Merge commit 'd26ed8388f100a12996c0b92a98040ef2ba7fa8e' as 'ast'

1 files changed, 3218 insertions, 0 deletions

diff --git a/ast/pcdmap.c b/ast/pcdmap.c
new file mode 100644
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+++ b/ast/pcdmap.c
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+/*
+*class++
+*  Name:
+*     PcdMap
+
+*  Purpose:
+*     Apply 2-dimensional pincushion/barrel distortion.
+
+*  Constructor Function:
+c     astPcdMap
+f     AST_PCDMAP
+
+*  Description:
+*     A PcdMap is a non-linear Mapping which transforms 2-dimensional
+*     positions to correct for the radial distortion introduced by some
+*     cameras and telescopes. This can take the form either of pincushion
+*     or barrel distortion, and is characterized by a single distortion
+*     coefficient.
+*
+*     A PcdMap is specified by giving this distortion coefficient and the
+*     coordinates of the centre of the radial distortion. The forward
+*     transformation of a PcdMap applies the distortion:
+*
+*        RD = R * ( 1 + C * R * R )
+*
+*     where R is the undistorted radial distance from the distortion
+*     centre (specified by attribute PcdCen), RD is the radial distance
+*     from the same centre in the presence of distortion, and C is the
+*     distortion coefficient (given by attribute Disco).
+*
+*     The inverse transformation of a PcdMap removes the distortion
+*     produced by the forward transformation. The expression used to derive
+*     R from RD is an approximate inverse of the expression above.
+
+*  Inheritance:
+*     The PcdMap class inherits from the Mapping class.
+
+*  Attributes:
+*     In addition to those attributes common to all Mappings, every
+*     PcdMap also has the following attributes:
+*
+*     - Disco: PcdMap pincushion/barrel distortion coefficient
+*     - PcdCen(axis): Centre coordinates of pincushion/barrel distortion
+
+*  Functions:
+c     The PcdMap class does not define any new functions beyond those
+f     The PcdMap class does not define any new routines beyond those
+*     which are applicable to all Mappings.
+
+*  Copyright:
+*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
+*     Research Councils
+
+*  Licence:
+*     This program is free software: you can redistribute it and/or
+*     modify it under the terms of the GNU Lesser General Public
+*     License as published by the Free Software Foundation, either
+*     version 3 of the License, or (at your option) any later
+*     version.
+*
+*     This program is distributed in the hope that it will be useful,
+*     but WITHOUT ANY WARRANTY; without even the implied warranty of
+*     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*     GNU Lesser General Public License for more details.
+*
+*     You should have received a copy of the GNU Lesser General
+*     License along with this program.  If not, see
+*     <http://www.gnu.org/licenses/>.
+
+*  Authors:
+*     DSB: David Berry (Starlink)
+
+*  History:
+*     18-MAY-1999 (DSB):
+*        Original version.
+*     25-OCT-1999 (DSB):
+*        Fixed memory leak in MapMerge.
+*     8-JAN-2003 (DSB):
+*        Changed private InitVtab method to protected astInitPcdMapVtab
+*        method.
+*     23-AUG-2006 (DSB):
+*        Override astEqual.
+*     23-APR-2015 (DSB):
+*        Improve MapMerge. If a PcdMap can merge with its next-but-one
+*        neighbour, then swap the PcdMap with its neighbour, so that
+*        it is then next its next-but-one neighbour, and then merge the
+*        two Mappings into a single Mapping. Previously, only the swap
+*        was performed - not the merger. And the swap was only performed
+*        if the intervening neighbour could not itself merge. This could
+*        result in an infinite simplification loop, which was detected by
+*        CmpMap and and aborted, resulting in no useful simplification.
+*class--
+*/
+
+/* Module Macros. */
+/* ============== */
+/* Set the name of the class we are implementing. This indicates to
+   the header files that define class interfaces that they should make
+   "protected" symbols available. */
+#define astCLASS PcdMap
+
+/* Include files. */
+/* ============== */
+/* Interface definitions. */
+/* ---------------------- */
+
+#include "globals.h"             /* Thread-safe global data access */
+#include "error.h"               /* Error reporting facilities */
+#include "memory.h"              /* Memory management facilities */
+#include "globals.h"             /* Thread-safe global data access */
+#include "object.h"              /* Base Object class */
+#include "pointset.h"            /* Sets of points/coordinates */
+#include "unitmap.h"             /* Unit mappings */
+#include "zoommap.h"             /* Zoom mappings */
+#include "permmap.h"             /* Axis permutations */
+#include "mapping.h"             /* Coordinate mappings (parent class) */
+#include "channel.h"             /* I/O channels */
+#include "pcdmap.h"              /* Interface definition for this class */
+
+/* Error code definitions. */
+/* ----------------------- */
+#include "ast_err.h"             /* AST error codes */
+
+/* C header files. */
+/* --------------- */
+#include <float.h>
+#include <math.h>
+#include <stdarg.h>
+#include <stddef.h>
+#include <stdio.h>
+#include <string.h>
+
+/* Module Variables. */
+/* ================= */
+
+/* Address of this static variable is used as a unique identifier for
+   member of this class. */
+static int class_check;
+
+/* Pointers to parent class methods which are extended by this class. */
+static AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static const char *(* parent_getattrib)( AstObject *, const char *, 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 * );
+
+/* Define macros for accessing each item of thread specific global data. */
+#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(PcdMap)
+
+/* Define macros for accessing each item of thread specific global data. */
+#define class_init astGLOBAL(PcdMap,Class_Init)
+#define class_vtab astGLOBAL(PcdMap,Class_Vtab)
+#define getattrib_buff astGLOBAL(PcdMap,GetAttrib_Buff)
+
+
+
+/* If thread safety is not needed, declare and initialise globals at static
+   variables. */
+#else
+
+static char getattrib_buff[ 101 ];
+
+
+/* Define the class virtual function table and its initialisation flag
+   as static variables. */
+static AstPcdMapVtab 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. */
+AstPcdMap *astPcdMapId_( double, const double [2], const char *, ... );
+
+/* Prototypes for Private Member Functions. */
+/* ======================================== */
+
+static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static const char *GetAttrib( AstObject *, const char *, int * );
+static double GetDisco( AstPcdMap *, int * );
+static double GetPcdCen( AstPcdMap *, int, int * );
+static int CanMerge( AstMapping *, AstMapping *, int, int, int * );
+static int CanSwap( AstMapping *, AstMapping *, int, int, int * );
+static int Equal( AstObject *, AstObject *, int * );
+static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
+static int TestAttrib( AstObject *, const char *, int * );
+static int TestDisco( AstPcdMap *, int * );
+static int TestPcdCen( AstPcdMap *, int, int * );
+static void ClearAttrib( AstObject *, const char *, int * );
+static void ClearDisco( AstPcdMap *, int * );
+static void ClearPcdCen( AstPcdMap *, int, int * );
+static void Dump( AstObject *, AstChannel *, int * );
+static void PcdPerm( AstMapping **, int *, int, int * );
+static void PcdZoom( AstMapping **, int *, int, int * );
+static void PermGet( AstPermMap *, int **, int **, double **, int * );
+static void SetAttrib( AstObject *, const char *, int * );
+static void SetDisco( AstPcdMap *, double, int * );
+static void SetPcdCen( AstPcdMap *, int, double, int * );
+
+/* Function Macros */
+/* =============== */
+/* Macros which return the maximum and minimum of two values. */
+#define MAX(aa,bb) ((aa)>(bb)?(aa):(bb))
+#define MIN(aa,bb) ((aa)<(bb)?(aa):(bb))
+
+/* Macro to check for equality of floating point values. We cannot
+compare bad values directory because of the danger of floating point
+exceptions, so bad values are dealt with explicitly. */
+#define EQUAL(aa,bb) (((aa)==AST__BAD)?(((bb)==AST__BAD)?1:0):(((bb)==AST__BAD)?0:(fabs((aa)-(bb))<=1.0E5*MAX((fabs(aa)+fabs(bb))*DBL_EPSILON,DBL_MIN))))
+
+/*
+*
+*  Name:
+*     MAKE_CLEAR
+
+*  Purpose:
+*     Implement a method to clear a single value in a multi-valued attribute.
+
+*  Type:
+*     Private macro.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     MAKE_CLEAR(attr,component,assign,nval)
+
+*  Class Membership:
+*     Defined by the PcdMap class.
+
+*  Description:
+*     This macro expands to an implementation of a private member function of
+*     the form:
+*
+*        static void Clear<Attribute>( AstPcdMap *this, int axis )
+*
+*     and an external interface function of the form:
+*
+*        void astClear<Attribute>_( AstPcdMap *this, int axis )
+*
+*     which implement a method for clearing a single value in a specified
+*     multi-valued attribute for an axis of a PcdMap.
+
+*  Parameters:
+*     attr
+*        The name of the attribute to be cleared, as it appears in the function
+*        name (e.g. PcdCen in "astClearPcdCen").
+*     component
+*        The name of the class structure component that holds the attribute
+*        value.
+*     assign
+*        An expression that evaluates to the value to assign to the component
+*        to clear its value.
+*     nval
+*        Specifies the number of values in the multi-valued attribute. The
+*        "axis" values supplied to the created function should be in the
+*        range zero to (nval - 1).
+
+*  Notes:
+*     -  To avoid problems with some compilers, you should not leave any white
+*     space around the macro arguments.
+*
+*/
+
+/* Define the macro. */
+#define MAKE_CLEAR(attr,component,assign,nval) \
+\
+/* Private member function. */ \
+/* ------------------------ */ \
+static void Clear##attr( AstPcdMap *this, int axis, int *status ) { \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return; \
+\
+/* Validate the axis index. */ \
+   if( axis < 0 || axis >= nval ){ \
+      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
+                #attr " - it should be in the range 1 to %d.", status, \
+                "astClear" #attr, astGetClass( this ), \
+                axis + 1, nval ); \
+\
+/* Report an error if the object has been cloned (i.e. has a reference \
+   count that is greater than one). */ \
+   } else if( astGetRefCount( this ) > 1 ) { \
+      astError( AST__IMMUT, "astClear(%s): The " #attr "attribute of " \
+                "the supplied %s cannot be cleared because the %s has " \
+                "been cloned (programming error).", status, \
+                astGetClass(this), astGetClass(this), astGetClass(this) ); \
+\
+/* Assign the "clear" value. */ \
+   } else { \
+      this->component[ axis ] = (assign); \
+   } \
+} \
+\
+/* External interface. */ \
+/* ------------------- */ \
+void astClear##attr##_( AstPcdMap *this, int axis, int *status ) { \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return; \
+\
+/* Invoke the required method via the virtual function table. */ \
+   (**astMEMBER(this,PcdMap,Clear##attr))( this, axis, status ); \
+}
+
+
+/*
+*
+*  Name:
+*     MAKE_GET
+
+*  Purpose:
+*     Implement a method to get a single value in a multi-valued attribute.
+
+*  Type:
+*     Private macro.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     MAKE_GET(attr,type,bad_value,assign,nval)
+
+*  Class Membership:
+*     Defined by the PcdMap class.
