upgrade ast 8.7.1

1 files changed, 7086 insertions, 0 deletions

diff --git a/ast/polygon.c b/ast/polygon.c
new file mode 100644
index 0000000..80b42ff
--- /dev/null
+++ b/ast/polygon.c
@@ -0,0 +1,7086 @@
+/*
+*class++
+*  Name:
+*     Polygon
+
+*  Purpose:
+*     A polygonal region within a 2-dimensional Frame.
+
+*  Constructor Function:
+c     astPolygon
+f     AST_POLYGON
+
+*  Description:
+*     The Polygon class implements a polygonal area, defined by a
+*     collection of vertices, within a 2-dimensional Frame. The vertices
+*     are connected together by geodesic curves within the encapsulated Frame.
+*     For instance, if the encapsulated Frame is a simple Frame then the
+*     geodesics will be straight lines, but if the Frame is a SkyFrame then
+*     the geodesics will be great circles. Note, the vertices must be
+*     supplied in an order such that the inside of the polygon is to the
+*     left of the boundary as the vertices are traversed. Supplying them
+*     in the reverse order will effectively negate the polygon.
+*
+*     Within a SkyFrame, neighbouring vertices are always joined using the
+*     shortest path. Thus if an edge of 180 degrees or more in length is
+*     required, it should be split into section each of which is less
+*     than 180 degrees. The closed path joining all the vertices in order
+*     will divide the celestial sphere into two disjoint regions. The
+*     inside of the polygon is the region which is circled in an
+*     anti-clockwise manner (when viewed from the inside of the celestial
+*     sphere) when moving through the list of vertices in the order in
+*     which they were supplied when the Polygon was created (i.e. the
+*     inside is to the left of the boundary when moving through the
+*     vertices in the order supplied).
+
+*  Inheritance:
+*     The Polygon class inherits from the Region class.
+
+*  Attributes:
+*     In addition to those attributes common to all Regions, every
+*     Polygon also has the following attributes:
+*     - SimpVertices: Simplify by transforming the vertices?
+
+*  Functions:
+c     In addition to those functions applicable to all Regions, the
+c     following functions may also be applied to all Polygons:
+f     In addition to those routines applicable to all Regions, the
+f     following routines may also be applied to all Polygons:
+*
+c     - astDownsize: Reduce the number of vertices in a Polygon.
+f     - AST_DOWNSIZE: Reduce the number of vertices in a Polygon.
+c     - astConvex<X>: Create a Polygon giving the convex hull of a pixel array
+f     - AST_CONVEX<X>: Create a Polygon giving the convex hull of a pixel array
+c     - astOutline<X>: Create a Polygon outlining values in a pixel array
+f     - AST_OUTLINE<X>: Create a Polygon outlining values in a pixel array
+
+*  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:
+*     26-OCT-2004 (DSB):
+*        Original version.
+*     28-MAY-2009 (DSB):
+*        Added astDownsize.
+*     29-MAY-2009 (DSB):
+*        Added astOutline<X>.
+*     30-JUN-2009 (DSB):
+*        Override astGetBounded.
+*     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-DEC-2013 (DSB):
+*        Reverse the order of the vertices when the Polygon is created,
+*        if necessary, to ensure that the unnegated Polygon is bounded.
+*        The parent Region class assumes that unnegated regions are
+*        bounded.
+*     6-JAN-2014 (DSB):
+*        Free edges when clearing the cache, not when establishing a new
+*        cache, as the number of edges may have changed.
+*     10-JAN-2014 (DSB):
+*        - Remove unused parameter description in prologue of for astOutline<X>
+*     24-FEB-2014 (DSB):
+*        Added astConvex<X>.
+*     25-FEB-2014 (DSB):
+*        Added attribute SimpVertices.
+*     7-SEP-2015 (DSB):
+*        Shrink outline polygons by a small fraction of a pixel, in order
+*        to avoid placing vertices exactly on pixel edges. This is because
+*        rounding errors in subsequent code may push the vertices into
+*        neighbouring pixels, which may have bad WCS coords (e.g.
