update ast 8.6.2

1 files changed, 5062 insertions, 0 deletions

diff --git a/ast/box.c b/ast/box.c
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index 0000000..99aa780
--- /dev/null
+++ b/ast/box.c
@@ -0,0 +1,5062 @@
+/*
+*class++
+*  Name:
+*     Box
+
+*  Purpose:
+*     A box region with sides parallel to the axes of a Frame.
+
+*  Constructor Function:
+c     astBox
+f     AST_BOX
+
+*  Description:
+*     The Box class implements a Region which represents a box with sides
+*     parallel to the axes of a Frame (i.e. an area which encloses a given
+*     range of values on each axis). A Box is similar to an Interval, the
+*     only real difference being that the Interval class allows some axis
+*     limits to be unspecified. Note, a Box will only look like a box if
+*     the Frame geometry is approximately flat. For instance, a Box centred
+*     close to a pole in a SkyFrame will look more like a fan than a box
+*     (the Polygon class can be used to create a box-like region close to a
+*     pole).
+
+*  Inheritance:
+*     The Box class inherits from the Region class.
+
+*  Attributes:
+*     The Box class does not define any new attributes beyond
+*     those which are applicable to all Regions.
+
+*  Functions:
+c     The Box class does not define any new functions beyond those
+f     The Box class does not define any new routines beyond those
+*     which are applicable to all Regions.
+
+*  Copyright:
+*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
+*     Research Councils
+*     Copyright (C) 2008-2009 Science & Technology Facilities Council.
+*     All Rights Reserved.
+
+*  Licence:
+*     This program is free software: you can redistribute it and/or
+*     modify it under the terms of the GNU Lesser General Public
+*     License as published by the Free Software Foundation, either
+*     version 3 of the License, or (at your option) any later
+*     version.
+*
+*     This program is distributed in the hope that it will be useful,
+*     but WITHOUT ANY WARRANTY; without even the implied warranty of
+*     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*     GNU Lesser General Public License for more details.
+*
+*     You should have received a copy of the GNU Lesser General
+*     License along with this program.  If not, see
+*     <http://www.gnu.org/licenses/>.
+
+*  Authors:
+*     DSB: David S. Berry (Starlink)
+
+*  History:
+*     22-MAR-2004 (DSB):
+*        Original version.
+*     14-FEB-2006 (DSB):
+*        Override astGetObjSize.
+*     5-JUN-2007 (DSB):
+*        Improve astSimplify algorithm.
+*     6-JUN-2007 (DSB):
+*        Change the iterating algorithm in MakeGrid so that it uses
+*        pixel index rather than axis value. This is more robust against
+*        rounding errors.
+*     9-OCT-2007 (DSB):
+*        - Fix bug in RegBaseMesh that could cause incorrect meshes for 2D
+*        Boxes.
+*        - In RegBaseMesh, use flat geometry if all axes come from simple
+*        frames or from 1-dimensional specialist frames.
+*     26-MAY-2008 (DSB):
+*        Fix bug in RegBaseMesh that caused an error to be reported if
+*        the Box occupies a single point.
+*     20-JAN-2009 (DSB):
+*        Over-ride astRegBasePick.
+*     26-JAN-2009 (DSB):
+*        Over-ride astMapMerge.
+*     12-JUL-2009 (DSB):
+*        Modify Simplify so that if a Box can be split into two
+*        simpler components and then joined together into a Prism, it
+*        does so. This is because being able to express a Region in
+*        its current Frame is more important than having the simplest
+*        possible structure.
+*     28-FEB-2011 (DSB):
+*        Do not assume the first axis value is good in function BestBox.
+*     22-MAR-2011 (DSB):
+*        Improve uniformity of points within grid produced by astRegBaseGrid.
+*     16-JUL-2013 (DSB):
+*        Use a more robust algorithm for determining the order of the
+*        vertices whan a Box is simplified to a Polygon. The old method
+*        sometimes resulted in an unbounded "inside-out" polygon.
+*     4-NOV-2013 (DSB):
+*        Modify RegPins so that it can handle uncertainty regions that straddle
+*        a discontinuity. Previously, such uncertainty Regions could have a huge
+*        bounding box resulting in matching region being far too big.
+*     10-APR-2014 (DSB):
+*        More work (in function Cache() ) on handling uncertainty regions that straddle
+*        a discontinuity. This time ensure that the extent of the box on each axis takes
+*        account of the possibly cyclic nature of the base Frame.
+*     25-4-2016 (DSB):
+*        Remove the unused box shrinking facility (a hang over from the
+*        days when the RegBaseGrid function operated by creating multiple
+*        meshes on the surface of the box, shrinking the box each time).
+*class--
+*/
+
+/* Module Macros. */
+/* ============== */
+/* Set the name of the class we are implementing. This indicates to
+   the header files that define class interfaces that they should make
+   "protected" symbols available. */
+#define astCLASS Box
+
+/* Include files. */
+/* ============== */
+/* Interface definitions. */
+/* ---------------------- */
+
+#include "globals.h"             /* Thread-safe global data access */
+#include "cmpmap.h"              /* Compound Mappings */
+#include "cmpframe.h"            /* Compound Frames */
+#include "error.h"               /* Error reporting facilities */
+#include "memory.h"              /* Memory allocation facilities */
+#include "object.h"              /* Base Object class */
+#include "pointset.h"            /* Sets of points/coordinates */
+#include "region.h"              /* Coordinate regions (parent class) */
+#include "channel.h"             /* I/O channels */
+#include "box.h"                 /* Interface definition for this class */
+#include "polygon.h"             /* Interface definition for this class */
+#include "mapping.h"             /* Position mappings */
+#include "unitmap.h"             /* Unit Mappings */
+#include "permmap.h"             /* Axis permutation Mappings */
+#include "interval.h"            /* Axis interval regions */
+#include "nullregion.h"          /* Empty regions */
+#include "pointlist.h"           /* List of points in a Frame */
+#include "prism.h"               /* Extruded regions */
+
+/* Error code definitions. */
+/* ----------------------- */
+#include "ast_err.h"             /* AST error codes */
+
+/* C header files. */
+/* --------------- */
+#include <float.h>
+#include <math.h>
+#include <stdarg.h>
+#include <stddef.h>
+#include <stdio.h>
+#include <string.h>
+
+/* Module Variables. */
+/* ================= */
+
+/* Address of this static variable is used as a unique identifier for
+   member of this class. */
+static int class_check;
+
+/* Pointers to parent class methods which are extended by this class. */
+static int (* parent_getobjsize)( AstObject *, int * );
+static AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static AstMapping *(* parent_simplify)( AstMapping *, int * );
+static void (* parent_setnegated)( AstRegion *, int, int * );
+static void (* parent_setclosed)( AstRegion *, int, int * );
+static void (* parent_clearnegated)( AstRegion *, int * );
+static void (* parent_clearclosed)( AstRegion *, int * );
+static void (* parent_setunc)( AstRegion *, AstRegion *, int * );
+static void (* parent_setregfs)( AstRegion *, AstFrame *, int * );
+static void (* parent_resetcache)( AstRegion *, int * );
+
+
+#ifdef THREAD_SAFE
+/* Define how to initialise thread-specific globals. */
+#define GLOBAL_inits \
+   globals->Class_Init = 0;
+
+/* Create the function that initialises global data for this module. */
+astMAKE_INITGLOBALS(Box)
+
+/* Define macros for accessing each item of thread specific global data. */
+#define class_init astGLOBAL(Box,Class_Init)
+#define class_vtab astGLOBAL(Box,Class_Vtab)
+
+
+#include <pthread.h>
+
+
+#else
+
+
+/* Define the class virtual function table and its initialisation flag
+   as static variables. */
+static AstBoxVtab class_vtab;   /* Virtual function table */
+static int class_init = 0;       /* Virtual function table initialised? */
+
+#endif
+
+/* External Interface Function Prototypes. */
+/* ======================================= */
+/* The following functions have public prototypes only (i.e. no
+   protected prototypes), so we must provide local prototypes for use
+   within this module. */
+AstBox *astBoxId_( void *, int, const double[], const double[], void *, const char *, ... );
+
+/* Prototypes for Private Member Functions. */
+/* ======================================== */
+static AstBox *BestBox( AstFrame *, AstPointSet *, AstRegion *, int * );
+static AstMapping *Simplify( AstMapping *, int * );
+static AstPointSet *RegBaseGrid( AstRegion *, int * );
+static AstPointSet *RegBaseMesh( AstRegion *, int * );
+static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static AstRegion *MergeBox( AstBox *, AstRegion *, int, int * );
+static AstRegion *RegBasePick( AstRegion *this, int, const int *, int * );
+static double *GeoCorner( AstFrame *, int, double *, double *, double *, int * );
+static double *GeoLengths( AstFrame *, int, double *, double *, double *, int * );
+static double *RegCentre( AstRegion *this, double *, double **, int, int, int * );
+static int GetObjSize( AstObject *, int * );
+static int MakeGrid( int, double **, int, double *, double *, int *, int, int, double, int * );
+static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
+static int RegPins( AstRegion *, AstPointSet *, AstRegion *, int **, int * );
+static int RegTrace( AstRegion *, int, double *, double **, int * );
+static void BoxPoints( AstBox *, double *, double *, int *);
+static void Cache( AstBox *, int, int * );
+static void ClearClosed( AstRegion *, int * );
+static void ClearNegated( AstRegion *, int * );
+static void Copy( const AstObject *, AstObject *, int * );
+static void Delete( AstObject *, int * );
+static void Dump( AstObject *, AstChannel *, int * );
+static void RegBaseBox( AstRegion *this, double *, double *, int * );
+static void ResetCache( AstRegion *this, int * );
+static void SetClosed( AstRegion *, int, int * );
+static void SetNegated( AstRegion *, int, int * );
+static void SetRegFS( AstRegion *, AstFrame *, int * );
+static void SetUnc( AstRegion *, AstRegion *, int * );
+
+/* Member functions. */
+/* ================= */
+
+void BoxPoints( AstBox *this, double *centre, double *corner, int *status) {
+/*
+*+
+*  Name:
+*     astBoxPoints
+
+*  Purpose:
+*     Return the defining points of a Box.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "box.h"
+*     astBoxPoints( AstBox *this, double *centre, double *corner )
+
+*  Class Membership:
+*     Region virtual function.
+
+*  Description:
+*     This function returns the axis values at the points defining the
+*     supplied Box.
+
+*  Parameters:
+*     this
+*        Pointer to the Box.
+*     centre
+*        A pointer to an array in which to return the centre position of
+*        the Box, in the base Frame of the encapsulated FrameSet.
+*     corner
+*        A pointer to an array in which to return the position of a corner
+*        of the Box, in the base Frame of the encapsulated FrameSet.
+
+*  Notes:
+*     - It is assumed that the length of the supplied arrays is at least
+*     equal to the number of axes in the base frame of the encapsulated
+*     FrameSet.
+*-
+*/
+
+/* Local Variables: */
+   AstPointSet *pset;
+   double **ptr;
+   int nc;
+   int i;
+
+/* Check the inherited status. */
+   if( !astOK ) return;
+
+/* Get a pointer to the PointSet holding the points defining the Box. */
+   pset = ((AstRegion *) this)->points;
+
+/* Get a pointer to the PointSet's data arrays. */
+   ptr = astGetPoints( pset );
+
+/* See how many axes each point in the PointSet has. */
+   nc = astGetNcoord( pset );
+
+/* Copy the centre and corner positions form the PointSet into the
+   supplied arrays. */
+   for( i = 0; i < nc; i++ ) {
+      centre[ i ] = ptr[ i ] [ 0 ];
+      corner[ i ] = ptr[ i ] [ 1 ];
+   }
+
+}
+
+static void ClearClosed( AstRegion *this, int *status ){
+/*
+*  Name:
+*     ClearClosed
+
+*  Purpose:
+*     Clear the Closed attribute of a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void ClearClosed( AstRegion *this, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the protected astClearClosed
+*     method inherited from the Region class).
+
+*  Description:
+*     This function clears the Closed attribute of the supplied Region.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   int old;
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get the original attribute value */
+   old = astGetClosed( this );
+
+/* Invoke the clear method inherited from the parent Region class */
+   (*parent_clearclosed)( this, status );
+
+/* If the new value is not the same as the old value, inidcatethat we
+   need to re-calculate the cached information in the Box. */
+   if( astGetClosed( this ) != old ) astResetCache( this );
+}
+
+static void ClearNegated( AstRegion *this, int *status ){
+/*
+*  Name:
+*     ClearNegated
+
+*  Purpose:
+*     Clear the Negated attribute of a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void ClearNegated( AstRegion *this, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the protected astClearNegated
+*     method inherited from the Region class).
+
+*  Description:
+*     This function clears the Negated attribute of the supplied Region.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   int old;
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get the original attribute value */
+   old = astGetNegated( this );
+
+/* Invoke the clear method inherited from the parent Region class */
+   (*parent_clearnegated)( this, status );
+
+/* If the new value is not the same as the old value, inidcatethat we
+   need to re-calculate the cached information in the Box. */
+   if( astGetNegated( this ) != old ) astResetCache( this );
+}
+
+static AstBox *BestBox( AstFrame *frm, AstPointSet *mesh, AstRegion *unc, int *status ){
+/*
+*  Name:
+*     BestBox
+
+*  Purpose:
+*     Find the best fitting Box through a given mesh of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstBox *BestBox( AstFrame *frm, AstPointSet *mesh, AstRegion *unc, int *status )
+
+*  Class Membership:
+*     Box member function
+
+*  Description:
+*     This function finds the best fitting Box through a given mesh of points.
+
+*  Parameters:
+*     frm
+*        Defines the geometry of the axes.
+*     mesh
+*        Pointer to a PointSet holding the mesh of points. They are
+*        assumed to be in the Frame represented by "unc".
+*     unc
+*        A Region representing the uncertainty associated with each point
+*        on the mesh.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the best fitting Region. It will inherit the positional
+*     uncertainty and Frame represented by "unc". NULL is returned if all
+*     the supplied positions are bad.
+
+*  Notes:
+*    - A NULL pointer is returned if an error has already occurred, or if
+*    this function should fail for any reason.
+
+*/
+
+/* Local Variables: */
+   AstBox *result;
+   double **ptr;
+   double *axval;
+   double *blbnd;
+   double *bubnd;
+   double *lbnd;
+   double *p;
+   double *ubnd;
+   double eps;
+   double lb;
+   double lim2;
+   double lim;
+   double liml;
+   double limu;
+   double mxl;
+   double mxu;
+   double org;
+   double sxl2;
+   double sxl;
+   double sxu2;
+   double sxu;
+   double ub;
+   double p0;
+   double d;
+   double dinc;
+   int ic;
+   int ip;
+   int nc;
+   int np;
+   int nxl;
+   int nxu;
+   int ok;
+
+/* Initialise */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get no. of points in the mesh, and the number of axis values per point. */
+   np = astGetNpoint( mesh );
+   nc = astGetNcoord( mesh );
+
+/* Get pointers to the axis values. */
+   ptr = astGetPoints( mesh );
+
+/* Allocate work space. */
+   lbnd = astMalloc( sizeof( double )*(size_t) nc );
+   ubnd = astMalloc( sizeof( double )*(size_t) nc );
+
+   blbnd = astMalloc( sizeof( double )*(size_t) nc );
+   bubnd = astMalloc( sizeof( double )*(size_t) nc );
+
+   axval = astMalloc( sizeof( double )*(size_t) np );
+
+/* Check pointers can be used safely */
+   if( axval ) {
+
+/* Get the bounding box of the uncertainty region. */
+      astGetRegionBounds( unc, lbnd, ubnd );
+
+/* We fit the box one axis at a time. */
+      ok = 1;
+      for( ic = 0; ic < nc; ic++ ) {
+
+/* Find the first good value on this axis. */
+         for( ip = 0; ip < np; ip++ ) {
+            org = ptr[ ic ][ ip ];
+            axval[ ip ] = org;
+            if( org != AST__BAD ) break;
+         }
+
+/* Abort if all the axis values werebad. */
+         if( ip >= np ) {
+            ok = 0;
+            break;
+         }
+
+/* Find the upper and lower limits of the supplied mesh on this axis. */
+         lb = 0.0;
+         ub = 0.0;
+         ip++;
+         p = ptr[ ic ] + ip;
+         p0 = org;
+         d = 0.0;
+         for( ; ip < np; ip++, p++ ) {
+            dinc = astAxDistance( frm, ic + 1, p0, *p );
+            if( dinc != AST__BAD ) {
+               d += dinc;
+               if( d < lb ) lb = d;
+               if( d > ub ) ub = d;
+            }
+            axval[ ip ] = org + d;
+            p0 = *p;
+         }
+
+/* Now convert these relative offsets to actual axis values. */
+         lb += org;
+         ub += org;
+
+/* Now scan the list of axis values again, looking for values which are
+   "close to" either lower or upper bound. These will be the points which
+   are on the faces of the box which are orthogonal to the current axis. Here
+   "close to" means within 20 times the uncertainty associated with this
+   axis, or one tenth of the box size (which ever is smaller). We find the
+   mean and standard deviation of such "close" values, and then do a
+   single sigma-clipping iteration (at 3-sigma) to get rid of any values
+   which are on one of the other faces of the box. */
+
+         lim = 20*( ubnd[ ic ] - lbnd[ ic ] );
+         lim2 = 0.1*( ub - lb );
+         if( lim2 < lim ) lim = lim2;
+
+         sxl = 0.0;
+         sxl2 = 0.0;
+         nxl = 0;
+         sxu = 0.0;
+         sxu2 = 0.0;
+         nxu = 0;
+
+         p = axval;
+         for( ip = 0; ip < np; ip++, p++ ) {
+            if( *p != AST__BAD ) {
+               if( fabs( *p - lb ) <= lim ) {
+                  sxl += *p;
+                  sxl2 += (*p)*(*p);
+                  nxl++;
+               } else if( fabs( *p - ub ) <= lim ) {
+                  sxu += *p;
+                  sxu2 += (*p)*(*p);
+                  nxu++;
+               }
+            }
+         }
+
+         if( nxl > 0 ) {
+            mxl = sxl/nxl;
+            liml = sxl2/nxl - mxl*mxl;
+            eps = 100*mxl*DBL_EPSILON;
+            if( liml < eps*eps ) {
+               liml = eps;
+            } else {
+               liml = 3.0*sqrt( liml );
+            }
+         } else {
+            mxl = lb;
+            liml = 0.0;
+         }
+
+         if( nxu > 0 ) {
+            mxu = sxu/nxu;
+            limu = sxu2/nxu - mxu*mxu;
+            eps = 100*mxu*DBL_EPSILON;
+            if( limu < eps*eps ) {
+               limu = eps;
+            } else {
+               limu = 3.0*sqrt( limu );
+            }
+
+         } else {
+            mxu = ub;
+            limu = 0.0;
+         }
+
+         sxl = 0.0;
+         nxl = 0;
+         sxu = 0.0;
+         nxu = 0;
+
+         p = axval;
+         for( ip = 0; ip < np; ip++, p++ ) {
+            if( *p != AST__BAD ) {
+               if( fabs( *p - mxl ) <= liml ) {
+                  sxl += *p;
+                  nxl++;
+               } else if( fabs( *p - mxu ) <= limu ) {
+                  sxu += *p;
+                  nxu++;
+               }
+            }
+         }
+
+         if( nxl > 0 ) {
+            mxl = sxl/nxl;
+         } else {
+            mxl = lb;
+         }
+
+         if( nxu > 0 ) {
+            mxu = sxu/nxu;
+         } else {
+            mxu = ub;
+         }
+
+/* The resulting mean axis values are the bounds of the required box on
+   the current axis.*/
+         blbnd[ ic ] = mxl;
+         bubnd[ ic ] = mxu;
+      }
+
+/* If possible, create the returned Box. */
+      if( ok ) result = astBox( unc, 1, blbnd, bubnd, unc, " ", status );
+   }
+
+/* Free resources */
+   lbnd = astFree( lbnd );
+   ubnd = astFree( ubnd );
+   blbnd = astFree( blbnd );
+   bubnd = astFree( bubnd );
+   axval = astFree( axval );
+
+/* Return NULL if anything went wrong. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return the result.*/
+   return result;
+}
+
+static void Cache( AstBox *this, int lohi, int *status ){
+/*
+*  Name:
+*     Cache
+
+*  Purpose:
+*     Calculate intermediate values and cache them in the Box structure.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void Cache( AstRegion *this, int lohi, int *status )
+
+*  Class Membership:
+*     Box member function
+
+*  Description:
+*     This function uses the PointSet stored in the parent Region to calculate
+*     some intermediate values which are useful in other methods. These
+*     values are stored within the Box structure.