+
+*  Description:
+*     This macro expands to an implementation of a private member function of
+*     the form:
+*
+*        static <Type> Get<Attribute>( AstPcdMap *this, int axis )
+*
+*     and an external interface function of the form:
+*
+*        <Type> astGet<Attribute>_( AstPcdMap *this, int axis )
+*
+*     which implement a method for getting a single value from a specified
+*     multi-valued attribute for an axis of a PcdMap.
+
+*  Parameters:
+*     attr
+*        The name of the attribute whose value is to be obtained, as it
+*        appears in the function name (e.g. PcdCen in "astGetPcdCen").
+*     type
+*        The C type of the attribute.
+*     bad_value
+*        A constant value to return if the global error status is set, or if
+*        the function fails.
+*     assign
+*        An expression that evaluates to the value to be returned. This can
+*        use the string "axis" to represent the zero-based value index.
+*     nval
+*        Specifies the number of values in the multi-valued attribute. The
+*        "axis" values supplied to the created function should be in the
+*        range zero to (nval - 1).
+
+*  Notes:
+*     -  To avoid problems with some compilers, you should not leave any white
+*     space around the macro arguments.
+*
+*/
+
+/* Define the macro. */
+#define MAKE_GET(attr,type,bad_value,assign,nval) \
+\
+/* Private member function. */ \
+/* ------------------------ */ \
+static type Get##attr( AstPcdMap *this, int axis, int *status ) { \
+   type result;                  /* Result to be returned */ \
+\
+/* Initialise */ \
+   result = (bad_value); \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return result; \
+\
+/* Validate the axis index. */ \
+   if( axis < 0 || axis >= nval ){ \
+      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
+                #attr " - it should be in the range 1 to %d.", status, \
+                "astGet" #attr, astGetClass( this ), \
+                axis + 1, nval ); \
+\
+/* Assign the result value. */ \
+   } else { \
+      result = (assign); \
+   } \
+\
+/* Check for errors and clear the result if necessary. */ \
+   if ( !astOK ) result = (bad_value); \
+\
+/* Return the result. */ \
+   return result; \
+} \
+/* External interface. */ \
+/* ------------------- */  \
+type astGet##attr##_( AstPcdMap *this, int axis, int *status ) { \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return (bad_value); \
+\
+/* Invoke the required method via the virtual function table. */ \
+   return (**astMEMBER(this,PcdMap,Get##attr))( this, axis, status ); \
+}
+
+/*
+*
+*  Name:
+*     MAKE_SET
+
+*  Purpose:
+*     Implement a method to set a single value in a multi-valued attribute.
+
+*  Type:
+*     Private macro.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     MAKE_SET(attr,type,component,assign,nval)
+
+*  Class Membership:
+*     Defined by the PcdMap class.
+
+*  Description:
+*     This macro expands to an implementation of a private member function of
+*     the form:
+*
+*        static void Set<Attribute>( AstPcdMap *this, int axis, <Type> value )
+*
+*     and an external interface function of the form:
+*
+*        void astSet<Attribute>_( AstPcdMap *this, int axis, <Type> value )
+*
+*     which implement a method for setting a single value in a specified
+*     multi-valued attribute for a PcdMap.
+
+*  Parameters:
+*      attr
+*         The name of the attribute to be set, as it appears in the function
+*         name (e.g. PcdCen in "astSetPcdCen").
+*      type
+*         The C type of the attribute.
+*      component
+*         The name of the class structure component that holds the attribute
+*         value.
+*      assign
+*         An expression that evaluates to the value to be assigned to the
+*         component.
+*      nval
+*         Specifies the number of values in the multi-valued attribute. The
+*         "axis" values supplied to the created function should be in the
+*         range zero to (nval - 1).
+
+*  Notes:
+*     -  To avoid problems with some compilers, you should not leave any white
+*     space around the macro arguments.
+*-
+*/
+
+/* Define the macro. */
+#define MAKE_SET(attr,type,component,assign,nval) \
+\
+/* Private member function. */ \
+/* ------------------------ */ \
+static void Set##attr( AstPcdMap *this, int axis, type value, int *status ) { \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return; \
+\
+/* Validate the axis index. */ \
+   if( axis < 0 || axis >= nval ){ \
+      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
+                #attr " - it should be in the range 1 to %d.", status, \
+                "astSet" #attr, astGetClass( this ), \
+                axis + 1, nval ); \
+\
+/* Report an error if the object has been cloned (i.e. has a reference \
+   count that is greater than one). */ \
+   } else if( astGetRefCount( this ) > 1 ) { \
+      astError( AST__IMMUT, "astSet(%s): The " #attr "attribute of " \
+                "the supplied %s cannot be changed because the %s has " \
+                "been cloned (programming error).", status, \
+                astGetClass(this), astGetClass(this), astGetClass(this) ); \
+\
+/* Store the new value in the structure component. */ \
+   } else { \
+      this->component[ axis ] = (assign); \
+   } \
+} \
+\
+/* External interface. */ \
+/* ------------------- */ \
+void astSet##attr##_( AstPcdMap *this, int axis, type value, int *status ) { \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return; \
+\
+/* Invoke the required method via the virtual function table. */ \
+   (**astMEMBER(this,PcdMap,Set##attr))( this, axis, value, status ); \
+}
+
+/*
+*
+*  Name:
+*     MAKE_TEST
+
+*  Purpose:
+*     Implement a method to test if a single value has been set in a
+*     multi-valued attribute.
+
+*  Type:
+*     Private macro.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     MAKE_TEST(attr,assign,nval)
+
+*  Class Membership:
+*     Defined by the PcdMap class.
+
+*  Description:
+*     This macro expands to an implementation of a private member function of
+*     the form:
+*
+*        static int Test<Attribute>( AstPcdMap *this, int axis )
+*
+*     and an external interface function of the form:
+*
+*        int astTest<Attribute>_( AstPcdMap *this, int axis )
+*
+*     which implement a method for testing if a single value in a specified
+*     multi-valued attribute has been set for a class.
+
+*  Parameters:
+*      attr
+*         The name of the attribute to be tested, as it appears in the function
+*         name (e.g. PcdCen in "astTestPcdCen").
+*      assign
+*         An expression that evaluates to 0 or 1, to be used as the returned
+*         value. This can use the string "axis" to represent the zero-based
+*         index of the value within the attribute.
+*      nval
+*         Specifies the number of values in the multi-valued attribute. The
+*         "axis" values supplied to the created function should be in the
+*         range zero to (nval - 1).
+
+*  Notes:
+*     -  To avoid problems with some compilers, you should not leave any white
+*     space around the macro arguments.
+*-
+*/
+
+/* Define the macro. */
+#define MAKE_TEST(attr,assign,nval) \
+\
+/* Private member function. */ \
+/* ------------------------ */ \
+static int Test##attr( AstPcdMap *this, int axis, int *status ) { \
+   int result;                   /* Value to return */ \
+\
+/* Initialise */ \
+   result = 0; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return result; \
+\
+\
+/* Validate the axis index. */ \
+   if( axis < 0 || axis >= nval ){ \
+      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
+                #attr " - it should be in the range 1 to %d.", status, \
+                "astTest" #attr, astGetClass( this ), \
+                axis + 1, nval ); \
+\
+/* Assign the result value. */ \
+   } else { \
+      result = (assign); \
+   } \
+\
+/* Check for errors and clear the result if necessary. */ \
+   if ( !astOK ) result = 0; \
+\
+/* Return the result. */ \
+   return result; \
+} \
+/* External interface. */ \
+/* ------------------- */ \
+int astTest##attr##_( AstPcdMap *this, int axis, int *status ) { \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return 0; \
+\
+/* Invoke the required method via the virtual function table. */ \
+   return (**astMEMBER(this,PcdMap,Test##attr))( this, axis, status ); \
+}
+
+/* Member functions. */
+/* ================= */
+static int CanMerge( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status ){
+/*
+*
+*  Name:
+*     CanMerge
+
+*  Purpose:
+*     Checks if two Mappings can be merged.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     int CanMerge( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status )
+
+*  Class Membership:
+*     PcdMap internal utility function.
+
+*  Description:
+*     This function checks the two supplied Mappings to see if they
+*     can be merged into a single Mapping. One of the pair must be a PcdMap.
+
+*  Parameters:
+*     map1
+*        A pointer to the first mapping.
+*     map2
+*        A pointer to the second mapping.
+*     inv1
+*        The invert flag to use with the first mapping.
+*     inv2
+*        The invert flag to use with the second mapping.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     1 if the Mappings can be merged, zero otherwise.
+
+*/
+
+   AstPcdMap  *pcd;          /* Pointer to PcdMap Mapping */
+   AstPcdMap  *pcd2;         /* Pointer to second PcdMap Mapping */
+   AstMapping *nopcd;        /* Pointer to non-PcdMap Mapping */
+   const char *class1;       /* Pointer to map1 class string */
+   const char *class2;       /* Pointer to map2 class string */
+   const char *nopcd_class;  /* Pointer to non-PcdMap class string */
+   int invert[ 2 ];          /* Original invert flags */
+   int ret;                  /* Returned flag */
+
+/* Check the global error status. */
+   if ( !astOK ) return 0;
+
+/* Initialise */
+   ret = 0;
+   pcd = NULL;
+   nopcd = NULL;
+
+/* Temporarily set the Invert attributes of both Mappings to the supplied
+   values. */
+   invert[ 0 ] = astGetInvert( map1 );
+   astSetInvert( map1, inv1 );
+
+   invert[ 1 ] = astGetInvert( map2 );
+   astSetInvert( map2, inv2 );
+
+/* Get the classes of the two mappings. */
+   class1 = astGetClass( map1 );
+   class2 = astGetClass( map2 );
+   if( astOK ){
+
+/* Get pointers to the PcdMap and the non-PcdMap Mapping. */
+      if( !strcmp( class1, "PcdMap" ) ){
+         pcd = (AstPcdMap * ) map1;
+         nopcd = map2;
+         nopcd_class = class2;
+      } else if( !strcmp( class2, "PcdMap" ) ){
+         nopcd = map1;
+         pcd = (AstPcdMap * ) map2;
+         nopcd_class = class1;
+      } else {
+         nopcd_class = "unusable";
+      }
+
+/* The Mappings can merge if the other Mapping is a UnitMap. */
+      if( !strcmp( nopcd_class, "UnitMap" ) ){
+         ret = 1;
+
+/* They can also merge if the other Mapping is also a PcdMap, and is the
+   invert of the other. */
+      } else if( !strcmp( nopcd_class, "PcdMap" ) ){
+         pcd2 = (AstPcdMap *) nopcd;
+
+/* Check the distortion coefficients are equal. */
+         if( EQUAL( astGetDisco( pcd ), astGetDisco( pcd2 ) ) ){
+
+/* Check the axis 0 centres are equal. */
+            if( EQUAL( astGetPcdCen( pcd, 0 ), astGetPcdCen( pcd2, 0 ) ) ){
+
+/* Check the axis 1 centres are equal. */
+               if( EQUAL( astGetPcdCen( pcd, 1 ), astGetPcdCen( pcd2, 1 ) ) ){
+
+/* Check the Invert flags are different. */
+                  if( astGetInvert( pcd ) != astGetInvert( pcd2 ) ){
+
+/* If the Mappings have passed all these tests, they can be merged. */
+                     ret = 1;
+                  }
+               }
+            }
+         }
+      }
+   }
+
+/* Re-instate the original settings of the Invert attributes for the
+   supplied Mappings. */
+   astSetInvert( map1, invert[ 0 ] );
+   astSetInvert( map2, invert[ 1 ] );
+
+/* Return the answer. */
+   return astOK ? ret : 0;
+}
+
+static int CanSwap( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status ){
+/*
+*  Name:
+*     CanSwap
+
+*  Purpose:
+*     Determine if two Mappings could be swapped.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     int CanSwap( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status )
+
+*  Class Membership:
+*     PcdMap member function
+
+*  Description:
+*     This function returns a flag indicating if the pair of supplied
+*     Mappings could be replaced by an equivalent pair of Mappings from the
+*     same classes as the supplied pair, but in reversed order. Each pair
+*     of Mappings is considered to be compounded in series. The supplied
+*     Mappings are not changed in any way.
