update ast 8.6.2

1 files changed, 0 insertions, 2093 deletions

diff --git a/ast/nullregion.c b/ast/nullregion.c
deleted file mode 100644
index 6ef9cfa..0000000
--- a/ast/nullregion.c
+++ /dev/null
@@ -1,2093 +0,0 @@
-/*
-*class++
-*  Name:
-*     NullRegion
-
-*  Purpose:
-*     A boundless region within a Frame.
-
-*  Constructor Function:
-c     astNullRegion
-f     AST_NULLREGION
-
-*  Description:
-*     The NullRegion class implements a Region with no bounds within a Frame.
-*     If the Negated attribute of a NullRegion is false, the NullRegion
-*     represents a Region containing no points. If the Negated attribute of
-*     a NullRegion is true, the NullRegion represents an infinite Region
-*     (that is, all points in the coordinate system are inside the NullRegion).
-
-*  Inheritance:
-*     The NullRegion class inherits from the Region class.
-
-*  Attributes:
-*     The NullRegion class does not define any new attributes beyond
-*     those which are applicable to all Regions.
-
-*  Functions:
-c     The NullRegion class does not define any new functions beyond those
-f     The NullRegion class does not define any new routines beyond those
-*     which are applicable to all Regions.
-
-*  Copyright:
-*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
-*     Research Councils
-*     Copyright (C) 2009 Science & Technology Facilities Council.
-*     All Rights Reserved.
-
-*  Licence:
-*     This program is free software: you can redistribute it and/or
-*     modify it under the terms of the GNU Lesser General Public
-*     License as published by the Free Software Foundation, either
-*     version 3 of the License, or (at your option) any later
-*     version.
-*     
-*     This program is distributed in the hope that it will be useful,
-*     but WITHOUT ANY WARRANTY; without even the implied warranty of
-*     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-*     GNU Lesser General Public License for more details.
-*     
-*     You should have received a copy of the GNU Lesser General
-*     License along with this program.  If not, see
-*     <http://www.gnu.org/licenses/>.
-
-*  Authors:
-*     DSB: David S. Berry (Starlink)
-
-*  History:
-*     11-OCT-2004 (DSB):
-*        Original version.
-*     20-JAN-2009 (DSB):
-*        Over-ride astRegBasePick.
-*     26-JAN-2009 (DSB):
-*        Over-ride astMapMerge.
-*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 NullRegion
-
-/* 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"              /* Coordinate regions (parent class) */
-#include "channel.h"             /* I/O channels */
-#include "nullregion.h"          /* Interface definition for this class */
-#include "mapping.h"             /* Position mappings */
-#include "circle.h"              /* Circle regions */
-#include "prism.h"               /* Extruded Regions */
-#include "unitmap.h"             /* Unit Mapping */
-#include "cmpframe.h"            /* Compound Frames */
-#include "cmpmap.h"              /* Compound Mappings */
-
-/* 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 * );
-
-
-#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(NullRegion)
-
-/* Define macros for accessing each item of thread specific global data. */
-#define class_init astGLOBAL(NullRegion,Class_Init)
-#define class_vtab astGLOBAL(NullRegion,Class_Vtab)
-
-
-#include <pthread.h>
-
-
-#else
-
-
-/* Define the class virtual function table and its initialisation flag
-   as static variables. */
-static AstNullRegionVtab 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. */
-AstNullRegion *astNullRegionId_( void *, void *, const char *, ... );
-
-/* Prototypes for Private Member Functions. */
-/* ======================================== */
-static AstMapping *Simplify( AstMapping *, int * );
-static AstPointSet *RegBaseMesh( AstRegion *, int * );
-static AstPointSet *RegMesh( 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 *MergeNullRegion( AstNullRegion *, AstRegion *, int, int * );
-static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
-static int Overlap( AstRegion *, AstRegion *, int * );
-static int OverlapX( AstRegion *, AstRegion *, int * );
-static void Dump( AstObject *, AstChannel *, int * );
-static void RegBaseBox( AstRegion *this, double *, double *, int * );
-static void GetRegionBounds( AstRegion *this, double *, double *, int * );
-
-/* Member functions. */
-/* ================= */
-static AstRegion *GetDefUnc( AstRegion *this, int *status ) {
-/*
-*+
-*  Name:
-*     astGetDefUnc
-
-*  Purpose:
-*     Obtain a pointer to the default uncertainty Region for a given Region.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstRegion *astGetDefUnc( AstRegion *this )
-
-*  Class Membership:
-*     NullRegion 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.
