Merge commit '7fde2daeed593684120d75de07598154f3ddaf2c' as 'ast'

1 files changed, 2052 insertions, 0 deletions

diff --git a/ast/sphmap.c b/ast/sphmap.c
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+/*
+*class++
+*  Name:
+*     SphMap
+
+*  Purpose:
+*     Map 3-d Cartesian to 2-d spherical coordinates
+
+*  Constructor Function:
+c     astSphMap
+f     AST_SPHMAP
+
+*  Description:
+*     A SphMap is a Mapping which transforms points from a
+*     3-dimensional Cartesian coordinate system into a 2-dimensional
+*     spherical coordinate system (longitude and latitude on a unit
+*     sphere centred at the origin). It works by regarding the input
+*     coordinates as position vectors and finding their intersection
+*     with the sphere surface. The inverse transformation always
+*     produces points which are a unit distance from the origin
+*     (i.e. unit vectors).
+
+*  Inheritance:
+*     The SphMap class inherits from the Mapping class.
+
+*  Attributes:
+*     In addition to those attributes common to all Mappings, every
+*     SphMap also has the following attributes:
+*
+*     - UnitRadius: SphMap input vectors lie on a unit sphere?
+*     - PolarLong: The longitude value to assign to either pole
+
+*  Functions:
+c     The SphMap class does not define any new functions beyond those
+f     The SphMap 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)
+*     RFWS: R.F. Warren-Smith (Starlink)
+
+*  History:
+*     24-OCT-1996 (DSB):
+*        Original version.
+*     5-MAR-1997 (RFWS):
+*        Tidied public prologues.
+*     24-MAR-1998 (RFWS):
+*        Override the astMapMerge method.
+*     4-SEP-1998 (DSB):
+*        Added UnitRadius attribute.
+*     8-JAN-2003 (DSB):
+*        Changed private InitVtab method to protected astInitSphMapVtab
+*        method.
+*     11-JUN-2003 (DSB):
+*        Added PolarLong attribute.
+*     10-MAY-2006 (DSB):
+*        Override astEqual.
+*     5-NOV-2013 (DSB):
+*        Modify MapMerge so that it can spot and simplify an
+*        (inverted SphMap,MatrixMap,SphMap) sequence in which the
+*        MatrixMap just magnifies or reflects the radius vector.
+*     25-MAR-2014 (DSB):
+*        Correct 5-NOV-2013 MapMerge change.
+*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 SphMap
+
+/* 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 "mapping.h"             /* Coordinate mappings (parent class) */
+#include "channel.h"             /* I/O channels */
+#include "unitmap.h"             /* Unit (identity) Mappings */
+#include "sphmap.h"              /* Interface definition for this class */
+#include "pal.h"                 /* SLA transformations */
+#include "wcsmap.h"              /* For the AST__DPIBY2 (etc) constants */
+#include "matrixmap.h"           /* Matrix mappings */
+#include "winmap.h"              /* Shift and scale mappings */
+#include "zoommap.h"             /* Scale mappings */
+
+/* Error code definitions. */
+/* ----------------------- */
+#include "ast_err.h"             /* AST error codes */
+
+/* C header files. */
+/* --------------- */
+#include <float.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(SphMap)
+
+/* Define macros for accessing each item of thread specific global data. */
+#define class_init astGLOBAL(SphMap,Class_Init)
+#define class_vtab astGLOBAL(SphMap,Class_Vtab)
+#define getattrib_buff astGLOBAL(SphMap,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 AstSphMapVtab 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. */
+AstSphMap *astSphMapId_( const char *, ...);
+
+/* Prototypes for Private Member Functions. */
+/* ======================================== */
+static int GetUnitRadius( AstSphMap *, int * );
+static int TestUnitRadius( AstSphMap *, int * );
+static void ClearUnitRadius( AstSphMap *, int * );
+static void SetUnitRadius( AstSphMap *, int, int * );
+
+static double GetPolarLong( AstSphMap *, int * );
+static int TestPolarLong( AstSphMap *, int * );
+static void ClearPolarLong( AstSphMap *, int * );
+static void SetPolarLong( AstSphMap *, double, int * );
+
+static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static const char *GetAttrib( AstObject *, const char *, 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 void ClearAttrib( AstObject *, const char *, int * );
+static void Copy( const AstObject *, AstObject *, int * );
+static void Delete( AstObject *, int * );
+static void Dump( AstObject *, AstChannel *, int * );
+static void SetAttrib( AstObject *, const char *, int * );
+
+/* Member functions. */
+/* ================= */
+static void ClearAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     ClearAttrib
+
+*  Purpose:
+*     Clear an attribute value for a SphMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     void ClearAttrib( AstObject *this, const char *attrib, int *status, int *status )
+
+*  Class Membership:
+*     SphMap 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
+*     SphMap, so that the default value will subsequently be used.
+
+*  Parameters:
+*     this
+*        Pointer to the SphMap.
+*     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.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstSphMap *this;             /* Pointer to the SphMap structure */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the SphMap structure. */
+   this = (AstSphMap *) this_object;
+
+/* UnitRadius */
+/* ---------- */
+   if ( !strcmp( attrib, "unitradius" ) ) {
+      astClearUnitRadius( this );
+
+/* PolarLong */
+/* --------- */
+   } else if ( !strcmp( attrib, "polarlong" ) ) {
+      astClearPolarLong( 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 SphMaps are equivalent.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     int Equal( AstObject *this, AstObject *that, int *status, int *status )
+
+*  Class Membership:
+*     SphMap 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 SphMaps are equivalent.
