update ast 8.6.2

1 files changed, 3407 insertions, 0 deletions

diff --git a/ast/pointlist.c b/ast/pointlist.c
new file mode 100644
index 0000000..61117c2
--- /dev/null
+++ b/ast/pointlist.c
@@ -0,0 +1,3407 @@
+/*
+*class++
+*  Name:
+*     PointList
+
+*  Purpose:
+*     A collection of points in a Frame.
+
+*  Constructor Function:
+c     astPointList
+f     AST_POINTLIST
+
+*  Description:
+*     The PointList class implements a Region which represents a collection
+*     of points in a Frame.
+
+*  Inheritance:
+*     The PointList class inherits from the Region class.
+
+*  Attributes:
+*     In addition to those attributes common to all Regions, every
+*     PointList also has the following attributes:
+*
+*     - ListSize: The number of positions stored in the PointList
+
+
+*  Functions:
+c     The PointList class does not define any new functions beyond those
+f     The PointList 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:
+*     22-MAR-2004 (DSB):
+*        Original version.
+*     20-JAN-2009 (DSB):
+*        Over-ride astRegBasePick.
+*     21-JAN-2009 (DSB):
+*        - Add methods astGetEnclosure, astSetEnclosure and astPoints, and
+*        attribute ListSize.
+*        - Override astGetObjSize and astEqual.
+*     26-JAN-2009 (DSB):
+*        Change protected constructor to accept a PointSet rather than an
+*        array of doubles.
+*     6-FEB-2009 (DSB):
+*        Over-ride astMapMerge.
+*     9-FEB-2009 (DSB):
+*        Move methods astGetEnclosure and astSetEnclosure to Region class.
+*     8-JUL-2009 (DSB):
+*        In Transform, use "ptr2", not "ptr", if we are creating a mask.
+*class--
+
+*  Implementation Deficiencies:
+*     - Use of simple arrays to hold lists  of points is probably not
+*     efficient for large numbers of points. For instance, use of k-tree
+*     structures instead of arrays could result in a much  more efficient
+*     implementation of the Transform function. Maybe the PointSet class
+*     should be extended to provide a k-tree representation as well as a
+*     simple array.
+
+*/
+
+/* 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 PointList
+
+/* 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 "pointlist.h"           /* Interface definition for this class */
+#include "mapping.h"             /* Position mappings */
+#include "unitmap.h"             /* Unit Mapping */
+#include "frame.h"               /* Coordinate systems */
+#include "cmpframe.h"            /* Compound Frames */
+#include "cmpmap.h"              /* Compound Mappings */
+#include "prism.h"               /* Extruded Regions */
+
+/* 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 AstMapping *(* parent_simplify)( AstMapping *, int * );
+static AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static const char *(* parent_getattrib)( AstObject *, const char *, int * );
+static int (* parent_getobjsize)( AstObject *, int * );
+static int (* parent_testattrib)( AstObject *, const char *, int * );
+static void (* parent_clearattrib)( AstObject *, const char *, int * );
+static void (* parent_setattrib)( AstObject *, const char *, int * );
+
+
+#ifdef THREAD_SAFE
+/* Define how to initialise thread-specific globals. */
+#define GLOBAL_inits \
+   globals->Class_Init = 0; \
+   globals->GetAttrib_Buff[ 0 ] = 0;
+
+/* Create the function that initialises global data for this module. */
+astMAKE_INITGLOBALS(PointList)
+
+/* Define macros for accessing each item of thread specific global data. */
+#define class_init astGLOBAL(PointList,Class_Init)
+#define class_vtab astGLOBAL(PointList,Class_Vtab)
+#define getattrib_buff astGLOBAL(PointList,GetAttrib_Buff)
+
+
+#include <pthread.h>
+
+
+#else
+
+static char getattrib_buff[ 101 ];
+
+/* Define the class virtual function table and its initialisation flag
+   as static variables. */
+static AstPointListVtab 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. */
+AstPointList *astPointListId_( void *, int, int, int, const double *, void *, const char *, ... );
+
+/* Prototypes for Private Member Functions. */
+/* ======================================== */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+static int MaskLD( AstRegion *, AstMapping *, int, int, const int[], const int ubnd[], long double [], long double, int * );
+#endif
+static int MaskB( AstRegion *, AstMapping *, int, int, const int[], const int[], signed char[], signed char, int * );
+static int MaskD( AstRegion *, AstMapping *, int, int, const int[], const int[], double[], double, int * );
+static int MaskF( AstRegion *, AstMapping *, int, int, const int[], const int[], float[], float, int * );
+static int MaskI( AstRegion *, AstMapping *, int, int, const int[], const int[], int[], int, int * );
+static int MaskL( AstRegion *, AstMapping *, int, int, const int[], const int[], long int[], long int, int * );
+static int MaskS( AstRegion *, AstMapping *, int, int, const int[], const int[], short int[], short int, int * );
+static int MaskUB( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned char[], unsigned char, int * );
+static int MaskUI( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned int[], unsigned int, int * );
+static int MaskUL( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned long int[], unsigned long int, int * );
+static int MaskUS( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned short int[], unsigned short int, int * );
+
+static AstMapping *Simplify( AstMapping *, int * );
+static AstPointSet *RegBaseMesh( AstRegion *, int * );
+static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static AstRegion *RegBasePick( AstRegion *, int, const int *, int * );
+static int GetClosed( AstRegion *, int * );
+static int GetListSize( AstPointList *, int * );
+static int GetObjSize( AstObject *, int * );
+static int RegPins( AstRegion *, AstPointSet *, AstRegion *, int **, int * );
+static void Copy( const AstObject *, AstObject *, int * );
+static void PointListPoints( AstPointList *, AstPointSet **, int *);
+static void Delete( AstObject *, int * );
+static void Dump( AstObject *, AstChannel *, int * );
+static void RegBaseBox( AstRegion *, double *, double *, int * );
+static AstRegion *MergePointList( AstPointList *, AstRegion *, int, int * );
+static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
+
+static const char *GetAttrib( AstObject *, const char *, int * );
+static int TestAttrib( AstObject *, const char *, int * );
+static void ClearAttrib( AstObject *, const char *, int * );
+static void SetAttrib( AstObject *, const char *, int * );
+
+
+/* Member functions. */
+/* ================= */
+
+static void ClearAttrib( AstObject *this_object, const char *attrib,
+                         int *status ) {
+/*
+*  Name:
+*     ClearAttrib
+
+*  Purpose:
+*     Clear an attribute value for a PointList.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     void ClearAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astClearAttrib
+*     protected method inherited from the Object class).
+
+*  Description:
+*     This function clears the value of a specified attribute for a
+*     PointList, so that the default value will subsequently be used.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     attrib
+*        Pointer to a null-terminated string specifying the attribute
+*        name.  This should be in lower case with no surrounding white
+*        space.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstPointList *this;            /* Pointer to the PointList structure */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the PointList structure. */
+   this = (AstPointList *) this_object;
+
+/* Check the attribute name and clear the appropriate attribute. */
+
+/* Test if the name matches any of the read-only attributes of this
+   class. If it does, then report an error. */
+   if ( !strcmp( attrib, "listsize" ) ) {
+      astError( AST__NOWRT, "astClear: Invalid attempt to clear the \"%s\" "
+                "value for a %s.", status, attrib, astGetClass( this ) );
+      astError( AST__NOWRT, "This is a read-only attribute." , status);
+
+/* If the attribute is still not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      (*parent_clearattrib)( this_object, attrib, status );
+   }
+}
+
+static const char *GetAttrib( AstObject *this_object, const char *attrib,
+                              int *status ) {
+/*
+*  Name:
+*     GetAttrib
+
+*  Purpose:
+*     Get the value of a specified attribute for a PointList.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     const char *GetAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the protected astGetAttrib
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a pointer to the value of a specified
+*     attribute for a PointList, formatted as a character string.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     attrib
+*        Pointer to a null-terminated string containing the name of
+*        the attribute whose value is required. This name should be in
+*        lower case, with all white space removed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     - Pointer to a null-terminated string containing the attribute
+*     value.
+
+*  Notes:
+*     - The returned string pointer may point at memory allocated
+*     within the PointList, or at static memory. The contents of the
+*     string may be over-written or the pointer may become invalid
+*     following a further invocation of the same function or any
+*     modification of the PointList. A copy of the string should
+*     therefore be made if necessary.
+*     - 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 */
+   AstPointList *this;           /* Pointer to the PointList structure */
+   const char *result;           /* Pointer value to return */
+   int ival;                     /* Integer attribute value */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(this_object);
+
+/* Obtain a pointer to the PointList structure. */
+   this = (AstPointList *) this_object;
+
+/* Compare "attrib" with each recognised attribute name in turn,
+   obtaining the value of the required attribute. If necessary, write
+   the value into "getattrib_buff" as a null-terminated string in an
+   appropriate format.  Set "result" to point at the result string. */
+
+/* ListSize. */
+/* -------- */
+   if ( !strcmp( attrib, "listsize" ) ) {
+      ival = astGetListSize( this );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%d", ival );
+         result = getattrib_buff;
+      }
+
+/* If the attribute name was not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      result = (*parent_getattrib)( this_object, attrib, status );
+   }
+
+/* Return the result. */
+   return result;
+}
+
+static int GetClosed( AstRegion *this, int *status ) {
+/*
+*  Name:
+*     GetClosed
+
+*  Purpose:
+*     Get the value of the CLosed attribute for a PointList.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     int GetClosed( AstRegion *this, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astGetClosed method
+*     inherited from the Region class).
+
+*  Description:
+*     This function returns the value of the Closed attribute for a
+*     PointList. Since points have zero volume they consist entirely of
+*     boundary. Therefore the Region is always considered to be closed
+*     unless it has been negated, in which case it is always assumed to
+*     be open.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     The value to use for the Closed attribute.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*/
+
+/* Check the global error status. */
+   if ( !astOK ) return 0;
+
+/* The value to be used for the Closed attribute is always the opposite
+   of the Negated attribute. */
+   return ( astGetNegated( this ) == 0 );
+}
+
+static int GetListSize( AstPointList *this, int *status ) {
+/*
+*+
+*  Name:
+*     astGetListSize
+
+*  Purpose:
+*     Determine how many points there are in a PointList.
