upgrade AST

1 files changed, 0 insertions, 4686 deletions

diff --git a/ast/interval.c b/ast/interval.c
deleted file mode 100644
index 73e23bc..0000000
--- a/ast/interval.c
+++ /dev/null
@@ -1,4686 +0,0 @@
-/*
-*class++
-*  Name:
-*     Interval
-
-*  Purpose:
-*     A region representing an interval on one or more axes of a Frame.
-
-*  Constructor Function:
-c     astInterval
-f     AST_INTERVAL
-
-*  Description:
-*     The Interval class implements a Region which represents upper
-*     and/or lower limits on one or more axes of a Frame. For a point to
-*     be within the region represented by the Interval, the point must
-*     satisfy all the restrictions placed on all the axes. The point is
-*     outside the region if it fails to satisfy any one of the restrictions.
-*     Each axis may have either an upper limit, a lower limit, both or
-*     neither. If both limits are supplied but are in reverse order (so
-*     that the lower limit is greater than the upper limit), then the
-*     interval is an excluded interval, rather than an included interval.
-*
-*     Note, The Interval class makes no allowances for cyclic nature of
-*     some coordinate systems (such as SkyFrame coordinates). A Box
-*     should usually be used in these cases since this requires the user
-*     to think about suitable upper and lower limits,
-
-*  Inheritance:
-*     The Interval class inherits from the Region class.
-
-*  Attributes:
-*     The Interval class does not define any new attributes beyond
-*     those which are applicable to all Regions.
-
-*  Functions:
-c     The Interval class does not define any new functions beyond those
-f     The Interval 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
-
-*  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:
-*     29-OCT-2004 (DSB):
-*        Original version.
-*     19-APR-2006 (DSB):
-*        Negate the cached equivalent Box if the Interval has been negated.
-*     28-MAY-2007 (DSB):
-*        Re-implemented BndBaseMesh.
-*     20-JAN-2009 (DSB):
-*        Over-ride astRegBasePick.
-*     26-JAN-2009 (DSB):
-*        Over-ride astMapMerge.
-*     4-NOV42-2013 (DSB):
-*        - Change RegCentre so that it does not report an error for an unbounded
-*        Interval if the centre is merely being inquired rather than set. This is
-*        the documented behaviour of the astRegCentre method.
-*        - 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.
-*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 Interval
-
-/* Include files. */
-/* ============== */
-/* Interface definitions. */
-/* ---------------------- */
-
-#include "globals.h"             /* Thread-safe global data access */
-#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"              /* Abstract coordinate regions (parent class) */
-#include "channel.h"             /* I/O channels */
-#include "box.h"                 /* Box Regions */
-#include "nullregion.h"          /* Null Regions */
-#include "wcsmap.h"              /* Definitons of AST__DPI etc */
-#include "interval.h"            /* Interface definition for this class */
-#include "ellipse.h"             /* Interface definition for ellipse class */
-#include "mapping.h"             /* Position mappings */
-#include "unitmap.h"             /* Unit Mappings */
-#include "cmpmap.h"              /* Compound Mappings */
-#include "cmpframe.h"            /* Compound Frames */
-#include "prism.h"               /* Prism regions */
-#include "pointlist.h"           /* Lists of points in a Frame */
-
-/* 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 AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
-static AstMapping *(* parent_simplify)( AstMapping *, int * );
-static int (* parent_overlap)( AstRegion *, AstRegion *, int * );
-static void (* parent_setregfs)( AstRegion *, AstFrame *, int * );
-static void (* parent_setunc)( AstRegion *, AstRegion *, int * );
-static void (* parent_resetcache)( AstRegion *, int * );
-
-#if defined(THREAD_SAFE)
-static int (* parent_managelock)( AstObject *, int, int, AstObject **, int * );
-#endif
-
-
-#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(Interval)
-
-/* Define macros for accessing each item of thread specific global data. */
-#define class_init astGLOBAL(Interval,Class_Init)
-#define class_vtab astGLOBAL(Interval,Class_Vtab)
-
-
-#include <pthread.h>
-
-
-#else
-
-
-/* Define the class virtual function table and its initialisation flag
-   as static variables. */
-static AstIntervalVtab 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. */
-AstInterval *astIntervalId_( void *, const double[], const double[], void *, const char *, ... );
-
-/* Prototypes for Private Member Functions. */
-/* ======================================== */
-static AstBox *Cache( AstInterval *, int * );
-static AstMapping *Simplify( AstMapping *, int * );
-static AstPointSet *BndBaseMesh( AstRegion *, double *, double *, int * );
-static AstPointSet *RegBaseMesh( AstRegion *, int * );
-static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
-static AstRegion *RegBasePick( AstRegion *this, int, const int *, int * );
-static AstRegion *GetDefUnc( AstRegion *, int * );
-static AstRegion *MergeInterval( AstInterval *, AstRegion *, int, int * );
-static double *RegCentre( AstRegion *this, double *, double **, int, int, int * );
-static int *OneToOne( AstMapping *, int * );
-static int GetBounded( AstRegion *, int * );
-static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
-static int Overlap( AstRegion *, AstRegion *, int * );
-static int RegPins( AstRegion *, AstPointSet *, AstRegion *, int **, int * );
-static int RegTrace( AstRegion *, int, double *, double **, int * );
-static void Copy( const AstObject *, AstObject *, int * );
-static void Delete( AstObject *, int * );
-static void Dump( AstObject *, AstChannel *, int * );
-static void IntervalPoints( AstInterval *, double *, double *, int *);
-static void RegBaseBox( AstRegion *this, double *, double *, int * );
-static void ResetCache( AstRegion *this, int * );
-static void SetRegFS( AstRegion *, AstFrame *, int * );
-static void SetUnc( AstRegion *, AstRegion *, int * );
-
-#if defined(THREAD_SAFE)
-static int ManageLock( AstObject *, int, int, AstObject **, int * );
-#endif
-
-/* Member functions. */
-/* ================= */
-
-static AstPointSet *BndBaseMesh( AstRegion *this, double *lbnd, double *ubnd, int *status ){
-/*
-*  Name:
-*     BndBaseMesh
-
-*  Purpose:
-*     Return a PointSet containing points spread around part of the boundary
-*     of a Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     AstPointSet *BndBaseMesh( AstRegion *this, double *lbnd, double *ubnd, int *status )
-
-*  Class Membership:
-*     Interval method (over-rides the astBndBaseMesh method inherited from
-*     the Region class).
-
-*  Description:
-*     This function returns a PointSet containing a set of points on the
-*     boundary of the intersection between the supplied Region and the
-*     supplied box. The points refer to the base Frame of the
-*     encapsulated FrameSet. If the boundary of the supplied Region does
-*     not intersect the supplied box, then a PointSet containing a single
-*     bad point is returned.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     lbnd
-*        Pointer to an array holding the lower limits of the axis values
-*        within the required box.
-*     ubnd
-*        Pointer to an array holding the upper limits of the axis values
-*        within the required box.
-*     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 uncertainties which were
-*     supplied when the Region was created.
-*
-*    If the Region does not intersect the supplied box, the returned
-*    PointSet will contain a single point with a value of AST__BAD on
-*    every axis.
-
-*  Notes:
-*    - A NULL pointer is returned if an error has already occurred, or if
-*    this function should fail for any reason.
-*/
-
-/* Local Variables: */
-   AstBox *box;
-   AstFrame *bfrm;
-   AstInterval *this_interval;
-   AstMapping *map;
-   AstPointSet *result;
-   double *lbndb;
-   double *ubndb;
-   double **ptr;
-   int closed;
-   int i;
-   int nbase;
-
-/* Initialise */
-   result = NULL;
-
-/* Check the local error status. */
-   if ( !astOK ) return result;
-
-/* Store a pointer to the interval. */
-   this_interval = (AstInterval *) this;
-
-/* If the Interval is effectively a Box, invoke the astBndBaseMesh
-   function on the equivalent Box. A pointer to the equivalent Box will
-   be stored in the Interval structure. */
-   box = Cache( (AstInterval *) this, status );
-   if( box ) {
-      result = astBndBaseMesh( box, lbnd, ubnd );
-
-/* If the Interval is not equivalent to a Box (i.e. if one or more bounds
-   are missing)... */
-   } else {
-
-/* Find the base frame box that just encloses the supplied current Frame
-   box. */
-      map = astGetMapping( this->frameset, AST__CURRENT, AST__BASE );
-      nbase = astGetNout( map );
-      lbndb = astMalloc( sizeof(double)*nbase );
-      ubndb = astMalloc( sizeof(double)*nbase );
-      if( astOK ) {
-         for( i = 0; i < nbase; i++ ) {
-            astMapBox( map, lbnd, ubnd, 1, i, lbndb + i, ubndb + i,
-                       NULL, NULL );
-         }
-
-/* Create a Box that is like this Interval except that missing bounds are
-   inherited from the supplied limits. Check that the resulting box is
-   closed. */
-         closed = 1;
-         for( i = 0; i < nbase; i++ ) {
-            if( this_interval->ubnd[ i ] != DBL_MAX ) ubndb[ i ] = this_interval->ubnd[ i ];
-            if( this_interval->lbnd[ i ] != -DBL_MAX ) lbndb[ i ] = this_interval->lbnd[ i ];
-            if( lbndb[ i ] > ubndb[ i ] ) closed = 0;
-         }
-
-/* Cannot create the required mesh if the box is not closed. */
-         if( closed ) {
-
-/* Create the Box. */
-            bfrm = astGetFrame( this->frameset, AST__BASE );
-            box = astBox( bfrm, 1, lbndb, ubndb, NULL, "", status );
-
-/* Create the required mesh. */
-            result = astRegBaseMesh( box );
-
-/* Free resources */
-            bfrm = astAnnul( bfrm );
-            box = astAnnul( box );
-
-/* If the boundary of the supplied Region does not intersect the box,
-   return a PointSet containing a single bad position. */
-         } else {
-            result = astPointSet( 1, nbase, "", status );
-            ptr = astGetPoints( result );
-            if( astOK ) {
-               for( i = 0; i < nbase; i++ ) ptr[ i ][ 0 ] = AST__BAD;
-            }
-         }
-      }
-
-/* Free resources. */
-      map = astAnnul( map );
-      lbndb = astFree( lbndb );
-      ubndb = astFree( ubndb );
-   }
-
-/* Return NULL if an error occurred. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return the required pointer. */
-   return result;
-}
-
-static AstBox *Cache( AstInterval *this, int *status ){
-/*
-*  Name:
-*     Cache
-
-*  Purpose:
-*     Calculate intermediate values and cache them in the Interval structure.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     AstBox *Cache( AstInterval *this, int *status )
-
-*  Class Membership:
-*     Interval 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 Interval structure.
-
-*  Parameters:
-*     this
-*        Pointer to the Interval.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     If the Interval is equivalent to a Box, then a pointer to the
-*     equivalent Box is returned. This is a copy of the pointer stored in
-*     the Interval structure and should not be annulled.
