upgrade ast 8.7.1

1 files changed, 0 insertions, 2902 deletions

diff --git a/ast/circle.c b/ast/circle.c
deleted file mode 100644
index b26771c..0000000
--- a/ast/circle.c
+++ /dev/null
@@ -1,2902 +0,0 @@
-/*
-*class++
-*  Name:
-*     Circle
-
-*  Purpose:
-*     A circular or spherical region within a Frame.
-
-*  Constructor Function:
-c     astCircle
-f     AST_CIRCLE
-
-*  Description:
-*     The Circle class implements a Region which represents a circle or
-*     sphere within a Frame.
-
-*  Inheritance:
-*     The Circle class inherits from the Region class.
-
-*  Attributes:
-*     The Circle class does not define any new attributes beyond
-*     those which are applicable to all Regions.
-
-*  Functions:
-c     In addition to those functions applicable to all Regions, the
-c     following functions may also be applied to all Circles:
-f     In addition to those routines applicable to all Regions, the
-f     following routines may also be applied to all Circles:
-*
-c     - astCirclePars: Get the geometric parameters of the Circle
-f     - AST_CIRCLEPARS: Get the geometric parameters of the Circle
-
-*  Copyright:
-*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
-*     Research Councils
-*     Copyright (C) 2009 Science & Technology Facilities Council.
-*     All Rights Reserved.
-
-*  Licence:
-*     This program is free software: you can redistribute it and/or
-*     modify it under the terms of the GNU Lesser General Public
-*     License as published by the Free Software Foundation, either
-*     version 3 of the License, or (at your option) any later
-*     version.
-*
-*     This program is distributed in the hope that it will be useful,
-*     but WITHOUT ANY WARRANTY; without even the implied warranty of
-*     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-*     GNU Lesser General Public License for more details.
-*
-*     You should have received a copy of the GNU Lesser General
-*     License along with this program.  If not, see
-*     <http://www.gnu.org/licenses/>.
-
-*  Authors:
-*     DSB: David S. Berry (Starlink)
-
-*  History:
-*     31-AUG-2004 (DSB):
-*        Original version.
-*     4-NOV-2013 (DSB):
-*        Modify RegPins so that it can handle uncertainty regions that straddle
-*        a discontinuity. Previously, such uncertainty Regions could have a huge
-*        bounding box resulting in matching region being far too big.
-*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 Circle
-
-/* Include files. */
-/* ============== */
-/* Interface definitions. */
-/* ---------------------- */
-
-#include "globals.h"             /* Thread-safe global data access */
-#include "error.h"               /* Error reporting facilities */
-#include "memory.h"              /* Memory allocation facilities */
-#include "object.h"              /* Base Object class */
-#include "pointset.h"            /* Sets of points/coordinates */
-#include "region.h"              /* Coordinate regions (parent class) */
-#include "channel.h"             /* I/O channels */
-#include "box.h"                 /* Box Regions */
-#include "wcsmap.h"              /* Definitons of AST__DPI etc */
-#include "circle.h"              /* Interface definition for this class */
-#include "ellipse.h"             /* Interface definition for ellipse class */
-#include "mapping.h"             /* Position mappings */
-#include "unitmap.h"             /* Unit Mapping */
-
-/* Error code definitions. */
-/* ----------------------- */
-#include "ast_err.h"             /* AST error codes */
-
-/* C header files. */
-/* --------------- */
-#include <float.h>
-#include <math.h>
-#include <stdarg.h>
-#include <stddef.h>
-#include <stdio.h>
-#include <string.h>
-
-/* Module Variables. */
-/* ================= */
-
-/* Address of this static variable is used as a unique identifier for
-   member of this class. */
-static int class_check;
-
-/* Pointers to parent class methods which are extended by this class. */
-static AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
-static AstMapping *(* parent_simplify)( AstMapping *, int * );
-static void (* parent_setregfs)( AstRegion *, AstFrame *, int * );
-static void (* parent_resetcache)( AstRegion *, int * );
-
-
-#ifdef THREAD_SAFE
-/* Define how to initialise thread-specific globals. */
-#define GLOBAL_inits \
-   globals->Class_Init = 0;
-
-/* Create the function that initialises global data for this module. */
-astMAKE_INITGLOBALS(Circle)
-
-/* Define macros for accessing each item of thread specific global data. */
-#define class_init astGLOBAL(Circle,Class_Init)
-#define class_vtab astGLOBAL(Circle,Class_Vtab)
-
-
-#include <pthread.h>
-
-
-#else
-
-
-/* Define the class virtual function table and its initialisation flag
-   as static variables. */
-static AstCircleVtab 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. */
-AstCircle *astCircleId_( void *, int, const double[], const double[], void *, const char *, ... );
-
-/* Prototypes for Private Member Functions. */
-/* ======================================== */
-static AstMapping *Simplify( AstMapping *, int * );
-static AstPointSet *RegBaseMesh( AstRegion *, int * );
-static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
-static double *CircumPoint( AstFrame *, int, const double *, double, int * );
-static double *RegCentre( AstRegion *this, double *, double **, int, int, int * );
-static int RegPins( AstRegion *, AstPointSet *, AstRegion *, int **, int * );
-static int RegTrace( AstRegion *, int, double *, double **, int * );
-static void Cache( AstCircle *, int * );
-static void CalcPars( AstFrame *, AstPointSet *, double *, double *, double *, int * );
-static void CirclePars( AstCircle *, double *, double *, double *, int * );
-static void Copy( const AstObject *, AstObject *, int * );
-static void Delete( AstObject *, int * );
-static void Dump( AstObject *, AstChannel *, int * );
-static void RegBaseBox( AstRegion *this, double *, double *, int * );
-static void ResetCache( AstRegion *this, int * );
-static void SetRegFS( AstRegion *, AstFrame *, int * );
-
-/* Member functions. */
-/* ================= */
-
-AstRegion *astBestCircle_( AstPointSet *mesh, double *cen, AstRegion *unc, int *status ){
-/*
-*+
-*  Name:
-*     astBestCircle
-
-*  Purpose:
-*     Find the best fitting Circle through a given mesh of points.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     AstRegion *astBestCircle( AstPointSet *mesh, double *cen, AstRegion *unc )
-
-*  Class Membership:
-*     Circle member function
-
-*  Description:
-*     This function finds the best fitting Circle through a given mesh of
-*     points.
-
-*  Parameters:
-*     mesh
-*        Pointer to a PointSet holding the mesh of points. They are
-*        assumed to be in the Frame represented by "unc".
-*     cen
-*        Pointer to an array holding the coordinates of the new Circle
-*        centre.
-*     unc
-*        A Region representing the uncertainty associated with each point
-*        on the mesh.
-
-*  Returned Value:
-*     Pointer to the best fitting Circle. It will inherit the positional
-*     uncertainty and Frame represented by "unc".
-
-*  Notes:
-*    - A NULL pointer is returned if an error has already occurred, or if
-*    this function should fail for any reason.
-
-*-
-*/
-
-/* Local Variables: */
-   AstRegion *result;
-   double *p;
-   double rad;
-   double **ptr;
-   double d;
-   double s2r;
-   double p0;
-   int ic;
-   int ip;
-   int n;
-   int nc;
-   int np;
-
-/* Initialise */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get no. of points in the mesh, and the number of axis values per point. */
-   np = astGetNpoint( mesh );
-   nc = astGetNcoord( mesh );
-
-/* Get pointers to the axis values. */
-   ptr = astGetPoints( mesh );
-
-/* Check pointers can be used safely */
-   if( astOK ) {
-
-/* We find ther sum of the squared axis increments from the supplied
-   centre to each of the supplied points. Initialise the sum to zero. */
-      s2r = 0.0;
-      n = 0;
-
-/* Loop round all axes. */
-      for( ic = 0; ic < nc; ic++ ) {
-         p = ptr[ ic ];
-         p0 = cen[ ic ];
-
-/* Loop round all values for this axis. */
-         for( ip = 0; ip < np; ip++, p++ ) {
-            if( *p != AST__BAD ) {
-
-/* Increment the sums */
-               d = *p - p0;
-               s2r += d*d;
-               n++;
-
-            }
-         }
-      }
-
-/* Find the RMS distance of the points from the supplied centre. This is
-   the radius of the best fitting circle. */
-      if( n > 0 ) {
-         rad = sqrt( nc*s2r/n );
-
-/* Create the returned Region. */
-         result = (AstRegion *) astCircle( unc, 1, cen, &rad, unc, "", status );
-      }
-   }
-
-/* Return NULL if anything went wrong. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return the result.*/
-   return result;
-}
-
-static void Cache( AstCircle *this, int *status ){
-/*
-*  Name:
-*     Cache
-
-*  Purpose:
-*     Calculate intermediate values and cache them in the Circle structure.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     void Cache( AstCircle *this, int *status )
-
-*  Class Membership:
-*     Circle member function
-
-*  Description:
-*     This function uses the PointSet stored in the parent Region to calculate
-*     some intermediate values which are useful in other methods. These
-*     values are stored within the Circle structure.
-
-*  Parameters:
-*     this
-*        Pointer to the Circle.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-/* Local Variables: */
-   AstFrame *frm;
-   double *centre;
-   double *lb;
-   double *ub;
-   double radius;
-   int i;
-   int nc;
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Do Nothing if the cached information is up to date. */
-   if( this->stale ) {
-
-/* Get a pointer to the base Frame and the number of base axes. */
-      frm = astGetFrame( ((AstRegion *) this)->frameset, AST__BASE );
-      nc = astGetNaxes( frm );
-
-/* Allocate memory to hold the centre coords. */
-      centre = astMalloc( sizeof( double )*astGetNaxes( frm ) );
-
-/* Get the radius and centre of the Circle in the base Frame, using the
-   centre and circumference positions stored in the parent Region structure. */
-      CalcPars( frm, ( (AstRegion *) this)->points, centre, &radius, NULL,
-                status );
-
-/* Allocate memory to store the base frame bounding box. This is just
-   initialised here. It is set properly when the astRegBaseMesh
-   function is called. This box should not be used unless the "basemesh"
-   component of the parent Region structure is set to a non-null value. */
-      lb = (double *) astMalloc( sizeof( double )*(size_t) nc );
-      ub = (double *) astMalloc( sizeof( double )*(size_t) nc );
-
-/* Initialise the bounding box. */
-      for( i = 0; astOK && i < nc; i++ ) {
-         lb[ i ] = -DBL_MAX;
-         ub[ i ] = DBL_MAX;
-      }
-
-/* If everything went OK, store these values in the Circle structure. */
-      if( astOK ) {
-         this->radius = radius;
-
-         astFree( this->centre );
-         this->centre = centre;
-         centre = NULL;
-
-         astFree( this->lb );
-         this->lb = lb;
-         lb = NULL;
-
-         astFree( this->ub );
-         this->ub = ub;
-         ub = NULL;
-      }
-
-/* Free resources */
-      frm = astAnnul( frm );
-      centre = astFree( centre );
-      lb = astFree( lb );
-      ub = astFree( ub );
-
-/* Indicate cached information is up to date. */
-      this->stale = 0;
-   }
-}
-
-static void CalcPars( AstFrame *frm, AstPointSet *pset, double *centre,
-                      double *radius, double *p1, int *status ){
-/*
-*  Name:
-*     CalcPars
-
-*  Purpose:
-*     Calculate the geometric parameters of the supplied Circle.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     double *CalcPars( AstFrame *frm, AstPointSet *pset, double *centre,
-*                       double *radius, double *p1, int *status )
-
-*  Class Membership:
-*     Circle member function
-
-*  Description:
-*     This function uses the supplied PointSet to calculate the geometric
-*     parameters that describe the a crcle. These values are returned in
-*     a newly allocated dynamic array.
