upgrade ast 8.7.1

1 files changed, 1720 insertions, 0 deletions

diff --git a/ast/normmap.c b/ast/normmap.c
new file mode 100644
index 0000000..3739739
--- /dev/null
+++ b/ast/normmap.c
@@ -0,0 +1,1720 @@
+/*
+*class++
+*  Name:
+*     NormMap
+
+*  Purpose:
+*     Normalise coordinates using a supplied Frame.
+
+*  Constructor Function:
+c     astNormMap
+f     AST_NORMMAP
+
+*  Description:
+*     The NormMap class implements a Mapping which normalises coordinate
+*     values using the
+c     astNorm function
+f     AST_NORM routine
+*     of a supplied Frame. The number of inputs and outputs of a NormMap
+*     are both equal to the number of axes in the supplied Frame.
+*
+*     The forward and inverse transformation of a NormMap are both
+*     defined but are identical (that is, they do not form a real inverse
+*     pair in that the inverse transformation does not undo the
+*     normalisation, instead it reapplies it). However, the
+c     astSimplify
+f     AST_SIMPLIFY
+*     function will replace neighbouring pairs of forward and inverse
+*     NormMaps by a single UnitMap (so long as the Frames encapsulated by
+*     the two NormMaps are equal - i.e. have the same class and the same
+*     attribute values). This means, for instance, that if a CmpMap contains
+*     a NormMap, the CmpMap will still cancel with its own inverse.
+
+*  Inheritance:
+*     The NormMap class inherits from the Mapping class.
+
+*  Attributes:
+*     The NormMap class does not define any new attributes beyond
+*     those which are applicable to all Mappings.
+
+*  Functions:
+c     The NormMap class does not define any new functions beyond those
+f     The NormMap class does not define any new routines beyond those
+*     which are applicable to all Mappings.
+
+*  Copyright:
+*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
+*     Research Councils
+
+*  Licence:
+*     This program is free software: you can redistribute it and/or
+*     modify it under the terms of the GNU Lesser General Public
+*     License as published by the Free Software Foundation, either
+*     version 3 of the License, or (at your option) any later
+*     version.
+*
+*     This program is distributed in the hope that it will be useful,
+*     but WITHOUT ANY WARRANTY; without even the implied warranty of
+*     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*     GNU Lesser General Public License for more details.
+*
+*     You should have received a copy of the GNU Lesser General
+*     License along with this program.  If not, see
+*     <http://www.gnu.org/licenses/>.
+
+*  Authors:
+*     DSB: David S. Berry (Starlink)
+
+*  History:
+*     11-JUL-2005 (DSB):
+*        Original version.
+*     23-AUG-2006 (DSB):
+*        Override astEqual.
+*     8-NOV-2016 (DSB):
+*        - Allow multiple identical NormMaps in series to be simplified to
+*        a single NormMap.
+*        - Allow a NormMap that contains a basic Frame to be simplified
+*        to a UnitMap.
+*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 NormMap
+
+/* 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 "mapping.h"             /* Coordinate mappings (parent class) */
+#include "channel.h"             /* I/O channels */
+#include "unitmap.h"             /* Unit Mappings */
+#include "normmap.h"             /* Interface definition for this class */
+
+/* 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 int *(* parent_mapsplit)( AstMapping *, int, const int *, AstMapping **, int * );
+
+#if defined(THREAD_SAFE)
+static int (* parent_managelock)( AstObject *, int, int, AstObject **, int * );
+#endif
+
+
+#ifdef THREAD_SAFE
+/* Define how to initialise thread-specific globals. */
+#define GLOBAL_inits \
+   globals->Class_Init = 0;
+
+/* Create the function that initialises global data for this module. */
+astMAKE_INITGLOBALS(NormMap)
+
+/* Define macros for accessing each item of thread specific global data. */
+#define class_init astGLOBAL(NormMap,Class_Init)
+#define class_vtab astGLOBAL(NormMap,Class_Vtab)
+
+
+#include <pthread.h>
+
+
+#else
+
+
+/* Define the class virtual function table and its initialisation flag
+   as static variables. */
+static AstNormMapVtab 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. */
+AstNormMap *astNormMapId_( void *, const char *, ... );
+
+/* Prototypes for Private Member Functions. */
+/* ======================================== */
+static AstMapping *RemoveRegions( AstMapping *, int * );
+static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static double Rate( AstMapping *, double *, int, int, int * );
+static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
+static void Copy( const AstObject *, AstObject *, int * );
+static void Delete( AstObject *, int * );
+static void Dump( AstObject *, AstChannel *, int * );
+static int Equal( AstObject *, AstObject *, int * );
+static int *MapSplit( AstMapping *, int, const int *, AstMapping **, int * );
+
+#if defined(THREAD_SAFE)
+static int ManageLock( AstObject *, int, int, AstObject **, int * );
+#endif
+
+
+/* Member functions. */
+/* ================= */
+
+static int Equal( AstObject *this_object, AstObject *that_object, int *status ) {
+/*
+*  Name:
+*     Equal
+
+*  Purpose:
+*     Test if two NormMaps are equivalent.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     int Equal( AstObject *this, AstObject *that, int *status )
+
+*  Class Membership:
+*     NormMap member function (over-rides the astEqual protected
+*     method inherited from the astMapping class).