-
-*/
-
-/* Local Variables: */
-   AstBox *bbox;            /* Equivalent base Box */
-   AstFrame *bfrm;          /* Interval base Frame */
-   AstFrame *cfrm;          /* Interval current Frame */
-   AstRegion *map;          /* Interval base->current Mapping */
-   AstRegion *reg;          /* Pointer to this Region structure */
-   AstRegion *unc;          /* Pointer to uncertainty Region */
-   double **ptr;            /* Pointer to data holding all axis limits */
-   double *lbnd;            /* Pointer to array of lower axis limits */
-   double *ubnd;            /* Pointer to array of upper axis limits */
-   int i;                   /* Axis index */
-   int isBox;               /* Is this Interval equivalent to a Box? */
-   int nc;                  /* Number of base Frame axes */
-   int neg;                 /* Is the equivalent Box negated? */
-
-/* Check the global error status. Also return if the cached information
-   is up to date (i.e. not stale). */
-   if( !this->stale || !astOK ) return this->box;
-
-/* Get a pointer to the Region structure */
-   reg = (AstRegion *) this;
-
-/* The Interval structure contains a pointer to an equivalent Box
-   structure. This Box structure is created below if the Interval is
-   equivalent to a Box. Annul any previous box. */
-   if( this->box ) this->box = astAnnul( this->box );
-
-/* Get the number of axes in the base Frame of the FrameSet encapsulated
-   by the parent Region structure. */
-   nc = astGetNin( reg->frameset );
-
-/* Get a pointer to the array holding the axis limits held in the PointSet
-   encapsulated in the parent Region structure. */
-   ptr = astGetPoints( reg->points );
-
-/* Allocate memory to hold the limits organised per point rather than per
-   axis. */
-   lbnd = astMalloc( sizeof( double )*(size_t)nc );
-   ubnd = astMalloc( sizeof( double )*(size_t)nc );
-
-/* Check these pointers can be used safely. */
-   if( ubnd ) {
-
-/* See if the Interval is effectively a (possibly negated) Box. Assume it
-   is to begin with.  */
-      isBox = 1;
-
-/* Initialisation to prevent compiler warnings. */
-      neg = 0;
-
-/* Check the limits on every axis. */
-      for( i = 0; i < nc; i++ ) {
-
-/* Copy the axis limits into the allocated arrays (these are needed by the
-   Box constructor later on). */
-         lbnd[ i ] = ptr[ i ][ 0 ];
-         ubnd[ i ] = ptr[ i ][ 1 ];
-
-/* The Interval is not a Box if any axis limit is missing. In this case
-   use -DBL_MAX or +DBL_MAX as the limit to be stored in the Interval
-   structure. */
-         if( lbnd[ i ] == AST__BAD ) lbnd[ i ] = -DBL_MAX;
-         if( fabs( lbnd[ i ] ) == DBL_MAX ) isBox = 0;
-
-         if( ubnd[ i ] == AST__BAD ) ubnd[ i ] = DBL_MAX;
-         if( fabs( ubnd[ i ] ) == DBL_MAX ) isBox = 0;
-
-/* If this is the first axis, note if the axis interval is included or
-   excluded. This is determined by whether the "lower limit" is greater
-   than or less than the "upper limit". If the axis interval is excluded
-   (lower limit greater than upper limit), then any equivalent Box will be
-   a negated Box (i.e. will represent the outside of a box rather than
-   the inside). */
-         if( i == 0 ){
-            neg = ( lbnd[ i ] > ubnd[ i ]  );
-
-/* The Interval is not a Box if the limits for this axis are not the same
-   way round as those of the first axis. */
-         } else {
-
-            if( neg ) {
-               if( lbnd[ i ] < ubnd[ i ]  ) isBox = 0;
-            } else {
-               if( lbnd[ i ] > ubnd[ i ]  ) isBox = 0;
-            }
-
-         }
-      }
-
-/* If the Interval is effectively an unnegated Box, create the equivalent Box,
-   and store a pointer to it in the Interval structure. */
-      if( isBox && !neg ) {
-         bfrm = astGetFrame( reg->frameset, AST__BASE );
-         cfrm = astGetFrame( reg->frameset, AST__CURRENT );
-         map = astGetMapping( reg->frameset, AST__BASE, AST__CURRENT );
-         unc = astTestUnc( reg ) ? astGetUncFrm( reg, AST__BASE ) : NULL;
-
-         bbox = astBox( bfrm, 1, lbnd, ubnd, unc, "", status );
-         if( astIsAUnitMap( map ) ){
-            this->box = astClone( bbox );
-         } else {
-            this->box = astMapRegion( bbox, map, cfrm );
-         }
-
-         if( unc ) unc = astAnnul( unc );
-         cfrm = astAnnul( cfrm );
-         bfrm = astAnnul( bfrm );
-         map = astAnnul( map );
-         bbox = astAnnul( bbox );
-
-/* If the supplied Interval has been negated, negate the equivalent Box. */
-         if( astGetNegated( this ) ) astNegate( this->box );
-
-/* If the supplied Interval is closed, ensure the equivalent Box is closed. */
-         astSetClosed( this->box, astGetClosed( this ) );
-      }
-
-/* Store the axis limits in the Interval structure. */
-      if( this->lbnd ) astFree( this->lbnd );
-      if( this->ubnd ) astFree( this->ubnd );
-      this->lbnd = lbnd;
-      this->ubnd = ubnd;
-   }
-
-/* Indicate the cached information is no longer stale, and return a
-   pointer to any equivalent Box. */
-   this->stale = 0;
-   return this->box;
-}
-
-static int GetBounded( AstRegion *this, int *status ) {
-/*
-*  Name:
-*     GetBounded
-
-*  Purpose:
-*     Is the Region bounded?
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     int GetBounded( AstRegion *this, int *status )
-
-*  Class Membership:
-*     Interval method (over-rides the astGetBounded method inherited from
-*     the Region class).
-
-*  Description:
-*     This function returns a flag indicating if the Region is bounded.
-*     The implementation provided by the base Region class is suitable
-*     for Region sub-classes representing the inside of a single closed
-*     curve (e.g. Circle, Interval, Box, etc). Other sub-classes (such as
-*     CmpRegion, PointList, etc ) may need to provide their own
-*     implementations.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     Non-zero if the Region is bounded. Zero otherwise.
-
-*/
-
-/* Local Variables: */
-   int result;                /* Returned result */
-
-/* Initialise */
-   result = 0;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* The unnegated Interval is bounded only if there is an equivalent Box
-   structure stored in the Interval structure. */
-   if( Cache( (AstInterval *) this, status ) ) result = 1;
-
-/* Return the required pointer. */
-   return result;
-}
-
-static AstRegion *GetDefUnc( AstRegion *this_region, int *status ) {
-/*
-*  Name:
-*     GetDefUnc
-
-*  Purpose:
-*     Obtain a pointer to the default uncertainty Region for a given Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     AstRegion *GetDefUnc( AstRegion *this, int *status )
-
-*  Class Membership:
-*     Interval member function (over-rides the astGetDefUnc protected
-*     method inherited from the Region class).
-
-*  Description:
-*     This function returns a pointer to a Region which represents the
-*     default uncertainty associated with a position on the boundary of the
-*     given Region. The returned Region refers to the base Frame within the
-*     FrameSet encapsulated by the supplied Region.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     A pointer to the Region. This should be annulled (using astAnnul)
-*     when no longer needed.
-
-*  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 *box;               /* Pointer to equivalent Box */
-   AstFrame *bfrm;            /* Base Frame of supplied Region */
-   AstInterval *this;         /* Pointer to Interval structure */
-   AstRegion *result;         /* Returned pointer */
-   double *lbnd;              /* Ptr. to array holding axis lower bounds */
-   double *ubnd;              /* Ptr. to array holding axis upper bounds */
-   double c;                  /* Central axis value */
-   double hw;                 /* Half width of uncertainty interval */
-   int i;                     /* Axis index */
-   int nax;                   /* Number of base Frame axes */
-
-/* Initialise */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the Interval structure. */
-   this = (AstInterval *) this_region;
-
-/* If this Interval is equivalent to a Box, get the default uncertainty
-   for the equivalent Box and return it. */
-   box = Cache( this, status );
-   if( box ) {
-      result = astGetDefUnc( box );
-
-/* Otherwise, we use a box covering 1.0E-6 of each axis interval, centred on
-   the origin. */
-   } else {
-
-/* Get a pointer to the base Frame. */
-      bfrm = astGetFrame( this_region->frameset, AST__BASE );
-
-/* Get the number of base Frame axes. */
-      nax = astGetNaxes( bfrm );
-
-/* Allocate arrays to hold the bounds of the uncertainty Box. */
-      lbnd = astMalloc( sizeof( double)*(size_t) nax );
-      ubnd = astMalloc( sizeof( double)*(size_t) nax );
-      if( astOK ) {
-
-/* Ensure cached information (e.g.bounds) is up to date. */
-         Cache( this, status );
-
-/* Do each axis in turn */
-         for( i = 0; i < nax; i++ ) {
-
-/* If this axis has both limits, use 1.0E-6 of the difference between the
-   limits. */
-            if( this->lbnd[ i ] != -DBL_MAX &&
-                this->ubnd[ i ] != DBL_MAX ) {
-               hw = fabs( 0.5E-6*(  this->ubnd[ i ] - this->lbnd[ i ] ) );
-               c = 0.5*(  this->ubnd[ i ] + this->lbnd[ i ] );
-               if( hw == 0.0 ) hw = c*0.5E-6;
-               ubnd[ i ] = c + hw;
-               lbnd[ i ] = c - hw;
-
-/* Otherwise use zero. */
-            } else {
-               ubnd[ i ] = 0.0;
-               lbnd[ i ] = 0.0;
-            }
-         }
-
-/* Create the Box. */
-         result = (AstRegion *) astBox( bfrm, 1, lbnd, ubnd, NULL, "", status );
-      }
-
-/* Free resources. */
-      lbnd = astFree( lbnd );
-      ubnd = astFree( ubnd );
-      bfrm = astAnnul( bfrm );
-   }
-
-/* Return NULL if an error occurred. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return the required pointer. */
-   return result;
-}
-
-void astInitIntervalVtab_(  AstIntervalVtab *vtab, const char *name, int *status ) {
-/*
-*+
-*  Name:
-*     astInitIntervalVtab
-
-*  Purpose:
-*     Initialise a virtual function table for a Interval.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     void astInitIntervalVtab( AstIntervalVtab *vtab, const char *name )
-
-*  Class Membership:
-*     Interval vtab initialiser.
-
-*  Description:
-*     This function initialises the component of a virtual function
-*     table which is used by the Interval 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 */
-   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
-   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
-   AstRegionVtab *region;        /* Pointer to Region 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 astIsAInterval) 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->IntervalPoints = IntervalPoints;
-
-/* 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;
-
-#if defined(THREAD_SAFE)
-   parent_managelock = object->ManageLock;
-   object->ManageLock = ManageLock;
-#endif
-
-   parent_transform = mapping->Transform;
-   mapping->Transform = Transform;
-
-   parent_simplify = mapping->Simplify;
-   mapping->Simplify = Simplify;
-
-   parent_overlap = region->Overlap;
-   region->Overlap = Overlap;
-
-   parent_setregfs = region->SetRegFS;
-   region->SetRegFS = SetRegFS;
-
-   parent_resetcache = region->ResetCache;
-   region->ResetCache = ResetCache;
-
-   parent_setunc = region->SetUnc;
-   region->SetUnc = SetUnc;
-
-/* Store replacement pointers for methods which will be over-ridden by
-   new member functions implemented here. */
-   mapping->MapMerge = MapMerge;
-
-   region->RegCentre = RegCentre;
-   region->GetBounded = GetBounded;
-   region->GetDefUnc = GetDefUnc;
-   region->RegPins = RegPins;
-   region->RegTrace = RegTrace;
-   region->RegBaseMesh = RegBaseMesh;
-   region->BndBaseMesh = BndBaseMesh;
-   region->RegBaseBox = RegBaseBox;
-   region->RegBasePick = RegBasePick;
-
-/* Declare the copy constructor, destructor and class dump
-   functions. */
-   astSetDelete( vtab, Delete );
-   astSetCopy( vtab, Copy );
-   astSetDump( vtab, Dump, "Interval", "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) );
-   }
-}
-
-void IntervalPoints( AstInterval *this, double *lbnd, double *ubnd,
-                     int *status) {
-/*
-*+
-*  Name:
-*     astIntervalPoints
-
-*  Purpose:
-*     Return the defining points of a Interval.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "box.h"
-*     astIntervalPoints( AstInterval *this, double *lbnd, double *ubnd )
-
-*  Class Membership:
-*     Region virtual function.
-
-*  Description:
-*     This function returns the axis values at the points defining the
-*     supplied Interval.
-
-*  Parameters:
-*     this
-*        Pointer to the Interval.
-*     lbnd
-*        A pointer to an array in which to return the "lbnd" values
-*        supplied when the Interval was constructed. These are in the
-*        base Frame of the encapsilated FrameSet.
-*     ubnd
-*        A pointer to an array in which to return the "ubnd" values
-*        supplied when the Interval was constructed. These are in the
-*        base Frame of the encapsilated 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 Interval. */
-   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 axis values from the PointSet into the supplied arrays. */
-   for( i = 0; i < nc; i++ ) {
-      lbnd[ i ] = ptr[ i ] [ 0 ];
-      ubnd[ i ] = ptr[ i ] [ 1 ];
-   }
-}
-
-#if defined(THREAD_SAFE)
-static int ManageLock( AstObject *this_object, int mode, int extra,
-                       AstObject **fail, int *status ) {
-/*
-*  Name:
-*     ManageLock
-
-*  Purpose:
-*     Manage the thread lock on an Object.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "object.h"
-*     AstObject *ManageLock( AstObject *this, int mode, int extra,
-*                            AstObject **fail, int *status )
-
-*  Class Membership:
-*     Interval member function (over-rides the astManageLock protected
-*     method inherited from the parent class).
-
-*  Description:
-*     This function manages the thread lock on the supplied Object. The
-*     lock can be locked, unlocked or checked by this function as
-*     deteremined by parameter "mode". See astLock for details of the way
-*     these locks are used.
-
-*  Parameters:
-*     this
-*        Pointer to the Object.
-*     mode
-*        An integer flag indicating what the function should do:
-*
-*        AST__LOCK: Lock the Object for exclusive use by the calling
-*        thread. The "extra" value indicates what should be done if the
-*        Object is already locked (wait or report an error - see astLock).
-*
-*        AST__UNLOCK: Unlock the Object for use by other threads.
-*
-*        AST__CHECKLOCK: Check that the object is locked for use by the
-*        calling thread (report an error if not).
-*     extra
-*        Extra mode-specific information.