+
+*  Parameters:
+*     this
+*        Pointer to the Box.
+*     lohi
+*        Are the lo and hi arrays to be used?
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Local Variables: */
+   AstFrame *frm;
+   AstPointSet *pset;
+   AstRegion *unc;
+   double **ptr;
+   double *centre;
+   double *extent;
+   double *hi;
+   double *lbnd_unc;
+   double *geolen;
+   double *lo;
+   double *ubnd_unc;
+   double wid;
+   int i;
+   int nc;
+
+/* Check the global error status. Also return if the currently cached
+   information is usable. */
+   if ( !astOK || !this->stale ) return;
+
+/* Get the number of base Frame axes. */
+   nc = astGetNin( ((AstRegion *)this)->frameset );
+
+/* Allocate memory to store the half-width of the box on each axis. */
+   extent = (double *) astMalloc( sizeof( double )*(size_t) nc );
+
+/* Allocate memory to store the centre of the box on each axis. */
+   centre = (double *) astMalloc( sizeof( double )*(size_t) nc );
+
+/* Allocate memory to store the high and low bounds. */
+   hi = (double *) astMalloc( sizeof( double )*(size_t) nc );
+   lo = (double *) astMalloc( sizeof( double )*(size_t) nc );
+
+/* Memory to store the uncertainty bounding box */
+   lbnd_unc = astMalloc( sizeof( double)*(size_t) nc );
+   ubnd_unc = astMalloc( sizeof( double)*(size_t) nc );
+
+/* Memory to store the geodesic half-dimensions of the box. */
+   geolen = astMalloc( sizeof( double)*(size_t) nc );
+
+/* Get pointers to the coordinate data in the parent Region structure. */
+   pset = ((AstRegion *) this)->points;
+   ptr = astGetPoints( pset );
+
+/* Check pointers can be used safely. */
+   if( ptr ) {
+
+/* Store the centre and corner axis values. */
+      for( i = 0; i < nc; i++ ) {
+         centre[ i ] = ptr[ i ][ 0 ];
+         hi[ i ] = ptr[ i ][ 1 ];
+      }
+
+/* Calculate the geodesic half-dimensions of the box. */
+      frm = astGetFrame( ((AstRegion *) this)->frameset, AST__BASE );
+      GeoLengths( frm, nc, centre, hi, geolen, status );
+
+/* Calculate the half-width and store in the above array. Also store the
+   lower and upper bounds. */
+      for( i = 0; i < nc; i++ ) {
+         extent[ i ] = fabs( astAxDistance( frm, i + 1, ptr[ i ][ 1 ],
+                                            centre[ i ] ) );
+         lo[ i ] = centre[ i ] - extent[ i ];
+         hi[ i ] = centre[ i ] + extent[ i ];
+      }
+
+      frm = astAnnul( frm );
+
+/* Store the pointers to these arrays in the Box structure, and indicate
+   the information is usable. */
+      if( astOK ) {
+         astFree( this->extent );
+         astFree( this->centre );
+         astFree( this->lo );
+         astFree( this->hi );
+         astFree( this->geolen );
+         this->extent = extent;
+         this->centre = centre;
+         this->lo = lo;
+         this->hi = hi;
+         this->geolen = geolen;
+         this->stale = 0;
+         extent = NULL;
+         centre = NULL;
+         lo = NULL;
+         hi = NULL;
+         geolen = NULL;
+      }
+
+/* If lo and hi values are to be used, ensure they are expanded to at
+   least the width of an uncertainty box. */
+      if( lohi ) {
+
+/* If we are dealing with an unnegated closed Box or a negated open
+   Box, ensure that the box does not have zero width on any axis. We do
+   this by ensuring that the extent on all axes is at least half the
+   width  of the bounding box of the uncertainty Region. */
+         if(  astGetNegated( this ) != astGetClosed( this ) ) {
+
+/* Get the bounding box of the uncertainty Region in the base Frame of
+   the supplied Box. */
+            unc = astGetUncFrm( this, AST__BASE );
+            astGetRegionBounds( unc, lbnd_unc, ubnd_unc );
+
+/* Ensure the extents are at least half the width of the uncertainty
+   bounding box. */
+            for ( i = 0; i < nc; i++ ) {
+               wid = 0.5*( ubnd_unc[ i ] - lbnd_unc[ i ] );
+               if( this->extent[ i ] < wid ) {
+                  this->extent[ i ] = wid;
+                  this->lo[ i ] = this->centre[ i ] - wid;
+                  this->hi[ i ] = this->centre[ i ] + wid;
+               }
+            }
+
+/* Free resources. */
+            unc = astAnnul( unc );
+         }
+      }
+   }
+
+/* Annul the memory allocated above if an error occurred. */
+   if( !astOK ) {
+      extent = astFree( extent );
+      centre = astFree( centre );
+      lo = astFree( lo );
+      hi = astFree( hi );
+   }
+
+/* Free other resources */
+   lbnd_unc = astFree( lbnd_unc );
+   ubnd_unc = astFree( ubnd_unc );
+
+}
+
+static double *GeoCorner( AstFrame *frm, int nc, double *centre,
+                          double *geolen, double *corner, int *status ){
+/*
+*  Name:
+*     GeoCorner
+
+*  Purpose:
+*     Find the corner position implied by the supplied centre position
+*     and geodesic box dimensions.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     double *GeoCorner( AstFrame *frm, int nc, double *centre,
+*                        double *geolen, double *corner, int *status )
+
+*  Class Membership:
+*     Box member function
+
+*  Description:
+*     This function returns the corner position that is implied by the
+*     supplied centre position and geodesic box dimensions. The returned
+*     corner position is found by offsetting away from the supplied
+*     centre position along each axis in turn, by the geodesic distance
+*     specified in "geolen".
+
+*  Parameters:
+*     frm
+*        Defines the geometry of the axes.
+*     nc
+*        The number of Frame axes.
+*     centre
+*        Pointer to an array holding the box centre axis values.
+*     geolen
+*        Pointer to an array holding the geodesic distance corresponding
+*        to each half axis of the box.
+*     corner
+*        Pointer to an array in which to store the axis values at the
+*        returned corner position. If this is NULL a new array is
+*        allocated and a pointer to it returned as the function value.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the array holding the corner axis values. If a non-NULL
+*     value is supplied for parameter "corner", then the same value will
+*     be returned as the function value. Otherwise, the returned value
+*     will be a pointer to a newly allocated array that should be freed
+*     using astFree when no longer needed.
+
+*/
+
+/* Local Variables: */
+   double *p1;
+   double *p2;
+   double *p3;
+   double *pt;
+   double *result;
+   double *work1;
+   double *work2;
+   double off;
+   double off0;
+   int i;
+
+/* Initialise */
+   result = corner;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Ensure we have a results array. */
+   if( ! result ) result = astMalloc( sizeof( double )*nc );
+
+/* Also allocate two work arrays to hold a single position. */
+   work1 = astMalloc( sizeof( double )*nc );
+   work2 = astMalloc( sizeof( double )*nc );
+
+/* Check the pointers can be used safely. */
+   if( astOK ) {
+
+/* Select which array to use as the initial results array so that the
+   final results end up in the returned array. */
+      if( ( nc % 2 ) == 0 ) {
+         p1 = result;
+         p2 = work1;
+         p3 = work2;
+      } else {
+         p1 = work2;
+         p2 = work1;
+         p3 = result;
+      }
+
+/* Initialise the current corner position to be at the centre of the box. */
+      for( i = 0; i < nc; i++ ) p1[ i ] = centre[ i ];
+
+/* Loop round offsetting along each side of the box. */
+      for( i = 0; i < nc; i++ ) {
+
+/* In the p2 array put the axis values at a point which is offset
+   slightly along the current axis away from the current "corner"
+   position (p1). */
+         memcpy( p2, p1, sizeof( double )*nc );
+
+         if( geolen[ i ] != 0.0 ) {
+            off = 0.0001*fabs( geolen[ i ] );
+         } else {
+            off = 1.0E-6;
+         }
+
+         off0 = fabs( 1.0E-10*centre[ i ] );
+         if( off < off0 ) off = off0;
+         p2[ i ] += off;
+
+/* Offset away from the current corner position (p1) towards the position
+   found above (p2), moving by the geodesic distance supplied for this axis.
+   Put the resulting axis values in p3. */
+         astOffset( frm, p1, p2, geolen[ i ], p3 );
+
+/* Swap the p3 and p1 arrays so that the offset position found above (p3)
+   becomes the starting position (p1) for the next offset. */
+         pt = p1;
+         p1 = p3;
+         p3 = pt;
+      }
+   }
+
+/* Free resources */
+   work1 = astFree( work1 );
+   work2 = astFree( work2 );
+
+/* Return the result */
+   return result;
+}
+
+static double *GeoLengths( AstFrame *frm, int nc, double *centre,
+                           double *corner, double *geolen, int *status ){
+/*
+*  Name:
+*     GeoLengths
+
+*  Purpose:
+*     Find the geodesic dimensions of a box.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*      double *GeoLengths( AstFrame *frm, int nc, double *centre,
+*                          double *corner, double *geolen, int *status )
+
+*  Class Membership:
+*     Box member function
+
+*  Description:
+*     This function returns half the geodesic distance along each edge of
+*     the supplied box.
+
+*  Parameters:
+*     frm
+*        Defines the geometry of the axes.
+*     nc
+*        The number of Frame axes.
+*     centre
+*        Pointer to an array holding rhe box centre axis values.
+*     corner
+*        Pointer to an array holding the axis values at the corner
+*        position.
+*     geolen
+*        Pointer to an array in which to return the geodesic distances
+*        corresponding to each half axis of the box. If this is NULL a
+*        new array is allocated and a pointer to it returned as the
+*        function value.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the array holding the geodesic half-dimensions of the box.
+*     If a non-NULL value is supplied for parameter "corner", then the same
+*     value will be returned as the function value. Otherwise, the
+*     returned value will be a pointer to a newly allocated array that
+*     should be freed using astFree when no longer needed.
+
+*/
+
+/* Local Variables: */
+   double *result;
+   double *p1;
+   double *p2;
+   int i;
+
+/* Initialise */
+   result = geolen;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Ensure we have a results array. */
+   if( ! result ) result = astMalloc( sizeof( double )*nc );
+
+/* Also allocate two work arrays to hold a single position. */
+   p1 = astMalloc( sizeof( double )*nc );
+   p2 = astMalloc( sizeof( double )*nc );
+
+/* Check the pointers can be used safely. */
+   if( astOK ) {
+
+/* Initialise the coords as the start and end of the line. */
+      memcpy( p1, centre, sizeof( double )*nc );
+      memcpy( p2, centre, sizeof( double )*nc );
+
+/* Loop round finding the geodesic half-length of each side of the box. */
+      for( i = 0; i < nc; i++ ) {
+
+/* The end of the line is the same as the start of the line, except that
+   it has the corner value for the current axis. */
+         p2[ i ] = corner[ i ];
+
+/* Find and return the geodesic distance along the line (i.e. from p1 to
+   p2). */
+         result[ i ] = astDistance( frm, p1, p2 );
+
+/* The start of the next line wil lbe at the end of the current line. */
+         p1[ i ] = corner[ i ];
+      }
+   }
+
+/* Free resources */
+   p1 = astFree( p1 );
+   p2 = astFree( p2 );
+
+/* Return the result */
+   return result;
+}
+
+static int GetObjSize( AstObject *this_object, int *status ) {
+/*
+*  Name:
+*     GetObjSize
+
+*  Purpose:
+*     Return the in-memory size of an Object.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     int GetObjSize( AstObject *this, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astGetObjSize protected
+*     method inherited from the parent class).
+
+*  Description:
+*     This function returns the in-memory size of the supplied Box,
+*     in bytes.
+
+*  Parameters:
+*     this
+*        Pointer to the Box.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     The Object size, in bytes.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global status set, or if it should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstBox *this;         /* Pointer to Box structure */
+   int result;                /* Result value to return */
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointers to the Box structure. */
+   this = (AstBox *) this_object;
+
+/* Invoke the GetObjSize method inherited from the parent class, and then
+   add on any components of the class structure defined by thsi class
+   which are stored in dynamically allocated memory. */
+   result = (*parent_getobjsize)( this_object, status );
+
+   result += astTSizeOf( this->extent );
+   result += astTSizeOf( this->centre );
+   result += astTSizeOf( this->lo );
+   result += astTSizeOf( this->hi );
+   result += astTSizeOf( this->geolen );
+
+/* If an error occurred, clear the result value. */
+   if ( !astOK ) result = 0;
+
+/* Return the result, */
+   return result;
+}
+
+void astInitBoxVtab_(  AstBoxVtab *vtab, const char *name, int *status ) {
+/*
+*+
+*  Name:
+*     astInitBoxVtab
+
+*  Purpose:
+*     Initialise a virtual function table for a Box.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void astInitBoxVtab( AstBoxVtab *vtab, const char *name )
+
+*  Class Membership:
+*     Box vtab initialiser.
+
+*  Description:
+*     This function initialises the component of a virtual function
+*     table which is used by the Box class.
+
+*  Parameters:
+*     vtab
+*        Pointer to the virtual function table. The components used by
+*        all ancestral classes will be initialised if they have not already
+*        been initialised.
+*     name
+*        Pointer to a constant null-terminated character string which contains
+*        the name of the class to which the virtual function table belongs (it
+*        is this pointer value that will subsequently be returned by the Object
+*        astClass function).
+*-
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
+   AstRegionVtab *region;        /* Pointer to Region component of Vtab */
+   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
+
+/* Check the local error status. */
+   if ( !astOK ) return;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Initialize the component of the virtual function table used by the
+   parent class. */
+   astInitRegionVtab( (AstRegionVtab *) vtab, name );
+
+/* Store a unique "magic" value in the virtual function table. This
+   will be used (by astIsABox) to determine if an object belongs
+   to this class.  We can conveniently use the address of the (static)
+   class_check variable to generate this unique value. */
+   vtab->id.check = &class_check;
+   vtab->id.parent = &(((AstRegionVtab *) vtab)->id);
+
+/* Initialise member function pointers. */
+/* ------------------------------------ */
+/* Store pointers to the member functions (implemented here) that provide
+   virtual methods for this class. */
+   vtab->BoxPoints = BoxPoints;
+
+/* Save the inherited pointers to methods that will be extended, and
+   replace them with pointers to the new member functions. */
+   object = (AstObjectVtab *) vtab;
+   mapping = (AstMappingVtab *) vtab;
+   region = (AstRegionVtab *) vtab;
+
+   parent_getobjsize = object->GetObjSize;
+   object->GetObjSize = GetObjSize;
+
+   parent_transform = mapping->Transform;
+   mapping->Transform = Transform;
+
+   parent_simplify = mapping->Simplify;
+   mapping->Simplify = Simplify;
+
+   parent_setnegated = region->SetNegated;
+   region->SetNegated = SetNegated;
+
+   parent_setunc = region->SetUnc;
+   region->SetUnc = SetUnc;
+
+   parent_setclosed = region->SetClosed;
+   region->SetClosed = SetClosed;
+
+   parent_clearnegated = region->ClearNegated;
+   region->ClearNegated = ClearNegated;
+
+   parent_clearclosed = region->ClearClosed;
+   region->ClearClosed = ClearClosed;
+
+   parent_setregfs = region->SetRegFS;
+   region->SetRegFS = SetRegFS;
+
+   parent_resetcache = region->ResetCache;
+   region->ResetCache = ResetCache;
+
+   mapping->MapMerge = MapMerge;
+
+/* Store replacement pointers for methods which will be over-ridden by
+   new member functions implemented here. */
+   region->RegBaseGrid = RegBaseGrid;
+   region->RegBaseMesh = RegBaseMesh;
+   region->RegBasePick = RegBasePick;
+   region->RegBaseBox = RegBaseBox;
+   region->RegPins = RegPins;
+   region->RegTrace = RegTrace;
+   region->RegCentre = RegCentre;
+
+/* Declare the copy constructor, destructor and class dump
+   functions. */
+   astSetDelete( vtab, Delete );
+   astSetCopy( vtab, Copy );
+   astSetDump( vtab, Dump, "Box", "Axis intervals" );
+
+/* If we have just initialised the vtab for the current class, indicate
+   that the vtab is now initialised, and store a pointer to the class
+   identifier in the base "object" level of the vtab. */
+   if( vtab == &class_vtab ) {
+      class_init = 1;
+      astSetVtabClassIdentifier( vtab, &(vtab->id) );
+   }
+}
+
+static int MakeGrid( int naxes, double **ptr, int ip, double *lbnd,
+                     double *ubnd, int *np_axes, int np_axis, int iaxis,
+                     double axval, int *status ){
+/*
+*  Name:
+*     MakeGrid
+
+*  Purpose:
+*     Create a grid covering the entire volume of a specified box.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     int MakeGrid( int naxes, double **ptr, int ip, double *lbnd,
+*                   double *ubnd, int *np_axes, int np_axis, int iaxis,
+*                   double axval, int *status )
+
+*  Class Membership:
+*     Box member function
+
+*  Description:
+*     This function creates an evenly sampled grid covering a given
+*     volume of n-D space, putting the coordinates at the sample points
+*     into a supplied array and returning the number of samples added.
+*     Optionally, the volume can be assumed to have a constant value on
+*     a specified axis.
+
+*  Parameters:
+*     naxes
+*        The number of axes.
+*     ptr
+*        Pointer to an array with "naxes" elements. Each element is a
+*        pointer to an array in which to store the values for the axis.
+*     ip
+*        The index of the first point to be added to the "ptr" arrays.
+*     lbnd
+*        Pointer to an array containing the lower axis bounds of the
+*        volume to be sampled.
+*     ubnd
+*        Pointer to an array containing the upper axis bounds of the
+*        volume to be sampled.
+*     np_axes
+*        Pointer to an array with one element for every axis, giving the
+*        number of samples along each axis (except, optionally, the axis
+*        specified by "iaxis"). The first sample (sample 0) for each axis
+*        will be at the lower bound given in "lbnd" and the last sample
+*        (sample "np_axes[iax]-1") will be at the upper bound given in
+*        "ubnd". If NULL, then the single scalar avalue given by
+*        "np_axis" is used for all axes.
+*     np_axis
+*        The constant number of samples along every axis (except, optionally,
+*        the axis specified by "iaxis"). The first sample (sample 0) for each
+*        axis will be at the lower bound given in "lbnd" and the last sample
+*        (sample "np_axis-1") will be at the upper bound given in "ubnd".
+*        The supplied value is only used if "np_axes" is NULL.
+*     iaxis
+*        The index of an axis which has constant value in the volume, or
+*        -1 if all axes are to span the full volume given by lbnd/ubnd.
+*        The values in "lbnd" and "ubnd" are ignored for this axis and all
+*        sample positions will have the axis value given by "axval".
+*     axval
+*        The constant value for the axis with index "iaxis". Ignored if
+*        "iaxis" is -1.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     The number of points added to the "ptr" arrays.