+
+*  Description:
+*     This function returns a boolean result (0 or 1) to indicate whether
+*     two NormMaps are equivalent.
+
+*  Parameters:
+*     this
+*        Pointer to the first Object (a NormMap).
+*     that
+*        Pointer to the second Object.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     One if the NormMaps are equivalent, zero otherwise.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global status set, or if it should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstNormMap *that;
+   AstNormMap *this;
+   int result;
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain pointers to the two NormMap structures. */
+   this = (AstNormMap *) this_object;
+   that = (AstNormMap *) that_object;
+
+/* Check the second object is a NormMap. We know the first is a
+   NormMap since we have arrived at this implementation of the virtual
+   function. */
+   if( astIsANormMap( that ) ) {
+
+/* Check the Invert flags for the two NormMaps are equal. */
+      if( astGetInvert( this ) == astGetInvert( that ) ) {
+
+/* Check the two Frames are equal. */
+         if( astEqual( this->frame, that->frame ) ) {
+            result = 1;
+         }
+      }
+   }
+
+/* If an error occurred, clear the result value. */
+   if ( !astOK ) result = 0;
+
+/* Return the result, */
+   return result;
+}
+
+void astInitNormMapVtab_(  AstNormMapVtab *vtab, const char *name, int *status ) {
+/*
+*+
+*  Name:
+*     astInitNormMapVtab
+
+*  Purpose:
+*     Initialise a virtual function table for a NormMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     void astInitNormMapVtab( AstNormMapVtab *vtab, const char *name )
+
+*  Class Membership:
+*     NormMap vtab initialiser.
+
+*  Description:
+*     This function initialises the component of a virtual function
+*     table which is used by the NormMap class.
+
+*  Parameters:
+*     vtab
+*        Pointer to the virtual function table. The components used by
+*        all ancestral classes will be initialised if they have not already
+*        been initialised.
+*     name
+*        Pointer to a constant null-terminated character string which contains
+*        the name of the class to which the virtual function table belongs (it
+*        is this pointer value that will subsequently be returned by the Object
+*        astClass function).
+*-
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
+   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
+
+/* 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. */
+   astInitMappingVtab( (AstMappingVtab *) vtab, name );
+
+/* Store a unique "magic" value in the virtual function table. This
+   will be used (by astIsANormMap) 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 = &(((AstMappingVtab *) 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. */
+   object = (AstObjectVtab *) vtab;
+   mapping = (AstMappingVtab *) vtab;
+
+   mapping->RemoveRegions = RemoveRegions;
+
+#if defined(THREAD_SAFE)
+   parent_managelock = object->ManageLock;
+   object->ManageLock = ManageLock;
+#endif
+
+   parent_transform = mapping->Transform;
+   mapping->Transform = Transform;
+
+   parent_mapsplit = mapping->MapSplit;
+   mapping->MapSplit = MapSplit;
+
+/* Store replacement pointers for methods which will be over-ridden by
+   new member functions implemented here. */
+   object->Equal = Equal;
+   mapping->MapMerge = MapMerge;
+   mapping->MapSplit = MapSplit;
+   mapping->Rate = Rate;
+
+/* Declare the copy constructor, destructor and class dump function. */
+   astSetDump( vtab, Dump, "NormMap", "Normalise axis values" );
+   astSetCopy( vtab, Copy );
+   astSetDelete( vtab, Delete );
+
+/* 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) );
+   }
+}
+
+#if defined(THREAD_SAFE)
+static int ManageLock( AstObject *this_object, int mode, int extra,
+                       AstObject **fail, int *status ) {
+/*
+*  Name:
+*     ManageLock
+
+*  Purpose:
+*     Manage the thread lock on an Object.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "object.h"
+*     AstObject *ManageLock( AstObject *this, int mode, int extra,
+*                            AstObject **fail, int *status )
+
+*  Class Membership:
+*     NormMap member function (over-rides the astManageLock protected
+*     method inherited from the parent class).
+
+*  Description:
+*     This function manages the thread lock on the supplied Object. The
+*     lock can be locked, unlocked or checked by this function as
+*     deteremined by parameter "mode". See astLock for details of the way
+*     these locks are used.
+
+*  Parameters:
+*     this
+*        Pointer to the Object.
+*     mode
+*        An integer flag indicating what the function should do:
+*
+*        AST__LOCK: Lock the Object for exclusive use by the calling
+*        thread. The "extra" value indicates what should be done if the
+*        Object is already locked (wait or report an error - see astLock).
+*
+*        AST__UNLOCK: Unlock the Object for use by other threads.