+
+*  Type:
+*     Protected virtual function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     int astGetListSize( AstPointList *this )
+
+*  Class Membership:
+*     PointList method.
+
+*  Description:
+*     This function returns the number of points stored in a Point|List.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+
+*  Returned Value:
+*     The number of points in the PointList.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*-
+*/
+
+/* Check the global error status. */
+   if ( !astOK ) return 0;
+
+/* Return the number of points by querying the PointSet that holds the
+   points. */
+   return astGetNpoint( ((AstRegion *) this)->points );
+}
+
+static int GetObjSize( AstObject *this_object, int *status ) {
+/*
+*  Name:
+*     GetObjSize
+
+*  Purpose:
+*     Return the in-memory size of an Object.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     int GetObjSize( AstObject *this, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astGetObjSize protected
+*     method inherited from the parent class).
+
+*  Description:
+*     This function returns the in-memory size of the supplied PointList,
+*     in bytes.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     The Object size, in bytes.
+
+*  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: */
+   AstPointList *this;         /* Pointer to PointList structure */
+   int result;                /* Result value to return */
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointers to the PointList structure. */
+   this = (AstPointList *) this_object;
+
+/* Invoke the GetObjSize method inherited from the parent class, and then
+   add on any components of the class structure defined by this class
+   which are stored in dynamically allocated memory. */
+   result = (*parent_getobjsize)( this_object, status );
+
+   result += astGetObjSize( this->lbnd );
+   result += astGetObjSize( this->ubnd );
+
+/* If an error occurred, clear the result value. */
+   if ( !astOK ) result = 0;
+
+/* Return the result, */
+   return result;
+}
+
+void astInitPointListVtab_(  AstPointListVtab *vtab, const char *name,
+                             int *status ) {
+/*
+*+
+*  Name:
+*     astInitPointListVtab
+
+*  Purpose:
+*     Initialise a virtual function table for a PointList.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     void astInitPointListVtab( AstPointListVtab *vtab, const char *name )
+
+*  Class Membership:
+*     PointList vtab initialiser.
+
+*  Description:
+*     This function initialises the component of a virtual function
+*     table which is used by the PointList class.
+
+*  Parameters:
+*     vtab
+*        Pointer to the virtual function table. The components used by
+*        all ancestral classes will be initialised if they have not already
+*        been initialised.
+*     name
+*        Pointer to a constant null-terminated character string which contains
+*        the name of the class to which the virtual function table belongs (it
+*        is this pointer value that will subsequently be returned by the Object
+*        astClass function).
+*-
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
+   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
+   AstRegionVtab *region;        /* Pointer to Region component of Vtab */
+
+/* Check the local error status. */
+   if ( !astOK ) return;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Initialize the component of the virtual function table used by the
+   parent class. */
+   astInitRegionVtab( (AstRegionVtab *) vtab, name );
+
+/* Store a unique "magic" value in the virtual function table. This
+   will be used (by astIsAPointList) to determine if an object belongs
+   to this class.  We can conveniently use the address of the (static)
+   class_check variable to generate this unique value. */
+   vtab->id.check = &class_check;
+   vtab->id.parent = &(((AstRegionVtab *) vtab)->id);
+
+/* Initialise member function pointers. */
+/* ------------------------------------ */
+/* Store pointers to the member functions (implemented here) that provide
+   virtual methods for this class. */
+   vtab->GetListSize = GetListSize;
+   vtab->PointListPoints = PointListPoints;
+
+/* Save the inherited pointers to methods that will be extended, and
+   replace them with pointers to the new member functions. */
+   object = (AstObjectVtab *) vtab;
+   mapping = (AstMappingVtab *) vtab;
+   region = (AstRegionVtab *) vtab;
+
+   parent_getobjsize = object->GetObjSize;
+   object->GetObjSize = GetObjSize;
+
+   parent_clearattrib = object->ClearAttrib;
+   object->ClearAttrib = ClearAttrib;
+
+   parent_getattrib = object->GetAttrib;
+   object->GetAttrib = GetAttrib;
+
+   parent_setattrib = object->SetAttrib;
+   object->SetAttrib = SetAttrib;
+
+   parent_testattrib = object->TestAttrib;
+   object->TestAttrib = TestAttrib;
+
+   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->RegBaseMesh = RegBaseMesh;
+   region->RegBaseBox = RegBaseBox;
+   region->RegBasePick = RegBasePick;
+   region->RegPins = RegPins;
+   region->GetClosed = GetClosed;
+   region->MaskB = MaskB;
+   region->MaskD = MaskD;
+   region->MaskF = MaskF;
+   region->MaskI = MaskI;
+   region->MaskL = MaskL;
+   region->MaskS = MaskS;
+   region->MaskUB = MaskUB;
+   region->MaskUI = MaskUI;
+   region->MaskUL = MaskUL;
+   region->MaskUS = MaskUS;
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+   region->MaskLD = MaskLD;
+#endif
+
+/* Declare the class dump function. There is no copy constructor or
+   destructor. */
+   astSetDelete( vtab, Delete );
+   astSetCopy( vtab, Copy );
+   astSetDump( vtab, Dump, "PointList", "Collection of points" );
+
+/* 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) );
+   }
+}
+
+/*
+*  Name:
+*     Mask<X>
+
+*  Purpose:
+*     Mask a region of a data grid.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     int Mask<X>( AstRegion *this, AstMapping *map, int inside, int ndim,
+*                  const int lbnd[], const int ubnd[], <Xtype> in[],
+*                  <Xtype> val )
+
+*  Class Membership:
+*     PointList function method (replaces the astMask<X> methods
+*     inherited from the parent Region class).
+
+*  Description:
+*     This is a set of functions for masking out regions within gridded data
+*     (e.g. an image). The functions modifies a given data grid by
+*     assigning a specified value to all samples which are inside (or outside
+*     if "inside" is zero) the specified Region.
+*
+*     You should use a masking function which matches the numerical
+*     type of the data you are processing by replacing <X> in
+*     the generic function name astMask<X> by an appropriate 1- or
+*     2-character type code. For example, if you are masking data
+*     with type "float", you should use the function astMaskF (see
+*     the "Data Type Codes" section below for the codes appropriate to
+*     other numerical types).
+
+*  Parameters:
+*     this
+*        Pointer to a Region.
+*     map
+*        Pointer to a Mapping. The forward transformation should map
+*        positions in the coordinate system of the supplied Region
+*        into pixel coordinates as defined by the "lbnd" and "ubnd"
+*        parameters. A NULL pointer can be supplied if the coordinate
+*        system of the supplied Region corresponds to pixel coordinates.
+*        This is equivalent to supplying a UnitMap.
+*
+*        The number of inputs for this Mapping (as given by its Nin attribute)
+*        should match the number of axes in the supplied Region (as given
+*        by the Naxes attribute of the Region). The number of outputs for the
+*        Mapping (as given by its Nout attribute) should match the number of
+*        grid dimensions given by the value of "ndim" below.
+*     inside
+*        A boolean value which indicates which pixel are to be masked. If
+*        a non-zero value is supplied, then all grid pixels which are inside
+*        the supplied Region are assigned the value given by "val",
+*        and all other pixels are left unchanged. If zero is supplied, then
+*        all grid pixels which are not inside the supplied Region are
+*        assigned the value given by "val", and all other pixels are left
+*        unchanged. Note, the Negated attribute of the Region is used to
+*        determine which pixel are inside the Region and which are outside.
+*        So the inside of a Region which has not been negated is the same as
+*        the outside of the corresponding negated Region.
+*     ndim
+*        The number of dimensions in the input grid. This should be at
+*        least one.
+*     lbnd
+*        Pointer to an array of integers, with "ndim" elements,
+*        containing the coordinates of the centre of the first pixel
+*        in the input grid along each dimension.
+*     ubnd
+*        Pointer to an array of integers, with "ndim" elements,
+*        containing the coordinates of the centre of the last pixel in
+*        the input grid along each dimension.
+*
+*        Note that "lbnd" and "ubnd" together define the shape
+*        and size of the input grid, its extent along a particular
+*        (j'th) dimension being ubnd[j]-lbnd[j]+1 (assuming the
+*        index "j" to be zero-based). They also define
+*        the input grid's coordinate system, each pixel having unit
+*        extent along each dimension with integral coordinate values
+*        at its centre.
+*     in
+*        Pointer to an array, with one element for each pixel in the
+*        input grid, containing the data to be masked.  The
+*        numerical type of this array should match the 1- or
+*        2-character type code appended to the function name (e.g. if
+*        you are using astMaskF, the type of each array element
+*        should be "float").
+*
+*        The storage order of data within this array should be such
+*        that the index of the first grid dimension varies most
+*        rapidly and that of the final dimension least rapidly
+*        (i.e. Fortran array indexing is used).
+*
+*        On exit, the samples specified by "inside" are set to the value
+*        of "val". All other samples are left unchanged.
+*     val
+*        This argument should have the same type as the elements of
+*        the "in" array. It specifies the value used to flag the
+*        masked data (see "inside").
+
+*  Returned Value:
+*     The number of pixels to which a value of "badval" has been assigned.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+
+*  Data Type Codes:
+*     To select the appropriate masking function, you should
+*     replace <X> in the generic function name astMask<X> with a
+*     1- or 2-character data type code, so as to match the numerical
+*     type <Xtype> of the data you are processing, as follows:
+*     - D: double
+*     - F: float
+*     - L: long int
+*     - UL: unsigned long int
+*     - I: int
+*     - UI: unsigned int
+*     - S: short int
+*     - US: unsigned short int
+*     - B: byte (signed char)
+*     - UB: unsigned byte (unsigned char)
+*
+*     For example, astMaskD would be used to process "double"
+*     data, while astMaskS would be used to process "short int"
+*     data, etc.