+
+*/
+
+/* Local Variables: */
+   double *step;         /* Pointer to array holding axis step sizes */
+   int *maxi;            /* Pointer to array of maximum index values */
+   int *pi;              /* Pointer to array holding current sample indices */
+   int i;                /* Axis index */
+   int ipp;              /* Index of next point */
+   int nsamp;            /* Number of samples along the axis */
+
+/* Check the global error status. */
+   if ( !astOK ) return 0;
+
+/* Allocate memory to hold the max indices on each axis. */
+   maxi = astMalloc( sizeof( int )*(size_t) naxes );
+
+/* Allocate memory to hold the indices of the current position.*/
+   pi = astMalloc( sizeof( int )*(size_t) naxes );
+
+/* Allocate memory to hold the step size for each axis. */
+   step = astMalloc( sizeof( double )*(size_t) naxes );
+   if( astOK ) {
+
+/* For every axis, set up the step size, initialise the current position to
+   the lower bound, and store a modified upper limit which includes some
+   safety marging to allow for rounding errors. */
+      for( i = 0; i < naxes; i++ ) {
+         nsamp = np_axes ? np_axes[ i ] : np_axis;
+         step[ i ] = ( ubnd[ i ] - lbnd[ i ] )/( nsamp - 1 );
+         pi[ i ] = 0;
+         maxi[ i ] = nsamp - 1;
+      }
+
+      if( iaxis >= 0 ) {
+         maxi[ iaxis ] = 0;
+         step[ iaxis ] = 0.0;
+         pi[ iaxis ] = 0;
+      }
+
+/* Initialise the index of the next position to store. */
+      ipp = ip;
+
+/* Loop round adding points to the array until the whole volume has been
+   done. */
+      i = 0;
+      while( i < naxes ) {
+
+/* Add the current point to the supplied array,and increment the index of
+   the next point to add. */
+         for( i = 0; i < naxes; i++ ) {
+            if( i == iaxis ) {
+               ptr[ i ][ ipp ] = axval;
+            } else {
+               ptr[ i ][ ipp ] = lbnd[ i ] + pi[ i ]*step[ i ];
+            }
+         }
+         ipp++;
+
+/* We now move the current position on to the next sample */
+         i = 0;
+         while( i < naxes ) {
+            pi[ i ]++;
+            if( pi[ i ] > maxi[ i ] ) {
+               pi[ i ] = 0;
+               i++;
+            } else {
+               break;
+            }
+         }
+      }
+   } else {
+      ipp = ip;
+   }
+
+/* Free resources. */
+   maxi = astFree( maxi );
+   pi = astFree( pi );
+   step = astFree( step );
+
+/* Return the result. */
+   return astOK ? ( ipp - ip ): 0 ;
+}
+
+static int MapMerge( AstMapping *this, int where, int series, int *nmap,
+                     AstMapping ***map_list, int **invert_list, int *status ) {
+/*
+*  Name:
+*     MapMerge
+
+*  Purpose:
+*     Simplify a sequence of Mappings containing a Box.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "mapping.h"
+*     int MapMerge( AstMapping *this, int where, int series, int *nmap,
+*                   AstMapping ***map_list, int **invert_list, int *status )
+
+*  Class Membership:
+*     Box method (over-rides the protected astMapMerge method
+*     inherited from the Region class).
+
+*  Description:
+*     This function attempts to simplify a sequence of Mappings by
+*     merging a nominated Box in the sequence with its neighbours,
+*     so as to shorten the sequence if possible.
+*
+*     In many cases, simplification will not be possible and the
+*     function will return -1 to indicate this, without further
+*     action.
+*
+*     In most cases of interest, however, this function will either
+*     attempt to replace the nominated Box with a Mapping which it
+*     considers simpler, or to merge it with the Mappings which
+*     immediately precede it or follow it in the sequence (both will
+*     normally be considered). This is sufficient to ensure the
+*     eventual simplification of most Mapping sequences by repeated
+*     application of this function.
+*
+*     In some cases, the function may attempt more elaborate
+*     simplification, involving any number of other Mappings in the
+*     sequence. It is not restricted in the type or scope of
+*     simplification it may perform, but will normally only attempt
+*     elaborate simplification in cases where a more straightforward
+*     approach is not adequate.
+
+*  Parameters:
+*     this
+*        Pointer to the nominated Box which is to be merged with
+*        its neighbours. This should be a cloned copy of the Box
+*        pointer contained in the array element "(*map_list)[where]"
+*        (see below). This pointer will not be annulled, and the
+*        Box it identifies will not be modified by this function.
+*     where
+*        Index in the "*map_list" array (below) at which the pointer
+*        to the nominated Box resides.
+*     series
+*        A non-zero value indicates that the sequence of Mappings to
+*        be simplified will be applied in series (i.e. one after the
+*        other), whereas a zero value indicates that they will be
+*        applied in parallel (i.e. on successive sub-sets of the
+*        input/output coordinates).
+*     nmap
+*        Address of an int which counts the number of Mappings in the
+*        sequence. On entry this should be set to the initial number
+*        of Mappings. On exit it will be updated to record the number
+*        of Mappings remaining after simplification.
+*     map_list
+*        Address of a pointer to a dynamically allocated array of
+*        Mapping pointers (produced, for example, by the astMapList
+*        method) which identifies the sequence of Mappings. On entry,
+*        the initial sequence of Mappings to be simplified should be
+*        supplied.
+*
+*        On exit, the contents of this array will be modified to
+*        reflect any simplification carried out. Any form of
+*        simplification may be performed. This may involve any of: (a)
+*        removing Mappings by annulling any of the pointers supplied,
+*        (b) replacing them with pointers to new Mappings, (c)
+*        inserting additional Mappings and (d) changing their order.
+*
+*        The intention is to reduce the number of Mappings in the
+*        sequence, if possible, and any reduction will be reflected in
+*        the value of "*nmap" returned. However, simplifications which
+*        do not reduce the length of the sequence (but improve its
+*        execution time, for example) may also be performed, and the
+*        sequence might conceivably increase in length (but normally
+*        only in order to split up a Mapping into pieces that can be
+*        more easily merged with their neighbours on subsequent
+*        invocations of this function).
+*
+*        If Mappings are removed from the sequence, any gaps that
+*        remain will be closed up, by moving subsequent Mapping
+*        pointers along in the array, so that vacated elements occur
+*        at the end. If the sequence increases in length, the array
+*        will be extended (and its pointer updated) if necessary to
+*        accommodate any new elements.
+*
+*        Note that any (or all) of the Mapping pointers supplied in
+*        this array may be annulled by this function, but the Mappings
+*        to which they refer are not modified in any way (although
+*        they may, of course, be deleted if the annulled pointer is
+*        the final one).
+*     invert_list
+*        Address of a pointer to a dynamically allocated array which,
+*        on entry, should contain values to be assigned to the Invert
+*        attributes of the Mappings identified in the "*map_list"
+*        array before they are applied (this array might have been
+*        produced, for example, by the astMapList method). These
+*        values will be used by this function instead of the actual
+*        Invert attributes of the Mappings supplied, which are
+*        ignored.
+*
+*        On exit, the contents of this array will be updated to
+*        correspond with the possibly modified contents of the
+*        "*map_list" array.  If the Mapping sequence increases in
+*        length, the "*invert_list" array will be extended (and its
+*        pointer updated) if necessary to accommodate any new
+*        elements.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     If simplification was possible, the function returns the index
+*     in the "map_list" array of the first element which was
+*     modified. Otherwise, it returns -1 (and makes no changes to the
+*     arrays supplied).
+
+*  Notes:
+*     - A value of -1 will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*/
+
+/* Local Variables: */
+   AstBox *oldbox;       /* Pointer to supplied Box */
+   AstMapping *map;      /* Pointer to adjacent Mapping */
+   AstMapping *new;      /* Simplified or merged Region */
+   int i1;               /* Index of first Mapping merged */
+   int i;                /* Loop counter */
+   int result;           /* Result value to return */
+
+/* Initialise. */
+   result = -1;
+   i1 = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the Box. */
+   oldbox = (AstBox *) this;
+
+/* First of all, see if the Box can be replaced by a simpler Region,
+   without reference to the neighbouring Regions in the list.           */
+/* =====================================================================*/
+
+/* Try to simplify the box. If the pointer value has changed, we assume
+   some simplification took place. */
+   new = astSimplify( oldbox );
+   if( new != (AstMapping *) oldbox ) {
+
+/* Annul the Box pointer in the list and replace it with the new Region
+   pointer, and indicate that the forward transformation of the returned
+   Region should be used (not really needed but keeps things clean). */
+      (void) astAnnul( ( *map_list )[ where ] );
+      ( *map_list )[ where ] = new;
+      ( *invert_list )[ where ] = 0;
+
+/* Return the index of the first modified element. */
+      result = where;
+
+/* If the Box itself could not be simplified, see if it can be merged
+   with the Regions on either side of it in the list. We can only merge
+   in parallel. */
+/* =====================================================================*/
+   } else if( ! series ){
+      new = astAnnul( new );
+
+/* Attempt to merge the Box with its lower neighbour (if any). */
+      if( where > 0 ) {
+         i1 = where - 1;
+         map = ( *map_list )[ where - 1 ];
+         if( astIsARegion( map ) ) {
+            new = (AstMapping *) MergeBox( oldbox, (AstRegion *) map, 0,
+                                           status );
+         }
+      }
+
+/* If this did not produced a merged Region, attempt to merge the Box with its
+   upper neighbour (if any). */
+      if( !new && where < *nmap - 1 ) {
+         i1 = where;
+         map = ( *map_list )[ where + 1 ];
+         if( astIsARegion( map ) ) {
+            new = (AstMapping *) MergeBox( oldbox, (AstRegion *) map, 1,
+                                           status );
+         }
+      }
+
+/* If succesfull... */
+      if( new ){
+
+/* Annul the first of the two Mappings, and replace it with the merged
+   Region. Also clear the invert flag. */
+         (void) astAnnul( ( *map_list )[ i1 ] );
+         ( *map_list )[ i1 ] = new;
+         ( *invert_list )[ i1 ] = 0;
+
+/* Annul the second of the two Mappings, and shuffle down the rest of the
+   list to fill the gap. */
+         (void) astAnnul( ( *map_list )[ i1 + 1 ] );
+         for ( i = i1 + 2; i < *nmap; i++ ) {
+            ( *map_list )[ i - 1 ] = ( *map_list )[ i ];
+            ( *invert_list )[ i - 1 ] = ( *invert_list )[ i ];
+         }
+
+/* Clear the vacated element at the end. */
+         ( *map_list )[ *nmap - 1 ] = NULL;
+         ( *invert_list )[ *nmap - 1 ] = 0;
+
+/* Decrement the Mapping count and return the index of the first
+   modified element. */
+         ( *nmap )--;
+         result = i1;
+      }
+
+   } else {
+      new = astAnnul( new );
+   }
+
+/* Return the result. */
+   return result;
+}
+
+static AstRegion *MergeBox( AstBox *this, AstRegion *reg, int boxfirst,
+                            int *status ) {
+/*
+*  Name:
+*     MergeBox
+
+*  Purpose:
+*     Attempt to merge a Box with another Region to form a Region of higher
+*     dimensionality.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstRegion *MergeBox( AstBox *this, AstRegion *reg, int boxfirst, int *status )
+
+*  Class Membership:
+*     Box member function.
+
+*  Description:
+*     This function attempts to combine the supplied Regions together
+*     into a Region of higher dimensionality.
+
+*  Parameters:
+*     this
+*        Pointer to a Box.
+*     reg
+*        Pointer to another Region.
+*     boxfirst
+*        If non-zero, then the Box axes are put first in the new Region.
+*        Otherwise, the other Region's axes are put first.
+*     status
+*        Pointer to the inherited status value.
+
+*  Returned Value:
+*     A pointer to a new region, or NULL if the supplied Regions could
+*     not be merged.
+*/
+
+/* Local Variables: */
+   AstFrame *bfrm;           /* Pointer to base Frame for "result" */
+   AstFrame *cfrm;           /* Pointer to current Frame for "result" */
+   AstFrame *frm_reg;        /* Pointer to Frame from "reg" */
+   AstFrame *frm_this;       /* Pointer to Frame from "this" */
+   AstMapping *bcmap;        /* Base->current Mapping for "result" */
+   AstMapping *map_reg;      /* Base->current Mapping from "reg" */
+   AstMapping *map_this;     /* Base->current Mapping from "this" */
+   AstMapping *sbunc;        /* Simplified uncertainty */
+   AstPointSet *pset_new;    /* PointSet holding PointList axis values for new */
+   AstPointSet *pset_reg;    /* PointSet holding PointList axis values for reg */
+   AstRegion *bunc;          /* Base Frame uncertainty Region */
+   AstRegion *new;           /* Pointer to new Interval in base Frame */
+   AstRegion *result;        /* Pointer to returned Interval in current Frame */
+   AstRegion *unc_reg;       /* Current Frame uncertainty Region from "reg" */
+   AstRegion *unc_this;      /* Current Frame uncertainty Region from "this" */
+   double **ptr_new;         /* Pointers to arrays holding new axis values */
+   double **ptr_reg;         /* Pointers to arrays holding reg axis values */
+   double *centre;           /* Array to hold box centre axis values */
+   double *corner;           /* Array to hold box corner axis values */
+   double *lbnd;             /* Array to hold lower axis bounds */
+   double *p;                /* Pointer to next input value */
+   double *q;                /* Pointer to next output value */
+   double *ubnd;             /* Array to hold upper axis bounds */
+   double fac_reg;           /* Ratio of used to default MeshSize for "reg" */
+   double fac_this;          /* Ratio of used to default MeshSize for "this" */
+   double temp;              /* Temporary storage */
+   int i;                    /* Loop count */
+   int j;                    /* Loop count */
+   int msz_reg;              /* Original MeshSize for "reg" */
+   int msz_reg_set;          /* Was MeshSize originally set for "reg"? */
+   int msz_this;             /* Original MeshSize for "this" */
+   int msz_this_set;         /* Was MeshSize originally set for "this"? */
+   int nax;                  /* Number of axes in "result" */
+   int nax_reg;              /* Number of axes in "reg" */
+   int nax_this;             /* Number of axes in "this" */
+   int neg_reg;              /* Negated attribute value for other supplied Region */
+   int neg_this;             /* Negated attribute value for supplied Box  */
+   int npnt;                 /* Number of points in PointList */
+   int ok;                   /* Can supplied Regions be merged? */
+
+/* Initialise */
+   result = NULL;
+
+/* Check the local error status. */
+   if ( !astOK ) return result;
+
+/* Get the Closed attributes of the two Regions. They must be the same in
+   each Region if we are to merge the Regions. In addition, in order to
+   merge, either both Regions must have a defined uncertainty, or neither
+   Region must have a defined Uncertainty. */
+   if( astGetClosed( this ) == astGetClosed( reg ) &&
+       astTestUnc( this ) == astTestUnc( reg ) ) {
+
+/* Get the Nagated attributes of the two Regions. */
+      neg_this = astGetNegated( this );
+      neg_reg = astGetNegated( reg );
+
+/* Get the number of axes in the two supplied Regions. */
+      nax_reg = astGetNaxes( reg );
+      nax_this = astGetNaxes( this );
+
+/* If the Regions can be combined, get the number of axes the
+   combination will have. */
+      nax = nax_reg + nax_this;
+
+/* Get the base Frames from the two Region FrameSets, and combine them
+   into a single CmpFrame that will be used to create any new Region. */
+      frm_this = astGetFrame( ((AstRegion *) this)->frameset, AST__BASE );
+      frm_reg = astGetFrame( reg->frameset, AST__BASE );
+
+      if( boxfirst ) {
+         bfrm = (AstFrame *) astCmpFrame( frm_this, frm_reg, "", status );
+      } else {
+         bfrm = (AstFrame *) astCmpFrame( frm_reg, frm_this, "", status );
+      }
+
+      frm_this = astAnnul( frm_this );
+      frm_reg = astAnnul( frm_reg );
+
+/* Indicate we do not yet have a merged Region. */
+      new = NULL;
+
+/* First attempt to merge with another Box. The result will be a Box. Both
+   Boxes must be un-negated. */
+      if( astIsABox( reg ) && !neg_this && !neg_reg ) {
+
+/* Allocate memory to store the centre and corner of the returned Box. */
+         centre = astMalloc( sizeof( double )*(size_t) nax );
+         corner = astMalloc( sizeof( double )*(size_t) nax );
+
+/* Copy the centres and corners from the supplied Boxes into the above
+   arrays, in the requested order. */
+         if( boxfirst ) {
+            astBoxPoints( this, centre, corner );
+            astBoxPoints( reg, centre + nax_this, corner + nax_this );
+         } else {
+            astBoxPoints( reg, centre, corner );
+            astBoxPoints( this, centre + nax_reg, corner + nax_reg );
+         }
+
+/*  Create the new Box, initially with no uncertainty. */
+         new = (AstRegion *) astBox( bfrm, 0, centre, corner, NULL, "",
+                                     status );
+
+/* Free resources .*/
+         centre = astFree( centre );
+         corner = astFree( corner );
+
+/* Now attempt to merge with an Interval. The result will be an Interval.
+   Both Intervals must be un-negated. */
+      } else if( astIsAInterval( reg )  && !neg_this && !neg_reg ) {
+
+/* Allocate memory to store the bounds of the returned Interval. */
+         lbnd = astMalloc( sizeof( double )*(size_t) nax );
+         ubnd = astMalloc( sizeof( double )*(size_t) nax );
+
+/* Copy the centre and corner from the supplied Box into the required part
+   of the above arrays. */
+         if( boxfirst ) {
+            centre = lbnd;
+            corner = ubnd;
+         } else {
+            centre = lbnd + nax_reg;
+            corner = ubnd + nax_reg;
+         }
+         astBoxPoints( this, centre, corner );
+
+/* Convert these centre and corner positions into upper and lower bounds. */
+         if( astOK ) {
+            for( i = 0; i < nax_this; i++ ) {
+               centre[ i ] = 2*centre[ i ] - corner[ i ];
+               if( centre[ i ] > corner[ i ] ) {
+                  temp = centre[ i ];
+                  centre[ i ] = corner[ i ];
+                  corner[ i ] = temp;
+               }
+            }
+         }
+
+/* Get the bounds from the interval and add them into the above arrays. */
+         if( boxfirst ) {
+            astIntervalPoints( reg, lbnd + nax_this, ubnd + nax_this );
+         } else {
+            astIntervalPoints( reg, lbnd, ubnd );
+         }
+
+/*  Create the new Interval, initially with no uncertainty. */
+         new = (AstRegion *) astInterval( bfrm, lbnd, ubnd, NULL, "",
+                                          status );
+
+/* Free resources .*/
+         lbnd = astFree( lbnd );
+         ubnd = astFree( ubnd );
+
+/* Now attempt to merge with a NullRegion. The result will be an
+   Interval. The NullRegion must be negated and the Box must not. */
+      } else if( astIsANullRegion( reg ) && !neg_this && neg_reg ) {
+
+/* Allocate memory to store the bounds of the returned Interval. */
+         lbnd = astMalloc( sizeof( double )*(size_t) nax );
+         ubnd = astMalloc( sizeof( double )*(size_t) nax );
+
+/* Copy the centre and corner from the supplied Box into the required part
+   of the above arrays. */
+         if( boxfirst ) {
+            centre = lbnd;
+            corner = ubnd;
+         } else {
+            centre = lbnd + nax_reg;
+            corner = ubnd + nax_reg;
+         }
+         astBoxPoints( this, centre, corner );
+
+/* Convert these centre and corner positions into upper and lower bounds. */
+         if( astOK ) {
+            for( i = 0; i < nax_this; i++ ) {
+               centre[ i ] = 2*centre[ i ] - corner[ i ];
+               if( centre[ i ] > corner[ i ] ) {
+                  temp = centre[ i ];
+                  centre[ i ] = corner[ i ];
+                  corner[ i ] = temp;
+               }
+            }
+
+/* Fill the other axes with bad values to indicate they are unbounded. */
+            if( boxfirst ) {
+               for( i = nax_this; i < nax; i++ ) {
+                  lbnd[ i ] = AST__BAD;
+                  ubnd[ i ] = AST__BAD;
+               }
+            } else {
+               for( i = 0; i < nax_reg; i++ ) {
+                  lbnd[ i ] = AST__BAD;
+                  ubnd[ i ] = AST__BAD;
+               }
+            }
+
+/*  Create the new Interval, initially with no uncertainty. */
+            new = (AstRegion *) astInterval( bfrm, lbnd, ubnd, NULL, "",
+                                             status );
+         }
+
+/* Free resources .*/
+         lbnd = astFree( lbnd );
+         ubnd = astFree( ubnd );
+
+/* Now attempt to merge with a PointList. The result will be a PointList.
+   Both Regions must be un-negated. */
+      } else if( astIsAPointList( reg ) && !neg_this && !neg_reg ) {
+
+/* We can only do this if the Box has zero width on each axis (i.e.
+   represents a point). Get the Box centre and corner. */
+         centre = astMalloc( sizeof( double )*(size_t) nax_this );
+         corner = astMalloc( sizeof( double )*(size_t) nax_this );
+         astBoxPoints( this, centre, corner );
+
+/* Get the size of the Box's uncertainty region. */
+         lbnd = astMalloc( sizeof( double )*(size_t) nax_this );
+         ubnd = astMalloc( sizeof( double )*(size_t) nax_this );
+         bunc = astGetUncFrm( this, AST__BASE );
+         astGetRegionBounds( bunc, lbnd, ubnd );
+
+/* Set "ok" to zero if the Box does not have zero width on any axis. Here
+   "zero width" means a width less than half the uncertainty on the axis. */
+         if( astOK ) {
+
+            ok = 1;
+            for( i = 0; i < nax_this; i++ ) {
+               if( fabs( centre[ i ] - corner[ i ] ) >
+                   0.25*fabs( ubnd[ i ] - lbnd[ i ] ) ) {
+                  ok = 0;
+                  break;
+               }
+            }
+
+/* If the Box is a point, we go on to create a new PointList. */
+            if( ok ) {
+
+/* Get a PointSet holding the axis values in the supplied PointList data.
