path: root/ast/interval.c

/*
*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 to 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;
}