-
-*  Parameters:
-*     frm
-*        Pointer to the Frame in which the circle is defined.
-*     pset
-*        Pointer to a PointSet. The first point should be the circle
-*        centre, and the second point should be a point on the circle
-*        circumference.
-*     centre
-*        An array in which to return the axis values at the circle centre.
-*        The length of this array should be no less than the number of
-*        axes in "frm".
-*     radius
-*        Pointer to a double in which to return the circle radius,
-*        expressed as a geodesic distance in the supplied Frame.
-*     p1
-*        An array in which to return the coordinates of a point on the
-*        circumference of the circle. The length of this array should be
-*        no less than the number of axes in "frm". Can be NULL if the
-*        circumference position is not needed.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-/* Local Variables: */
-   double **ptr;
-   double *circum;
-   int i;
-   int nc;
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Get and the number of axes. */
-   nc = astGetNaxes( frm );
-
-/* Get pointers to the coordinate data in the supplied PointSet. */
-   ptr = astGetPoints( pset );
-
-/* If no p1 array was supplied, create a temporary work array to hold the
-   circumference position. */
-   if( !p1 ) {
-      circum = astMalloc( sizeof( double )*nc );
-   } else {
-      circum = p1;
-   }
-
-/* Check pointers can be used safely. */
-   if( ptr ) {
-
-/* Copy the two points in to the allocated memory. */
-      for( i = 0; i < nc; i++ ) {
-         centre[ i ] = ptr[ i ][ 0 ];
-         circum[ i ] = ptr[ i ][ 1 ];
-      }
-
-/* Return the geodesic distance between these two points as the radius. */
-      *radius = astDistance( frm, centre, circum );
-   }
-
-/* Free any work array. */
-   if( !p1 ) circum = astFree( circum );
-}
-
-static void CirclePars( AstCircle *this, double *centre, double *radius,
-                        double *p1, int *status ){
-/*
-*++
-*  Name:
-c     astCirclePars
-f     AST_CIRCLEPARS
-
-*  Purpose:
-*     Returns the geometric parameters of an Circle.
-
-*  Type:
-*     Public virtual function.
-
-*  Synopsis:
-c     #include "circle.h"
-c     void astCirclePars( AstCircle *this, double *centre, double *radius,
-c                         double *p1 )
-f     CALL AST_CIRCLEPARS( THIS, CENTRE, RADIUS, P1, STATUS )
-
-*  Class Membership:
-*     Region method.
-
-*  Description:
-c     This function
-f     This routine
-*     returns the geometric parameters describing the supplied Circle.
-
-*  Parameters:
-c     this
-f     THIS = INTEGER (Given)
-*        Pointer to the Region.
-c     centre
-f     CENTRE( * ) = DOUBLE PRECISION (Returned)
-c        Pointer to an array
-f        An array
-*        in which to return the coordinates of the Circle centre.
-*        The length of this array should be no less than the number of
-*        axes in the associated coordinate system.
-c     radius
-f     RADIUS = DOUBLE PRECISION (Returned)
-*        Returned holding the radius of the Circle, as an geodesic
-*        distance in the associated coordinate system.
-c     p1
-f     P1( * ) = DOUBLE PRECISION (Returned)
-c        Pointer to an array
-f        An array
-*        in which to return the coordinates of a point on the
-*        circumference of the Circle. The length of this array should be
-*        no less than the number of axes in the associated coordinate system.
-c        A NULL pointer can be supplied if the circumference position is
-c        not needed.
-f     STATUS = INTEGER (Given and Returned)
-f        The global status.
-
-*  Notes:
-*     - If the coordinate system represented by the Circle has been
-*     changed since it was first created, the returned parameters refer
-*     to the new (changed) coordinate system, rather than the original
-*     coordinate system. Note however that if the transformation from
-*     original to new coordinate system is non-linear, the shape
-*     represented by the supplied Circle object may not be an accurate
-*     circle.
-*--
-*/
-
-/* Local Variables: */
-   AstRegion *this_region;  /* Parent Region pointer */
-   AstFrame *frm;           /* Current Frame represented by the Circle */
-   AstPointSet *pset;       /* PointSet holding PointList axis values */
-
-/* Check the inherited status. */
-   if( !astOK ) return;
-
-/* Store a pointer to the parent region structure. */
-   this_region = (AstRegion *) this;
-
-/* Transform the base Frame axis values into the current Frame. */
-   pset = astTransform( this_region->frameset, this_region->points, 1, NULL );
-
-/* Get the Circle frame. */
-   frm = astGetFrame( this_region->frameset, AST__CURRENT );
-
-/* Calculate the required parameters. */
-   CalcPars( frm, pset, centre, radius, p1, status );
-
-/* Free resources */
-   frm = astAnnul( frm );
-   pset = astAnnul( pset );
-}
-
-static double *CircumPoint( AstFrame *frm, int nax, const double *centre,
-                            double radius, int *status ){
-/*
-*  Name:
-*     CircumPoint
-
-*  Purpose:
-*     Find a point on the circumference of the circle.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     double *CircumPoint( AstFrame *frm, int nax, const double *centre,
-*                          double radius, int *status )
-
-*  Class Membership:
-*     Circle member function
-
-*  Description:
-*     This function returns a dynamically allocated array containing the
-*     axis values at a point on the circumference of the circle specified
-*     by a given centre and radius. The returned point is the point at
-*     which the circle crosses the first axis.
-
-*  Parameters:
-*     frm
-*        Pointer to the Frame in which the circle is defined.
-*     nax
-*        The number of axes in the Frame.
-*     centre
-*        An array holding the axis values at the circle centre.
-*     radius
-*        The circle radius, expressed as a geodesic distance in the
-*        supplied Frame.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     A pointer to a 1D array holding the axis values at the point where
-*     the circle crosses the first frame axis. The length of this array
-*     will equal the number of axes in the supsplied Frame. It should be
-*     freed using astFree when no longer needed.
-
-*/
-
-/* Local Variables: */
-   double *circum;
-   double *work;
-   int i;
-
-/* Check the global error status. */
-   if ( !astOK ) return NULL;
-
-/* Allocate the returned array. */
-   circum = astMalloc( sizeof( double)*(size_t) nax );
-
-/* Allocate work space */
-   work = astMalloc( sizeof( double)*(size_t) nax );
-
-/* Check pointers can be used safely. */
-   if( astOK ) {
-
-/* Find the coords of a point that is offset away from the centre
-   position along the first axis. We use the supplied radius value as a
-   convenient offset length, but the actual length used is not critical. */
-      for( i = 0; i < nax; i++ ) work[ i ] = centre[ i ];
-      work[ 0 ] = astAxOffset( frm, 1, work[ 0 ], radius );
-
-/* Offset away from the centre position, towards the position found
-   above, going the distance specified by the supplied radius. */
-      astOffset( frm, centre, work, radius, (double *) circum );
-   }
-
-/* Free resources. */
-   work = astFree( work );
-
-/* Return the result. */
-   return circum;
-}
-
-void astInitCircleVtab_(  AstCircleVtab *vtab, const char *name, int *status ) {
-/*
-*+
-*  Name:
-*     astInitCircleVtab
-
-*  Purpose:
-*     Initialise a virtual function table for a Circle.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     void astInitCircleVtab( AstCircleVtab *vtab, const char *name )
-
-*  Class Membership:
-*     Circle vtab initialiser.
-
-*  Description:
-*     This function initialises the component of a virtual function
-*     table which is used by the Circle class.
-
-*  Parameters:
-*     vtab
-*        Pointer to the virtual function table. The components used by
-*        all ancestral classes will be initialised if they have not already
-*        been initialised.
-*     name
-*        Pointer to a constant null-terminated character string which contains
-*        the name of the class to which the virtual function table belongs (it
-*        is this pointer value that will subsequently be returned by the Object
-*        astClass function).
-*-
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
-   AstRegionVtab *region;        /* Pointer to Region component of Vtab */
-
-/* Check the local error status. */
-   if ( !astOK ) return;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Initialize the component of the virtual function table used by the
-   parent class. */
-   astInitRegionVtab( (AstRegionVtab *) vtab, name );
-
-/* Store a unique "magic" value in the virtual function table. This
-   will be used (by astIsACircle) to determine if an object belongs
-   to this class.  We can conveniently use the address of the (static)
-   class_check variable to generate this unique value. */
-   vtab->id.check = &class_check;
-   vtab->id.parent = &(((AstRegionVtab *) vtab)->id);
-
-/* Initialise member function pointers. */
-/* ------------------------------------ */
-/* Store pointers to the member functions (implemented here) that provide
-   virtual methods for this class. */
-   vtab->CirclePars = CirclePars;
-
-/* Save the inherited pointers to methods that will be extended, and
-   replace them with pointers to the new member functions. */
-   mapping = (AstMappingVtab *) vtab;
-   region = (AstRegionVtab *) vtab;
-
-   parent_transform = mapping->Transform;
-   mapping->Transform = Transform;
-
-   parent_simplify = mapping->Simplify;
-   mapping->Simplify = Simplify;
-
-   parent_setregfs = region->SetRegFS;
-   region->SetRegFS = SetRegFS;
-
-   parent_resetcache = region->ResetCache;
-   region->ResetCache = ResetCache;
-
-   region->RegPins = RegPins;
-   region->RegTrace = RegTrace;
-   region->RegBaseMesh = RegBaseMesh;
-   region->RegBaseBox = RegBaseBox;
-   region->RegCentre = RegCentre;
-
-/* Store replacement pointers for methods which will be over-ridden by
-   new member functions implemented here. */
-
-/* Declare the copy constructor, destructor and class dump
-   functions. */
-   astSetDelete( vtab, Delete );
-   astSetCopy( vtab, Copy );
-   astSetDump( vtab, Dump, "Circle", "Circular or spherical region" );
-
-/* If we have just initialised the vtab for the current class, indicate
-   that the vtab is now initialised, and store a pointer to the class
-   identifier in the base "object" level of the vtab. */
-   if( vtab == &class_vtab ) {
-      class_init = 1;
-      astSetVtabClassIdentifier( vtab, &(vtab->id) );
-   }
-}
-
-static void RegBaseBox( AstRegion *this_region, double *lbnd, double *ubnd, int *status ){
-/*
-*  Name:
-*     RegBaseBox
-
-*  Purpose:
-*     Returns the bounding box of an un-negated Region in the base Frame of
-*     the encapsulated FrameSet.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     void RegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status )
-
-*  Class Membership:
-*     Circle member function (over-rides the astRegBaseBox protected
-*     method inherited from the Region class).