+   Also get the number of points in the PointSet and pointers to the arrays
+   holding the axis values. */
+               astPointListPoints( reg, &pset_reg );
+               npnt = astGetNpoint( pset_reg );
+               ptr_reg = astGetPoints( pset_reg );
+
+/*  Create a new PointSet with room for the same number of points, but
+    with the extra required axes. Get pointers to its axis arrays. */
+               pset_new = astPointSet( npnt, nax, "", status );
+               ptr_new = astGetPoints( pset_new );
+
+/* Copy the PointList axis values into the new PointSet, and then include
+   the extra axis values defined by the Box to each point. */
+               if( astOK ) {
+
+                  for( j = 0; j < nax_reg; j++ ) {
+                     p = ptr_reg[ j ];
+                     q = ptr_new[ boxfirst ? nax_this + j : j ];
+                     for( i = 0; i < npnt; i++ ) *(q++) = *(p++);
+                  }
+
+                  for( j = 0; j < nax_this; j++ ) {
+                     p = centre + j;
+                     q = ptr_new[ boxfirst ? j : nax_reg + j ];
+                     for( i = 0; i < npnt; i++ ) *(q++) = *p;
+                  }
+
+/*  Create the new PointList, initially with no uncertainty. */
+                  new = (AstRegion *) astPointList( bfrm, pset_new, NULL,
+                                                    "", status );
+               }
+
+/* Free resources .*/
+               pset_new = astAnnul( pset_new );
+               pset_reg = astAnnul( pset_reg );
+            }
+         }
+         centre = astFree( centre );
+         corner = astFree( corner );
+         lbnd = astFree( lbnd );
+         ubnd = astFree( ubnd );
+         bunc = astAnnul( bunc );
+
+      }
+
+/* If a new Region was created above, propagate remaining attributes of
+   the supplied Region to it. */
+      if( new ) {
+         astRegOverlay( new, this, 1 );
+
+/* The above Prism constructors create the Prism with the correct value
+   for the Nagated attribute (i.e. zero). Ensure the above call to
+   astRegOverlay has not changed this. */
+         astClearNegated( new );
+
+/* If both the supplied Regions have uncertainty, assign the new Region an
+   uncertainty. */
+         if( astTestUnc( this ) && astTestUnc( reg ) ) {
+
+/* Get the uncertainties from the two supplied Regions. */
+            unc_this = astGetUncFrm( this, AST__BASE );
+            unc_reg = astGetUncFrm( reg, AST__BASE );
+
+/* Combine them into a single Region (a Prism), in the correct order. */
+            if( boxfirst ) {
+               bunc = (AstRegion *) astPrism( unc_this, unc_reg, "", status );
+            } else {
+               bunc = (AstRegion *) astPrism( unc_reg, unc_this, "", status );
+            }
+
+/* Attempt to simplify the Prism. */
+            sbunc = astSimplify( bunc );
+
+/* Use the simplified Prism as the uncertainty for the returned Region. */
+            astSetUnc( new, sbunc );
+
+/* Free resources. */
+            sbunc = astAnnul( sbunc );
+            bunc = astAnnul( bunc );
+            unc_reg = astAnnul( unc_reg );
+            unc_this = astAnnul( unc_this );
+         }
+
+/* Get the current Frames from the two Region FrameSets, and combine them
+   into a single CmpFrame. */
+         frm_this = astGetFrame( ((AstRegion *) this)->frameset, AST__CURRENT );
+         frm_reg = astGetFrame( reg->frameset, AST__CURRENT );
+
+         if( boxfirst ) {
+            cfrm = (AstFrame *) astCmpFrame( frm_this, frm_reg, "", status );
+         } else {
+            cfrm = (AstFrame *) astCmpFrame( frm_reg, frm_this, "", status );
+         }
+
+/* Get the base -> current Mappings from the two Region FrameSets, and
+   combine them into a single parallel CmpMap that connects bfrm and cfrm. */
+         map_this = astGetMapping( ((AstRegion *) this)->frameset, AST__BASE,
+                                   AST__CURRENT );
+         map_reg = astGetMapping( reg->frameset, AST__BASE, AST__CURRENT );
+
+         if( boxfirst ) {
+            bcmap = (AstMapping *) astCmpMap( map_this, map_reg, 0, "",
+                                              status );
+         } else {
+            bcmap = (AstMapping *) astCmpMap( map_reg, map_this, 0, "",
+                                              status );
+         }
+
+/* Map the new Region into the new current Frame. */
+         result = astMapRegion( new, bcmap, cfrm );
+
+/* The filling factor in the returned is the product of the filling
+   factors for the two supplied Regions. */
+         if( astTestFillFactor( reg ) || astTestFillFactor( this ) ) {
+            astSetFillFactor( result, astGetFillFactor( reg )*
+                                      astGetFillFactor( this ) );
+         }
+
+/* If the MeshSize value is set in either supplied Region, set a value
+   for the returned Region which scales the default value by the
+   product of the scaling factors for the two supplied Regions. First see
+   if either MeshSize value is set. */
+         msz_this_set = astTestMeshSize( this );
+         msz_reg_set = astTestMeshSize( reg );
+         if( msz_this_set || msz_reg_set ) {
+
+/* If so, get the two MeshSize values (one of which may be a default
+   value), and then clear them so that the default value will be returned
+   in future. */
+            msz_this = astGetMeshSize( this );
+            msz_reg = astGetMeshSize( reg );
+            astClearMeshSize( this );
+            astClearMeshSize( reg );
+
+/* Get the ratio of the used MeshSize to the default MeshSize for both
+   Regions. */
+            fac_this = (double)msz_this/(double)astGetMeshSize( this );
+            fac_reg = (double)msz_reg/(double)astGetMeshSize( reg );
+
+/* The MeshSize of the returned Returned is the default value scaled by
+   the product of the two ratios found above. */
+            astSetMeshSize( result, fac_this*fac_reg*astGetMeshSize( result ) );
+
+/* Re-instate the original MeshSize values for the supplied Regions (if
+   set) */
+            if( msz_this_set ) astSetMeshSize( this, msz_this );
+            if( msz_reg_set ) astSetMeshSize( reg, msz_reg );
+         }
+
+/* Free remaining resources */
+         frm_this = astAnnul( frm_this );
+         frm_reg = astAnnul( frm_reg );
+         map_this = astAnnul( map_this );
+         map_reg = astAnnul( map_reg );
+         bcmap = astAnnul( bcmap );
+         new = astAnnul( new );
+         cfrm = astAnnul( cfrm );
+      }
+      bfrm = astAnnul( bfrm );
+   }
+
+/* If an error has occurred, annul the returned pointer. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static void RegBaseBox( AstRegion *this_region, double *lbnd, double *ubnd, int *status ){
+/*
+*  Name:
+*     RegBaseBox
+
+*  Purpose:
+*     Returns the bounding box of an un-negated Region in the base Frame of
+*     the encapsulated FrameSet.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void RegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astRegBaseBox protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns the upper and lower axis bounds of a Region in
+*     the base Frame of the encapsulated FrameSet, assuming the Region
+*     has not been negated. That is, the value of the Negated attribute
+*     is ignored.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     lbnd
+*        Pointer to an array in which to return the lower axis bounds
+*        covered by the Region in the base Frame of the encapsulated
+*        FrameSet. It should have at least as many elements as there are
+*        axes in the base Frame.
+*     ubnd
+*        Pointer to an array in which to return the upper axis bounds
+*        covered by the Region in the base Frame of the encapsulated
+*        FrameSet. It should have at least as many elements as there are
+*        axes in the base Frame.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Local Variables: */
+   AstBox *this;                 /* Pointer to Box structure */
+   double axcen;                 /* Central axis value */
+   double axlen;                 /* Half width of box on axis */
+   int i;                        /* Axis index */
+   int nc;                       /* No. of axes in base Frame */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get a pointer to the Box structure */
+   this = (AstBox *) this_region;
+
+/* Ensure cached information is up to date. */
+   Cache( this, 0, status );
+
+/* Get the number of base Frame axes in the Region. */
+   nc = astGetNin( this_region->frameset );
+
+/* The first point is the centre of the box, the second point is the half
+   size of the box on each axis.*/
+   for( i = 0; i < nc; i++ ) {
+      axcen = this->centre[ i ];
+      axlen = this->extent[ i ];
+      lbnd[ i ] = axcen - axlen;
+      ubnd[ i ] = axcen + axlen;
+   }
+}
+
+static AstPointSet *RegBaseGrid( AstRegion *this, int *status ){
+/*
+*  Name:
+*     RegBaseGrid
+
+*  Purpose:
+*     Return a PointSet containing points spread through the volume of a
+*     Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstPointSet *RegBaseGrid( AstRegion *this, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astRegBaseGrid protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a PointSet containing a set of points spread
+*     through the volume of the supplied Box. The points refer to the base
+*     Frame of the encapsulated FrameSet.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the PointSet. If the Region is unbounded, a NULL pointer
+*     will be returned.
+
+*  Notes:
+*    - A NULL pointer is returned if an error has already occurred, or if
+*    this function should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstFrame *frm;                 /* Base Frame in encapsulated FrameSet */
+   AstPointSet *result;           /* Returned pointer */
+   double *lbnd;                  /* Pointer to array of lower bounds of box */
+   double *ubnd;                  /* Pointer to array of upper bounds of box */
+   int meshsize;                  /* Requested size of grid */
+   int naxes;                     /* No. of axes in base Frame */
+
+/* Initialise */
+   result = NULL;
+
+/* Check the local error status. */
+   if ( !astOK ) return NULL;
+
+/* If the Region structure contains a pointer to a PointSet holding
+   a previously created grid, return it. */
+   if( this->basegrid ) {
+      result = astClone( this->basegrid );
+
+/* Otherwise, create a new one, but only if the Box is bounded. */
+   } else if( astGetBounded( this ) ) {
+
+/* Get the base Frame in the Region's FrameSet. */
+      frm = astGetFrame( this->frameset, AST__BASE );
+
+/* Get the number of axes in the base Frame */
+      naxes = astGetNaxes( frm );
+
+/* Get the bounds of the Region in the base Frame. */
+      lbnd = astMalloc( sizeof( double )*(size_t) naxes );
+      ubnd = astMalloc( sizeof( double )*(size_t) naxes );
+      astRegBaseBox( this, lbnd, ubnd );
+
+/* Get the number of points which would be used to create a boundary
+   mesh. We use the same number to determine the number of points in the
+   grid. */
+      meshsize = astGetMeshSize( this );
+
+/* Create the PointSet holding the grid. */
+      result = astFrameGrid( frm, meshsize, lbnd, ubnd );
+
+/* Save the returned pointer in the Region structure so that it does not
+   need to be created again next time this function is called. */
+      if( astOK && result ) this->basegrid = astClone( result );
+
+/* Free remaining resources. */
+      frm = astAnnul( frm );
+      lbnd = astFree( lbnd );
+      ubnd = astFree( ubnd );
+   }
+
+/* Annul the result if an error occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return the result */
+   return result;
+}
+
+static AstPointSet *RegBaseMesh( AstRegion *this, int *status ){
+/*
+*  Name:
+*     RegBaseMesh
+
+*  Purpose:
+*     Return a PointSet containing a mesh of points on the boundary of a
+*     Region in its base Frame.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstPointSet *RegBaseMesh( AstRegion *this, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astRegBaseMesh protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a PointSet containing a mesh of points on the
+*     boundary of the Region. The points refer to the base Frame of
+*     the encapsulated FrameSet.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the PointSet. The axis values in this PointSet will have
+*     associated accuracies derived from the accuracies which were
+*     supplied when the Region was created.
+
+*  Notes:
+*    - A NULL pointer is returned if an error has already occurred, or if
+*    this function should fail for any reason.
+
+*/
+
+/* Local Constants: */
+#define NP_EDGE 50                /* No. of points for determining geodesic
+                                     length of each axis. */
+
+/* Local Variables: */
+   AstFrame *frm;                 /* Base Frame in encapsulated FrameSet */
+   AstFrame *pfrm0;               /* Primary Frame defining axis 0 */
+   AstFrame *pfrm1;               /* Primary Frame defining axis 1 */
+   AstPointSet *result;           /* Returned pointer */
+   const char *class0;            /* Pointer to class string from pfrm0 */
+   const char *class1;            /* Pointer to class string from pfrm1 */
+   double **ptr;                  /* Pointers to data */
+   double *ax;                    /* Pointer to next first axis value */
+   double *ay;                    /* Pointer to next second axis value */
+   double *lbnd;                  /* Pointer to array of lower bounds of box */
+   double *ubnd;                  /* Pointer to array of lower bounds of box */
+   double c[ 5 ][ 2 ];            /* Positions of corners for 2D boxes */
+   double dx;                     /* Increment along first axis of 2D box */
+   double dy;                     /* Increment along second axis of 2D box */
+   double edge_len[ 4 ];          /* Length of each edge of 2D boundary */
+   double lax;                    /* Previous value on first axis */
+   double lay;                    /* Previous value on second axis */
+   double len;                    /* Length of edge of 2D boundary */
+   double p0[ 2 ];                /* Position in 2D Frame */
+   double p1[ 2 ];                /* Position in 2D Frame */
+   double ppd;                    /* Points per unit distance */
+   double total_len;              /* Total length of 2D boundary */
+   int flat;                      /* Assume Frame geometry is flat? */
+   int i;                         /* Point index */
+   int iaxis;                     /* Axis index */
+   int iedge;                     /* Edge index */
+   int ip;                        /* Index of next point */
+   int metric;                    /* Does Frame have a usable metric? */
+   int nax0;                      /* No. of axes in first primary Frame */
+   int nax1;                      /* No. of axes in second primary Frame */
+   int naxes;                     /* No. of axes in base Frame */
+   int np;                        /* No. of points in returned PointSet */
+   int np0;                       /* No. of points per edge */
+   int np_axis;                   /* No. of points per axis in ND box */
+   int np_edge[ 4 ];              /* No. of points per edge in 2D box */
+   int paxis;                     /* Axis index in primary Frame */
+   int single;                    /* Does the Box occupy a single point? */
+
+/* Initialise */
+   result= NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* If the Region structure contains a pointer to a PointSet holding
+   a previously created mesh, return it. */
+   if( this->basemesh ) {
+      result = astClone( this->basemesh );
+
+/* Otherwise, create a new mesh. */
+   } else {
+
+/* Get the base Frame in the Region's FrameSet. */
+      frm = astGetFrame( this->frameset, AST__BASE );
+
+/* Get the number of axes in the base Frame */
+      naxes = astGetNaxes( frm );
+
+/* Get the bounds of the Region in the base Frame. */
+      lbnd = astMalloc( sizeof( double )*(size_t) naxes );
+      ubnd = astMalloc( sizeof( double )*(size_t) naxes );
+      astRegBaseBox( this, lbnd, ubnd );
+
+/* Get the requested number of points to put on the mesh. */
+      np = astGetMeshSize( this );
+
+/* See if the box occupies a single point. */
+      single = 1;
+      for( i = 0; i < naxes; i++ ) {
+         if( ubnd[ i ] > lbnd[ i ] ) {
+            single = 0;
+            break;
+         }
+      }
+
+/* If so, we return a PointSet holding a single point. */
+      if( single ) {
+         result = astPointSet( 1, naxes, "", status );
+         ptr = astGetPoints( result );
+         if( astOK ) {
+            for( i = 0; i < naxes; i++ ) {
+               ptr[ i ][ 0 ] = 0.5*( lbnd[ 0 ] + ubnd[ 0 ] );
+            }
+         }
+
+/* Otherwise, first deal with 1-D boxes. */
+      } else if( naxes == 1 ) {
+
+/* The boundary of a 1-D box consists of 2 points - the two extreme values.
+   Create a PointSet to hold 2 1-D values, and store the extreme values. */
+         result = astPointSet( 2, 1, "", status );
+         ptr = astGetPoints( result );
+         if( astOK ) {
+            ptr[ 0 ][ 0 ] = lbnd[ 0 ];
+            ptr[ 0 ][ 1 ] = ubnd[ 0 ];
+         }
+
+/* Now deal with 2-D boxes. */
+      } else if( naxes == 2 ){
+
+/* Store the coords of each corner for easy access. */
+         c[ 0 ][ 0 ] = lbnd[ 0 ];
+         c[ 0 ][ 1 ] = lbnd[ 1 ];
+         c[ 1 ][ 0 ] = lbnd[ 0 ];
+         c[ 1 ][ 1 ] = ubnd[ 1 ];
+         c[ 2 ][ 0 ] = ubnd[ 0 ];
+         c[ 2 ][ 1 ] = ubnd[ 1 ];
+         c[ 3 ][ 0 ] = ubnd[ 0 ];
+         c[ 3 ][ 1 ] = lbnd[ 1 ];
+         c[ 4 ][ 0 ] = lbnd[ 0 ];
+         c[ 4 ][ 1 ] = lbnd[ 1 ];
+
+/* See if we can assume that the frame has flat geometry. This is the case
+   if both axes belong to simple Frames, or are 1D, but may not be the case
+   if either axis does not belong to a simple Frame that has more than 1
+   axis. */
+         astPrimaryFrame( frm, 0, &pfrm0, &paxis );
+         astPrimaryFrame( frm, 1, &pfrm1, &paxis );
+         class0 = astGetClass( pfrm0 );
+         class1 = astGetClass( pfrm1 );
+         nax0 = astGetNaxes( pfrm0 );
+         nax1 = astGetNaxes( pfrm1 );
+         if( astOK ) {
+            flat = ( !strcmp( class0, "Frame" ) || nax0 == 1 ) &&
+                   ( !strcmp( class1, "Frame" ) || nax1 == 1 );
+         } else {
+            flat = 0;
+         }
+
+/* Our choice of distribution of points depends on whether the axes have the
+   same units or not. If the axes have the same units, or if they share the
+   same primary Frame, then we assume that the axes span some space in which
+   a single "distance" is defined. If not, (e.g. for a Frame representing
+   frequency in Hz on one axis - typical value 1.0E10, and slit position in
+   metres on the other axis - typical value 1.0E-2) we assume that "distance"
+   is defined differently for each axis. The primary frame requirement is
+   because some classes of Frame (e.g. SkyFrame) have a defined distance,
+   even though the Units attributes for its axes may differ (since Units
+   refers to the external representation - e.g. hours and degrees for a
+   SkyFrame - rather than the internal representation). */
+         if( astOK && !strcmp( astGetUnit( frm, 0 ), astGetUnit( frm, 1 ) ) ) {
+            metric = 1;
+         } else {
+            metric = ( pfrm0 == pfrm1 );
+         }
+
+/* If we have a usable metric, distribute the points according to the aspect
+   ratio of the box (i.e. the shorter box sides gets fewer points). */
+         if( metric ){
+
+/* Find the approximate geodesic length of each edge of the box. Since
+   the edges of the box may not correspond to single geodesic (e.g. a
+   line of constant latitude is not a geodesic), we do this by testing
+   a set of points along each edge of the box and finding the total of the
+   geodesic distances between each pair of adjacent points. Initialise the
+   total length round all edges. */
+            total_len = 0.0;
+
+/* Do each edge in turn.*/
+            for( iedge = 0; iedge < 4; iedge++ ) {
+
+/* Find the increment in x and y between adjacent points along this edge.