+*/
+/* Define a macro to implement the function for a specific data
+   type. */
+#define MAKE_MASK(X,Xtype) \
+static int Mask##X( AstRegion *this, AstMapping *map, int inside, int ndim, \
+                    const int lbnd[], const int ubnd[], \
+                    Xtype in[], Xtype val, int *status ) { \
+\
+/* Local Variables: */ \
+   AstFrame *grid_frame;         /* Pointer to Frame describing grid coords */ \
+   AstPointSet *pset1;           /* Pointer to base Frame positions */ \
+   AstPointSet *pset2;           /* Pointer to current Frame positions */ \
+   AstRegion *used_region;       /* Pointer to Region to be used by astResample */ \
+   Xtype *temp;                  /* Pointer to temp storage for retained points */ \
+   double **ptr2;                /* Pointer to pset2 data values */ \
+   int *iv;                      /* Pointer to index array */ \
+   int i;                        /* Point index */ \
+   int idim;                     /* Loop counter for coordinate dimensions */ \
+   int ii;                       /* Vectorised point index */ \
+   int j;                        /* Axis index */ \
+   int nax;                      /* Number of Region axes */ \
+   int negated;                  /* Has Region been negated? */ \
+   int nin;                      /* Number of Mapping input coordinates */ \
+   int nout;                     /* Number of Mapping output coordinates */ \
+   int npnt;                     /* Number of points in PointList */ \
+   int result;                   /* Result value to return */ \
+   int vlen;                     /* Length of vectorised array */ \
+\
+/* Initialise. */ \
+   result = 0; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return result; \
+\
+/* Obtain value for the Naxes attribute of the Region. */ \
+   nax = astGetNaxes( this ); \
+\
+/* If supplied, obtain values for the Nin and Nout attributes of the Mapping. */ \
+   if( map ) { \
+      nin = astGetNin( map ); \
+      nout = astGetNout( map ); \
+\
+/* If OK, check that the number of mapping inputs matches the \
+   number of axes in the Region. Report an error if necessary. */ \
+      if ( astOK && ( nax != nin ) ) { \
+         astError( AST__NGDIN, "astMask"#X"(%s): Bad number of mapping " \
+                   "inputs (%d).", status, astGetClass( this ), nin ); \
+         astError( AST__NGDIN, "The %s given requires %d coordinate value%s " \
+                   "to specify a position.", status, \
+                   astGetClass( this ), nax, ( nax == 1 ) ? "" : "s" ); \
+      } \
+\
+/* If OK, check that the number of mapping outputs matches the \
+   number of grid dimensions. Report an error if necessary. */ \
+      if ( astOK && ( ndim != nout ) ) { \
+         astError( AST__NGDIN, "astMask"#X"(%s): Bad number of mapping " \
+                   "outputs (%d).", status, astGetClass( this ), nout ); \
+         astError( AST__NGDIN, "The pixel grid requires %d coordinate value%s " \
+                   "to specify a position.", status, \
+                   ndim, ( ndim == 1 ) ? "" : "s" ); \
+      } \
+\
+/* Create a new Region by mapping the supplied Region with the supplied \
+   Mapping.*/ \
+      grid_frame = astFrame( ndim, "Domain=grid", status ); \
+      used_region = astMapRegion( this, map, grid_frame ); \
+      grid_frame = astAnnul( grid_frame ); \
+\
+/* If no Mapping was supplied check that the number of grid dimensions \
+   matches the number of axes in the Region.*/ \
+   } else if ( astOK && ( ( ndim != nax ) || ( ndim < 1 ) ) ) { \
+      used_region = NULL; \
+      astError( AST__NGDIN, "astMask"#X"(%s): Bad number of input grid " \
+                "dimensions (%d).", status, astGetClass( this ), ndim ); \
+      if ( ndim != nax ) { \
+         astError( AST__NGDIN, "The %s given requires %d coordinate value%s " \
+                   "to specify an input position.", status, \
+                   astGetClass( this ), nax, ( nax == 1 ) ? "" : "s" ); \
+      } \
+\
+/* If no Mapping was supplied and the parameters look OK, clone the \
+   supplied Region pointer for use later on. */  \
+   } else { \
+      used_region = astClone( this );  \
+   }  \
+\
+/* Check that the lower and upper bounds of the input grid are \
+   consistent. Report an error if any pair is not. */ \
+   if ( astOK ) { \
+      for ( idim = 0; idim < ndim; idim++ ) { \
+         if ( lbnd[ idim ] > ubnd[ idim ] ) { \
+            astError( AST__GBDIN, "astMask"#X"(%s): Lower bound of " \
+                      "input grid (%d) exceeds corresponding upper bound " \
+                      "(%d).", status, astGetClass( this ), \
+                      lbnd[ idim ], ubnd[ idim ] ); \
+            astError( AST__GBDIN, "Error in input dimension %d.", status, \
+                      idim + 1 ); \
+            break; \
+         } \
+      } \
+   } \
+\
+/* Get the PointSet in the base Frame of the Region's FrameSet, and \
+   transform to the current (GRID) Frame. */ \
+   pset1 = used_region->points; \
+   pset2 = astRegTransform( used_region, pset1, 1, NULL, NULL ); \
+   ptr2 =astGetPoints( pset2 ); \
+\
+/* Allocate memory to hold the corresponding vector indices. */ \
+   npnt = astGetNpoint( pset2 ); \
+   iv = astMalloc( sizeof(int)*(size_t) npnt ); \
+   if( astOK ) { \
+\
+/* Convert the transformed GRID positions into integer indices into the \
+   vectorised data array. Also form the total size of the data array. */ \
+      vlen = 0; \
+      for( i = 0; i < npnt; i++ ) { \
+         vlen = 1; \
+         ii = 0; \
+         for( j = 0; j < ndim; j++ ) { \
+            ii += vlen*( (int)( ptr2[ j ][ i ] + 0.5 ) - lbnd[ j ] ); \
+            vlen *= ubnd[ i ] - lbnd[ i ] + 1; \
+         }  \
+         iv[ i ] = ii; \
+      } \
+\
+/* See if the Region is negated. */ \
+      negated = astGetNegated( used_region ); \
+\
+/* If necessary, set the transformed pixel coords to the supplied value. */ \
+      if( ( inside && !negated ) || ( !inside && negated ) ) { \
+         for( i = 0; i < npnt; i++ ) in[ iv[ i ] ] = val; \
+         result = npnt; \
+\
+/* If necessary, set all except the transformed pixel coords to the supplied  \
+   value. */ \
+      } else { \
+         temp = astMalloc( sizeof( Xtype )*(size_t)npnt ); \
+         if( astOK ) { \
+            for( i = 0; i < npnt; i++ ) temp[ i ] = in[ iv[ i ] ]; \
+            for( i = 0; i < vlen; i++ ) in[ i ] = val; \
+            for( i = 0; i < npnt; i++ ) in[ iv[ i ] ] = temp[ i ]; \
+            result = vlen - npnt; \
+         } \
+         temp = astFree( temp ); \
+      } \
+   } \
+\
+/* Free resources */ \
+   iv = astFree( iv ); \
+   pset2 = astAnnul( pset2 ); \
+   used_region = astAnnul( used_region ); \
+\
+/* If an error occurred, clear the returned result. */ \
+   if ( !astOK ) result = 0; \
+\
+/* Return the result. */ \
+   return result; \
+}
+
+/* Expand the above macro to generate a function for each required
+   data type. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKE_MASK(LD,long double)
+#endif
+MAKE_MASK(D,double)
+MAKE_MASK(F,float)
+MAKE_MASK(L,long int)
+MAKE_MASK(UL,unsigned long int)
+MAKE_MASK(I,int)
+MAKE_MASK(UI,unsigned int)
+MAKE_MASK(S,short int)
+MAKE_MASK(US,unsigned short int)
+MAKE_MASK(B,signed char)
+MAKE_MASK(UB,unsigned char)
+
+/* Undefine the macro. */
+#undef MAKE_MASK
+
+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 PointList.
+
+*  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:
+*     PointList 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 PointList 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 PointList 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 PointList which is to be merged with
+*        its neighbours. This should be a cloned copy of the PointList
+*        pointer contained in the array element "(*map_list)[where]"
+*        (see below). This pointer will not be annulled, and the
+*        PointList it identifies will not be modified by this function.
+*     where
+*        Index in the "*map_list" array (below) at which the pointer
+*        to the nominated PointList 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: */
+   AstPointList *oldint;  /* Pointer to supplied PointList */
+   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 PointList. */
+   oldint = (AstPointList *) this;
+
+/* First of all, see if the PointList can be replaced by a simpler Region,
+   without reference to the neighbouring Regions in the list.           */
+/* =====================================================================*/
+
+/* Try to simplify the PointList. If the pointer value has changed, we assume
+   some simplification took place. */
+   new = astSimplify( oldint );
+   if( new != (AstMapping *) oldint ) {
+
+/* Annul the PointList 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 PointList 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 PointList with its lower neighbour (if any). */
+      if( where > 0 ) {
+         i1 = where - 1;
+         map = ( *map_list )[ where - 1 ];
+         if( astIsARegion( map ) ) {
+            new = (AstMapping *) MergePointList( oldint, (AstRegion *) map,
+                                                  0, status );
+         }
+      }
+
+/* If this did not produced a merged Region, attempt to merge the PointList
+   with its upper neighbour (if any). */
+      if( !new && where < *nmap - 1 ) {
+         i1 = where;
+         map = ( *map_list )[ where + 1 ];
+         if( astIsARegion( map ) ) {
+            new = (AstMapping *) MergePointList( 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 *MergePointList( AstPointList *this, AstRegion *reg,
+                                   int plsfirst, int *status ) {
+/*
+*  Name:
+*     MergePointList
+
+*  Purpose:
+*     Attempt to merge a PointList with another Region to form a Region of
+*     higher dimensionality.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     AstRegion *MergePointList( AstPointList *this, AstRegion *reg,
+*                                 int plsfirst, int *status )
+
+*  Class Membership:
+*     PointList member function.
+
+*  Description:
+*     This function attempts to combine the supplied Regions together
+*     into a Region of higher dimensionality.
+
+*  Parameters:
+*     this
+*        Pointer to a PointList.
+*     reg
+*        Pointer to another Region.
+*     plsfirst
+*        If non-zero, then the PointList axes are put first in the new Region.
+*        Otherwise, the other Region's axes are put first.
+*     status
+*        Pointer to the inherited status value.
