upgrade ast 8.7.1

1 files changed, 3055 insertions, 0 deletions

diff --git a/ast/ellipse.c b/ast/ellipse.c
new file mode 100644
index 0000000..5efa2a7
--- /dev/null
+++ b/ast/ellipse.c
@@ -0,0 +1,3055 @@
+/*
+*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 = astFree( *mask );
+   }
+
+/* Return the result. */
+   return result;
+}
+
+static int RegTrace( AstRegion *this_region, int n, double *dist, double **ptr,
+                     int *status ){
+/*
+*+
+*  Name:
+*     RegTrace
+
+*  Purpose:
+*     Return requested positions on the boundary of a 2D Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "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 ? astVerifyRegion( 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 );
+}
+
+
+
+
+
+