+   We put a point at each end of the edge. Note, one of dx or dy will be
+   zero since the edges are parallel to the axes. */
+               dx = ( c[ iedge + 1 ][ 0 ] - c[ iedge ][ 0 ] )/( NP_EDGE - 1 );
+               dy = ( c[ iedge + 1 ][ 1 ] - c[ iedge ][ 1 ] )/( NP_EDGE - 1 );
+
+/* Store the coords of the first point. */
+               p0[ 0 ] = c[ iedge ][ 0 ];
+               p0[ 1 ] = c[ iedge ][ 1 ];
+
+/* Initialise the length of this edge and loop round the remaining points. */
+               len = 0.0;
+               for( i = 1; i < NP_EDGE; i++ ) {
+
+/* Save the position of the previous point. */
+                  p1[ 0 ] = p0[ 0 ];
+                  p1[ 1 ] = p0[ 1 ];
+
+/* Find the position of the new point. */
+                  p0[ 0 ] = p1[ 0 ] + dx;
+                  p0[ 1 ] = p1[ 1 ] + dy;
+
+/* Increment the length of the edge by the geodesic distance from this point
+   to the previous point. If the Frame is flat, this is simple (given that we
+   know that one of dx and dy must be zero). */
+                  if( flat ) {
+                     len += fabs( dx + dy );
+                  } else {
+                     len += astDistance( frm, p0, p1 );
+                  }
+               }
+
+/* Save the length of this edge, and also form the total length round all
+   edges. */
+               edge_len[ iedge ] = len;
+               total_len += len;
+            }
+
+/* Find the average number of points per unit geodesic distance around the
+   boundary. */
+            if( total_len > 0.0 ) {
+               ppd = np / total_len;
+
+/* Use this, with the geodesic length of each edge found above, to find the
+   number of points to put along each edge of the boundary, and update the
+   total number of points to use. In the returned boundary we put a point at
+   the start of each edge but not at the end (since the end of one edge will
+   be the start of the next edge). */
+               np = 0;
+               for( iedge = 0; iedge < 4; iedge++ ) {
+                  np_edge[ iedge ] = (int) ( edge_len[ iedge ]*ppd );
+                  if( np_edge[ iedge ] == 0 ) np_edge[ iedge ] = 1;
+                  np += np_edge[ iedge ];
+               }
+
+/* Report error if total length round box is zero. */
+            } else if( astOK ) {
+               astError( AST__INTER, "astRegBaseMesh(%s): Distance around "
+                         "box perimeter is zero (internal AST programming "
+                         "error).", status, astGetClass( this ) );
+            }
+
+/* If the Frame has no usable metric, give an equal number of points
+   (equal to a quarter of the total) to all 4 sides of the box. */
+         } else {
+            np0 = (int) ( 0.25*np );
+            np = 0;
+            for( iedge = 0; iedge < 4; iedge++ ) {
+               np_edge[ iedge ] = np0;
+               np += np_edge[ iedge ];
+            }
+         }
+
+/* Create a PointSet with enough room and get a pointer to its data arrays. */
+         result = astPointSet( np, 2, "", status );
+         ptr = astGetPoints( result );
+         if( astOK ) {
+
+/* Initialise pointers to the first element for each axis in the returned
+   PointSet. */
+            ax = ptr[ 0 ];
+            ay = ptr[ 1 ];
+
+/* Loop round each edge. */
+            for( iedge = 0; iedge < 4; iedge++ ) {
+
+/* Find the increment in x and y between adjacent points along this edge. */
+               dx = ( c[ iedge + 1 ][ 0 ] - c[ iedge ][ 0 ] )/ np_edge[ iedge ];
+               dy = ( c[ iedge + 1 ][ 1 ] - c[ iedge ][ 1 ] )/ np_edge[ iedge ];
+
+/* Store the first point. */
+               lax = c[ iedge ][ 0 ];
+               lay = c[ iedge ][ 1 ];
+               *(ax++) = lax;
+               *(ay++) = lay;
+
+/* Loop round the remaining points, incrementing the pointers at the same
+   time. */
+               for( i = 1; i < np_edge[ iedge ]; i++, ax++, ay++ ) {
+
+/* Find the position of the new point and store it. */
+                  lax += dx;
+                  lay += dy;
+                  *ax = lax;
+                  *ay = lay;
+               }
+            }
+         }
+
+/* Free resources. */
+         pfrm0 = astAnnul( pfrm0 );
+         pfrm1 = astAnnul( pfrm1 );
+
+/* Now deal with boxes with more than 2 dimensions. */
+      } else {
+
+/* Number of samples along each edge of the hyper-cube. */
+         np_axis = 1 + (int) pow( np/(2*naxes), 1.0/(naxes-1) );
+         if( np_axis < 2 ) np_axis = 2;
+
+/* Each face of the hyper-cube will have np_axis**(naxes-1) points, and there
+   are 2*naxes faces. Create a PointSet with the correct number of
+   points. */
+         np = 2*naxes;
+         for( iaxis = 1; iaxis < naxes; iaxis++ ) np *= np_axis;
+         result = astPointSet( np, naxes, "", status );
+         ptr = astGetPoints( result );
+         if( astOK ) {
+
+/* Initialise the index of the next point to add into the PointSet. */
+            ip = 0;
+
+/* Create the upper and lower faces for each axis in turn. */
+            for( iaxis = 0; iaxis < naxes; iaxis++ ) {
+
+/* First do the upper face for this axis. */
+               ip += MakeGrid( naxes, ptr, ip, lbnd, ubnd, NULL, np_axis,
+                               iaxis, ubnd[ iaxis ], status );
+
+/* Now do the lower face for this axis. */
+               ip += MakeGrid( naxes, ptr, ip, lbnd, ubnd, NULL, np_axis,
+                               iaxis, lbnd[ iaxis ], status );
+            }
+
+/* Remove any unused space at the end of the PointSet. */
+            if( ip < np ) astSetNpoint( result, ip );
+         }
+      }
+
+/* Same the returned pointer in the Region structure so that it does not
+   need to be created again next time this function is called. */
+      if( astOK && result ) this->basemesh = astClone( result );
+
+/* Free resources. */
+      frm = astAnnul( frm );
+      lbnd = astFree( lbnd );
+      ubnd = astFree( ubnd );
+   }
+
+/* Annul the result if an error has occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return a pointer to the output PointSet. */
+   return result;
+
+/* Undefine macros local to this function. */
+#undef NP_EDGE
+
+}
+
+static AstRegion *RegBasePick( AstRegion *this_region, int naxes, const int *axes,
+                               int *status ){
+/*
+*  Name:
+*     RegBasePick
+
+*  Purpose:
+*     Return a Region formed by picking selected base Frame axes from the
+*     supplied Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstRegion *RegBasePick( AstRegion *this, int naxes, const int *axes,
+*                             int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astRegBasePick protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function attempts to return a Region that is spanned by selected
+*     axes from the base Frame of the encapsulated FrameSet of the supplied
+*     Region. This may or may not be possible, depending on the class of
+*     Region. If it is not possible a NULL pointer is returned.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     naxes
+*        The number of base Frame axes to select.
+*     axes
+*        An array holding the zero-based indices of the base Frame axes
+*        that are to be selected.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the Region, or NULL if no region can be formed.
+
+*  Notes:
+*    - A NULL pointer is returned if an error has already occurred, or if
+*    this function should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstFrame *bfrm;         /* The base Frame in the supplied Region */
+   AstFrame *frm;          /* The base Frame in the returned Region */
+   AstPointSet *pset;      /* Holds axis values defining the supplied Region */
+   AstRegion *bunc;        /* The uncertainty in the supplied Region */
+   AstRegion *result;      /* Returned Region */
+   AstRegion *unc;         /* The uncertainty in the returned Region */
+   double **ptr;           /* Holds axis values defining the supplied Region */
+   double *cen;            /* Base Frm axis values at centre of returned Box */
+   double *cor;            /* Base Frm axis values at a corner of returned Box */
+   int i;                  /* Index of axis within returned Region */
+
+/* Initialise */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the base Frame of the encapsulated FrameSet. */
+   bfrm = astGetFrame( this_region->frameset, AST__BASE );
+
+/* Create a Frame by picking the selected axes from the base Frame of the
+   encapsulated FrameSet. */
+   frm = astPickAxes( bfrm, naxes, axes, NULL );
+
+/* Get the uncertainty Region (if any) within the base Frame of the supplied
+   Region, and select the required axes from it. If the resulting Object
+   is not a Region, annul it so that the returned Region will have no
+   uncertainty. */
+   if( astTestUnc( this_region ) ) {
+      bunc = astGetUncFrm( this_region, AST__BASE );
+      unc = astPickAxes( bunc, naxes, axes, NULL );
+      bunc = astAnnul( bunc );
+
+      if( ! astIsARegion( unc ) ) unc = astAnnul( unc );
+
+   } else {
+      unc = NULL;
+   }
+
+/* Get pointers to the coordinate data in the parent Region structure. */
+   pset = this_region->points;
+   ptr = astGetPoints( pset );
+
+/* Get space to hold the centre and corner of the Box in the new Frame. */
+   cen = astMalloc( sizeof( *cen )*naxes );
+   cor = astMalloc( sizeof( *cor )*naxes );
+
+/* Check pointers can be used safely. */
+   if( astOK ) {
+
+/* Copy the centre and corner axis values for the selected axes into the
+   arrays allocated above. */
+      for( i = 0; i < naxes; i++ ) {
+         cen[ i ] = ptr[ axes[ i ] ][ 0 ];
+         cor[ i ] = ptr[ axes[ i ] ][ 1 ];
+      }
+
+/* Create the new Box. */
+      result = (AstRegion *) astBox( frm, 0, cen, cor, unc, "", status );
+   }
+
+/* Free resources */
+   frm = astAnnul( frm );
+   bfrm = astAnnul( bfrm );
+   if( unc ) unc = astAnnul( unc );
+   cen = astFree( cen );
+   cor = astFree( cor );
+
+/* Return a NULL pointer if an error has occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static double *RegCentre( AstRegion *this_region, double *cen, double **ptr,
+                          int index, int ifrm, int *status ){
+/*
+*  Name:
+*     RegCentre
+
+*  Purpose:
+*     Re-centre a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     double *RegCentre( AstRegion *this, double *cen, double **ptr,
+*                        int index, int ifrm, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astRegCentre protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function shifts the centre of the supplied Region to a
+*     specified position, or returns the current centre of the Region.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     cen
+*        Pointer to an array of axis values, giving the new centre.
+*        Supply a NULL value for this in order to use "ptr" and "index" to
+*        specify the new centre.
+*     ptr
+*        Pointer to an array of points, one for each axis in the Region.
+*        Each pointer locates an array of axis values. This is the format
+*        returned by the PointSet method astGetPoints. Only used if "cen"
+*        is NULL.
+*     index
+*        The index of the point within the arrays identified by "ptr" at
+*        which is stored the coords for the new centre position. Only used
+*        if "cen" is NULL.
+*     ifrm
+*        Should be AST__BASE or AST__CURRENT. Indicates whether the centre
+*        position is supplied and returned in the base or current Frame of
+*        the FrameSet encapsulated within "this".
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     If both "cen" and "ptr" are NULL then a pointer to a newly
+*     allocated dynamic array is returned which contains the centre
+*     coords of the Region. This array should be freed using astFree when
+*     no longer needed. If either of "ptr" or "cen" is not NULL, then a
+*     NULL pointer is returned.
+
+*  Notes:
+*    - Some Region sub-classes do not have a centre. Such classes will report
+*    an AST__INTER error code if this method is called with either "ptr" or
+*    "cen" not NULL. If "ptr" and "cen" are both NULL, then no error is
+*    reported if this method is invoked on a Region of an unsuitable class,
+*    but NULL is always returned.
+
+*/
+
+/* Local Variables: */
+   AstBox *this;       /* Pointer to Box structure */
+   AstFrame *frm;      /* Pointer to Box's base Frame */
+   double **rptr;      /* Data pointers for Region PointSet */
+   double *bc;         /* Base Frame centre position */
+   double *corner;     /* Array holding corner axis values */
+   double *result;     /* Returned pointer */
+   double *tmp;        /* Temporary array pointer */
+   double axval;       /* Axis value */
+   int ic;             /* Coordinate index */
+   int ncb;            /* Number of base frame coordinate values per point */
+   int ncc;            /* Number of current frame coordinate values per point */
+
+/* Initialise */
+   result = NULL;
+
+/* Check the local error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the Box structure. */
+   this = (AstBox *) this_region;
+
+/* First ensure cached information (which includes the centre coords)
+   is up to date. */
+   Cache( this, 0, status );
+
+/* Get the number of axis values per point in the base and current Frames. */
+   ncb = astGetNin( this_region->frameset );
+   ncc = astGetNout( this_region->frameset );
+
+/* If the centre coords are to be returned, return either a copy of the
+   base Frame centre coords, or transform the base Frame centre coords
+   into the current Frame. First ensure cached information (which
+   includes the centre coords) is up to date. */
+   if( !ptr && !cen ) {
+      if( ifrm == AST__CURRENT ) {
+         result = astRegTranPoint( this_region, this->centre, 1, 1 );
+      } else {
+         result = astStore( NULL, this->centre, sizeof( double )*ncb );
+      }
+
+/* Otherwise, we store the supplied new centre coords and return a NULL
+   pointer. */
+   } else {
+
+/* Get a pointer to the axis values stored in the Region structure. */
+      rptr = astGetPoints( this_region->points );
+
+/* Check pointers can be used safely */
+      if( astOK ) {
+
+/* If the centre position was supplied in the current Frame, find the
+   corresponding base Frame position... */
+         if( ifrm == AST__CURRENT ) {
+            if( cen ) {
+               bc = astRegTranPoint( this_region, cen, 1, 0 );
+            } else {
+               tmp = astMalloc( sizeof( double)*(size_t)ncc );
+               if( astOK ) {
+                  for( ic = 0; ic < ncc; ic++ ) tmp[ ic ] = ptr[ ic ][ index ];
+               }
+               bc = astRegTranPoint( this_region, tmp, 1, 0 );
+               tmp = astFree( tmp );
+            }
+
+/* Replace any bad centre values with their current values. */
+            for( ic = 0; ic < ncb; ic++ ) {
+               if( bc[ ic ] ==  AST__BAD ) bc[ ic ] = this->centre[ ic ];
+            }
+
+/* If the centre position was supplied in the base Frame, store the
+   centre coords in this->centre, skipping bad values. */
+         } else {
+            bc = this->centre;
+            for( ic = 0; ic < ncb; ic++ ) {
+               axval = cen ? cen[ ic ] : ptr[ ic ][ index ];
+               if( axval != AST__BAD ) bc[ ic ] = axval;
+            }
+         }
+
+/* Find the coordinates at the new box corner. */
+         frm = astGetFrame( this_region->frameset, AST__BASE );
+         corner = GeoCorner( frm, ncb, bc, this->geolen, NULL, status );
+         frm = astAnnul( frm );
+
+/* ... and change the coords in the parent Region structure. */
+         for( ic = 0; ic < ncb; ic++ ) {
+            rptr[ ic ][ 0 ] = bc[ ic ];
+            rptr[ ic ][ 1 ] = corner[ ic ];
+         }
+
+/* Free resources */
+         if( ifrm == AST__CURRENT ) bc = astFree( bc );
+         corner = astFree( corner );
+
+/* Indicate the cached info in the Box structure is out of date. */
+         astResetCache( this );
+
+/* Any base Frame mesh or grid is now no good, so annul it. */
+         if( this_region->basemesh ) this_region->basemesh = astAnnul( this_region->basemesh );
+         if( this_region->basegrid ) this_region->basegrid = astAnnul( this_region->basegrid );
+
+      }
+   }
+
+
+/* Return the result. */
+   return result;
+}
+
+static int RegPins( AstRegion *this_region, AstPointSet *pset, AstRegion *unc,
+                    int **mask, int *status ){
+/*
+*  Name:
+*     RegPins
+
+*  Purpose:
+*     Check if a set of points fall on the boundary of a given Box.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     int RegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
+*                  int **mask, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astRegPins protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a flag indicating if the supplied set of
+*     points all fall on the boundary of the given Box.
+*
+*     Some tolerance is allowed, as specified by the uncertainty Region
+*     stored in the supplied Box "this", and the supplied uncertainty
+*     Region "unc" which describes the uncertainty of the supplied points.
+
+*  Parameters:
+*     this
+*        Pointer to the Box.
+*     pset
+*        Pointer to the PointSet. The points are assumed to refer to the
+*        base Frame of the FrameSet encapsulated by "this".
+*     unc
+*        Pointer to a Region representing the uncertainties in the points
+*        given by "pset". The Region is assumed to represent the base Frame
+*        of the FrameSet encapsulated by "this". Zero uncertainity is assumed
+*        if NULL is supplied.
+*     mask
+*        Pointer to location at which to return a pointer to a newly
+*        allocated dynamic array of ints. The number of elements in this
+*        array is equal to the value of the Npoint attribute of "pset".
+*        Each element in the returned array is set to 1 if the
+*        corresponding position in "pset" is on the boundary of the Region
+*        and is set to zero otherwise. A NULL value may be supplied
+*        in which case no array is created. If created, the array should
+*        be freed using astFree when no longer needed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Non-zero if the points all fall on the boundary of the given
+*     Region, to within the tolerance specified. Zero otherwise.
+
+*/
+
+/* Local variables: */
+   AstBox *large_box;           /* Box slightly larger than "this" */
+   AstBox *small_box;           /* Box slightly smaller than "this" */
+   AstBox *this;                /* Pointer to the Box structure. */
+   AstFrame *frm;               /* Base Frame in supplied Box */
+   AstPointSet *ps1;            /* Points masked by larger Box */
+   AstPointSet *ps2;            /* Points masked by larger and smaller Boxes */
+   AstRegion *tunc;             /* Uncertainity Region from "this" */
+   double **ptr;                /* Pointer to axis values in "ps2" */
+   double *large;               /* A corner position in the larger Box */
+   double *safe;                /* An interior point in "this" */
+   double *lbnd_tunc;           /* Lower bounds of "this" uncertainty Region */
+   double *lbnd_unc;            /* Lower bounds of supplied uncertainty Region */
+   double *p;                   /* Pointer to next axis value */
+   double *small;               /* A corner position in the smaller Box */
+   double *ubnd_tunc;           /* Upper bounds of "this" uncertainty Region */
+   double *ubnd_unc;            /* Upper bounds of supplied uncertainty Region */
+   double *wid;                 /* Widths of "this" border */
+   int i;                       /* Axis index */
+   int j;                       /* Point index */
+   int nc;                      /* No. of axes in Box base frame */
+   int np;                      /* No. of supplied points */
+   int result;                  /* Returned flag */
+
+/* Initialise */
+   result = 0;
+   if( mask ) *mask = NULL;
+
+/* Check the inherited status. */
+   if( !astOK ) return result;
+
+/* Get a pointer to the Box structure. */
+   this = (AstBox *) this_region;
+
+/* Ensure cached information is up to date. */
+   Cache( this, 0, status );
+
+/* Get the number of base Frame axes in the Box, and check the supplied
+   PointSet has the same number of axis values per point. */
+   frm = astGetFrame( this_region->frameset, AST__BASE );
+   nc = astGetNaxes( frm );
+   if( astGetNcoord( pset ) != nc && astOK ) {
+      astError( AST__INTER, "astRegPins(%s): Illegal number of axis "
+                "values per point (%d) in the supplied PointSet - should be "
+                "%d (internal AST programming error).", status, astGetClass( this ),
+                astGetNcoord( pset ), nc );
+   }
+
+/* Get the number of axes in the uncertainty Region and check it is the
+   same as above. */
+   if( unc && astGetNaxes( unc ) != nc && astOK ) {
+      astError( AST__INTER, "astRegPins(%s): Illegal number of axes (%d) "
+                "in the supplied uncertainty Region - should be "
+                "%d (internal AST programming error).", status, astGetClass( this ),
+                astGetNaxes( unc ), nc );
+   }
+
+/* Get the centre of the region in the base Frame. We use this as a "safe"
+   interior point within the region. */
+   safe = astRegCentre( this, NULL, NULL, 0, AST__BASE );
+
+/* We now find the maximum distance on each axis that a point can be from the
+   boundary of the Box for it still to be considered to be on the boundary.