-
-*  Description:
-*     This function returns the upper and lower axis bounds of a Region in
-*     the base Frame of the encapsulated FrameSet, assuming the Region
-*     has not been negated. That is, the value of the Negated attribute
-*     is ignored.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     lbnd
-*        Pointer to an array in which to return the lower axis bounds
-*        covered by the Region in the base Frame of the encapsulated
-*        FrameSet. It should have at least as many elements as there are
-*        axes in the base Frame.
-*     ubnd
-*        Pointer to an array in which to return the upper axis bounds
-*        covered by the Region in the base Frame of the encapsulated
-*        FrameSet. It should have at least as many elements as there are
-*        axes in the base Frame.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-/* Local Variables: */
-   AstCircle *this;              /* Pointer to Circle structure */
-   AstFrame *frm;                /* Pointer to base Frame */
-   const char *class;            /* Pointer to class name */
-   int i;                        /* Axis index */
-   int nb;                       /* No. of axes in base Frame */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Get a pointer to the Circle structure */
-   this = (AstCircle *) this_region;
-
-/* Ensure cached information is available. */
-   Cache( this, status );
-
-/* Get a pointer to the base Frame in the Region, and get the number of
-   axes. */
-   frm = astGetFrame( this_region->frameset, AST__BASE );
-   nb = astGetNaxes( frm );
-
-/* If the Frame is a simple Frame, we can assume plane geometry. */
-   class = astGetClass( frm );
-   if( class && !strcmp( class, "Frame" ) ) {
-      for( i = 0; i < nb; i++ ) {
-         lbnd[ i ] = ( this->centre )[ i ] - this->radius;
-         ubnd[ i ] = ( this->centre )[ i ] + this->radius;
-      }
-
-/* If the Frame is not a simple Frame we cannot assume plane geometry. */
-   } else {
-
-/* The bounding box of the mesh returned by astRegBaseMesh is used as the
-   bounding box of the Circle. These bounds are cached in the Circle
-   structure by astRegBaseMesh. Ensure astRegBaseMesh has been invoked,
-   so that it is safe to use the cached bounding box. */
-      if( !this_region->basemesh ) (void) astAnnul( astRegBaseMesh( this ) );
-
-/* Store the bounding box. */
-      for( i = 0; i < nb; i++ ) {
-         lbnd[ i ] = this->lb[ i ];
-         ubnd[ i ] = this->ub[ i ];
-      }
-   }
-
-/* Free resources. */
-   frm = astAnnul( frm );
-}
-
-static AstPointSet *RegBaseMesh( AstRegion *this_region, int *status ){
-/*
-*  Name:
-*     RegBaseMesh
-
-*  Purpose:
-*     Return a PointSet containing a mesh of points on the boundary of a
-*     Region in its base Frame.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     AstPointSet *astRegBaseMesh( AstRegion *this, int *status )
-
-*  Class Membership:
-*     Circle member function (over-rides the astRegBaseMesh protected
-*     method inherited from the Region class).
-
-*  Description:
-*     This function returns a PointSet containing a mesh of points on the
-*     boundary of the Region. The points refer to the base Frame of
-*     the encapsulated FrameSet.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     Pointer to the PointSet. The axis values in this PointSet will have
-*     associated accuracies derived from the accuracies which were
-*     supplied when the Region was created.
-
-*  Notes:
-*    - A NULL pointer is returned if an error has already occurred, or if
-*    this function should fail for any reason.
-
-*/
-
-/* Local Constants: */
-#define NP_EDGE 50                /* No. of points for determining geodesic */
-
-/* Local Variables: */
-   AstBox *box;                   /* Bounding box for this Circle */
-   AstCircle *this;               /* The Circle structure */
-   AstRegion *reg;                /* Copy of supplied Circle */
-   AstFrame *frm;                 /* Base Frame in encapsulated FrameSet */
-   AstPointSet *result;           /* Returned pointer */
-   double **ptr;                  /* Pointers to data */
-   double *p1;                    /* Pointer to array holding a single point */
-   double *p2;                    /* Pointer to array holding a single point */
-   double angle;                  /* Angular position of point */
-   double delta;                  /* Angular separation of points */
-   double dist;                   /* Offset along an axis */
-   double lbx;                    /* Lower x bound of mesh bounding box */
-   double lby;                    /* Lower y bound of mesh bounding box */
-   double p[ 2 ];                 /* Position in 2D Frame */
-   double ubx;                    /* Upper x bound of mesh bounding box */
-   double uby;                    /* Upper y bound of mesh bounding box */
-   int i;                         /* Point index */
-   int j;                         /* Axis index */
-   int naxes;                     /* No. of axes in base Frame */
-   int np;                        /* No. of points in returned PointSet */
-
-/* Initialise */
-   result= NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* If the Region structure contains a pointer to a PointSet holding
-   a previously created mesh, return it. */
-   if( this_region->basemesh ) {
-      result = astClone( this_region->basemesh );
-
-/* Otherwise, create a new mesh. */
-   } else {
-
-/* Get a pointer to the Circle structure. */
-      this = (AstCircle *) this_region;
-
-/* Get a pointer to the base Frame in the encapsulated FrameSet. */
-      frm = astGetFrame( this_region->frameset, AST__BASE );
-
-/* Get the number of axes in the base Frame */
-      naxes = astGetNaxes( frm );
-
-/* Get the requested number of points to put on the mesh. */
-      np = astGetMeshSize( this );
-
-/* Ensure cached information is available. */
-      Cache( (AstCircle *) this, status );
-
-/* First deal with 1-D "circles" (where we ignore MeshSize). */
-      if( naxes == 1 ) {
-
-/* The boundary of a 1-D circle consists of 2 points - the two extreme values.
-   Create a PointSet to hold 2 1-D values, and store the extreme values. */
-         result = astPointSet( 2, 1, "", status );
-         ptr = astGetPoints( result );
-         if( astOK ) {
-            ptr[ 0 ][ 0 ] = ( this->centre )[ 0 ] - this->radius;
-            ptr[ 0 ][ 1 ] = ( this->centre )[ 0 ] + this->radius;
-         }
-
-/* Store the bounding box in the Circle structure. */
-         this->lb[ 0 ] = ptr[ 0 ][ 0 ];
-         this->ub[ 0 ] = ptr[ 0 ][ 1 ];
-
-/* Now deal with 2-D circles. */
-      } else if( naxes == 2 ){
-
-/* Store the angular increment between points. */
-         delta = 2*AST__DPI/np;
-
-/* Create a suitable PointSet to hold the returned positions. */
-         result = astPointSet( np, 2, "", status );
-         ptr = astGetPoints( result );
-         if( astOK ) {
-
-/* Initialise the bounding box of the mesh points. */
-            lbx = DBL_MAX;
-            ubx = -DBL_MAX;
-            lby = DBL_MAX;
-            uby = -DBL_MAX;
-
-/* Loop round each point. */
-            angle = 0.0;
-            for( i = 0; i < np; i++ ) {
-
-/* Work out where the end of the radius vector at this angle is, and
-   store in the returned PointSet. */
-               astOffset2( frm, this->centre, angle, this->radius, p );
-               ptr[ 0 ][ i ] = p[ 0 ];
-               ptr[ 1 ][ i ] = p[ 1 ];
-
-/* Update the bounds of the mesh bounding box. The box is expressed in
-   terms of axis offsets from the centre, in order to avoid problems with
-   boxes that cross RA=0 or RA=12h */
-               if( p[ 0 ] != AST__BAD && p[ 1 ] != AST__BAD ){
-                  dist =  astAxDistance( frm, 1, this->centre[ 0 ], p[ 0 ] );
-                  if( dist < lbx ) {
-                     lbx = dist;
-                  } else if( dist > ubx ) {
-                     ubx = dist;
-                  }
-                  dist =  astAxDistance( frm, 2, this->centre[ 1 ], p[ 1 ] );
-                  if( dist < lby ) {
-                     lby = dist;
-                  } else if( dist > uby ) {
-                     uby = dist;
-                  }
-               }
-
-/* Increment the angular position of the next mesh point. */
-               angle += delta;
-            }
-
-/* Store the bounding box in the Circle structure. */
-            this->lb[ 0 ] = this->centre[ 0 ] + lbx;
-            this->lb[ 1 ] = this->centre[ 1 ] + lby;
-            this->ub[ 0 ] = this->centre[ 0 ] + ubx;
-            this->ub[ 1 ] = this->centre[ 1 ] + uby;
-         }
-
-/* Now deal with circles with more than 2 dimensions. Producing an evenly
-   spread mesh of points over a sphere is a complex task (see e.g.
-   http://www.eso.org/science/healpix/ ). This implementation does not
-   attempt to produce a genuinely even spread. Instead it simply uses the
-   mesh for the bounding box of the sphere, and projects each point on to
-   the surface of the sphere. */
-      } else {
-
-/* Allocate memory to hold an approximation of the circle bounding box. */
-         p1 = astMalloc( sizeof( double )*(size_t) naxes );
-         p2 = astMalloc( sizeof( double )*(size_t) naxes );
-
-/* Get an approximation to the bounding box, and initialise the real
-   bounding box of the mesh points. */
-         if( astOK ) {
-            memcpy( p1, this->centre, sizeof( double )*(size_t) naxes );
-            for( j = 0; j < naxes; j++ ) {
-               p1[ j ] += this->radius;
-               astOffset( frm, this->centre, p1, this->radius, p2 );
-               p1[ j ] = this->centre[ j ];
-               this->ub[ j ] = p2[ j ];
-            }
-         }
-
-/* Create a Box region which just encompasses the circle. */
-         box = astBox( frm, 0, this->centre, this->ub, NULL, "", status );
-
-/* Get a mesh covering this box. */
-         astSetMeshSize( box, np );
-         result = astRegBaseMesh( box );
-         ptr = astGetPoints( result );
-         np = astGetNpoint( result  );
-
-/* Allocate memory for a single point */
-         if( astOK ) {
-
-/* Initialise the real bounding box of the mesh points. */
-            for( j = 0; j < naxes; j++ ) {
-               this->lb[ j ] = DBL_MAX;
-               this->ub[ j ] = -DBL_MAX;
-            }
-
-/* Move each point in this mesh radially so that its distance from the centre
-   equals the radius of this Circle. */
-            for( i = 0; i < np; i++ ) {
-               for( j = 0; j < naxes; j++ ) p1[ j ] = ptr[ j ][ i ];
-               astOffset( frm, this->centre, p1, this->radius, p2 );
-
-               for( j = 0; j < naxes; j++ ) {
-                  ptr[ j ][ i ] = p2[ j ];
-
-/* Update the bounds of the mesh bounding box. */
-                  if( p2[ j ] != AST__BAD ){
-                     if( p2[ j ] < this->lb[ j ] ) {
-                        this->lb[ j ] = p2[ j ];
-                     } else if( p2[ j ] > this->ub[ j ] ) {
-                        this->ub[ j ] = p2[ j ];
-                     }
-                  }
-               }
-            }
-         }
-
-/* Same the returned pointer in the Region structure so that it does not
-   need to be created again next time this function is called. */
-         if( astOK && result ) this_region->basemesh = astClone( result );
-
-/* Free resources. */
-         p1 = astFree( p1 );
-         p2 = astFree( p2 );
-         box = astAnnul( box );
-      }
-
-/* Extend the bounding box if it contains any singularies. The astNormBox
-   requires a Mapping which can be used to test points in the base Frame.