+
+*  Parameters:
+*     map1
+*        The Mapping to be applied first.
+*     map2
+*        The Mapping to be applied second.
+*     inv1
+*        The invert flag to use with map1. A value of zero causes the forward
+*        mapping to be used, and a non-zero value causes the inverse
+*        mapping to be used.
+*     inv2
+*        The invert flag to use with map2.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     1 if the Mappings could be swapped, 0 otherwise.
+
+*  Notes:
+*     -  One of the supplied pair of Mappings must be a PcdMap.
+*     -  A value of 0 is returned if the two Mappings could be merged into
+*     a single Mapping.
+*     -  A value of 0 is returned if an error has already occurred, or if
+*     this function should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstMapping *nopcd;        /* Pointer to non-PcdMap Mapping */
+   const char *class1;       /* Pointer to map1 class string */
+   const char *class2;       /* Pointer to map2 class string */
+   const char *nopcd_class;  /* Pointer to non-PcdMap class string */
+   double *consts;           /* Pointer to constants array */
+   int *inperm;              /* Pointer to input axis permutation array */
+   int *outperm;             /* Pointer to output axis permutation array */
+   int invert[ 2 ];          /* Original invert flags */
+   int nin;                  /* No. of input coordinates for the PermMap */
+   int nout;                 /* No. of output coordinates for the PermMap */
+   int ret;                  /* Returned flag */
+
+/* Check the global error status. */
+   if ( !astOK ) return 0;
+
+/* Initialise */
+   ret = 0;
+
+/* Temporarily set the Invert attributes of both Mappings to the supplied
+   values. */
+   invert[ 0 ] = astGetInvert( map1 );
+   astSetInvert( map1, inv1 );
+
+   invert[ 1 ] = astGetInvert( map2 );
+   astSetInvert( map2, inv2 );
+
+/* Get the classes of the two mappings. */
+   class1 = astGetClass( map1 );
+   class2 = astGetClass( map2 );
+   if( astOK ){
+
+/* Get a pointer to the non-PcdMap Mapping. */
+      if( !strcmp( class1, "PcdMap" ) ){
+         nopcd = map2;
+         nopcd_class = class2;
+      } else {
+         nopcd = map1;
+         nopcd_class = class1;
+      }
+
+/* If the other Mapping is a ZoomMap, the Mappings can be swapped. */
+      if( !strcmp( nopcd_class, "ZoomMap" ) ){
+         ret = 1;
+
+/* If it is a PermMap, the Mappings can be swapped so long as the PermMap
+   simply swaps the two axes. */
+      } else if( !strcmp( nopcd_class, "PermMap" ) ){
+
+/* Get the number of input and output coordinates for the PermMap. */
+         nin = astGetNin( nopcd );
+         nout = astGetNout( nopcd );
+
+/* Must be 2-dimensional to swap. */
+         if( nin == 2 && nout == 2 ) {
+
+/* Get the axis permutation arrays and constants array for the PermMap. */
+            PermGet( (AstPermMap *) nopcd, &outperm, &inperm, &consts, status );
+            if( astOK ) {
+
+/* If the PermMap simply swaps the 2 axes (in both direction) we can
+   swap the two mappings. */
+               ret = ( outperm[0] == 1 && outperm[1] == 0 &&
+                       inperm[0] == 1 && inperm[1] == 0 );
+
+/* Free the axis permutation and constants arrays. */
+               outperm = (int *) astFree( (void *) outperm );
+               inperm = (int *) astFree( (void *) inperm );
+               consts = (double *) astFree( (void *) consts );
+            }
+         }
+      }
+   }
+
+/* Re-instate the original settings of the Invert attributes for the
+   supplied Mappings. */
+   astSetInvert( map1, invert[ 0 ] );
+   astSetInvert( map2, invert[ 1 ] );
+
+/* Return the answer. */
+   return astOK ? ret : 0;
+}
+
+static void ClearAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     ClearAttrib
+
+*  Purpose:
+*     Clear an attribute value for a PcdMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     void ClearAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     PcdMap member function (over-rides the astClearAttrib protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function clears the value of a specified attribute for a
+*     PcdMap, so that the default value will subsequently be used.
+
+*  Parameters:
+*     this
+*        Pointer to the PcdMap.
+*     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: */
+   AstPcdMap *this;              /* Pointer to the PcdMap structure */
+   int axis;                     /* Axis number */
+   int len;                      /* Length of attrib string */
+   int nc;                       /* No. characters read by astSscanf */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the PcdMap structure. */
+   this = (AstPcdMap *) this_object;
+
+/* Obtain the length of the "attrib" string. */
+   len = strlen( attrib );
+
+/* Check the attribute name and clear the appropriate attribute. */
+
+/* PcdCen(axis). */
+/* ------------- */
+   if ( nc = 0,
+               ( 1 == astSscanf( attrib, "pcdcen(%d)%n", &axis, &nc ) )
+               && ( nc >= len ) ) {
+      astClearPcdCen( this, axis - 1 );
+
+/* PcdCen. */
+/* ------- */
+   } else if ( !strcmp( attrib, "pcdcen" ) ) {
+      astClearPcdCen( this, 0 );
+      astClearPcdCen( this, 1 );
+
+/* Disco. */
+/* ------ */
+   } else if ( !strcmp( attrib, "disco" ) ) {
+      astClearDisco( this );
+
+/* 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 int Equal( AstObject *this_object, AstObject *that_object, int *status ) {
+/*
+*  Name:
+*     Equal
+
+*  Purpose:
+*     Test if two PcdMaps are equivalent.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     int Equal( AstObject *this, AstObject *that, int *status )
+
+*  Class Membership:
+*     PcdMap member function (over-rides the astEqual protected
+*     method inherited from the astMapping class).
+
+*  Description:
+*     This function returns a boolean result (0 or 1) to indicate whether
+*     two PcdMaps are equivalent.
+
+*  Parameters:
+*     this
+*        Pointer to the first Object (a PcdMap).
+*     that
+*        Pointer to the second Object.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     One if the PcdMaps are equivalent, zero otherwise.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global status set, or if it should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstPcdMap *that;
+   AstPcdMap *this;
+   int result;
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain pointers to the two PcdMap structures. */
+   this = (AstPcdMap *) this_object;
+   that = (AstPcdMap *) that_object;
+
+/* Check the second object is a PcdMap. We know the first is a
+   PcdMap since we have arrived at this implementation of the virtual
+   function. */
+   if( astIsAPcdMap( that ) ) {
+
+/* Check the Invert flags for the two PcdMaps are equal. */
+      if( astGetInvert( this ) == astGetInvert( that ) ) {
+
+/* Check all the attributes are equal. */
+         if( astEQUAL( this->pcdcen[0], that->pcdcen[0] ) &&
+             astEQUAL( this->pcdcen[1], that->pcdcen[1] ) &&
+             astEQUAL( this->disco, that->disco ) ) {
+            result = 1;
+         }
+      }
+   }
+
+/* If an error occurred, clear the result value. */
+   if ( !astOK ) result = 0;
+
+/* Return the result, */
+   return result;
+}
+
+static const char *GetAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     GetAttrib
+
+*  Purpose:
+*     Get the value of a specified attribute for a PcdMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     const char *GetAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     PcdMap member function (over-rides the protected astGetAttrib
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function returns a pointer to the value of a specified
+*     attribute for a PcdMap, formatted as a character string.
+
+*  Parameters:
+*     this
+*        Pointer to the PcdMap.
+*     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 PcdMap, 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 PcdMap. 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 */
+   AstPcdMap *this;              /* Pointer to the PcdMap structure */
+   const char *result;           /* Pointer value to return */
+   double dval;                  /* Double attribute value */
+   int axis;                     /* Axis number */
+   int len;                      /* Length of attrib string */
+   int nc;                       /* No. characters read by astSscanf */
+
+/* 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 PcdMap structure. */
+   this = (AstPcdMap *) this_object;
+
+/* Obtain the length of the attrib string. */
+   len = strlen( attrib );
+
+/* 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. */
+
+/* Disco. */
+/* ------ */
+   if ( !strcmp( attrib, "disco" ) ) {
+      dval = astGetDisco( this );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%.*g", DBL_DIG, dval );
+         result = getattrib_buff;
+      }
+
+/* PcdCen(axis). */
+/* ------------- */
+   } else if ( nc = 0,
+               ( 1 == astSscanf( attrib, "pcdcen(%d)%n", &axis, &nc ) )
+               && ( nc >= len ) ) {
+      dval = astGetPcdCen( this, axis - 1 );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%.*g", DBL_DIG, dval );
+         result = getattrib_buff;
+      }
+
+/* PcdCen. */
+/* ------- */
+   } else if ( !strcmp( attrib, "pcdcen" ) ) {
+      dval = astGetPcdCen( this, 0 );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%.*g", DBL_DIG, dval );
+         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;
+}
+
+void astInitPcdMapVtab_(  AstPcdMapVtab *vtab, const char *name, int *status ) {
+/*
+*+
+*  Name:
+*     astInitPcdMapVtab
+
+*  Purpose:
+*     Initialise a virtual function table for a PcdMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     void astInitPcdMapVtab( AstPcdMapVtab *vtab, const char *name )
+
+*  Class Membership:
+*     PcdMap vtab initialiser.
+
+*  Description:
+*     This function initialises the component of a virtual function
+*     table which is used by the PcdMap class.
+
+*  Parameters:
+*     vtab
+*        Pointer to the virtual function table. The components used by
+*        all ancestral classes will be initialised if they have not already
+*        been initialised.
+*     name
+*        Pointer to a constant null-terminated character string which contains
+*        the name of the class to which the virtual function table belongs (it
+*        is this pointer value that will subsequently be returned by the Object
+*        astClass function).