+
+*  Parameters:
+*     this
+*        Pointer to the first Object (a SphMap).
+*     that
+*        Pointer to the second Object.
+*     status
+*        Pointer to the inherited status variable.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     One if the SphMaps 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: */
+   AstSphMap *that;
+   AstSphMap *this;
+   int nin;
+   int nout;
+   int result;
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain pointers to the two SphMap structures. */
+   this = (AstSphMap *) this_object;
+   that = (AstSphMap *) that_object;
+
+/* Check the second object is a SphMap. We know the first is a
+   SphMap since we have arrived at this implementation of the virtual
+   function. */
+   if( astIsASphMap( that ) ) {
+
+/* Get the number of inputs and outputs and check they are the same for both. */
+      nin = astGetNin( this );
+      nout = astGetNout( this );
+      if( astGetNin( that ) == nin && astGetNout( that ) == nout ) {
+
+/* If the Invert flags for the two SphMaps differ, it may still be possible
+   for them to be equivalent. First compare the SphMaps if their Invert
+   flags are the same. In this case all the attributes of the two SphMaps
+   must be identical. */
+         if( astGetInvert( this ) == astGetInvert( that ) ) {
+
+            if( astEQUAL( this->polarlong, that->polarlong ) &&
+                          this->unitradius == that->unitradius ){
+               result = 1;
+            }
+
+/* If the Invert flags for the two SphMaps differ, the attributes of the two
+   SphMaps must be inversely related to each other. */
+         } else {
+
+/* In the specific case of a SphMap, Invert flags must be equal. */
+            result = 0;
+
+         }
+      }
+   }
+
+/* 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 SphMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     const char *GetAttrib( AstObject *this, const char *attrib, int *status, int *status )
+
+*  Class Membership:
+*     SphMap 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 SphMap, formatted as a character string.
+
+*  Parameters:
+*     this
+*        Pointer to the SphMap.
+*     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.
+*     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 SphMap, 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 SphMap. 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 */
+   AstSphMap *this;              /* Pointer to the SphMap structure */
+   const char *result;           /* Pointer value to return */
+   double dval;                  /* Double precision attribute value */
+   int ival;                     /* Int attribute value */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(this_object);
+
+/* Obtain a pointer to the SphMap structure. */
+   this = (AstSphMap *) this_object;
+
+/* UnitRadius. */
+/* ----------- */
+   if ( !strcmp( attrib, "unitradius" ) ) {
+      ival = astGetUnitRadius( this );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%d", ival );
+         result = getattrib_buff;
+      }
+
+/* PolarLong */
+/* --------- */
+   } else if ( !strcmp( attrib, "polarlong" ) ) {
+      dval = astGetPolarLong( this );
+      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 astInitSphMapVtab_(  AstSphMapVtab *vtab, const char *name, int *status ) {
+/*
+*+
+*  Name:
+*     astInitSphMapVtab
+
+*  Purpose:
+*     Initialise a virtual function table for a SphMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     void astInitSphMapVtab( AstSphMapVtab *vtab, const char *name )
+
+*  Class Membership:
+*     SphMap vtab initialiser.
+
+*  Description:
+*     This function initialises the component of a virtual function
+*     table which is used by the SphMap 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 astIsASphMap) 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->ClearUnitRadius = ClearUnitRadius;
+   vtab->SetUnitRadius = SetUnitRadius;
+   vtab->GetUnitRadius = GetUnitRadius;
+   vtab->TestUnitRadius = TestUnitRadius;
+
+   vtab->ClearPolarLong = ClearPolarLong;
+   vtab->SetPolarLong = SetPolarLong;
+   vtab->GetPolarLong = GetPolarLong;
+   vtab->TestPolarLong = TestPolarLong;
+
+/* 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;
+
+   parent_transform = mapping->Transform;
+   mapping->Transform = Transform;
+
+/* Store replacement pointers for methods which will be over-ridden by
+   new member functions implemented here. */
+   object->Equal = Equal;
+   mapping->MapMerge = MapMerge;
+
+/* Declare the class dump, copy and delete functions.*/
+   astSetDump( vtab, Dump, "SphMap", "Cartesian to Spherical mapping" );
+   astSetCopy( (AstObjectVtab *) vtab, Copy );
+   astSetDelete( (AstObjectVtab *) vtab, Delete );
+
+/* If we have just initialised the vtab for the current class, indicate
+   that the vtab is now initialised, and store a pointer to the class
+   identifier in the base "object" level of the vtab. */
+   if( vtab == &class_vtab ) {
+      class_init = 1;
+      astSetVtabClassIdentifier( vtab, &(vtab->id) );
+   }
+}
+
+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 SphMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     int MapMerge( AstMapping *this, int where, int series, int *nmap,
+*                   AstMapping ***map_list, int **invert_list, int *status, int *status )
+
+*  Class Membership:
+*     SphMap 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 SphMap 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 SphMap with one which it
+*     considers simpler, or to merge it with the Mappings which
+*     immediately precede it or follow it in the sequence (both will
+*     normally be considered). This is sufficient to ensure the
+*     eventual simplification of most Mapping sequences by repeated
+*     application of this function.
+*
+*     In some cases, the function may attempt more elaborate
+*     simplification, involving any number of other Mappings in the
+*     sequence. It is not restricted in the type or scope of
+*     simplification it may perform, but will normally only attempt
+*     elaborate simplification in cases where a more straightforward
+*     approach is not adequate.