-   Create a copy of the Circle and then set its FrameSet so that the current
-   Frame in the copy is the same as the base Frame in the original. */
-      reg = astCopy( this );
-      astSetRegFS( reg, frm );
-      astSetNegated( reg, 0 );
-
-/* Normalise this box. */
-      astNormBox( frm, this->lb, this->ub, reg );
-
-/* Free resources. */
-      reg = astAnnul( reg );
-      frm = astAnnul( frm );
-   }
-
-/* Annul the result if an error has occurred. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return a pointer to the output PointSet. */
-   return result;
-}
-
-static double *RegCentre( AstRegion *this_region, double *cen, double **ptr,
-                          int index, int ifrm, int *status ){
-/*
-*  Name:
-*     RegCentre
-
-*  Purpose:
-*     Re-centre a Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     double *RegCentre( AstRegion *this, double *cen, double **ptr,
-*                        int index, int ifrm, int *status )
-
-*  Class Membership:
-*     Circle member function (over-rides the astRegCentre protected
-*     method inherited from the Region class).
-
-*  Description:
-*     This function shifts the centre of the supplied Region to a
-*     specified position, or returns the current centre of the Region.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     cen
-*        Pointer to an array of axis values, giving the new centre.
-*        Supply a NULL value for this in order to use "ptr" and "index" to
-*        specify the new centre.
-*     ptr
-*        Pointer to an array of pointers, one for each axis in the Region.
-*        Each pointer locates an array of axis values. This is the format
-*        returned by the PointSet method astGetPoints. Only used if "cen"
-*        is NULL.
-*     index
-*        The index of the point within the arrays identified by "ptr" at
-*        which is stored the coords for the new centre position. Only used
-*        if "cen" is NULL.
-*     ifrm
-*        Should be AST__BASE or AST__CURRENT. Indicates whether the centre
-*        position is supplied and returned in the base or current Frame of
-*        the FrameSet encapsulated within "this".
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     If both "cen" and "ptr" are NULL then a pointer to a newly
-*     allocated dynamic array is returned which contains the centre
-*     coords of the Region. This array should be freed using astFree when
-*     no longer needed. If either of "ptr" or "cen" is not NULL, then a
-*     NULL pointer is returned.
-
-*  Notes:
-*    - Some Region sub-classes do not have a centre. Such classes will report
-*    an AST__INTER error code if this method is called.
-*/
-
-/* Local Variables: */
-   AstFrame *frm;      /* Pointer to base Frame */
-   AstCircle *this;    /* Pointer to Circle structure */
-   double **rptr;      /* Data pointers for Region PointSet */
-   double *bc;         /* Base Frame centre position */
-   double *circum;     /* Base frame circumference position */
-   double *result;     /* Returned pointer */
-   double *tmp;        /* Temporary array pointer */
-   double axval;       /* Axis value */
-   int ic;             /* Coordinate index */
-   int ncb;            /* Number of base frame coordinate values per point */
-   int ncc;            /* Number of current frame coordinate values per point */
-
-/* Initialise */
-   result = NULL;
-
-/* Check the local error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the Circle structure. */
-   this = (AstCircle *) this_region;
-
-/* Get the number of axis values per point in the base and current Frames. */
-   ncb = astGetNin( this_region->frameset );
-   ncc = astGetNout( this_region->frameset );
-
-/* Ensure cached information is available. */
-   Cache( this, status );
-
-/* If the centre coords are to be returned, return either a copy of the
-   base Frame centre coords, or transform the base Frame centre coords
-   into the current Frame. */
-   if( !ptr && !cen ) {
-      if( ifrm == AST__CURRENT ) {
-         result = astRegTranPoint( this_region, this->centre, 1, 1 );
-      } else {
-         result = astStore( NULL, this->centre, sizeof( double )*ncb );
-      }
-
-/* Otherwise, we store the supplied new centre coords and return a NULL
-   pointer. */
-   } else {
-
-/* Get a pointer to the base Frame in the Region's FrameSet. */
-      frm = astGetFrame( this_region->frameset, AST__BASE );
-
-/* Get a pointer to the axis values stored in the Region structure. */
-      rptr = astGetPoints( this_region->points );
-
-/* Check pointers can be used safely */
-      if( astOK ) {
-
-/* If the centre position was supplied in the current Frame, find the
-   corresponding base Frame position... */
-         if( ifrm == AST__CURRENT ) {
-            if( cen ) {
-               bc = astRegTranPoint( this_region, cen, 1, 0 );
-            } else {
-               tmp = astMalloc( sizeof( double)*(size_t)ncc );
-               if( astOK ) {
-                  for( ic = 0; ic < ncc; ic++ ) tmp[ ic ] = ptr[ ic ][ index ];
-               }
-               bc = astRegTranPoint( this_region, tmp, 1, 0 );
-               tmp = astFree( tmp );
-            }
-
-/* Replace any bad centre values with their current values. */
-            for( ic = 0; ic < ncb; ic++ ) {
-               if( bc[ ic ] ==  AST__BAD ) bc[ ic ] = this->centre[ ic ];
-            }
-
-/* ... and change the coords in the parent Region structure and the cached
-   coords in the Circle structure. */
-            circum = CircumPoint( frm, ncb, bc, this->radius, status );
-            if( circum ) {
-               for( ic = 0; ic < ncb; ic++ ) {
-                  rptr[ ic ][ 0 ] = bc[ ic ];
-                  rptr[ ic ][ 1 ] = circum[ ic ];
-                  this->centre[ ic ] = bc[ ic ];
-               }
-            }
-
-/* Free resources */
-            circum = astFree( circum );
-            bc = astFree( bc );
-
-/* If the centre position was supplied in the base Frame, use the
-   supplied "cen" or "ptr" pointer directly to change the coords in the
-   parent Region structure and the cached coords in the Circle structure. */
-         } else {
-            for( ic = 0; ic < ncb; ic++ ) {
-               axval = cen ? cen[ ic ] : ptr[ ic ][ index ];
-               if( axval != AST__BAD ) this->centre[ ic ] = axval;
-            }
-
-            circum = CircumPoint( frm, ncb, this->centre, this->radius,
-                                  status );
-            if( circum ) {
-               for( ic = 0; ic < ncb; ic++ ) {
-                  rptr[ ic ][ 0 ] = this->centre[ ic ];
-                  rptr[ ic ][ 1 ] = circum[ ic ];
-               }
-               circum = astFree( circum );
-            }
-         }
-      }
-
-/* Free resources */
-      frm = astAnnul( frm );
-   }
-
-/* Return the result. */
-   return result;
-}
-
-static int RegPins( AstRegion *this_region, AstPointSet *pset, AstRegion *unc,
-                    int **mask, int *status ){
-/*
-*  Name:
-*     RegPins
-
-*  Purpose:
-*     Check if a set of points fall on the boundary of a given Circle.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     int RegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
-*                  int **mask, int *status ){
-
-*  Class Membership:
-*     Circle member function (over-rides the astRegPins protected
-*     method inherited from the Region class).
-
-*  Description:
-*     This function returns a flag indicating if the supplied set of
-*     points all fall on the boundary of the given Circle.
-*
-*     Some tolerance is allowed, as specified by the uncertainty Region
-*     stored in the supplied Circle "this", and the supplied uncertainty
-*     Region "unc" which describes the uncertainty of the supplied points.
-
-*  Parameters:
-*     this
-*        Pointer to the Circle.
-*     pset
-*        Pointer to the PointSet. The points are assumed to refer to the
-*        base Frame of the FrameSet encapsulated by "this".
-*     unc
-*        Pointer to a Region representing the uncertainties in the points
-*        given by "pset". The Region is assumed to represent the base Frame
-*        of the FrameSet encapsulated by "this". Zero uncertainity is assumed
-*        if NULL is supplied.
-*     mask
-*        Pointer to location at which to return a pointer to a newly
-*        allocated dynamic array of ints. The number of elements in this
-*        array is equal to the value of the Npoint attribute of "pset".
-*        Each element in the returned array is set to 1 if the
-*        corresponding position in "pset" is on the boundary of the Region
-*        and is set to zero otherwise. A NULL value may be supplied
-*        in which case no array is created. If created, the array should
-*        be freed using astFree when no longer needed.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     Non-zero if the points all fall on the boundary of the given
-*     Region, to within the tolerance specified. Zero otherwise.
-
-*/
-
-/* Local variables: */
-   AstCircle *large_circle;     /* Circle slightly larger than "this" */
-   AstCircle *small_circle;     /* Circle slightly smaller than "this" */
-   AstCircle *this;             /* Pointer to the Circle structure. */
-   AstFrame *frm;               /* Base Frame in supplied Circle */
-   AstPointSet *ps1;            /* Points masked by larger Circle */
-   AstPointSet *ps2;            /* Points masked by larger and smaller Circlees */
-   AstRegion *tunc;             /* Uncertainity Region from "this" */
-   double **ptr;                /* Pointer to axis values in "ps2" */
-   double *lbnd_tunc;           /* Lower bounds of "this" uncertainty Region */
-   double *lbnd_unc;            /* Lower bounds of supplied uncertainty Region */
-   double *p;                   /* Pointer to next axis value */
-   double *safe;                /* An interior point in "this" */
-   double *ubnd_tunc;           /* Upper bounds of "this" uncertainty Region */
-   double *ubnd_unc;            /* Upper bounds of supplied uncertainty Region */
-   double drad;                 /* Radius increment corresponding to border width */
-   double l1;                   /* Length of bounding box diagonal */
-   double l2;                   /* Length of bounding box diagonal */
-   double rad;                  /* Radius of Circle */
-   int i;                       /* Axis index */
-   int j;                       /* Point index */
-   int nc;                      /* No. of axes in Circle base frame */
-   int np;                      /* No. of supplied points */
-   int result;                  /* Returned flag */
-
-/* Initialise */
-   result = 0;
-   if( mask ) *mask = NULL;
-
-/* Check the inherited status. */
-   if( !astOK ) return result;
-
-/* Get a pointer to the Circle structure. */
-   this = (AstCircle *) this_region;
-
-/* Get the number of base Frame axes in the Circle, and check the supplied
-   PointSet has the same number of axis values per point. */
-   frm = astGetFrame( this_region->frameset, AST__BASE );
-   nc = astGetNaxes( frm );
-   if( astGetNcoord( pset ) != nc && astOK ) {
-      astError( AST__INTER, "astRegPins(%s): Illegal number of axis "
-                "values per point (%d) in the supplied PointSet - should be "
-                "%d (internal AST programming error).", status, astGetClass( this ),
-                astGetNcoord( pset ), nc );
-   }
-
-/* Get the number of axes in the uncertainty Region and check it is the
-   same as above. */
-   if( unc && astGetNaxes( unc ) != nc && astOK ) {
-      astError( AST__INTER, "astRegPins(%s): Illegal number of axes (%d) "
-                "in the supplied uncertainty Region - should be "
-                "%d (internal AST programming error).", status, astGetClass( this ),
-                astGetNaxes( unc ), nc );
-   }
-
-/* Get the centre of the region in the base Frame. We use this as a "safe"
-   interior point within the region. */
-   safe = astRegCentre( this, NULL, NULL, 0, AST__BASE );
-
-/* We now find the maximum distance on each axis that a point can be from the
-   boundary of the Circle for it still to be considered to be on the boundary.
