upgrade ast 8.7.1

1 files changed, 0 insertions, 3055 deletions

diff --git a/ast/ellipse.c b/ast/ellipse.c
deleted file mode 100644
index 1e23724..0000000
--- a/ast/ellipse.c
+++ /dev/null
@@ -1,3055 +0,0 @@
-/*
-*class++
-*  Name:
-*     Ellipse
-
-*  Purpose:
-*     An elliptical region within a 2-dimensional Frame.
-
-*  Constructor Function:
-c     astEllipse
-f     AST_ELLIPSE
-
-*  Description:
-*     The Ellipse class implements a Region which represents a ellipse
-*     within a 2-dimensional Frame.
-
-*  Inheritance:
-*     The Ellipse class inherits from the Region class.
-
-*  Attributes:
-*     The Ellipse 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 Ellipses:
-f     In addition to those routines applicable to all Regions, the
-f     following routines may also be applied to all Ellipses:
-*
-c     - astEllipsePars: Get the geometric parameters of the Ellipse
-f     - AST_ELLIPSEPARS: Get the geometric parameters of the Ellipse
-
-*  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:
-*     7-SEP-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.
-*     6-JAN-2014 (DSB):
-*        Ensure cached information is available in RegCentre even if no new
-*        centre is supplied.
-*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 Ellipse
-
-/* 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 circle class */
-#include "ellipse.h"             /* Interface definition for this class */
-#include "mapping.h"             /* Position mappings */
-#include "unitmap.h"             /* Unit Mapping */
-#include "pal.h"                 /* Positional astronomy library */
-
-/* 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(Ellipse)
-
-/* Define macros for accessing each item of thread specific global data. */
-#define class_init astGLOBAL(Ellipse,Class_Init)
-#define class_vtab astGLOBAL(Ellipse,Class_Vtab)
-
-
-#include <pthread.h>
-
-
-#else
-
-
-/* Define the class virtual function table and its initialisation flag
-   as static variables. */
-static AstEllipseVtab 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. */
-AstEllipse *astEllipseId_( void *, int, const double[2], const double[2], const double[2], 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 *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( AstEllipse *, int * );
-static void CalcPars( AstFrame *, double[2], double[2], double[2], double *, double *, double *, int * );
-static void Copy( const AstObject *, AstObject *, int * );
-static void Delete( AstObject *, int * );
-static void Dump( AstObject *, AstChannel *, int * );
-static void EllipsePars( AstEllipse *, double[2], double *, double *, double *, double[2], double[2], int * );
-static void RegBaseBox( AstRegion *this, double *, double *, int * );
-static void ResetCache( AstRegion *this, int * );
-static void SetRegFS( AstRegion *, AstFrame *, int * );
-
-/* Member functions. */
-/* ================= */
-
-AstRegion *astBestEllipse_( AstPointSet *mesh, double *cen, AstRegion *unc, int *status ){
-/*
-*+
-*  Name:
-*     astBestEllipse
-
-*  Purpose:
-*     Find the best fitting Ellipse through a given mesh of points.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     AstRegion *astBestEllipse( AstPointSet *mesh, double *cen, AstRegion *unc )
-
-*  Class Membership:
-*     Ellipse member function
-
-*  Description:
-*     This function finds the best fitting Ellipse through a given mesh of
-*     points. Ellispes are always 2-dimensional.
-
-*  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 Ellipse
-*        centre.
-*     unc
-*        A Region representing the uncertainty associated with each point
-*        on the mesh.
-
-*  Returned Value:
-*     Pointer to the best fitting Ellipse. It will inherit the positional
-*     uncertainty and Frame represented by "unc".
-
-*  Implementation Deficiencies:
-*    - The method used by this function is not very accurate, and assumes
-*    that the supplied mesh provides uniform coverage of the entire ellipse.
-
-*  Notes:
-*    - A NULL pointer is returned if an error has already occurred, or if
-*    this function should fail for any reason.
-
-*-
-*/
-
-/* Local Variables: */
-   AstFrame *frm;
-   AstPointSet *ps2;
-   AstRegion *result;
-   double **ptr2;
-   double **ptr;
-   double *ang;
-   double *dist;
-   double *px;
-   double *py;
-   double a0;
-   double a;
-   double aa[2];
-   double at;
-   double b;
-   double c0;
-   double c1;
-   double c2;
-   double c;
-   double d;
-   double den;
-   double e;
-   double f;
-   double mn;
-   double mx;
-   double p[2];
-   double pa[2];
-   double pb[2];
-   double r1;
-   double r2;
-   double r3;
-   double smn;
-   double t1;
-   double t2;
-   double t3;
-   int ip;
-   int maxat;
-   int np;
-   double sw;
-
-/* Initialise */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get no. of points in the mesh. */
-   np = astGetNpoint( mesh );
-
-/* Get pointers to the axis values. */
-   ptr = astGetPoints( mesh );
-
-/* Allocate work space */
-   dist = astMalloc( sizeof( double )*(size_t) np );
-   ang = astMalloc( sizeof( double )*(size_t) np );
-
-/* Get a pointer to the Frame represented by "unc". This is the Frame to
-   which the supplied mesh points refer. */
-   frm = astGetFrame( unc->frameset, AST__CURRENT );
-
-/* Check pointers can be used safely */
-   if( astOK ) {
-
-/* Find the first mesh point which is at a non-zero distance from the
-   centre. */
-      px = ptr[ 0 ];
-      py = ptr[ 1 ];
-      for( ip = 0; ip < np; ip++, px++, py++ ) {
-         p[ 0 ] = *px;
-         p[ 1 ] = *py;
-         dist[ ip ] = astDistance( frm, cen, p );
-         if( dist[ ip ] != AST__BAD && dist[ ip ] != 0.0 ) {
-            break;
-         } else {
-            ang[ ip ] = AST__BAD;
-            dist[ ip ] = AST__BAD;
-         }
-      }
-
-/* Find a point which is this distance away from the centre along the second
-   axis. This point is used to define zero angle when calling astAngle
-   below. */
-      astOffset2( frm, cen, 0.0, dist[ ip ], aa );
-      ang[ ip ] = astAngle( frm, aa, cen, p );
-
-/* Get the distance from the centre to each of the remaining mesh points. Also
-   find the orientation of the radial lines through the centre to each mesh
-   point. At the same time, find the index of the point with the largest
-   radial distance. */
-      maxat = ip;
-      r2 = dist[ maxat ];
-      ip++;
-      px++;
-      py++;
-      for( ; ip < np; ip++, px++, py++ ) {
-         p[ 0 ] = *px;
-         p[ 1 ] = *py;
-         dist[ ip ] = astDistance( frm, cen, p );
-         ang[ ip ] = astAngle( frm, aa, cen, p );
-         if( dist[ ip ] != AST__BAD && dist[ ip ] > r2 ) {
-            r2 = dist[ ip ];
-            maxat = ip;
-         }
-      }
-
-/* Find the higher index neighbouring point, wrapping back to the start
-   of the list when the end is reached. Note the radius and position angle
-   at this neighbouring point. */
-      t2 = 0.0;
-      r3 = AST__BAD;
-      t3 = AST__BAD;
-      a0 = ang[ maxat ];
-      for( ip = maxat + 1; ip < np; ip++ ) {
-         if( dist[ ip ] != AST__BAD ) {
-            r3 = dist[ ip ];
-            t3 = palDrange( ang[ ip ] - a0 );
-            break;
-         }
-      }
-      if( r3 == AST__BAD ) {
-         for( ip = 0; ip < maxat; ip++ ) {
-            if( dist[ ip ] != AST__BAD ) {
-               r3 = dist[ ip ];
-               t3 = palDrange( ang[ ip ] - a0 );
-               break;
-            }
-         }
-      }
-
-/* Find the lower index neighbouring point, wrapping back to the end
-   of the list when the start is reached. Note the radius and position angle
-   at this neighbouring point. */
-      r1 = AST__BAD;
-      t1 = AST__BAD;
-      for( ip = maxat - 1; ip > -1; ip-- ) {
-         if( dist[ ip ] != AST__BAD ) {
-            r1 = dist[ ip ];
-            t1 = palDrange( ang[ ip ] - a0 );
-            break;
-         }
-      }
-      if( r1 == AST__BAD ) {