+
+*  Parameters:
+*     this
+*        Pointer to the nominated SphMap which is to be merged with
+*        its neighbours. This should be a cloned copy of the SphMap
+*        pointer contained in the array element "(*map_list)[where]"
+*        (see below). This pointer will not be annulled, and the
+*        SphMap it identifies will not be modified by this function.
+*     where
+*        Index in the "*map_list" array (below) at which the pointer
+*        to the nominated SphMap 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.
+*     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 *new;              /* Pointer to replacement Mapping */
+   AstMatrixMap *mm;             /* Pointer to MatrixMap */
+   AstWinMap *wm;                /* The new WinMap */
+   const char *class;            /* Pointer to Mapping class string */
+   double absval;                /* Absolute value fo each diagonal element */
+   double diag[ 3 ];             /* The diagonal matrix elements */
+   double polarlong;             /* Value of PolarLong attribute */
+   int imap1;                    /* Index of first SphMap */
+   int imap2;                    /* Index of second SphMap */
+   int imap;                     /* Loop counter for Mappings */
+   int result;                   /* Result value to return */
+   int simpler;                  /* Mappings simplified? */
+
+/* Initialise the returned result. */
+   result = -1;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Further initialisation. */
+   new = NULL;
+   simpler = 0;
+
+/* We will only handle the case of SphMaps in series and will consider
+   merging the nominated SphMap with the Mapping which follows
+   it. Check that there is such a Mapping. */
+   if ( series && ( ( where + 1 ) < *nmap ) ) {
+
+/* Obtain the indices of the two potential SphMaps to be merged. */
+      imap1 = where;
+      imap2 = where + 1;
+
+/* Obtain the Class string of the second Mapping and determine if it
+   is a SphMap. */
+      class = astGetClass( ( *map_list )[ imap2 ] );
+      if ( astOK && !strcmp( class, "SphMap" ) ) {
+
+/* Check if the first SphMap is applied in the inverse direction and
+   the second in the forward direction. This combination can be
+   simplified if the PolarLongitude attributes are equal.. */
+         if( ( *invert_list )[ imap1 ] && !( *invert_list )[ imap2 ] ) {
+            simpler = astEQUAL( astGetPolarLong( ( *map_list )[ imap1 ] ),
+                                astGetPolarLong( ( *map_list )[ imap2 ] ) );
+
+/* If the first SphMap is applied in the forward direction and the second in
+   the inverse direction, the combination can only be simplified if the
+   input vectors to the first SphMap all have unit length (as indicated by
+   the UnitRadius attribute). */
+         } else if( !( *invert_list )[ imap1 ] && ( *invert_list )[ imap2 ] ) {
+            simpler = astGetUnitRadius( ( *map_list )[ imap1 ] );
+         }
+      }
+
+/* If the two SphMaps can be simplified, create a UnitMap to replace
+   them. */
+      if ( simpler ) {
+         new = (AstMapping *) astUnitMap( 2, "", status );
+
+/* Annul the pointers to the SphMaps. */
+         if ( astOK ) {
+            ( *map_list )[ imap1 ] = astAnnul( ( *map_list )[ imap1 ] );
+            ( *map_list )[ imap2 ] = astAnnul( ( *map_list )[ imap2 ] );
+
+/* Insert the pointer to the replacement Mapping and initialise its
+   invert flag. */
+            ( *map_list )[ imap1 ] = new;
+            ( *invert_list )[ imap1 ] = 0;
+
+/* Loop to close the resulting gap by moving subsequent elements down
+   in the arrays. */
+            for ( imap = imap2 + 1; imap < *nmap; imap++ ) {
+               ( *map_list )[ imap - 1 ] = ( *map_list )[ imap ];
+               ( *invert_list )[ imap - 1 ] = ( *invert_list )[ imap ];
+            }
+
+/* Clear the vacated elements 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 = imap1;
+         }
+      }
+   }
+
+/* Another possible simplification is if the nominated Mapping is an inverted
+   SphMap followed in series by a ZoomMap or diagonal MatrixMap that has
+   diagonal elements of equal magnitude, which is then followed by a
+   non-inverted SphMap. This is equivalent to a 3D rotation of a pair of
+   (longitude,latitude) angles. The MatrixMap/ZoomMap may magnify the
+   radius vector, but this will not alter the angles. Any difference in
+   signs amongst the diagonal elements will cause a reflection or reversal
+   of the corresponbding angles, which can be represented by a WinMap. We
+   do not need to consider the other possibility (that the nominated
+   SphMap is the *last* Mapping in such a sequence of three), since we
+   will already have discovered such a sequence on an earlier invocation
+   of this function. */
+   if( series && !simpler && ( *invert_list )[ where ] &&
+       where + 2 < *nmap  ) {
+
+/* Check the third Mapping is a non-inverted SphMap. */
+      class = astGetClass( ( *map_list )[ where + 2 ] );
+      if( astOK && !strcmp( class, "SphMap" ) &&
+          !( *invert_list )[ where + 2 ] ) {
+
+/* Check the second Mapping is a ZoomMap, or a diagonal MatrixMap that
+   has diagonal elements of equal magnitude. Since the Mapping is
+   sandwiched between the two SphMaps, we know it must have 3 inputs and
+   3 outputs. Record the corresponding diagonal values. The state of the