+*
+*        AST__CHECKLOCK: Check that the object is locked for use by the
+*        calling thread (report an error if not).
+*     extra
+*        Extra mode-specific information.
+*     fail
+*        If a non-zero function value is returned, a pointer to the
+*        Object that caused the failure is returned at "*fail". This may
+*        be "this" or it may be an Object contained within "this". Note,
+*        the Object's reference count is not incremented, and so the
+*        returned pointer should not be annulled. A NULL pointer is
+*        returned if this function returns a value of zero.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*    A local status value:
+*        0 - Success
+*        1 - Could not lock or unlock the object because it was already
+*            locked by another thread.
+*        2 - Failed to lock a POSIX mutex
+*        3 - Failed to unlock a POSIX mutex
+*        4 - Bad "mode" value supplied.
+
+*  Notes:
+*     - This function attempts to execute even if an error has already
+*     occurred.
+*/
+
+/* Local Variables: */
+   AstNormMap *this;       /* Pointer to NormMap structure */
+   int result;             /* Returned status value */
+
+/* Initialise */
+   result = 0;
+
+/* Check the supplied pointer is not NULL. */
+   if( !this_object ) return result;
+
+/* Obtain a pointers to the NormMap structure. */
+   this = (AstNormMap *) this_object;
+
+/* Invoke the ManageLock method inherited from the parent class. */
+   if( !result ) result = (*parent_managelock)( this_object, mode, extra,
+                                                fail, status );
+
+/* Invoke the astManageLock method on any Objects contained within
+   the supplied Object. */
+   if( !result ) result = astManageLock( this->frame, mode, extra, fail );
+
+   return result;
+
+}
+#endif
+
+static int MapMerge( AstMapping *this, int where, int series, int *nmap,
+                     AstMapping ***map_list, int **invert_list, int *status ) {
+/*
+*  Name:
+*     MapMerge
+
+*  Purpose:
+*     Simplify a sequence of Mappings containing a NormMap.
+
+*  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:
+*     NormMap method (over-rides the protected astMapMerge method
+*     inherited from the Mapping class).
+
+*  Description:
+*     This function attempts to simplify a sequence of Mappings by
+*     merging a nominated NormMap 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 NormMap with one 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 NormMap which is to be merged with
+*        its neighbours. This should be a cloned copy of the NormMap
+*        pointer contained in the array element "(*map_list)[where]"
+*        (see below). This pointer will not be annulled, and the
+*        NormMap it identifies will not be modified by this function.
+*     where
+*        Index in the "*map_list" array (below) at which the pointer
+*        to the nominated NormMap 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: */
+   AstFrame *frm1;
+   AstFrame *frm2;
+   AstMapping *smap;
+   AstNormMap *map;
+   AstNormMap *nmap1;
+   AstNormMap *nmap2;
+   const char *class;
+   int cancel;
+   int map_inv;
+   int nax;
+   int result;
+
+/* Initialise. */
+   result = -1;
+
+/* Check the inherited status. */
+   if ( !astOK ) return result;
+
+/* Initialisation to avoid compiler warnings. */
+   nax = 0;
+
+/* Get a pointer to this NormMap. */
+   map = (AstNormMap *) this;
+
+/* Temporarily set its Invert flag to the requested value. */
+   map_inv = astGetInvert( map );
+   astSetInvert( map, ( *invert_list )[ where ] );
+
+/* First try to simplify the NormMap by simplifying its encapsulated
+   Frame. Get its class. */
+   smap = astSimplify( map->frame );
+   class = astGetClass( smap );
+
+/* If any simplification took place, create a new NormMap with the
+   simplified Frame. */
+   if( smap != (AstMapping *) map->frame ) {
+      (void) astAnnul( ( *map_list )[ where ] );
+      ( *map_list )[ where ] = (AstMapping *) astNormMap( (AstFrame *) smap,
+                                                          "", status );
+      result = where;
+
+/* If the encapsulated Frame is a basic Frame, we can safely assume that
+   the astNorm method does nothing, and so we can replace the NormMap with
+   a UnitMap. */
+   } else if( class && !strcmp( class, "Frame" ) ) {
+      nax = astGetNin( smap );
+      (void) astAnnul( ( *map_list )[ where ] );
+      ( *map_list )[ where ] = (AstMapping *) astUnitMap( nax, "", status );
+      result = where;
+
+/* The only other simplications which can be performed are a) to cancel a NormMap
+   with its own inverse in series, or b) to remove duplicated adjacent
+   NormMaps in series. */
+   } else if( series ) {
+