+*-
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
+   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
+
+/* Check the local error status. */
+   if ( !astOK ) return;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Initialize the component of the virtual function table used by the
+   parent class. */
+   astInitMappingVtab( (AstMappingVtab *) vtab, name );
+
+/* Store a unique "magic" value in the virtual function table. This
+   will be used (by astIsAPcdMap) to determine if an object belongs
+   to this class.  We can conveniently use the address of the (static)
+   class_check variable to generate this unique value. */
+   vtab->id.check = &class_check;
+   vtab->id.parent = &(((AstMappingVtab *) vtab)->id);
+
+/* Initialise member function pointers. */
+/* ------------------------------------ */
+/* Store pointers to the member functions (implemented here) that provide
+   virtual methods for this class. */
+   vtab->ClearDisco = ClearDisco;
+   vtab->SetDisco = SetDisco;
+   vtab->GetDisco = GetDisco;
+   vtab->TestDisco = TestDisco;
+   vtab->ClearPcdCen = ClearPcdCen;
+   vtab->SetPcdCen = SetPcdCen;
+   vtab->GetPcdCen = GetPcdCen;
+   vtab->TestPcdCen = TestPcdCen;
+
+/* 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;
+
+   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;
+   object->Equal = Equal;
+
+   parent_transform = mapping->Transform;
+   mapping->Transform = Transform;
+
+/* Store replacement pointers for methods which will be over-ridden by
+   new member functions implemented here. */
+   mapping->MapMerge = MapMerge;
+
+/* Declare the class dump function.*/
+   astSetDump( vtab, Dump, "PcdMap", "Apply pincushion distortion" );
+
+/* If we have just initialised the vtab for the current class, indicate
+   that the vtab is now initialised, and store a pointer to the class
+   identifier in the base "object" level of the vtab. */
+   if( vtab == &class_vtab ) {
+      class_init = 1;
+      astSetVtabClassIdentifier( vtab, &(vtab->id) );
+   }
+}
+
+static int MapMerge( AstMapping *this, int where, int series, int *nmap,
+                     AstMapping ***map_list, int **invert_list, int *status ) {
+/*
+*  Name:
+*     MapMerge
+
+*  Purpose:
+*     Simplify a sequence of Mappings containing a PcdMap.
+
+*  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:
+*     PcdMap method (over-rides the protected astMapMerge method
+*     inherited from the Mapping class).
+
+*  Description:
+*     This function attempts to simplify a sequence of Mappings by
+*     merging a nominated PcdMap 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 PcdMap 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 PcdMap which is to be merged with
+*        its neighbours. This should be a cloned copy of the PcdMap
+*        pointer contained in the array element "(*map_list)[where]"
+*        (see below). This pointer will not be annulled, and the
+*        PcdMap it identifies will not be modified by this function.
+*     where
+*        Index in the "*map_list" array (below) at which the pointer
+*        to the nominated PcdMap 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: */
+   AstMapping **maplt;   /* New mappings list pointer */
+   AstMapping *map2;     /* First mapping to check */
+   AstMapping *newmap;   /* Pointer to replacement Mapping */
+   AstMapping *mc[2];    /* Copies of supplied Mappings to swap */
+   AstMapping *smc0;     /* Simplied Mapping */
+   AstMapping *smc1;     /* Simplied Mapping */
+   const char *class1;   /* Pointer to first Mapping class string */
+   const char *class2;   /* Pointer to second Mapping class string */
+   const char *nclass;   /* Pointer to neighbouring Mapping class */
+   int i1;               /* Index of first PcdMap to merge */
+   int i2;               /* Index of last PcdMap to merge */
+   int i;                /* Loop counter */
+   int ic[2];            /* Copies of supplied invert flags to swap */
+   int invert;           /* Should the inverted Mapping be used? */
+   int *invlt;           /* New invert flags list pointer */
+   int nmapt;            /* No. of Mappings in list */
+   int nstep1;           /* No. of Mappings backwards to next mergable Mapping */
+   int nstep2;           /* No. of Mappings forward to next mergable Mapping */
+   int result;           /* Result value to return */
+   int swaphi;           /* Can PcdMap be swapped with higher neighbour? */
+   int swaplo;           /* Can PcdMap be swapped with lower neighbour? */
+
+/* Initialise. */
+   result = -1;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Initialise variables to avoid "used of uninitialised variable"
+   messages from dumb compilers. */
+   i1 = 0;
+   i2 = 0;
+
+/* First of all, see if the PcdMap can be replaced by a simpler Mapping,
+   without reference to the neighbouring Mappings in the list.           */
+/* ======================================================================*/
+/* If the distortion coefficient in the PcdMap is zero, the PcdMap can be
+   replaced by a UnitMap. */
+   if( EQUAL( astGetDisco( (AstPcdMap *) ( *map_list )[ where ] ), 0.0 ) ){
+
+/* Annul the PcdMap pointer in the list and replace it with a UnitMap
+   pointer, and indicate that the forward transformation of the returned
+   UnitMap should be used. */
+      (void) astAnnul( ( *map_list )[ where ] );
+      ( *map_list )[ where ] = (AstMapping *) astUnitMap( 2, "", status );
+      ( *invert_list )[ where ] = 0;
+
+/* Return the index of the first modified element. */
+      result = where;
+
+/* If the PcdMap itself could not be simplified, see if it can be merged
+   with the Mappings on either side of it in the list. */
+   } else {
+
+/* Store the classes of the neighbouring Mappings in the list. */
+       class1 = ( where > 0 ) ? astGetClass( ( *map_list )[ where - 1 ] ) : NULL;
+       class2 = ( where < *nmap - 1 ) ? astGetClass( ( *map_list )[ where + 1 ] ) : NULL;
+
+/* In series. */
+/* ========== */
+      if ( series ) {
+
+/* We first look to see if the PcdMap can be merged with one of its
+   neighbours, resulting in a reduction of one in the number of Mappings
+   in the list. A PcdMap can only merge directly with its own inverse, or
+   a UnitMap. */
+         if( class1 && CanMerge(  ( *map_list )[ where - 1 ],
+                                  ( *map_list )[ where ],
+                                  ( *invert_list )[ where - 1 ],
+                                  ( *invert_list )[ where ], status ) ){
+            nclass = class1;
+            i1 = where - 1;
+            i2 = where;
+
+         } else if( class2 && CanMerge(  ( *map_list )[ where ],
+                                  ( *map_list )[ where + 1 ],
+                                  ( *invert_list )[ where ],
+                                  ( *invert_list )[ where + 1 ], status ) ){
+            nclass = class2;
+            i1 = where;
+            i2 = where + 1;
+
+         } else {
+            nclass = NULL;
+         }
+
+/* If the PcdMap can merge with one of its neighbours, create the merged
+   Mapping. */
+         if( nclass ){
+
+/* If the neighbour is a PcdMap, it must be the inverse of the nominated
+   Mapping, and so they merge to form a UnitMap. */
+            if( !strcmp( nclass, "PcdMap" ) ){
+               newmap = (AstMapping *) astUnitMap( 2, "", status );
+               invert = 0;
+
+/* If the neighbour is a UnitMap, they merge to form a clone of the
+   nominated PcdMap. */
+            } else {
+               newmap = (AstMapping *) astClone( ( *map_list )[ where ] );
+               invert = ( *invert_list )[ where ];
+            }
+
+/* If succesfull... */
+            if( astOK ){
+
+/* Annul the first of the two Mappings, and replace it with the merged
+   Mapping. Also set the invert flag. */
+               (void) astAnnul( ( *map_list )[ i1 ] );
+               ( *map_list )[ i1 ] = newmap;
+               ( *invert_list )[ i1 ] = invert;
+
+/* Annul the second of the two Mappings, and shuffle down the rest of the
+   list to fill the gap. */
+               (void) astAnnul( ( *map_list )[ i2 ] );
+               for ( i = i2 + 1; 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;
+
+            }
+
+/* If the PcdMap could not merge directly with either of its neighbours,
+   we consider whether it would be worthwhile to swap the PcdMap with
+   either of its neighbours. This can only be done for certain classes
+   of Mapping (ZoomMaps & some PermMaps), and will usually require both
+   Mappings to be modified (unless they are commutative). The advantage of
+   swapping the order of the Mappings is that it may result in the PcdMap
+   being adjacent to a Mapping with which it can merge directly on the next
+   invocation of this function, thus reducing the number of Mappings
+   in the list. */
+         } else {
+
+/* Set a flag if we could swap the PcdMap with its higher neighbour. */
+            if( where + 1 < *nmap ){
+               swaphi = CanSwap(  ( *map_list )[ where ],
+                                  ( *map_list )[ where + 1 ],
+                                  ( *invert_list )[ where ],
+                                  ( *invert_list )[ where + 1 ], status );
+            } else {
+               swaphi = 0;
+            }
+
+/* If so, step through each of the Mappings which follow the PcdMap,
+   looking for a Mapping with which the PcdMap could merge directly. Stop
+   when such a Mapping is found, or if a Mapping is found with which the
+   PcdMap could definitely not swap. Note the number of Mappings which
+   separate the PcdMap from the Mapping with which it could merge (if
+   any). */
+            nstep2 = -1;
+            if( swaphi ){
+               for( i2 = where + 1; i2 < *nmap; i2++ ){
+
+/* See if we may be able to merge with this Mapping. If so, note the number
+   of steps between the two Mappings and leave the loop. */
+                  nclass = astGetClass( ( *map_list )[ i2 ] );
+
+                  if( !strcmp( nclass, "UnitMap" ) ||
+                      !strcmp( nclass, "PcdMap" ) ){
+                     nstep2 = i2 - where - 1;
+                     break;
+                  }
+
+/* If there is no chance that we can swap with this Mapping, leave the loop
+   with -1 for the number of steps to indicate that no merging is possible.