+   Invert flag does not matter since it will only affect the degree to
+   which the radius vector is magnified - it will not change the signs of
+   any diagonal elements. */
+         class = astGetClass( ( *map_list )[ where + 1 ] );
+         if( astOK && !strcmp( class, "ZoomMap" ) ) {
+            diag[ 0 ] = astGetZoom( ( *map_list )[ where + 1 ] );
+            if( diag[ 0 ] != 0.0 ) {
+               diag[ 1 ] = diag[ 0 ];
+               diag[ 2 ] = diag[ 0 ];
+            } else {
+               class = NULL;
+            }
+
+         } else if( astOK && !strcmp( class, "MatrixMap" ) ) {
+            mm = (AstMatrixMap *)  ( *map_list )[ where + 1 ];
+            if( mm->form == 1 && mm->f_matrix ) {
+               diag[ 0 ] = mm->f_matrix[ 0 ];
+               if( diag[ 0 ] != 0.0 ) {
+                  diag[ 1 ] = mm->f_matrix[ 1 ];
+                  diag[ 2 ] = mm->f_matrix[ 2 ];
+
+                  absval = fabs( diag[ 0 ] );
+                  if( !astEQUAL( fabs( diag[ 1 ] ), absval ) ||
+                      !astEQUAL( fabs( diag[ 2 ] ), absval ) ) {
+                     class = NULL;
+                  }
+
+               } else {
+                  class = NULL;
+               }
+
+            } else {
+               class = NULL;
+            }
+
+         } else {
+            class = NULL;
+         }
+
+      } else {
+         class = NULL;
+      }
+
+/* We can only make changes if above conditions were met. */
+      if( class ) {
+
+/* Create a WinMap that modifies the (longitude,latitude) values, initially
+   with undefined corners. */
+         wm = astWinMap( 2, NULL, NULL, NULL, NULL, "", status );
+
+/* Store appropriate scales and offsets in the WinMap. These just depend on
+   the signs of the matrix diagonal elements since we know the magnitudes of
+   these elements are all equal. */
+         if( diag[ 0 ] < 0.0 ) {
+            if( diag[ 1 ] < 0.0 ) {
+               wm->a[ 0 ] = AST__DPI;
+               wm->b[ 0 ] = 1.0;
+            } else {
+               wm->a[ 0 ] = AST__DPI;
+               wm->b[ 0 ] = -1.0;
+            }
+
+         } else {
+            if( diag[ 1 ] < 0.0 ) {
+               wm->a[ 0 ] = 0.0;
+               wm->b[ 0 ] = -1.0;
+            } else {
+               wm->a[ 0 ] = 0.0;
+               wm->b[ 0 ] = 1.0;
+            }
+         }
+
+         if( diag[ 2 ] < 0.0 ) {
+            wm->a[ 1 ] = 0.0;
+            wm->b[ 1 ] = -1.0;
+         } else {
+            wm->a[ 1 ] = 0.0;
+            wm->b[ 1 ] = 1.0;
+         }
+
+/* We are aiming to replace the supplied (SphMap,MatrixMap,SphMap)
+   combination with (WinMap,SphMap,SphMap), leaving us with an inverted
+   and non-inverted SphMap side by side. This is on the understanding
+   that a subsequent call to this function will combine these two
+   adjacent SphMaps into a UnitMap. But this will only happen if the
+   adjacent SphMaps have equal values for their PolarLong attributes. The
+   change of (SphMap,MatrixMap) to (WinMap,SphMap) will change the value
+   of the PolarLong attribute in the first SphMap, so we need to work out
+   this changed value and check that it is the same as the PolarLong
+   value of the second SphMap. If they are different, there is no point
+   making any changes since the two SphMaps cannot be merged into a
+   UnitMap. So get the PolarLong value from the supplied first SphMap. */
+         polarlong = astGetPolarLong( ( *map_list )[ where ] );
+
+/* Modified the PolarLong value to take account of the change from
+   (SphMap,MatrixMap) to (WinMap,SphMap). */
+         polarlong =  wm->a[ 0 ] + wm->b[ 0 ]*polarlong;
+
+/* Check this is the same as the PolarLong value in the second SphMap. */
+         if( astEQUAL( polarlong, astGetPolarLong( ( *map_list )[ where + 2 ] ) ) ) {
+
+/* All is good, so we can now change the supplied Mappings list. First
+   change the PolarLong value in the first SphMap. */
+            astSetPolarLong( ( *map_list )[ where ], polarlong );
+
+/* Annul The MatrixMap or ZoomMap. */
+            (void) astAnnul( ( *map_list )[ where + 1 ] );
+
+/* Move the first SphMap to the slot left vacant by the annulled
+   MatrixMap or ZoomMap. */
+            ( *map_list )[ where + 1 ] = ( *map_list )[ where ];
+            ( *invert_list )[ where + 1 ] = ( *invert_list )[ where ];
+
+/* Store the new WinMap in the place of the SphMap. */
+            ( *map_list )[ where ] = astClone( wm );
+            ( *invert_list )[ where ] = 0;
+
+/* Return the index of the first modified element. */
+            result = where;
+         }
+
+/* Free resources. */
+         wm = astAnnul( wm );
+      }
+   }
+
+/* If an error occurred, clear the returned result. */
+   if ( !astOK ) result = -1;
+
+/* Return the result. */
+   return result;
+}
+
+static void SetAttrib( AstObject *this_object, const char *setting, int *status ) {
+/*
+*  Name:
+*     SetAttrib
+
+*  Purpose:
+*     Set an attribute value for a SphMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     void SetAttrib( AstObject *this, const char *setting )
+
+*  Class Membership:
+*     SphMap member function (over-rides the astSetAttrib protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function assigns an attribute value for a SphMap, 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 SphMap.