+/* Indicate we have nothing to cancel with as yet. */
+      cancel = -1;
+
+/* First consider the lower neighbour. */
+      if( where > 0 && astIsANormMap( ( *map_list )[ where - 1 ] ) ) {
+
+/* Check the Invert flags are opposite */
+         if( ( *invert_list )[ where ] != ( *invert_list )[ where - 1 ] ) {
+            nmap1 = map;
+            nmap2 = (AstNormMap *) ( *map_list )[ where - 1 ];
+
+/* Check the encapsulated Frames are equal. */
+            frm1 = nmap1->frame;
+            frm2 = nmap2->frame;
+            if( astEqual( frm1, frm2 ) ) cancel = where - 1;
+            nax = astGetNout( nmap1 );
+         }
+      }
+
+/* Likewise consider the upper neighbour. */
+      if( cancel == -1 && where + 1 < *nmap &&
+          astIsANormMap( ( *map_list )[ where + 1 ] ) ) {
+
+         if( ( *invert_list )[ where ] != ( *invert_list )[ where + 1 ] ) {
+            nmap1 = map;
+            nmap2 = (AstNormMap *) ( *map_list )[ where + 1 ];
+            frm1 = nmap1->frame;
+            frm2 = nmap2->frame;
+            if( astEqual( frm1, frm2 ) ) cancel = where + 1;
+            nax = astGetNin( nmap1 );
+         }
+      }
+
+/* If we can cancel with a neightbour, do so. */
+      if( cancel != -1 ) {
+         (void) astAnnul( ( *map_list )[ where ] );
+         (void) astAnnul( ( *map_list )[ cancel ] );
+         ( *map_list )[ where ] = (AstMapping *) astUnitMap( nax, "", status );
+         ( *invert_list )[ where ] = 0;
+         ( *map_list )[ cancel ] = (AstMapping *) astUnitMap( nax, "", status );
+         ( *invert_list )[ cancel ] = 0;
+          result = ( cancel < where ) ? cancel : where;
+
+/* Otherwise, see if the nominated NormMap is followed by one or more
+   identical NormMaps, in which case we can remove all but one of the
+   NormMaps. */
+      } else {
+
+/* Loop round all subsequent Mappings until the end of the list is
+   reached, or a Mapping that is not a NormMap is reached. On each pass
+   we replace the NormMap with a UnitMap. */
+         nax = astGetNin( map );
+         cancel = where;
+         while( ++cancel < *nmap &&
+                astIsANormMap( ( *map_list )[ cancel ] ) ) {
+
+/* Check the Invert flags are equal. */
+            if( ( *invert_list )[ where ] == ( *invert_list )[ cancel ] ) {
+
+/* Check the Frames are equal .*/
+               nmap2 = (AstNormMap *) ( *map_list )[ cancel ];
+               if( astEqual( map->frame, nmap2->frame ) ) {
+
+/* Replace the later NormMap with a UnitMap. */
+                  (void) astAnnul( ( *map_list )[ cancel ] );
+                  ( *map_list )[ cancel ] = (AstMapping *) astUnitMap( nax,
+                                                               "", status );
+
+/* We return the index of the first modified Mapping in the list, so do
+   not update "result" if this is not the first change. */
+                  if( result == -1 ) result = cancel;
+               }
+            }
+         }
+      }
+   }
+
+/* Free resources. */
+   smap = astAnnul( smap );
+
+/* Reset the original Invert attribute for the specified NormMap */
+   astSetInvert( map, map_inv );
+
+/* If an error occurred, clear the result value. */
+   if ( !astOK ) result = -1;
+
+/* Return the result. */
+   return result;
+}
+
+static int *MapSplit( AstMapping *this_map, int nin, const int *in, AstMapping **map, int *status ){
+/*
+*  Name:
+*     MapSplit
+
+*  Purpose:
+*     Create a Mapping representing a subset of the inputs of an existing
+*     NormMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     int *MapSplit( AstMapping *this, int nin, const int *in, AstMapping **map, int *status )
+
+*  Class Membership:
+*     NormMap method (over-rides the protected astMapSplit method
+*     inherited from the Mapping class).
+
+*  Description:
+*     This function creates a new Mapping by picking specified inputs from
+*     an existing NormMap. This is only possible if the specified inputs
+*     correspond to some subset of the NormMap outputs. That is, there
+*     must exist a subset of the NormMap outputs for which each output
+*     depends only on the selected NormMap inputs, and not on any of the
+*     inputs which have not been selected. If this condition is not met
+*     by the supplied NormMap, then a NULL Mapping is returned.
+
+*  Parameters:
+*     this
+*        Pointer to the NormMap to be split (the NormMap is not actually
+*        modified by this function).
+*     nin
+*        The number of inputs to pick from "this".
+*     in
+*        Pointer to an array of indices (zero based) for the inputs which
+*        are to be picked. This array should have "nin" elements. If "Nin"
+*        is the number of inputs of the supplied NormMap, then each element
+*        should have a value in the range zero to Nin-1.
