Merge commit 'd26ed8388f100a12996c0b92a98040ef2ba7fa8e' as 'ast'

1 files changed, 4686 insertions, 0 deletions

diff --git a/ast/interval.c b/ast/interval.c
new file mode 100644
index 0000000..73e23bc
--- /dev/null
+++ b/ast/interval.c
@@ -0,0 +1,4686 @@
+/*
+*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;
+}
+
+
+
+
+
+