+*     setting
+*        Pointer to a null-terminated string specifying the new attribute
+*        value.
+*/
+
+/* Local Variables: */
+   AstSphMap *this;              /* Pointer to the SphMap structure */
+   double dval;                  /* Double precision attribute value */
+   int len;                      /* Length of setting string */
+   int ival;                     /* Int attribute value */
+   int nc;                       /* Number of characters read by astSscanf */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the SphMap structure. */
+   this = (AstSphMap *) this_object;
+
+/* Obtain the length of the setting string. */
+   len = (int) strlen( setting );
+
+/* UnitRadius */
+/* ---------- */
+   if ( nc = 0,
+        ( 1 == astSscanf( setting, "unitradius= %d %n", &ival, &nc ) )
+        && ( nc >= len ) ) {
+      astSetUnitRadius( this, ival );
+
+/* PolarLong */
+/* --------- */
+   } else if ( nc = 0,
+        ( 1 == astSscanf( setting, "polarlong= %lf %n", &dval, &nc ) )
+        && ( nc >= len ) ) {
+      astSetPolarLong( this, 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 SphMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     int TestAttrib( AstObject *this, const char *attrib, int *status, int *status )
+
+*  Class Membership:
+*     SphMap 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 SphMap's attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the SphMap.
+*     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.
+*     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: */
+   AstSphMap *this;             /* Pointer to the SphMap structure */
+   int result;                   /* Result value to return */
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the SphMap structure. */
+   this = (AstSphMap *) this_object;
+
+/* UnitRadius */
+/* ---------- */
+   if ( !strcmp( attrib, "unitradius" ) ) {
+      result = astTestUnitRadius( this );
+
+/* PolarLong */
+/* --------- */
+   } else if ( !strcmp( attrib, "polarlong" ) ) {
+      result = astTestPolarLong( this );
+
+/* 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 SphMap to transform a set of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+*                             int forward, AstPointSet *out, int *status, int *status )
+
+*  Class Membership:
+*     SphMap member function (over-rides the astTransform protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function takes a SphMap and a set of points encapsulated in a
+*     PointSet and transforms the points from Cartesian coordinates to
+*     spherical coordinates.
+
+*  Parameters:
+*     this
+*        Pointer to the SphMap.
+*     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.
+*     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 SphMap 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 */
+   AstSphMap *map;               /* Pointer to SphMap to be applied */
+   double **ptr_in;              /* Pointer to input coordinate data */
+   double **ptr_out;             /* Pointer to output coordinate data */
+   int npoint;                   /* Number of points */
+   int point;                    /* Loop counter for points */
+   double *p0;                   /* Pointer to x axis value */
+   double *p1;                   /* Pointer to y axis value */
+   double *p2;                   /* Pointer to z axis value */
+   double *q0;                   /* Pointer to longitude value */
+   double *q1;                   /* Pointer to latitude value */
+   double mxerr;                 /* Largest value which is effectively zero */
+   double polarlong;             /* Longitude at either pole */
+   double v[3];                  /* Vector for a single point */
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain a pointer to the SphMap. */
+   map = (AstSphMap *) 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;
+
+/* Perform coordinate arithmetic. */
+/* ------------------------------ */
+   if( astOK ){
+
+/* First deal with forward mappings from Cartesian to Spherical. */
+      if( forward ){
+
+/* Get the longitude to return at either pole. */
+         polarlong = astGetPolarLong( this );
+
+/* Store pointers to the input Cartesian axes. */
+         p0 = ptr_in[ 0 ];
+         p1 = ptr_in[ 1 ];
+         p2 = ptr_in[ 2 ];
+
+/* Store pointers to the output Spherical axes. */
+         q0 = ptr_out[ 0 ];
+         q1 = ptr_out[ 1 ];
+
+/* Apply the mapping to every point. */
+         for( point = 0; point < npoint; point++ ){
+            if( *p0 != AST__BAD && *p1 != AST__BAD && *p2 != AST__BAD ){
+               v[0] = *p0;
+               v[1] = *p1;
+               v[2] = *p2;
+
+/* At either pole, return the longitude equal to PolarLong attribute. */
+               mxerr = fabs( 1000.0*v[ 2 ] )*DBL_EPSILON;
+               if( fabs( v[ 0 ] ) < mxerr && fabs( v[ 1 ] ) < mxerr ) {
+                  if( v[ 2 ] < 0.0 ) {
+                     *(q0++) = polarlong;
+                     *(q1++) = -AST__DPIBY2;
+                  } else if( v[ 2 ] > 0.0 ) {
+                     *(q0++) = polarlong;
+                     *(q1++) = AST__DPIBY2;
+                  } else {
+                     *(q0++) = AST__BAD;
+                     *(q1++) = AST__BAD;
+                  }
+
+/* Otherwise use a SLALIB function to do the conversion (SLALIB always
+   returns zero at either pole which is why we make the above check). */
+               } else {
+                  palDcc2s( v, q0++, q1++ );
+               }
+
+            } else {
+               *(q0++) = AST__BAD;
+               *(q1++) = AST__BAD;
+            }
+            p0++;
+            p1++;
+            p2++;
+         }
+
+/* Now deal with inverse mappings from Spherical to Cartesian. */
+      } else {
+
+/* Store pointers to the input Spherical axes. */
+         q0 = ptr_in[ 0 ];
+         q1 = ptr_in[ 1 ];
+
+/* Store pointers to the output Cartesian axes. */
+         p0 = ptr_out[ 0 ];
+         p1 = ptr_out[ 1 ];
+         p2 = ptr_out[ 2 ];
+
+/* Apply the mapping to every point. */
+         for( point = 0; point < npoint; point++ ){
+            if( *q0 != AST__BAD && *q1 != AST__BAD ){
+               palDcs2c( *q0, *q1, v );
+               *(p0++) = v[ 0 ];
+               *(p1++) = v[ 1 ];
+               *(p2++) = v[ 2 ];
+            } else {
+               *(p0++) = AST__BAD;
+               *(p1++) = AST__BAD;
+               *(p2++) = AST__BAD;
+
+            }
+            q0++;
+            q1++;
+         }
+
+      }
+
+   }
+
+/* Return a pointer to the output PointSet. */
+   return result;
+}
+
+/* Functions which access class attributes. */
+/* ---------------------------------------- */
+/* Implement member functions to access the attributes associated with
+   this class using the macros defined for this purpose in the
+   "object.h" file. For a description of each attribute, see the class
+   interface (in the associated .h file). */
+
+/* UnitRadius */
+/* ---------- */
+/*
+*att++
+*  Name:
+*     UnitRadius
+
+*  Purpose:
+*     SphMap input vectors lie on a unit sphere?