-*     fail
-*        If a non-zero function value is returned, a pointer to the
-*        Object that caused the failure is returned at "*fail". This may
-*        be "this" or it may be an Object contained within "this". Note,
-*        the Object's reference count is not incremented, and so the
-*        returned pointer should not be annulled. A NULL pointer is
-*        returned if this function returns a value of zero.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*    A local status value:
-*        0 - Success
-*        1 - Could not lock or unlock the object because it was already
-*            locked by another thread.
-*        2 - Failed to lock a POSIX mutex
-*        3 - Failed to unlock a POSIX mutex
-*        4 - Bad "mode" value supplied.
-
-*  Notes:
-*     - This function attempts to execute even if an error has already
-*     occurred.
-*/
-
-/* Local Variables: */
-   AstInterval *this;       /* Pointer to Interval structure */
-   int result;              /* Returned status value */
-
-/* Initialise */
-   result = 0;
-
-/* Check the supplied pointer is not NULL. */
-   if( !this_object ) return result;
-
-/* Obtain a pointers to the Interval structure. */
-   this = (AstInterval *) this_object;
-
-/* Invoke the ManageLock method inherited from the parent class. */
-   if( !result ) result = (*parent_managelock)( this_object, mode, extra,
-                                                fail, status );
-
-/* Invoke the astManageLock method on any Objects contained within
-   the supplied Object. */
-   if( !result ) result = astManageLock( this->box, mode, extra, fail );
-
-   return result;
-
-}
-#endif
-
-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 Interval.
-
-*  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:
-*     Interval 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 Interval 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 Interval 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 Interval which is to be merged with
-*        its neighbours. This should be a cloned copy of the Interval
-*        pointer contained in the array element "(*map_list)[where]"
-*        (see below). This pointer will not be annulled, and the
-*        Interval it identifies will not be modified by this function.
-*     where
-*        Index in the "*map_list" array (below) at which the pointer
-*        to the nominated Interval 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: */
-   AstInterval *oldint;  /* Pointer to supplied Interval */
-   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 = -1;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the Interval. */
-   oldint = (AstInterval *) this;
-
-/* First of all, see if the Interval can be replaced by a simpler Region,
-   without reference to the neighbouring Regions in the list.           */
-/* =====================================================================*/
-
-/* Try to simplify the Interval. If the pointer value has changed, we assume
-   some simplification took place. */
-   new = astSimplify( oldint );
-   if( new != (AstMapping *) oldint ) {
-
-/* Annul the Interval 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 Interval 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 Interval with its lower neighbour (if any). */
-      if( where > 0 ) {
-         i1 = where - 1;
-         map = ( *map_list )[ where - 1 ];
-         if( astIsARegion( map ) ) {
-            new = (AstMapping *) MergeInterval( oldint, (AstRegion *) map,
-                                                0, status );
-         }
-      }
-
-/* If this did not produced a merged Region, attempt to merge the Interval
-   with its upper neighbour (if any). */
-      if( !new && where < *nmap - 1 ) {
-         i1 = where;
-         map = ( *map_list )[ where + 1 ];
-         if( astIsARegion( map ) ) {
-            new = (AstMapping *) MergeInterval( oldint, (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 *MergeInterval( AstInterval *this, AstRegion *reg,
-                                 int intfirst, int *status ) {
-/*
-*  Name:
-*     MergeInterval
-
-*  Purpose:
-*     Attempt to merge a Interval with another Region to form a Region of
-*     higher dimensionality.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "box.h"
-*     AstRegion *MergeInterval( AstInterval *this, AstRegion *reg,
-*                               int intfirst, int *status )
-
-*  Class Membership:
-*     Interval member function.
-
-*  Description:
-*     This function attempts to combine the supplied Regions together
-*     into a Region of higher dimensionality.
-
-*  Parameters:
-*     this
-*        Pointer to a Interval.
-*     reg
-*        Pointer to another Region.
-*     intfirst
-*        If non-zero, then the Interval 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 Interval centre axis values */
-   double *corner;           /* Array to hold Interval corner axis values */
-   double *lbnd;             /* Array to hold lower axis bounds */
-   double *lbnd_unc;         /* Array to hold uncertainty lower bounds */
-   double *p;                /* Pointer to next input value */
-   double *q;                /* Pointer to next output value */
-   double *ubnd;             /* Array to hold upper axis bounds */
-   double *ubnd_unc;         /* Array to hold uncertainty upper 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 Interval  */
-   int npnt;                 /* Number of points in PointList */
-   int ok;                   /* Can supplied Regions be merged? */
-
-/* Initialise */
-   result = NULL;
-   lbnd = NULL;
-   ubnd = 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( intfirst ) {
-         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 Interval. The result will be an
-   Interval. Both Intervals must be un-negated. */
-      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 limits from the supplied Intervals into the above arrays,
-   in the requested order. */
-         if( intfirst ) {
-            astIntervalPoints( this, lbnd, ubnd );
-            astIntervalPoints( reg, lbnd + nax_this, ubnd + nax_this );
-         } else {
-            astIntervalPoints( reg, lbnd, ubnd );
-            astIntervalPoints( this, lbnd + nax_reg, ubnd + nax_reg );
-         }
-
-/*  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 Box. The result will be an Interval. Both
-   Regions must be un-negated. */
-      } else if( astIsABox( 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 );
-
-/* Get the bounds from the Interval and add them into the above arrays. */
-         if( intfirst ) {
-            astIntervalPoints( this, lbnd, ubnd );
-         } else {
-            astIntervalPoints( this, lbnd + nax_reg, ubnd + nax_reg );
-         }
-
-/* Copy the centre and corner from the supplied Box into the required part
-   of the above arrays. */
-         if( intfirst ) {
-            centre = lbnd + nax_this;
-            corner = ubnd + nax_this;
-         } else {
-            centre = lbnd;
-            corner = ubnd;
-         }
-         astBoxPoints( reg, centre, corner );
-
-/* Convert these centre and corner positions into upper and lower bounds. */
-         if( astOK ) {
-            for( i = 0; i < nax_reg; i++ ) {
-               centre[ i ] = 2*centre[ i ] - corner[ i ];
-               if( centre[ i ] > corner[ i ] ) {
-                  temp = centre[ i ];
-                  centre[ i ] = corner[ i ];
-                  corner[ i ] = temp;
-               }
-            }
-         }
-
-/*  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 Interval 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 limits from the supplied Interval into the above arrays.
-   Store bad values for the other axes indicating they are unbounded. */
-         if( intfirst ) {
-            astIntervalPoints( this, lbnd, ubnd );
-            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;
-            }
-            astIntervalPoints( this, lbnd + nax_reg, ubnd + nax_reg );
-         }
-
-/*  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 Interval has zero width on each axis (i.e.
-   represents a point). Get the Interval bounds.  */
-         lbnd = astMalloc( sizeof( double )*(size_t) nax_this );
-         ubnd = astMalloc( sizeof( double )*(size_t) nax_this );
-         astRegBaseBox( this, lbnd, ubnd );
-
-/* Get the size of the Interval's uncertainty region. */
-         lbnd_unc = astMalloc( sizeof( double )*(size_t) nax_this );
-         ubnd_unc = astMalloc( sizeof( double )*(size_t) nax_this );
-         bunc = astGetUncFrm( this, AST__BASE );
-         astGetRegionBounds( bunc, lbnd, ubnd );
-
-/* Set "ok" to zero if the Interval does not have zero width on any axis. Here
-   "zero width" means a width less than half the uncertainty on the axis.
-   We also replace the lower bound values in the "lbnd" array by the central
-   values in the Interval. */
-         if( astOK ) {
-            ok = 1;
-            for( i = 0; i < nax_this; i++ ) {
-               if( fabs( lbnd[ i ] - lbnd[ i ] ) >
-                   0.25*fabs( ubnd_unc[ i ] - lbnd_unc[ i ] ) ) {
-                  ok = 0;
-                  break;
-               } else {
-                  lbnd[ i ] = 0.5*( lbnd[ i ] + ubnd[ i ] );
-               }
-            }
-
-/* If the Interval 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 Interval to each point. */
-               if( astOK ) {
-
-                  for( j = 0; j < nax_reg; j++ ) {
-                     p = ptr_reg[ j ];
-                     q = ptr_new[ intfirst ? nax_this + j : j ];
-                     for( i = 0; i < npnt; i++ ) *(q++) = *(p++);
-                  }
-
-                  for( j = 0; j < nax_this; j++ ) {
-                     p = lbnd + j;
-                     q = ptr_new[ intfirst ? 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 );
-            }
-         }
-         lbnd = astFree( lbnd );
-         ubnd = astFree( ubnd );
-         lbnd_unc = astFree( lbnd_unc );
-         ubnd_unc = astFree( ubnd_unc );
-         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( intfirst ) {
-               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( intfirst ) {
-            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( intfirst ) {
-            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 int *OneToOne( AstMapping *map, int *status ){
-/*
-*  Name:
-*     OneToOne
-
-*  Purpose:
-*     Does each output of the supplied Mapping depend on only one input?
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     int OneToOne( AstMapping *map, int *status )
-
-*  Class Membership:
-*     Interval method
-
-*  Description:
-*     This function returns a flag indicating if the Mapping is 1-to-1.
-*     That is, if each output depends only on one input.
-
-*  Parameters:
-*     map
-*        Pointer to the Mapping.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     If the Mapping is 1-to-1, a pointer to an array of ints is returned
-*     (NULL is returned otherwise). There is one int for each output of
-*     the supplied Mapping. The value of each int is the index of the
-*     corresponding input which feeds the output. The array should be
-*     freed using astFree when no longer needed.
-
-*/
-
-/* Local Variables: */
-   int *result;
-   const char *class;
-   int nout;
-   int i;
-   int *tt;
-   AstMapping *tmap;
-
-/* Initialise */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get the number of outputs for the Mapping. */
-   nout = astGetNout( map );
-
-/* The Mapping cannot be 1-to-1 if the number of inputs is different.*/
-   if( astGetNin( map ) == nout ) {
-
-/* Allocate an output array on the assumption that the Mapping is 1-to-1. */
-      result = astMalloc( sizeof( int )*(size_t) nout );
-      if( result ) {
-
-/* Check known specal cases for speed. */
-         class = astGetClass( map );
-         if( !strcmp( class, "WinMap" ) ||
-             !strcmp( class, "ZoomMap" ) ||
-             !strcmp( class, "UnitMap" ) ||
-             !strcmp( class, "ShiftMap" ) ){
-
-/* Each output is fed by the corresponding input for these classes of
-   Mapping. */
-            for( i = 0; i < nout; i++ ) result[ i ] = i;
-
-/* Now do the general case. */
-         } else {
-
-/* Loop round each input axis. */
-            for( i = 0; i < nout; i++ ) {
-
-/* Use astMapSplit to see if this input corresponds to a single output. */
-               tt = astMapSplit( map, 1, &i, &tmap );
-
-/* If not, annul the returned array and break. */
-               if( !tmap ) {
-                  result = astFree( result );
-                  break;
-
-/* If so, store the index of the corresponding input in the returned
-   array and free resources. */
-               } else {
-                 result[ tt[ 0 ] ] = i;
-                 tt = astFree( tt );
-                 if( astGetNout( tmap ) != 1 ) result = astFree( result );
-                 tmap = astAnnul( tmap );
-                 if( !result ) break;
-               }
-            }
-         }
-      }
-   }
-
-/* Return the result */
-   return result;
-}
-
-static int Overlap( AstRegion *this, AstRegion *that, int *status ){
-/*
-*  Name:
-*     Overlap
-
-*  Purpose:
-*     Test if two regions overlap each other.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     int Overlap( AstRegion *this, AstRegion *that, int *status )
-
-*  Class Membership:
-*     Interval member function (over-rides the astOverlap method inherited
-*     from the Region class).
-
-*  Description:
-*     This function returns an integer value indicating if the two
-*     supplied Regions overlap. The two Regions are converted to a commnon
-*     coordinate system before performing the check. If this conversion is
-*     not possible (for instance because the two Regions represent areas in
-*     different domains), then the check cannot be performed and a zero value
-*     is returned to indicate this.
-
-*  Parameters:
-*     this
-*        Pointer to the first Region.
-*     that
-*        Pointer to the second Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     astOverlap()
-*        A value indicating if there is any overlap between the two Regions.
-*        Possible values are:
-*
-*        0 - The check could not be performed because the second Region
-*            could not be mapped into the coordinate system of the first
-*            Region.
-*
-*        1 - There is no overlap between the two Regions.
-*
-*        2 - The first Region is completely inside the second Region.
-*
-*        3 - The second Region is completely inside the first Region.
-*
-*        4 - There is partial overlap between the two Regions.
-*
-*        5 - The Regions are identical.
-*
-*        6 - The second Region is the negation of the first Region.
-
-*  Notes:
-*     - The returned values 5 and 6 do not check the value of the Closed
-*     attribute in the two Regions.