+   First get the Region which defines the uncertainty within the Box being
+   checked (in its base Frame), re-centre it on the interior point found
+   above (to avoid problems if the uncertainty region straddles a
+   discontinuity), and get its bounding box. */
+   tunc = astGetUncFrm( this, AST__BASE );
+   if( safe ) astRegCentre( tunc, safe, NULL, 0, AST__CURRENT );
+   lbnd_tunc = astMalloc( sizeof( double )*(size_t) nc );
+   ubnd_tunc = astMalloc( sizeof( double )*(size_t) nc );
+   astGetRegionBounds( tunc, lbnd_tunc, ubnd_tunc );
+
+/* Also get the Region which defines the uncertainty of the supplied
+   points and get its bounding box. First re-centre the uncertainty at the
+   interior position to avoid problems from uncertainties that straddle a
+   discontinuity. */
+   if( unc ) {
+      if( safe ) astRegCentre( unc, safe, NULL, 0, AST__CURRENT );
+      lbnd_unc = astMalloc( sizeof( double )*(size_t) nc );
+      ubnd_unc = astMalloc( sizeof( double )*(size_t) nc );
+      astGetRegionBounds( unc, lbnd_unc, ubnd_unc );
+   } else {
+      lbnd_unc = NULL;
+      ubnd_unc = NULL;
+   }
+
+/* The required border width for each axis is half of the total width
+   of the two bounding boxes. Use a zero sized box "unc" if no box was
+   supplied. */
+   wid = astMalloc( sizeof( double )*(size_t) nc );
+   large = astMalloc( sizeof( double )*(size_t) nc );
+   small = astMalloc( sizeof( double )*(size_t) nc );
+   if( astOK ) {
+      if( unc ) {
+         for( i = 0; i < nc; i++ ) {
+            wid[ i ] = 0.5*( fabs( astAxDistance( frm, i + 1, lbnd_tunc[ i ], ubnd_tunc[ i ] ) )
+                           + fabs( astAxDistance( frm, i + 1, lbnd_unc[ i ], ubnd_unc[ i ] ) ) );
+         }
+      } else {
+         for( i = 0; i < nc; i++ ) {
+            wid[ i ] = fabs( 0.5*astAxDistance( frm, i + 1, lbnd_tunc[ i ], ubnd_tunc[ i ] ) );
+         }
+      }
+
+/* Create two new Boxes, one of which is larger than "this" by the widths
+   found above, and the other of which is smaller than "this" by the widths
+   found above. */
+      for( i = 0; i < nc; i++ ) {
+         large[ i ] = this->centre[ i ]  + this->extent[ i ] + wid[ i ];
+         small[ i ] = this->extent[ i ] - wid[ i ];
+         if( small[ i ] < 0.0 ) small[ i ] = 0.0;
+         small[ i ] += this->centre[ i ];
+      }
+
+      large_box = astBox( frm, 0, this->centre, large, NULL, "", status );
+      small_box = astBox( frm, 0, this->centre, small, NULL, "", status );
+
+/* Negate the smaller region.*/
+      astNegate( small_box );
+
+/* Points are on the boundary of "this" if they are inside both the large
+   box and the negated smallbox. First transform the supplied PointSet
+   using the large box, then transform them using the negated smaller Box. */
+      ps1 = astTransform( large_box, pset, 1, NULL );
+      ps2 = astTransform( small_box, ps1, 1, NULL );
+
+/* Get a point to the resulting axis values, and the number of axis
+   values per axis. */
+      ptr = astGetPoints( ps2 );
+      np = astGetNpoint( ps2 );
+
+/* If a mask array is to be returned, create one. */
+      if( mask ) {
+         *mask = astMalloc( sizeof(int)*(size_t) np );
+
+/* Check all the resulting points, setting mask values for all of them. */
+         if( astOK ) {
+
+/* Initialise the mask elements on the basis of the first axis values */
+            result = 1;
+            p = ptr[ 0 ];
+            for( j = 0; j < np; j++ ) {
+               if( *(p++) == AST__BAD ) {
+                  result = 0;
+                  (*mask)[ j ] = 0;
+               } else {
+                  (*mask)[ j ] = 1;
+               }
+            }
+
+/* Now check for bad values on other axes. */
+            for( i = 1; i < nc; i++ ) {
+               p = ptr[ i ];
+               for( j = 0; j < np; j++ ) {
+                  if( *(p++) == AST__BAD ) {
+                     result = 0;
+                     (*mask)[ j ] = 0;
+                  }
+               }
+            }
+         }
+
+/* If no output mask is to be made, we can break out of the check as soon
+   as the first bad value is found. */
+      } else if( astOK ) {
+         result = 1;
+         for( i = 0; i < nc && result; i++ ) {
+            p = ptr[ i ];
+            for( j = 0; j < np; j++ ) {
+               if( *(p++) == AST__BAD ) {
+                  result = 0;
+                  break;
+               }
+            }
+         }
+      }
+
+/* Free resources. */
+      large_box = astAnnul( large_box );
+      small_box = astAnnul( small_box );
+      ps1 = astAnnul( ps1 );
+      ps2 = astAnnul( ps2 );
+   }
+
+   tunc = astAnnul( tunc );
+   frm = astAnnul( frm );
+   lbnd_tunc = astFree( lbnd_tunc );
+   ubnd_tunc = astFree( ubnd_tunc );
+   if( unc ) lbnd_unc = astFree( lbnd_unc );
+   if( unc ) ubnd_unc = astFree( ubnd_unc );
+   wid = astFree( wid );
+   large = astFree( large );
+   small = astFree( small );
+   safe = astFree( safe );
+
+/* If an error has occurred, return zero. */
+   if( !astOK ) {
+      result = 0;
+      if( mask ) *mask = astAnnul( *mask );
+   }
+
+/* Return the result. */
+   return result;
+}
+
+static int RegTrace( AstRegion *this_region, int n, double *dist, double **ptr,
+                     int *status ){
+/*
+*+
+*  Name:
+*     RegTrace
+
+*  Purpose:
+*     Return requested positions on the boundary of a 2D Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     int astTraceRegion( AstRegion *this, int n, double *dist, double **ptr );
+
+*  Class Membership:
+*     Box member function (overrides the astTraceRegion method
+*     inherited from the parent Region class).
+
+*  Description:
+*     This function returns positions on the boundary of the supplied
+*     Region, if possible. The required positions are indicated by a
+*     supplied list of scalar parameter values in the range zero to one.
+*     Zero corresponds to some arbitrary starting point on the boundary,
+*     and one corresponds to the end (which for a closed region will be
+*     the same place as the start).
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     n
+*        The number of positions to return. If this is zero, the function
+*        returns without action (but the returned function value still
+*        indicates if the method is supported or not).
+*     dist
+*        Pointer to an array of "n" scalar parameter values in the range
+*        0 to 1.0.
+*     ptr
+*        A pointer to an array of pointers. The number of elements in
+*        this array should equal tthe number of axes in the Frame spanned
+*        by the Region. Each element of the array should be a pointer to
+*        an array of "n" doubles, in which to return the "n" values for
+*        the corresponding axis. The contents of the arrays are unchanged
+*        if the supplied Region belongs to a class that does not
+*        implement this method.
+
+*  Returned Value:
+*     Non-zero if the astTraceRegion method is implemented by the class
+*     of Region supplied, and zero if not.
+
+*-
+*/
+
+/* Local Variables; */
+   AstMapping *map;
+   AstPointSet *bpset;
+   AstPointSet *cpset;
+   double **bptr;
+   double d;
+   double lbnd[ 2 ];
+   double ubnd[ 2 ];
+   int i;
+   int ncur;
+   int result;
+
+/* Initialise */
+   result = 0;
+
+/* Check inherited status. */
+   if( ! astOK ) return result;
+
+/* Check it is 2-dimensional. */
+   if( astGetNin( this_region->frameset ) == 2 ) result = 1;
+
+/* Check we have some points to find. */
+   if( result && n > 0 ) {
+
+/* We first determine the required positions in the base Frame of the
+   Region, and then transform them into the current Frame. Get the
+   base->current Mapping, and the number of current Frame axes. */
+      map = astGetMapping( this_region->frameset, AST__BASE, AST__CURRENT );
+
+/* If it's a UnitMap we do not need to do the transformation, so put the
+   base Frame positions directly into the supplied arrays. */
+      if( astIsAUnitMap( map ) ) {
+         bpset = NULL;
+         bptr = ptr;
+         ncur = 2;
+
+/* Otherwise, create a PointSet to hold the base Frame positions. */
+      } else {
+         bpset = astPointSet( n, 2, " ", status );
+         bptr = astGetPoints( bpset );
+         ncur = astGetNout( map );
+      }
+
+/* Check the pointers can be used safely. */
+      if( astOK ) {
+
+/* Get the bounds of the Region in the base Frame. */
+         astRegBaseBox( this_region, lbnd, ubnd );
+
+/* Loop round each point. Each edge of the box covers a parameteric
+   distance of 0.25, regardless of the aspect ratio of the box. */
+         for( i = 0; i < n; i++ ) {
+
+/* The right hand edge starts at 0.75 (parameter increases top to bottom). */
+            d = 4*dist[ i ] - 3;
+            if( d > 0 ) {
+               bptr[ 0 ][ i ] = ubnd[ 0 ];
+               bptr[ 1 ][ i ] = ( 1.0 - d )*ubnd[ 1 ] + d*lbnd[ 1 ];
+
+/* The top edge starts at 0.5 (parameter increases left to right). */
+            } else {
+               d += 1.0;
+               if( d > 0 ) {
+                  bptr[ 0 ][ i ] = ( 1.0 - d )*lbnd[ 0 ] + d*ubnd[ 0 ];
+                  bptr[ 1 ][ i ] = ubnd[ 1 ];
+
+/* The left hand edge starts at 0.25 (parameter increases bottom to top). */
+               } else {
+                  d += 1.0;
+                  if( d > 0 ) {
+                     bptr[ 0 ][ i ] = lbnd[ 0 ];
+                     bptr[ 1 ][ i ] = ( 1.0 - d )*lbnd[ 1 ] + d*ubnd[ 1 ];
+
+/* The bottom edge starts at 0.0 (parameter increases right to left). */
+                  } else {
+                     d += 1.0;
+                     bptr[ 0 ][ i ] = ( 1.0 - d )*ubnd[ 0 ] + d*lbnd[ 0 ];
+                     bptr[ 1 ][ i ] = lbnd[ 1 ];
+                  }
+               }
+            }
+         }
+      }
+
+/* If required, transform the base frame positions into the current
+   Frame, storing them in the supplied array. Then free resources. */
+      if( bpset ) {
+         cpset = astPointSet( n, ncur, " ", status );
+         astSetPoints( cpset, ptr );
+
+         (void) astTransform( map, bpset, 1, cpset );
+
+         cpset = astAnnul( cpset );
+         bpset = astAnnul( bpset );
+      }
+
+/* Free remaining resources. */
+      map = astAnnul( map );
+   }
+
+/* Return the result. */
+   return result;
+}
+
+static void ResetCache( AstRegion *this, int *status ){
+/*
+*  Name:
+*     ResetCache
+
+*  Purpose:
+*     Clear cached information within the supplied Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void ResetCache( AstRegion *this, int *status )
+
+*  Class Membership:
+*     Region member function (overrides the astResetCache method
+*     inherited from the parent Region class).
+
+*  Description:
+*     This function clears cached information from the supplied Region
+*     structure.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     status
+*        Pointer to the inherited status variable.
+*/
+   if( this ) {
+      ((AstBox *) this )->stale = 1;
+      (*parent_resetcache)( this, status );
+   }
+}
+
+static void SetClosed( AstRegion *this, int value, int *status ){
+/*
+*  Name:
+*     SetClosed
+
+*  Purpose:
+*     Set a value for the Closed attribute of a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void SetClosed( AstRegion *this, int value, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the protected astSetClosed
+*     method inherited from the Region class).
+
+*  Description:
+*     This function sets a new value for the Closed attribute of a Region.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     value
+*        The new attribute value.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   int old;
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get the original attribute value */
+   old = astGetClosed( this );
+
+/* Invoke the set method inherited from the parent Region class */
+   (*parent_setclosed)( this, value, status );
+
+/* If the new value is not the same as the old value, indicate that we
+   need to re-calculate the cached information in the Box. */
+   if( value != old ) astResetCache( this );
+}
+
+static void SetNegated( AstRegion *this, int value, int *status ){
+/*
+*  Name:
+*     SetNegated
+
+*  Purpose:
+*     Set a value for the Negated attribute of a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void SetNegated( AstRegion *this, int value, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the protected astSetNegated
+*     method inherited from the Region class).
+
+*  Description:
+*     This function sets a new value for the Negated attribute of a Region.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     value
+*        The new attribute value.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   int old;
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get the original attribute value */
+   old = astGetNegated( this );
+
+/* Invoke the set method inherited from the parent Region class */
+   (*parent_setnegated)( this, value, status );
+
+/* If the new value is not the same as the old value, indicate that we
+   need to re-calculate the cached information in the Box. */
+   if( value != old ) astResetCache( this );
+}
+
+static void SetRegFS( AstRegion *this_region, AstFrame *frm, int *status ) {
+/*
+*  Name:
+*     SetRegFS
+
+*  Purpose:
+*     Stores a new FrameSet in a Region
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void SetRegFS( AstRegion *this_region, AstFrame *frm, int *status )
+
+*  Class Membership:
+*     Box method (over-rides the astSetRegFS method inherited from
+*     the Region class).
+
+*  Description:
+*     This function creates a new FrameSet and stores it in the supplied
+*     Region. The new FrameSet contains two copies of the supplied
+*     Frame, connected by a UnitMap.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     frm
+*        The Frame to use.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Invoke the parent method to store the FrameSet in the parent Region
+   structure. */
+   (* parent_setregfs)( this_region, frm, status );
+
+/* Indicate that we need to re-calculate the cached information in the Box. */
+   astResetCache( this_region );
+}
+
+static void SetUnc( AstRegion *this, AstRegion *unc, int *status ){
+/*
+*  Name:
+*     SetUnc
+
+*  Purpose:
+*     Store uncertainty information in a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     void SetUnc( AstRegion *this, AstRegion *unc, int *status )
+
+*  Class Membership:
+*     Box method (over-rides the astSetUnc method inherited from the
+*     Region class).
+
+*  Description:
+*     Each Region (of any class) can have an "uncertainty" which specifies
+*     the uncertainties associated with the boundary of the Region. This
+*     information is supplied in the form of a second Region. The uncertainty
+*     in any point on the boundary of a Region is found by shifting the
+*     associated "uncertainty" Region so that it is centred at the boundary
+*     point being considered. The area covered by the shifted uncertainty
+*     Region then represents the uncertainty in the boundary position.
+*     The uncertainty is assumed to be the same for all points.
+*
+*     The uncertainty is usually specified when the Region is created, but
+*     this function allows it to be changed at any time.
+
+*  Parameters:
+*     this
+*        Pointer to the Region which is to be assigned a new uncertainty.
+*     unc
+*        Pointer to the new uncertainty Region. This must be either a Box,
+*        a Circle or an Ellipse. A deep copy of the supplied Region will be
+*        taken, so subsequent changes to the uncertainty Region using the
+*        supplied pointer will have no effect on the Region "this".
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Check the inherited status. */
+   if( !astOK ) return;
+
+/* Invoke the astSetUnc method inherited from the parent Region class. */
+   (*parent_setunc)( this, unc, status );
+
+/* Indicate that we need to re-calculate the cached information in the Box. */
+   astResetCache( this );
+}
+
+static AstMapping *Simplify( AstMapping *this_mapping, int *status ) {
+/*
+*  Name:
+*     Simplify
+
+*  Purpose:
+*     Simplify the Mapping represented by a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstMapping *Simplify( AstMapping *this, int *status )
+
+*  Class Membership:
+*     Box method (over-rides the astSimplify method inherited
+*     from the Region class).
+
+*  Description:
+*     This function invokes the parent Region Simplify method, and then
+*     performs any further region-specific simplification.
+*
+*     If the Mapping from base to current Frame is not a UnitMap, this
+*     will include attempting to fit a new Region to the boundary defined
+*     in the current Frame.
+
+*  Parameters:
+*     this
+*        Pointer to the original Region.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     A pointer to the simplified Region. A cloned pointer to the
+*     supplied Region will be returned if no simplication could be
+*     performed.
+
+*  Notes:
+*     - A NULL pointer value will be returned if this function is
+*     invoked with the AST error status set, or if it should fail for
+*     any reason.
+*/
+
+/* Local Variables: */
+   AstBox *box;                  /* Pointer to Box structure */
+   AstBox *newbox;               /* Pointer to simpler Box */
+   AstFrame *frm;                /* Pointer to current Frame */
+   AstMapping *map;              /* Base -> current Mapping */
+   AstMapping *result;           /* Result pointer to return */
+   AstPointSet *basemesh;        /* Mesh of base Frame positions */
+   AstPointSet *mesh;            /* Mesh of current Frame positions */
+   AstPointSet *ps1;             /* Box corners in base Frame */
+   AstPointSet *ps2;             /* Box corners in current Frame */
+   AstPolygon *newpoly;          /* New Polygon to replace Box */
+   AstRegion *prism;             /* Prism combining all axes */
+   AstRegion *new;               /* Pointer to simplified Region */
+   AstRegion *this;              /* Pointer to supplied Region structure */
+   AstRegion *unc;               /* Pointer to uncertainty Region */
+   double **ptr1;                /* Pointers to axis values in ps1 */
+   double **ptr2;                /* Pointers to axis values in ps2 */
+   double *constants;            /* Axis constants array */
+   double *lbnd;                 /* Lower bounds for new Box */
+   double *ubnd;                 /* Upper bounds for new Box */
+   double corners[8];            /* Box corners in current Frame */
+   double k;                     /* Axis constant value */
+   double lb;                    /* Lower axis bound */
+   double ub;                    /* Upper axis bound */
+   int *inperm;                  /* Input axis permutation array */
+   int *outperm;                 /* Output axis permutation array */
+   int closed;                   /* Was original Region closed? */
+   int feed;                     /* Source of value for current axis */
+   int right_handed;             /* Is the new Frame right handed? */
+   int ic;                       /* Axis index */
+   int isInterval;               /* Is the simplified Box an Interval */
+   int isNull;                   /* Is the simplified Box a NullRegion? */
+   int neg;                      /* Was original Region negated? */
+   int nin;                      /* No. of base Frame axes (Mapping inputs) */
+   int nout;                     /* No. of current Frame axes (Mapping outputs) */
+   int simpler;                  /* Has some simplication taken place? */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the Region structure. */
+   this = (AstRegion *) this_mapping;
+
+/* Invoke the parent Simplify method inherited from the Region class. This
+   will simplify the encapsulated FrameSet and uncertainty Region. */
+   new = (AstRegion *) (*parent_simplify)( this_mapping, status );
+
+/* Note if any simplification took place. This is assumed to be the case
+   if the pointer returned by the above call is different to the supplied
+   pointer. */
+   simpler = ( new != this );
+
+/* Get the Mapping from base to current Frame. */
+   map = astGetMapping( new->frameset, AST__BASE, AST__CURRENT );
+
+/* Get the number of inputs and outputs for the PermMap */
+   nin = astGetNin( map );
+   nout = astGetNout( map );
+
+/* If the Mapping from base to current Frame is a PermMap, we now explicitly
+   how to swap the axes of the Box to produce either a new Box or an
+   Interval. */
+   if( astIsAPermMap( map ) ){
+
+/* See if the new Box is Negated and/or Closed.*/
+      neg = astGetNegated( new );
+      closed = astGetClosed( new );
+
+/* Get a pointer to the Box structure. */
+      newbox = (AstBox *) new;
+
+/* Ensure cached information is up to date. */
+      Cache( newbox, 0, status );
+
+/* Get the input and output permutation arrays and the array of constants
+   from the PermMap. */
+      inperm = astGetInPerm( map );
+      outperm = astGetOutPerm( map );
+      constants = astGetConstants( map );
+
+/* Allocate memory to hold the axis bounds for the box in the current
+   Frame. */
+      lbnd = astMalloc( sizeof( double )*(size_t) nout );
+      ubnd = astMalloc( sizeof( double )*(size_t) nout );
+
+/* Check pointers can be used safely. */
+      if( astOK ) {
+
+/* Set flags indicating that the Box can be simplified, and does not result
+   in a NullRegion or an Interval. */
+         simpler = 1;
+         isNull = 0;
+         isInterval = 0;
+
+/* Check each output (which corresponds to an axis in the current Frame
+   of the Box). */
+         for( ic = 0; ic < nout; ic++ ) {
+
+/* Find the input (a base Frame axis) which feeds this output when the
+   forward transformation of the PermMap is used. */
+            feed = outperm[ ic ];
+
+/* If this output is fed a constant (i.e. does not depend on any of the
+   inputs), then the output axis limits are equal to this constant. */
+            if( feed < 0 ) {
+               lbnd[ ic ] = constants[ (-feed) - 1 ];
+               ubnd[ ic ] = constants[ (-feed) - 1 ];
+
+/* If this output is fed the constant AST__BAD (i.e. does not depend on any of
+   the inputs), then the output axis is unbounded and we will consequently
+   create an Interval rather than a Box. */
+            } else if( feed >= nin ) {
+               lbnd[ ic ] = AST__BAD;
+               ubnd[ ic ] = AST__BAD;
+
+/* If this output is fed the value of an input, then the output limits
+   are equal to the corresponding input limits. */
+            } else {
+               lbnd[ ic ] = newbox->centre[ feed ] - newbox->extent[ feed ];
+               ubnd[ ic ] = newbox->centre[ feed ] + newbox->extent[ feed ];
+            }
+
+/* If either bound is missing we will produce an Interval rather than a
+   Box. */
+            if( lbnd[ ic ] == AST__BAD || ubnd[ ic ] == AST__BAD ) {
+               isInterval = 1;
+            }
+         }
+
+/* If any base Frame axes are not present in the current Frame, we need
+   to check that the PermMap selects a slice which intersects the base
+   Frame box. If the slice does not intersect the base Frame box, then
+   the resulting Region willbe NullRegion. To do this, we check each
+   element in the input axis permutation array, "inperm". */
+         for( ic = 0; ic < nin; ic++ ) {
+
+/* Find the output (a current Frame axis) which feeds this input when the
+   inverse transformation of the PermMap is used. */
+            feed = inperm[ ic ];
+
+/* If this input is fed a constant (i.e. does not depend on any of the
+   outputs), then we must check that this constant is within the range of
+   axis values covered by the Box. If not then the simplified Box represents
+   a slice through the coordinate system which does not pass through the
+   original Box. In this case the simplified Region is a NullRegion
+   instead of a Box. */
+            if( feed < 0 ) {
+               k = constants[ (-feed) - 1 ];
+               lb = newbox->centre[ ic ] - newbox->extent[ ic ];
+               ub = newbox->centre[ ic ] + newbox->extent[ ic ];
+
+               if( closed == neg ) {
+                  isNull = ( k <= lb || k >= ub );
+               } else {
+                  isNull = ( k < lb || k > ub );
+               }
+
+/* If this input is fed the constant AST__BAD (i.e. does not depend on any of
+   the outputs), then the input axis is unbounded and will consequently
+   extend beyond the Box. In this case the simplified Region will be a
+   NullRegion. */
+            } else if( feed >= nout ) {
+               isNull = 1;
+
+/* If this input is fed the value of an output, then check that the
+   relationship is bi-directional. If it is not, we cannot simplify the
+   Box. */
+            } else if( outperm[ feed ] != ic ) {
+               simpler = 0;
+               break;
+            }
+         }
+
+/* If the Box can be simplified, create a new Region of an appropriate
+   class. */
+         if( simpler ) {
+
+/* Get any uncertainty from the supplied Box (it will already have been
+   simplified by the parent Simplify method). */
+            unc = astTestUnc( new ) ? astGetUncFrm( new, AST__CURRENT ) : NULL;
+
+/* Get the Frame represented by the Region. */
+            frm = astGetFrame( new->frameset, AST__CURRENT );
+
+/* We can now replace the original Region with the simplified Region so annul
+   the original pointer. */
+            new = astAnnul( new );
+
+/* Create a new Region of the required class. */
+            if( isNull ) {
+               new = (AstRegion *) astNullRegion( frm, unc, "", status );
+
+            } else if( isInterval ){
+               new = (AstRegion *) astInterval( frm, lbnd, ubnd, unc, "", status );
+
+            } else {
+               new = (AstRegion *) astBox( frm, 1, lbnd, ubnd, unc, "", status );
+            }
+
+/* If the original box was Negated. Negate the new one. */
+            if( neg ) astNegate( new );
+
+/* Free resources */
+            if( unc ) unc = astAnnul( unc );
+            frm = astAnnul( frm );
+
+         }
+      }
+
+/* Free resources */
+      inperm = astFree( inperm );
+      outperm = astFree( outperm );
+      constants = astFree( constants );
+      lbnd = astFree( lbnd );
+      ubnd = astFree( ubnd );
+
+/* If the Mapping from base to current Frame is not a PermMap or a UnitMap, we
+   attempt to simplify the Box by re-defining it within its current Frame.