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Integer (boolean).
+
+*  Description:
+*     This is a boolean attribute which indicates whether the
+*     3-dimensional vectors which are supplied as input to a SphMap
+*     are known to always have unit length, so that they lie on a unit
+*     sphere centred on the origin.
+*
+c     If this condition is true (indicated by setting UnitRadius
+c     non-zero), it implies that a CmpMap which is composed of a
+c     SphMap applied in the forward direction followed by a similar
+c     SphMap applied in the inverse direction may be simplified
+c     (e.g. by astSimplify) to become a UnitMap. This is because the
+c     input and output vectors will both have unit length and will
+c     therefore have the same coordinate values.
+f     If this condition is true (indicated by setting UnitRadius
+f     non-zero), it implies that a CmpMap which is composed of a
+f     SphMap applied in the forward direction followed by a similar
+f     SphMap applied in the inverse direction may be simplified
+f     (e.g. by AST_SIMPLIFY) to become a UnitMap. This is because the
+f     input and output vectors will both have unit length and will
+f     therefore have the same coordinate values.
+*
+*     If UnitRadius is zero (the default), then although the output
+*     vector produced by the CmpMap (above) will still have unit
+*     length, the input vector may not have. This will, in general,
+*     change the coordinate values, so it prevents the pair of SphMaps
+*     being simplified.
+
+*  Notes:
+*     - This attribute is intended mainly for use when SphMaps are
+*     involved in a sequence of Mappings which project (e.g.) a
+*     dataset on to the celestial sphere. By regarding the celestial
+*     sphere as a unit sphere (and setting UnitRadius to be non-zero)
+*     it becomes possible to cancel the SphMaps present, along with
+*     associated sky projections, when two datasets are aligned using
+*     celestial coordinates. This often considerably improves
+*     performance.
+*     - Such a situations often arises when interpreting FITS data and
+*     is handled automatically by the FitsChan class.
+*     - The value of the UnitRadius attribute is used only to control
+*     the simplification of Mappings and has no effect on the value of
+*     the coordinates transformed by a SphMap. The lengths of the
+*     input 3-dimensional Cartesian vectors supplied are always
+*     ignored, even if UnitRadius is non-zero.
+*     - The value of this attribute may changed only if the SphMap
+*     has no more than one reference. That is, an error is reported if the
+*     SphMap 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:
+*     SphMap
+*        All SphMaps have this attribute.
+*att--
+*/
+astMAKE_CLEAR1(SphMap,UnitRadius,unitradius,-1)
+astMAKE_GET(SphMap,UnitRadius,int,0,(this->unitradius == -1 ? 0 : this->unitradius))
+astMAKE_SET1(SphMap,UnitRadius,int,unitradius,( value ? 1 : 0 ))
+astMAKE_TEST(SphMap,UnitRadius,( this->unitradius != -1 ))
+
+/* PolarLong */
+/* --------- */
+/*
+*att++
+*  Name:
+*     PolarLong
+
+*  Purpose:
+*     The longitude value to assign to either pole
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Double precision.
+
+*  Description:
+*     This attribute holds the longitude value, in radians, to be
+*     returned when a Cartesian position corresponding to either the north
+*     or south pole is transformed into spherical coordinates. The
+*     default value is zero.
+*
+*     Note, the value of this attribute may changed only if the SphMap
+*     has no more than one reference. That is, an error is reported if the
+*     SphMap 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:
+*     SphMap
+*        All SphMaps have this attribute.
+*att--
+*/
+astMAKE_CLEAR1(SphMap,PolarLong,polarlong,AST__BAD)
+astMAKE_GET(SphMap,PolarLong,double,0.0,(this->polarlong == AST__BAD ? 0.0 : this->polarlong))
+astMAKE_SET1(SphMap,PolarLong,double,polarlong,value)
+astMAKE_TEST(SphMap,PolarLong,( this->polarlong != AST__BAD ))
+
+/* Copy constructor. */
+/* ----------------- */
+static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
+/*
+*  Name:
+*     Copy
+
+*  Purpose:
+*     Copy constructor for SphMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Copy( const AstObject *objin, AstObject *objout, int *status, int *status, int *status )
+
+*  Description:
+*     This function implements the copy constructor for SphMap objects.