-   First get the Region which defines the uncertainty within the Circle being
-   checked (in its base Frame), re-centre it on the interior point found
-   above (to avoid problems if the uncertainty region straddles a
-   discontinuity), and get its bounding box. */
-   tunc = astGetUncFrm( this, AST__BASE );
-   if( safe ) astRegCentre( tunc, safe, NULL, 0, AST__CURRENT );
-   lbnd_tunc = astMalloc( sizeof( double )*(size_t) nc );
-   ubnd_tunc = astMalloc( sizeof( double )*(size_t) nc );
-   astGetRegionBounds( tunc, lbnd_tunc, ubnd_tunc );
-
-/* Find the geodesic length within the base Frame of "this" of the diagonal of
-   the bounding box. */
-   l1 = astDistance( frm, lbnd_tunc, ubnd_tunc );
-
-/* Also get the Region which defines the uncertainty of the supplied
-   points and get its bounding box. First re-centre the uncertainty at the
-   interior position to avoid problems from uncertainties that straddle a
-   discontinuity. */
-   if( unc ) {
-      if( safe ) astRegCentre( unc, safe, NULL, 0, AST__CURRENT );
-      lbnd_unc = astMalloc( sizeof( double )*(size_t) nc );
-      ubnd_unc = astMalloc( sizeof( double )*(size_t) nc );
-      astGetRegionBounds( unc, lbnd_unc, ubnd_unc );
-
-/* Find the geodesic length of the diagonal of this bounding box. */
-      l2 = astDistance( frm, lbnd_unc, ubnd_unc );
-
-/* Use a zero sized box "unc" if no box was supplied. */
-   } else {
-      lbnd_unc = NULL;
-      ubnd_unc = NULL;
-      l2 = 0.0;
-   }
-
-/* Ensure cached information is available. */
-   Cache( this, status );
-
-/* The required border width is half of the total diagonal of the two bounding
-   boxes. */
-   if( astOK ) {
-      drad = 0.5*( l1 + l2 );
-
-/* Create two new Circle, one of which is larger than "this" by the amount
-   found above, and the other of which is smaller than "this" by the amount
-   found above. */
-      rad = this->radius + 0.5*drad;
-      large_circle = astCircle( frm, 1, this->centre, &rad, NULL, "", status );
-      rad = this->radius - 0.5*drad;
-      small_circle = astCircle( frm, 1, this->centre, &rad, NULL, "", status );
-
-/* Negate the smaller region.*/
-      astNegate( small_circle );
-
-/* Points are on the boundary of "this" if they are inside both the large
-   Circle and the negated small Circle. First transform the supplied PointSet
-   using the large Circle, then transform them using the negated smaller
-   Circle. */
-      ps1 = astTransform( large_circle, pset, 1, NULL );
-      ps2 = astTransform( small_circle, ps1, 1, NULL );
-
-/* Get a point to the resulting axis values, and the number of axis
-   values per axis. */
-      ptr = astGetPoints( ps2 );
-      np = astGetNpoint( ps2 );
-
-/* If a mask array is to be returned, create one. */
-      if( mask ) {
-         *mask = astMalloc( sizeof(int)*(size_t) np );
-
-/* Check all the resulting points, setting mask values for all of them. */
-         if( astOK ) {
-
-/* Initialise the mask elements on the basis of the first axis values */
-            result = 1;
-            p = ptr[ 0 ];
-            for( j = 0; j < np; j++ ) {
-               if( *(p++) == AST__BAD ) {
-                  result = 0;
-                  (*mask)[ j ] = 0;
-               } else {
-                  (*mask)[ j ] = 1;
-               }
-            }
-
-/* Now check for bad values on other axes. */
-            for( i = 1; i < nc; i++ ) {
-               p = ptr[ i ];
-               for( j = 0; j < np; j++ ) {
-                  if( *(p++) == AST__BAD ) {
-                     result = 0;
-                     (*mask)[ j ] = 0;
-                  }
-               }
-            }
-         }
-
-/* If no output mask is to be made, we can break out of the check as soon
-   as the first bad value is found. */
-      } else if( astOK ) {
-         result = 1;
-         for( i = 0; i < nc && result; i++ ) {
-            p = ptr[ i ];
-            for( j = 0; j < np; j++ ) {
-               if( *(p++) == AST__BAD ) {
-                  result = 0;
-                  break;
-               }
-            }
-         }
-      }
-
-/* Free resources. */
-      large_circle = astAnnul( large_circle );
-      small_circle = astAnnul( small_circle );
-      ps1 = astAnnul( ps1 );
-      ps2 = astAnnul( ps2 );
-   }
-
-   tunc = astAnnul( tunc );
-   frm = astAnnul( frm );
-   lbnd_tunc = astFree( lbnd_tunc );
-   ubnd_tunc = astFree( ubnd_tunc );
-   if( unc ) lbnd_unc = astFree( lbnd_unc );
-   if( unc ) ubnd_unc = astFree( ubnd_unc );
-   safe = astFree( safe );
-
-/* If an error has occurred, return zero. */
-   if( !astOK ) {
-      result = 0;
-      if( mask ) *mask = astFree( *mask );
-   }
-
-/* Return the result. */
-   return result;
-}
-
-static int RegTrace( AstRegion *this_region, int n, double *dist, double **ptr,
-                     int *status ){
-/*
-*+
-*  Name:
-*     RegTrace
-
-*  Purpose:
-*     Return requested positions on the boundary of a 2D Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     int astTraceRegion( AstRegion *this, int n, double *dist, double **ptr );
-
-*  Class Membership:
-*     Circle member function (overrides the astTraceRegion method
-*     inherited from the parent Region class).
-
-*  Description:
-*     This function returns positions on the boundary of the supplied
-*     Region, if possible. The required positions are indicated by a
-*     supplied list of scalar parameter values in the range zero to one.
-*     Zero corresponds to some arbitrary starting point on the boundary,
-*     and one corresponds to the end (which for a closed region will be
-*     the same place as the start).
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     n
-*        The number of positions to return. If this is zero, the function
-*        returns without action (but the returned function value still
-*        indicates if the method is supported or not).
-*     dist
-*        Pointer to an array of "n" scalar parameter values in the range
-*        0 to 1.0.
-*     ptr
-*        A pointer to an array of pointers. The number of elements in
-*        this array should equal tthe number of axes in the Frame spanned
-*        by the Region. Each element of the array should be a pointer to
-*        an array of "n" doubles, in which to return the "n" values for
-*        the corresponding axis. The contents of the arrays are unchanged
-*        if the supplied Region belongs to a class that does not
-*        implement this method.
-
-*  Returned Value:
-*     Non-zero if the astTraceRegion method is implemented by the class
-*     of Region supplied, and zero if not.
-
-*-
-*/
-
-/* Local Variables; */
-   AstCircle *this;
-   AstFrame *frm;
-   AstMapping *map;
-   AstPointSet *bpset;
-   AstPointSet *cpset;
-   double **bptr;
-   double angle;
-   double p[ 2 ];
-   int i;
-   int ncur;
-   int result;
-
-/* Initialise */
-   result = 0;
-
-/* Check inherited status. */
-   if( ! astOK ) return result;
-
-/* Get a pointer to the base Frame in the encapsulated FrameSet. */
-   frm = astGetFrame( this_region->frameset, AST__BASE );
-
-/* Check it is 2-dimensional. */
-   if( astGetNaxes( frm ) == 2 ) result = 1;
-
-/* Check we have some points to find. */
-   if( result && n > 0 ) {
-
-/* Get a pointer to the Circle structure. */
-      this = (AstCircle *) this_region;
-
-/* Ensure cached information is available. */
-      Cache( this, status );
-
-/* We first determine the required positions in the base Frame of the
-   Region, and then transform them into the current Frame. Get the
-   base->current Mapping, and the number of current Frame axes. */
-      map = astGetMapping( this_region->frameset, AST__BASE, AST__CURRENT );
-
-/* If it's a UnitMap we do not need to do the transformation, so put the
-   base Frame positions directly into the supplied arrays. */
-      if( astIsAUnitMap( map ) ) {
-         bpset = NULL;
-         bptr = ptr;
-         ncur = 2;
-
-/* Otherwise, create a PointSet to hold the base Frame positions. */
-      } else {
-         bpset = astPointSet( n, 2, " ", status );
-         bptr = astGetPoints( bpset );
-         ncur = astGetNout( map );
-      }
-
-/* Check the pointers can be used safely. */
-      if( astOK ) {
-
-/* Loop round each point. Get the angle around the circle, and offset
-   along that angle to find the point that is one radius away from the
-   centre. Copy the results into the required arrays. */
-         for( i = 0; i < n; i++ ) {
-            angle = dist[ i ]*2*AST__DPI;
-            astOffset2( frm, this->centre, angle, this->radius, p );
-            bptr[ 0 ][ i ] = p[ 0 ];
-            bptr[ 1 ][ i ] = p[ 1 ];
-         }
-
-      }
-
-/* If required, transform the base frame positions into the current
-   Frame, storing them in the supplied array. Then free resources. */
-      if( bpset ) {
-         cpset = astPointSet( n, ncur, " ", status );
-         astSetPoints( cpset, ptr );
-
-         (void) astTransform( map, bpset, 1, cpset );
-
-         cpset = astAnnul( cpset );
-         bpset = astAnnul( bpset );
-      }
-
-/* Free remaining resources. */
-      map = astAnnul( map );
-   }
-   frm = astAnnul( frm );
-
-/* Return the result. */
-   return result;
-}
-
-static void ResetCache( AstRegion *this, int *status ){
-/*
-*  Name:
-*     ResetCache
-
-*  Purpose:
-*     Clear cached information within the supplied Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     void ResetCache( AstRegion *this, int *status )
-
-*  Class Membership:
-*     Region member function (overrides the astResetCache method
-*     inherited from the parent Region class).