-         for( ip = np - 1; ip > maxat; ip-- ) {
-            if( dist[ ip ] != AST__BAD ) {
-               r1 = dist[ ip ];
-               t1 = palDrange( ang[ ip ] - a0 );
-               break;
-            }
-         }
-      }
-
-/* Fit a quadratic through the three pairs of (radius,angle) values. The
-   centre point (r2,t2) is the point which is furthest from the centre,
-   and the other two are the neighbouring points found above. */
-      a = r2 - r1;
-      b = t2 - t1;
-      c = t2*t2 - t1*t1;
-      d = r3 - r2;
-      e = t3 - t2;
-      f = t3*t3 - t2*t2;
-
-      den = c*e - b*f;
-      if( den != 0.0 ) {
-
-/* The co-efficients of the interpolating polynomial... */
-         c1 = ( d*c - a*f )/den;
-         c2 = ( a*e - d*b )/den;
-         c0 = r1 - c1*t1 - c2*t1*t1;
-
-/* Find the largest radius (the turning point of the quadratic), and the
-   angle at which it occurs. */
-         if( c2 < 0.0 ) {
-            mx = ( 4*c0*c2 - c1*c1 )/( 4*c2 );
-            at = a0 - c1/( 2*c2 );
-         } else {
-            mx = r2;
-            at = a0 - t2;
-         }
-
-/* This point is the end of the ellipse primary axis. Find its (x,y)
-   coords, and store in "pa". */
-         astOffset2( frm, cen, at, mx, pa );
-
-/* Resolve all the supplied points into components parallel and
-   perpendicular to the line joining the centre and "pa". */
-         ps2 = astResolvePoints( frm, cen, pa, mesh, NULL );
-         ptr2 = astGetPoints( ps2 );
-         if( astOK ) {
-
-/* For each other mesh point, work out the length of the secondary
-   axis which would result if we used that point to define the ellipse.
-   Find the mean of these secondary axis lengths, weighted by the length
-   of the y component to reduce influence of poor conditioning at very
-   low y. */
-            smn = 0.0;
-            sw = 0.0;
-            px = ptr2[ 0 ];
-            py = ptr2[ 1 ];
-            for( ip = 0; ip < np; ip++, px++, py++ ) {
-               if( *px != AST__BAD && *py != AST__BAD ) {
-                  den = mx*mx - (*px)*(*px);
-                  if( den > 0.0 ) {
-                     smn += fabs( mx*(*py)*(*py) )/sqrt( den );
-                     sw += fabs( *py );
-                  }
-               }
-            }
-
-            if( sw > 0 ) {
-               mn = smn/sw;
-
-/* Find the coords at the end of the mean secondary axis. */
-               astOffset2( frm, cen, at + AST__DPIBY2, mn, pb );
-
-/* Create the Ellipse to return. */
-               result = (AstRegion *) astEllipse( frm, 0, cen, pa, pb, unc, "", status );
-            }
-         }
-
-/* Free resources. */
-         ps2 = astAnnul( ps2 );
-
-      }
-   }
-
-   dist = astFree( dist );
-   ang = astFree( ang );
-   frm = astAnnul( frm );
-
-/* Return NULL if anything went wrong. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return the result.*/
-   return result;
-}
-
-void astInitEllipseVtab_(  AstEllipseVtab *vtab, const char *name, int *status ) {
-/*
-*+
-*  Name:
-*     astInitEllipseVtab
-
-*  Purpose:
-*     Initialise a virtual function table for a Ellipse.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     void astInitEllipseVtab( AstEllipseVtab *vtab, const char *name )
-
-*  Class Membership:
-*     Ellipse vtab initialiser.
-
-*  Description:
-*     This function initialises the component of a virtual function
-*     table which is used by the Ellipse 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 astIsAEllipse) 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->EllipsePars = EllipsePars;
-
-/* 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->RegBaseMesh = RegBaseMesh;
-   region->RegBaseBox = RegBaseBox;
-   region->RegCentre = RegCentre;
-   region->RegTrace = RegTrace;
-
-/* 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, "Ellipse", "Elliptical 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 Cache( AstEllipse *this, int *status ){
-/*
-*  Name:
-*     Cache
-
-*  Purpose:
-*     Calculate intermediate values and cache them in the Ellipse structure.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     void Cache( AstEllipse *this, int *status )
-
-*  Class Membership:
-*     Ellipse 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 Ellipse structure.
-
-*  Parameters:
-*     this
-*        Pointer to the Ellipse.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-/* Local Variables: */
-   AstFrame *frm;       /* Pointer to base Frame in Ellipse */
-   double **ptr;        /* Pointer to data in the encapsulated PointSet */
-   double *centre;      /* Array holding centre coords */
-   double *point1;      /* Array holding coords at end of primary axis */
-   double *point2;      /* Array holding coords at another point on ellipse */
-   double a;            /* The half-length of the primary axis */
-   double angle;        /* Orientation of primary axis */
-   double b;            /* The half-length of the secondary axis */
-   int i;               /* Axis index */
-
-/* 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. */
-      frm = astGetFrame( ((AstRegion *) this)->frameset, AST__BASE );
-
-/* Allocate memory. */
-      centre = (double *) astMalloc( sizeof( double )*2 );
-      point1 = (double *) astMalloc( sizeof( double )*2 );
-      point2 = (double *) astMalloc( sizeof( double )*2 );
-
-/* Get pointers to the coordinate data in the parent Region structure. */
-      ptr = astGetPoints( ((AstRegion *) this)->points );
-
-/* Check pointers can be used safely. */
-      if( astOK ) {
-
-/* Copy the points in to the allocated memory. */
-         for( i = 0; i < 2; i++ ) {
-            centre[ i ] = ptr[ i ][ 0 ];
-            point1[ i ] = ptr[ i ][ 1 ];
-            point2[ i ] = ptr[ i ][ 2 ];
-         }
-
-/* Calculate the geometric parameters of the ellipse. */
-         CalcPars( frm, centre, point1, point2, &a, &b, &angle, status );
-
-/* Check the returned values. */
-         if( a <= 0.0 || a == AST__BAD || b <= 0.0 || b == AST__BAD ) {
-            if( astOK ) astError( AST__BADIN, "astInitEllipse(%s): The "
-                                  "supplied points do not determine an "
-                                  "ellipse.", status, astGetClass( this ) );
-         }
-
-/* Store useful things in the Ellipse structure. */
-         if( astOK ) {
-           astFree( this->centre );
-           this->centre = centre;
-           centre = NULL;
-
-           astFree( this->point1 );
-           this->point1 = point1;
-           point1 = NULL;
-
-           this->a = a;
-           this->b = b;
-           this->angle = angle;
-         }
-      }
-
-/* Initialise the bounding box. This is set properly when the astRegBaseMesh
-   function is called. These variables should not be used unless the
-   "basemesh" component of the parent Region structure is set to a non-null
-   value. */
-      this->lbx = -DBL_MAX;
-      this->ubx = DBL_MAX;
-      this->lby = -DBL_MAX;
-      this->uby = DBL_MAX;
-
-/* Free resources */
-      frm = astAnnul( frm );
-      if( centre ) centre = astFree( centre );
-      if( point1 ) point1 = astFree( point1 );
-      point2 = astFree( point2 );
-
-/* Indicate cached information is up to date. */
-      this->stale = 0;
-
-   }
-}
-
-static void CalcPars( AstFrame *frm, double centre[2], double point1[2],
-                      double point2[2], double *a, double *b,
-                      double *angle, int *status ){
-/*
-*  Name:
-*     CalcPars
-
-*  Purpose:
-*     Calculate ellipse parameters.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     void CalcPars( AstFrame *frm, double centre[2], double point1[2],
-*                    double point2[2], double *a, double *b, double *angle,
-*                    int *status )
-
-*  Class Membership:
-*     Ellipse member function
-
-*  Description:
-*     This function uses the supplied positions to calculate the
-*     geometric parameters of an ellipse.