-*     - A value of zero will be returned if this function is invoked with the
-*     AST error status set, or if it should fail for any reason.
-
-*/
-
-/* Local Variables: */
-   AstFrame *frm;
-   AstFrameSet *fs;
-   AstMapping *map;
-   AstMapping *map1;
-   AstMapping *map2;
-   AstMapping *map3;
-   AstMapping *smap;
-   AstMapping *tmap;
-   AstPointSet *pset_that;
-   AstRegion *unc_temp;
-   AstRegion *unc_that;
-   AstRegion *unc_this;
-   double **ptr_that;
-   double **ptr_thato;
-   double **ptr_this;
-   double *lbndu_that;
-   double *lbndu_this;
-   double *ubndu_that;
-   double *ubndu_this;
-   double err;
-   double err_that;
-   double err_this;
-   double lb_that;
-   double lb_this;
-   double tmp;
-   double ub_that;
-   double ub_this;
-   int *outperm;
-   int ic;
-   int inc_that;
-   int inc_this;
-   int lb_equal;
-   int nc;
-   int neg_that;
-   int neg_this;
-   int ov;
-   int result;
-   int ub_equal;
-
-   static int newResult[ 5 ][ 5 ] = { { 1, 1, 1, 1, 1},
-                                      { 1, 2, 4, 4, 2},
-                                      { 1, 4, 3, 4, 3},
-                                      { 1, 4, 4, 4, 4},
-                                      { 1, 2, 3, 4, 5} };
-
-/* Initialise */
-   result = 0;
-
-/* Check the inherited status. */
-   if ( !astOK ) return result;
-
-/* If both Regions are Intervals, we provide a specialised implementation.
-   The implementation in the parent Region class assumes that at least one of
-   the two Regions can be represented using a finite mesh of points on the
-   boundary which is not the case with Intervals. The implementation in this
-   class sees if the Mapping between the base Frames of the Intervals allows
-   the axis limits to be transferred from one Frame ot the other. */
-   if( astIsAInterval( this ) && astIsAInterval( that ) ) {
-
-/* Get a FrameSet which connects the Frame represented by the second Interval
-   to the Frame represented by the first Interval. Check that the conection is
-   defined. */
-      fs = astConvert( that, this, "" );
-      if( fs ) {
-
-/* Get a pointer to the Mapping from base to current Frame in the second
-   Interval */
-         map1 = astGetMapping( that->frameset, AST__BASE, AST__CURRENT );
-
-/* Get the Mapping from the current Frame of the second Interval to the
-   current Frame of the first Interval. */
-         map2 = astGetMapping( fs, AST__BASE, AST__CURRENT );
-
-/* Get a pointer to the Mapping from current to base Frame in the first
-   Interval. */
-         map3 = astGetMapping( this->frameset, AST__CURRENT, AST__BASE );
-
-/* Combine these Mappings to get the Mapping from the base Frame of the
-   second Interval to the base Frame of the first Interval. */
-         tmap = (AstMapping *) astCmpMap( map1, map2, 1, "", status );
-         map = (AstMapping *) astCmpMap( tmap, map3, 1, "", status );
-
-/* Simplify this Mapping. */
-         smap = astSimplify( map );
-
-/* We can only proceed if each output of the simplified Mapping depends
-   on only one input. Test this. */
-         outperm = OneToOne( smap, status );
-         if( outperm ){
-
-/* Get the uncertainty Regions for both Intervals, expressed in the base
-   Frames of the Intervals. */
-            unc_this = astGetUncFrm( this, AST__BASE );
-            unc_temp = astGetUncFrm( that, AST__BASE );
-
-/* Map the uncertainty Region for the second Interval from the base Frame
-   of the second Interval into the base Frame of the first Interval. */
-            frm = astGetFrame( this->frameset, AST__BASE );
-            unc_that = astMapRegion( unc_temp, smap, frm );
-
-/* Get the bounding boxes of the two uncertainty Regions in the base
-   Frame of the first Interval. */
-            nc = astGetNaxes( frm );
-            lbndu_this = astMalloc( sizeof( double )*(size_t)nc );
-            ubndu_this = astMalloc( sizeof( double )*(size_t)nc );
-            astGetRegionBounds( unc_this, lbndu_this, ubndu_this );
-
-            lbndu_that = astMalloc( sizeof( double )*(size_t)nc );
-            ubndu_that = astMalloc( sizeof( double )*(size_t)nc );
-            astGetRegionBounds( unc_that, lbndu_that, ubndu_that );
-
-/* Transform the PointSet holding the limits for the second Interval into
-   the Frame of the first Interval. */
-            pset_that = astTransform( smap, that->points, 1, NULL );
-
-/* Get pointers for accesing the limits of the two Intervals, expressed
-   in a common Frame (the base Frame of the first Interval). */
-            ptr_that = astGetPoints( pset_that );
-            ptr_thato = astGetPoints( that->points );
-            ptr_this = astGetPoints( this->points );
-            if( astOK ) {
-
-/* Check the limits on each base Frame axis in turn. */
-               for( ic = 0; ic < nc; ic++ ) {
-
-/* Get the widths of the two uncertainty boxes on this axis. */
-                  err_this = ubndu_this[ ic ] - lbndu_this[ ic ];
-                  err_that = ubndu_that[ ic ] - lbndu_that[ ic ];
-
-/* Add this together in quadrature to get the tolerance for two values on
-   the current axis to be considered equal. */
-                  err = sqrt( err_that*err_that + err_this*err_this );
-
-/* Get the limits on this axis from both Intervals. */
-                  lb_this = ptr_this[ ic ][ 0 ];
-                  ub_this = ptr_this[ ic ][ 1 ];
-                  lb_that = ptr_that[ ic ][ 0 ];
-                  ub_that = ptr_that[ ic ][ 1 ];
-
-/* The limits for "that" have been mapped, which may have resulted in
-   them being swapped. We need to unswap them in this case to prevent the
-   swapping being used as an indication of a desire to use an excluded
-   interval rather than an included interval. */
-                   if( lb_that != AST__BAD && ub_that != AST__BAD ) {
-                      if( ptr_thato[ ic ][ 0 ] < ptr_thato[ ic ][ 1 ] ) {
-                         if( lb_that > ub_that ) {
-                            tmp = lb_that;
-                            lb_that = ub_that;
-                            ub_that = tmp;
-                         }
-                      } else {
-                         if( lb_that < ub_that ) {
-                            tmp = lb_that;
-                            lb_that = ub_that;
-                            ub_that = tmp;
-                         }
-                      }
-                   }
-
-/* If the regions are not closed, reduce the limits by the smallest
-   amount possible. */
-                  if( !astGetClosed( that ) ) {
-                     if( lb_that != AST__BAD && lb_that < DBL_MAX )
-                         lb_that += DBL_EPSILON*fabs(lb_that);
-                     if( ub_that != AST__BAD && ub_that > -DBL_MAX )
-                         ub_that -= DBL_EPSILON*fabs(ub_that);
-                  }
-                  if( !astGetClosed( this ) ) {
-                     if( lb_this != AST__BAD && lb_this < DBL_MAX )
-                         lb_this += DBL_EPSILON*fabs(lb_this);
-                     if( ub_this != AST__BAD && ub_this > -DBL_MAX )
-                         ub_this -= DBL_EPSILON*fabs(ub_this);
-                  }
-
-/* Replace any missing limits with suitable extreme values */
-                  if( lb_this == AST__BAD ) lb_this = -DBL_MAX;
-                  if( ub_this == AST__BAD ) ub_this = DBL_MAX;
-                  if( lb_that == AST__BAD ) lb_that = -DBL_MAX;
-                  if( ub_that == AST__BAD ) ub_that = DBL_MAX;
-
-/* If the bounds are the wrong way round (indicating an excluded rather
-   than an included axis range), swap them. Also set a flag indicating if
-   the limits define an included or excluded range. */
-                  inc_this = ( lb_this <= ub_this );
-                  if( !inc_this ) {
-                     tmp = lb_this;
-                     lb_this = ub_this;
-                     ub_this = tmp;
-                  }
-
-                  inc_that = ( lb_that <= ub_that );
-                  if( !inc_that ) {
-                     tmp = lb_that;
-                     lb_that = ub_that;
-                     ub_that = tmp;
-                  }
-
-
-/* Are the lower limits from the two Intervals effectively equal? Take care
-   about DBL_MAX values causing overflow. */
-                  lb_equal = astEQUALS( lb_this, lb_that, 1.0E9 );
-
-                  if( !lb_equal && fabs(lb_this) != DBL_MAX &&
-                                   fabs(lb_that) != DBL_MAX ) {
-                     lb_equal = ( fabs( lb_this - lb_that) <= err );
-                  }
-
-/* Are the upper limits from the two Intervals effectively equal? */
-                  ub_equal = astEQUALS( ub_this, ub_that, 1.0E9 );
-                  if( !ub_equal && fabs(ub_this) != DBL_MAX &&
-                                   fabs(ub_that) != DBL_MAX ) {
-                     ub_equal = ( fabs( ub_this - ub_that) <= err );
-                  }
-
-
-
-/* If both the limits on this axis are effectively equal for the two Intervals,
-   set "ov" to 5 if both Interval ranges are inclusive or both are exclusive,
-   and set "ov" to 6 if one Interval range is exclusive and the other is
-   inclusive. */
-                  if( lb_equal && ub_equal ) {
-                     ov = ( inc_this == inc_that ) ? 5 : 6;
-
-/* See if the limits on this axis indicate overlap for the two Intervals. "ov"
-   is set to 1 if there is no overlap, 2 if the first Interval range is
-   completely inside the second Interval range, 3 if the second Interval
-   range is completely inside the first Interval range, and 4 if there is
-   partial overlap between the Interval ranges. */
-                  } else if( inc_this ) {
-                     if( inc_that ) {
-                        if( lb_that <= lb_this && ub_that >= ub_this ) {
-                           ov = 2;
-                        } else if( lb_that >= lb_this && ub_that <= ub_this ) {
-                           ov = 3;
-                        } else if( ub_that >= lb_this && lb_that <= ub_this ) {
-                           ov = 4;
-                        } else {
-                           ov = 1;
-                        }
-
-                     } else {
-
-                        if( lb_that <= lb_this && ub_that >= ub_this ) {
-                           ov = 1;
-                        } else if( lb_that >= ub_this || ub_that <= lb_this ) {
-                           ov = 2;
-                        } else if( lb_this == -DBL_MAX && ub_this == DBL_MAX ) {
-                           ov = 3;
-                        } else {
-                           ov = 4;
-                        }
-                     }
-
-                  } else {
-
-                     if( inc_that ) {
-                        if( lb_this <= lb_that && ub_this >= ub_that ) {
-                           ov = 1;
-                        } else if( lb_this >= ub_that || ub_this <= lb_that ) {
-                           ov = 3;
-                        } else if( lb_that == -DBL_MAX && ub_that == DBL_MAX ) {
-                           ov = 2;
-                        } else {
-                           ov = 4;
-                        }
-
-                     } else {
-                        ov = 4;
-                     }
-                  }
-
-/* The returned value is initialised on the basis of the first axis
-   overlap. */
-                  if( ic == 0 ) {
-                     result = ov;
-
-/* For subsequent axes, combine the old result value with the new ov value
-   to get the new result value. */
-                  } else {
-                     result = newResult[ result - 1 ][ ov - 1 ];
-                  }
-
-/* If we now know there is no overlap, there is no point in checking any
-   remaining axes. */
-                  if( result == 1 ) break;
-
-               }
-
-/* The above logic assumed that neither of the Intervals has been negated.