-
-*  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: */
-   AstRegion *result;
-   double *cen;
-   double rad;
-   int i;
-   int n;
-
-/* Initialise */
-   result = NULL;
-
-/* Check inherited status */
-   if( !astOK ) return result;
-
-/* Create a Circle centred on the origin with zero radius. */
-   n = astGetNaxes( this );
-   cen = astMalloc( sizeof(double)*(size_t) n );
-   if( cen ) {
-      for( i = 0; i < n; i++ ) cen[ i ] = 0.0;
-      rad = 0.0;
-      result = (AstRegion *) astCircle( this, 1, cen, &rad, NULL, "", status );
-      cen = astFree( cen );
-   }
-
-/* Return the default uncertainty Region. */
-   return result;
-}
-
-void astInitNullRegionVtab_(  AstNullRegionVtab *vtab, const char *name, int *status ) {
-/*
-*+
-*  Name:
-*     astInitNullRegionVtab
-
-*  Purpose:
-*     Initialise a virtual function table for a NullRegion.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     void astInitNullRegionVtab( AstNullRegionVtab *vtab, const char *name )
-
-*  Class Membership:
-*     NullRegion vtab initialiser.
-
-*  Description:
-*     This function initialises the component of a virtual function
-*     table which is used by the NullRegion class.
-
-*  Parameters:
-*     vtab
-*        Pointer to the virtual function table. The components used by
-*        all ancestral classes will be initialised if they have not already
-*        been initialised.
-*     name
-*        Pointer to a constant null-terminated character string which contains
-*        the name of the class to which the virtual function table belongs (it
-*        is this pointer value that will subsequently be returned by the Object
-*        astClass function).
-*-
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
-   AstRegionVtab *region;        /* Pointer to Region component of Vtab */
-
-/* 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 astIsANullRegion) 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. */
-
-/* Save the inherited pointers to methods that will be extended, and
-   replace them with pointers to the new member functions. */
-   mapping = (AstMappingVtab *) vtab;
-   region = (AstRegionVtab *) vtab;
-
-   parent_transform = mapping->Transform;
-   mapping->Transform = Transform;
-
-   parent_simplify = mapping->Simplify;
-   mapping->Simplify = Simplify;
-
-/* Store replacement pointers for methods which will be over-ridden by
-   new member functions implemented here. */
-   mapping->MapMerge = MapMerge;
-
-   region->GetDefUnc = GetDefUnc;
-   region->Overlap = Overlap;
-   region->OverlapX = OverlapX;
-   region->RegBaseBox = RegBaseBox;
-   region->RegBaseMesh = RegBaseMesh;
-   region->GetRegionBounds = GetRegionBounds;
-   region->RegMesh = RegMesh;
-   region->RegBasePick = RegBasePick;
-
-/* Declare the copy constructor, destructor and class dump
-   functions. */
-   astSetDump( vtab, Dump, "NullRegion", "Boundless region" );
-
-/* If we have just initialised the vtab for the current class, indicate
-   that the vtab is now initialised, and store a pointer to the class
-   identifier in the base "object" level of the vtab. */
-   if( vtab == &class_vtab ) {
-      class_init = 1;
-      astSetVtabClassIdentifier( vtab, &(vtab->id) );
-   }
-}
-
-static int 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 NullRegion.
-
-*  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:
-*     NullRegion 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 NullRegion 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 NullRegion 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 NullRegion which is to be merged with
-*        its neighbours. This should be a cloned copy of the NullRegion
-*        pointer contained in the array element "(*map_list)[where]"
-*        (see below). This pointer will not be annulled, and the
-*        NullRegion it identifies will not be modified by this function.