-
-*  Description:
-*     This function clears cached information from the supplied Region
-*     structure.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     status
-*        Pointer to the inherited status variable.
-*/
-   if( this ) {
-      ( (AstCircle *) this )->stale = 1;
-      (*parent_resetcache)( this, status );
-   }
-}
-
-static void SetRegFS( AstRegion *this_region, AstFrame *frm, int *status ) {
-/*
-*  Name:
-*     SetRegFS
-
-*  Purpose:
-*     Stores a new FrameSet in a Region
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     void SetRegFS( AstRegion *this_region, AstFrame *frm, int *status )
-
-*  Class Membership:
-*     Circle method (over-rides the astSetRegFS method inherited from
-*     the Region class).
-
-*  Description:
-*     This function creates a new FrameSet and stores it in the supplied
-*     Region. The new FrameSet contains two copies of the supplied
-*     Frame, connected by a UnitMap.
-
-*  Parameters:
-*     this
-*        Pointer to the Region.
-*     frm
-*        The Frame to use.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Invoke the parent method to store the FrameSet in the parent Region
-   structure. */
-   (* parent_setregfs)( this_region, frm, status );
-
-/* Re-calculate cached information. */
-   astResetCache( this_region );
-}
-
-static AstMapping *Simplify( AstMapping *this_mapping, int *status ) {
-/*
-*  Name:
-*     Simplify
-
-*  Purpose:
-*     Simplify the Mapping represented by a Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     AstMapping *Simplify( AstMapping *this, int *status )
-
-*  Class Membership:
-*     Circle method (over-rides the astSimplify method inherited
-*     from the Region class).
-
-*  Description:
-*     This function invokes the parent Region Simplify method, and then
-*     performs any further region-specific simplification.
-*
-*     If the Mapping from base to current Frame is not a UnitMap, this
-*     will include attempting to fit a new Region to the boundary defined
-*     in the current Frame.
-
-*  Parameters:
-*     this
-*        Pointer to the original Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     A pointer to the simplified Region. A cloned pointer to the
-*     supplied Region will be returned if no simplication could be
-*     performed.
-
-*  Notes:
-*     - A NULL pointer value will be returned if this function is
-*     invoked with the AST error status set, or if it should fail for
-*     any reason.
-*/
-
-/* Local Variables: */
-   AstMapping *map;           /* Base -> current Mapping */
-   AstMapping *result;        /* Result pointer to return */
-   AstPointSet *mesh;         /* Mesh of current Frame positions */
-   AstPointSet *ps2;          /* Circle PointSet in current Frame */
-   AstRegion *new;            /* Pointer to simplified Region */
-   AstRegion *newreg;         /* Equivalent circle or ellipse */
-   AstRegion *this;           /* Pointer to supplied Region structure */
-   AstRegion *unc;            /* Pointer to uncertainty Region */
-   double **ptr2;             /* Pointer axis values in "ps2" */
-   double *cen;               /* Pointer to array holding new centre coords */
-   int ic;                    /* Axis index */
-   int nc;                    /* No. of axis values per point */
-   int ok;                    /* Was the new centre found OK? */
-   int simpler;               /* Has some simplication taken place? */
-
-/* Initialise. */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the supplied Region structure. */
-   this = (AstRegion *) this_mapping;
-
-/* Invoke the parent Simplify method inherited from the Region class. This
-   will simplify the encapsulated FrameSet and uncertainty Region. */
-   new = (AstRegion *) (*parent_simplify)( this_mapping, status );
-
-/* Note if any simplification took place. This is assumed to be the case
-   if the pointer returned by the above call is different to the supplied
-   pointer. */
-   simpler = ( new != this );
-
-/* If the Mapping from base to current Frame is not a UnitMap, we attempt
-   to simplify the Circle by re-defining it within its current Frame.
-   Transforming the Circle from its base to its current Frame may result in
-   the region no longer being a circle. We test this by transforming a set of
-   bounds on the Circle boundary. */
-   map = astGetMapping( new->frameset, AST__BASE, AST__CURRENT );
-   if( !astIsAUnitMap( map ) ){
-
-/* Get a mesh of points covering the Circle in its current Frame. */
-      mesh = astRegMesh( new );
-
-/* Get the Region describing the positional uncertainty within the Circle in
-   its current Frame. */
-      unc = astGetUncFrm( new, AST__CURRENT );
-
-/* Transform the PointSet holding the circle centre into the current
-   Frame, and copy the axis values into a new array. */
-      ps2 = astRegTransform( this, this->points, 1, NULL, NULL );
-      nc = astGetNcoord( ps2 );
-      cen = astMalloc( sizeof( double )*(size_t) nc );
-      ptr2 = astGetPoints( ps2 );
-      if( astOK ) {
-
-         ok = 1;
-         for( ic = 0; ic < nc; ic++ ) {
-            cen[ ic ] = ptr2[ ic ][ 0 ];
-            if( cen[ ic ] == AST__BAD ) ok = 0;
-         }
-
-/* Find the best fitting Circle (defined in the current Frame) through these
-   points */
-         newreg = ok ? astBestCircle( mesh, cen, unc ) : NULL;
-
-/* See if all points within this mesh fall on the boundary of the best
-   fitting Circle, to within the uncertainty of the Region. */
-         if( newreg && astRegPins( newreg, mesh, NULL, NULL ) ) {
-
-/* If so, use the new Circle in place of the original. */
-            (void) astAnnul( new );
-            new = astClone( newreg );
-
-/* Otherwise, if the region is 2-d we see if an Ellipse can represent the
-   mesh. */
-         } else if( ok && nc == 2 ){
-
-/* Find the best fitting Ellipse (defined in the current Frame) through these
-   points */
-            if( newreg ) (void) astAnnul( newreg );
-            newreg = astBestEllipse( mesh, cen, unc );
-
-/* See if all points within this mesh fall on the boundary of the best
-   fitting Ellipse, to within the uncertainty of the Region. */
-            if( newreg && astRegPins( newreg, mesh, NULL, NULL ) ) {
-
-/* If so, use the new Ellipse in place of the original. */
-               (void) astAnnul( new );
-               new = astClone( newreg );
-               simpler = 1;
-            }
-         }
-
-/* Free resources. */
-         if( newreg ) newreg = astAnnul( newreg );
-      }
-
-      ps2 = astAnnul( ps2 );
-      cen = astFree( cen );
-      mesh = astAnnul( mesh );
-      unc = astAnnul( unc );
-   }
-   map = astAnnul( map );
-
-/* If any simplification could be performed, copy Region attributes from
-   the supplied Region to the returned Region, and return a pointer to it.
-   If the supplied Region had no uncertainty, ensure the returned Region
-   has no uncertainty. Otherwise, return a clone of the supplied pointer. */
-   if( simpler ){
-      astRegOverlay( new, this, 1 );
-      result = (AstMapping *) new;
-
-   } else {
-      new = astAnnul( new );
-      result = astClone( this );
-   }
-
-/* If an error occurred, annul the returned pointer. */
-   if ( !astOK ) result = astAnnul( result );
-
-/* Return the result. */
-   return result;
-}
-
-static AstPointSet *Transform( AstMapping *this_mapping, AstPointSet *in,
-                               int forward, AstPointSet *out, int *status ) {
-/*
-*  Name:
-*     Transform
-
-*  Purpose:
-*     Apply a Circle to transform a set of points.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-*                             int forward, AstPointSet *out, int *status )
-
-*  Class Membership:
-*     Circle member function (over-rides the astTransform protected
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function takes a Circle and a set of points encapsulated in a
-*     PointSet and transforms the points by setting axis values to
-*     AST__BAD for all points which are outside the region. Points inside
-*     the region are copied unchanged from input to output.
-
-*  Parameters:
-*     this
-*        Pointer to the Circle.
-*     in
-*        Pointer to the PointSet holding the input coordinate data.
-*     forward
-*        A non-zero value indicates that the forward coordinate transformation
-*        should be applied, while a zero value requests the inverse
-*        transformation.
-*     out
-*        Pointer to a PointSet which will hold the transformed (output)
-*        coordinate values. A NULL value may also be given, in which case a
-*        new PointSet will be created by this function.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     Pointer to the output (possibly new) PointSet.
-
-*  Notes:
-*     -  The forward and inverse transformations are identical for a
-*     Region.
-*     -  A null pointer will be returned if this function is invoked with the
-*     global error status set, or if it should fail for any reason.
-*     -  The number of coordinate values per point in the input PointSet must
-*     match the number of axes in the Frame represented by the Circle.