+
+*  Parameters:
+*     objin
+*        Pointer to the SphMap to be copied.
+*     objout
+*        Pointer to the SphMap being constructed.
+*     status
+*        Pointer to the inherited status variable.
+*     status
+*        Pointer to the inherited status variable.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+}
+
+/* Destructor. */
+/* ----------- */
+static void Delete( AstObject *obj, int *status ) {
+/*
+*  Name:
+*     Delete
+
+*  Purpose:
+*     Destructor for SphMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Delete( AstObject *obj, int *status, int *status )
+
+*  Description:
+*     This function implements the destructor for SphMap objects.
+
+*  Parameters:
+*     obj
+*        Pointer to the SphMap to be deleted.
+*     status
+*        Pointer to the inherited status variable.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     - This destructor does nothing and exists only to maintain a
+*     one-to-one correspondence between destructors and copy
+*     constructors.
+*/
+
+
+}
+
+/* Dump function. */
+/* -------------- */
+static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
+/*
+*  Name:
+*     Dump
+
+*  Purpose:
+*     Dump function for SphMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Dump( AstObject *this, AstChannel *channel, int *status, int *status, int *status, int *status )
+
+*  Description:
+*     This function implements the Dump function which writes out data
+*     for the SphMap class to an output Channel.
+
+*  Parameters:
+*     this
+*        Pointer to the SphMap whose data are being written.
+*     channel
+*        Pointer to the Channel to which the data are being written.
+*     status
+*        Pointer to the inherited status variable.
+*     status
+*        Pointer to the inherited status variable.
+*     status
+*        Pointer to the inherited status variable.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstSphMap *this;              /* Pointer to the SphMap structure */
+   double dval;                  /* Double precision attribute value */
+   int ival;                     /* Integer value */
+   int set;                      /* Attribute value set? */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the SphMap structure. */
+   this = (AstSphMap *) this_object;
+
+/* Write out values representing the instance variables for the
+   SphMap 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. */
+
+/* UnitRadius. */
+/* ------- */
+   set = TestUnitRadius( this, status );
+   ival = set ? GetUnitRadius( this, status ) : astGetUnitRadius( this );
+   if( ival ) {
+      astWriteInt( channel, "UntRd", set, 0, ival, "All input vectors have unit length" );
+   } else {
+      astWriteInt( channel, "UntRd", set, 0, ival, "Input vectors do not all have unit length" );
+   }
+
+/* PolarLong. */
+/* ---------- */
+   set = TestPolarLong( this, status );
+   dval = set ? GetPolarLong( this, status ) : astGetPolarLong( this );
+   astWriteDouble( channel, "PlrLg", set, 1, dval, "Polar longitude (rad.s)" );
+
+}
+
+/* Standard class functions. */
+/* ========================= */
+/* Implement the astIsASphMap and astCheckSphMap functions using the macros
+   defined for this purpose in the "object.h" header file. */
+astMAKE_ISA(SphMap,Mapping)
+astMAKE_CHECK(SphMap)
+
+AstSphMap *astSphMap_( const char *options, int *status, ...) {
+/*
+*++
+*  Name:
+c     astSphMap
+f     AST_SPHMAP
+
+*  Purpose:
+*     Create a SphMap.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "sphmap.h"
+c     AstSphMap *astSphMap( const char *options, ... )
+f     RESULT = AST_SPHMAP( OPTIONS, STATUS )
+
+*  Class Membership:
+*     SphMap constructor.
+
+*  Description:
+*     This function creates a new SphMap and optionally initialises
+*     its attributes.
+*
+*     A SphMap is a Mapping which transforms points from a
+*     3-dimensional Cartesian coordinate system into a 2-dimensional
+*     spherical coordinate system (longitude and latitude on a unit
+*     sphere centred at the origin). It works by regarding the input
+*     coordinates as position vectors and finding their intersection
+*     with the sphere surface. The inverse transformation always
+*     produces points which are a unit distance from the origin
+*     (i.e. unit vectors).
+
+*  Parameters:
+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 SphMap. 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 SphMap. 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     astSphMap()
+f     AST_SPHMAP = INTEGER
+*        A pointer to the new SphMap.
+
+*  Notes:
+*     - The spherical coordinates are longitude (positive
+*     anti-clockwise looking from the positive latitude pole) and
+*     latitude. The Cartesian coordinates are right-handed, with the x
+*     axis (axis 1) at zero longitude and latitude, and the z axis
+*     (axis 3) at the positive latitude pole.
+*     - At either pole, the longitude is set to the value of the
+*     PolarLong attribute.
+*     - If the Cartesian coordinates are all zero, then the longitude
+*     and latitude are set to the value AST__BAD.
+*     - 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".
+
+
+*  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".
+
+
+*  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 */
+   AstSphMap *new;              /* Pointer to new SphMap */
+   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 SphMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitSphMap( NULL, sizeof( AstSphMap ), !class_init, &class_vtab,
+                        "SphMap" );
+
+/* 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 SphMap'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 SphMap. */
+   return new;
+}
+
+AstSphMap *astSphMapId_( const char *options, ...) {
+/*
+*  Name:
+*     astSphMapId_
+
+*  Purpose:
+*     Create a SphMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     AstSphMap *astSphMapId_( const char *options, ... )
+
+*  Class Membership:
+*     SphMap constructor.