-*     where
-*        Index in the "*map_list" array (below) at which the pointer
-*        to the nominated NullRegion 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: */
-   AstNullRegion *oldint;  /* Pointer to supplied NullRegion */
-   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 NullRegion. */
-   oldint = (AstNullRegion *) this;
-
-/* First of all, see if the NullRegion can be replaced by a simpler Region,
-   without reference to the neighbouring Regions in the list.           */
-/* =====================================================================*/
-
-/* Try to simplify the NullRegion. If the pointer value has changed, we assume
-   some simplification took place. */
-   new = astSimplify( oldint );
-   if( new != (AstMapping *) oldint ) {
-
-/* Annul the NullRegion 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 NullRegion 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 NullRegion with its lower neighbour (if any). */
-      if( where > 0 ) {
-         i1 = where - 1;
-         map = ( *map_list )[ where - 1 ];
-         if( astIsARegion( map ) ) {
-            new = (AstMapping *) MergeNullRegion( oldint, (AstRegion *) map,
-                                                  0, status );
-         }
-      }
-
-/* If this did not produced a merged Region, attempt to merge the NullRegion
-   with its upper neighbour (if any). */
-      if( !new && where < *nmap - 1 ) {
-         i1 = where;
-         map = ( *map_list )[ where + 1 ];
-         if( astIsARegion( map ) ) {
-            new = (AstMapping *) MergeNullRegion( 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 *MergeNullRegion( AstNullRegion *this, AstRegion *reg,
-                                   int intfirst, int *status ) {
-/*
-*  Name:
-*     MergeNullRegion
-
-*  Purpose:
-*     Attempt to merge a NullRegion with another Region to form a Region of
-*     higher dimensionality.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstRegion *MergeNullRegion( AstNullRegion *this, AstRegion *reg,
-*                                 int intfirst, int *status )
-
-*  Class Membership:
-*     NullRegion member function.
-
-*  Description:
-*     This function attempts to combine the supplied Regions together
-*     into a Region of higher dimensionality.
-
-*  Parameters:
-*     this
-*        Pointer to a NullRegion.
-*     reg
-*        Pointer to another Region.
-*     intfirst
-*        If non-zero, then the NullRegion 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 */
-   AstRegion *bunc;          /* Base Frame uncertainty Region */
-   AstRegion *new;           /* Pointer to new NullRegion in base Frame */
-   AstRegion *result;        /* Pointer to returned NullRegion in current Frame */
-   AstRegion *unc_reg;       /* Current Frame uncertainty Region from "reg" */
-   AstRegion *unc_this;      /* Current Frame uncertainty Region from "this" */
-   double fac_reg;           /* Ratio of used to default MeshSize for "reg" */
-   double fac_this;          /* Ratio of used to default MeshSize for "this" */
-   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 NullRegion  */
-
-/* Initialise */
-   result = NULL;
-
-/* Check the local error status. */
-   if ( !astOK ) return result;
-
-/* Get the Closed attributes of the two Regions. They must be the same in
-   each Region if we are to merge the Regions. In addition, in order to
-   merge, either both Regions must have a defined uncertainty, or neither
-   Region must have a defined Uncertainty. */
-   if( astGetClosed( this ) == astGetClosed( reg ) &&
-       astTestUnc( this ) == astTestUnc( reg ) ) {
-
-/* Get the Nagated attributes of the two Regions. */
-      neg_this = astGetNegated( this );
-      neg_reg = astGetNegated( reg );
-
-/* Get the number of axes in the two supplied Regions. */
-      nax_reg = astGetNaxes( reg );
-      nax_this = astGetNaxes( this );
-
-/* If the Regions can be combined, get the number of axes the
-   combination will have. */
-      nax = nax_reg + nax_this;
-
-/* Get the base Frames from the two Region FrameSets, and combine them
-   into a single CmpFrame that will be used to create any new Region. */
-      frm_this = astGetFrame( ((AstRegion *) this)->frameset, AST__BASE );
-      frm_reg = astGetFrame( reg->frameset, AST__BASE );
-
-      if( 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;
-
-/* We only check for merging with another NullRegion (other classes such
-   as Box and Interval check for merging of NullRegions with other classes).