+*     map
+*        Address of a location at which to return a pointer to the new
+*        Mapping. This Mapping will have "nin" inputs (the number of
+*        outputs may be different to "nin"). A NULL pointer will be
+*        returned if the supplied NormMap has no subset of outputs which
+*        depend only on the selected inputs.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     A pointer to a dynamically allocated array of ints. The number of
+*     elements in this array will equal the number of outputs for the
+*     returned Mapping. Each element will hold the index of the
+*     corresponding output in the supplied NormMap. The array should be
+*     freed using astFree when no longer needed. A NULL pointer will
+*     be returned if no output Mapping can be created.
+
+*  Notes:
+*     - If this function is invoked with the global error status set,
+*     or if it should fail for any reason, then NULL values will be
+*     returned as the function value and for the "map" pointer.
+*/
+
+/* Local Variables: */
+   AstFrame *frm2;            /* Pointer to new Frame */
+   AstNormMap *this;          /* Pointer to NormMap structure */
+   int *result;               /* Pointer to returned array */
+
+/* Initialise */
+   result = NULL;
+   *map = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Invoke the parent astMapSplit method to see if it can do the job. */
+   result = (*parent_mapsplit)( this_map, nin, in, map, status );
+
+/* If not, we provide a special implementation here. */
+   if( !result ) {
+
+/* Get a pointer to the NormMap structure. */
+      this = (AstNormMap *) this_map;
+
+/* Pick the requried axes from the encapsulated Frame. */
+      frm2 = astPickAxes( this->frame, nin, in, NULL );
+
+/* Create a new NormMap from this. */
+      *map = (AstMapping *) astNormMap( frm2, "", status );
+
+/* The returned list of output axes is a copy the supplied list of input
+   axes. */
+      result = astStore( NULL, in, sizeof( int )*(size_t) nin );
+
+/* Free resources. */
+      frm2 = astAnnul( frm2 );
+   }
+
+/* Free returned resources if an error has occurred. */
+   if( !astOK ) {
+      result = astFree( result );
+      *map = astAnnul( *map );
+   }
+
+/* Return the list of output indices. */
+   return result;
+}
+
+static double Rate( AstMapping *this, double *at, int ax1, int ax2, int *status ){
+/*
+*  Name:
+*     Rate
+
+*  Purpose:
+*     Calculate the rate of change of a Mapping output.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     result = Rate( AstMapping *this, double *at, int ax1, int ax2, int *status )
+
+*  Class Membership:
+*     NormMap member function (overrides the astRate method inherited
+*     from the Mapping class ).
+
+*  Description:
+*     This function returns the rate of change of a specified output of
+*     the supplied Mapping with respect to a specified input, at a
+*     specified input position.
+
+*  Parameters:
+*     this
+*        Pointer to the Mapping to be applied.
+*     at
+*        The address of an array holding the axis values at the position
+*        at which the rate of change is to be evaluated. The number of
+*        elements in this array should equal the number of inputs to the
+*        Mapping.
+*     ax1
+*        The index of the Mapping output for which the rate of change is to
+*        be found (output numbering starts at 0 for the first output).
+*     ax2
+*        The index of the Mapping input which is to be varied in order to
+*        find the rate of change (input numbering starts at 0 for the first
+*        input).
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     The rate of change of Mapping output "ax1" with respect to input
+*     "ax2", evaluated at "at", or AST__BAD if the value cannot be
+*     calculated.
+
+*/
+
+   return ( ax1 == ax2 ) ? 1.0 : 0.0;
+}
+
+static AstMapping *RemoveRegions( AstMapping *this_mapping, int *status ) {
+/*
+*  Name:
+*     RemoveRegions
+
+*  Purpose:
+*     Remove any Regions from a Mapping.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     AstMapping *RemoveRegions( AstMapping *this, int *status )
+
+*  Class Membership:
+*     NormMap method (over-rides the astRemoveRegions method inherited
+*     from the Mapping class).
+
+*  Description:
+*     This function searches the supplied Mapping (which may be a
+*     compound Mapping such as a CmpMap) for any component Mappings
+*     that are instances of the AST Region class. It then creates a new
+*     Mapping from which all Regions have been removed. If a Region
+*     cannot simply be removed (for instance, if it is a component of a
+*     parallel CmpMap), then it is replaced with an equivalent UnitMap
+*     in the returned Mapping.
+*
+*     The implementation provided by the NormMap class invokes the
+*     astRemoveRegions method on the encapsulated Frame, and returns a
+*     new NormMap containing the resulting Frame.
+
+*  Parameters:
+*     this
+*        Pointer to the original Region.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     A pointer to the modified mapping.