+   Transforming the box from its base to its current FRame may result in
+   the region no longer being a box. We test this by transforming a set of
+   bounds on the box boundary. */
+   } else if( !astIsAUnitMap( map ) ){
+
+/* Get pointer to current Frame. */
+      frm = astGetFrame( new->frameset, AST__CURRENT );
+
+/* Get a mesh of points covering the Box in its current Frame. */
+      mesh = astRegMesh( new );
+
+/* Get the Region describing the positional uncertainty within the Box in
+   its current Frame. */
+      unc = astGetUncFrm( new, AST__CURRENT );
+
+/* Find the best fitting box (defined in the current Frame) through these
+   points */
+      newbox = BestBox( frm, mesh, unc, status );
+
+/* See if all points within this mesh fall on the boundary of the best
+   fitting Box, to within the uncertainty of the Region. */
+      if( newbox && astRegPins( newbox, mesh, NULL, NULL ) ) {
+
+/* If so, check that the inverse is true (we need to transform the
+   simplified boxes mesh into the base Frame of he original box for use by
+   astRegPins). */
+         (void) astAnnul( mesh );
+         mesh = astRegMesh( newbox );
+         basemesh = astTransform( map, mesh, 0, NULL );
+         if( astRegPins( new, basemesh, NULL, NULL ) ) {
+
+/* If so, use the new Box in place of the original Box. */
+            (void) astAnnul( new );
+            new = astClone( newbox );
+            simpler = 1;
+         }
+
+/* Free resources. */
+         basemesh = astAnnul( basemesh );
+
+/* If the transformed Box is not itself a Box, see if it can be
+   represented accurately by a Polygon. This is only possible for
+   2-dimensional Boxes. */
+      } else if( nin == 2 && nout == 2 ) {
+
+/* Create a PointSet holding the base Frame axis values at the four
+   corners of the Box. */
+         ps1 = astPointSet( 4, 2, "", status );
+         ptr1 = astGetPoints( ps1 );
+         if( astOK ) {
+            box = (AstBox *) new;
+            Cache( box, 0, status );
+
+/* The order in which the polygon vertices are stored determines whether
+   the interior or exterior of the polygon forms the inside of the
+   Region. We want the inside to be the interior. First create a Polygon
+   in which the vertices are stored in clockwise order within the
+   new coordinate Frame. If the new Polygon is not bounded, use
+   anti-clockwise order. */
+            for( right_handed = 0; right_handed < 2; right_handed++ ) {
+
+               if( right_handed ) {
+                  ptr1[ 0 ][ 0 ] = box->centre[ 0 ] - box->extent[ 0 ];
+                  ptr1[ 1 ][ 0 ] = box->centre[ 1 ] + box->extent[ 1 ];
+
+                  ptr1[ 0 ][ 1 ] = box->centre[ 0 ] - box->extent[ 0 ];
+                  ptr1[ 1 ][ 1 ] = box->centre[ 1 ] - box->extent[ 1 ];
+
+                  ptr1[ 0 ][ 2 ] = box->centre[ 0 ] + box->extent[ 0 ];
+                  ptr1[ 1 ][ 2 ] = box->centre[ 1 ] - box->extent[ 1 ];
+
+                  ptr1[ 0 ][ 3 ] = box->centre[ 0 ] + box->extent[ 0 ];
+                  ptr1[ 1 ][ 3 ] = box->centre[ 1 ] + box->extent[ 1 ];
+
+               } else {
+                  ptr1[ 0 ][ 3 ] = box->centre[ 0 ] - box->extent[ 0 ];
+                  ptr1[ 1 ][ 3 ] = box->centre[ 1 ] + box->extent[ 1 ];
+
+                  ptr1[ 0 ][ 2 ] = box->centre[ 0 ] - box->extent[ 0 ];
+                  ptr1[ 1 ][ 2 ] = box->centre[ 1 ] - box->extent[ 1 ];
+
+                  ptr1[ 0 ][ 1 ] = box->centre[ 0 ] + box->extent[ 0 ];
+                  ptr1[ 1 ][ 1 ] = box->centre[ 1 ] - box->extent[ 1 ];
+
+                  ptr1[ 0 ][ 0 ] = box->centre[ 0 ] + box->extent[ 0 ];
+                  ptr1[ 1 ][ 0 ] = box->centre[ 1 ] + box->extent[ 1 ];
+               }
+
+/* Transform the Box corners into the current Frame. */
+               ps2 = astTransform( map, ps1, 1, NULL );
+               ptr2 = astGetPoints( ps2 );
+               if( astOK ) {
+
+/* Create a Polygon from these points. */
+                  for( ic = 0; ic < 4; ic++ ) {
+                     corners[ ic ] = ptr2[ 0 ][ ic ];
+                     corners[ 4 + ic ] = ptr2[ 1 ][ ic ];
+                  }
+                  newpoly = astPolygon( frm, 4, 4, corners, unc, "", status );
+
+/* If the Polygon is bounded, break out of the loop. */
+                  if( astGetBounded( newpoly ) ) break;
+               }
+
+/* Free resources. */
+               newpoly = astAnnul( newpoly );
+               ps2 = astAnnul( ps2 );
+            }
+
+/* See if all points within the Box mesh fall on the boundary of this
+   Polygon, to within the uncertainty of the Region. */
+            if( astRegPins( newpoly, mesh, NULL, NULL ) ) {
+
+/* If so, use the new Polygon in place of the original Box. */
+               (void) astAnnul( new );
+               new = astClone( newpoly );
+               simpler = 1;
+            }
+
+/* Free resources. */
+            newpoly = astAnnul( newpoly );
+         }
+
+         ps1 = astAnnul( ps1 );
+      }
+
+/* If we have yet been able to produce a simpler region, we now try
+   splitting the Box into two separate Boxes defined in separate
+   coordinate Frames. If either of these two Boxes can be simplified,
+   create a Prism containing the two simplified Boxes, and attempt to
+   simplify the Prism. Otherwise a clone of "new" is returned by
+   astConvertToPrism. */
+      if( !simpler ) {
+         prism = astConvertToPrism( new );
+
+         if( prism != new ) {
+            simpler = 1;
+            (void) astAnnul( new );
+            new = prism;
+
+         } else {
+            prism = astAnnul( prism );
+         }
+      }
+
+      frm = astAnnul( frm );
+      mesh = astAnnul( mesh );
+      unc = astAnnul( unc );
+      if( newbox ) newbox = astAnnul( newbox );
+   }
+
+   map = astAnnul( map );
+
+/* If any simplification could be performed, copy Region attributes from
+   the supplied Region to the returned Region, and return a pointer to it.
+   If the supplied Region had no uncertainty, ensure the returned Region
+   has no uncertainty. Otherwise, return a clone of the supplied pointer. */
+   if( simpler ){
+      astRegOverlay( new, this, 1 );
+      result = (AstMapping *) new;
+
+   } else {
+      new = astAnnul( new );
+      result = astClone( this );
+   }
+
+/* If an error occurred, annul the returned pointer. */
+   if ( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+                               int forward, AstPointSet *out, int *status ) {
+/*
+*  Name:
+*     Transform
+
+*  Purpose:
+*     Apply a Box to transform a set of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+*                             int forward, AstPointSet *out, int *status )
+
+*  Class Membership:
+*     Box member function (over-rides the astTransform protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function takes a Box and a set of points encapsulated in a
+*     PointSet and transforms the points by setting axis values to
+*     AST__BAD for all points which are outside the region. Points inside
+*     the region are copied unchanged from input to output.
+
+*  Parameters:
+*     this
+*        Pointer to the Box.
+*     in
+*        Pointer to the PointSet holding the input coordinate data.
+*     forward
+*        A non-zero value indicates that the forward coordinate transformation
+*        should be applied, while a zero value requests the inverse
+*        transformation.
+*     out
+*        Pointer to a PointSet which will hold the transformed (output)
+*        coordinate values. A NULL value may also be given, in which case a
+*        new PointSet will be created by this function.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the output (possibly new) PointSet.
+
+*  Notes:
+*     -  The forward and inverse transformations are identical for a
+*     Region.
+*     -  A null pointer will be returned if this function is invoked with the
+*     global error status set, or if it should fail for any reason.
+*     -  The number of coordinate values per point in the input PointSet must
+*     match the number of axes in the Frame represented by the Box.
+*     -  If an output PointSet is supplied, it must have space for sufficient
+*     number of points and coordinate values per point to accommodate the
+*     result. Any excess space will be ignored.
+*/
+
+/* Local Variables: */
+   AstBox *box;                  /* Pointer to Box */
+   AstFrame *frm;                /* Pointer to base Frame in FrameSet */
+   AstPointSet *pset_tmp;        /* Pointer to PointSet holding base Frame positions*/
+   AstPointSet *result;          /* Pointer to output PointSet */
+   AstRegion *reg;               /* Pointer to Region */
+   double **ptr_out;             /* Pointer to output coordinate data */
+   double **ptr_tmp;             /* Pointer to base Frame coordinate data */
+   double axval;                 /* Input axis value */
+   int closed;                   /* Is the boundary part of the Region? */
+   int coord;                    /* Zero-based index for coordinates */
+   int ncoord_out;               /* No. of coordinates per output point */
+   int ncoord_tmp;               /* No. of coordinates per base Frame point */
+   int neg;                      /* Is the Box negated?*/
+   int npoint;                   /* No. of points */
+   int ok;                       /* Is the point inside the Region? */
+   int point;                    /* Loop counter for points */
+
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain pointers to the Regionand to the Box. */
+   reg = (AstRegion *) this;
+   box = (AstBox *) this;
+
+/* Apply the parent mapping using the stored pointer to the Transform member
+   function inherited from the parent Region class. This function validates
+   all arguments and generates an output PointSet if necessary,
+   containing a copy of the input PointSet. */
+   result = (*parent_transform)( this, in, forward, out, status );
+
+/* We will now extend the parent astTransform method by performing the
+   calculations needed to generate the output coordinate values. */
+
+/* First use the encapsulated FrameSet to transform the supplied positions
+   from the current Frame in the encapsulated FrameSet (the Frame
+   represented by the Region), to the base Frame (the Frame in which the
+   Region is defined). This call also returns a pointer to the base Frame
+   of the encapsulated FrameSet. Note, the returned pointer may be a
+   clone of the "in" pointer, and so we must be carefull not to modify the
+   contents of the returned PointSet. */
+   pset_tmp = astRegTransform( reg, in, 0, NULL, &frm );
+
+/* Determine the numbers of points and coordinates per point from the base
+   Frame PointSet and obtain pointers for accessing the base Frame and output
+   coordinate values. */
+   npoint = astGetNpoint( pset_tmp );
+   ncoord_tmp = astGetNcoord( pset_tmp );
+   ptr_tmp = astGetPoints( pset_tmp );
+   ncoord_out = astGetNcoord( result );
+   ptr_out = astGetPoints( result );
+
+/* See if the boundary is part of the Region. */
+   closed = astGetClosed( reg );
+
+/* See if the Box is negated */
+   neg = astGetNegated( reg );
+
+/* Ensire the cached information is up to date. */
+   Cache( box, 1, status );
+
+/* Perform coordinate arithmetic. */
+/* ------------------------------ */
+   if ( astOK ) {
+
+/* The logic used to combine axis values for negated and un-negated boxes
+   is different. For negated boxes, a position is in the region if *any
+   one* axis is not "close" to the box centre. */
+      if( neg ) {
+
+/* Loop round each point */
+         for ( point = 0; point < npoint; point++ ) {
+
+/* Assume the point is outside the Region (since the Region is
+   negated, this means assuming it is within the box). */
+            ok = 0;
+
+/* Loop round each axis value at this point. We break as soon as we find
+   a bad axis value or an axis value which is outside the box. */
+            for ( coord = 0; coord < ncoord_tmp; coord++ ) {
+
+/* The point is definiately not in the Region if any input axis value is bad. */
+               axval = ptr_tmp[ coord ][ point ];
+               if( axval == AST__BAD ) {
+                  break;
+
+/* Otherwise check the current axis value, depending on whether the
+   boundary is included in the Region or not. Break as soon as an axis
+   value is found which is outside the box limits (i.e. in the Region). */
+               } else if( !astAxIn( frm, coord, box->lo[ coord ], box->hi[ coord ],
+                                    axval, !closed ) ) {
+                  ok = 1;
+                  break;
+               }
+            }
+
+/* If this point is not inside the Region store bad output axis values. */
+            if( !ok ) {
+               for ( coord = 0; coord < ncoord_out; coord++ ) {
+                  ptr_out[ coord ][ point ] = AST__BAD;
+               }
+            }
+         }
+
+/* For un-negated boxes, a position is in the region if *all* axes are "close"
+   to the box centre. */
+      } else {
+
+/* Loop round each point */
+         for ( point = 0; point < npoint; point++ ) {
+
+/* Assume the point is within the Region (i.e.inside the box). */
+            ok = 1;
+
+/* Loop round each axis value at this point. We break when we find a bad
+   input point or if any axis value is outside the box. */
+            for ( coord = 0; coord < ncoord_tmp; coord++ ) {
+
+/* The point is not in the Region if any input axis value is bad. */
+               axval = ptr_tmp[ coord ][ point ];
+               if( axval == AST__BAD ) {
+                  ok = 0;
+                  break;
+
+/* Otherwise check the current axis value, depending on whether the
+   boundary is included in the Region or not. Break as soon as an axis
+   value is found which is outside the box limits (i.e. outside the Region). */
+               } else if( !astAxIn( frm, coord, box->lo[ coord ], box->hi[ coord ],
+                                    axval, closed ) ) {
+                  ok = 0;
+                  break;
+               }
+            }
+
+/* If this point is outside the Region store bad output axis values. */
+            if( !ok ) {
+               for ( coord = 0; coord < ncoord_out; coord++ ) {
+                  ptr_out[ coord ][ point ] = AST__BAD;
+               }
+            }
+         }
+      }
+   }
+
+/* Free resources */
+   pset_tmp = astAnnul( pset_tmp );
+   frm = astAnnul( frm );
+
+/* Annul the result if an error has occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return a pointer to the output PointSet. */
+   return result;
+}
+
+/* Functions which access class attributes. */
+/* ---------------------------------------- */
+/* Implement member functions to access the attributes associated with
+   this class using the macros defined for this purpose in the
+   "object.h" file. For a description of each attribute, see the class
+   interface (in the associated .h file). */
+
+/* Copy constructor. */
+/* ----------------- */
+static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
+/*
+*  Name:
+*     Copy
+
+*  Purpose:
+*     Copy constructor for Region objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Copy( const AstObject *objin, AstObject *objout, int *status )
+
+*  Description:
+*     This function implements the copy constructor for Region objects.
+
+*  Parameters:
+*     objin
+*        Pointer to the object to be copied.
+*     objout
+*        Pointer to the object being constructed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     -  This constructor makes a deep copy.
+*/
+
+/* Local Variables: */
+   AstBox *in;                /* Pointer to input Box */
+   AstBox *out;               /* Pointer to output Box */
+   int nax;                   /* Number of base Frame axes */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain pointers to the input and output Boxs. */
+   in = (AstBox *) objin;
+   out = (AstBox *) objout;
+
+/* For safety, first clear any references to the input memory from
+   the output Box. */
+   out->extent = NULL;
+   out->centre = NULL;
+   out->lo = NULL;
+   out->hi = NULL;
+   out->geolen = NULL;
+
+/* Copy dynamic memory contents */
+   nax = astGetNin( ((AstRegion *) in)->frameset );
+   out->extent = astStore( NULL, in->extent,
+                           sizeof( double )*(size_t)nax );
+   out->centre = astStore( NULL, in->centre,
+                           sizeof( double )*(size_t)nax );
+   out->lo = astStore( NULL, in->lo,
+                           sizeof( double )*(size_t)nax );
+   out->hi = astStore( NULL, in->hi,
+                           sizeof( double )*(size_t)nax );
+   out->geolen = astStore( NULL, in->geolen,
+                           sizeof( double )*(size_t)nax );
+}
+
+
+/* Destructor. */
+/* ----------- */
+static void Delete( AstObject *obj, int *status ) {
+/*
+*  Name:
+*     Delete
+
+*  Purpose:
+*     Destructor for Box objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Delete( AstObject *obj, int *status )
+
+*  Description:
+*     This function implements the destructor for Box objects.
+
+*  Parameters:
+*     obj
+*        Pointer to the object to be deleted.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     This function attempts to execute even if the global error status is
+*     set.
+*/
+
+/* Local Variables: */
+   AstBox *this;                 /* Pointer to Box */
+
+/* Obtain a pointer to the Box structure. */
+   this = (AstBox *) obj;
+
+/* Annul all resources. */
+   this->extent = astFree( this->extent );
+   this->centre = astFree( this->centre );
+   this->lo = astFree( this->lo );
+   this->hi = astFree( this->hi );
+   this->geolen = astFree( this->geolen );
+}
+
+/* Dump function. */
+/* -------------- */
+static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
+/*
+*  Name:
+*     Dump
+
+*  Purpose:
+*     Dump function for Box objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Dump( AstObject *this, AstChannel *channel, int *status )
+
+*  Description:
+*     This function implements the Dump function which writes out data
+*     for the Box class to an output Channel.
+
+*  Parameters:
+*     this
+*        Pointer to the Box whose data are being written.
