Merge commit '7fde2daeed593684120d75de07598154f3ddaf2c' as 'ast'

1 files changed, 2900 insertions, 0 deletions

diff --git a/ast/circle.c b/ast/circle.c
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+++ b/ast/circle.c
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+/*
+*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 );
+      if( centre ) centre = astFree( centre );
+
+/* 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 = astAnnul( *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 ? astCheckRegion( 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 );
+}
+
+
+
+
+
+