-   Decide on the value to return, taking into account whether either of
-   the Intervals has been negated. */
-               neg_this = astGetNegated( this );
-               neg_that = astGetNegated( that );
-
-               if( result == 1 ) {
-                  if( neg_this ) {
-                     result = neg_that ? 4 : 3;
-                  } else if( neg_that ){
-                     result = 2;
-                  }
-
-               } else if( result == 2) {
-                  if( neg_this ) {
-                     result = neg_that ? 3 : 4;
-                  } else if( neg_that ){
-                     result = 1;
-                  }
-
-               } else if( result == 3) {
-                  if( neg_this ) {
-                     result = neg_that ? 2 : 1;
-                  } else if( neg_that ){
-                     result = 4;
-                  }
-
-               } else if( result == 4) {
-                  result = 4;
-
-               } else if( result == 5) {
-                  if( neg_this ) {
-                     result = neg_that ? 5 : 6;
-                  } else if( neg_that ){
-                     result = 6;
-                  }
-               }
-            }
-
-/* Free resources. */
-            pset_that = astAnnul( pset_that );
-            unc_this = astAnnul( unc_this );
-            unc_that = astAnnul( unc_that );
-            unc_temp = astAnnul( unc_temp );
-            frm = astAnnul( frm );
-            lbndu_this = astFree( lbndu_this );
-            ubndu_this = astFree( ubndu_this );
-            lbndu_that = astFree( lbndu_that );
-            ubndu_that = astFree( ubndu_that );
-            outperm = astFree( outperm );
-         }
-
-         smap = astAnnul( smap );
-         map = astAnnul( map );
-         tmap = astAnnul( tmap );
-         map3 = astAnnul( map3 );
-         map2 = astAnnul( map2 );
-         map1 = astAnnul( map1 );
-         fs = astAnnul( fs );
-      }
-   }
-
-/* If overlap could not be determined using the above implementation, try
-   using the implementation inherited from the parent Region class. */
-   if( !result ) result = (*parent_overlap)( this, that, status );
-
-/* If not OK, return zero. */
-   if( !astOK ) result = 0;
-
-/* 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 "interval.h"
-*     void RegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status )
-
-*  Class Membership:
-*     Interval 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: */
-   AstInterval *this;
-   int nax;
-   int i;
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Get a pointer to the Interval structure */
-   this = (AstInterval *) this_region;
-
-/* Ensure the cached bounds are up to date. */
-   Cache( this, status );
-
-/* Copy the cached bounds into the supplied arrays. */
-   nax = astGetNin( this_region->frameset );
-   for( i = 0; i < nax; i++ ) {
-      lbnd[ i ] = this->lbnd[ i ];
-      ubnd[ i ] = this->ubnd[ i ];
-   }
-}
-
-static AstPointSet *RegBaseMesh( AstRegion *this_region, 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 "interval.h"
-*     AstPointSet *astRegBaseMesh( AstRegion *this, int *status )
-
-*  Class Membership:
-*     Interval 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 Variables: */
-   AstBox *box;                  /* The equivalent Box */
-   AstPointSet *result;          /* Returned pointer */
-
-/* Initialise */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* If the Interval is effectively a Box, invoke the astRegBaseMesh
-   function on the equivalent Box. A pointer to the equivalent Box will
-   be stored in the Interval structure. */
-   box = Cache( (AstInterval *) this_region, status );
-   if( box ) {
-      result = astRegBaseMesh( box );
-
-/* If the Interval is not equivalent to a Box, report an error. */
-   } else {
-      astError( AST__INTER, "astRegBaseMesh(%s): The %s given is "
-                "unbounded and therefore no boundary mesh can be "
-                "produced (internal AST programming error).", status,
-                astGetClass( this_region ), astGetClass( this_region ) );
-   }
-
-/* Return a pointer to the output PointSet. */
-   return result;
-}
-
-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 "interval.h"
-*     AstRegion *RegBasePick( AstRegion *this, int naxes, const int *axes,
-*                             int *status )
-
-*  Class Membership:
-*     Interval 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 *lbnd;           /* Base Frm lower bound axis values */
-   double *ubnd;           /* Base Frm upper bound axis values */
-   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 limits of the Interval in the new Frame. */
-   lbnd = astMalloc( sizeof( *lbnd )*naxes );
-   ubnd = astMalloc( sizeof( *ubnd )*naxes );
-
-/* Check pointers can be used safely. */
-   if( astOK ) {
-
-/* Copy the limits for the selected axes into the arrays allocated above. */
-      for( i = 0; i < naxes; i++ ) {
-         lbnd[ i ] = ptr[ axes[ i ] ][ 0 ];
-         ubnd[ i ] = ptr[ axes[ i ] ][ 1 ];
-      }
-
-/* Create the new Interval. */
-      result = (AstRegion *) astInterval( frm, lbnd, ubnd, unc, "", status );
-
-   }
-
-/* Free resources */
-   frm = astAnnul( frm );
-   bfrm = astAnnul( bfrm );
-   if( unc ) unc = astAnnul( unc );
-   lbnd = astFree( lbnd );
-   ubnd = astFree( ubnd );
-
-/* 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 "interval.h"
-*     double *RegCentre( AstRegion *this, double *cen, double **ptr,
-*                        int index, int ifrm, int *status )
-
-*  Class Membership:
-*     Interval 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: */
-   AstInterval *this;  /* Pointer to Interval structure */
-   AstBox *box;        /* Pointer to equivalent Box structure */
-   double **bptr;      /* Data pointers for Region PointSet */
-   double *lbnd;       /* Pointer to new lower bound values */
-   double *ubnd;       /* Pointer to new upper bound values */
-   double *result;     /* Returned pointer */
-   int i;              /* Coordinate index */
-   int nax;            /* Number of axes */
-
-/* Initialise */
-   result = NULL;
-
-/* Check the local error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the Interval structure. */
-   this = (AstInterval *) this_region;
-
-/* The Interval can only be re-centred if it is effectively a Box. */
-   box = Cache( (AstInterval *) this_region, status );
-   if( box ) {
-
-/* If the centre is being changed... */
-      if( cen || ptr ) {
-
-/* Set the new centre in the equivalent box. */
-         astRegCentre( box, cen, ptr, index, ifrm );
-
-/* Get the new base Frame bounds from the Box. */
-         nax = astGetNin( this_region->frameset );
-         lbnd = astMalloc( sizeof( double )*nax );
-         ubnd = astMalloc( sizeof( double )*nax );
-         astRegBaseBox( box, lbnd, ubnd );
-
-/* Store these bounds in the Interval structure. */
-         bptr = astGetPoints( this_region->points );
-         if( astOK ) {
-            for( i = 0; i < nax; i++ ) {
-               bptr[ i ][ 0 ] = lbnd[ i ];
-               bptr[ i ][ 1 ] = ubnd[ i ];
-            }
-         }
-
-/* Free resources. */
-         lbnd = astFree( lbnd );
-         ubnd = astFree( ubnd );
-
-/* If the centre is not being changed, just invoke the method on the
-   equivalent box. */
-      } else {
-         result = astRegCentre( box, NULL, NULL, 0, AST__BASE );
-      }
-
-/* If the Interval is not equivalent to a Box, report an error */
-   } else if( cen || ptr ) {
-      astError( AST__REGCN, "astRegCentre(%s): The supplied %s is not a "
-                "closed Interval and so cannot be re-centred.", status,
-                astGetClass( this ), astGetClass( this ) );
-   }
-
-/* 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 Interval.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     int RegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
-*                  int **mask, int *status )
-
-*  Class Membership:
-*     Interval 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 Interval.
-*
-*     Some tolerance is allowed, as specified by the uncertainty Region
-*     stored in the supplied Interval "this", and the supplied uncertainty
-*     Region "unc" which describes the uncertainty of the supplied points.
-
-*  Parameters:
-*     this
-*        Pointer to the Interval.
-*     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 *box;              /* The equivalent Box */
-   AstInterval *large_int;   /* Interval slightly larger than "this" */
-   AstInterval *small_int;   /* Interval slightly smaller than "this" */
-   AstInterval *this;        /* Pointer to the Interval structure. */
-   AstFrame *frm;            /* Base Frame in supplied Interval */
-   AstPointSet *ps1;         /* Points masked by larger Interval */
-   AstPointSet *ps2;         /* Points masked by larger and smaller Intervals */
-   AstRegion *tunc;          /* Uncertainity Region from "this" */
-   double **ptr;             /* Pointer to axis values in "ps2" */
-   double *large_lbnd;       /* Lower bounds of larger interval */
-   double *large_ubnd;       /* Upper bounds of larger interval */
-   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 *safe;             /* An interior point in "this" */
-   double *small_lbnd;       /* Lower bounds of smaller interval */
-   double *small_ubnd;       /* Upper bounds of smaller interval */
-   double *ubnd_tunc;        /* Upper bounds of "this" uncertainty Region */
-   double *ubnd_unc;         /* Upper bounds of supplied uncertainty Region */
-   double *wid;              /* Widths of "this" border */
-   double lb;                /* Lower bound */
-   double ub;                /* Upper bound */
-   double t;                 /* Swap space */
-   double w;                 /* Width */
-   int i;                    /* Axis index */
-   int j;                    /* Point index */
-   int nc;                   /* No. of axes in Interval 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 Interval structure. */
-   this = (AstInterval *) this_region;
-
-/* If the Interval is effectively a Box, invoke the astRegPins function on
-   the equivalent Box. A pointer to the equivalent Box will be stored in the
-   Interval structure. */
-   box = Cache( this, status );
-   if( box ) return astRegPins( box, pset, unc, mask );
-
-/* Arrive here only if the Interval is not equivalent to a box (i.e. has
-   at least one infinite boundary). Get the number of base Frame axes in the
-   Interval, 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 Interval for it still to be considered to be on the
-   boundary. First get the Region which defines the uncertainty within the
-   Interval 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_lbnd = astMalloc( sizeof( double )*(size_t) nc );
-   large_ubnd = astMalloc( sizeof( double )*(size_t) nc );
-   small_lbnd = astMalloc( sizeof( double )*(size_t) nc );
-   small_ubnd = astMalloc( sizeof( double )*(size_t) nc );
-   if( small_ubnd ) {
-      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 ] = 0.5*fabs( astAxDistance( frm, i + 1, lbnd_tunc[ i ],
-                                                ubnd_tunc[ i ] ) );
-         }
-      }
-
-/* Create two new Intervals, 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++ ) {
-         lb = this->lbnd[ i ];
-         ub = this->ubnd[ i ];
-         if( lb > ub ) {
-            t = ub;
-            ub = lb;
-            lb = t;
-         }
-
-         w = fabs( wid[ i ] );
-         if( lb != -DBL_MAX ){
-            large_lbnd[ i ] = lb - w;
-            small_lbnd[ i ] = lb + w;
-         } else {
-            large_lbnd[ i ] = AST__BAD;
-            small_lbnd[ i ] = AST__BAD;
-         }
-
-         if( ub != DBL_MAX ){
-            large_ubnd[ i ] = ub + w;
-            small_ubnd[ i ] = ub - w;
-         } else {
-            large_ubnd[ i ] = AST__BAD;
-            small_ubnd[ i ] = AST__BAD;
-         }
-
-         if( small_lbnd[ i ] > small_ubnd[ i ] ) {
-            small_lbnd[ i ] = small_ubnd[ i ];
-         }
-      }
-
-      large_int = astInterval( frm, large_lbnd, large_ubnd, NULL, "", status );
-      small_int = astInterval( frm, small_lbnd, small_ubnd, NULL, "", status );
-
-/* Negate the smaller interval.*/
-      astNegate( small_int );
-
-/* Points are on the boundary of "this" if they are inside both the large
-   interval and the negated small interval. First transform the supplied
-   PointSet using the large interval, then transform them using the negated
-   smaller Interval. */
-      ps1 = astTransform( large_int, pset, 1, NULL );
-      ps2 = astTransform( small_int, 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_int = astAnnul( large_int );
-      small_int = astAnnul( small_int );
-      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_lbnd = astFree( large_lbnd );
-   large_ubnd = astFree( large_ubnd );
-   small_lbnd = astFree( small_lbnd );
-   small_ubnd = astFree( small_ubnd );
-   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 "interval.h"
-*     int astTraceRegion( AstRegion *this, int n, double *dist, double **ptr );
-
-*  Class Membership:
-*     Interval 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; */
-   AstBox *box;
-   int result;
-
-/* Initialise */
-   result = 0;
-
-/* Check inherited status. */
-   if( ! astOK ) return result;
-
-/* If the Interval is effectively a Box, invoke the astRegTrace function on
-   the equivalent Box. A pointer to the equivalent Box will be stored in the
-   Interval structure. */
-   box = Cache( (AstInterval *) this_region, status );
-   if( box ) result = astRegTrace( box, n, dist, ptr );
-
-/* 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 "interval.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 ) {
-      ( (AstInterval *) this )->stale = 1;
-      (*parent_resetcache)( this, status );
-   }
-}
-
-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 "interval.h"
-*     void SetRegFS( AstRegion *this_region, AstFrame *frm, int *status )
-
-*  Class Membership:
-*     Interval 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 the cached intermediate information is now stale and
-   should be recreated when next needed. */
-   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 "interval.h"
-*     void SetUnc( AstRegion *this, AstRegion *unc, int *status )
-
-*  Class Membership:
-*     Interval 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 the cached intermediate information is now stale and
-   should be recreated when next needed. */
-   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 "interval.h"
-*     AstMapping *Simplify( AstMapping *this, int *status )
-
-*  Class Membership:
-*     Interval 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 *box2;              /* Box used to determine 1-to-1 axis correspondance */
-   AstBox *box;               /* Box used to determine 1-to-1 axis correspondance */
-   AstInterval *this_interval;/* Pointer to Interval structure */
-   AstMapping *bfrm;          /* Pointer to base Frame in supplied Interval */
-   AstMapping *cfrm;          /* Pointer to current Frame in supplied Interval */
-   AstMapping *map;           /* Base -> current Mapping after parent simplification */
-   AstMapping *result;        /* Result pointer to return */
-   AstPointSet *pset2;        /* PointSet containing current Frame test points */
-   AstPointSet *pset3;        /* PointSet containing base Frame test points */
-   AstPointSet *psetb;        /* PointSet holding base positions */
-   AstPointSet *psetc;        /* PointSet holding current positions */
-   AstRegion *new;            /* Pointer to Region simplfied by parent class */
-   AstRegion *sreg;           /* Pointer to simplified Box */