-
-*  Parameters:
-*     frm
-*        Pointer to the Frame in which the positions are defined.
-*     centre;
-*        Array holding centre coords.
-*     point1
-*        Array holding coords at end of primary axis
-*     point2
-*        Array holding coords at another point on ellipse. On exit it
-*        holds the coords at the end of the secondary axis.
-*     a
-*        Pointer to location at which to store the half-length of the
-*        primary axis.
-*     b
-*        Pointer to location at which to store the half-length of the
-*        secondary axis.
-*     angle
-*        Pointer to location at which to store the angle from the
-*        positive direction of the second Frame axis to the primary
-*        ellipse axis, in radians. Rotation from the second to the first
-*        Frame axis is positive.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-/* Local Variables: */
-   double point3[ 2 ];  /* Array holding a point on the primary axis */
-   double x;            /* The offset parallel to the primary axis */
-   double y;            /* The offset perpendicular to the primary axis */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Get the geodesic distance between the centre and point 1 (the end of
-   the primary axis of the ellipse). This is the half length of the
-   primary axis of the ellipse (the axis which joins the centre position to
-   point 1). */
-   *a = astDistance( frm, centre, point1 );
-
-/* Find the point (point3) on the primary axis which is closest to point 2,
-   and thus get the geodesic offsets (resolved parallel and perpendicular to
-   the primary axis) between the centre and point 2. */
-   if( *a > 0.0 ) {
-      astResolve( frm, centre, point1, point2, point3, &x, &y );
-
-/* Find the half-length of the secondary ellipse axis. */
-      if( astOK ) {
-         *b = (*a)*(*a) - x*x;
-         if( *b > 0.0 ) *b = (*a)*y/sqrt( *b );
-      } else {
-         *b = *a;
-      }
-
-/* Find the angle from the positive direction of the second axis to the
-   primary ellipse axis. */
-      point3[ 0 ] = centre[ 0 ];
-      point3[ 1 ] = centre[ 1 ] + fabs( 0.1*(*a) );
-      *angle = astAngle( frm, point3, centre, point1 );
-
-/* Find the end point of the secondary axis. */
-      (void) astOffset2( frm, centre, *angle + AST__DPIBY2, *b, point2 );
-   }
-}
-
-static void EllipsePars( AstEllipse *this, double centre[2], double *a,
-                         double *b, double *angle, double p1[2],
-                         double p2[2], int *status ){
-/*
-*++
-*  Name:
-c     astEllipsePars
-f     AST_ELLIPSEPARS
-
-*  Purpose:
-*     Returns the geometric parameters of an Ellipse.
-
-*  Type:
-*     Public virtual function.
-
-*  Synopsis:
-c     #include "ellipse.h"
-c     void astEllipsePars( AstEllipse *this, double centre[2], double *a,
-c                          double *b, double *angle, double p1[2], double p2[2] )
-f     CALL AST_ELLIPSEPARS( THIS, CENTRE, A, B, ANGLE, P1, P2, STATUS )
-
-*  Class Membership:
-*     Region method.
-
-*  Description:
-c     This function
-f     This routine
-*     returns the geometric parameters describing the supplied ellipse.
-
-*  Parameters:
-c     this
-f     THIS = INTEGER (Given)
-*        Pointer to the Region.
-c     centre
-f     CENTRE( 2 ) = DOUBLE PRECISION (Returned)
-*        The coordinates of the Ellipse centre are returned in this arrays.
-c     a
-f     A = DOUBLE PRECISION (Returned)
-*        Returned holding the half-length of the first axis of the
-*        ellipse.
-c     b
-f     B = DOUBLE PRECISION (Returned)
-*        Returned holding the half-length of the second axis of the
-*        ellipse.
-c     angle
-f     ANGLE = DOUBLE PRECISION (Returned)
-*        If the coordinate system in which the Ellipse is defined has
-*        axes (X,Y), then
-c        "*angle"
-f        ANGLE
-*        is returned holding the angle from the positive direction of
-*        the Y axis to the first axis of the ellipse, in radians.
-*        Positive rotation is in the same sense as rotation from the
-*        positive direction of Y to the positive direction of X.
-c     p1
-f     P1( 2 ) = DOUBLE PRECISION (Returned)
-*        An array in which to return the coordinates at one of the two ends
-*        of the first axis  of the ellipse.
-c        A NULL pointer can be supplied if these coordinates are not needed.
-c     p2
-f     P2( 2 ) = DOUBLE PRECISION (Returned)
-*        An array in which to return the coordinates at one of the two ends
-*        of the second axis  of the ellipse.
-c        A NULL pointer can be supplied if these coordinates are not needed.
-f     STATUS = INTEGER (Given and Returned)
-f        The global status.
-
-*  Notes:
-*     - If the coordinate system represented by the Ellipse 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 Ellipse object may not be an accurate
-*     ellipse.
-*     - Values of AST__BAD are returned for the parameters without error
-*     if the ellipse is degenerate or undefined.