+
+*  Returned Value:
+*     A pointer to a new region, or NULL if the supplied Regions could
+*     not be merged.
+*/
+
+/* Local Variables: */
+   AstFrame *bfrm;           /* Pointer to base Frame for "result" */
+   AstFrame *cfrm;           /* Pointer to current Frame for "result" */
+   AstFrame *frm_reg;        /* Pointer to Frame from "reg" */
+   AstFrame *frm_this;       /* Pointer to Frame from "this" */
+   AstMapping *bcmap;        /* Base->current Mapping for "result" */
+   AstMapping *map_reg;      /* Base->current Mapping from "reg" */
+   AstMapping *map_this;     /* Base->current Mapping from "this" */
+   AstMapping *sbunc;        /* Simplified uncertainty */
+   AstPointSet *pset_new;    /* PointSet for new PointList */
+   AstPointSet *pset_reg;    /* PointSet from reg */
+   AstPointSet *pset_this;   /* PointSet from this */
+   AstRegion *bunc;          /* Base Frame uncertainty Region */
+   AstRegion *new;           /* Pointer to new PointList in base Frame */
+   AstRegion *result;        /* Pointer to returned PointList in current Frame */
+   AstRegion *unc_reg;       /* Current Frame uncertainty Region from "reg" */
+   AstRegion *unc_this;      /* Current Frame uncertainty Region from "this" */
+   double **ptr_new;         /* PointSet data pointers for new PointList */
+   double **ptr_reg;         /* PointSet data pointers for reg */
+   double **ptr_this;        /* PointSet data pointers for this */
+   double fac_reg;           /* Ratio of used to default MeshSize for "reg" */
+   double fac_this;          /* Ratio of used to default MeshSize for "this" */
+   int i;                    /* Axis index */
+   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 PointList  */
+
+/* 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 );
+
+/* We only check for merging with another PointList (other classes such
+   as Box and Interval check for merging of PointLists with other classes).
+   The result will be an PointList. Both Regions must have the same value
+   for the Negated flag, and can contain only a single point. */
+      if( astIsAPointList( reg ) && neg_this == neg_reg &&
+          astGetListSize( this ) == 1 &&
+          astGetListSize( (AstPointList *) reg ) == 1 ) {
+
+/* Get the number of axes in the two supplied Regions. */
+         nax_reg = astGetNaxes( reg );
+         nax_this = astGetNaxes( this );
+
+/* 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 the new Region. */
+         frm_this = astGetFrame( ((AstRegion *) this)->frameset, AST__BASE );
+         frm_reg = astGetFrame( reg->frameset, AST__BASE );
+
+         if( plsfirst ) {
+            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 );
+
+/* Get pointers to the coordinate data in the two PointLists */
+         pset_this = ((AstRegion *) this)->points;
+         ptr_this = astGetPoints( pset_this );
+         pset_reg = reg->points;
+         ptr_reg = astGetPoints( pset_reg );
+
+/* Create a PointSet to hold the points for the returned PointList. */
+         pset_new = astPointSet( 1, nax, "", status );
+
+/* Get pointers to its data. */
+         ptr_new = astGetPoints( pset_new );
+
+/* Check pointers can be used safely. */
+         if( astOK ) {
+
+/* Copy the point positions fon the selected axes into the arrays allocated
+   above, in the requested order. */
+            if( plsfirst ) {
+               for( i = 0; i < nax_this; i++ ) {
+                  ptr_new[ i ][ 0 ] = ptr_this[ i ][ 0 ];
+               }
+               for( ; i < nax; i++ ) {
+                  ptr_new[ i ][ 0 ] = ptr_reg[ i - nax_this ][ 0 ];
+               }
+
+            } else {
+               for( i = 0; i < nax_reg; i++ ) {
+                  ptr_new[ i ][ 0 ] = ptr_reg[ i ][ 0 ];
+               }
+               for( ; i < nax; i++ ) {
+                  ptr_new[ i ][ 0 ] = ptr_this[ i - nax_reg ][ 0 ];
+               }
+            }
+
+/* Create the new PointList. */
+            new = (AstRegion *) astPointList( bfrm, pset_new, 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 PointList. */
+            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( plsfirst ) {
+                  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( plsfirst ) {
+               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( plsfirst ) {
+               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 );
+            cfrm = astAnnul( cfrm );
+            new = astAnnul( new );
+         }
+         bfrm = astAnnul( bfrm );
+         pset_new = astAnnul( pset_new );
+
+      }
+   }
+
+/* If an error has occurred, annul the returned pointer. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+void PointListPoints( AstPointList *this, AstPointSet **pset, int *status) {
+/*
+*+
+*  Name:
+*     astPointListPoints
+
+*  Purpose:
+*     Return the defining points of a PointList.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     astPointListPoints( AstPointList *this, AstPointSet **pset )
+
+*  Class Membership:
+*     Region virtual function.
+
+*  Description:
+*     This function returns the axis values at the points defining the
+*     supplied PointList.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     pset
+*        Address of a location at which to return a pointer to a PointSet
+*        holding the points in the PointList, in the base Frame of the
+*        encapsulated FrameSet. The returned Pointer should be annulled
+*        when no longer needed.
+
+*-
+*/
+
+/* Check the inherited status. */
+   if( !astOK ) return;
+
+/* Return a clone of the PointSet holding the points defining the PointList. */
+   *pset = astClone( ((AstRegion *) this)->points );
+
+}
+
+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 "pointlist.h"
+*     void astRegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status )
+
+*  Class Membership:
+*     PointList 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: */
+   AstFrame *frm;                /* Pointer to encapsulated Frame */
+   AstPointList *this;           /* Pointer to PointList structure */
+   AstPointSet *pset;            /* Pointer to PointSet defining the Region */
+   double **ptr;                 /* Pointer to PointSet data */
+   double *p;                    /* Pointer to next axis value */
+   double *lb;                   /* Pointer to lower limit array */
+   double *ub;                   /* Pointer to upper limit array */
+   double d;                     /* Axis offset from refernce value */
+   double p0;                    /* Reference axis value */
+   int ic;                       /* Axis index */
+   int ip;                       /* Point index */
+   int nb;                       /* Number of bytes to be copied */
+   int nc;                       /* No. of axes in base Frame */
+   int np;                       /* No. of points in PointSet */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get a pointer to the PointList structure. */
+   this = (AstPointList *) this_region;
+
+/* Calculate the number of bytes in each array. */
+   nb = sizeof( double )*(size_t) astGetNaxes( this );
+
+/* If the base Frame bounding box has not yet been found, find it now and
+   store it in the PointList structure. */
+   if( !this->lbnd || !this->ubnd ) {
+
+/* Allocate memory to store the bounding box in the PointList structure. */
+      lb = astMalloc( nb );
+      ub = astMalloc( nb );
+
+/* Get the axis values for the PointSet which defines the location and
+   extent of the region in the base Frame of the encapsulated FrameSet. */
+      pset = this_region->points;
+      ptr = astGetPoints( pset );
+      nc = astGetNcoord( pset );
+      np = astGetNpoint( pset );
+
+/* Get a pointer to the base Frame in the encaposulated FrameSet. */
+      frm = astGetFrame( this_region->frameset, AST__BASE );
+
+/* Check pointers can be used safely. */
+      if( astOK ) {
+
+/* Find the bounds on each axis in turn. */
+         for( ic = 0; ic < nc; ic++ ) {
+
+/* We first find the max and min axis offsets from the first point. We
+   used astAxDistance to cater for the possbility that the Frame may be a
+   SkyFrame and thus have circular redundancy. */
+            p = ptr[ ic ] + 1;
+            p0 = p[ -1 ];
+            lb[ ic ] = 0.0;
+            ub[ ic ] = 0.0;
+            for( ip = 1; ip < np; ip++, p++ ) {
+               d = astAxDistance( frm, ic + 1, p0, *p );
+               if( d < lb[ ic ] ) lb[ ic ] = d;
+               if( d > ub[ ic ] ) ub[ ic ] = d;
+            }
+
+/* Now convert these offsets to actual axis values. */
+            lb[ ic ] = astAxOffset( frm, ic + 1, p0, lb[ ic ] );
+            ub[ ic ] = astAxOffset( frm, ic + 1, p0, ub[ ic ] );
+
+         }
+      }
+
+/* Free resources */
+      frm = astAnnul( frm );
+
+/* Store the pointers in the PointList structure. */
+      if( astOK ) {
+         this->lbnd = lb;
+         this->ubnd = ub;
+      } else {
+         this->lbnd = astFree( this->lbnd );
+         this->ubnd = astFree( this->ubnd );
+      }
+   }
+
+/* If the bounding box has been found succesfully, copy it into the supplied
+   arrays. */
+   if( astOK ) {
+      memcpy( lbnd, this->lbnd, nb );
+      memcpy( ubnd, this->ubnd, nb );
+   }
+
+}
+
+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 "pointlist.h"
+*     AstPointSet *astRegBaseMesh( AstRegion *this, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astRegBaseMesh protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a PointSet containing a mesh of points on the
+*     boundary of the Region. The points refer to the base Frame of
+*     the encapsulated FrameSet.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the PointSet. The axis values in this PointSet will have
+*     associated accuracies derived from the accuracies which were
+*     supplied when the Region was created.
+
+*  Notes:
+*    - A NULL pointer is returned if an error has already occurred, or if
+*    this function should fail for any reason.
+
+*/
+
+/* Local Variables: */
+   AstPointSet *result;
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* 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 {
+
+/* It is just a copy of the encapsulated PointSet. */
+      result = astCopy( this->points );
+
+/* 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 );
+   }
+
+/* Annul the result if an error has occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return a pointer to the output PointSet. */
+   return result;
+}
+
+static AstRegion *RegBasePick( AstRegion *this_region, int naxes,
+                               const int *axes, int *status ){
+/*
+*  Name:
+*     RegBasePick
+
+*  Purpose:
+*     Return a Region formed by picking selected base Frame axes from the
+*     supplied Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     AstRegion *RegBasePick( AstRegion *this, int naxes, const int *axes,
+*                             int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astRegBasePick protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function attempts to return a Region that is spanned by selected
+*     axes from the base Frame of the encapsulated FrameSet of the supplied
+*     Region. This may or may not be possible, depending on the class of
+*     Region. If it is not possible a NULL pointer is returned.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     naxes
+*        The number of base Frame axes to select.