+*        vertices on the boundary of a polar cusp in an HPX map).
+*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 Polygon
+
+/* Define a macro for testing if a pixel value <V> satisfies the requirements
+   specified by <Oper> and <Value>. Compiler optimisation should remove
+   all the "if" testing from this expression. */
+#define ISVALID(V,OperI,Value) ( \
+   ( OperI == AST__LT ) ? ( (V) < Value ) : ( \
+      ( OperI == AST__LE ) ? ( (V) <= Value ) : ( \
+         ( OperI == AST__EQ ) ? ( (V) == Value ) : ( \
+            ( OperI == AST__GE ) ? ( (V) >= Value ) : ( \
+               ( OperI == AST__NE ) ? ( (V) != Value ) : ( \
+                  (V) > Value \
+               ) \
+            ) \
+         ) \
+      ) \
+   ) \
+)
+
+/* Macros specifying whether a point is inside, outside or on the
+   boundary of the polygon. */
+#define UNKNOWN 0
+#define IN      1
+#define OUT     2
+#define ON      3
+
+/* Size of pertubation (in pixels) used to avoid placing vertices exactly
+   on a pixel edge. */
+#define DELTA 0.01
+
+/* 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 "polygon.h"             /* Interface definition for this class */
+#include "mapping.h"             /* Position mappings */
+#include "unitmap.h"             /* Unit Mapping */
+#include "pal.h"                 /* SLALIB library interface */
+#include "frame.h"               /* Coordinate system description */
+
+/* Error code definitions. */
+/* ----------------------- */
+#include "ast_err.h"             /* AST error codes */
+
+/* C header files. */
+/* --------------- */
+#include <float.h>
+#include <math.h>
+#include <stdarg.h>
+#include <stdlib.h>
+#include <stddef.h>
+#include <stdio.h>
+#include <string.h>
+#include <limits.h>
+
+/* Type definitions. */
+/* ================= */
+
+/* A structure that holds information about an edge of the new Polygon
+   being created by astDownsize. The edge is a line betweeen two of the
+   vertices of the original Polygon. */
+typedef struct Segment {
+   int i1;        /* Index of starting vertex within old Polygon */
+   int i2;        /* Index of ending vertex within old Polygon */
+   double error;  /* Max geodesic distance from any old vertex to the line */
+   int imax;      /* Index of the old vertex at which max error is reached */
+   struct Segment *next;/* Pointer to next Segment in a double link list */
+   struct Segment *prev;/* Pointer to previous Segment in a double link list */
+} Segment;
+
+
+/* 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 * );
+static const char *(* parent_getattrib)( AstObject *, const char *, int * );
+static int (* parent_testattrib)( AstObject *, const char *, int * );
+static void (* parent_clearattrib)( AstObject *, const char *, int * );
+static void (* parent_setattrib)( AstObject *, const char *, int * );
+
+
+#ifdef THREAD_SAFE
+/* Define how to initialise thread-specific globals. */
+#define GLOBAL_inits \
+   globals->Class_Init = 0; \
+   globals->GetAttrib_Buff[ 0 ] = 0;
+
+/* Create the function that initialises global data for this module. */
+astMAKE_INITGLOBALS(Polygon)
+
+/* Define macros for accessing each item of thread specific global data. */
+#define class_init astGLOBAL(Polygon,Class_Init)
+#define class_vtab astGLOBAL(Polygon,Class_Vtab)
+#define getattrib_buff astGLOBAL(Polygon,GetAttrib_Buff)
+
+
+#include <pthread.h>
+
+
+#else
+
+static char getattrib_buff[ 51 ];
+