-   The result will be an NullRegion. Both Regions must have the same value
-   for the Negated flag. */
-      if( astIsANullRegion( reg ) && neg_this == neg_reg ) {
-         new = (AstRegion *) astNullRegion( bfrm, NULL, "", status );
-
-/* Propagate remaining attributes of the supplied Region to it. */
-         astRegOverlay( new, this, 1 );
-
-/* Ensure the Negated flag is set correctly in the returned NullRegion. */
-         if( neg_this ) {
-            astSetNegated( new, neg_this );
-         } else {
-            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 );
-      }
-   }
-
-/* If an error has occurred, annul the returned pointer. */
-   if( !astOK ) result = astAnnul( result );
-
-/* 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 "nullregion.h"
-*     int Overlap( AstRegion *this, AstRegion *that )
-
-*  Class Membership:
-*     NullRegion 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.
-
-*  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.
-
-* Implementation Notes:
-*    - This function is simply a wrap-up for the OverlapX function
-*    which performs the required processing but swaps the order of the
-*    two arguments. This is a trick to allow the astOverlap
-*    method to be over-ridden by derived classes on the basis of the
-*    class of either of the two arguments.
-*/
-
-/* Check the inherited status. */
-   if ( !astOK ) return 0;
-
-/* Invoke the private "OverlapX" member function with the two arguments
-   swapped. */
-   return OverlapX( that, this, status );
-}
-
-static int OverlapX( AstRegion *that, AstRegion *this, int *status ){
-/*
-*  Name:
-*     OverlapX
-
-*  Purpose:
-*     Test if two regions overlap each other.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     int OverlapX( AstRegion *that, AstRegion *this )
-
-*  Class Membership:
-*     NullRegion member function (over-rides the astOverlapX method inherited
-*     from the Region class).
-
-*  Description:
-*     This function performs the processing for the public astOverlap
-*     method (as inherited from the Region class and over-ridden by the
-*     NullRegion class) and has exactly the same interface except that
-*     the order of the two arguments is swapped. This is a trick
-*     to allow the astOverlap method to be over-ridden by derived
-*     classes on the basis of the class of either of its two
-*     arguments.
-*
-*     See the astOverlap method for details of the interface.
-
-*/
-
-/* Local Variables: */
-   AstFrameSet *fs;               /* FrameSet connecting Region Frames */
-   int result;                    /* Returned value */
-
-/* Initialise. */
-   result = 0;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Check that the Regions can be compared meaningfully. */
-   fs = astConvert( this, that, "" );
-   if( fs ) {
-      fs = astAnnul( fs );
-
-/* If both the supplied Regions are NullRegion... */
-      if( astIsANullRegion( this ) && astIsANullRegion( that ) ) {
-
-/* If the Negated attributes are equal, the Regions are identical.
-   Otherwise they are mutually exclusive. */
-         if( astGetNegated( this ) == astGetNegated( that ) ) {
-            result = 5;
-         } else {
-            result = 6;
-         }
-
-/* If one of the supplied Region is a NullRegion containing no points,
-   then there is no overlap. */
-      } else if( ( astIsANullRegion( this ) && !astGetNegated( this ) ) ||
-                 ( astIsANullRegion( that ) && !astGetNegated( that ) ) ) {
-         result = 1;
-
-/* If "that" is infinite and "this" is not infinite, then "this" is
-   entirely inside "that". */
-      } else if( astIsANullRegion( that ) && astGetNegated( that ) ) {
-         result = 2;
-
-/* If "this" is infinite and "that" is not infinite, then "that" is
-   entirely inside "this". */
-      } else if( astIsANullRegion( this ) && astGetNegated( this ) ){
-         result = 3;
-
-/* Otherwise there is partial overlap. */
-      } else {
-         result = 4;
-      }
-   }
-
-/* 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 "nullregion.h"
-*     void RegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status )
-
-*  Class Membership:
-*     NullRegion 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: */
-   AstNullRegion *this;          /* Pointer to NullRegion structure */
-   int i;                        /* Axis index */
-   int nc;                       /* No. of axes in base Frame */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Get a pointer to the NullRegion structure */
-   this = (AstNullRegion *) this_region;
-
-/* Get the number of base Frame axes. */
-   nc = astGetNin( this_region->frameset );
-
-/* Set the upper bound less than the lower bound to indicate that the region
-   contains no points. */
-   for( i = 0; i < nc; i++ ) {
-      lbnd[ i ] = 1.0;
-      ubnd[ i ] = -1.0;
-   }
-
-}
-
-static AstPointSet *RegBaseMesh( AstRegion *this, int *status ){
-/*
-*  Name:
-*     RegBaseMesh
-
-*  Purpose:
-*     Return a PointSet containing a mesh of points on the boundary of a
-*     Region in its base Frame.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstPointSet *astRegBaseMesh( AstRegion *this, int *status )
-
-*  Class Membership:
-*     NullRegion 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. Note, a NullRegion has no boundary. This
-*     is indicated by returned a PointSet containing a single point with a
-*     value of AST__BAD on every axis.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*    Pointer to a new PointSet containing a single point with value of
-*    AST__BAD on every axis.