+*     axes
+*        An array holding the zero-based indices of the base Frame axes
+*        that are to be selected.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the Region, or NULL if no region can be formed.
+
+*  Notes:
+*    - A NULL pointer is returned if an error has already occurred, or if
+*    this function should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstFrame *bfrm;         /* The base Frame in the supplied Region */
+   AstFrame *frm;          /* The base Frame in the returned Region */
+   AstPointSet *pset;      /* Holds axis values defining the supplied Region */
+   AstPointSet *pset_new;  /* Holds axis values defining the returned Region */
+   AstRegion *bunc;        /* The uncertainty in the supplied Region */
+   AstRegion *result;      /* Returned Region */
+   AstRegion *unc;         /* The uncertainty in the returned Region */
+   double **ptr;           /* Holds axis values defining the supplied Region */
+   double **ptr_new;       /* Holds axis values defining the returned Region */
+   double *p;              /* Pointer to next input axis value */
+   double *q;              /* Pointer to next output axis value */
+   int i;                  /* Index of axis within returned Region */
+   int j;                  /* Point index */
+   int npnt;               /* Number of points in PointList */
+
+/* Initialise */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the base Frame of the encapsulated FrameSet. */
+   bfrm = astGetFrame( this_region->frameset, AST__BASE );
+
+/* Create a Frame by picking the selected axes from the base Frame of the
+   encapsulated FrameSet. */
+   frm = astPickAxes( bfrm, naxes, axes, NULL );
+
+/* Get the uncertainty Region (if any) within the base Frame of the supplied
+   Region, and select the required axes from it. If the resulting Object
+   is not a Region, annul it so that the returned Region will have no
+   uncertainty. */
+   if( astTestUnc( this_region ) ) {
+      bunc = astGetUncFrm( this_region, AST__BASE );
+      unc = astPickAxes( bunc, naxes, axes, NULL );
+      bunc = astAnnul( bunc );
+
+      if( ! astIsARegion( unc ) ) unc = astAnnul( unc );
+
+   } else {
+      unc = NULL;
+   }
+
+/* Get pointers to the coordinate data in the parent Region structure. */
+   pset = this_region->points;
+   ptr = astGetPoints( pset );
+   npnt = astGetNpoint( pset );
+
+/* Create a PointSet to hold the points for the returned PointList. */
+   pset_new = astPointSet( npnt, naxes, "", status );
+
+/* Get pointers to its data. */
+   ptr_new = astGetPoints( pset_new );
+
+/* Check pointers can be used safely. */
+   if( astOK ) {
+
+/* Copy the point positions on the selected axes into the arrays allocated
+   above. */
+      for( i = 0; i < naxes; i++ ) {
+         p = ptr[ axes[ i ] ];
+         q = ptr_new[ i ];
+         for( j = 0; j < npnt; j++ ) *(q++) = *(p++);
+      }
+
+/* Create the new PointList. */
+      result = (AstRegion *) astPointList( frm, pset_new, unc, "", status );
+   }
+
+/* Free resources */
+   frm = astAnnul( frm );
+   bfrm = astAnnul( bfrm );
+   if( unc ) unc = astAnnul( unc );
+   pset_new = astAnnul( pset_new );
+
+/* Return a NULL pointer if an error has occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static int RegPins( AstRegion *this_region, AstPointSet *pset, AstRegion *unc,
+                    int **mask, int *status ){
+/*
+*  Name:
+*     RegPins
+
+*  Purpose:
+*     Check if a set of points fall on the boundary of a given PointList.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     int RegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
+*                  int **mask, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astRegPins protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a flag indicating if the supplied set of
+*     points all fall on the boundary of the given PointList.
+*
+*     Some tolerance is allowed, as specified by the uncertainty Region
+*     stored in the supplied PointList "this", and the supplied uncertainty
+*     Region "unc" which describes the uncertainty of the supplied points.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     pset
+*        Pointer to the PointSet. The points are assumed to refer to the
+*        base Frame of the FrameSet encapsulated by "this".
+*     unc
+*        Pointer to a Region representing the uncertainties in the points
+*        given by "pset". The Region is assumed to represent the base Frame
+*        of the FrameSet encapsulated by "this". Zero uncertainity is assumed
+*        if NULL is supplied.
+*     mask
+*        Pointer to location at which to return a pointer to a newly
+*        allocated dynamic array of ints. The number of elements in this
+*        array is equal to the value of the Npoint attribute of "this".
+*        Each element in the returned array is set to 1 if the
+*        corresponding position in "this" is on the boundary of the Region
+*        and is set to zero otherwise. A NULL value may be supplied
+*        in which case no array is created. If created, the array should
+*        be freed using astFree when no longer needed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Non-zero if the points all fall on the boundary of the given
+*     Region, to within the tolerance specified. Zero otherwise.
+
+*/
+
+/* Local variables: */
+   AstPointList *pl;            /* Pointer to PointList holding supplied points */
+   AstPointList *this;          /* Pointer to the PointList structure. */
+   AstPointSet *pset2;          /* Supplied points masked by this PointList */
+   AstPointSet *pset3;          /* This PointList masked by supplied points */
+   double **ptr2;               /* Pointer to axis values in "pset2" */
+   double **ptr3;               /* Pointer to axis values in "pset3" */
+   double **ptr;                /* Pointer to axis values in "this" */
+   double *p;                   /* Pointer to next axis value to read */
+   int ic;                      /* Axis index */
+   int icurr;                   /* Index of original current Frame in "this" */
+   int ip;                      /* Point index */
+   int nc;                      /* No. of axes in Box base frame */
+   int neg_old;                 /* Original Negated flag for "this" */
+   int np;                      /* No. of supplied points */
+   int result;                  /* Returned flag */
+
+/* Initialise */
+   result = 0;
+   if( mask ) *mask = NULL;
+
+/* Check the inherited status. */
+   if( !astOK ) return result;
+
+/* Get a pointer to the Box structure. */
+   this = (AstPointList *) this_region;
+
+/* Temporarily ensure that the current Frame in "this" is the same as the
+   base Frame. We need to do this since the supplied points are in the
+   base Frame of "this", but the astTransform method below assumes
+   that it is transforming points in the current Frame of the Region. */
+   icurr = astGetCurrent( this_region->frameset );
+   astSetCurrent( this_region->frameset, AST__BASE );
+
+/* Get pointer to the supplied axis values, the number of points and the
+   number of axis values per point. */
+   ptr = astGetPoints( pset );
+   np = astGetNpoint( pset );
+   nc = astGetNcoord( pset );
+
+/* All the supplied points should be within the supplied PointsList region
+   (given that "within" implies some tolerance). Transform the positions
+   using this PointList and check if any of the resulting points fell
+   outside this PointList. We need to ensure that the PointList is not
+   negated first. */
+   neg_old = astGetNegated( this );
+   astSetNegated( this, 0 );
+   pset2 = astTransform( this, pset, 1, NULL );
+   ptr2 = astGetPoints( pset2 );
+
+/* Check pointers can be used. */
+   if( astOK ) {
+
+/* Check there are no bad points (i.e. check that none of the points are
+   outside the supplied PointList). The algorithm used to do this depends
+   on whether we need to create an output mask. */
+      result = 1;
+      if( mask ) {
+
+/* Create the returned mask array. */
+         *mask = astMalloc( np );
+         if( astOK ) {
+
+/* Initialise the mask elements on the basis of the first axis values */
+            result = 1;
+            p = ptr2[ 0 ];
+            for( ip = 0; ip < np; ip++ ) {
+               if( *(p++) == AST__BAD ) {
+                  result = 0;
+                  (*mask)[ ip ] = 0;
+               } else {
+                  (*mask)[ ip ] = 1;
+               }
+            }
+
+/* Now check for bad values on other axes. */
+            for( ic = 1; ic < nc; ic++ ) {
+               p = ptr2[ ic ];
+               for( ip = 0; ip < np; ip++ ) {
+                  if( *(p++) == AST__BAD ) {
+                     result = 0;
+                     (*mask)[ ip ] = 0;
+                  }
+               }
+            }
+         }
+
+/* If no output mask is to be made, we can break out of the check as soon
+   as the first bad value is found. */
+      } else {
+         for( ic = 0; ic < nc && result; ic++ ){
+            p = ptr2[ ic ];
+            for( ip = 0; ip < np; ip++,p++ ){
+               if( *p == AST__BAD ) {
+                  result = 0;
+                  break;
+               }
+            }
+         }
+      }
+
+/* If this check was passed, we perform a similar check in the opposite
+   direction: we create a new PointList from the supplied list of points,
+   and then we transform the points associated with the supplied PointList
+   using the new PointList. This checks that all the points in the
+   supplied PointList are close to the supplied points. Create the new
+   PointList holding the supplied points. */
+      if( result ) {
+         pl = astPointList( unc, pset, unc, "", status );
+
+/* Transform the points in "this" PointList using the new PointList as a
+   Mapping. */
+         pset3 = astTransform( pl, this_region->points, 1, NULL );
+         ptr3 = astGetPoints( pset3 );
+
+/* Check pointers can be used. */
+         if( astOK ) {
+            for( ic = 0; ic < nc && result; ic++ ){
+               p = ptr3[ ic ];
+               for( ip = 0; ip < np; ip++,p++ ){
+                  if( *p == AST__BAD ) {
+                     result = 0;
+                     break;
+                  }
+               }
+            }
+         }
+
+/* Free resources. */
+         pl = astAnnul( pl );
+         pset3 = astAnnul( pset3 );
+
+      }
+   }
+
+   pset2 = astAnnul( pset2 );
+
+/* Re-instate the original current Frame in "this". */
+   astSetCurrent( this_region->frameset, icurr );
+
+/* Re-instate the original Negated flag for "this". */
+   astSetNegated( this, neg_old );
+
+/* If an error has occurred, return zero. */
+   if( !astOK ) {
+      result = 0;
+      if( mask ) *mask = astAnnul( *mask );
+   }
+
+/* Return the result. */
+   return result;
+}
+
+static void SetAttrib( AstObject *this_object, const char *setting,
+                       int *status ) {
+/*
+*  Name:
+*     SetAttrib
+
+*  Purpose:
+*     Set an attribute value for a PointList.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     void SetAttrib( AstObject *this, const char *setting )
+
+*  Class Membership:
+*     PointList member function (over-rides the astSetAttrib protected
+*     method inherited from the Object class).