+
+*  Description:
+*     This function implements the external (public) interface to the
+*     astSphMap constructor function. It returns an ID value (instead
+*     of a true C pointer) to external users, and must be provided
+*     because astSphMap_ 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 astSphMap_ 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 astSphMap_.
+
+*  Returned Value:
+*     The ID value associated with the new SphMap.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstSphMap *new;              /* Pointer to new SphMap */
+   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 SphMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitSphMap( NULL, sizeof( AstSphMap ), !class_init, &class_vtab,
+                        "SphMap" );
+
+/* 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 SphMap'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 SphMap. */
+   return astMakeId( new );
+}
+
+AstSphMap *astInitSphMap_( void *mem, size_t size, int init,
+                           AstSphMapVtab *vtab, const char *name, int *status ) {
+/*
+*+
+*  Name:
+*     astInitSphMap
+
+*  Purpose:
+*     Initialise a SphMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     AstSphMap *astInitSphMap( void *mem, size_t size, int init,
+*                               AstSphMapVtab *vtab, const char *name )
+
+*  Class Membership:
+*     SphMap initialiser.
+
+*  Description:
+*     This function is provided for use by class implementations to initialise
+*     a new SphMap object. It allocates memory (if necessary) to accommodate
+*     the SphMap plus any additional data associated with the derived class.
+*     It then initialises a SphMap 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 SphMap at the start of the memory passed via the
+*     "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory in which the SphMap is to be initialised.
+*        This must be of sufficient size to accommodate the SphMap data
+*        (sizeof(SphMap)) 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 SphMap (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 SphMap
+*        structure, so a valid value must be supplied even if not required for
+*        allocating memory.
+*     init
+*        A logical flag indicating if the SphMap'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 SphMap.
+*     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).
+
+*  Returned Value:
+*     A pointer to the new SphMap.
+
+*  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: */
+   AstSphMap *new;              /* Pointer to new SphMap */
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* If necessary, initialise the virtual function table. */
+   if ( init ) astInitSphMapVtab( vtab, name );
+
+/* Initialise. */
+   new = NULL;
+
+/* Initialise a Mapping structure (the parent class) as the first component
+   within the SphMap structure, allocating memory if necessary. Specify that
+   the Mapping should be defined in both the forward and inverse directions. */
+   new = (AstSphMap *) astInitMapping( mem, size, 0,
+                                       (AstMappingVtab *) vtab, name,
+                                       3, 2, 1, 1 );
+
+   if ( astOK ) {
+
+/* Initialise the SphMap data. */
+/* --------------------------- */
+/* Are all input vectors of unit length? Store a value of -1 to indicate that
+   no value has yet been set. This will cause a default value of 0 (no, i.e.
+   input vectors are not all of unit length) to be used. */
+      new->unitradius = -1;
+      new->polarlong = AST__BAD;
+
+   }
+
+/* Return a pointer to the new SphMap. */
+   return new;
+}
+
+AstSphMap *astLoadSphMap_( void *mem, size_t size,
+                           AstSphMapVtab *vtab, const char *name,
+                           AstChannel *channel, int *status ) {
+/*
+*+
+*  Name:
+*     astLoadSphMap
+
+*  Purpose:
+*     Load a SphMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "sphmap.h"
+*     AstSphMap *astLoadSphMap( void *mem, size_t size,
+*                               AstSphMapVtab *vtab, const char *name,
+*                               AstChannel *channel )
+
+*  Class Membership:
+*     SphMap loader.
+
+*  Description:
+*     This function is provided to load a new SphMap 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
+*     SphMap 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 SphMap at the start of the memory
+*     passed via the "vtab" parameter.
+
+
+*  Parameters:
+*     mem
+*        A pointer to the memory into which the SphMap is to be
+*        loaded.  This must be of sufficient size to accommodate the
+*        SphMap data (sizeof(SphMap)) 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 SphMap (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 SphMap 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(AstSphMap) is used instead.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new SphMap. If this is NULL, a pointer
+*        to the (static) virtual function table for the SphMap 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 "SphMap" is used instead.
+
+*  Returned Value:
+*     A pointer to the new SphMap.
+
+*  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.
+*-
+*/
+
+#define KEY_LEN 50               /* Maximum length of a keyword */
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstSphMap *new;               /* Pointer to the new SphMap */
+
+/* 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 SphMap. In this case the
+   SphMap belongs to this class, so supply appropriate values to be
+   passed to the parent class loader (and its parent, etc.). */
+   if ( !vtab ) {
+      size = sizeof( AstSphMap );
+      vtab = &class_vtab;
+      name = "SphMap";
+
+/* If required, initialise the virtual function table for this class. */
+      if ( !class_init ) {
+         astInitSphMapVtab( 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 SphMap. */
+   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, "SphMap" );
+
+/* 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. */
+
+/* UnitRadius. */
+/* ----------- */
+      new->unitradius = astReadInt( channel, "untrd", -1 );
+      if ( TestUnitRadius( new, status ) ) SetUnitRadius( new, new->unitradius, status );
+
+/* PolarLong. */
+/* ---------- */
+      new->polarlong = astReadDouble( channel, "plrlg", AST__BAD );
+      if ( TestPolarLong( new, status ) ) SetPolarLong( new, new->polarlong, status );
+
+   }
+
+/* If an error occurred, clean up by deleting the new SphMap. */
+   if ( !astOK ) new = astDelete( new );
+
+/* Return the new SphMap 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. */
+
+
+
+
+