update ast 8.6.3

1 files changed, 2093 insertions, 0 deletions

diff --git a/ast/nullregion.c b/ast/nullregion.c
new file mode 100644
index 0000000..6ef9cfa
--- /dev/null
+++ b/ast/nullregion.c
@@ -0,0 +1,2093 @@
+/*
+*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. */
+
+
+
+
+
+
+
+
+
+