+   PcdMaps can swap with ZoomMaps and some PermMaps. */
+                  if( strcmp( nclass, "ZoomMap" ) &&
+                      strcmp( nclass, "PermMap" ) ) {
+                     break;
+                  }
+
+               }
+
+            }
+
+/* Do the same working forward from the PcdMap towards the start of the map
+   list. */
+            if( where > 0 ){
+               swaplo = CanSwap(  ( *map_list )[ where - 1 ],
+                                  ( *map_list )[ where ],
+                                  ( *invert_list )[ where - 1 ],
+                                  ( *invert_list )[ where ], status );
+            } else {
+               swaplo = 0;
+            }
+
+            nstep1 = -1;
+            if( swaplo ){
+               for( i1 = where - 1; i1 >= 0; i1-- ){
+
+                  nclass = astGetClass( ( *map_list )[ i1 ] );
+
+                  if( !strcmp( nclass, "UnitMap" ) ||
+                      !strcmp( nclass, "PcdMap" ) ){
+                     nstep1 = where - 1 - i1;
+                     break;
+                  }
+
+                  if( strcmp( nclass, "ZoomMap" ) &&
+                      strcmp( nclass, "PermMap" ) ) {
+                     break;
+                  }
+
+               }
+
+            }
+
+/* Choose which neighbour to swap with so that the PcdMap moves towards the
+   nearest Mapping with which it can merge. */
+            if( nstep1 != -1 && ( nstep2 == -1 || nstep2 > nstep1 ) ){
+               nclass = class1;
+               i1 = where - 1;
+               i2 = where;
+            } else if( nstep2 != -1 ){
+               nclass = class2;
+               i1 = where;
+               i2 = where + 1;
+            } else {
+               nclass = NULL;
+            }
+
+/* If there is a target Mapping in the list with which the PcdMap could
+   merge, replace the supplied Mappings with swapped Mappings to bring a
+   PcdMap closer to the target Mapping. */
+            if( nclass ){
+
+/* Swap the Mappings. */
+               if( !strcmp( nclass, "ZoomMap" ) ){
+                  PcdZoom( (*map_list) + i1, (*invert_list) + i1, where - i1, status );
+
+               } else if( !strcmp( nclass, "PermMap" ) ){
+                  PcdPerm( (*map_list) + i1, (*invert_list) + i1, where - i1, status );
+               }
+
+/* And then merge them. */
+               if( where == i1 && where + 1 < *nmap ) {    /* Merging upwards */
+                  map2 = astClone( (*map_list)[ where + 1 ] );
+                  nmapt = *nmap - where - 1;
+                  maplt = *map_list + where + 1;
+                  invlt = *invert_list + where + 1;
+
+                  (void) astMapMerge( map2, 0, series, &nmapt, &maplt, &invlt );
+                  map2 = astAnnul( map2 );
+                  *nmap = where + 1 + nmapt;
+
+               } else if( where - 2 >= 0 ) {               /* Merging downwards */
+                  map2 = astClone( (*map_list)[ where - 2 ] );
+                  nmapt = *nmap - where + 2;
+                  maplt = *map_list + where - 2 ;
+                  invlt = *invert_list + where - 2;
+
+                  (void) astMapMerge( map2, 0, series, &nmapt, &maplt, &invlt );
+                  map2 = astAnnul( map2 );
+                  *nmap = where - 2 + nmapt;
+               }
+
+               result = i1;
+
+/* If there is no Mapping available for merging, it may still be
+   advantageous to swap with a neighbour because the swapped Mapping may
+   be simpler than the original Mappings. */
+            } else if( swaphi || swaplo ) {
+
+/* Try swapping with each possible neighbour in turn. */
+               for( i = 0; i < 2; i++ ) {
+
+/*  Set up the class and pointers for the mappings to be swapped, first
+    the lower neighbour, then the upper neighbour. */
+                  if( i == 0 && swaplo ){
+                     nclass = class1;
+                     i1 = where - 1;
+                     i2 = where;
+
+                  } else if( i == 1 && swaphi ){
+                     nclass = class2;
+                     i1 = where;
+                     i2 = where + 1;
+
+                  } else {
+                     nclass = NULL;
+                  }
+
+/* If we have a Mapping to swap with... */
+                  if( nclass ) {
+
+/* Take copies of the Mapping and Invert flag arrays so we do not change
+   the supplied values. */
+                     mc[ 0 ] = (AstMapping *) astCopy( ( (*map_list) + i1 )[0] );
+                     mc[ 1 ] = (AstMapping *) astCopy( ( (*map_list) + i1 )[1] );
+                     ic[ 0 ] = ( (*invert_list) + i1 )[0];
+                     ic[ 1 ] = ( (*invert_list) + i1 )[1];
+
+/* Swap these Mappings. */
+                     if( !strcmp( nclass, "ZoomMap" ) ){
+                        PcdZoom( mc, ic, where - i1, status );
+                     } else if( !strcmp( nclass, "PermMap" ) ){
+                        PcdPerm( mc, ic, where - i1, status );
+                     }
+
+/* If neither of the swapped Mappings can be simplified further, then there
+   is no point in swapping the Mappings, so just annul the map copies. */
+                     smc0 = astSimplify( mc[0] );
+                     smc1 = astSimplify( mc[1] );
+
+                     if( astGetClass( smc0 ) == astGetClass( mc[0] ) &&
+                         astGetClass( smc1 ) == astGetClass( mc[1] ) ) {
+
+                        mc[ 0 ] = (AstMapping *) astAnnul( mc[ 0 ] );
+                        mc[ 1 ] = (AstMapping *) astAnnul( mc[ 1 ] );
+
+/* If one or both of the swapped Mappings could be simplified, then annul
+   the supplied Mappings and return the swapped mappings, storing the index
+   of the first modified Mapping. */
+                     } else {
+                        (void ) astAnnul( ( (*map_list) + i1 )[0] );
+                        (void ) astAnnul( ( (*map_list) + i1 )[1] );
+
+                        ( (*map_list) + i1 )[0] = mc[ 0 ];
+                        ( (*map_list) + i1 )[1] = mc[ 1 ];
+
+                        ( (*invert_list) + i1 )[0] = ic[ 0 ];
+                        ( (*invert_list) + i1 )[1] = ic[ 1 ];
+
+                        result = i1;
+                        break;
+                     }
+
+/* Annul the simplied Mappings */
+                     smc0 = astAnnul( smc0 );
+                     smc1 = astAnnul( smc1 );
+
+                  }
+               }
+            }
+         }
+
+/* In parallel. */
+/* ============ */
+/* PcdMaps cannot combine in parallel with any other Mappings. */
+      }
+   }
+
+/* Return the result. */
+   return result;
+}
+
+static void PermGet( AstPermMap *map, int **outperm, int **inperm,
+                     double **consts, int *status ){
+/*
+*  Name:
+*     PermGet
+
+*  Purpose:
+*     Get the axis permutation and constants array for a PermMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     void PermGet( AstPermMap *map, int **outperm, int **inperm,
+*                   double **const, int *status )
+
+*  Class Membership:
+*     PcdMap member function
+
+*  Description:
+*     This function returns axis permutation and constants arrays which can
+*     be used to create a PermMap which is equivalent to the supplied PermMap.
+
+*  Parameters:
+*     map
+*        The PermMap.
+*     outperm
+*        An address at which to return a popinter to an array of ints
+*        holding the output axis permutation array. The array should be
+*        released using astFree when no longer needed.
+*     inperm
+*        An address at which to return a popinter to an array of ints
+*        holding the input axis permutation array. The array should be
+*        released using astFree when no longer needed.
+*     consts
+*        An address at which to return a popinter to an array of doubles
+*        holding the constants array. The array should be released using
+*        astFree when no longer needed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     -  NULL pointers are returned if an error has already occurred, or if
+*     this function should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstPointSet *pset1;       /* PointSet holding input positions for PermMap */
+   AstPointSet *pset2;       /* PointSet holding output positions for PermMap */
+   double **ptr1;            /* Pointer to pset1 data */
+   double **ptr2;            /* Pointer to pset2 data */
+   double *cnst;             /* Pointer to constants array */
+   double cn;                /* Potential new constant value */
+   double ip;                /* Potential output axis index */
+   double op;                /* Potential input axis index */
+   int *inprm;               /* Pointer to input axis permutation array */
+   int *outprm;              /* Pointer to output axis permutation array */
+   int i;                    /* Axis count */
+   int nc;                   /* Number of constants stored so far */
+   int nin;                  /* No. of input coordinates for the PermMap */
+   int nout;                 /* No. of output coordinates for the PermMap */
+
+/* Initialise. */
+   if( outperm ) *outperm = NULL;
+   if( inperm ) *inperm = NULL;
+   if( consts ) *consts = NULL;
+
+/* Check the global error status and the supplied pointers. */
+   if ( !astOK || !outperm || !inperm || !consts ) return;
+
+/* Initialise variables to avoid "used of uninitialised variable"
+   messages from dumb compilers. */
+   nc = 0;
+
+/* Get the number of input and output axes for the supplied PermMap. */
+   nin = astGetNin( map );
+   nout = astGetNout( map );
+
+/* Allocate the memory for the returned arrays. */
+   outprm = (int *) astMalloc( sizeof( int )* (size_t) nout );
+   inprm = (int *) astMalloc( sizeof( int )* (size_t) nin );
+   cnst = (double *) astMalloc( sizeof( double )* (size_t) ( nout + nin ) );
+
+/* Returned the pointers to these arrays.*/
+   *outperm = outprm;
+   *inperm = inprm;
+   *consts = cnst;
+
+/* Create two PointSets, each holding two points, which can be used for
+   input and output positions with the PermMap. */
+   pset1 = astPointSet( 2, nin, "", status );
+   pset2 = astPointSet( 2, nout, "", status );
+
+/* Set up the two input positions to be [0,1,2...] and [-1,-1,-1,...]. The
+   first position is used to enumerate the axes, and the second is used to
+   check for constant axis values. */
+   ptr1 = astGetPoints( pset1 );
+   if( astOK ){
+      for( i = 0; i < nin; i++ ){
+         ptr1[ i ][ 0 ] = ( double ) i;
+         ptr1[ i ][ 1 ] = -1.0;
+      }
+   }
+
+/* Use the PermMap to transform these positions in the forward direction. */
+   (void) astTransform( map, pset1, 1, pset2 );
+
+/* Look at the mapped positions to determine the output axis permutation
+   array. */
+   ptr2 = astGetPoints( pset2 );
+   if( astOK ){
+
+/* No constant axis valeus found yet. */
+      nc = 0;
+
+/* Do each output axis. */
+      for( i = 0; i < nout; i++ ){
+
+/* If the output axis value is copied from an input axis value, the index
+   of the appropriate input axis will be in the mapped first position. */
+         op = ptr2[ i ][ 0 ];
+
+/* If the output axis value is assigned a constant value, the result of
+   mapping the two different input axis values will be the same. */
+         cn = ptr2[ i ][ 1 ];
+         if( op == cn ) {
+
+/* We have found another constant. Store it in the constants array, and
+   store the index of the constant in the output axis permutation array. */
+            cnst[ nc ] = cn;
+            outprm[ i ] = -( nc + 1 );
+            nc++;
+
+/* If the output axis values are different, then the output axis value
+   must be copied from the input axis value. */
+         } else {
+            outprm[ i ] = (int) ( op + 0.5 );
+         }
+      }
+   }
+
+/* Now do the same thing to determine the input permutation array. */
+   if( astOK ){
+      for( i = 0; i < nout; i++ ){
+         ptr2[ i ][ 0 ] = ( double ) i;
+         ptr2[ i ][ 1 ] = -1.0;
+      }
+   }
+
+   (void) astTransform( map, pset2, 0, pset1 );
+
+   if( astOK ){
+
+      for( i = 0; i < nin; i++ ){
+
+         ip = ptr1[ i ][ 0 ];
+         cn = ptr1[ i ][ 1 ];
+         if( ip == cn ) {
+
+            cnst[ nc ] = cn;
+            inprm[ i ] = -( nc + 1 );
+            nc++;
+
+         } else {
+            inprm[ i ] = (int) ( ip + 0.5 );
+         }
+      }
+   }
+
+/* Annul the PointSets. */
+   pset1 = astAnnul( pset1 );
+   pset2 = astAnnul( pset2 );
+
+/* If an error has occurred, attempt to free the returned arrays. */
+   if( !astOK ) {
+      *outperm = (int *) astFree( (void *) *outperm );
+      *inperm = (int *) astFree( (void *) *inperm );
+      *consts = (double *) astFree( (void *) *consts );
+   }
+
+/* Return. */
+   return;
+}
+
+static void SetAttrib( AstObject *this_object, const char *setting, int *status ) {
+/*
+*  Name:
+*     SetAttrib
+
+*  Purpose:
+*     Set an attribute value for a PcdMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     void SetAttrib( AstObject *this, const char *setting, int *status )
+
+*  Class Membership:
+*     PcdMap member function (over-rides the astSetAttrib protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function assigns an attribute value for a PcdMap, 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 PcdMap.