-*--
-*/
-
-/* Local Variables: */
-   AstFrame *frm;           /* Current Frame represented by the Ellipse */
-   AstPointSet *pset;       /* PointSet holding PointList axis values */
-   AstRegion *this_region;  /* Parent Region pointer */
-   double **ptr;            /* Pointer to axes values in the PointList */
-   double *point1;          /* Pointer to "p1" or "buf1" */
-   double *point2;          /* Pointer to "p2" or "buf2" */
-   double buf1[2];          /* Local substitute array for "p1" */
-   double buf2[2];          /* Local substitute array for "p2" */
-   int i;                   /* Axis index */
-
-/* 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 pointers to the coordinate data. */
-   ptr = astGetPoints( pset );
-
-/* Choose the arrays to use - supplied arrays if possible, local arrays
-   otherwise. */
-   if( p1 ) {
-      point1 = p1;
-   } else {
-      point1 = buf1;
-   }
-   if( p2 ) {
-      point2 = p2;
-   } else {
-      point2 = buf2;
-   }
-
-/* Check pointers can be used safely. */
-   if( astOK ) {
-
-/* Copy the points in to separate arrays. */
-      for( i = 0; i < 2; i++ ) {
-         centre[ i ] = ptr[ i ][ 0 ];
-         point1[ i ] = ptr[ i ][ 1 ];
-         point2[ i ] = ptr[ i ][ 2 ];
-      }
-
-/* Get the Ellipse frame. */
-      frm = astGetFrame( this_region->frameset, AST__CURRENT );
-
-/* Calculate the geometric parameters of the ellipse. */
-      CalcPars( frm, centre, point1, point2, a, b, angle, status );
-
-/* Ensure no zero values are returned. */
-      if( *a <= 0.0  || *b <= 0.0 ) {
-         *a = AST__BAD;
-         *b = AST__BAD;
-         *angle = AST__BAD;
-      }
-
-/* Free resources */
-      frm = astAnnul( frm );
-   }
-   pset = astAnnul( pset );
-}
-
-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 "ellipse.h"
-*     void RegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status )
-
-*  Class Membership:
-*     Ellipse 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: */
-   AstEllipse *this;             /* Pointer to Ellipse structure */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Get a pointer to the Ellipse structure */
-   this = (AstEllipse *) this_region;
-
-/* The bounding box of the mesh returned by astRegBaseMesh is used as the
-   bounding box of the Ellipse. These bounds are cached in the Ellipse
-   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. */
-   lbnd[ 0 ] = this->lbx;
-   ubnd[ 0 ] = this->ubx;
-   lbnd[ 1 ] = this->lby;
-   ubnd[ 1 ] = this->uby;
-
-}
-
-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 "ellipse.h"
-*     AstPointSet *astRegBaseMesh( AstRegion *this, int *status )
-
-*  Class Membership:
-*     Ellipse 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. Annul the pointer using astAnnul when it
-*     is no longer needed.
-
-*  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: */
-   AstEllipse *this;              /* The Ellipse structure */
-   AstFrame *frm;                 /* Base Frame in encapsulated FrameSet */
-   AstPointSet *result;           /* Returned pointer */
-   AstRegion *reg;                /* Copy of supplied Ellipse */
-   double **ptr;                  /* Pointers to data */
-   double ang;                    /* Position angular of primary axis at "dx" */
-   double angle;                  /* Ellipse parametric angle at point */
-   double delta;                  /* Angular separation of points */
-   double dist;                   /* Offset along an axis */
-   double dx;                     /* Primary axis offset */
-   double dy;                     /* Secondary axis offset */
-   double lbnd[2];                /* Lower bounding box bounds */
-   double lbx;                    /* Lower x bound of mesh bounding box */
-   double lby;                    /* Lower y bound of mesh bounding box */
-   double p2[ 2 ];                /* Position in 2D Frame */
-   double p[ 2 ];                 /* Position in 2D Frame */
-   double ubnd[2];                /* Upper bounding box bounds */
-   double ubx;                    /* Upper x bound of mesh bounding box */
-   double uby;                    /* Upper y bound of mesh bounding box */
-   int i;                         /* Point index */
-   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 {
-
-/* Initialise the bounding box of the mesh points. */
-      lbx = DBL_MAX;
-      ubx = -DBL_MAX;
-      lby = DBL_MAX;
-      uby = -DBL_MAX;
-
-/* Get a pointer to the Ellipse structure. */
-      this = (AstEllipse *) this_region;
-
-/* Ensure cached information is available. */
-      Cache( this, status );
-
-/* Get a pointer to the base Frame in the encapsulated FrameSet. */
-      frm = astGetFrame( this_region->frameset, AST__BASE );
-
-/* Get the requested number of points to put on the mesh. */
-      np = astGetMeshSize( this );
-
-/* 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 ) {
-
-/* Loop round each point. The angle is the parametric angle, phi, where
-   the ellipse is defined by:
-
-   dx = a.cos( phi )
-   dy = a.sin( phi )
-
-   measured from the primary ellipse. Positive in the sense of rotation from
-   axis 2 to axis 1.  */
-         angle = 0.0;
-         for( i = 0; i < np; i++ ) {
-
-/* Find the offsets from the centre. "dx" is geodesic distance along the
-   primary axis, and dy is geodesic distance along the secondary axis. */
-            dx = this->a*cos( angle );
-            dy = this->b*sin( angle );
-
-/* Now find the point which corresponds to this dx and dy, taking account
-   of the potential spherical geometry of hte coordinate system. First
-   move a distance "dx" from the centre along the primary axis. The
-   function value returned is the direction of the geodesic curve at the
-   end point. That is, the angle (in radians) between the positive direction
-   of the second axis and the continuation of the geodesic curve at the
-   requested end point. */
-            ang = astOffset2( frm, this->centre, this->angle, dx, p );
-
-/* Now move a distance "dy" from the point found above at right angles to
-   the primary axis. */
-            astOffset2( frm, p, ang + AST__DPIBY2, dy, p2 );
-
-/* Store the resulting axis values. */
-            ptr[ 0 ][ i ] = p2[ 0 ];
-            ptr[ 1 ][ i ] = p2[ 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( p2[ 0 ] != AST__BAD && p2[ 1 ] != AST__BAD ){
-
-               dist =  astAxDistance( frm, 1, this->centre[ 0 ], p2[ 0 ] );
-               if( dist < lbx ) {
-                  lbx = dist;
-               } else if( dist > ubx ) {
-                  ubx = dist;
-               }
-
-               dist =  astAxDistance( frm, 1, this->centre[ 1 ], p2[ 1 ] );
-               if( dist < lby ) {
-                  lby = dist;
-               } else if( dist > uby ) {
-                  uby = dist;
-               }
-            }
-
-/* Increment the angular position of the next mesh point. */
-            angle += delta;
-         }
-      }
-
-/* Save the returned pointer in the Region structure so that it does not
-   need to be created again next time this function is called. Also cache
-   the bounding box in the Ellipse structure. */
-      if( astOK && result ) {
-         this_region->basemesh = astClone( result );
-
-/* 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. */
-         lbnd[ 0 ] = this->centre[ 0 ] + lbx;
-         lbnd[ 1 ] = this->centre[ 1 ] + lby;
-         ubnd[ 0 ] = this->centre[ 0 ] + ubx;
-         ubnd[ 1 ] = this->centre[ 1 ] + uby;
-         astNormBox( frm, lbnd, ubnd, reg );
-
-/* Save this box */
-         this->lbx = lbnd[ 0 ];
-         this->ubx = ubnd[ 0 ];
-         this->lby = lbnd[ 1 ];
-         this->uby = ubnd[ 1 ];
-
-/* 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 "ellipse.h"
-*     double *RegCentre( AstRegion *this, double *cen, double **ptr,
-*                        int index, int ifrm, int *status )
-
-*  Class Membership:
-*     Ellipse 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 points, 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: */
-   AstEllipse *this;   /* Pointer to Ellipse structure */
-   AstFrame *frm;      /* Base Frame */
-   double **rptr;      /* Data pointers for Region PointSet */
-   double *bc;         /* Base Frame centre position */
-   double *result;     /* Returned pointer */
-   double *tmp;        /* Temporary array pointer */
-   double a[ 2 ];      /* Original position */
-   double angle;       /* Orietentation of offset from old to new centre */
-   double axval;       /* Axis value */
-   double b[ 2 ];      /* New position */
-   double dist;        /* Distance from old to new centre */
-   double newcen[ 2 ]; /* New centre */
-   int ic;             /* Coordinate index */
-   int ip;             /* Position 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 Ellipse structure. */
-   this = (AstEllipse *) this_region;
-
-/* Ensure cached information is available. */
-   Cache( this, status );
-
-/* Get the number of axis values per point in the current Frame. */
-   ncc = astGetNout( this_region->frameset );
-
-/* An ellipse always has 2 base frame axes. */
-   ncb = 2;
-
-/* 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 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 ];
-            }
-
-/* 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 Ellipse structure. */
-         } else {
-            bc = newcen;
-            for( ic = 0; ic < ncb; ic++ ) {
-               axval = cen ? cen[ ic ] : ptr[ ic ][ index ];
-               newcen[ ic ] = ( axval != AST__BAD ) ? axval : this->centre[ ic ];
-            }
-         }
-
-/* Find the direction and length of the offset between the old and new
-   centre. */
-         frm = astGetFrame( this_region->frameset, AST__BASE );
-         angle = astAxAngle( frm, this->centre, bc, 2 );
-         dist = astDistance( frm, this->centre, bc );
-
-/* Shift each point in the parent Region structure by the same length and
-   direction. */
-         for( ip = 0; ip < 3; ip++ ) {
-            a[ 0 ] = rptr[ ip ][ 0 ];
-            a[ 1 ] = rptr[ ip ][ 1 ];
-            astOffset2( frm, a, angle, dist, b );
-            rptr[ ip ][ 0 ] = b[ 0 ];
-            rptr[ ip ][ 1 ] = b[ 1 ];
-         }
-
-/* Indicate that the cache is stale. */
-         astResetCache( this );
-
-/* Free resources */
-         frm = astAnnul( frm );
-         if( bc != newcen ) bc = astFree( bc );
-      }
-   }
-
-/* 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 Ellipse.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     int RegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
-*                  int **mask, int *status )
-
-*  Class Membership:
-*     Ellipse 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 Ellipse.