-
-*-
-*/
-
-/* Local Variables: */
-   AstPointSet *result;
-   double **ptr;
-   int i;
-   int nc;
-
-/* Initialise */
-   result = NULL;
-
-/* Check the inherited status */
-   if( !astOK ) return result;
-
-/* If the Region structure contains a pointer to a PointSet holding
-   a previously created mesh, return it. */
-   if( this->basemesh ) {
-      result = astClone( this->basemesh );
-
-/* Otherwise, create a new mesh. */
-   } else {
-
-/* Get the number of base Frame axes */
-      nc = astGetNin( this->frameset );
-
-/* Create the PointSet. */
-      result = astPointSet( 1, nc, "", status );
-
-/* Get a pointer to the axis values. */
-      ptr = astGetPoints( result );
-
-/* If OK, store AST__BAD on every axis. */
-      if( ptr ) for( i = 0; i < nc; i++ ) ptr[ i ][ 0 ] = AST__BAD;
-
-/* Same the returned pointer in the Region structure so that it does not
-   need to be created again next time this function is called. */
-      if( astOK && result ) this->basemesh = astClone( result );
-
-   }
-
-/* Return the result. */
-   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 "nullregion.h"
-*     AstRegion *RegBasePick( AstRegion *this, int naxes, const int *axes,
-*                             int *status )
-
-*  Class Membership:
-*     NullRegion 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 */
-   AstRegion *bunc;        /* The uncertainty in the supplied Region */
-   AstRegion *result;      /* Returned Region */
-   AstRegion *unc;         /* The uncertainty in the 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;
-   }
-
-/* Create the new NullRegion. */
-   result = (AstRegion *) astNullRegion( frm, unc, "", status );
-
-/* Free resources */
-   frm = astAnnul( frm );
-   bfrm = astAnnul( bfrm );
-   if( unc ) unc = astAnnul( unc );
-
-/* Return a NULL pointer if an error has occurred. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return the result. */
-   return result;
-}
-
-static void GetRegionBounds( AstRegion *this_region, double *lbnd, double *ubnd, int *status ){
-/*
-*  Name:
-*     GetRegionBounds
-
-*  Purpose:
-*     Returns the bounding box of an un-negated Region in the current Frame of
-*     the encapsulated FrameSet.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     void astGetRegionBounds( AstRegion *this, double *lbnd, double *ubnd, int *status )
-
-*  Class Membership:
-*     NullRegion member function (over-rides the astGetRegionBounds protected
-*     method inherited from the Region class).
-
-*  Description:
-*     This function returns the upper and lower axis bounds of a Region in
-*     the current 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 current Frame of the encapsulated
-*        FrameSet. It should have at least as many elements as there are
-*        axes in the Region.
-*     ubnd
-*        Pointer to an array in which to return the upper axis bounds
-*        covered by the Region in the current Frame of the encapsulated
-*        FrameSet. It should have at least as many elements as there are
-*        axes in the Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-/* Local Variables: */
-   AstNullRegion *this;          /* Pointer to NullRegion structure */
-   int i;                        /* Axis index */
-   int nc;                       /* No. of axes in base Frame */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Get a pointer to the NullRegion structure */
-   this = (AstNullRegion *) this_region;
-
-/* Get the number of base Frame axes. */
-   nc = astGetNin( this_region->frameset );
-
-/* Set the upper bound less than the lower bound to indicate that the region
-   contains no points. */
-   for( i = 0; i < nc; i++ ) {
-      lbnd[ i ] = 1.0;
-      ubnd[ i ] = -1.0;
-   }
-
-}
-
-static AstPointSet *RegMesh( AstRegion *this, int *status ){
-/*
-*  Name:
-*     RegMesh
-
-*  Purpose:
-*     Return a PointSet containing points spread over the boundary of a
-*     Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstPointSet *astRegMesh( AstRegion *this, int *status )
-
-*  Class Membership:
-*     NullRegion member function (over-rides the astRegMesh 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 current Frame of
-*     the encapsulated FrameSet. Note, a NullRegion has no boundary and
-*     so an error is reported if this function is called.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     NULL pointer.