+*     setting
+*        Pointer to a null terminated string specifying the new attribute
+*        value.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstPcdMap *this;              /* Pointer to the PcdMap structure */
+   double dval;                  /* Double attribute value */
+   int axis;                     /* Index for the axis */
+   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 PcdMap structure. */
+   this = (AstPcdMap *) 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. */
+
+/* Disco. */
+/* ------ */
+   if ( nc = 0,
+        ( 1 == astSscanf( setting, "disco= %lg %n", &dval, &nc ) )
+        && ( nc >= len ) ) {
+      astSetDisco( this, dval );
+
+/* PcdCen(axis). */
+/* ------------ */
+   } else if ( nc = 0,
+               ( 2 == astSscanf( setting, "pcdcen(%d)= %lg %n",
+                              &axis, &dval, &nc ) )
+               && ( nc >= len ) ) {
+      astSetPcdCen( this, axis - 1, dval );
+
+/* PcdCen. */
+/* ------- */
+   } else if ( nc = 0,
+        ( 1 == astSscanf( setting, "pcdcen= %lg %n", &dval, &nc ) )
+        && ( nc >= len ) ) {
+      astSetPcdCen( this, 0, dval );
+      astSetPcdCen( this, 1, dval );
+
+/* If the attribute is still not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      (*parent_setattrib)( this_object, setting, status );
+   }
+
+}
+
+static int TestAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     TestAttrib
+
+*  Purpose:
+*     Test if a specified attribute value is set for a PcdMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     int TestAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     PcdMap member function (over-rides the astTestAttrib protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function returns a boolean result (0 or 1) to indicate whether
+*     a value has been set for one of a PcdMap's attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the PcdMap.
+*     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: */
+   AstPcdMap *this;              /* Pointer to the PcdMap structure */
+   int axis;                     /* Axis number */
+   int len;                      /* Length of attrib string */
+   int nc;                       /* No. characters read by astSscanf */
+   int result;                   /* Result value to return */
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the PcdMap structure. */
+   this = (AstPcdMap *) this_object;
+
+/* Obtain the length of the attrib string. */
+   len = strlen( attrib );
+
+/* Check the attribute name and test the appropriate attribute. */
+
+/* Disco. */
+/* ------ */
+   if ( !strcmp( attrib, "disco" ) ) {
+      result = astTestDisco( this );
+
+/* PcdCen. */
+/* ------- */
+   } else if ( !strcmp( attrib, "pcdcen" ) ) {
+      result = astTestPcdCen( this, 0 );
+
+/* PcdCen(axis). */
+/* ---------- */
+   } else if ( nc = 0,
+               ( 1 == astSscanf( attrib, "pcdcen(%d)%n", &axis, &nc ) )
+               && ( nc >= len ) ) {
+      result = astTestPcdCen( this, axis - 1 );
+
+/* 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, AstPointSet *in,
+                               int forward, AstPointSet *out, int *status ) {
+/*
+*  Name:
+*     Transform
+
+*  Purpose:
+*     Apply a PcdMap to transform a set of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+*                             int forward, AstPointSet *out, int *status )
+
+*  Class Membership:
+*     PcdMap member function (over-rides the astTransform protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function takes a PcdMap and a set of points encapsulated in a
+*     PointSet and transforms the points so as to map them into the
+*     required window.
+
+*  Parameters:
+*     this
+*        Pointer to the PcdMap.
+*     in
+*        Pointer to the PointSet holding the input coordinate data.
+*     forward
+*        A non-zero value indicates that the forward coordinate transformation
+*        should be applied, while a zero value requests the inverse
+*        transformation.
+*     out
+*        Pointer to a PointSet which will hold the transformed (output)
+*        coordinate values. A NULL value may also be given, in which case a
+*        new PointSet will be created by this function.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the output (possibly new) PointSet.
+
+*  Notes:
+*     -  A null pointer will be returned if this function is invoked with the
+*     global error status set, or if it should fail for any reason.
+*     -  The number of coordinate values per point in the input PointSet must
+*     match the number of coordinates for the PcdMap being applied.
+*     -  If an output PointSet is supplied, it must have space for sufficient
+*     number of points and coordinate values per point to accommodate the
+*     result. Any excess space will be ignored.
+*/
+
+/* Local Variables: */
+   AstPointSet *result;          /* Pointer to output PointSet */
+   AstPcdMap *map;               /* Pointer to PcdMap to be applied */
+   double **ptr_in;              /* Pointer to input coordinate data */
+   double **ptr_out;             /* Pointer to output coordinate data */
+   double *axin_0;               /* Pointer to next input axis 0 value */
+   double *axin_1;               /* Pointer to next input axis 1 value */
+   double *axout_0;              /* Pointer to next output axis 0 value */
+   double *axout_1;              /* Pointer to next output axis 1 value */
+   int npoint;                   /* Number of points */
+   int point;                    /* Loop counter for points */
+   double dx;                    /* Undistorted X increment from centre  */
+   double dy;                    /* Undistorted Y increment from centre */
+   double dxp;                   /* Distorted X increment from centre  */
+   double dyp;                   /* Distorted Y increment from centre */
+   double disco;                 /* Distortion coefficient */
+   double cen0;                  /* Centre of distortion on axis 0 */
+   double cen1;                  /* Centre of distortion on axis 1 */
+   double cr2;                   /* Constant */
+   double a;                     /* Constant */
+   double cr2a2;                 /* Constant */
+   double f;                     /* Expansion factor */
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain a pointer to the PcdMap. */
+   map = (AstPcdMap *) this;
+
+/* Apply the parent mapping using the stored pointer to the Transform member
+   function inherited from the parent Mapping class. This function validates
+   all arguments and generates an output PointSet if necessary, but does not
+   actually transform any coordinate values. */
+   result = (*parent_transform)( this, in, forward, out, status );
+
+/* We will now extend the parent astTransform method by performing the
+   calculations needed to generate the output coordinate values. */
+
+/* Determine the numbers of points and coordinates per point from the input
+   PointSet and obtain pointers for accessing the input and output coordinate
+   values. */
+   npoint = astGetNpoint( in );
+   ptr_in = astGetPoints( in );
+   ptr_out = astGetPoints( result );
+
+/* Determine whether to apply the forward or inverse mapping, according to the
+   direction specified and whether the mapping has been inverted. */
+   if ( astGetInvert( map ) ) forward = !forward;
+
+/* Get the distortion coefficient and centre. */
+   disco = astGetDisco( map );
+   cen0 = astGetPcdCen( map, 0 );
+   cen1 = astGetPcdCen( map, 1 );
+
+/* Perform coordinate arithmetic. */
+/* ------------------------------ */
+   if( astOK ){
+
+/* Store pointers to the first input and output values on both axes. */
+      axin_0 = ptr_in[ 0 ];
+      axin_1 = ptr_in[ 1 ];
+      axout_0 = ptr_out[ 0 ];
+      axout_1 = ptr_out[ 1 ];
+
+/* First deal with forward transformations. */
+      if( forward ){
+
+         for( point = 0; point < npoint; point++ ){
+            if( *axin_0 != AST__BAD && *axin_1 != AST__BAD ){
+               dx = ( *axin_0 - cen0 );
+               dy = ( *axin_1 - cen1 );
+               f = 1.0 + disco*( dx*dx + dy*dy );
+               dxp = dx*f;
+               dyp = dy*f;
+               *(axout_0++) = dxp + cen0;
+               *(axout_1++) = dyp + cen1;
+
+            } else {
+               *(axout_0++) = AST__BAD;
+               *(axout_1++) = AST__BAD;
+            }
+            axin_0++;
+            axin_1++;
+         }
+
+/* Now deal with inverse transformations. */
+      } else {
+
+         for( point = 0; point < npoint; point++ ){
+            if( *axin_0 != AST__BAD && *axin_1 != AST__BAD ){
+               dxp = ( *axin_0 - cen0 );
+               dyp = ( *axin_1 - cen1 );
+
+               cr2 = disco*( dxp*dxp + dyp*dyp );
+               a = ( 2.0*cr2 + 1.0 )/( 3.0*cr2 + 1.0 );
+               cr2a2 = cr2*a*a;
+               f = ( 2.0*cr2a2*a + 1.0 )/( 3.0*cr2a2 + 1.0 );
+
+               dx = dxp*f;
+               dy = dyp*f;
+
+/* The above approximate inverse is taken from SLA_UNPCD. If more accuracy
+c   is needed, the following code can be uncommented to iterate to a better
+c   solution.
+c
+c               fl = 1.0 + disco*( dx*dx + dy*dy );
+c               dx = dxp/fl;
+c               dy = dyp/fl;
+c
+c               df = fabs( fl );
+c               while( df > fabs( fl*1.0E-6 ) ){
+c                  f = 1.0 + disco*( dx*dx + dy*dy );
+c                  df = fabs( f - fl );
+c                  fl = f;
+c
+c                  dx = dxp/f;
+c                  dy = dyp/f;
+c               }
+*/
+               *(axout_0++) = dx + cen0;
+               *(axout_1++) = dy + cen1;
+
+            } else {
+               *(axout_0++) = AST__BAD;
+               *(axout_1++) = AST__BAD;
+            }
+            axin_0++;
+            axin_1++;
+         }
+
+      }
+
+   }
+
+/* Return a pointer to the output PointSet. */
+   return result;
+}
+
+static void PcdZoom( AstMapping **maps, int *inverts, int ipc, int *status ){
+/*
+*  Name:
+*     PcdZoom
+
+*  Purpose:
+*     Swap a PcdMap and a ZoomMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     void PcdZoom( AstMapping **maps, int *inverts, int ipc, int *status )
+
+*  Class Membership:
+*     PcdMap member function
+
+*  Description:
+*     A list of two Mappings is supplied containing a PcdMap and a
+*     ZoomMap. These Mappings are annulled, and replaced with
+*     another pair of Mappings consisting of a PcdMap and a ZoomMap
+*     in the opposite order. These Mappings are chosen so that their
+*     combined effect is the same as the original pair of Mappings.
+
+*  Parameters:
+*     maps
+*        A pointer to an array of two Mapping pointers.
+*     inverts
+*        A pointer to an array of two invert flags.