-*
-*     Some tolerance is allowed, as specified by the uncertainty Region
-*     stored in the supplied Ellipse "this", and the supplied uncertainty
-*     Region "unc" which describes the uncertainty of the supplied points.
-
-*  Parameters:
-*     this
-*        Pointer to the Ellipse.
-*     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: */
-   AstEllipse *large_ellipse;   /* Ellipse slightly larger than "this" */
-   AstEllipse *small_ellipse;   /* Ellipse slightly smaller than "this" */
-   AstEllipse *this;            /* Pointer to the Ellipse structure. */
-   AstFrame *frm;               /* Base Frame in supplied Ellipse */
-   AstPointSet *ps1;            /* Points masked by larger Ellipse */
-   AstPointSet *ps2;            /* Points masked by larger and smaller Ellipsees */
-   AstRegion *tunc;             /* Uncertainity Region from "this" */
-   double **ptr;                /* Pointer to axis values in "ps2" */
-   double *p;                   /* Pointer to next axis value */
-   double *safe;                /* An interior point in "this" */
-   double drad;                 /* Radius increment corresponding to border width */
-   double l1;                   /* Length of bounding box diagonal */
-   double l2;                   /* Length of bounding box diagonal */
-   double lbnd_tunc[2];         /* Lower bounds of "this" uncertainty Region */
-   double lbnd_unc[2];          /* Lower bounds of supplied uncertainty Region */
-   double lim;                  /* Smallest semi-minor/major axis length */
-   double p1[2];                /* New ellipse axis lengths */
-   double ubnd_tunc[2];         /* Upper bounds of "this" uncertainty Region */
-   double ubnd_unc[2];          /* Upper bounds of supplied uncertainty Region */
-   int i;                       /* Axis index */
-   int j;                       /* Point index */
-   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 Ellipse structure. */
-   this = (AstEllipse *) this_region;
-
-/* Check the supplied PointSet has 2 axis values per point. */
-   if( astGetNcoord( pset ) != 2 && astOK ) {
-      astError( AST__INTER, "astRegPins(%s): Illegal number of axis "
-                "values per point (%d) in the supplied PointSet - should be "
-                "2 (internal AST programming error).", status, astGetClass( this ),
-                astGetNcoord( pset ) );
-   }
-
-/* Get the number of axes in the uncertainty Region and check it is also 2. */
-   if( unc && astGetNaxes( unc ) != 2 && astOK ) {
-      astError( AST__INTER, "astRegPins(%s): Illegal number of axes (%d) "
-                "in the supplied uncertainty Region - should be 2 "
-                "(internal AST programming error).", status, astGetClass( this ),
-                astGetNaxes( unc ) );
-   }
-
-/* 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 Ellipse for it still to be considered to be on the boundary.
-   First get the Region which defines the uncertainty within the Ellipse 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 );
-   astGetRegionBounds( tunc, lbnd_tunc, ubnd_tunc );
-
-/* Find the geodesic length within the base Frame of "this" of the diagonal of
-   the bounding box. */
-   frm = astGetFrame( this_region->frameset, AST__BASE );
-   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 );
-      astGetRegionBounds( unc, lbnd_unc, ubnd_unc );
-
-/* Find the geodesic length of the diagonal of this bounding box. */
-      l2 = astDistance( frm, lbnd_unc, ubnd_unc );
-
-/* Assume zero uncertainty if no "unc" Region was supplied. */
-   } else {
-      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 Ellipse, 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. */
-      p1[ 0 ] = this->a + 0.5*drad;
-      p1[ 1 ] = this->b + 0.5*drad;
-      large_ellipse = astEllipse( frm, 1, this->centre, p1, &(this->angle),
-                                  NULL, " ", status );
-
-      p1[ 0 ] = this->a - 0.5*drad;
-      p1[ 1 ] = this->b - 0.5*drad;
-      lim = 1.0E-6*drad;
-      if( p1[ 0 ] < lim ) p1[ 0 ] = lim;
-      if( p1[ 1 ] < lim ) p1[ 1 ] = lim;
-      small_ellipse = astEllipse( frm, 1, this->centre, p1, &(this->angle),
-                                  NULL, " ", status );
-
-/* Negate the smaller region.*/
-      astNegate( small_ellipse );
-
-/* Points are on the boundary of "this" if they are inside both the large
-   Ellipse and the negated small Ellipse. First transform the supplied PointSet
-   using the large Ellipse, then transform them using the negated smaller
-   Ellipse. */
-      ps1 = astTransform( large_ellipse, pset, 1, NULL );
-      ps2 = astTransform( small_ellipse, 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 < 2; 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 < 2 && result; i++ ) {
-            p = ptr[ i ];
-            for( j = 0; j < np; j++ ) {
-               if( *(p++) == AST__BAD ) {
-                  result = 0;
-                  break;
-               }
-            }
-         }
-      }
-
-/* Free resources. */
-      large_ellipse = astAnnul( large_ellipse );
-      small_ellipse = astAnnul( small_ellipse );
-      ps1 = astAnnul( ps1 );
-      ps2 = astAnnul( ps2 );
-   }
-
-   tunc = astAnnul( tunc );
-   frm = astAnnul( frm );
-   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 "ellipse.h"
-*     int astTraceRegion( AstRegion *this, int n, double *dist, double **ptr );
-
-*  Class Membership:
-*     Ellipse 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; */
-   AstEllipse *this;
-   AstFrame *frm;
-   AstMapping *map;
-   AstPointSet *bpset;
-   AstPointSet *cpset;
-   double **bptr;
-   double ang;
-   double angle;
-   double dx;
-   double dy;
-   double p2[ 2 ];
-   double p[ 2 ];
-   int i;
-   int ncur;
-
-/* Check inherited status, and the number of points to return, returning
-   a non-zero value to indicate that this class supports the astRegTrace
-   method. */
-   if( ! astOK || n == 0 ) return 1;
-
-/* Get a pointer to the Ellipse structure. */
-   this = (AstEllipse *) this_region;
-
-/* Ensure cached information is available. */
-   Cache( this, status );
-
-/* Get a pointer to the base Frame in the encapsulated FrameSet. */
-   frm = astGetFrame( this_region->frameset, AST__BASE );
-
-/* 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 (known
-   to be 2D since this is an ellipse). */
-   } 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. */
-      for( i = 0; i < n; i++ ) {
-
-/* The supplied scalar parameter values are the parametric angles, phi,
-   where the ellipse is defined by:
-
-   dx = a.cos( phi )
-   dy = a.sin( phi )
-
-   measured from the primary ellipse. Positive in the sense of rotation from
-   axis 2 to axis 1.  */
-         angle = dist[ i ]*2*AST__DPI;
-
-/* Find the offsets from the centre. "dx" is geodesic distance along the
-   primary axis, and dy is geodesic distance along the secondary axis. */
-         dx = this->a*cos( angle );
-         dy = this->b*sin( angle );
-
-/* Now find the point which corresponds to this dx and dy, taking account
-   of the potential spherical geometry of hte coordinate system. First
-   move a distance "dx" from the centre along the primary axis. The
-   function value returned is the direction of the geodesic curve at the
-   end point. That is, the angle (in radians) between the positive direction
-   of the second axis and the continuation of the geodesic curve at the
-   requested end point. */
-         ang = astOffset2( frm, this->centre, this->angle, dx, p );
-
-/* Now move a distance "dy" from the point found above at right angles to
-   the primary axis. */
-         astOffset2( frm, p, ang + AST__DPIBY2, dy, p2 );
-
-/* Store the resulting axis values. */
