upgrade ast 8.7.1

1 files changed, 0 insertions, 5065 deletions

diff --git a/ast/box.c b/ast/box.c
deleted file mode 100644
index b0b22dd..0000000
--- a/ast/box.c
+++ /dev/null
@@ -1,5065 +0,0 @@
-/*
-*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 ) ) {
-                     ps2 = astAnnul( ps2 );
-                     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;
-}
-
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