+*     ipc
+*        The index within "maps" of the PcdMap.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Local Variables: */
+   AstPcdMap *pm2;               /* Pointer to the returned PcdMap */
+   AstPcdMap *pm;                /* Pointer to the supplied PcdMap */
+   AstZoomMap *zm2;              /* Pointer to the returned ZoomMap */
+   AstZoomMap *zm;               /* Pointer to the supplied ZoomMap */
+   double cen[2];                /* New distortion centre */
+   double disc;                  /* Distortion coeff. for returned PcdMap */
+   double disco;                 /* Distortion coeff. for supplied PcdMap */
+   double xcen;                  /* Axis 0 centre for supplied PcdMap */
+   double ycen;                  /* Axis 1 centre for supplied PcdMap */
+   double zoom;                  /* Zoom factor for supplied ZoomMap */
+   int old_pinv;                 /* Invert value for the supplied PcdMap */
+   int old_zinv;                 /* Invert value for the supplied ZoomMap */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Store pointers to the supplied PcdMap and the ZoomMap. */
+   pm = (AstPcdMap *) maps[ ipc ];
+   zm = (AstZoomMap *) maps[ 1 - ipc ];
+
+/* Temporarily set the Invert attribute of the supplied Mappings to the
+   supplied values. */
+   old_pinv = astGetInvert( pm );
+   astSetInvert( pm, inverts[ ipc ] );
+
+   old_zinv = astGetInvert( zm );
+   astSetInvert( zm, inverts[ 1 - ipc ] );
+
+/* Get the zoom factor from the ZoomMap. */
+   zoom = astGetZoom( zm );
+
+/* Get the distortion coefficient from the PcdMap. */
+   disco = astGetDisco( pm );
+
+/* Get the distortion centre from the PcdMap. */
+   xcen = astGetPcdCen( pm, 0 );
+   ycen = astGetPcdCen( pm, 1 );
+
+/* Re-instate the original value of the Invert attributes of the supplied
+   Mappings. */
+   astSetInvert( pm, old_pinv );
+   astSetInvert( zm, old_zinv );
+
+/* Create the returned ZoomMap. */
+   zm2 = astZoomMap( 2, zoom, "", status );
+
+/* Find the attributes of the returned PcdMap. If the PCD map is applied
+   first... */
+   if( ipc == 0 ) {
+      cen[ 0 ] = xcen*zoom;
+      cen[ 1 ] = ycen*zoom;
+      disc = disco/(zoom*zoom);
+
+/* If the PCD map is applied second... */
+   } else {
+      cen[ 0 ] = xcen/zoom;
+      cen[ 1 ] = ycen/zoom;
+      disc = disco*zoom*zoom;
+   }
+
+/* Create the returned PcdMap. */
+   pm2 = astPcdMap( disc, cen, "", status );
+   if( inverts[ ipc ] ) astInvert( pm2 );
+
+/* Replace the supplied Mappings with the ones created above, swapping the
+   order. */
+   if( astOK ){
+      (void) astAnnul( pm );
+      (void) astAnnul( zm );
+
+      maps[ 1 - ipc ] = (AstMapping *) pm2;
+      inverts[ 1 - ipc  ] = inverts[ ipc ];
+
+      maps[ ipc ] = (AstMapping *) zm2;
+      inverts[ ipc ] = 0;
+
+   }
+
+/* Return. */
+   return;
+}
+
+static void PcdPerm( AstMapping **maps, int *inverts, int ipc, int *status ){
+/*
+*  Name:
+*     PcdPerm
+
+*  Purpose:
+*     Swap a PcdMap and a PermMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     void PcdPerm( AstMapping **maps, int *inverts, int ipc, int *status )
+
+*  Class Membership:
+*     PcdMap member function
+
+*  Description:
+*     A list of two Mappings is supplied containing a PcdMap and a
+*     PermMap. These Mappings are annulled, and replaced with
+*     another pair of Mappings consisting of a PcdMap and a PermMap
+*     in the opposite order. These Mappings are chosen so that their
+*     combined effect is the same as the original pair of Mappings.
+
+*  Parameters:
+*     maps
+*        A pointer to an array of two Mapping pointers.
+*     inverts
+*        A pointer to an array of two invert flags.
+*     ipc
+*        The index within "maps" of the PcdMap.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     -  It should have been checked previously that the PermMap simply
+*     swaps axes 0 and 1. This is the only sort of PermMap which can be
+*     used here.
+
+*/
+
+   AstPermMap *rm;               /* Pointer to the supplied PermMap */
+   AstPermMap *rm2;              /* Pointer to the returned PermMap */
+   AstPcdMap *pm;                /* Pointer to the supplied PcdMap */
+   AstPcdMap *pm2;               /* Pointer to the returned PcdMap */
+   double cen[2];                /* Centre for new PcdMap */
+   double disco;                 /* Distortion coeff. for supplied PcdMap */
+   double xcen;                  /* Axis 0 centre for supplied PcdMap */
+   double ycen;                  /* Axis 1 centre for supplied PcdMap */
+   int old_rinv;                 /* Invert value for the supplied PermMap */
+   int old_pinv;                 /* Invert value for the supplied PcdMap */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Store pointers to the supplied PcdMap and the PermMap. */
+   pm = (AstPcdMap *) maps[ ipc ];
+   rm = (AstPermMap *) maps[ 1 - ipc ];
+
+/* Temporarily set the Invert attribute of the supplied Mappings to the
+   supplied values. */
+   old_pinv = astGetInvert( pm );
+   astSetInvert( pm, inverts[ ipc ] );
+
+   old_rinv = astGetInvert( rm );
+   astSetInvert( rm, inverts[ 1 - ipc ] );
+
+/* Get the distortion coefficient from the PcdMap. */
+   disco = astGetDisco( pm );
+
+/* Get the distortion centre from the PcdMap. */
+   xcen = astGetPcdCen( pm, 0 );
+   ycen = astGetPcdCen( pm, 1 );
+
+/* Re-instate the original value of the Invert attributes of the supplied
+   Mappings. */
+   astSetInvert( pm, old_pinv );
+   astSetInvert( rm, old_rinv );
+
+/* Create the returned PermMap (unchanged). */
+   rm2 = astClone( rm );
+
+/* Create the returned PcdMap. */
+   cen[ 0 ] = ycen;
+   cen[ 1 ] = xcen;
+   pm2 = astPcdMap( disco, cen, "", status );
+   if( inverts[ ipc ] ) astInvert( pm2 );
+
+/* Replace the supplied Mappings with the ones created above, swapping the
+   order. */
+   if( astOK ){
+      (void) astAnnul( pm );
+      (void) astAnnul( rm );
+
+      old_pinv = inverts[ ipc ];
+
+      maps[ ipc ] = (AstMapping *) rm2;
+      inverts[ ipc ] = inverts[ 1 - ipc ];
+
+      maps[ 1 - ipc ] = (AstMapping *) pm2;
+      inverts[ 1 - ipc  ] = old_pinv;
+   }
+
+/* Return. */
+   return;
+}
+
+/* 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:
+*     Disco
+
+*  Purpose:
+*     PcdMap pincushion/barrel distortion coefficient.
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Double precision.
+
+*  Description:
+*     This attribute specifies the pincushion/barrel distortion coefficient
+*     used by a PcdMap. This coefficient is set when the PcdMap is created,
+*     but may later be modified. If the attribute is cleared, its default
+*     value is zero, which gives no distortion. For pincushion distortion,
+*     the value should be positive. For barrel distortion, it should be
+*     negative.
+*
+*     Note that the forward transformation of a PcdMap applies the
+*     distortion specified by this attribute and the inverse
+*     transformation removes this distortion. If the PcdMap is inverted
+c     (e.g. using astInvert), then the forward transformation will
+f     (e.g. using AST_INVERT), then the forward transformation will
+*     remove the distortion and the inverse transformation will apply
+*     it. The distortion itself will still be given by the same value of
+*     Disco.
+*
+*     Note, the value of this attribute may changed only if the PcdMap
+*     has no more than one reference. That is, an error is reported if the
+*     PcdMap has been cloned, either by including it within another object
+*     such as a CmpMap or FrameSet or by calling the
+c     astClone
+f     AST_CLONE
+*     function.
+
+*  Applicability:
+*     PcdMap
+*        All PcdMaps have this attribute.
+
+*att--
+*/
+/* This ia a double value with a value of AST__BAD when undefined but
+   yielding a default of 0.0. */
+astMAKE_CLEAR1(PcdMap,Disco,disco,AST__BAD)
+astMAKE_GET(PcdMap,Disco,double,0.0,( ( this->disco == AST__BAD ) ?
+                                      0.0 : this->disco ))
+astMAKE_SET1(PcdMap,Disco,double,disco,value)
+astMAKE_TEST(PcdMap,Disco,( this->disco != AST__BAD ))
+
+
+/*
+*att++
+*  Name:
+*     PcdCen(axis)
+
+*  Purpose:
+*     Centre coordinates of pincushion/barrel distortion.
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Floating point.
+
+*  Description:
+*     This attribute specifies the centre of the pincushion/barrel
+*     distortion implemented by a PcdMap. It takes a separate value for
+*     each axis of the PcdMap so that, for instance, the settings
+*     "PcdCen(1)=345.0,PcdCen(2)=-104.4" specify that the pincushion
+*     distortion is centred at positions of 345.0 and -104.4 on axes 1 and 2
+*     respectively. This attribute is set when a PcdMap is created, but may
+*     later be modified. If the attribute is cleared, the default value for
+*     both axes is zero.
+*
+*     Note, the value of this attribute may changed only if the PcdMap
+*     has no more than one reference. That is, an error is reported if the
+*     PcdMap has been cloned, either by including it within another object
+*     such as a CmpMap or FrameSet or by calling the
+c     astClone
+f     AST_CLONE
+*     function.
+
+*  Applicability:
+*     PcdMap
+*        All PcdMaps have this attribute.
+
+*  Notes:
+*     - If no axis is specified, (e.g. "PcdCen" instead of
+*     "PcdCen(2)"), then a "set" or "clear" operation will affect
+*     the attribute value of both axes, while a "get" or "test"
+*     operation will use just the PcdCen(1) value.
+*att--
+*/
+/* The centre of the distortion. AST__BAD is stored if no value has been
+   supplied, resulting in default values of zero being used. */
+MAKE_CLEAR(PcdCen,pcdcen,AST__BAD,2)
+MAKE_SET(PcdCen,double,pcdcen,value,2)
+MAKE_TEST(PcdCen,( this->pcdcen[axis] != AST__BAD ),2)
+MAKE_GET(PcdCen,double,0.0,(( this->pcdcen[axis] == AST__BAD ) ?
+                              0.0 : this->pcdcen[axis] ),2)
+
+/* Copy constructor. */
+/* ----------------- */
+/* No copy constructor is needed, as a byte-by-byte copy suffices. */
+
+/* Destructor. */
+/* ----------- */
+/* No destructor is needed as no memory, etc. needs freeing. */
+
+/* Dump function. */
+/* -------------- */
+static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
+/*
+*  Name:
+*     Dump
+
+*  Purpose:
+*     Dump function for PcdMap 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 PcdMap class to an output Channel.
+
+*  Parameters:
+*     this
+*        Pointer to the PcdMap 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: */
+   AstPcdMap *this;              /* Pointer to the PcdMap structure */
+   double dval;                  /* Attribute value */
+   int set;                      /* Is a value set? */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the PcdMap structure. */
+   this = (AstPcdMap *) this_object;
+
+/* Write out values representing the instance variables for the
+   PcdMap 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. */
+
+/* PcdCen(0). */
+/* ---------- */
+   set = TestPcdCen( this, 0, status );
+   dval = set ? GetPcdCen( this, 0, status ) : astGetPcdCen( this, 0 );
+   astWriteDouble( channel, "PcdCn0", set, 1, dval, "Distortion centre on first axis" );
+
+/* PcdCen(1). */
+/* ---------- */
+   set = TestPcdCen( this, 1, status );
+   dval = set ? GetPcdCen( this, 1, status ) : astGetPcdCen( this, 1 );
+   astWriteDouble( channel, "PcdCn1", set, 1, dval, "Distortion centre on second axis" );
+
+/* Disco. */
+/* ------ */
+   set = TestDisco( this, status );
+   dval = set ? GetDisco( this, status ) : astGetDisco( this );
+   astWriteDouble( channel, "Disco", set, 1, dval, "Distortion coefficient" );
+
+}
+
+/* Standard class functions. */
+/* ========================= */
+/* Implement the astIsAPcdMap and astCheckPcdMap functions using the macros
+   defined for this purpose in the "object.h" header file. */
+astMAKE_ISA(PcdMap,Mapping)
+astMAKE_CHECK(PcdMap)
+
+AstPcdMap *astPcdMap_( double disco, const double pcdcen[2],
+                       const char *options, int *status, ...) {
+/*
+*++
+*  Name:
+c     astPcdMap
+f     AST_PCDMAP
+
+*  Purpose:
+*     Create a PcdMap.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "pcdmap.h"
+c     AstPcdMap *astPcdMap( double disco, const double pcdcen[2],
+c                           const char *options, ... )
+f     RESULT = AST_PCDMAP( DISCO, PCDCEN, OPTIONS, STATUS )
+
+*  Class Membership:
+*     PcdMap constructor.