-         bptr[ 0 ][ i ] = p2[ 0 ];
-         bptr[ 1 ][ i ] = p2[ 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 a non-zero value to indicate that this class supports the
-   astRegTrace method. */
-   return 1;
-}
-
-static void ResetCache( AstRegion *this, int *status ){
-/*
-*  Name:
-*     ResetCache
-
-*  Purpose:
-*     Clear cached information within the supplied Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ellipse.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 ) {
-      ( (AstEllipse *) 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 "ellipse.h"
-*     void SetRegFS( AstRegion *this_region, AstFrame *frm, int *status )
-
-*  Class Membership:
-*     Ellipse 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 );
-
-/* Indicate that cached information will need to be re-calculated before
-   it is next used. */
-   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 "ellipse.h"
-*     AstMapping *Simplify( AstMapping *this, int *status )
-
-*  Class Membership:
-*     Ellipse 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;          /* Ellipse 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 );
-
-/* We attempt to simplify the Ellipse by re-defining it within its current
-   Frame. Transforming the Ellipse from its base to its current Frame may
-   result in the region no longer being an ellipse. We test this by
-   transforming a set of bounds on the Ellipse boundary. */
-   map = astGetMapping( new->frameset, AST__BASE, AST__CURRENT );
-
-/* Get a mesh of points covering the Ellipse in its current Frame. */
-   mesh = astRegMesh( new );
-
-/* Get the Region describing the positional uncertainty within the Ellipse in
-   its current Frame. */
-   unc = astGetUncFrm( new, AST__CURRENT );
-
-/* Transform the PointSet holding the ellipse 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 Region. */
-         (void) astAnnul( new );
-         new = astClone( newreg );
-         simpler =1;
-
-/* 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 Region. */
-            (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 Ellipse to transform a set of points.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-*                             int forward, AstPointSet *out, int *status )
-
-*  Class Membership:
-*     Ellipse member function (over-rides the astTransform protected
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function takes a Ellipse 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 Ellipse.
-*     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 Ellipse.
-*     -  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: */
-   AstEllipse *this;             /* Pointer to Ellipse */
-   AstFrame *frm;                /* Pointer to base Frame in FrameSet */
-   AstPointSet *pset_res;        /* Pointer to PointSet holding resolved components */
-   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_res;             /* Pointer to resolved components coordinate data */
-   double *px;                   /* Pointer to array of primary axis components */
-   double *py;                   /* Pointer to array of secondary axis components */
-   double c1;                    /* Constant */
-   double c2;                    /* Constant */
-   double d;                     /* Elliptical distance to current 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 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 Ellipse structure. */
-   this = (AstEllipse *) 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 );
-
-/* Ensure cached information is available. */
-   Cache( this, 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 );
-
-/* Resolve all the base Frame positions into components parallel to and
-   perpendicular to the primary axis, relative to the ellipse centre. The
-   components are returned in a new PointSet. */
-   pset_res = astResolvePoints( frm, this->centre, this->point1, pset_tmp, NULL );
-
-/* Determine the numbers of points from the component PointSet and obtain
-   pointers for accessing the component and output coordinate values. */
-   npoint = astGetNpoint( pset_res );
-   ptr_res = astGetPoints( pset_res );
-   ncoord_out = astGetNcoord( result );
-   ptr_out = astGetPoints( result );
-
-/* See if the boundary is part of the Region. */
-   closed = astGetClosed( this );
-
-/* See if the Region has been negated. */
-   neg = astGetNegated( this );
-
-/* Form some frequently needed constants. */
-   c1 = 1.0/(this->a*this->a);
-   c2 = 1.0/(this->b*this->b);
-
-/* Perform coordinate arithmetic. */
-/* ------------------------------ */
-   if ( astOK ) {
-      px = ptr_res[ 0 ];
-      py = ptr_res[ 1 ];
-
-/* Loop round each point */
-      for ( point = 0; point < npoint; point++, px++, py++ ) {
-
-/* Bad input points result in bad output points */
-         if( *px == AST__BAD || *py == AST__BAD ) {
-            inside = 0;
-
-/* If the input points are good... */
-         } else {
-
-/* Find the elliptical distance from the centre to the supplied point (the
-   ellipse circumference has an "elliptical distance" of 1.0 at all points).*/
-            d = c1*(*px)*(*px) + c2*(*py)*(*py);
-
-/* Now consider whether this radius value puts the point in or out of the
-   Ellipse. */
-            if( d != AST__BAD ){
-               if( neg ) {
-                  if( closed ) {
-                     inside = ( d >= 1.0 );
-                  } else {
-                     inside = ( d > 1.0 );
-                  }
-               } else {
-                  if( closed ) {
-                     inside = ( d <= 1.0 );
-                  } else {
-                     inside = ( d < 1.0 );
-                  }
-               }
-            } 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 */
-   pset_tmp = astAnnul( pset_tmp );
-   pset_res = astAnnul( pset_res );
-   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 Ellipse objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Copy( const AstObject *objin, AstObject *objout, int *status )
-
-*  Description:
-*     This function implements the copy constructor for Ellipse 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: */
-   AstEllipse *in;             /* Pointer to input Ellipse */
-   AstEllipse *out;            /* Pointer to output Ellipse */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain pointers to the input and output Ellipses. */
-   in = (AstEllipse *) objin;
-   out = (AstEllipse *) objout;
-
-/* For safety, first clear any references to the input memory from
-   the output Ellipse. */
-   out->centre = NULL;
-   out->point1 = NULL;
-
-/* Copy dynamic memory contents */
-   out->centre = astStore( NULL, in->centre, sizeof( double )*2 );
-   out->point1 = astStore( NULL, in->point1, sizeof( double )*2 );
-}
-
-
-/* Destructor. */
-/* ----------- */
-static void Delete( AstObject *obj, int *status ) {
-/*
-*  Name:
-*     Delete
-
-*  Purpose:
-*     Destructor for Ellipse objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Delete( AstObject *obj, int *status )
-
-*  Description:
-*     This function implements the destructor for Ellipse 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: */
-   AstEllipse *this;                 /* Pointer to Ellipse */
-
-/* Obtain a pointer to the Ellipse structure. */
-   this = (AstEllipse *) obj;
-
-/* Annul all resources. */
-   this->centre = astFree( this->centre );
-   this->point1 = astFree( this->point1 );
-}
-
-/* Dump function. */
-/* -------------- */
-static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
-/*
-*  Name:
-*     Dump
-
-*  Purpose:
-*     Dump function for Ellipse 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 Ellipse class to an output Channel.