-   AstRegion *this;           /* Pointer to supplied Region structure */
-   AstRegion *unc;            /* Pointer to uncertainty Region */
-   double **ptr2;             /* Pointer axis values in "pset2" */
-   double **ptr3;             /* Pointer axis values in "pset3" */
-   double **ptr;              /* Pointer to base Frame values defining Interval */
-   double **ptrb;             /* Pointer to "psetb" axis values */
-   double **sptr;             /* Pointer to simplified Interval bounds */
-   double *lbnd;              /* Pointer to array of base Frame lower bounds */
-   double *slbnd;             /* Pointer to array of current Frame lower bounds */
-   double *subnd;             /* Pointer to array of current Frame upper bounds */
-   double *ubnd;              /* Pointer to array of base Frame upper bounds */
-   double d;                  /* Distance between axis values */
-   double lb;                 /* Lower bound on axis values */
-   double lwid;               /* Axis width below the Interval lower limit */
-   double maxd;               /* Maximum currenrt Frame axis offset between test points */
-   double tmp;                /* Temporary storage for swapping variable values */
-   double ub;                 /* Upperbound on axis values */
-   double uwid;               /* Axis width above the Interval upper limit */
-   int bax;                   /* Base Frame axis index corresponding to "ic" */
-   int ic;                    /* Axis index */
-   int jc;                    /* Axis index */
-   int nc;                    /* No. of base Frame axis values per point */
-   int simpler;               /* Has some simplication taken place? */
-   int snc;                   /* No. of current Frame axis values per point */
-
-/* Initialise. */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the supplied Region structure. */
-   this = (AstRegion *) this_mapping;
-
-/* Get a pointer to the supplied Interval structure. */
-   this_interval = (AstInterval *) this;
-
-/* If this Interval is equivalent to a Box, use the astTransform method of
-   the equivalent Box. */
-   box = Cache( this_interval, status );
-   if( box ) {
-      result = astSimplify( box );
-
-/* Otherwise, we use a new implementation appropriate for unbounded
-   intervals. */
-   } else {
-
-/* 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 );
-      if( new ) {
-
-/* 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 );
-
-/* If the Mapping from base to current Frame is not a UnitMap, we attempt
-   to simplify the Interval by re-defining it within its current Frame. */
-         map = astGetMapping( new->frameset, AST__BASE, AST__CURRENT );
-         if( !astIsAUnitMap( map ) ){
-
-/* Take a copy of the Interval bounds (defined in the base Frame of the
-   Intervals FrameSet) and replace any missing limits with arbitrary
-   non-BAD values. This will give us a complete set of bounds defining a
-   box within the base Frame of the Interval. */
-            ptr = astGetPoints( new->points );
-            nc = astGetNcoord( new->points );
-
-            lbnd = astMalloc( sizeof( double )*(size_t) nc );
-            ubnd = astMalloc( sizeof( double )*(size_t) nc );
-
-            if( astOK ) {
-               for( ic = 0; ic < nc; ic++ ) {
-                  lbnd[ ic ] = ptr[ ic ][ 0 ];
-                  ubnd[ ic ] = ptr[ ic ][ 1 ];
-
-/* Ensure we have a good upper bound for this axis. */
-                  if( ubnd[ ic ] == AST__BAD ) {
-                     if( lbnd[ ic ] == AST__BAD ) {
-                        ubnd[ ic ] = 1.0;
-
-                     } else if( lbnd[ ic ] > 0.0 ) {
-                        ubnd[ ic ] = lbnd[ ic ]*1.01;
-
-                     } else if( lbnd[ ic ] < 0.0 ) {
-                        ubnd[ ic ] = lbnd[ ic ]*0.99;
-
-                     } else {
-                        ubnd[ ic ] = 1.0;
-                     }
-                  }
-
-/* Ensure we have a good lower bound for this axis. */
-                  if( lbnd[ ic ] == AST__BAD ) {
-                     if( ubnd[ ic ] > 0.0 ) {
-                        lbnd[ ic ] = ubnd[ ic ]*0.99;
-
-                     } else if( ubnd[ ic ] < 0.0 ) {
-                        lbnd[ ic ] = ubnd[ ic ]*1.01;
-
-                     } else {
-                        lbnd[ ic ] = 1.0;
-                     }
-                  }
-               }
-            }
-
-/* Transform the box corners found above into the current frame and then back
-   into the base Frame, and ensure that the box encloses both the original
-   and the new bounds. PermMaps with fewer outputs than inputs can cause the
-   resulting base Frame positions to differ significantly from the original. */
-            psetb =astPointSet( 2, nc,"", status );
-            ptrb =astGetPoints( psetb );
-            if( astOK ) {
-               for( ic = 0; ic < nc; ic++ ) {
-                  ptrb[ ic ][ 0 ] = lbnd[ ic ];
-                  ptrb[ ic ][ 1 ] = ubnd[ ic ];
-               }
-            }
-            psetc = astTransform( map, psetb, 1, NULL );
-            (void) astTransform( map, psetc, 0, psetb );
-            if( astOK ) {
-               for( ic = 0; ic < nc; ic++ ) {
-                  lb = ptrb[ ic ][ 0 ];
-                  if( lb != AST__BAD ) {
-                     if( lb < lbnd[ ic ] ) lbnd[ ic ] = lb;
-                     if( lb > ubnd[ ic ] ) ubnd[ ic ] = lb;
-                  }
-                  ub = ptrb[ ic ][ 1 ];
-                  if( ub != AST__BAD ) {
-                     if( ub < lbnd[ ic ] ) lbnd[ ic ] = ub;
-                     if( ub > ubnd[ ic ] ) ubnd[ ic ] = ub;
-                  }
-               }
-            }
-            psetb = astAnnul( psetb );
-            psetc = astAnnul( psetc );
-
-/* Limit this box to not exceed the limits imposed by the Interval.*/
-            Cache( this_interval, status );
-            for( ic = 0; ic < nc; ic++ ) {
-               lb = this_interval->lbnd[ ic ] ;
-               ub = this_interval->ubnd[ ic ] ;
-               if( lb <= ub ) {
-                  if( lbnd[ ic ] < lb ) {
-                     lbnd[ ic ] = lb;
-                  } else if( lbnd[ ic ] > ub ) {
-                     lbnd[ ic ] = ub;
-                  }
-                  if( ubnd[ ic ] < lb ) {
-                     ubnd[ ic ] = lb;
-                  } else if( ubnd[ ic ] > ub ) {
-                     ubnd[ ic ] = ub;
-                  }
-               } else {
-                  lwid = lb - lbnd[ ic ];
-                  uwid = ubnd[ ic ] - ub;
-                  if( lwid > uwid ) {
-                    if( lbnd[ ic ] > lb ) lbnd[ ic ] = lb;
-                    if( ubnd[ ic ] > lb ) ubnd[ ic ] = lb;
-                  } else {
-                    if( lbnd[ ic ] < ub ) lbnd[ ic ] = ub;
-                    if( ubnd[ ic ] < ub ) ubnd[ ic ] = ub;
-                  }
-               }
-
-/* Ensure the bounds are not equal */
-               if( lbnd[ ic ] == 0.0 && ubnd[ ic ] == 0.0 ) {
-                  ubnd[ ic ] = 1.0;
-
-               } else if( astEQUALS( lbnd[ ic ], ubnd[ ic ], 1.0E9 ) ) {
-                  ubnd[ ic ] = astMAX( ubnd[ ic ], lbnd[ ic ] )*( 1.0E6*DBL_EPSILON );
-               }
-            }
-
-/* Create a new Box representing the box found above. */
-            bfrm = astGetFrame( new->frameset, AST__BASE );
-            unc = astTestUnc( new ) ? astGetUncFrm( new, AST__BASE ) : NULL;
-            box = astBox( bfrm, 1, lbnd, ubnd, unc, "", status );
-            if( unc ) unc = astAnnul( unc );
-
-/* Modify this Box so that it has the same current Frame as this Interval. */
-            cfrm = astGetFrame( new->frameset, AST__CURRENT );
-            box2 = astMapRegion( box, map, cfrm );
-
-/* Try simplifying the Box. */
-            sreg = (AstRegion *) astSimplify( box2 );
-
-/* Only proceed if the Box was simplified */
-            if( sreg != (AstRegion *) box2 ) {
-
-/* If the simplified Box is a NullRegion return it. */
-               if( astIsANullRegion( sreg ) ) {
-                  (void) astAnnul( new );
-                  new = astClone( sreg );
-                  simpler = 1;
-
-/* If the simplified Box is a Box or an Interval... */
-               } else if( astIsABox( sreg ) || astIsAInterval( sreg ) ) {
-
-/* Get the bounds of the simplified Box. We assume that the base and
-   current Frames in the simplified Box are the same. */
-                  snc = astGetNin( sreg->frameset );
-                  slbnd = astMalloc( sizeof( double )*(size_t)snc );
-                  subnd = astMalloc( sizeof( double )*(size_t)snc );
-                  if(  astIsAInterval( sreg ) ) {
-                     sptr = astGetPoints( sreg->points );
-                     if( astOK ) {
-                        for( ic = 0; ic < snc; ic++ ) {
-                           slbnd[ ic ] = sptr[ ic ][ 0 ];
-                           subnd[ ic ] = sptr[ ic ][ 1 ];
-                        }
-                     }
-                  } else {
-                     astRegBaseBox( sreg, slbnd, subnd );
-                  }
-
-/* Now create a PointSet containing one point for each axis in the
-   current (or equivalently, base ) Frame of the simplified Box, plus an
-   extra point. */
-                  pset2 = astPointSet( snc + 1, snc, "", status );
-                  ptr2 = astGetPoints( pset2 );
-
-/* Put the lower bounds of the simplified Box into the first point in
-   this PointSet. The remaining points are displaced from this first point
-   along each axis in turn. The length of each displacement is determined
-   by the length of the box on the axis. */
-                  if( astOK ) {
-                     for( ic = 0; ic < snc; ic++ ) {
-                        for( jc = 0; jc < snc + 1; jc++ ) {
-                           ptr2[ ic ][ jc ] = slbnd[ ic ];
-                        }
-                        ptr2[ ic ][ ic + 1 ] = subnd[ ic ];
-                     }
-                  }
-
-/* Transform this PointSet into the base Frame of this Interval using the
-   inverse of the base->current Mapping. */
-                  pset3 = astTransform( map, pset2, 0, NULL );
-                  ptr3 = astGetPoints( pset3 );
-                  if( astOK ) {
-
-/* Now consider each axis of the Interval's current Frame (i.e. each base
-   Frame axis in the simplified Box). */
-                     for( ic = 0; ic < snc; ic++ ) {
-
-/* Given that the Box simplified succesfully, we know that there is a one
-   to one connection between the axes of the base and current Frame in this
-   Interval, but we do not yet know which base Frame axis corresponds to
-   which current Frame axis (and the number of base and current Frame axes
-   need not be equal). We have two points on a line parallel to current
-   Frame axis number "ic" (points zero and "ic+1" in "pset2"). Look at the
-   corresponding base Frame positions (in "pset3), and see which base Frame
-   axis they are parallel to. We look for the largest base Frame axis
-   increment (this allows small non-zero displacements to occur on the
-   other axes due to rounding errors). */
-                        maxd = -DBL_MAX;
-                        bax = -1;
-                        for( jc = 0; jc < nc; jc++ ) {
-                           d = fabs( astAxDistance( bfrm, jc + 1, ptr3[ jc ][ 0 ],
-                                                    ptr3[ jc ][ ic + 1 ] ) );
-                           if( d != AST__BAD && d > maxd ) {
-                              maxd = d;
-                              bax = jc;
-                           }
-                        }
-
-/* If the largest base Frame axis increment is zero, it must mean that
-   the current Frame axis is not present in the base Frame. The only
-   plausable cause of this is if the base->current Mapping contains a
-   PermMap which introduces an extra axis, in which case the axis will
-   have a fixed value (any other Mapping arrangement would have prevented
-   the Box from simplifying). Therefore, set upper and lower limits for
-   this axis to the same value. */
-                        if( maxd <= 0.0 ) {
-                           if( slbnd[ ic ] == AST__BAD ||
-                               subnd[ ic ] == AST__BAD ) {
-                              slbnd[ ic ] = AST__BAD;
-                           } else {
-                              slbnd[ ic ] = 0.5*( slbnd[ ic ] + subnd[ ic ] );
-                           }
-                           subnd[ ic ] = slbnd[ ic ];
-
-/* If we have found a base Frame axis which corresponds to the current
-   Frame axis "ic", then look to see which limits are specified for the
-   base Frame axis, and transfer missing limits to the current Frame. */
-                        } else {
-                           if( ptr[ bax ][ 0 ] == AST__BAD ) slbnd[ ic ] = AST__BAD;
-                           if( ptr[ bax ][ 1 ] == AST__BAD ) subnd[ ic ] = AST__BAD;
-
-/* If the original limits were equal, ensure the new limits are equal
-   (the code above modified the upper limit to ensure it was different to
-   the lower limit). */
-                           if( ptr[ bax ][ 1 ] == ptr[ bax ][ 0 ] ) {
-                              subnd[ ic ] = slbnd[ ic ];
-
-/* If the original interval was an inclusion (ubnd > lbnd), ensure the new
-   interval is also an inclusion by swapping the limits if required. */
-                           } else if( ptr[ bax ][ 1 ] > ptr[ bax ][ 0 ] ) {
-                              if( subnd[ ic ] < slbnd[ ic ] ) {
-                                 tmp = subnd[ ic ];
-                                 subnd[ ic ] = slbnd[ ic ];
-                                 slbnd[ ic ] = tmp;
-                              }
-
-/* If the original interval was an exclusion (ubnd < lbnd), ensure the new
-   interval is also an exlusion by swapping the limits if required. */
-                           } else if( ptr[ bax ][ 1 ] < ptr[ bax ][ 0 ] ) {
-                              if( subnd[ ic ] > slbnd[ ic ] ) {
-                                 tmp = subnd[ ic ];
-                                 subnd[ ic ] = slbnd[ ic ];
-                                 slbnd[ ic ] = tmp;
-                              }
-                           }
-                        }
-                     }
-
-/* Create the simplified Interval from the current Frame limits found
-   above, and use it in place of the original. */
-                     unc = astTestUnc( new ) ? astGetUncFrm( new, AST__CURRENT ) : NULL;
-                     (void) astAnnul( new );
-                     new = (AstRegion *) astInterval( cfrm, slbnd, subnd, unc, "", status );
-                     if( unc ) unc = astAnnul( unc );
-                     simpler = 1;
-                  }
-
-/* Free resources */
-                  pset2 = astAnnul( pset2 );
-                  pset3 = astAnnul( pset3 );
-                  slbnd = astFree( slbnd );
-                  subnd = astFree( subnd );
-               }
-            }
-
-/* Free resources */
-            bfrm = astAnnul( bfrm );
-            cfrm = astAnnul( cfrm );
-            box = astAnnul( box );
-            box2 = astAnnul( box2 );
-            sreg = astAnnul( sreg );
-            lbnd = astFree( lbnd );
-            ubnd = astFree( ubnd );
-         }
-
-/* Free resources */
-         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_mapping, AstPointSet *in,
-                               int forward, AstPointSet *out, int *status ) {
-/*
-*  Name:
-*     Transform
-
-*  Purpose:
-*     Apply a Interval to transform a set of points.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-*                             int forward, AstPointSet *out, int *status )
-
-*  Class Membership:
-*     Interval member function (over-rides the astTransform protected
-*     method inherited from the Region class).