+
+*  Description:
+*     This function creates a new PcdMap and optionally initialises its
+*     attributes.
+*
+*     A PcdMap is a non-linear Mapping which transforms 2-dimensional
+*     positions to correct for the radial distortion introduced by some
+*     cameras and telescopes. This can take the form either of pincushion
+*     or barrel distortion, and is characterized by a single distortion
+*     coefficient.
+*
+*     A PcdMap is specified by giving this distortion coefficient and the
+*     coordinates of the centre of the radial distortion. The forward
+*     transformation of a PcdMap applies the distortion:
+*
+*        RD = R * ( 1 + C * R * R )
+*
+*     where R is the undistorted radial distance from the distortion
+*     centre (specified by attribute PcdCen), RD is the radial distance
+*     from the same centre in the presence of distortion, and C is the
+*     distortion coefficient (given by attribute Disco).
+*
+*     The inverse transformation of a PcdMap removes the distortion
+*     produced by the forward transformation. The expression used to derive
+*     R from RD is an approximate inverse of the expression above, obtained
+*     from two iterations of the Newton-Raphson method. The mismatch between
+*     the forward and inverse expressions is negligible for astrometric
+*     applications (to reach 1 milliarcsec at the edge of the Anglo-Australian
+*     Telescope triplet or a Schmidt field would require field diameters of
+*     2.4 and 42 degrees respectively).
+*
+c     If a PcdMap is inverted (e.g. using astInvert) then the roles of the
+f     If a PcdMap is inverted (e.g. using AST_INVERT) then the roles of the
+*     forward and inverse transformations are reversed; the forward
+*     transformation will remove the distortion, and the inverse
+*     transformation will apply it.
+
+*  Parameters:
+c     disco
+f     DISCO = DOUBLE PRECISION (Given)
+*        The distortion coefficient. Negative values give barrel
+*        distortion, positive values give pincushion distortion, and
+*        zero gives no distortion.
+c     pcdcen
+f     PCDCEN( 2 ) = DOUBLE PRECISION (Given)
+c        A 2-element array containing the coordinates of the centre of the
+f        An array containing the coordinates of the centre of the
+*        distortion.
+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 PcdMap. 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 PcdMap. 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     astPcdMap()
+f     AST_PCDMAP = INTEGER
+*        A pointer to the new PcdMap.
+
+*  Notes:
+*     - A null Object pointer (AST__NULL) will be returned if this
+c     function is invoked with the AST error status set, or if it
+f     function is invoked with STATUS set to an error value, or if it
+*     should fail for any reason.
+
+*  Status Handling:
+*     The protected interface to this function includes an extra
+*     parameter at the end of the parameter list descirbed above. This
+*     parameter is a pointer to the integer inherited status
+*     variable: "int *status".
+
+*--
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstPcdMap *new;              /* Pointer to new PcdMap */
+   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;
+
+/* Initialise the PcdMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitPcdMap( NULL, sizeof( AstPcdMap ), !class_init, &class_vtab,
+                        "PcdMap", disco, pcdcen );
+
+/* 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 PcdMap'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 PcdMap. */
+   return new;
+}
+
+AstPcdMap *astPcdMapId_( double disco, const double pcdcen[2],
+                         const char *options, ... ) {
+/*
+*  Name:
+*     astPcdMapId_
+
+*  Purpose:
+*     Create a PcdMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     AstPcdMap *astPcdMapId_( double disco, const double pcdcen[2],
+*                              const char *options, ... )
+
+*  Class Membership:
+*     PcdMap constructor.
+
+*  Description:
+*     This function implements the external (public) interface to the
+*     astPcdMap constructor function. It returns an ID value (instead
+*     of a true C pointer) to external users, and must be provided
+*     because astPcdMap_ has a variable argument list which cannot be
+*     encapsulated in a macro (where this conversion would otherwise
+*     occur).
+*
+*     The variable argument list also prevents this function from
+*     invoking astPcdMap_ directly, so it must be a re-implementation
+*     of it in all respects, except for the final conversion of the
+*     result to an ID value.
+
+*  Parameters:
+*     As for astPcdMap_.
+
+*  Returned Value:
+*     The ID value associated with the new PcdMap.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstPcdMap *new;              /* Pointer to new PcdMap */
+   va_list args;                /* Variable argument list */
+
+   int *status;                  /* Pointer to inherited status value */
+
+/* Get a pointer to the inherited status value. */
+   status = astGetStatusPtr;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* Initialise the PcdMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitPcdMap( NULL, sizeof( AstPcdMap ), !class_init, &class_vtab,
+                        "PcdMap", disco, pcdcen );
+
+/* 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 PcdMap's attributes. */
+      va_start( args, options );
+      astVSet( new, options, NULL, args );
+      va_end( args );
+
+/* If an error occurred, clean up by deleting the new object. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return an ID value for the new PcdMap. */
+   return astMakeId( new );
+}
+
+AstPcdMap *astInitPcdMap_( void *mem, size_t size, int init,
+                           AstPcdMapVtab *vtab, const char *name,
+                           double disco, const double pcdcen[2], int *status ){
+/*
+*+
+*  Name:
+*     astInitPcdMap
+
+*  Purpose:
+*     Initialise a PcdMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     AstPcdMap *astInitPcdMap( void *mem, size_t size, int init,
+*                               AstPcdMapVtab *vtab, const char *name,
+*                               double disco, const double pcdcen[2] )
+
+*  Class Membership:
+*     PcdMap initialiser.
+
+*  Description:
+*     This function is provided for use by class implementations to initialise
+*     a new PcdMap object. It allocates memory (if necessary) to accommodate
+*     the PcdMap plus any additional data associated with the derived class.
+*     It then initialises a PcdMap 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 PcdMap at the start of the memory passed via the
+*     "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory in which the PcdMap is to be initialised.
+*        This must be of sufficient size to accommodate the PcdMap data
+*        (sizeof(PcdMap)) 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 PcdMap (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 PcdMap
+*        structure, so a valid value must be supplied even if not required for
+*        allocating memory.
+*     init
+*        A logical flag indicating if the PcdMap'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 PcdMap.
+*     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).
+*     disco
+*        Distortion coefficient.
+*     pcdcen
+*        Distortion centre.
+
+*  Returned Value:
+*     A pointer to the new PcdMap.
+
+*  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: */
+   AstPcdMap *new;              /* Pointer to new PcdMap */
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* If necessary, initialise the virtual function table. */
+   if ( init ) astInitPcdMapVtab( vtab, name );
+
+/* Initialise. */
+   new = NULL;
+
+/* Initialise a Mapping structure (the parent class) as the first component
+   within the PcdMap structure, allocating memory if necessary. Specify that
+   the Mapping should be defined in both the forward and inverse directions. */
+   new = (AstPcdMap *) astInitMapping( mem, size, 0,
+                                       (AstMappingVtab *) vtab, name,
+                                       2, 2, 1, 1 );
+
+   if ( astOK ) {
+
+/* Initialise the PcdMap data. */
+/* ---------------------------- */
+/* Store the shift and scale for each axis. */
+      new->pcdcen[0] = pcdcen[0];
+      new->pcdcen[1] = pcdcen[1];
+      new->disco = disco;
+
+/* If an error occurred, clean up by deleting the new PcdMap. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return a pointer to the new PcdMap. */
+   return new;
+}
+
+AstPcdMap *astLoadPcdMap_( void *mem, size_t size,
+                           AstPcdMapVtab *vtab, const char *name,
+                           AstChannel *channel, int *status ) {
+/*
+*+
+*  Name:
+*     astLoadPcdMap
+
+*  Purpose:
+*     Load a PcdMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "pcdmap.h"
+*     AstPcdMap *astLoadPcdMap( void *mem, size_t size,
+*                               AstPcdMapVtab *vtab, const char *name,
+*                               AstChannel *channel )
+
+*  Class Membership:
+*     PcdMap loader.
+
+*  Description:
+*     This function is provided to load a new PcdMap 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
+*     PcdMap 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 PcdMap at the start of the memory
+*     passed via the "vtab" parameter.
+
+
+*  Parameters:
+*     mem
+*        A pointer to the memory into which the PcdMap is to be
+*        loaded.  This must be of sufficient size to accommodate the
+*        PcdMap data (sizeof(PcdMap)) 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 PcdMap (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 PcdMap 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(AstPcdMap) is used instead.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new PcdMap. If this is NULL, a pointer
+*        to the (static) virtual function table for the PcdMap 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 "PcdMap" is used instead.
+
+*  Returned Value:
+*     A pointer to the new PcdMap.
+
+*  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 */
+   AstPcdMap *new;              /* Pointer to the new PcdMap */
+
+/* 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 PcdMap. In this case the
+   PcdMap belongs to this class, so supply appropriate values to be
+   passed to the parent class loader (and its parent, etc.). */
+   if ( !vtab ) {
+      size = sizeof( AstPcdMap );
+      vtab = &class_vtab;
+      name = "PcdMap";
+
+/* If required, initialise the virtual function table for this class. */
+      if ( !class_init ) {
+         astInitPcdMapVtab( 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 PcdMap. */
+   new = astLoadMapping( mem, size, (AstMappingVtab *) vtab, name,
+                         channel );
+
+   if ( astOK ) {
+
+/* Read input data. */
+/* ================ */
+/* Request the input Channel to read all the input data appropriate to
+   this class into the internal "values list". */
+      astReadClassData( channel, "PcdMap" );
+
+/* 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. */
+
+/* PcdCen(0). */
+/* ---------- */
+      new->pcdcen[0] = astReadDouble( channel, "pcdcn0", AST__BAD );
+      if ( TestPcdCen( new, 0, status ) ) SetPcdCen( new, 0, new->pcdcen[0], status );
+
+/* PcdCen(1). */
+/* ---------- */
+      new->pcdcen[1] = astReadDouble( channel, "pcdcn1", AST__BAD );
+      if ( TestPcdCen( new, 1, status ) ) SetPcdCen( new, 1, new->pcdcen[1], status );
+
+/* Disco. */
+/* ------ */
+      new->disco = astReadDouble( channel, "disco", AST__BAD );
+      if ( TestDisco( new, status ) ) SetDisco( new, new->disco, status );
+
+/* If an error occurred, clean up by deleting the new PcdMap. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return the new PcdMap 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. */
+
+
+
+
+