-
-*  Notes:
-*     - This implementation reports and error and returns NULL since a
-*     NullRegion has no boundary.
-*-
-*/
-
-   astError( AST__INTER, "astRegMesh(%s): The %s class does not implement "
-             "the astRegMesh method inherited from the Region class "
-             "(internal AST programming error).", status, astGetClass( this ),
-             astGetClass( this ) );
-   return NULL;
-}
-
-static AstMapping *Simplify( AstMapping *this_mapping, int *status ) {
-/*
-*  Name:
-*     Simplify
-
-*  Purpose:
-*     Simplify the Mapping represented by a Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstMapping *Simplify( AstMapping *this, int *status )
-
-*  Class Membership:
-*     NullRegion 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: */
-   AstFrame *frm;             /* Current Frame */
-   AstMapping *map;           /* Base->current Mapping */
-   AstMapping *result;        /* Result pointer to return */
-   AstRegion *new;            /* Simplified Region */
-   AstRegion *this;           /* Pointer to supplied Region structure */
-
-/* Initialise. */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the supplied Region structure. */
-   this = (AstRegion *) this_mapping;
-
-/* Invoke the parent Simplify method inherited from the Region class. This
-   will simplify the encapsulated FrameSet and uncertainty Region. */
-   new = (AstRegion *) (*parent_simplify)( this_mapping, status );
-
-/* Is the Mapping from base Frame to current Frame in the Region a
-   UnitMap? If so, no simplification is possible. */
-   map = astGetMapping( new->frameset, AST__BASE, AST__CURRENT );
-   if( astIsAUnitMap( map ) ){
-      result = astClone( new );
-
-   } else {
-
-/* Create a NullRegion from the current Frame. */
-      frm = astGetFrame( new->frameset, AST__CURRENT );
-      result = (AstMapping *) astNullRegion( frm, astGetUnc( new, 0 ), "", status );
-
-/* Free resources. */
-      frm = astAnnul( frm );
-
-   }
-   map = astAnnul( map );
-   new = astAnnul( new );
-
-/* 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( result != this_mapping ) astRegOverlay( result, this, 1 );
-
-/* 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 NullRegion to transform a set of points.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-*                             int forward, AstPointSet *out, int *status )
-
-*  Class Membership:
-*     NullRegion member function (over-rides the astTransform protected
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function takes a NullRegion 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 NullRegion.
-*     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 NullRegion.
-*     -  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: */
-   AstNullRegion *this;          /* Pointer to NullRegion */
-   AstPointSet *result;          /* Pointer to output PointSet */
-   double **ptr_out;             /* Pointer to output coordinate data */
-   double *p;                    /* Pointer to next axis value */
-   int coord;                    /* Zero-based index for coordinates */
-   int ncoord_out;               /* No. of coordinates per output point */
-   int npoint_out;               /* No. of points */
-   int point;                    /* Loop counter for points */
-
-/* Check the global error status. */
-   if ( !astOK ) return NULL;
-
-/* Obtain a pointer to the NullRegion structure. */
-   this = (AstNullRegion *) this_mapping;
-
-/* 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. */
-
-/* If the NullRegion has been inverted, it represents an infinite region
-   which includes all points, so just retain the copy of the supplied
-   PointSet created by the parent Transform method above. If the NullRegion
-   has not been inverted, it contains no points and so set all output points
-   bad. */
-   if( !astGetNegated( this ) ) {
-      ncoord_out = astGetNcoord( result );
-      npoint_out = astGetNpoint( result );
-      ptr_out = astGetPoints( result );
-      if ( astOK ) {
-         for ( coord = 0; coord < ncoord_out; coord++ ) {
-            p = ptr_out[ coord ];
-            for ( point = 0; point < npoint_out; point++ ) {
-               *(p++) = AST__BAD;
-            }
-         }
-      }
-   }
-
-/* 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. */
-/* ----------------- */
-/* None */
-
-/* Destructor. */
-/* ----------- */
-/* None */
-
-/* Dump function. */
-/* -------------- */
-static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
-/*
-*  Name:
-*     Dump
-
-*  Purpose:
-*     Dump function for NullRegion 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 NullRegion class to an output Channel.