+
+*  Description:
+*     This function assigns an attribute value for a PointList, the
+*     attribute and its value being specified by means of a string of
+*     the form:
+*
+*        "attribute= value "
+*
+*     Here, "attribute" specifies the attribute name and should be in
+*     lower case with no white space present. The value to the right
+*     of the "=" should be a suitable textual representation of the
+*     value to be assigned and this will be interpreted according to
+*     the attribute's data type.  White space surrounding the value is
+*     only significant for string attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     setting
+*        Pointer to a null-terminated string specifying the new
+*        attribute value.
+*/
+
+/* Local Variables: */
+   AstPointList *this;            /* Pointer to the PointList structure */
+   int len;                      /* Length of setting string */
+   int nc;                       /* Number of characters read by astSscanf */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the PointList structure. */
+   this = (AstPointList *) this_object;
+
+/* Obtain the length of the setting string. */
+   len = (int) strlen( setting );
+
+/* Test for each recognised attribute in turn, using "astSscanf" to parse
+   the setting string and extract the attribute value (or an offset to
+   it in the case of string values). In each case, use the value set
+   in "nc" to check that the entire string was matched. Once a value
+   has been obtained, use the appropriate method to set it. */
+
+/* Define a macro to see if the setting string matches any of the
+   read-only attributes of this class. */
+#define MATCH(attrib) \
+        ( nc = 0, ( 0 == astSscanf( setting, attrib "=%*[^\n]%n", &nc ) ) && \
+                  ( nc >= len ) )
+
+/* Use this macro to report an error if a read-only attribute has been
+   specified. */
+   if ( MATCH( "listsize" ) ) {
+      astError( AST__NOWRT, "astSet: The setting \"%s\" is invalid for a %s.",
+                status, setting, astGetClass( this ) );
+      astError( AST__NOWRT, "This is a read-only attribute." , status );
+
+/* If the attribute is still not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      (*parent_setattrib)( this_object, setting, status );
+   }
+
+/* Undefine macros local to this function. */
+#undef MATCH
+}
+
+static AstMapping *Simplify( AstMapping *this_mapping, int *status ) {
+/*
+*  Name:
+*     Simplify
+
+*  Purpose:
+*     Simplify the Mapping represented by a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     AstMapping *Simplify( AstMapping *this, int *status )
+
+*  Class Membership:
+*     PointList 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 *fr;                 /* Pointer to encapsulated Frame */
+   AstMapping *map;              /* Pointer to frameset Mapping */
+   AstMapping *result;           /* Result pointer to return */
+   AstPointList *new2;           /* Pointer to simplified Region */
+   AstPointSet *pset1;           /* Original base Frame positions */
+   AstPointSet *pset2;           /* Current Frame Frame positions */
+   AstRegion *new;               /* Pointer to simplified Region */
+   AstRegion *this;              /* Pointer to original Region structure */
+   AstRegion *unc;               /* Pointer to new uncertainty Region */
+   double **ptr2;                /* Pointer to current Frame points */
+   int simpler;                  /* Has some simplication taken place? */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the 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 );
+
+/* Note if any simplification took place. This is assumed to be the case
+   if the pointer returned by the above call is different to the supplied
+   pointer. */
+   simpler = ( new != this );
+
+/* Get the Mapping from base to current Frame. We can modify the PointList so
+   that a UnitMap can be used. This is good because it means that the
+   serialised PointList is simpler since the Dump function only needs to
+   record one Frame instead of the whole FrameSet. */
+   map = astGetMapping( new->frameset, AST__BASE, AST__CURRENT );
+   if( !astIsAUnitMap( map ) ){
+
+/* Get a pointer to the current Region Frame */
+      fr = astGetFrame( this->frameset, AST__CURRENT );
+
+/* Get the PointSet which holds the base Frame positions defining this
+   PointList. */
+      pset1 = this->points;
+
+/* Transform the PointSet using this Mapping. */
+      pset2 = astTransform( map, pset1, 1, NULL );
+      ptr2 = astGetPoints( pset2 );
+
+/* Get the Region describing the positional uncertainty within the
+   supplied PointList, in its current Frame. */
+      unc = astGetUncFrm( new, AST__CURRENT );
+
+/* Create a new PointList, and use it in place of the original. */
+      new2 = astPointList( fr, pset2, unc, "", status );
+      (void) astAnnul( new );
+      new = (AstRegion *) new2;
+      simpler = 1;
+
+/* Free resources. */
+      fr = astAnnul( fr );
+      pset2 = astAnnul( pset2 );
+      unc = astAnnul( unc );
+   }
+
+/* Free resources. */
+   map = astAnnul( map );
+
+/* If any simplification could be performed, copy Region attributes from
+   the supplied Region to the returned Region, and return a pointer to it.
+   If the supplied Region had no uncertainty, ensure the returned Region
+   has no uncertainty. Otherwise, return a clone of the supplied pointer. */
+   if( simpler ){
+      astRegOverlay( new, this, 1 );
+      result = (AstMapping *) new;
+
+   } else {
+      new = astAnnul( new );
+      result = astClone( this );
+   }
+
+/* If an error occurred, annul the returned pointer. */
+   if ( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static int TestAttrib( AstObject *this_object, const char *attrib,
+                       int *status ) {
+/*
+*  Name:
+*     TestAttrib
+
+*  Purpose:
+*     Test if a specified attribute value is set for a PointList.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     int TestAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astTestAttrib protected
+*     method inherited from the Object class).
+
+*  Description:
+*     This function returns a boolean result (0 or 1) to indicate
+*     whether a value has been set for one of a PointList's attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     attrib
+*        Pointer to a null-terminated string specifying the attribute
+*        name.  This should be in lower case with no surrounding white
+*        space.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     One if a value has been set, otherwise zero.
+
+*  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: */
+   AstPointList *this;            /* Pointer to the PointList structure */
+   int result;                   /* Result value to return */
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the PointList structure. */
+   this = (AstPointList *) this_object;
+
+/* Check the attribute name and test the appropriate attribute. */
+
+/* Test if the name matches any of the read-only attributes of this
+   class. If it does, then return zero. */
+   if ( !strcmp( attrib, "listsize" ) ){
+      result = 0;
+
+/* If the attribute is still not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      result = (*parent_testattrib)( this_object, attrib, status );
+   }
+
+/* Return the result, */
+   return result;
+}
+
+static AstPointSet *Transform( AstMapping *this_mapping, AstPointSet *in,
+                               int forward, AstPointSet *out, int *status ) {
+/*
+*  Name:
+*     Transform
+
+*  Purpose:
+*     Apply a PointList to transform a set of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+*                             int forward, AstPointSet *out, int *status )
+
+*  Class Membership:
+*     PointList member function (over-rides the astTransform protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function takes a PointList 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 covered by the
+*     PointList. PointList inside the region are copied unchanged from input
+*     to output.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList.
+*     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 PointList.