-
-*  Parameters:
-*     this
-*        Pointer to the Ellipse 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: */
-   AstEllipse *this;                 /* Pointer to the Ellipse structure */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the Ellipse structure. */
-   this = (AstEllipse *) this_object;
-
-/* Write out values representing the instance variables for the
-   Ellipse 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 astIsAEllipse and astCheckEllipse functions using the macros
-   defined for this purpose in the "object.h" header file. */
-astMAKE_ISA(Ellipse,Region)
-astMAKE_CHECK(Ellipse)
-
-AstEllipse *astEllipse_( void *frame_void, int form, const double centre[2],
-                         const double point1[2], const double point2[2],
-                         AstRegion *unc, const char *options, int *status, ...) {
-/*
-*++
-*  Name:
-c     astEllipse
-f     AST_ELLIPSE
-
-*  Purpose:
-*     Create a Ellipse.
-
-*  Type:
-*     Public function.
-
-*  Synopsis:
-c     #include "ellipse.h"
-c     AstEllipse *astEllipse( AstFrame *frame, int form, const double centre[2],
-c                             const double point1[2], const double point2[2],
-c                             AstRegion *unc, const char *options, ... )
-f     RESULT = AST_ELLIPSE( FRAME, FORM, CENTRE, POINT1, POINT2, UNC, OPTIONS,
-f                           STATUS )
-
-*  Class Membership:
-*     Ellipse constructor.
-
-*  Description:
-*     This function creates a new Ellipse and optionally initialises its
-*     attributes.
-*
-*     A Ellipse is a Region which represents a elliptical area within the
-*     supplied 2-dimensional Frame.
-
-*  Parameters:
-c     frame
-f     FRAME = INTEGER (Given)
-*        A pointer to the Frame in which the region is defined. It must
-*        have exactly 2 axes. 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 ellipse is described by the remaining parameters.
-*        A value of zero indicates that the ellipse is specified by a
-*        centre position and two positions on the circumference. A value of
-*        one indicates that the ellipse is specified by its centre position,
-*        the half-lengths of its two axes, and the orientation of its first
-*        axis.
-c     centre
-f     CENTRE( 2 ) = DOUBLE PRECISION (Given)
-c        An array of 2 doubles,
-f        An array
-*        containing the coordinates at the centre of
-*        the ellipse.
-c     point1
-f     POINT1( 2 ) = DOUBLE PRECISION (Given)
-c        An array of 2 doubles. If "form"
-f        If FORM
-*        is zero, this array should contain the coordinates of one of the four
-*        points where an axis of the ellipse crosses the circumference of the
-*        ellipse.
-c        If "form"
-f        If FORM
-*        is one, it should contain the lengths of semi-major and
-*        semi-minor axes of the ellipse, given as geodesic distances
-*        within the Frame.
-c     point2
-f     POINT2( 2 ) = DOUBLE PRECISION (Given)
-c        An array of 2 doubles. If "form"
-f        If FORM
-*        is zero, this array should containing the coordinates at some other
-*        point on the circumference of the ellipse, distinct from
-c        "point1". If "form"
-f        POINT1. If FORM
-*        is one, the first element of this array should hold the angle
-*        between the second axis of the Frame and the first ellipse axis
-*        (i.e. the ellipse axis which is specified first in the
-c        "point1"
-f        POINT1
-*        array), and the second element will be ignored. The angle should be
-*        given in radians, measured positive in the same sense as rotation
-*        from the positive direction of the second Frame axis to the positive
-*        direction of the first Frame axis.
-c     unc
-f     UNC = INTEGER (Given)
-*        An optional pointer to an existing Region which specifies the
-*        uncertainties associated with the boundary of the Ellipse being created.
-*        The uncertainty in any point on the boundary of the Ellipse 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 Ellipse. 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 Ellipse 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 Ellipse. 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 Ellipse. 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     astEllipse()
-f     AST_ELLIPSE = INTEGER
-*        A pointer to the new Ellipse.
-
-*  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 */
-   AstEllipse *new;              /* Pointer to new Ellipse */
-   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 Ellipse, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitEllipse( NULL, sizeof( AstEllipse ), !class_init, &class_vtab,
-                         "Ellipse", frame, form, centre, point1, point2, 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 Ellipse'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 Ellipse. */
-   return new;
-}
-
-AstEllipse *astEllipseId_( void *frame_void, int form, const double centre[2],
-                         const double point1[2], const double point2[2],
-                         void *unc_void, const char *options, ... ) {
-/*
-*  Name:
-*     astEllipseId_
-
-*  Purpose:
-*     Create a Ellipse.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     AstEllipse *astEllipseId( void *frame_void, int form, const double centre[2],
-*                         const double point1[2], const double point2[2],
-*                         void *unc_void, const char *options, ..., int *status )
-
-*  Class Membership:
-*     Ellipse constructor.
-
-*  Description:
-*     This function implements the external (public) interface to the
-*     astEllipse constructor function. It returns an ID value (instead
-*     of a true C pointer) to external users, and must be provided
-*     because astEllipse_ 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 astEllipse_ 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 astEllipse_.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     The ID value associated with the new Ellipse.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstFrame *frame;              /* Pointer to Frame structure */
-   AstEllipse *new;              /* Pointer to new Ellipse */
-   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 Ellipse, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitEllipse( NULL, sizeof( AstEllipse ), !class_init, &class_vtab,
-                        "Ellipse", frame, form, centre, point1, point2, 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 Ellipse'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 Ellipse. */
-   return astMakeId( new );
-}
-
-AstEllipse *astInitEllipse_( void *mem, size_t size, int init, AstEllipseVtab *vtab,
-                             const char *name, AstFrame *frame, int form,
-                             const double centre[2], const double point1[2],
-                             const double point2[2], AstRegion *unc, int *status ){
-/*
-*+
-*  Name:
-*     astInitEllipse
-
-*  Purpose:
-*     Initialise a Ellipse.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     AstEllipse *astInitEllipse( void *mem, size_t size, int init,
-*                                 AstEllipseVtab *vtab, const char *name,
-*                                 AstFrame *frame, const double centre[2],
-*                                 const double point1[2], const double point2[2],
-*                                 AstRegion *unc )
-
-*  Class Membership:
-*     Ellipse initialiser.
-
-*  Description:
-*     This function is provided for use by class implementations to initialise
-*     a new Ellipse object. It allocates memory (if necessary) to accommodate
-*     the Ellipse plus any additional data associated with the derived class.
-*     It then initialises a Ellipse 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 Ellipse at the start of the memory passed via the
-*     "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory in which the Ellipse is to be initialised.