-*     -  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: */
-   AstCircle *this;            /* Pointer to Circle */
-   AstFrame *frm;                /* Pointer to base Frame in FrameSet */
-   AstPointSet *pset_tmp;        /* Pointer to PointSet holding base Frame positions*/
-   AstPointSet *result;          /* Pointer to output PointSet */
-   double **ptr_out;             /* Pointer to output coordinate data */
-   double **ptr_tmp;             /* Pointer to base Frame coordinate data */
-   double *work;                 /* Pointer to array holding single base point */
-   double d;                     /* Base-Frame distance from centre to point */
-   int closed;                   /* Is the boundary part of the Region? */
-   int coord;                    /* Zero-based index for coordinates */
-   int inside;                   /* Is the point inside the Region? */
-   int ncoord_out;               /* No. of coordinates per output point */
-   int ncoord_tmp;               /* No. of coordinates per base Frame point */
-   int neg;                      /* Has the Region been negated? */
-   int npoint;                   /* No. of points */
-   int point;                    /* Loop counter for points */
-
-/* Check the global error status. */
-   if ( !astOK ) return NULL;
-
-/* Obtain a pointer to the Circle structure. */
-   this = (AstCircle *) this_mapping;
-
-/* Apply the parent mapping using the stored pointer to the Transform member
-   function inherited from the parent Region class. This function validates
-   all arguments and generates an output PointSet if necessary,
-   containing a copy of the input PointSet. */
-   result = (*parent_transform)( this_mapping, in, forward, out, status );
-
-/* We will now extend the parent astTransform method by performing the
-   calculations needed to generate the output coordinate values. */
-
-/* First use the encapsulated FrameSet to transform the supplied positions
-   from the current Frame in the encapsulated FrameSet (the Frame
-   represented by the Region), to the base Frame (the Frame in which the
-   Region is defined). This call also returns a pointer to the base Frame
-   of the encapsulated FrameSet. Note, the returned pointer may be a
-   clone of the "in" pointer, and so we must be carefull not to modify the
-   contents of the returned PointSet. */
-   pset_tmp = astRegTransform( this, in, 0, NULL, &frm );
-
-/* Determine the numbers of points and coordinates per point from the base
-   Frame PointSet and obtain pointers for accessing the base Frame and output
-   coordinate values. */
-   npoint = astGetNpoint( pset_tmp );
-   ncoord_tmp = astGetNcoord( pset_tmp );
-   ptr_tmp = astGetPoints( pset_tmp );
-   ncoord_out = astGetNcoord( result );
-   ptr_out = astGetPoints( result );
-
-/* Get work space for one base Frame position */
-   work = astMalloc( sizeof( double )*(size_t) ncoord_tmp );
-
-/* See if the boundary is part of the Region. */
-   closed = astGetClosed( this );
-
-/* See if the Region has been negated. */
-   neg = astGetNegated( this );
-
-/* Perform coordinate arithmetic. */
-/* ------------------------------ */
-   if ( astOK ) {
-
-/* Ensure cached information is available. */
-      Cache( this, status );
-
-/* Loop round each point */
-      for ( point = 0; point < npoint; point++ ) {
-
-/* Copy the base Frame position into a work array. */
-         for ( coord = 0; coord < ncoord_tmp; coord++ ) {
-            work[ coord ] = ptr_tmp[ coord ][ point ];
-         }
-
-/* Find the geodesic distance from the centre of the Circle in the base
-   Frame. */
-         d = astDistance( frm, this->centre, work );
-
-/* Now consider whether this radius value puts the point in or out of the
-   Circle. */
-         if( d != AST__BAD ){
-            if( neg ) {
-               if( closed ) {
-                  inside = ( d >= this->radius );
-               } else {
-                  inside = ( d > this->radius );
-               }
-            } else {
-               if( closed ) {
-                  inside = ( d <= this->radius );
-               } else {
-                  inside = ( d < this->radius );
-               }
-            }
-         } else {
-            inside = 0;
-         }
-
-/* If the point is outside, store bad output values. */
-         if( !inside ) {
-            for ( coord = 0; coord < ncoord_out; coord++ ) {
-               ptr_out[ coord ][ point ] = AST__BAD;
-            }
-         }
-      }
-   }
-
-/* Free resources */
-   work = astFree( work );
-   pset_tmp = astAnnul( pset_tmp );
-   frm = astAnnul( frm );
-
-/* Annul the result if an error has occurred. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return a pointer to the output PointSet. */
-   return result;
-}
-
-/* Functions which access class attributes. */
-/* ---------------------------------------- */
-/* Implement member functions to access the attributes associated with
-   this class using the macros defined for this purpose in the
-   "object.h" file. For a description of each attribute, see the class
-   interface (in the associated .h file). */
-
-/* Copy constructor. */
-/* ----------------- */
-static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
-/*
-*  Name:
-*     Copy
-
-*  Purpose:
-*     Copy constructor for Region objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Copy( const AstObject *objin, AstObject *objout, int *status )
-
-*  Description:
-*     This function implements the copy constructor for Region objects.
-
-*  Parameters:
-*     objin
-*        Pointer to the object to be copied.
-*     objout
-*        Pointer to the object being constructed.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Notes:
-*     -  This constructor makes a deep copy.
-*/
-
-/* Local Variables: */
-   AstCircle *in;             /* Pointer to input Circle */
-   AstCircle *out;            /* Pointer to output Circle */
-   int nax;                   /* Number of base Frame axes */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain pointers to the input and output Circles. */
-   in = (AstCircle *) objin;
-   out = (AstCircle *) objout;
-
-/* For safety, first clear any references to the input memory from
-   the output Circle. */
-   out->centre = NULL;
-   out->lb = NULL;
-   out->ub = NULL;
-
-/* Copy dynamic memory contents */
-   nax = astGetNin( ((AstRegion *) in)->frameset );
-   out->centre = astStore( NULL, in->centre,
-                           sizeof( double )*(size_t)nax );
-   out->lb = astStore( NULL, in->lb, sizeof( double )*(size_t)nax );
-   out->ub = astStore( NULL, in->ub, sizeof( double )*(size_t)nax );
-}
-
-
-/* Destructor. */
-/* ----------- */
-static void Delete( AstObject *obj, int *status ) {
-/*
-*  Name:
-*     Delete
-
-*  Purpose:
-*     Destructor for Circle objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Delete( AstObject *obj, int *status )
-
-*  Description:
-*     This function implements the destructor for Circle objects.
-
-*  Parameters:
-*     obj
-*        Pointer to the object to be deleted.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Notes:
-*     This function attempts to execute even if the global error status is
-*     set.
-*/
-
-/* Local Variables: */
-   AstCircle *this;                 /* Pointer to Circle */
-
-/* Obtain a pointer to the Circle structure. */
-   this = (AstCircle *) obj;
-
-/* Annul all resources. */
-   this->centre = astFree( this->centre );
-   this->lb = astFree( this->lb );
-   this->ub = astFree( this->ub );
-}
-
-/* Dump function. */
-/* -------------- */
-static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
-/*
-*  Name:
-*     Dump
-
-*  Purpose:
-*     Dump function for Circle 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 Circle class to an output Channel.
-
-*  Parameters:
-*     this
-*        Pointer to the Circle 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: */
-   AstCircle *this;                 /* Pointer to the Circle structure */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the Circle structure. */
-   this = (AstCircle *) this_object;
-
-/* Write out values representing the instance variables for the
-   Circle class.  Accompany these with appropriate comment strings,
-   possibly depending on the values being written.*/
-
-/* In the case of attributes, we first use the appropriate (private)
-   Test...  member function to see if they are set. If so, we then use
-   the (private) Get... function to obtain the value to be written
-   out.
-
-   For attributes which are not set, we use the astGet... method to
-   obtain the value instead. This will supply a default value
-   (possibly provided by a derived class which over-rides this method)
-   which is more useful to a human reader as it corresponds to the
-   actual default attribute value.  Since "set" will be zero, these
-   values are for information only and will not be read back. */
-
-/* There are no values to write, so return without further action. */
-}
-
-/* Standard class functions. */
-/* ========================= */
-/* Implement the astIsACircle and astCheckCircle functions using the macros
-   defined for this purpose in the "object.h" header file. */
-astMAKE_ISA(Circle,Region)
-astMAKE_CHECK(Circle)
-
-AstCircle *astCircle_( void *frame_void, int form, const double centre[],
-                       const double point[], AstRegion *unc,
-                       const char *options, int *status, ...) {
-/*
-*++
-*  Name:
-c     astCircle
-f     AST_CIRCLE
-
-*  Purpose:
-*     Create a Circle.
-
-*  Type:
-*     Public function.
-
-*  Synopsis:
-c     #include "circle.h"
-c     AstCircle *astCircle( AstFrame *frame, int form, const double centre[],
-c                           const double point[], AstRegion *unc,
-c                           const char *options, ... )
-f     RESULT = AST_CIRCLE( FRAME, FORM, CENTRE, POINT, UNC, OPTIONS, STATUS )
-
-*  Class Membership:
-*     Circle constructor.
-
-*  Description:
-*     This function creates a new Circle and optionally initialises its
-*     attributes.
-*
-*     A Circle is a Region which represents a circle or sphere within the
-*     supplied Frame.
-
-*  Parameters:
-c     frame
-f     FRAME = INTEGER (Given)
-*        A pointer to the Frame in which the region is defined. A deep
-*        copy is taken of the supplied Frame. This means that any
-*        subsequent changes made to the Frame using the supplied pointer
-*        will have no effect the Region.
-c     form
-f     FORM = INTEGER (Given)
-*        Indicates how the circle is described by the remaining parameters.
-*        A value of zero indicates that the circle is specified by a
-*        centre position and a position on the circumference. A value of one
-*        indicates that the circle is specified by a centre position and a
-*        scalar radius.
-c     centre
-f     CENTRE( * ) = DOUBLE PRECISION (Given)
-c        An array of double, with one element for each Frame axis
-f        An array with one element for each Frame axis
-*        (Naxes attribute) containing the coordinates at the centre of
-*        the circle or sphere.
-c     point
-f     POINT( * ) = DOUBLE PRECISION (Given)
-c        If "form"
-f        If FORM
-*        is zero, then this array should have one element for each Frame
-*        axis (Naxes attribute), and should be supplied holding the
-*        coordinates at a point on the circumference of the circle or sphere.
-c        If "form"
-f        If FORM
-*        is one, then this array should have one element only which should
-*        be supplied holding the scalar radius of the circle or sphere,
-*        as a geodesic distance within the Frame.
-c     unc
-f     UNC = INTEGER (Given)
-*        An optional pointer to an existing Region which specifies the
-*        uncertainties associated with the boundary of the Circle being created.
-*        The uncertainty in any point on the boundary of the Circle is found by
-*        shifting the supplied "uncertainty" Region so that it is centred at
-*        the boundary point being considered. The area covered by the
-*        shifted uncertainty Region then represents the uncertainty in the
-*        boundary position. The uncertainty is assumed to be the same for
-*        all points.
-*
-*        If supplied, the uncertainty Region must be of a class for which
-*        all instances are centro-symetric (e.g. Box, Circle, Ellipse, etc.)
-*        or be a Prism containing centro-symetric component Regions. A deep
-*        copy of the supplied Region will be taken, so subsequent changes to
-*        the uncertainty Region using the supplied pointer will have no
-*        effect on the created Circle. Alternatively,
-f        a null Object pointer (AST__NULL)
-c        a NULL Object pointer
-*        may be supplied, in which case a default uncertainty is used
-*        equivalent to a box 1.0E-6 of the size of the Circle being created.
-*
-*        The uncertainty Region has two uses: 1) when the
-c        astOverlap
-f        AST_OVERLAP
-*        function compares two Regions for equality the uncertainty
-*        Region is used to determine the tolerance on the comparison, and 2)
-*        when a Region is mapped into a different coordinate system and
-*        subsequently simplified (using
-c        astSimplify),
-f        AST_SIMPLIFY),
-*        the uncertainties are used to determine if the transformed boundary
-*        can be accurately represented by a specific shape of Region.
-c     options
-f     OPTIONS = CHARACTER * ( * ) (Given)
-c        Pointer to a null-terminated string containing an optional
-c        comma-separated list of attribute assignments to be used for
-c        initialising the new Circle. 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 Circle. 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     astCircle()
-f     AST_CIRCLE = INTEGER
-*        A pointer to the new Circle.
-
-*  Notes:
-*     - A null Object pointer (AST__NULL) will be returned if this
-c     function is invoked with the AST error status set, or if it
-f     function is invoked with STATUS set to an error value, or if it
-*     should fail for any reason.
-*--
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstFrame *frame;              /* Pointer to Frame structure */
-   AstCircle *new;               /* Pointer to new Circle */
-   va_list args;                 /* Variable argument list */
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* Obtain and validate a pointer to the supplied Frame structure. */
-   frame = astCheckFrame( frame_void );
-
-/* Initialise the Circle, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitCircle( NULL, sizeof( AstCircle ), !class_init, &class_vtab,
-                        "Circle", frame, form, centre, point, unc );
-
-/* If successful, note that the virtual function table has been
-   initialised. */
-   if ( astOK ) {
-      class_init = 1;
-
-/* Obtain the variable argument list and pass it along with the options string
-   to the astVSet method to initialise the new Circle'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 Circle. */
-   return new;
-}
-
-AstCircle *astCircleId_( void *frame_void, int form, const double centre[],
-                         const double point[], void *unc_void,
-                         const char *options, ... ) {
-/*
-*  Name:
-*     astCircleId_
-
-*  Purpose:
-*     Create a Circle.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     AstCircle *astCircleId_( AstFrame *frame, int form, const double centre[],
-*                              const double point[], AstRegion *unc,
-*                              const char *options, ... )
-
-*  Class Membership:
-*     Circle constructor.