+/* Define the class virtual function table and its initialisation flag
+   as static variables. */
+static AstPolygonVtab 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. */
+AstPolygon *astPolygonId_( void *, int, int, const double *, void *, const char *, ... );
+
+/* Prototypes for Private Member Functions. */
+/* ======================================== */
+
+/* Define a macro that expands to a single prototype for function
+   FindInsidePoint for a given data type and operation. */
+#define FINDINSIDEPOINT_PROTO0(X,Xtype,Oper) \
+static void FindInsidePoint##Oper##X( Xtype, const Xtype *, const int[2], const int[2], int *, int *, int *, int * );
+
+/* Define a macro that expands to a set of prototypes for all operations
+   for function FindInsidePoint for a given data type. */
+#define FINDINSIDEPOINT_PROTO(X,Xtype) \
+FINDINSIDEPOINT_PROTO0(X,Xtype,LT) \
+FINDINSIDEPOINT_PROTO0(X,Xtype,LE) \
+FINDINSIDEPOINT_PROTO0(X,Xtype,EQ) \
+FINDINSIDEPOINT_PROTO0(X,Xtype,GE) \
+FINDINSIDEPOINT_PROTO0(X,Xtype,GT) \
+FINDINSIDEPOINT_PROTO0(X,Xtype,NE)
+
+/* Use the above macros to define all FindInsidePoint prototypes for all
+   data types and operations. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+FINDINSIDEPOINT_PROTO(LD,long double)
+#endif
+FINDINSIDEPOINT_PROTO(D,double)
+FINDINSIDEPOINT_PROTO(L,long int)
+FINDINSIDEPOINT_PROTO(UL,unsigned long int)
+FINDINSIDEPOINT_PROTO(I,int)
+FINDINSIDEPOINT_PROTO(UI,unsigned int)
+FINDINSIDEPOINT_PROTO(S,short int)
+FINDINSIDEPOINT_PROTO(US,unsigned short int)
+FINDINSIDEPOINT_PROTO(B,signed char)
+FINDINSIDEPOINT_PROTO(UB,unsigned char)
+FINDINSIDEPOINT_PROTO(F,float)
+
+/* Define a macro that expands to a single prototype for function
+   TraceEdge for a given data type and operation. */
+#define TRACEEDGE_PROTO0(X,Xtype,Oper) \
+static AstPointSet *TraceEdge##Oper##X( Xtype, const Xtype *, const int[2], const int[2], int, int, int, int, int, int * );
+
+/* Define a macro that expands to a set of prototypes for all operations
+   for function TraceEdge for a given data type. */
+#define TRACEEDGE_PROTO(X,Xtype) \
+TRACEEDGE_PROTO0(X,Xtype,LT) \
+TRACEEDGE_PROTO0(X,Xtype,LE) \
+TRACEEDGE_PROTO0(X,Xtype,EQ) \
+TRACEEDGE_PROTO0(X,Xtype,GE) \
+TRACEEDGE_PROTO0(X,Xtype,GT) \
+TRACEEDGE_PROTO0(X,Xtype,NE)
+
+/* Use the above macros to define all TraceEdge prototypes for all
+   data types and operations. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+TRACEEDGE_PROTO(LD,long double)
+#endif
+TRACEEDGE_PROTO(D,double)
+TRACEEDGE_PROTO(L,long int)
+TRACEEDGE_PROTO(UL,unsigned long int)
+TRACEEDGE_PROTO(I,int)
+TRACEEDGE_PROTO(UI,unsigned int)
+TRACEEDGE_PROTO(S,short int)
+TRACEEDGE_PROTO(US,unsigned short int)
+TRACEEDGE_PROTO(B,signed char)
+TRACEEDGE_PROTO(UB,unsigned char)
+TRACEEDGE_PROTO(F,float)
+
+/* Define a macro that expands to a single prototype for function
+   PartHull for a given data type and operation. */
+#define PARTHULL_PROTO0(X,Xtype,Oper) \
+static void PartHull##Oper##X( Xtype, const Xtype[], int, int, int, int, int, int, int, const int[2], double **, double **, int *, int * );
+
+/* Define a macro that expands to a set of prototypes for all operations
+   for function PartHull for a given data type. */
+#define PARTHULL_PROTO(X,Xtype) \
+PARTHULL_PROTO0(X,Xtype,LT) \
+PARTHULL_PROTO0(X,Xtype,LE) \
+PARTHULL_PROTO0(X,Xtype,EQ) \
+PARTHULL_PROTO0(X,Xtype,GE) \
+PARTHULL_PROTO0(X,Xtype,GT) \
+PARTHULL_PROTO0(X,Xtype,NE)
+
+/* Use the above macros to define all PartHull prototypes for all