+*     channel
+*        Pointer to the Channel to which the data are being written.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Write out values representing the instance variables for the
+   Box class.  Accompany these with appropriate comment strings,
+   possibly depending on the values being written.*/
+
+/* In the case of attributes, we first use the appropriate (private)
+   Test...  member function to see if they are set. If so, we then use
+   the (private) Get... function to obtain the value to be written
+   out.
+
+   For attributes which are not set, we use the astGet... method to
+   obtain the value instead. This will supply a default value
+   (possibly provided by a derived class which over-rides this method)
+   which is more useful to a human reader as it corresponds to the
+   actual default attribute value.  Since "set" will be zero, these
+   values are for information only and will not be read back. */
+
+/* There are no values to write, so return without further action. */
+}
+
+/* Standard class functions. */
+/* ========================= */
+/* Implement the astIsABox and astCheckBox functions using the macros
+   defined for this purpose in the "object.h" header file. */
+astMAKE_ISA(Box,Region)
+astMAKE_CHECK(Box)
+
+AstBox *astBox_( void *frame_void, int form, const double point1[],
+                 const double point2[], AstRegion *unc, const char *options, int *status, ...) {
+/*
+*++
+*  Name:
+c     astBox
+f     AST_BOX
+
+*  Purpose:
+*     Create a Box.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "box.h"
+c     AstBox *astBox( AstFrame *frame, int form, const double point1[],
+c                     const double point2[], AstRegion *unc,
+c                     const char *options, ... )
+f     RESULT = AST_BOX( FRAME, FORM, POINT1, POINT2, UNC, OPTIONS, STATUS )
+
+*  Class Membership:
+*     Box constructor.
+
+*  Description:
+*     This function creates a new Box and optionally initialises its
+*     attributes.
+*
+*     The Box class implements a Region which represents a box with sides
+*     parallel to the axes of a Frame (i.e. an area which encloses a given
+*     range of values on each axis). A Box is similar to an Interval, the
+*     only real difference being that the Interval class allows some axis
+*     limits to be unspecified. Note, a Box will only look like a box if
+*     the Frame geometry is approximately flat. For instance, a Box centred
+*     close to a pole in a SkyFrame will look more like a fan than a box
+*     (the Polygon class can be used to create a box-like region close to a
+*     pole).
+
+*  Parameters:
+c     frame
+f     FRAME = INTEGER (Given)
+*        A pointer to the Frame in which the region is defined. A deep
+*        copy is taken of the supplied Frame. This means that any
+*        subsequent changes made to the Frame using the supplied pointer
+*        will have no effect the Region.
+c     form
+f     FORM = INTEGER (Given)
+*        Indicates how the box is described by the remaining parameters.
+*        A value of zero indicates that the box is specified by a centre
+*        position and a corner position. A value of one indicates that the
+*        box is specified by a two opposite corner positions.
+c     point1
+f     POINT1( * ) = DOUBLE PRECISION (Given)
+c        An array of double, with one element for each Frame axis
+f        An array with one element for each Frame axis
+*        (Naxes attribute). If
+c        "form"
+f        FORM
+*        is zero, this array should contain the coordinates at the centre of
+*        the box.
+c        If "form"
+f        If FORM
+*        is one, it should contain the coordinates at the corner of the box
+*        which is diagonally opposite the corner specified by
+c        "point2".
+f        POINT2.
+c     point2
+f     POINT2( * ) = DOUBLE PRECISION (Given)
+c        An array of double, with one element for each Frame axis
+f        An array with one element for each Frame axis
+*        (Naxes attribute) containing the coordinates at any corner of the
+*        box.
+c     unc
+f     UNC = INTEGER (Given)
+*        An optional pointer to an existing Region which specifies the
+*        uncertainties associated with the boundary of the Box being created.
+*        The uncertainty in any point on the boundary of the Box is found by
+*        shifting the supplied "uncertainty" Region so that it is centred at
+*        the boundary point being considered. The area covered by the
+*        shifted uncertainty Region then represents the uncertainty in the
+*        boundary position. The uncertainty is assumed to be the same for
+*        all points.
+*
+*        If supplied, the uncertainty Region must be of a class for which
+*        all instances are centro-symetric (e.g. Box, Circle, Ellipse, etc.)
+*        or be a Prism containing centro-symetric component Regions. A deep
+*        copy of the supplied Region will be taken, so subsequent changes to
+*        the uncertainty Region using the supplied pointer will have no
+*        effect on the created Box. Alternatively,
+f        a null Object pointer (AST__NULL)
+c        a NULL Object pointer
+*        may be supplied, in which case a default uncertainty is used
+*        equivalent to a box 1.0E-6 of the size of the Box being created.
+*
+*        The uncertainty Region has two uses: 1) when the
+c        astOverlap
+f        AST_OVERLAP
+*        function compares two Regions for equality the uncertainty
+*        Region is used to determine the tolerance on the comparison, and 2)
+*        when a Region is mapped into a different coordinate system and
+*        subsequently simplified (using
+c        astSimplify),
+f        AST_SIMPLIFY),
+*        the uncertainties are used to determine if the transformed boundary
+*        can be accurately represented by a specific shape of Region.
+c     options
+f     OPTIONS = CHARACTER * ( * ) (Given)
+c        Pointer to a null-terminated string containing an optional
+c        comma-separated list of attribute assignments to be used for
+c        initialising the new Box. The syntax used is identical to
+c        that for the astSet function and may include "printf" format
+c        specifiers identified by "%" symbols in the normal way.
+f        A character string containing an optional comma-separated
+f        list of attribute assignments to be used for initialising the
+f        new Box. The syntax used is identical to that for the
+f        AST_SET routine.
+c     ...
+c        If the "options" string contains "%" format specifiers, then
+c        an optional list of additional arguments may follow it in
+c        order to supply values to be substituted for these
+c        specifiers. The rules for supplying these are identical to
+c        those for the astSet function (and for the C "printf"
+c        function).
+f     STATUS = INTEGER (Given and Returned)
+f        The global status.
+
+*  Returned Value:
+c     astBox()
+f     AST_BOX = INTEGER
+*        A pointer to the new Box.
+
+*  Notes:
+*     - A null Object pointer (AST__NULL) will be returned if this
+c     function is invoked with the AST error status set, or if it
+f     function is invoked with STATUS set to an error value, or if it
+*     should fail for any reason.
+
+*  Status Handling:
+*     The protected interface to this function includes an extra
+*     parameter at the end of the parameter list descirbed above. This
+*     parameter is a pointer to the integer inherited status
+*     variable: "int *status".
+
+*--
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstFrame *frame;              /* Pointer to Frame structure */
+   AstBox *new;                  /* Pointer to new Box */
+   va_list args;                 /* Variable argument list */
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain and validate a pointer to the supplied Frame structure. */
+   frame = astCheckFrame( frame_void );
+
+/* Initialise the Box, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitBox( NULL, sizeof( AstBox ), !class_init, &class_vtab,
+                     "Box", frame, form, point1, point2, unc );
+
+/* If successful, note that the virtual function table has been
+   initialised. */
+   if ( astOK ) {
+      class_init = 1;
+
+/* Obtain the variable argument list and pass it along with the options string
+   to the astVSet method to initialise the new Box's attributes. */
+      va_start( args, status );
+      astVSet( new, options, NULL, args );
+      va_end( args );
+
+/* If an error occurred, clean up by deleting the new object. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return a pointer to the new Box. */
+   return new;
+}
+
+AstBox *astBoxId_( void *frame_void, int form, const double point1[],
+                   const double point2[], void *unc_void, const char *options,
+                   ... ) {
+/*
+*  Name:
+*     astBoxId_
+
+*  Purpose:
+*     Create a Box.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstBox *astBoxId_( AstFrame *frame, int form, const double point1[],
+*                        const double point2[], AstRegion *unc,
+*                        const char *options, ... )
+
+*  Class Membership:
+*     Box constructor.
+
+*  Description:
+*     This function implements the external (public) interface to the
+*     astBox constructor function. It returns an ID value (instead
+*     of a true C pointer) to external users, and must be provided
+*     because astBox_ has a variable argument list which cannot be
+*     encapsulated in a macro (where this conversion would otherwise
+*     occur).
+*
+*     The variable argument list also prevents this function from
+*     invoking astBox_ directly, so it must be a re-implementation
+*     of it in all respects, except for the final conversion of the
+*     result to an ID value.
+
+*  Parameters:
+*     As for astBox_.
+
+*  Returned Value:
+*     The ID value associated with the new Box.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstFrame *frame;              /* Pointer to Frame structure */
+   AstBox *new;                  /* Pointer to new Box */
+   AstRegion *unc;               /* Pointer to Region structure */
+   va_list args;                 /* Variable argument list */
+
+   int *status;                  /* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Pointer to inherited status value */
+
+/* Get a pointer to the inherited status value. */
+   status = astGetStatusPtr;
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain a Frame pointer from the supplied ID and validate the
+   pointer to ensure it identifies a valid Frame. */
+   frame = astVerifyFrame( astMakePointer( frame_void ) );
+
+/* Obtain a Region pointer from the supplied "unc" ID and validate the
+   pointer to ensure it identifies a valid Region . */
+   unc = unc_void ? astCheckRegion( astMakePointer( unc_void ) ) : NULL;
+
+/* Initialise the Box, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitBox( NULL, sizeof( AstBox ), !class_init, &class_vtab,
+                     "Box", frame, form, point1, point2, unc );
+
+/* If successful, note that the virtual function table has been
+   initialised. */
+   if ( astOK ) {
+      class_init = 1;
+
+/* Obtain the variable argument list and pass it along with the options string
+   to the astVSet method to initialise the new Box's attributes. */
+      va_start( args, options );
+      astVSet( new, options, NULL, args );
+      va_end( args );
+
+/* If an error occurred, clean up by deleting the new object. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return an ID value for the new Box. */
+   return astMakeId( new );
+}
+
+AstBox *astInitBox_( void *mem, size_t size, int init, AstBoxVtab *vtab,
+                     const char *name, AstFrame *frame, int form,
+                     const double point1[], const double point2[],
+                     AstRegion *unc, int *status ) {
+/*
+*+
+*  Name:
+*     astInitBox
+
+*  Purpose:
+*     Initialise a Box.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstBox *astInitBox_( void *mem, size_t size, int init, AstBoxVtab *vtab,
+*                         const char *name, AstFrame *frame, int form,
+*                         const double point1[], const double point2[],
+*                         AstRegion *unc )
+
+*  Class Membership:
+*     Box initialiser.
+
+*  Description:
+*     This function is provided for use by class implementations to initialise
+*     a new Box object. It allocates memory (if necessary) to accommodate
+*     the Box plus any additional data associated with the derived class.
+*     It then initialises a Box structure at the start of this memory. If
+*     the "init" flag is set, it also initialises the contents of a virtual
+*     function table for a Box at the start of the memory passed via the
+*     "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory in which the Box is to be initialised.
+*        This must be of sufficient size to accommodate the Box data
+*        (sizeof(Box)) plus any data used by the derived class. If a value
+*        of NULL is given, this function will allocate the memory itself using
+*        the "size" parameter to determine its size.
+*     size
+*        The amount of memory used by the Box (plus derived class data).
+*        This will be used to allocate memory if a value of NULL is given for
+*        the "mem" parameter. This value is also stored in the Box
+*        structure, so a valid value must be supplied even if not required for
+*        allocating memory.
+*     init
+*        A logical flag indicating if the Box's virtual function table is
+*        to be initialised. If this value is non-zero, the virtual function
+*        table will be initialised by this function.
+*     vtab
+*        Pointer to the start of the virtual function table to be associated
+*        with the new Box.
+*     name
+*        Pointer to a constant null-terminated character string which contains
+*        the name of the class to which the new object belongs (it is this
+*        pointer value that will subsequently be returned by the astGetClass
+*        method).
+*     frame
+*        A pointer to the Frame in which the region is defined.
+*     form
+*        Indicates how the box is described by the remaining parameters.
+*        A value of zero indicates that the box is specified by a centre
+*        position and a corner position. A value of one indicates that the
+*        box is specified by a two opposite corner positions.
+*     point1
+*        An array of double, with one element for each Frame axis (Naxes
+*        attribute). If "form" is zero, this array should contain the
+*        coordinates at the centre of the box. If "form" is one, it should
+*        contain the coordinates at the corner of the box which is diagonally
+*        opposite the corner specified by "point2".
+*     point2
+*        An array of double, with one element for each Frame axis (Naxes
+*        attribute) containing the coordinates at any of the corners of
+*        the box.
+*     unc
+*        A pointer to a Region which specifies the uncertainty in the
+*        supplied positions (all points on the boundary of the new Box
+*        being initialised are assumed to have the same uncertainty). A NULL
+*        pointer can be supplied, in which case default uncertainties equal to
+*        1.0E-6 of the dimensions of the new Box's bounding box are used.
+*        If an uncertainty Region is supplied, it must be either a Box, a
+*        Circle or an Ellipse, and its encapsulated Frame must be related
+*        to the Frame supplied for parameter "frame" (i.e. astConvert
+*        should be able to find a Mapping between them). Two positions
+*        the "frame" Frame are considered to be co-incident if their
+*        uncertainty Regions overlap. The centre of the supplied
+*        uncertainty Region is immaterial since it will be re-centred on the
+*        point being tested before use. A deep copy is taken of the supplied
+*        Region.
+
+*  Returned Value:
+*     A pointer to the new Box.
+
+*  Notes:
+*     -  A null pointer will be returned if this function is invoked with the
+*     global error status set, or if it should fail for any reason.
+*-
+*/
+
+/* Local Variables: */
+   AstBox *new;              /* Pointer to new Box */
+   AstPointSet *pset;        /* PointSet to pass to Region initialiser */
+   double **ptr;             /* Pointer to coords data in pset */
+   int i;                    /* axis index */
+   int nc;                   /* No. of axes */
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* If necessary, initialise the virtual function table. */
+   if ( init ) astInitBoxVtab( vtab, name );
+
+/* Initialise. */
+   new = NULL;
+
+/* Get the number of axis values required for each position. */
+   nc = astGetNaxes( frame );
+
+/* Create a PointSet to hold the supplied values, and get points to the
+   data arrays. */
+   pset = astPointSet( 2, nc, "", status );
+   ptr = astGetPoints( pset );
+
+/* Copy the supplied coordinates into the PointSet, checking that no bad
+   values have been supplied. */
+   for( i = 0; astOK && i < nc; i++ ) {
+      if( point1[ i ] == AST__BAD ) {
+         astError( AST__BADIN, "astInitBox(%s): The value of axis %d is "
+                   "undefined at point 1 of the box.", status, name, i + 1 );
+         break;
+      }
+      if( point2[ i ] == AST__BAD ) {
+         astError( AST__BADIN, "astInitBox(%s): The value of axis %d is "
+                   "undefined at point 2 of the box.", status, name, i + 1 );
+         break;
+      }
+      ptr[ i ][ 0 ] = point1[ i ];
+      ptr[ i ][ 1 ] = point2[ i ];
+   }
+
+/* If two corners were supplied, find and store the centre. */
+   if( form == 1 ) {
+      for( i = 0; i < nc; i++ ) {
+         ptr[ i ][ 0 ] = 0.5*( point1[ i ] + point2[ i ] );
+      }
+   }
+
+/* Check pointers can be used safely. */
+   if( astOK ) {
+
+/* Initialise a Region structure (the parent class) as the first component
+   within the Box structure, allocating memory if necessary. */
+      new = (AstBox *) astInitRegion( mem, size, 0, (AstRegionVtab *) vtab,
+                                      name, frame, pset, unc );
+
+      if ( astOK ) {
+
+/* Initialise the Box data. */
+/* ------------------------ */
+         new->extent = NULL;
+         new->centre = NULL;
+         new->lo = NULL;
+         new->hi = NULL;
+         new->geolen = NULL;
+         new->stale = 1;
+
+/* If an error occurred, clean up by deleting the new Box. */
+         if ( !astOK ) new = astDelete( new );
+      }
+   }
+
+/* Free resources. */
+   pset = astAnnul( pset );
+
+/* Return a pointer to the new Box. */
+   return new;
+}
+
+AstBox *astLoadBox_( void *mem, size_t size, AstBoxVtab *vtab,
+                     const char *name, AstChannel *channel, int *status ) {
+/*
+*+
+*  Name:
+*     astLoadBox
+
+*  Purpose:
+*     Load a Box.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "box.h"
+*     AstBox *astLoadBox( void *mem, size_t size, AstBoxVtab *vtab,
+*                         const char *name, AstChannel *channel )
+
+*  Class Membership:
+*     Box loader.
+
+*  Description:
+*     This function is provided to load a new Box using data read
+*     from a Channel. It first loads the data used by the parent class
+*     (which allocates memory if necessary) and then initialises a
+*     Box structure in this memory, using data read from the input
+*     Channel.
+*
+*     If the "init" flag is set, it also initialises the contents of a
+*     virtual function table for a Box at the start of the memory
+*     passed via the "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory into which the Box is to be
+*        loaded.  This must be of sufficient size to accommodate the
+*        Box data (sizeof(Box)) plus any data used by derived
+*        classes. If a value of NULL is given, this function will
+*        allocate the memory itself using the "size" parameter to
+*        determine its size.
+*     size
+*        The amount of memory used by the Box (plus derived class
+*        data).  This will be used to allocate memory if a value of
+*        NULL is given for the "mem" parameter. This value is also
+*        stored in the Box structure, so a valid value must be
+*        supplied even if not required for allocating memory.
+*
+*        If the "vtab" parameter is NULL, the "size" value is ignored
+*        and sizeof(AstBox) is used instead.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new Box. If this is NULL, a pointer
+*        to the (static) virtual function table for the Box class
+*        is used instead.
+*     name
+*        Pointer to a constant null-terminated character string which
+*        contains the name of the class to which the new object
+*        belongs (it is this pointer value that will subsequently be
+*        returned by the astGetClass method).
+*
+*        If the "vtab" parameter is NULL, the "name" value is ignored
+*        and a pointer to the string "Box" is used instead.
+
+*  Returned Value:
+*     A pointer to the new Box.
+
+*  Notes:
+*     - A null pointer will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*-
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstBox *new;              /* Pointer to the new Box */
+
+/* Initialise. */
+   new = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return new;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(channel);
+
+/* If a NULL virtual function table has been supplied, then this is
+   the first loader to be invoked for this Box. In this case the
+   Box belongs to this class, so supply appropriate values to be
+   passed to the parent class loader (and its parent, etc.). */
+   if ( !vtab ) {
+      size = sizeof( AstBox );
+      vtab = &class_vtab;
+      name = "Box";
+
+/* If required, initialise the virtual function table for this class. */
+      if ( !class_init ) {
+          astInitBoxVtab( vtab, name );
+         class_init = 1;
+      }
+   }
+
+/* Invoke the parent class loader to load data for all the ancestral
+   classes of the current one, returning a pointer to the resulting
+   partly-built Box. */
+   new = astLoadRegion( mem, size, (AstRegionVtab *) vtab, name,
+                        channel );
+
+   if ( astOK ) {
+
+/* Read input data. */
+/* ================ */
+/* Request the input Channel to read all the input data appropriate to
+   this class into the internal "values list". */
+      astReadClassData( channel, "Box" );
+
+/* Now read each individual data item from this list and use it to
+   initialise the appropriate instance variable(s) for this class. */
+
+/* In the case of attributes, we first read the "raw" input value,
+   supplying the "unset" value as the default. If a "set" value is
+   obtained, we then use the appropriate (private) Set... member
+   function to validate and set the value properly. */
+
+/* There are no values to read. */
+/* ---------------------------- */
+
+/* Initialise Box data */
+      new->extent = NULL;
+      new->centre = NULL;
+      new->lo = NULL;
+      new->hi = NULL;
+      new->geolen = NULL;
+      new->stale = 1;
+
+/* If an error occurred, clean up by deleting the new Box. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return the new Box pointer. */
+   return new;
+}
+
+/* Virtual function interfaces. */
+/* ============================ */
+/* These provide the external interface to the virtual functions defined by
+   this class. Each simply checks the global error status and then locates and
+   executes the appropriate member function, using the function pointer stored
+   in the object's virtual function table (this pointer is located using the
+   astMEMBER macro defined in "object.h").
+
+   Note that the member function may not be the one defined here, as it may
+   have been over-ridden by a derived class. However, it should still have the
+   same interface. */
+
+
+void astBoxPoints_( AstBox *this, double *centre, double *corner,
+                    int *status) {
+   if ( !astOK ) return;
+   (**astMEMBER(this,Box,BoxPoints))( this, centre, corner, status );
+   return;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+