-
-*  Description:
-*     This function implements the external (public) interface to the
-*     astCircle constructor function. It returns an ID value (instead
-*     of a true C pointer) to external users, and must be provided
-*     because astCircle_ 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 astCircle_ 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 astCircle_.
-
-*  Returned Value:
-*     The ID value associated with the new Circle.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstFrame *frame;              /* Pointer to Frame structure */
-   AstCircle *new;               /* Pointer to new Circle */
-   AstRegion *unc;               /* Pointer to Region structure */
-   va_list args;                 /* Variable argument list */
-
-   int *status;                  /* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Pointer to inherited status value */
-
-/* Get a pointer to the inherited status value. */
-   status = astGetStatusPtr;
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* Obtain a Frame pointer from the supplied ID and validate the
-   pointer to ensure it identifies a valid Frame. */
-   frame = astVerifyFrame( astMakePointer( frame_void ) );
-
-/* Obtain a Region pointer from the supplied "unc" ID and validate the
-   pointer to ensure it identifies a valid Region . */
-   unc = unc_void ? astVerifyRegion( astMakePointer( unc_void ) ) : NULL;
-
-/* Initialise the Circle, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitCircle( NULL, sizeof( AstCircle ), !class_init, &class_vtab,
-                        "Circle", frame, form, centre, point, unc );
-
-/* If successful, note that the virtual function table has been
-   initialised. */
-   if ( astOK ) {
-      class_init = 1;
-
-/* Obtain the variable argument list and pass it along with the options string
-   to the astVSet method to initialise the new Circle'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 Circle. */
-   return astMakeId( new );
-}
-
-AstCircle *astInitCircle_( void *mem, size_t size, int init, AstCircleVtab *vtab,
-                           const char *name, AstFrame *frame, int form,
-                           const double centre[], const double point[],
-                           AstRegion *unc, int *status ) {
-/*
-*+
-*  Name:
-*     astInitCircle
-
-*  Purpose:
-*     Initialise a Circle.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     AstCircle *astInitCircle_( void *mem, size_t size, int init, AstCircleVtab *vtab,
-*                                const char *name, AstFrame *frame, int form,
-*                                const double centre[], const double point[],
-*                                AstRegion *unc )
-
-*  Class Membership:
-*     Circle initialiser.
-
-*  Description:
-*     This function is provided for use by class implementations to initialise
-*     a new Circle object. It allocates memory (if necessary) to accommodate
-*     the Circle plus any additional data associated with the derived class.
-*     It then initialises a Circle 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 Circle at the start of the memory passed via the
-*     "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory in which the Circle is to be initialised.
-*        This must be of sufficient size to accommodate the Circle data
-*        (sizeof(Circle)) 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 Circle (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 Circle
-*        structure, so a valid value must be supplied even if not required for
-*        allocating memory.
-*     init
-*        A logical flag indicating if the Circle'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 Circle.
-*     name
-*        Pointer to a constant null-terminated character string which contains
-*        the name of the class to which the new object belongs (it is this
-*        pointer value that will subsequently be returned by the astGetClass
-*        method).
-*     frame
-*        A pointer to the Frame in which the region is defined.
-*     form
-*        Indicates how the "point" parameter should be interpreted.
-*        Should be either 0 or 1.
-*     centre
-*        An array of double, with one element for each Frame axis (Naxes
-*        attribute) containing the coordinates of the circle centre.
-*     point
-*        If "form" is zero, this should be an array of double, with one
-*        element for each Frame axis (Naxes attribute) containing the
-*        coordinates at any point on the circumference. If "form" is one,
-*        this should be the address of a double containing the scalar
-*        radius of the circle or sphere.
-*     unc
-*        A pointer to a Region which specifies the uncertainty in the
-*        supplied positions (all points on the boundary of the new Circle
-*        being initialised are assumed to have the same uncertainty). A NULL
-*        pointer can be supplied, in which case default uncertainties equal to
-*        1.0E-6 of the dimensions of the new Circle's bounding box are used.
-*        If an uncertainty Region is supplied, it must be either a Box, a
-*        Circle or an Ellipse, and its encapsulated Frame must be related
-*        to the Frame supplied for parameter "frame" (i.e. astConvert
-*        should be able to find a Mapping between them). Two positions
-*        the "frame" Frame are considered to be co-incident if their
-*        uncertainty Regions overlap. The centre of the supplied
-*        uncertainty Region is immaterial since it will be re-centred on the
-*        point being tested before use. A deep copy is taken of the supplied
-*        Region.
-
-*  Returned Value:
-*     A pointer to the new Circle.
-
-*  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: */
-   AstCircle *new;           /* Pointer to new Circle */
-   AstPointSet *pset;        /* PointSet to pass to Region initialiser */
-   const double *circum;     /* Pointer to circumference position */
-   double **ptr;             /* Pointer to coords data in pset */
-   int i;                    /* Axis index */
-   int nc;                   /* No. of axes */
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* If necessary, initialise the virtual function table. */
-   if ( init ) astInitCircleVtab( vtab, name );
-
-/* Initialise. */
-   new = NULL;
-
-/* Check the supplied value for "form" is legal. */
-   if( form != 0 && form != 1 && astOK ) {
-      astError( AST__BADIN, "astInitCircle(%s): The value supplied for "
-                "parameter \"form\" (%d) is illegal - it should be 0 or 1 "
-                "(programming error).", status, name, form );
-   }
-
-/* Get the number of axis values required for each position. */
-   nc = astGetNaxes( frame );
-
-/* If the circle radius has been supplied, find a point on the circle
-   circumference. */
-   if( form == 1 ) {
-      circum = CircumPoint( frame, nc, centre, *point, status );
-
-/* Otherwise, use the supplied circumference point. */
-   } else {
-      circum = point;
-   }
-
-/* Create a PointSet to hold the centre position, and a point on the
-   circumference, and get points to the data arrays. */
-   pset = astPointSet( 2, nc, "", status );
-   ptr = astGetPoints( pset );
-
-/* Copy the centre and circumference coordinates into the PointSet, checking
-   that no bad values have been supplied. */
-   for( i = 0; astOK && i < nc; i++ ) {
-      if( centre[ i ] == AST__BAD ) {
-         astError( AST__BADIN, "astInitCircle(%s): The value of axis %d is "
-                   "undefined at the circle centre.", status, name, i + 1 );
-      }
-      if( astOK && circum[ i ] == AST__BAD ) {
-         astError( AST__BADIN, "astInitCircle(%s): The value of axis %d is "
-                   "undefined on the circumference of the circle.", status, name, i + 1 );
-      }
-      ptr[ i ][ 0 ] = centre[ i ];
-      ptr[ i ][ 1 ] = circum[ i ];
-   }
-
-/* Check pointers can be used safely. */
-   if( astOK ) {
-
-/* Initialise a Region structure (the parent class) as the first component
-   within the Circle structure, allocating memory if necessary. */
-      new = (AstCircle *) astInitRegion( mem, size, 0, (AstRegionVtab *) vtab,
-                                         name, frame, pset, unc );
-
-      if ( astOK ) {
-
-/* Initialise the Circle data. */
-/* ------------------------ */
-         new->stale = 1;
-         new->centre = NULL;
-         new->lb = NULL;
-         new->ub = NULL;
-         Cache( new, status );
-
-/* If an error occurred, clean up by deleting the new Circle. */
-         if ( !astOK ) new = astDelete( new );
-      }
-   }
-
-/* Free resources. */
-   pset = astAnnul( pset );
-   if( form == 1 ) circum = astFree( (void *) circum );
-
-/* Return a pointer to the new Circle. */
-   return new;
-}
-
-AstCircle *astLoadCircle_( void *mem, size_t size, AstCircleVtab *vtab,
-                           const char *name, AstChannel *channel, int *status ) {
-/*
-*+
-*  Name:
-*     astLoadCircle
-
-*  Purpose:
-*     Load a Circle.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "circle.h"
-*     AstCircle *astLoadCircle( void *mem, size_t size, AstCircleVtab *vtab,
-*                               const char *name, AstChannel *channel )
-
-*  Class Membership:
-*     Circle loader.
-
-*  Description:
-*     This function is provided to load a new Circle 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
-*     Circle 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 Circle at the start of the memory
-*     passed via the "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory into which the Circle is to be
-*        loaded.  This must be of sufficient size to accommodate the
-*        Circle data (sizeof(Circle)) 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 Circle (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 Circle 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(AstCircle) is used instead.
-*     vtab
-*        Pointer to the start of the virtual function table to be
-*        associated with the new Circle. If this is NULL, a pointer
-*        to the (static) virtual function table for the Circle 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 "Circle" is used instead.
-
-*  Returned Value:
-*     A pointer to the new Circle.
-
-*  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 */
-   AstCircle *new;              /* Pointer to the new Circle */
-
-/* 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 Circle. In this case the
-   Circle belongs to this class, so supply appropriate values to be
-   passed to the parent class loader (and its parent, etc.). */
-   if ( !vtab ) {
-      size = sizeof( AstCircle );
-      vtab = &class_vtab;
-      name = "Circle";
-
-/* If required, initialise the virtual function table for this class. */
-      if ( !class_init ) {
-         astInitCircleVtab( 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 Circle. */
-   new = astLoadRegion( mem, size, (AstRegionVtab *) vtab, name,
-                        channel );
-
-   if ( astOK ) {
-
-/* Read input data. */
-/* ================ */
-/* Request the input Channel to read all the input data appropriate to
-   this class into the internal "values list". */
-      astReadClassData( channel, "Circle" );
-
-/* Now read each individual data item from this list and use it to
-   initialise the appropriate instance variable(s) for this class. */
-
-/* In the case of attributes, we first read the "raw" input value,
-   supplying the "unset" value as the default. If a "set" value is
-   obtained, we then use the appropriate (private) Set... member
-   function to validate and set the value properly. */
-
-/* There are no values to read. */
-/* ---------------------------- */
-
-/* Cache intermediate results in the Circle structure */
-      new->centre = NULL;
-      new->lb = NULL;
-      new->ub = NULL;
-      new->stale = 1;
-      Cache( new, status );
-
-/* If an error occurred, clean up by deleting the new Circle. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return the new Circle 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. */
-
-
-void astCirclePars_( AstCircle *this, double *centre, double *radius,
-                     double *p1, int *status ){
-   if ( !astOK ) return;
-   (**astMEMBER(this,Circle,CirclePars))( this, centre, radius,
-                                          p1, status );
-}
-
-
-
-
-
-