+   data types and operations. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+PARTHULL_PROTO(LD,long double)
+#endif
+PARTHULL_PROTO(D,double)
+PARTHULL_PROTO(L,long int)
+PARTHULL_PROTO(UL,unsigned long int)
+PARTHULL_PROTO(I,int)
+PARTHULL_PROTO(UI,unsigned int)
+PARTHULL_PROTO(S,short int)
+PARTHULL_PROTO(US,unsigned short int)
+PARTHULL_PROTO(B,signed char)
+PARTHULL_PROTO(UB,unsigned char)
+PARTHULL_PROTO(F,float)
+
+/* Define a macro that expands to a single prototype for function
+   ConvexHull for a given data type and operation. */
+#define CONVEXHULL_PROTO0(X,Xtype,Oper) \
+static AstPointSet *ConvexHull##Oper##X( Xtype, const Xtype[], const int[2], int, int, int, int * );
+
+/* Define a macro that expands to a set of prototypes for all operations
+   for function ConvexHull for a given data type. */
+#define CONVEXHULL_PROTO(X,Xtype) \
+CONVEXHULL_PROTO0(X,Xtype,LT) \
+CONVEXHULL_PROTO0(X,Xtype,LE) \
+CONVEXHULL_PROTO0(X,Xtype,EQ) \
+CONVEXHULL_PROTO0(X,Xtype,GE) \
+CONVEXHULL_PROTO0(X,Xtype,GT) \
+CONVEXHULL_PROTO0(X,Xtype,NE)
+
+/* Use the above macros to define all ConvexHull prototypes for all
+   data types and operations. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+CONVEXHULL_PROTO(LD,long double)
+#endif
+CONVEXHULL_PROTO(D,double)
+CONVEXHULL_PROTO(L,long int)
+CONVEXHULL_PROTO(UL,unsigned long int)
+CONVEXHULL_PROTO(I,int)
+CONVEXHULL_PROTO(UI,unsigned int)
+CONVEXHULL_PROTO(S,short int)
+CONVEXHULL_PROTO(US,unsigned short int)
+CONVEXHULL_PROTO(B,signed char)
+CONVEXHULL_PROTO(UB,unsigned char)
+CONVEXHULL_PROTO(F,float)
+
+/* Define a macro that expands to a single prototype for function
+   FindBoxEdge for a given data type and operation. */
+#define FINDBOXEDGE_PROTO0(X,Xtype,Oper) \
+static void FindBoxEdge##Oper##X( Xtype, const Xtype[], int, int, int, int, int *, int *, int *, int * );
+
+/* Define a macro that expands to a set of prototypes for all operations
+   for function FindBoxEdge for a given data type. */
+#define FINDBOXEDGE_PROTO(X,Xtype) \
+FINDBOXEDGE_PROTO0(X,Xtype,LT) \
+FINDBOXEDGE_PROTO0(X,Xtype,LE) \
+FINDBOXEDGE_PROTO0(X,Xtype,EQ) \
+FINDBOXEDGE_PROTO0(X,Xtype,GE) \
+FINDBOXEDGE_PROTO0(X,Xtype,GT) \
+FINDBOXEDGE_PROTO0(X,Xtype,NE)
+
+/* Use the above macros to define all FindBoxEdge prototypes for all
+   data types and operations. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+FINDBOXEDGE_PROTO(LD,long double)
+#endif
+FINDBOXEDGE_PROTO(D,double)
+FINDBOXEDGE_PROTO(L,long int)
+FINDBOXEDGE_PROTO(UL,unsigned long int)
+FINDBOXEDGE_PROTO(I,int)
+FINDBOXEDGE_PROTO(UI,unsigned int)
+FINDBOXEDGE_PROTO(S,short int)
+FINDBOXEDGE_PROTO(US,unsigned short int)
+FINDBOXEDGE_PROTO(B,signed char)
+FINDBOXEDGE_PROTO(UB,unsigned char)
+FINDBOXEDGE_PROTO(F,float)
+
+
+
+
+
+
+
+
+
+/* Non-generic function prototypes. */
+static AstMapping *Simplify( AstMapping *, int * );
+static AstPointSet *DownsizePoly( AstPointSet *, double, int, AstFrame *, int * );
+static AstPointSet *RegBaseMesh( AstRegion *, int * );
+static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static AstPolygon *Downsize( AstPolygon *, double, int, int * );
+static Segment *AddToChain( Segment *, Segment *, int * );
+static Segment *NewSegment( Segment *, int, int, int, int * );
+static Segment *RemoveFromChain( Segment *, Segment *, int * );
+static double Polywidth( AstFrame *, AstLineDef **, int, int, double[ 2 ], int * );
+static int GetBounded( AstRegion *, int * );
