    {
+	if (numSpans < 9)
+	{
+	    /* Do insertion sort */
+	    register 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. */
+		    DDXPointRec 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);
+}
+
+#define NextBand()						    \
+{								    \
+    clipy1 = pboxBandStart->y1;					    \
+    clipy2 = pboxBandStart->y2;					    \
+    pboxBandEnd = pboxBandStart + 1;				    \
+    while (pboxBandEnd != pboxLast && pboxBandEnd->y1 == clipy1) {  \
+	pboxBandEnd++;						    \
+    }								    \
+    for (; ppt != pptLast && ppt->y < clipy1; ppt++, pwidth++) {} \
+}
+
+/*
+    Clip a list of scanlines to a region.  The caller has allocated the
+    space.  FSorted is non-zero if the scanline origins are in ascending
+    order.
+    returns the number of new, clipped scanlines.
+*/
+
+int
+miClipSpans(prgnDst, ppt, pwidth, nspans, pptNew, pwidthNew, fSorted)
+    RegionPtr		    prgnDst;
+    register DDXPointPtr    ppt;
+    register int	    *pwidth;
+    int			    nspans;
+    register DDXPointPtr    pptNew;
+    int			    *pwidthNew;
+    int			    fSorted;
+{
+    register DDXPointPtr pptLast;
+    int			*pwidthNewStart;	/* the vengeance of Xerox! */
+    register int	y, x1, x2;
+    register int	numRects;
+
+    good(prgnDst);
+    pptLast = ppt + nspans;
+    pwidthNewStart = pwidthNew;
+
+    if (!prgnDst->data)
+    {
+	/* Do special fast code with clip boundaries in registers(?) */
+	/* It doesn't pay much to make use of fSorted in this case, 
+	   so we lump everything together. */
+
+	register    int clipx1, clipx2, clipy1, clipy2;
+
+	clipx1 = prgnDst->extents.x1;
+	clipy1 = prgnDst->extents.y1;
+	clipx2 = prgnDst->extents.x2;
+	clipy2 = prgnDst->extents.y2;
+	    
+	for (; ppt != pptLast; ppt++, pwidth++)
+	{
+	    y = ppt->y;
+	    x1 = ppt->x;
+	    if (clipy1 <= y && y < clipy2)
+	    {
+		x2 = x1 + *pwidth;
+		if (x1 < clipx1)    x1 = clipx1;
+		if (x2 > clipx2)    x2 = clipx2;
+		if (x1 < x2)
+		{
+		    /* part of span in clip rectangle */
+		    pptNew->x = x1;
+		    pptNew->y = y;
+		    *pwidthNew = x2 - x1;
+		    pptNew++;
+		    pwidthNew++;
+		}
+	    }
+	} /* end for */
+
+    }
+    else if (numRects = prgnDst->data->numRects)
+    {
+	/* Have to clip against many boxes */
+	BoxPtr		pboxBandStart, pboxBandEnd;
+	register BoxPtr pbox;
+	register BoxPtr pboxLast;
+	register int	clipy1, clipy2;
+
+	/* In this case, taking advantage of sorted spans gains more than
+	   the sorting costs. */
+	if ((! fSorted) && (nspans > 1))
+	    QuickSortSpans(ppt, pwidth, nspans);
+
+	pboxBandStart = REGION_BOXPTR(prgnDst);
+	pboxLast = pboxBandStart + numRects;
+    
+	NextBand();
+
+	for (; ppt != pptLast; )
+	{
+	    y = ppt->y;
+	    if (y < clipy2)
+	    {
+		/* span is in the current band */
+		pbox = pboxBandStart;
+		x1 = ppt->x;
+		x2 = x1 + *pwidth;
+		do
+		{ /* For each box in band */
+		    register int    newx1, newx2;
+
+		    newx1 = x1;
+		    newx2 = x2;
+		    if (newx1 < pbox->x1)   newx1 = pbox->x1;
+		    if (newx2 > pbox->x2)   newx2 = pbox->x2;
+		    if (newx1 < newx2)
+		    {
+			/* Part of span in clip rectangle */
+			pptNew->x = newx1;
+			pptNew->y = y;
+			*pwidthNew = newx2 - newx1;
+			pptNew++;
+			pwidthNew++;
+		    }
+		    pbox++;
+		} while (pbox != pboxBandEnd);
+		ppt++;
+		pwidth++;
+	    }
+	    else
+	    {
+		/* Move to next band, adjust ppt as needed */
+		pboxBandStart = pboxBandEnd;
+		if (pboxBandStart == pboxLast)
+		    break; /* We're completely done */
+		NextBand();
+	    }
+	}
+    }
+    return (pwidthNew - pwidthNewStart);
+}
+
+/* find the band in a region with the most rectangles */
+int
+miFindMaxBand(prgn)
+    RegionPtr prgn;
+{
+    register int nbox;
+    register BoxPtr pbox;
+    register int nThisBand;
+    register int nMaxBand = 0;
+    short yThisBand;
+
+    good(prgn);
+    nbox = REGION_NUM_RECTS(prgn);
+    pbox = REGION_RECTS(prgn);
+
+    while(nbox > 0)
+    {
+	yThisBand = pbox->y1;
+	nThisBand = 0;
+	while((nbox > 0) && (pbox->y1 == yThisBand))
+	{
+	    nbox--;
+	    pbox++;
+	    nThisBand++;
+	}
+	if (nThisBand > nMaxBand)
+	    nMaxBand = nThisBand;
+    }
+    return (nMaxBand);
+}