+
+*  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 *newfrm;             /* New component Frame */
+   AstMapping *result;           /* Result pointer to return */
+   AstNormMap *new;              /* Pointer to new MormMap */
+   AstNormMap *this;             /* Pointer to NormMap structure */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the NormMap. */
+   this = (AstNormMap *) this_mapping;
+
+/* Invoke the astRemoveRegions method on the component Frame. */
+   newfrm = astRemoveRegions( this->frame );
+
+/* If the Frame was not modified, just return a clone of the supplied
+   pointer. */
+   if( this->frame == newfrm ) {
+      result = astClone( this );
+
+/* Otherwise, we need to create a new NormMap to return. We take a deep
+   copy of the supplied NormMap and then modify the Frame so that we
+   retain any extra information in the supplied NormMap. */
+   } else {
+      new = astCopy( this );
+      (void) astAnnul( new->frame );
+      new->frame = astClone( newfrm );
+      result = (AstMapping *) new;
+   }
+
+/* Free resources. */
+   newfrm = astAnnul( newfrm );
+
+/* Annul the returned Mapping if an error has occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+                               int forward, AstPointSet *out, int *status ) {
+/*
+*  Name:
+*     Transform
+
+*  Purpose:
+*     Apply a NormMap to transform a set of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+*                             int forward, AstPointSet *out, int *status )
+
+*  Class Membership:
+*     NormMap member function (over-rides the astTransform protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function takes a NormMap and a set of points encapsulated in a
+*     PointSet and transforms the points so as to apply the required zoom
+*     factor.
+
+*  Parameters:
+*     this
+*        Pointer to the NormMap.
+*     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:
+*     -  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 coordinates for the NormMap being applied.
+*     -  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: */
+   AstPointSet *result;          /* Pointer to output PointSet */
+   AstNormMap *map;              /* Pointer to NormMap to be applied */
+   double **ptr_in;              /* Pointer to input coordinate data */
+   double **ptr_out;             /* Pointer to output coordinate data */
+   double *work;                 /* Work space for a single point */
+   int coord;                    /* Loop counter for coordinates */
+   int ncoord_in;                /* Number of coordinates per input point */
+   int npoint;                   /* Number of points */
+   int point;                    /* Loop counter for points */
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain a pointer to the NormMap. */
+   map = (AstNormMap *) this;
+
+/* Apply the parent mapping using the stored pointer to the Transform member
+   function inherited from the parent Mapping class. This function validates
+   all arguments and generates an output PointSet if necessary, but does not
+   actually transform any coordinate values. */
+   result = (*parent_transform)( this, in, forward, out, status );
+
+/* We will now extend the parent astTransform method by performing the
+   calculations needed to generate the output coordinate values. */
+
+/* Determine the numbers of points and coordinates per point from the input
+   PointSet and obtain pointers for accessing the input and output coordinate
+   values. */
+   ncoord_in = astGetNcoord( in );
+   npoint = astGetNpoint( in );
+   ptr_in = astGetPoints( in );
+   ptr_out = astGetPoints( result );
+   work = astMalloc( sizeof( double )* ncoord_in );
+
+/* Perform coordinate arithmetic. */
+/* ------------------------------ */
+   if ( astOK ) {
+      for ( point = 0; point < npoint; point++ ) {
+         for ( coord = 0; coord < ncoord_in; coord++ ) {
+            work[ coord ] = ptr_in[ coord ][ point ];
+         }
+         astNorm( map->frame, work );
+         for ( coord = 0; coord < ncoord_in; coord++ ) {
+            ptr_out[ coord ][ point ] = work[ coord ];
+         }
+      }
+   }
+
+/* Free resources */
+   work = astFree( work );
+
+/* Return a pointer to the output PointSet. */
+   return result;
+}
+
+/* Functions which access class attributes. */
+/* ---------------------------------------- */
+/* Implement member functions to access the attributes associated with
+   this class using the macros defined for this purpose in the
+   "object.h" file. For a description of each attribute, see the class
+   interface (in the associated .h file). */
+
+/* Copy constructor. */
+/* ----------------- */
+static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
+/*
+*  Name:
+*     Copy
+
+*  Purpose:
+*     Copy constructor for NormMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Copy( const AstObject *objin, AstObject *objout, int *status )
+
+*  Description:
+*     This function implements the copy constructor for NormMap objects.
+
+*  Parameters:
+*     objin
+*        Pointer to the object to be copied.
+*     objout
+*        Pointer to the object being constructed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     void
+
+*  Notes:
+*     -  This constructor makes a deep copy, including a copy of the
+*     Frame within the NormMap.
+*/
+
+/* Local Variables: */
+   AstNormMap *in;                /* Pointer to input NormMap */
+   AstNormMap *out;               /* Pointer to output NormMap */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+   in = (AstNormMap *) objin;
+   out = (AstNormMap *) objout;
+   out->frame = astCopy( in->frame );
+}
+
+/* Destructor. */
+/* ----------- */
+static void Delete( AstObject *obj, int *status ) {
+/*
+*  Name:
+*     Delete
+
+*  Purpose:
+*     Destructor for NormMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Delete( AstObject *obj, int *status )
+
+*  Description:
+*     This function implements the destructor for NormMap objects.
+
+*  Parameters:
+*     obj
+*        Pointer to the object to be deleted.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     void
+
+*  Notes:
+*     This function attempts to execute even if the global error status is
+*     set.