-
-*  Description:
-*     This function takes a Interval 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 Interval.
-*     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 Interval.
-*     -  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 equivalent Box */
-   AstInterval *this;            /* Pointer to Interval structure */
-   AstPointSet *pset_tmp;        /* Pointer to PointSet holding base Frame positions*/
-   AstPointSet *result;          /* Pointer to output PointSet */
-   AstRegion *reg;               /* Pointer to Region structure */
-   AstRegion *unc;               /* Uncertainty Region */
-   double **ptr_lims;            /* Pointer to limits array */
-   double **ptr_out;             /* Pointer to output coordinate data */
-   double **ptr_tmp;             /* Pointer to base Frame coordinate data */
-   double *lbnd_unc;             /* Lower bounds of uncertainty Region */
-   double *ubnd_unc;             /* Upper bounds of uncertainty Region */
-   double lb;                    /* Base Frame axis lower bound */
-   double p;                     /* Input base Frame axis value */
-   double ub;                    /* Base Frame axis upper bound */
-   double wid;                   /* Half width of uncertainy 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;                      /* Has the Region been negated? */
-   int npoint;                   /* No. of points */
-   int pass;                     /* Does this point pass the axis test? */
-   int point;                    /* Loop counter for points */
-   int setbad;                   /* Set the output point bad? */
-
-/* Check the global error status. */
-   if ( !astOK ) return NULL;
-
-/* Obtain pointers to the Region and to the Interval. */
-   reg = (AstRegion *) this_mapping;
-   this = (AstInterval *) this_mapping;
-
-/* If this Interval is equivalent to a Box, use the astTransform method of
-   the equivalent Box. */
-   box = Cache( this, status );
-   if( box ) {
-      result = astTransform( box, in, forward, out );
-
-/* Otherwise, we use a new implementation appropriate for unbounded
-   intervals. */
-   } else {
-
-/* 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_mapping, 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, NULL );
-
-/* 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 );
-
-/* Get a pointer to the array of axis limits */
-      ptr_lims = astGetPoints( reg->points );
-
-/* See if the Region is negated. */
-      neg = astGetNegated( reg );
-
-/* Indicate we have not yet got the bounding box of the uncertainty
-   Region. */
-      lbnd_unc = NULL;
-      ubnd_unc = NULL;
-      unc = NULL;
-
-/* Perform coordinate arithmetic. */
-      if ( astOK ) {
-
-/* First deal with closed unnegated Intervals. */
-/* ------------------------------------------- */
-         if( astGetClosed( reg ) ) {
-            if( !neg ) {
-
-/* Loop round each point. */
-               for ( point = 0; point < npoint; point++ ) {
-
-/* Assume this point is inside the Region. We change this flag when we find
-   the first axis for which the point does not pass the axis test. */
-                  setbad = 0;
-
-/* Loop round each base Frame axis */
-                  Cache( this, status );
-                  for ( coord = 0; coord < ncoord_tmp; coord++ ) {
-                     p = ptr_tmp[ coord ][ point ];
-                     lb = (this->lbnd)[ coord ];
-                     ub = (this->ubnd)[ coord ];
-
-/* If the limits are equal separate them slightly to give some tolerance. */
-                     if( lb == ub ) {
-
-/* If not yet done so, get the bounding box of the uncertainty Region in the
-   base Frame of the Interval */
-                        if( !unc ) {
-                           unc = astGetUncFrm( reg, AST__BASE );
-                           lbnd_unc = astMalloc( sizeof( double)*(size_t) ncoord_tmp );
-                           ubnd_unc = astMalloc( sizeof( double)*(size_t) ncoord_tmp );
-                           astGetRegionBounds( unc, lbnd_unc, ubnd_unc );
-                        }
-
-/* Set the gap between the limits to be equal to the uincertainty on this
-   axis. */
-                        if( astOK ) {
-                           wid = 0.5*( ubnd_unc[ coord ] - lbnd_unc[ coord ] );
-                           lb -= wid;
-                           ub += wid;
-                        }
-                     }
-
-/* Bad input points should always be bad in the output. */
-                     if( p == AST__BAD ) {
-                        setbad = 1;
-                        break;
-
-/* Does the current axis value pass the limits test for this axis? */
-                     } else if( lb <= ub ) {
-                        pass = ( lb <= p && p <= ub );
-                     } else {
-                        pass = ( p <= ub || lb <= p );
-                     }
-
-/* If this point does not pass the test for this axis, then indicate that
-   we should set the resulting output point bad and break since we now have
-   a definite value for the inside/outside flag. */
-                     if( !pass ) {
-                        setbad = 1;
-                        break;
-                     }
-                  }
-
-/* Set the axis values bad for this output point if required. */
-                  if( setbad ) {
-                     for ( coord = 0; coord < ncoord_out; coord++ ) {
-                        ptr_out[ coord ][ point ] = AST__BAD;
-                     }
-                  }
-               }
-
-/* Now deal with closed negated Intervals. */
-/* --------------------------------------- */
-            } else  {
-
-/* Loop round each point. */
-               for ( point = 0; point < npoint; point++ ) {
-
-/* Assume this point is outside the negated Region (i.e. inside the
-   unnegated Region). We change this flag when we find the first axis for
-   which the point passes the axis test. */
-                  setbad = 1;
-
-/* Loop round each base Frame axis */
-                  Cache( this, status );
-                  for ( coord = 0; coord < ncoord_tmp; coord++ ) {
-                     p = ptr_tmp[ coord ][ point ];
-                     lb = (this->lbnd)[ coord ];
-                     ub = (this->ubnd)[ coord ];
-
-/* Bad input points should always be bad in the output. */
-                     if( p == AST__BAD ) {
-                        setbad = 1;
-                        break;
-
-/* Does the current axis value pass the limits test for this axis? */
-                     } else if( lb <= ub ) {
-                        pass = ( p <= lb || ub <= p );
-                     } else {
-                        pass = ( ub <= p && p <= lb );
-                     }
-
-/* If this point passes the test for this axis, then indicate that we should
-   not set the resulting output point bad and break since we now have a
-   definite value for the inside/outside flag. */
-                     if( pass ) {
-                        setbad = 0;
-                        break;
-                     }
-                  }
-
-/* Set the axis values bad for this output point if required. */
-                  if( setbad ) {
-                     for ( coord = 0; coord < ncoord_out; coord++ ) {
-                        ptr_out[ coord ][ point ] = AST__BAD;
-                     }
-                  }
-               }
-            }
-
-/* Now deal with open unnegated Intervals. */
-/* --------------------------------------- */
-         } else {
-            if( !neg ) {
-
-/* Loop round each point. */
-               for ( point = 0; point < npoint; point++ ) {
-
-/* Assume this point is inside the Region. We change this flag when we find
-   the first axis for which the point does not pass the axis test. */
-                  setbad = 0;
-
-/* Loop round each base Frame axis */
-                  Cache( this, status );
-                  for ( coord = 0; coord < ncoord_tmp; coord++ ) {
-                     p = ptr_tmp[ coord ][ point ];
-                     lb = (this->lbnd)[ coord ];
-                     ub = (this->ubnd)[ coord ];
-
-/* Bad input points should always be bad in the output. */
-                     if( p == AST__BAD ) {
-                        setbad = 1;
-                        break;
-
-/* Does the current axis value pass the limits test for this axis? */
-                     } else if( lb <= ub ) {
-                        pass = ( lb < p && p < ub );
-                     } else {
-                        pass = ( p < ub || lb < p );
-                     }
-
-/* If this point does not pass the test for this axis, then indicate that
-   we should set the resulting output point bad and break since we now have
-   a definite value for the inside/outside flag. */
-                     if( !pass ) {
-                        setbad = 1;
-                        break;
-                     }
-                  }
-
-/* Set the axis values bad for this output point if required. */
-                  if( setbad ) {
-                     for ( coord = 0; coord < ncoord_out; coord++ ) {
-                        ptr_out[ coord ][ point ] = AST__BAD;
-                     }
-                  }
-               }
-
-/* Now deal with open negated Intervals. */
-/* ------------------------------------- */
-            } else  {
-
-/* Loop round each point. */
-               for ( point = 0; point < npoint; point++ ) {
-
-/* Assume this point is outside the negated Region (i.e. inside the
-   unnegated Region). We change this flag when we find the first axis for
-   which the point passes the axis test. */
-                  setbad = 1;
-
-/* Loop round each base Frame axis */
-                  Cache( this, status );
-                  for ( coord = 0; coord < ncoord_tmp; coord++ ) {
-                     p = ptr_tmp[ coord ][ point ];
-                     lb = (this->lbnd)[ coord ];
-                     ub = (this->ubnd)[ coord ];
-
-/* If the limits are equal separate them slightly to give some tolerance. */
-                     if( lb == ub ) {
-
-/* If not yet done so, get the bounding box of the uncertainty Region in the
-   base Frame of the Interval */
-                        if( !unc ) {
-                           unc = astGetUncFrm( reg, AST__BASE );
-                           lbnd_unc = astMalloc( sizeof( double)*(size_t) ncoord_tmp );
-                           ubnd_unc = astMalloc( sizeof( double)*(size_t) ncoord_tmp );
-                           astGetRegionBounds( unc, lbnd_unc, ubnd_unc );
-                        }
-
-/* Set the gap between the limits to be equal to the uincertainty on this
-   axis. */
-                        if( astOK ) {
-                           wid = 0.5*( ubnd_unc[ coord ] - lbnd_unc[ coord ] );
-                           lb -= wid;
-                           ub += wid;
-                        }
-                     }
-
-/* Bad input points should always be bad in the output. */
-                     if( p == AST__BAD ) {
-                        setbad = 1;
-                        break;
-
-/* Does the current axis value pass the limits test for this axis? */
-                     } else if( lb <= ub ) {
-                        pass = ( p < lb || ub < p );
-                     } else {
-                        pass = ( ub < p && p < lb );
-                     }
-
-/* If this point passes the test for this axis, then indicate that we should
-   not set the resulting output point bad and break since we now have a
-   definite value for the inside/outside flag. */
-                     if( pass ) {
-                        setbad = 0;
-                        break;
-                     }
-                  }
-
-/* Set the axis values bad for this output point if required. */
-                  if( setbad ) {
-                     for ( coord = 0; coord < ncoord_out; coord++ ) {
-                        ptr_out[ coord ][ point ] = AST__BAD;
-                     }
-                  }
-               }
-            }
-         }
-      }
-
-/* Free resources */
-      pset_tmp = astAnnul( pset_tmp );
-      if( lbnd_unc ) lbnd_unc = astFree( lbnd_unc );
-      if( ubnd_unc ) ubnd_unc = astFree( ubnd_unc );
-      if( unc ) unc = astAnnul( unc );
-   }
-
-/* 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 Interval 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: */
-   AstInterval *in;             /* Pointer to input Interval */
-   AstInterval *out;            /* Pointer to output Interval */
-   size_t nb;                   /* Number of bytes in limits array */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain pointers to the input and output Intervals. */
-   in = (AstInterval *) objin;
-   out = (AstInterval *) objout;
-
-/* For safety, first clear any references to the input memory from
-   the output Interval. */
-   out->box = NULL;
-   out->lbnd = NULL;
-   out->ubnd = NULL;
-
-/* Note the number of bytes in each limits array */
-   nb = sizeof( double )*(size_t) astGetNin( ((AstRegion *) in)->frameset );
-
-/* Copy dynamic memory contents */
-   if( in->box ) out->box = astCopy( in->box );
-   out->lbnd = astStore( NULL, in->lbnd, nb );
-   out->ubnd = astStore( NULL, in->ubnd, nb );
-}
-
-
-/* Destructor. */
-/* ----------- */
-static void Delete( AstObject *obj, int *status ) {
-/*
-*  Name:
-*     Delete
-
-*  Purpose:
-*     Destructor for Interval objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Delete( AstObject *obj, int *status )
-
-*  Description:
-*     This function implements the destructor for Interval 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: */
-   AstInterval *this;                 /* Pointer to Interval */
-
-/* Obtain a pointer to the Interval structure. */
-   this = (AstInterval *) obj;
-
-/* Annul all resources. */
-   if( this->box ) this->box = astAnnul( this->box );
-   this->lbnd = astFree( this->lbnd );
-   this->ubnd = astFree( this->ubnd );
-}
-
-/* Dump function. */
-/* -------------- */
-static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
-/*
-*  Name:
-*     Dump
-
-*  Purpose:
-*     Dump function for Interval 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 Interval class to an output Channel.