-*        This must be of sufficient size to accommodate the Ellipse data
-*        (sizeof(Ellipse)) 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 Ellipse (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 Ellipse
-*        structure, so a valid value must be supplied even if not required for
-*        allocating memory.
-*     init
-*        A logical flag indicating if the Ellipse'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 Ellipse.
-*     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 ellipse centre.
-*     point1
-*        An array of double, with one element for each Frame axis (Naxes
-*        attribute). If "form" is zero, it should contain the coordinates at
-*        the end of one of the axes of the ellipse. If "form" is one, it
-*        should contain the semi-major and semi-minor axes of the ellipse.
-*     point2
-*        An array of double, with one element for each Frame axis (Naxes
-*        attribute). If "form" is zero, it should contain the coordinates at
-*        some other point on the circumference of the ellipse. If "form" is
-*        one, element [1] is ignored and element [0] should contain the
-*        angle from the second frame axis to the first ellipse axis, given in
-*        radians, measured positive in the same sense as rotation from the
-*        positive direction of the second Frame axis to the positive
-*        direction of the first Frame axis. The "first" ellipse axis is
-*        whichever of the semi-major or semi-minor axis is specified first in
-*        the "point1" array.
-*     unc
-*        A pointer to a Region which specifies the uncertainty in the
-*        supplied positions (all points on the boundary of the new Ellipse
-*        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 Ellipse'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 Ellipse.
-
-*  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: */
-   AstEllipse *new;          /* Pointer to new Ellipse */
-   AstPointSet *pset;        /* PointSet to pass to Region initialiser */
-   double **ptr;             /* Pointer to coords data in pset */
-   const double *p1;         /* Pointer to circumference point 1 */
-   const double *p2;         /* Pointer to circumference point 2 */
-   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 ) astInitEllipseVtab( vtab, name );
-
-/* Initialise. */
-   new = NULL;
-
-/* Check the supplied value for "form" is legal. */
-   if( form != 0 && form != 1 && astOK ) {
-      astError( AST__BADIN, "astInitEllipse(%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 );
-
-/* Report an error if the Frame is not 2-dimensional. */
-   if( nc != 2 ) {
-      astError( AST__BADIN, "astInitEllipse(%s): The supplied %s has %d "
-                "axes - ellipses must have exactly 2 axes.", status, name,
-                astGetClass( frame ), nc );
-   }
-
-/* If the ellipse is specified by axis lengths and orientation, find two
-   points on the circumference (ends of the two ellipse axes). */
-   if( form == 1 ) {
-      p1 = astMalloc( sizeof( double )*2 );
-      p2 = astMalloc( sizeof( double )*2 );
-      if( astOK ) {
-         astOffset2( frame, centre, *point2, point1[ 0 ], (double *) p1 );
-         astOffset2( frame, centre, *point2 + AST__DPIBY2, point1[ 1 ],
-                     (double *) p2 );
-      }
-
-/* If the ellipse is specified by two points on the circumference, use
-   them. */
-   } else {
-      p1 = point1;
-      p2 = point2;
-   }
-
-/* Create a PointSet to hold the supplied values, and get points to the
-   data arrays. */
-   pset = astPointSet( 3, nc, " ", status );
-   ptr = astGetPoints( pset );
-
-/* Copy the supplied 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, "astInitEllipse(%s): The value of axis %d is "
-                   "undefined at the ellipse centre.", status, name, i + 1 );
-      }
-      if( astOK && p1[ i ] == AST__BAD ) {
-         astError( AST__BADIN, "astInitEllipse(%s): The value of axis %d is "
-                   "undefined at point 1 on the circumference of "
-                   "the ellipse.", status, name, i + 1 );
-      }
-      if( astOK && p2[ i ] == AST__BAD ) {
-         astError( AST__BADIN, "astInitEllipse(%s): The value of axis %d is "
-                   "undefined at point 2 on the circumference of "
-                   "the ellipse.", status, name, i + 1 );
-      }
-      ptr[ i ][ 0 ] = centre[ i ];
-      ptr[ i ][ 1 ] = p1[ i ];
-      ptr[ i ][ 2 ] = p2[ i ];
-   }
-
-/* Check pointers can be used safely. */
-   if( astOK ) {
-
-/* Initialise a Region structure (the parent class) as the first component
-   within the Ellipse structure, allocating memory if necessary. */
-      new = (AstEllipse *) astInitRegion( mem, size, 0, (AstRegionVtab *) vtab,
-                                         name, frame, pset, unc );
-
-      if ( astOK ) {
-
-/* Initialise the Ellipse data. */
-/* ------------------------ */
-         new->stale = 1;
-
-/* If an error occurred, clean up by deleting the new Ellipse. */
-         if ( !astOK ) new = astDelete( new );
-      }
-   }
-
-/* Free resources. */
-   pset = astAnnul( pset );
-   if( form == 1 ) {
-      p1 = astFree( (void *) p1 );
-      p2 = astFree( (void *) p2 );
-   }
-
-/* Return a pointer to the new Ellipse. */
-   return new;
-}
-
-AstEllipse *astLoadEllipse_( void *mem, size_t size, AstEllipseVtab *vtab,
-                           const char *name, AstChannel *channel, int *status ) {
-/*
-*+
-*  Name:
-*     astLoadEllipse
-
-*  Purpose:
-*     Load a Ellipse.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ellipse.h"
-*     AstEllipse *astLoadEllipse( void *mem, size_t size, AstEllipseVtab *vtab,
-*                               const char *name, AstChannel *channel )
-
-*  Class Membership:
-*     Ellipse loader.
-
-*  Description:
-*     This function is provided to load a new Ellipse 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
-*     Ellipse 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 Ellipse at the start of the memory
-*     passed via the "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory into which the Ellipse is to be
-*        loaded.  This must be of sufficient size to accommodate the
-*        Ellipse data (sizeof(Ellipse)) 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 Ellipse (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 Ellipse 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(AstEllipse) is used instead.
-*     vtab
-*        Pointer to the start of the virtual function table to be
-*        associated with the new Ellipse. If this is NULL, a pointer
-*        to the (static) virtual function table for the Ellipse 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 "Ellipse" is used instead.
-
-*  Returned Value:
-*     A pointer to the new Ellipse.
-
-*  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 */
-   AstEllipse *new;              /* Pointer to the new Ellipse */
-
-/* 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 Ellipse. In this case the
-   Ellipse belongs to this class, so supply appropriate values to be
-   passed to the parent class loader (and its parent, etc.). */
-   if ( !vtab ) {
-      size = sizeof( AstEllipse );
-      vtab = &class_vtab;
-      name = "Ellipse";
-
-/* If required, initialise the virtual function table for this class. */
-      if ( !class_init ) {
-         astInitEllipseVtab( 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 Ellipse. */
-   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, "Ellipse" );
-
-/* 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. */
-/* ---------------------------- */
-
-/* Indicate that no cache intermediate results are yet available in the
-   Ellipse structure */
-      new->stale = 1;
-
-/* If an error occurred, clean up by deleting the new Ellipse. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return the new Ellipse 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 astEllipsePars_( AstEllipse *this, double centre[2], double *a,
-                      double *b, double *angle, double p1[2], double p2[2],
-                      int *status ){
-   if ( !astOK ) return;
-   (**astMEMBER(this,Ellipse,EllipsePars))( this, centre, a, b,
-                                            angle, p1, p2, status );
-}
-
-
-
-
-
-