+*/
+
+/* Local Variables: */
+   AstNormMap *this;              /* Pointer to NormMap */
+
+   this = (AstNormMap *) obj;
+   this->frame = astAnnul( this->frame );
+
+}
+
+/* Dump function. */
+/* -------------- */
+static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
+/*
+*  Name:
+*     Dump
+
+*  Purpose:
+*     Dump function for NormMap 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 NormMap class to an output Channel.
+
+*  Parameters:
+*     this
+*        Pointer to the NormMap 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: */
+   AstNormMap *this;             /* Pointer to the NormMap structure */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the NormMap structure. */
+   this = (AstNormMap *) this_object;
+
+/* Write out values representing the instance variables for the
+   NormMap class.  Accompany these with appropriate comment strings,
+   possibly depending on the values being written.*/
+
+/* Frame. */
+/* ------ */
+   astWriteObject( channel, "Frame", 1, 1, this->frame,
+                   "Frame defining the normalisation" );
+}
+
+/* Standard class functions. */
+/* ========================= */
+/* Implement the astIsANormMap and astCheckNormMap functions using the macros
+   defined for this purpose in the "object.h" header file. */
+astMAKE_ISA(NormMap,Mapping)
+astMAKE_CHECK(NormMap)
+
+AstNormMap *astNormMap_( void *frame_void, const char *options, int *status, ...) {
+/*
+*++
+*  Name:
+c     astNormMap
+f     AST_NORMMAP
+
+*  Purpose:
+*     Create a NormMap.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "normmap.h"
+c     AstNormMap *astNormMap( AstFrame *frame, const char *options, ... )
+f     RESULT = AST_NORMMAP( FRAME, OPTIONS, STATUS )
+
+*  Class Membership:
+*     NormMap constructor.
+
+*  Description:
+*     This function creates a new NormMap and optionally initialises its
+*     attributes.
+*
+*     A NormMap is a Mapping which normalises coordinate values using the
+c     astNorm function
+f     AST_NORM routine
+*     of the supplied Frame. The number of inputs and outputs of a NormMap
+*     are both equal to the number of axes in the supplied Frame.
+*
+*     The forward and inverse transformation of a NormMap are both
+*     defined but are identical (that is, they do not form a real inverse
+*     pair in that the inverse transformation does not undo the
+*     normalisation, instead it reapplies it). However, the
+c     astSimplify
+f     AST_SIMPLIFY
+*     function will replace neighbouring pairs of forward and inverse
+*     NormMaps by a single UnitMap (so long as the Frames encapsulated by
+*     the two NormMaps are equal - i.e. have the same class and the same
+*     attribute values). This means, for instance, that if a CmpMap contains
+*     a NormMap, the CmpMap will still cancel with its own inverse.
+
+*  Parameters:
+c     frame
+f     FRAME = INTEGER (Given)
+*        A pointer to the Frame which is to be used to normalise the
+*        supplied axis values.
+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 NormMap. 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 NormMap. 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     astNormMap()
+f     AST_NORMMAP = INTEGER
+*        A pointer to the new NormMap.
+
+*  Notes:
+*     - A null Object pointer (AST__NULL) will be returned if this
+c     function is invoked with the AST error status set, or if it
+f     function is invoked with STATUS set to an error value, or if it
+*     should fail for any reason.
+
+*  Status Handling:
+*     The protected interface to this function includes an extra
+*     parameter at the end of the parameter list descirbed above. This
+*     parameter is a pointer to the integer inherited status
+*     variable: "int *status".
+
+*--
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstFrame *frame;              /* The Frame pointer */
+   AstNormMap *new;              /* Pointer to new NormMap */
+   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 pointers to the Frame structures provided. */
+   frame = astCheckFrame( frame_void );
+
+/* Initialise the NormMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitNormMap( NULL, sizeof( AstNormMap ), !class_init, &class_vtab,
+                         "NormMap", frame );
+   if( astOK ) {
+
+/* 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 NormMap'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 NormMap. */
+   return new;
+}
+
+AstNormMap *astNormMapId_( void *frame_void, const char *options, ... ) {
+/*
+*  Name:
+*     astNormMapId_
+
+*  Purpose:
+*     Create a NormMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     AstNormMap *astNormMapId_( int ncoord, double zoom,
+*                                const char *options, ... )
+
+*  Class Membership:
+*     NormMap constructor.
+
+*  Description:
+*     This function implements the external (public) interface to the
+*     astNormMap constructor function. It returns an ID value (instead
+*     of a true C pointer) to external users, and must be provided
+*     because astNormMap_ 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 astNormMap_ 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 astNormMap_.