-
-*  Parameters:
-*     this
-*        Pointer to the NullRegion 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: */
-   AstNullRegion *this;                 /* Pointer to the NullRegion structure */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the NullRegion structure. */
-   this = (AstNullRegion *) this_object;
-
-/* Write out values representing the instance variables for the
-   NullRegion 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 astIsANullRegion and astCheckNullRegion functions using the macros
-   defined for this purpose in the "object.h" header file. */
-astMAKE_ISA(NullRegion,Region)
-astMAKE_CHECK(NullRegion)
-
-AstNullRegion *astNullRegion_( void *frame_void, AstRegion *unc, const char *options, int *status, ...) {
-/*
-*++
-*  Name:
-c     astNullRegion
-f     AST_NULLREGION
-
-*  Purpose:
-*     Create a NullRegion.
-
-*  Type:
-*     Public function.
-
-*  Synopsis:
-c     #include "nullregion.h"
-c     AstNullRegion *astNullRegion( AstFrame *frame, AstRegion *unc, const char *options, ... )
-f     RESULT = AST_NULLREGION( FRAME, UNC, OPTIONS, STATUS )
-
-*  Class Membership:
-*     NullRegion constructor.
-
-*  Description:
-*     This function creates a new NullRegion and optionally initialises its
-*     attributes.
-*
-*     A NullRegion is a Region with no bounds. If the Negated attribute of a
-*     NullRegion is false, the NullRegion represents a Region containing no
-*     points. If the Negated attribute of a NullRegion is true, the NullRegion
-*     represents an infinite Region containing all points within the
-*     coordinate system.
-
-*  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     unc
-f     UNC = INTEGER (Given)
-*        An optional pointer to an existing Region which specifies the
-*        uncertainties associated with positions in the supplied Frame.
-*        The uncertainty in any point in the Frame is found by shifting the
-*        supplied "uncertainty" Region so that it is centred at the point
-*        being considered. The area covered by the shifted uncertainty
-*        Region then represents the uncertainty in the 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 NullRegion. Alternatively,
-f        a null Object pointer (AST__NULL)
-c        a NULL Object pointer
-*        may be supplied, in which case a default uncertainty of zero is
-*        used.
-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 NullRegion. 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 NullRegion. 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     astNullRegion()
-f     AST_NULLREGION = INTEGER
-*        A pointer to the new NullRegion.
-
-*  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.
-*--
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstFrame *frame;              /* Pointer to Frame structure */
-   AstNullRegion *new;           /* Pointer to new NullRegion */
-   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 NullRegion, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitNullRegion( NULL, sizeof( AstNullRegion ), !class_init,
-                            &class_vtab, "NullRegion", frame, 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 NullRegion'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 NullRegion. */
-   return new;
-}
-
-AstNullRegion *astNullRegionId_( void *frame_void, void *unc_void,
-                                 const char *options, ... ) {
-/*
-*  Name:
-*     astNullRegionId_
-
-*  Purpose:
-*     Create a NullRegion.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstNullRegion *astNullRegionId_( AstFrame *frame, AstRegion *unc, const char *options, ... )
-
-*  Class Membership:
-*     NullRegion constructor.
-
-*  Description:
-*     This function implements the external (public) interface to the
-*     astNullRegion constructor function. It returns an ID value (instead
-*     of a true C pointer) to external users, and must be provided
-*     because astNullRegion_ 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 astNullRegion_ 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 astNullRegion_.