-
-*  Parameters:
-*     this
-*        Pointer to the Interval whose data are being written.
-*     channel
-*        Pointer to the Channel to which the data are being written.
-*     status
-*        Pointer to the inherited status variable.
-*/
-
-/* Local Variables: */
-   AstInterval *this;                 /* Pointer to the Interval structure */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the Interval structure. */
-   this = (AstInterval *) this_object;
-
-/* Write out values representing the instance variables for the
-   Interval 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 astIsAInterval and astCheckInterval functions using the macros
-   defined for this purpose in the "object.h" header file. */
-astMAKE_ISA(Interval,Region)
-astMAKE_CHECK(Interval)
-
-AstInterval *astInterval_( void *frame_void, const double lbnd[],
-                           const double ubnd[], AstRegion *unc,
-                           const char *options, int *status, ...) {
-/*
-*++
-*  Name:
-c     astInterval
-f     AST_INTERVAL
-
-*  Purpose:
-*     Create a Interval.
-
-*  Type:
-*     Public function.
-
-*  Synopsis:
-c     #include "interval.h"
-c     AstInterval *astInterval( AstFrame *frame, const double lbnd[],
-c                               const double ubnd[], AstRegion *unc,
-c                               const char *options, ... )
-f     RESULT = AST_INTERVAL( FRAME, LBND, UBND, UNC, OPTIONS, STATUS )
-
-*  Class Membership:
-*     Interval constructor.
-
-*  Description:
-*     This function creates a new Interval and optionally initialises its
-*     attributes.
-*
-*     A Interval is a Region which represents upper and/or lower limits on
-*     one or more axes of a Frame. For a point to be within the region
-*     represented by the Interval, the point must satisfy all the
-*     restrictions placed on all the axes. The point is outside the region
-*     if it fails to satisfy any one of the restrictions. Each axis may have
-*     either an upper limit, a lower limit, both or neither. If both limits
-*     are supplied but are in reverse order (so that the lower limit is
-*     greater than the upper limit), then the interval is an excluded
-*     interval, rather than an included interval.
-*
-*     At least one axis limit must be supplied.
-*
-*     Note, The Interval class makes no allowances for cyclic nature of
-*     some coordinate systems (such as SkyFrame coordinates). A Box
-*     should usually be used in these cases since this requires the user
-*     to think about suitable upper and lower limits,
-
-*  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     lbnd
-f     LBND( * ) = 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 lower limits on each axis.
-*        Set a value to AST__BAD to indicate that the axis has no lower
-*        limit.
-c     ubnd
-f     UBND( * ) = 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 upper limits on each axis.
-*        Set a value to AST__BAD to indicate that the axis has no upper
-*        limit.
-c     unc
-f     UNC = INTEGER (Given)
-*        An optional pointer to an existing Region which specifies the
-*        uncertainties associated with the boundary of the Interval being created.
-*        The uncertainty in any point on the boundary of the Interval 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 Interval. 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 Interval 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 Interval. 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 Interval. 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     astInterval()
-f     AST_INTERVAL = INTEGER
-*        A pointer to the new Interval.
-
-*  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 */
-   AstInterval *new;             /* Pointer to new Interval */
-   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 Interval, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitInterval( NULL, sizeof( AstInterval ), !class_init,
-                          &class_vtab, "Interval", frame, lbnd, ubnd, 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 Interval'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 Interval. */
-   return new;
-}
-
-AstInterval *astIntervalId_( void *frame_void, const double lbnd[],
-                             const double ubnd[], void *unc_void,
-                             const char *options, ... ) {
-/*
-*  Name:
-*     astIntervalId_
-
-*  Purpose:
-*     Create a Interval.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     AstInterval *astIntervalId_( AstFrame *frame, const double lbnd[],
-*                                  const double ubnd[], AstRegion *unc,
-*                                  const char *options, ... )
-
-*  Class Membership:
-*     Interval constructor.
-
-*  Description:
-*     This function implements the external (public) interface to the
-*     astInterval constructor function. It returns an ID value (instead
-*     of a true C pointer) to external users, and must be provided
-*     because astInterval_ 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 astInterval_ 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 astInterval_.
-
-*  Returned Value:
-*     The ID value associated with the new Interval.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstFrame *frame;              /* Pointer to Frame structure */
-   AstInterval *new;             /* Pointer to new Interval */
-   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 Interval, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitInterval( NULL, sizeof( AstInterval ), !class_init, &class_vtab,
-                        "Interval", frame, lbnd, ubnd, 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 Interval'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 Interval. */
-   return astMakeId( new );
-}
-
-AstInterval *astInitInterval_( void *mem, size_t size, int init, AstIntervalVtab *vtab,
-                               const char *name, AstFrame *frame,
-                               const double lbnd[], const double ubnd[],
-                               AstRegion *unc, int *status ) {
-/*
-*+
-*  Name:
-*     astInitInterval
-
-*  Purpose:
-*     Initialise a Interval.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     AstInterval *astInitInterval( void *mem, size_t size, int init, AstIntervalVtab *vtab,
-*                                   const char *name, AstFrame *frame,
-*                                   const double lbnd[], const double ubnd[],
-*                                   AstRegion *unc )
-
-*  Class Membership:
-*     Interval initialiser.
-
-*  Description:
-*     This function is provided for use by class implementations to initialise
-*     a new Interval object. It allocates memory (if necessary) to accommodate
-*     the Interval plus any additional data associated with the derived class.
-*     It then initialises a Interval 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 Interval at the start of the memory passed via the
-*     "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory in which the Interval is to be initialised.
-*        This must be of sufficient size to accommodate the Interval data
-*        (sizeof(Interval)) 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 Interval (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 Interval
-*        structure, so a valid value must be supplied even if not required for
-*        allocating memory.
-*     init
-*        A logical flag indicating if the Interval'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 Interval.
-*     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.
-*     lbnd
-*        An array of double, with one element for each Frame axis
-*        (Naxes attribute) containing the lower limits on each axis.
-*        Set a value to AST__BAD to indicate that the axis has no lower
-*        limit. Upper and ower limits can be reversed to create an
-*        excluded interval rather than an included interval.
-*     ubnd
-*        An array of double, with one element for each Frame axis
-*        (Naxes attribute) containing the upper limits on each axis.
-*        Set a value to AST__BAD to indicate that the axis has no upper
-*        limit.
-*     unc
-*        A pointer to a Region which specifies the uncertainty in the
-*        supplied positions (all points on the boundary of the new Interval
-*        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 Interval'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 Interval.
-
-*  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 */
-   AstInterval *new;         /* Pointer to new Interval */
-   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;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* If necessary, initialise the virtual function table. */
-   if ( init ) astInitIntervalVtab( &class_vtab, name );
-
-/* Initialise. */
-   new = NULL;
-
-/* Get the number of axis values required for each position. */
-   nc = astGetNaxes( frame );
-
-/* Create a PointSet to hold the upper and lower bounds, and get pointers to
-   the data arrays. */
-   pset = astPointSet( 2, nc, "", status );
-   ptr = astGetPoints( pset );
-   if( astOK ) {
-
-/* Copy the limits into the PointSet.  */
-      for( i = 0; i < nc; i++ ) {
-         ptr[ i ][ 0 ] = lbnd[ i ];
-         ptr[ i ][ 1 ] = ubnd[ i ];
-      }
-
-/* Initialise a Region structure (the parent class) as the first component
-   within the Interval structure, allocating memory if necessary. */
-      new = (AstInterval *) astInitRegion( mem, size, 0, (AstRegionVtab *) vtab,
-                                           name, frame, pset, unc );
-
-      if ( astOK ) {
-
-/* Initialise the Interval data. */
-/* ----------------------------- */
-         new->lbnd = NULL;
-         new->ubnd = NULL;
-         new->box = NULL;
-         new->stale = 1;
-
-/* If an error occurred, clean up by deleting the new Interval. */
-         if ( !astOK ) new = astDelete( new );
-      }
-   }
-
-/* Free resources. */
-   pset = astAnnul( pset );
-
-/* Return a pointer to the new Interval. */
-   return new;
-}
-
-AstInterval *astLoadInterval_( void *mem, size_t size, AstIntervalVtab *vtab,
-                               const char *name, AstChannel *channel, int *status ) {
-/*
-*+
-*  Name:
-*     astLoadInterval
-
-*  Purpose:
-*     Load a Interval.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "interval.h"
-*     AstInterval *astLoadInterval( void *mem, size_t size, AstIntervalVtab *vtab,
-*                                   const char *name, AstChannel *channel )
-
-*  Class Membership:
-*     Interval loader.
-
-*  Description:
-*     This function is provided to load a new Interval 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
-*     Interval 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 Interval at the start of the memory
-*     passed via the "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory into which the Interval is to be
-*        loaded.  This must be of sufficient size to accommodate the
-*        Interval data (sizeof(Interval)) 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 Interval (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 Interval 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(AstInterval) is used instead.
-*     vtab
-*        Pointer to the start of the virtual function table to be
-*        associated with the new Interval. If this is NULL, a pointer
-*        to the (static) virtual function table for the Interval 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 "Interval" is used instead.
-
-*  Returned Value:
-*     A pointer to the new Interval.
-
-*  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 */
-   AstInterval *new;              /* Pointer to the new Interval */
-
-/* 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 Interval. In this case the
-   Interval belongs to this class, so supply appropriate values to be
-   passed to the parent class loader (and its parent, etc.). */
-   if ( !vtab ) {
-      size = sizeof( AstInterval );
-      vtab = &class_vtab;
-      name = "Interval";
-
-/* If required, initialise the virtual function table for this class. */
-      if ( !class_init ) {
-         astInitIntervalVtab( 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 Interval. */
-   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, "Interval" );
-
-/* 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. */
-/* ---------------------------- */
-      new->lbnd = NULL;
-      new->ubnd = NULL;
-      new->box = NULL;
-      new->stale = 1;
-
-/* If an error occurred, clean up by deleting the new Interval. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return the new Interval 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 astIntervalPoints_( AstInterval *this, double *lbnd, double *ubnd,
-                         int *status) {
-   if ( !astOK ) return;
-   (**astMEMBER(this,Interval,IntervalPoints))( this, lbnd, ubnd, status );
-   return;
-}
-
-
-
-
-
-