+
+*  Returned Value:
+*     The ID value associated with the new NormMap.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstFrame *frame;              /* The Frame pointer */
+   AstNormMap *new;              /* Pointer to new NormMap */
+   va_list args;                 /* Variable argument list */
+
+   int *status;                  /* Pointer to inherited status value */
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Get a pointer to the inherited status value. */
+   status = astGetStatusPtr;
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain and validate pointers to the Frame structures provided. */
+   frame = astVerifyFrame( astMakePointer( frame_void ) );
+
+/* Initialise the NormMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitNormMap( NULL, sizeof( AstNormMap ), !class_init, &class_vtab,
+                         "NormMap", frame );
+
+/* 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 NormMap'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 NormMap. */
+   return astMakeId( new );
+}
+
+AstNormMap *astInitNormMap_( void *mem, size_t size, int init,
+                             AstNormMapVtab *vtab, const char *name,
+                             AstFrame *frame, int *status ) {
+/*
+*+
+*  Name:
+*     astInitNormMap
+
+*  Purpose:
+*     Initialise a NormMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     AstNormMap *astInitNormMap( void *mem, size_t size, int init,
+*                                 AstNormMapVtab *vtab, const char *name,
+*                                 AstFrame *frame )
+
+*  Class Membership:
+*     NormMap initialiser.
+
+*  Description:
+*     This function is provided for use by class implementations to initialise
+*     a new NormMap object. It allocates memory (if necessary) to accommodate
+*     the NormMap plus any additional data associated with the derived class.
+*     It then initialises a NormMap 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 NormMap at the start of the memory passed via the
+*     "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory in which the NormMap is to be initialised.
+*        This must be of sufficient size to accommodate the NormMap data
+*        (sizeof(NormMap)) 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 NormMap (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 NormMap
+*        structure, so a valid value must be supplied even if not required for
+*        allocating memory.
+*     init
+*        A logical flag indicating if the NormMap'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 NormMap.
+*     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
+*        The Frame to use to do the normalisations.
+
+*  Returned Value:
+*     A pointer to the new NormMap.
+
+*  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: */
+   AstNormMap *new;              /* Pointer to new NormMap */
+   int ncoord;                   /* Number of input and output coords */
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* If necessary, initialise the virtual function table. */
+   if ( init ) astInitNormMapVtab( vtab, name );
+
+/* Initialise. */
+   new = NULL;
+
+/* Get the number of axes in the Frame. */
+   ncoord = astGetNaxes( frame );
+
+/* Initialise a Mapping structure (the parent class) as the first component
+   within the NormMap structure, allocating memory if necessary. Specify that
+   the Mapping should be defined in both the forward and inverse directions. */
+   new = (AstNormMap *) astInitMapping( mem, size, 0,
+                                        (AstMappingVtab *) vtab, name,
+                                        ncoord, ncoord, 1, 1 );
+
+   if ( astOK ) {
+
+/* Initialise the NormMap data. */
+/* ---------------------------- */
+/* Store a pointer to the Frame. */
+      new->frame = astClone( frame );
+
+/* If an error occurred, clean up by deleting the new NormMap. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return a pointer to the new NormMap. */
+   return new;
+}
+
+AstNormMap *astLoadNormMap_( void *mem, size_t size,
+                             AstNormMapVtab *vtab, const char *name,
+                             AstChannel *channel, int *status ) {
+/*
+*+
+*  Name:
+*     astLoadNormMap
+
+*  Purpose:
+*     Load a NormMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "normmap.h"
+*     AstNormMap *astLoadNormMap( void *mem, size_t size,
+*                                 AstNormMapVtab *vtab, const char *name,
+*                                 AstChannel *channel )
+
+*  Class Membership:
+*     NormMap loader.
+
+*  Description:
+*     This function is provided to load a new NormMap 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
+*     NormMap 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 NormMap at the start of the memory
+*     passed via the "vtab" parameter.
+
+
+*  Parameters:
+*     mem
+*        A pointer to the memory into which the NormMap is to be
+*        loaded.  This must be of sufficient size to accommodate the
+*        NormMap data (sizeof(NormMap)) 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 NormMap (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 NormMap 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(AstNormMap) is used instead.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new NormMap. If this is NULL, a pointer
+*        to the (static) virtual function table for the NormMap 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 "NormMap" is used instead.
+
+*  Returned Value:
+*     A pointer to the new NormMap.
+
+*  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 */
+   AstNormMap *new;              /* Pointer to the new NormMap */
+
+/* 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 NormMap. In this case the
+   NormMap belongs to this class, so supply appropriate values to be
+   passed to the parent class loader (and its parent, etc.). */
+   if ( !vtab ) {
+      size = sizeof( AstNormMap );
+      vtab = &class_vtab;
+      name = "NormMap";
+
+/* If required, initialise the virtual function table for this class. */
+      if ( !class_init ) {
+         astInitNormMapVtab( 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 NormMap. */
+   new = astLoadMapping( mem, size, (AstMappingVtab *) 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, "NormMap" );
+
+/* 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. */
+
+/* Frame. */
+/* ------ */
+      new->frame = astReadObject( channel, "frame", NULL );
+
+/* If an error occurred, clean up by deleting the new NormMap. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return the new NormMap 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. */
+
+
+
+