-
-*  Returned Value:
-*     The ID value associated with the new NullRegion.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstFrame *frame;              /* Pointer to Frame structure */
-   AstNullRegion *new;           /* Pointer to new NullRegion */
-   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 NullRegion, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitNullRegion( NULL, sizeof( AstNullRegion ), !class_init,
-                            &class_vtab, "NullRegion", frame, 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 NullRegion'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 NullRegion. */
-   return astMakeId( new );
-}
-
-AstNullRegion *astInitNullRegion_( void *mem, size_t size, int init,
-                                   AstNullRegionVtab *vtab, const char *name,
-                                   AstFrame *frame, AstRegion *unc, int *status ) {
-/*
-*+
-*  Name:
-*     astInitNullRegion
-
-*  Purpose:
-*     Initialise a NullRegion.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstNullRegion *astInitNullRegion_( void *mem, size_t size, int init,
-*                                        AstNullRegionVtab *vtab, const char *name,
-*                                        AstFrame *frame, AstRegion *unc  )
-
-*  Class Membership:
-*     NullRegion initialiser.
-
-*  Description:
-*     This function is provided for use by class implementations to initialise
-*     a new NullRegion object. It allocates memory (if necessary) to accommodate
-*     the NullRegion plus any additional data associated with the derived class.
-*     It then initialises a NullRegion 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 NullRegion at the start of the memory passed via the
-*     "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory in which the NullRegion is to be initialised.
-*        This must be of sufficient size to accommodate the NullRegion data
-*        (sizeof(NullRegion)) 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 NullRegion (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 NullRegion
-*        structure, so a valid value must be supplied even if not required for
-*        allocating memory.
-*     init
-*        A logical flag indicating if the NullRegion'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 NullRegion.
-*     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.
-*     unc
-*        A pointer to a Region which specifies the uncertainty of positions
-*        within the supplied Frame. A NULL pointer can be supplied, in which
-*        case default uncertainties of zero 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). 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 NullRegion.
-
-*  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: */
-   AstNullRegion *new;       /* Pointer to new NullRegion */
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* If necessary, initialise the virtual function table. */
-   if ( init ) astInitNullRegionVtab( vtab, name );
-
-/* Initialise a Region structure (the parent class) as the first component
-   within the NullRegion structure, allocating memory if necessary. */
-   new = (AstNullRegion *) astInitRegion( mem, size, 0, (AstRegionVtab *) vtab,
-                                          name, frame, NULL, unc );
-
-/* If an error occurred, clean up by deleting the new NullRegion. */
-   if ( !astOK ) new = astDelete( new );
-
-/* Return a pointer to the new NullRegion. */
-   return new;
-}
-
-AstNullRegion *astLoadNullRegion_( void *mem, size_t size, AstNullRegionVtab *vtab,
-                                   const char *name, AstChannel *channel, int *status ) {
-/*
-*+
-*  Name:
-*     astLoadNullRegion
-
-*  Purpose:
-*     Load a NullRegion.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "nullregion.h"
-*     AstNullRegion *astLoadNullRegion( void *mem, size_t size, AstNullRegionVtab *vtab,
-*                                       const char *name, AstChannel *channel )
-
-*  Class Membership:
-*     NullRegion loader.
-
-*  Description:
-*     This function is provided to load a new NullRegion 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
-*     NullRegion 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 NullRegion at the start of the memory
-*     passed via the "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory into which the NullRegion is to be
-*        loaded.  This must be of sufficient size to accommodate the
-*        NullRegion data (sizeof(NullRegion)) 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 NullRegion (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 NullRegion 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(AstNullRegion) is used instead.
-*     vtab
-*        Pointer to the start of the virtual function table to be
-*        associated with the new NullRegion. If this is NULL, a pointer
-*        to the (static) virtual function table for the NullRegion 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 "NullRegion" is used instead.
-
-*  Returned Value:
-*     A pointer to the new NullRegion.
-
-*  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 */
-   AstNullRegion *new;              /* Pointer to the new NullRegion */
-
-/* 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 NullRegion. In this case the
-   NullRegion belongs to this class, so supply appropriate values to be
-   passed to the parent class loader (and its parent, etc.). */
-   if ( !vtab ) {
-      size = sizeof( AstNullRegion );
-      vtab = &class_vtab;
-      name = "NullRegion";
-
-/* If required, initialise the virtual function table for this class. */
-      if ( !class_init ) {
-         astInitNullRegionVtab( 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 NullRegion. */
-   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, "NullRegion" );
-
-/* 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. */
-/* ---------------------------- */
-
-/* If an error occurred, clean up by deleting the new NullRegion. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return the new NullRegion 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. */
-
-
-
-
-
-
-
-
-
-