+*     -  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 *in_base;         /* Pointer to PointSet holding base Frame positions*/
+   AstPointSet *ps1;             /* Pointer to accumulation PointSet */
+   AstPointSet *ps2;             /* Pointer to accumulation PointSet */
+   AstPointSet *ps3;             /* Pointer for swapping PointSet pointers */
+   AstPointSet *pset_base;       /* PointList positions in "unc" base Frame */
+   AstPointSet *pset_reg;        /* Pointer to Region PointSet */
+   AstPointSet *result;          /* Pointer to output PointSet */
+   AstRegion *this;              /* Pointer to the Region structure */
+   AstRegion *unc;               /* Pointer to uncertainty Region */
+   double **ptr1;                /* Pointer to mask pointer array */
+   double **ptr_base;            /* Pointer to axis values for "pset_base" */
+   double **ptr_out;             /* Pointer to output coordinate data */
+   double *cen_orig;             /* Pointer to array holding original centre coords */
+   double *mask;                 /* Pointer to mask axis values */
+   int coord;                    /* Zero-based index for coordinates */
+   int ncoord_base;              /* No. of coordinates per base Frame point */
+   int ncoord_out;               /* No. of coordinates per output point */
+   int npoint;                   /* No. of supplied input test points */
+   int nrp;                      /* No. of points in Region PointSet */
+   int point;                    /* Loop counter for points */
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Avoid -Wall compiler warnings. */
+   ps1 = NULL;
+   ps2 = NULL;
+
+/* Obtain a pointer to the Region structure. */
+   this = (AstRegion *) 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. */
+
+/* First use the encapsulated FrameSet to transform the supplied positions
+   from the current Frame in the encapsulated FrameSet (the Frame
+   represented by the Region), to the base Frame (the Frame in which the
+   Region is defined). */
+   in_base = astRegTransform( this, in, 0, NULL, NULL );
+
+/* The PointSet pointer returned above may be a clone of the "in"
+   pointer. If so take a copy of the PointSet so we can change it safely. */
+   if( in_base == in ) {
+      ps3 = astCopy( in_base );
+      (void) astAnnul( in_base );
+      in_base = ps3;
+      ps3 = NULL;
+   }
+
+/* Determine the numbers of points and coordinates per point from the base
+   Frame PointSet and obtain pointers for accessing the base Frame and output
+   coordinate values. */
+   npoint = astGetNpoint( in_base );
+   ncoord_base = astGetNcoord( in_base );
+   ncoord_out = astGetNcoord( result );
+   ptr_out = astGetPoints( result );
+
+/* Get the axis values for the PointSet which defines the location and
+   extent of the region in the base Frame, and check them. */
+   pset_reg = this->points;
+   nrp = astGetNpoint( pset_reg );
+   if( astGetNcoord( pset_reg ) != ncoord_base && astOK ) {
+      astError( AST__INTER, "astTransform(PointList): Illegal number of "
+                "coords (%d) in the Region - should be %d "
+                "(internal AST programming error).", status, astGetNcoord( pset_reg ),
+                ncoord_base );
+   }
+
+/* Get the base Frame uncertainty Region. Temporarily set its negated flag. */
+   unc = astGetUncFrm( this, AST__BASE );
+   astSetNegated( unc, 1 );
+
+/* Transform the PointList PointSet into the base Frame of the uncertainty
+   Region, and get pointers to the corresponding axis value. */
+   pset_base = astRegTransform( unc, pset_reg, 0, NULL, NULL );
+   ptr_base = astGetPoints( pset_base );
+
+/* Perform coordinate arithmetic. */
+/* ------------------------------ */
+   if ( astOK ) {
+
+/* Save the original base Frame centre coords of the uncertainty Region. */
+      cen_orig = astRegCentre( unc, NULL, NULL, 0, AST__BASE );
+
+/* We use the PointSet created above as the initial input to astTransform
+   below. Also indicate we currently have no output PointSet. This will
+   cause a new PointSet to be created on the first pass through the loop
+   below. */
+      ps1 = astClone( in_base );
+      ps2 = NULL;
+
+/* Loop round all the points in the PointList. */
+      for ( point = 0; point < nrp; point++ ) {
+
+/* Centre the uncertainty Region at this PointList position. Note, the
+   base Frame of the PointList should be the same as the current Frame
+   of the uncertainty Region. */
+         astRegCentre( unc, NULL, ptr_base, point, AST__BASE );
+
+/* Use the uncertainty Region to transform the supplied PointSet. This
+   will set supplied points bad if they are within the uncertainty Region
+   (since the uncertainty Region has been negated above). */
+         ps2 = astTransform( unc, ps1, 0, ps2 );
+
+/* Use the output PointSet created above as the input for the next
+   position. This causes bad points to be accumulated in the output
+   PointSet. */
+         ps3 = ps2;
+         ps2 = ps1;
+         ps1 = ps3;
+
+      }
+
+/* Re-instate the original centre coords of the uncertainty Region. */
+      astRegCentre( unc, cen_orig, NULL, 0, AST__BASE );
+      cen_orig = astFree( cen_orig );
+
+/* The ps1 PointSet will now be a copy of the supplied PointSet but with
+   positions set to bad if they are inside any of the re-centred uncertainty
+   Regions.  If this PointList has been negated, this is what we want so
+   we just transfer this bad position mask to the result PointSet. If this
+   PointList has not been negated we need to invert the bad position
+   mask. Get a pointer to the first axis of the resulting PointSet. */
+      ptr1 = astGetPoints( ps1 );
+      if( astOK ) {
+         mask = ptr1[ 0 ];
+
+/* Apply the mask to the returned PointSet, inverted if necessary. */
+         if( astGetNegated( this ) ) {
+            for ( point = 0; point < npoint; point++, mask++ ) {
+               if( *mask == AST__BAD ) {
+                  for( coord = 0; coord < ncoord_out; coord++ ) {
+                     ptr_out[ coord ][ point ] = AST__BAD;
+                  }
+               }
+            }
+
+         } else {
+            for ( point = 0; point < npoint; point++, mask++ ) {
+               if( *mask != AST__BAD ) {
+                  for( coord = 0; coord < ncoord_out; coord++ ) {
+                     ptr_out[ coord ][ point ] = AST__BAD;
+                  }
+               }
+            }
+         }
+      }
+   }
+
+/* Clear the negated flag for the uncertainty Region. */
+   astClearNegated( unc );
+
+/* Free resources */
+   in_base = astAnnul( in_base );
+   pset_base = astAnnul( pset_base );
+   unc = astAnnul( unc );
+   if( ps2 ) ps2 = astAnnul( ps2 );
+   if( ps1 ) ps1 = astAnnul( ps1 );
+
+/* 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). */
+
+/*
+*att++
+*  Name:
+*     ListSize
+
+*  Purpose:
+*     Number of points in a PointList.
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Integer, read-only.
+
+*  Description:
+*     This is a read-only attribute giving the number of points in a
+*     PointList. This value is determined when the PointList is created.
+
+*  Applicability:
+*     PointList
+*        All PointLists have this attribute.
+*att--
+*/
+
+
+/* Copy constructor. */
+/* ----------------- */
+static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
+/*
+*  Name:
+*     Copy
+
+*  Purpose:
+*     Copy constructor for PointList objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Copy( const AstObject *objin, AstObject *objout, int *status )
+
+*  Description:
+*     This function implements the copy constructor for PointList objects.
+
+*  Parameters:
+*     objin
+*        Pointer to the object to be copied.
+*     objout
+*        Pointer to the object being constructed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     -  This constructor makes a deep copy.
+*/
+
+/* Local Variables: */
+   AstPointList *in;             /* Pointer to input PointList */
+   AstPointList *out;            /* Pointer to output PointList */
+   int nb;                       /* Number of bytes */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain pointers to the input and output PointLists. */
+   in = (AstPointList *) objin;
+   out = (AstPointList *) objout;
+
+/* For safety, first clear any references to the input memory from
+   the output PointList. */
+   out->lbnd = NULL;
+   out->ubnd = NULL;
+
+/* Copy dynamic memory contents */
+   if( in->lbnd && in->ubnd ) {
+      nb = sizeof( double )*astGetNaxes( in );
+      out->lbnd = astStore( NULL, in->lbnd, nb );
+      out->ubnd = astStore( NULL, in->ubnd, nb );
+   }
+}
+
+
+/* Destructor. */
+/* ----------- */
+static void Delete( AstObject *obj, int *status ) {
+/*
+*  Name:
+*     Delete
+
+*  Purpose:
+*     Destructor for PointList objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Delete( AstObject *obj, int *status )
+
+*  Description:
+*     This function implements the destructor for PointList objects.
+
+*  Parameters:
+*     obj
+*        Pointer to the object to be deleted.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     This function attempts to execute even if the global error status is
+*     set.
+*/
+
+/* Local Variables: */
+   AstPointList *this;                 /* Pointer to PointList */
+
+/* Obtain a pointer to the PointList structure. */
+   this = (AstPointList *) obj;
+
+/* Annul all resources. */
+   this->lbnd = astFree( this->lbnd );
+   this->ubnd = astFree( this->ubnd );
+}
+
+/* Dump function. */
+/* -------------- */
+static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
+/*
+*  Name:
+*     Dump
+
+*  Purpose:
+*     Dump function for PointList 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 PointList class to an output Channel.
+
+*  Parameters:
+*     this
+*        Pointer to the PointList 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: */
+   AstPointList *this;                 /* Pointer to the PointList structure */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the PointList structure. */
+   this = (AstPointList *) this_object;
+
+/* Write out values representing the instance variables for the
+   PointList 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. */
+
+}
+
+/* Standard class functions. */
+/* ========================= */
+/* Implement the astIsAPointList and astCheckPointList functions using the macros
+   defined for this purpose in the "object.h" header file. */
+astMAKE_ISA(PointList,Region)
+astMAKE_CHECK(PointList)
+
+AstPointList *astPointList_( void *frame_void, AstPointSet *points,
+                             AstRegion *unc, const char *options,
+                             int *status, ...) {
+/*
+*+
+*  Name:
+*     astPointList
+
+*  Purpose:
+*     Create a PointList.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     AstPointList *astPointList( AstFrame *frame, AstPointSet *points,
+*                                 AstRegion *unc, const char *options,
+*                                 int *status, ...) {
+
+*  Class Membership:
+*     PointList constructor.
+
+*  Description:
+*     This function implements the protected interface to the astPointList
+*     constructor function, returning a true C pointer. The parameter list
+*     differs from the public constructor, in that the positions are
+*     defined by a PointSet rather than an array of doubles.
+
+*  Parameters:
+*     frame
+*        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.
+*     points
+*        A PointSet holding the physical coordinates of the points.
+*     unc
+*        An optional pointer to an existing Region which specifies the
+*        uncertainties associated with each point in the PointList being
+*        created. The uncertainty at any point in the PointList 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 Box. Alternatively, a NULL Object pointer
+*        may be supplied, in which case a default uncertainty is used
+*        equivalent to a box 1.0E-6 of the size of the bounding box of the
+*        PointList being created.
+*
+*        The uncertainty Region has two uses: 1) when the astOverlap
+*        function compares two Regions for equality the uncertainty Region
+*        is used to determine the tolerance on the comparison, and 2)
+*        when a Region is mapped into a different coordinate system and
+*        subsequently simplified (using astSimplify), the uncertainties are
+*        used to determine if the transformed boundary can be accurately
+*        represented by a specific shape of Region.
+*     options
+*        Pointer to a null-terminated string containing an optional
+*        comma-separated list of attribute assignments to be used for
+*        initialising the new PointList. The syntax used is identical to
+*        that for the astSet function and may include "printf" format
+*        specifiers identified by "%" symbols in the normal way.
+*     status
+*        Pointer to the inherited status value.
+*     ...
+*        If the "options" string contains "%" format specifiers, then
+*        an optional list of additional arguments may follow it in
+*        order to supply values to be substituted for these
+*        specifiers. The rules for supplying these are identical to
+*        those for the astSet function (and for the C "printf"
+*        function).
+
+*  Returned Value:
+*     A pointer to the new PointList.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstFrame *frame;              /* Pointer to Frame structure */
+   AstPointList *new;            /* Pointer to new PointList */
+   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 PointList, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitPointList( NULL, sizeof( AstPointList ), !class_init,
+                           &class_vtab, "PointList", frame, points, 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 PointList'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 PointList. */
+   return new;
+}
+
+AstPointList *astPointListId_( void *frame_void, int npnt, int ncoord, int dim,
+                               const double *points, void *unc_void,
+                               const char *options, ... ) {
+/*
+*++
+*  Name:
+c     astPointList
+f     AST_POINTLIST
+
+*  Purpose:
+*     Create a PointList.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "pointlist.h"
+c     AstPointList *astPointList( AstFrame *frame, int npnt, int ncoord, int dim,
+c                                 const double *points, AstRegion *unc,
+c                                 const char *options, ... )
+f     RESULT = AST_POINTLIST( FRAME, NPNT, COORD, DIM, POINTS, UNC, OPTIONS, STATUS )
+
+*  Class Membership:
+*     PointList constructor.
+
+*  Description:
+*     This function creates a new PointList object and optionally initialises
+*     its attributes.
+*
+*     A PointList object is a specialised type of Region which represents a
+*     collection of points in a coordinate Frame.
+
+*  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     npnt
+f     NPNT = INTEGER (Given)
+*        The number of points in the Region.
+c     ncoord
+f     NCOORD = INTEGER (Given)
+*        The number of coordinates being supplied for each point. This
+*        must equal the number of axes in the supplied Frame, given by
+*        its Naxes attribute.
+c     dim
+f     DIM = INTEGER (Given)
+c        The number of elements along the second dimension of the "points"
+f        The number of elements along the first dimension of the POINTS
+*        array (which contains the point coordinates). This value is
+*        required so that the coordinate values can be correctly
+*        located if they do not entirely fill this array. The value
+c        given should not be less than "npnt".
+f        given should not be less than NPNT.
+c     points
+f     POINTS( DIM, NCOORD ) = DOUBLE PRECISION (Given)
+c        The address of the first element of a 2-dimensional array of
+c        shape "[ncoord][dim]" giving the physical coordinates of the
+c        points. These should be stored such that the value of coordinate
+c        number "coord" for point number "pnt" is found in element
+c        "in[coord][pnt]".
+f        A 2-dimensional array giving the physical coordinates of the
+f        points. These should be stored such that the value of coordinate
+f        number COORD for point number PNT is found in element IN(PNT,COORD).
+c     unc
+f     UNC = INTEGER (Given)
+*        An optional pointer to an existing Region which specifies the uncertainties
+*        associated with each point in the PointList being created. The
+*        uncertainty at any point in the PointList 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 Box. Alternatively,
+f        a null Object pointer (AST__NULL)
+c        a NULL Object pointer
+*        may be supplied, in which case a default uncertainty is used
+*        equivalent to a box 1.0E-6 of the size of the bounding box of the
+*        PointList being created.
+*
+*        The uncertainty Region has two uses: 1) when the
+c        astOverlap
+f        AST_OVERLAP
+*        function compares two Regions for equality the uncertainty
+*        Region is used to determine the tolerance on the comparison, and 2)
+*        when a Region is mapped into a different coordinate system and
+*        subsequently simplified (using
+c        astSimplify),
+f        AST_SIMPLIFY),
+*        the uncertainties are used to determine if the transformed boundary
+*        can be accurately represented by a specific shape of Region.
+c     options
+f     OPTIONS = CHARACTER * ( * ) (Given)
+c        Pointer to a null-terminated string containing an optional
+c        comma-separated list of attribute assignments to be used for
+c        initialising the new PointList. 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 PointList. 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     astPointList()
+f     AST_POINTLIST = INTEGER
+*        A pointer to the new PointList.
+
+*  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: */
+   AstFrame *frame;          /* Pointer to Frame structure */
+   AstPointList *new;        /* Pointer to new PointList */
+   AstPointSet *pset;        /* Pointer to PointSet holding points */
+   AstRegion *unc;           /* Pointer to Region structure */
+   astDECLARE_GLOBALS        /* Pointer to thread-specific global data */
+   const double *q;          /* Pointer to next supplied axis value */
+   double **ptr;             /* Pointer to data in pset */
+   double *p;                /* Pointer to next PointSet axis value */
+   int *status;              /* Pointer to inherited status value */
+   int i;                    /* Axis index */
+   int j;                    /* Point index */
+   va_list args;             /* Variable argument list */
+
+/* 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 a Frame pointer from the supplied ID and validate the
+   pointer to ensure it identifies a valid Frame. */
+   frame = astVerifyFrame( astMakePointer( frame_void ) );
+
+/* Create a PointSet and store the supplied points in it. */
+   pset = astPointSet( npnt, ncoord , "", status );
+   ptr = astGetPoints( pset );
+   if( astOK ) {
+      for( i = 0; i < ncoord; i++ ) {
+         p = ptr[ i ];
+         q = points + i*dim;
+         for( j = 0; j < npnt; j++ ) *(p++) = *(q++);
+      }
+   }
+
+/* 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 PointList, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitPointList( NULL, sizeof( AstPointList ), !class_init,
+                           &class_vtab, "PointList", frame, pset, 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 PointList'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 );
+   }
+
+/* Free resources. */
+   pset = astAnnul( pset );
+
+/* Return an ID value for the new PointList. */
+   return astMakeId( new );
+}
+
+AstPointList *astInitPointList_( void *mem, size_t size, int init,
+                                 AstPointListVtab *vtab, const char *name,
+                                 AstFrame *frame, AstPointSet *points,
+                                 AstRegion *unc, int *status ) {
+/*
+*+
+*  Name:
+*     astInitPointList
+
+*  Purpose:
+*     Initialise a PointList.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     AstPointList *astInitPointList( void *mem, size_t size, int init,
+*                                     AstPointListVtab *vtab, const char *name,
+*                                     AstFrame *frame, AstPointSet *points,
+*                                     AstRegion *unc, int *status )
+
+*  Class Membership:
+*     PointList initialiser.
+
+*  Description:
+*     This function is provided for use by class implementations to initialise
+*     a new PointList object. It allocates memory (if necessary) to accommodate
+*     the PointList plus any additional data associated with the derived class.
+*     It then initialises a PointList 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 PointList at the start of the memory passed via the
+*     "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory in which the PointList is to be initialised.
+*        This must be of sufficient size to accommodate the PointList data
+*        (sizeof(PointList)) 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 PointList (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 PointList
+*        structure, so a valid value must be supplied even if not required for
+*        allocating memory.
+*     init
+*        A logical flag indicating if the PointList'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 PointList.
+*     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.
+*     points
+*        A PointSet containing the Points for the PointList.
+*     unc
+*        A pointer to a Region which specifies the uncertainty in the
+*        supplied positions (all points in the new PointList being
+*        initialised are assumed to have the same uncertainty). A NULL
+*        pointer can be supplied, in which case default uncertainties equal
+*        to 1.0E-6 of the dimensions of the new PointList's bounding box are
+*        used. If an uncertainty Region is supplied, it must be either a Box,
+*        a Circle or an Ellipse, and its encapsulated Frame must be related
+*        to the Frame supplied for parameter "frame" (i.e. astConvert
+*        should be able to find a Mapping between them). Two positions
+*        the "frame" Frame are considered to be co-incident if their
+*        uncertainty Regions overlap. The centre of the supplied
+*        uncertainty Region is immaterial since it will be re-centred on the
+*        point being tested before use. A deep copy is taken of the supplied
+*        Region.
+
+*  Returned Value:
+*     A pointer to the new PointList.
+
+*  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: */
+   AstPointList *new;        /* Pointer to new PointList */
+   int ncoord;               /* No. of axes in PointSet */
+   int nin;                  /* No. of axes in Frame */
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* If necessary, initialise the virtual function table. */
+   if ( init ) astInitPointListVtab( vtab, name );
+
+/* Initialise. */
+   new = NULL;
+
+/* Check the number of axis values per position is correct. */
+   nin = astGetNaxes( frame );
+   ncoord = astGetNcoord( points );
+   if( nin != ncoord ) {
+      astError( AST__NCPIN, "astInitPointList(): Bad number of coordinate "
+                "values (%d).", status, ncoord );
+      astError( AST__NCPIN, "The %s given requires %d coordinate value(s) for "
+                "each input point.", status, astGetClass( frame ), nin );
+   }
+
+/* Initialise a Region structure (the parent class) as the first component
+   within the PointList structure, allocating memory if necessary. */
+   if( astOK ) {
+      new = (AstPointList *) astInitRegion( mem, size, 0, (AstRegionVtab *) vtab,
+                                            name, frame, points, unc );
+      if ( astOK ) {
+
+/* Initialise the PointList data. */
+/* ------------------------------ */
+         new->lbnd = NULL;
+         new->ubnd = NULL;
+
+/* If an error occurred, clean up by deleting the new PointList. */
+         if ( !astOK ) new = astDelete( new );
+      }
+   }
+
+/* Return a pointer to the new PointList. */
+   return new;
+}
+
+AstPointList *astLoadPointList_( void *mem, size_t size, AstPointListVtab *vtab,
+                                 const char *name, AstChannel *channel, int *status ) {
+/*
+*+
+*  Name:
+*     astLoadPointList
+
+*  Purpose:
+*     Load a PointList.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pointlist.h"
+*     AstPointList *astLoadPointList( void *mem, size_t size, AstPointListVtab *vtab,
+*                                     const char *name, AstChannel *channel )
+
+*  Class Membership:
+*     PointList loader.
+
+*  Description:
+*     This function is provided to load a new PointList 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
+*     PointList 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 PointList at the start of the memory
+*     passed via the "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory into which the PointList is to be
+*        loaded.  This must be of sufficient size to accommodate the
+*        PointList data (sizeof(PointList)) 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 PointList (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 PointList 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(AstPointList) is used instead.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new PointList. If this is NULL, a pointer
+*        to the (static) virtual function table for the PointList 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 "PointList" is used instead.
+
+*  Returned Value:
+*     A pointer to the new PointList.
+
+*  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 */
+   AstPointList *new;              /* Pointer to the new PointList */
+
+/* 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 PointList. In this case the
+   PointList belongs to this class, so supply appropriate values to be
+   passed to the parent class loader (and its parent, etc.). */
+   if ( !vtab ) {
+      size = sizeof( AstPointList );
+      vtab = &class_vtab;
+      name = "PointList";
+
+/* If required, initialise the virtual function table for this class. */
+      if ( !class_init ) {
+         astInitPointListVtab( 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 PointList. */
+   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, "PointList" );
+
+/* 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. */
+
+/* If an error occurred, clean up by deleting the new PointList. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return the new PointList 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. */
+
+int astGetListSize_( AstPointList *this, int *status ) {
+   if ( !astOK ) return 0;
+   return (**astMEMBER(this,PointList,GetListSize))( this, status );
+}
+void astPointListPoints_( AstPointList *this, AstPointSet **pset, int *status) {
+   if ( !astOK ) return;
+   (**astMEMBER(this,PointList,PointListPoints))( this, pset, status );
+   return;
+}
+