+static int IntCmp( const void *, const void * );
+static int RegPins( AstRegion *, AstPointSet *, AstRegion *, int **, int * );
+static int RegTrace( AstRegion *, int, double *, double **, int * );
+static void Cache( AstPolygon *, int * );
+static void Copy( const AstObject *, AstObject *, int * );
+static void Delete( AstObject *, int * );
+static void Dump( AstObject *, AstChannel *, int * );
+static void EnsureInside( AstPolygon *, int * );
+static void FindMax( Segment *, AstFrame *, double *, double *, int, int, int * );
+static void RegBaseBox( AstRegion *this, double *, double *, int * );
+static void ResetCache( AstRegion *this, int * );
+static void SetPointSet( AstPolygon *, AstPointSet *, int * );
+static void SetRegFS( AstRegion *, AstFrame *, int * );
+static void SmoothPoly( AstPointSet *, int, double, int * );
+
+static const char *GetAttrib( AstObject *, const char *, int * );
+static void ClearAttrib( AstObject *, const char *, int * );
+static void SetAttrib( AstObject *, const char *, int * );
+static int TestAttrib( AstObject *, const char *, int * );
+
+static int GetSimpVertices( AstPolygon *, int * );
+static int TestSimpVertices( AstPolygon *, int * );
+static void ClearSimpVertices( AstPolygon *, int * );
+static void SetSimpVertices( AstPolygon *, int, int * );
+
+
+/* Member functions. */
+/* ================= */
+static Segment *AddToChain( Segment *head, Segment *seg, int *status ){
+/*
+*  Name:
+*     AddToChain
+
+*  Purpose:
+*     Add a Segment into the linked list of Segments, maintaining the
+*     required order in the list.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     Segment *AddToChain( Segment *head, Segment *seg, int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     The linked list of Segments maintained by astDownsize is searched
+*     from the high error end (the head), until a Segment is foound which
+*     has a lower error than the supplied segment. The supplied Segment
+*     is then inserted into the list at that point.
+
+*  Parameters:
+*     head
+*        The Segment structure at the head of the list (i.e. the segment
+*        with maximum error).
+*     seg
+*        The Segment to be added into the list.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the link head (which will have changed if "seg" has a
+*     higher error than the original head).
+
+*/
+
+/* Local Variables: */
+   Segment *tseg;
+
+/* Check the global error status. */
+   if ( !astOK ) return head;
+
+/* If the list is empty, return the supplied segment as the new list
+   head. */
+   if( !head ) {
+      head = seg;
+
+/* If the supplied segment has a higher error than the original head,
+   insert the new segment in front of the original head. */
+   } else if( seg->error > head->error ){
+      seg->next = head;
+      head->prev = seg;
+      head = seg;
+
+/* Otherwise, move down the list from the head until a segment is found
+   which has a lower error than the supplied Segment. Then insert the
+   supplied segment into the list in front of it. */
+   } else {
+      tseg = head;
+      seg->next = NULL;
+
+      while( tseg->next ) {
+         if( seg->error > tseg->next->error ) {
+            seg->next = tseg->next;
+            seg->prev = tseg;
+            tseg->next->prev = seg;
+            tseg->next = seg;
+            break;
+         }
+         tseg = tseg->next;
+      }
+
+      if( !seg->next ) {
+         tseg->next = seg;
+         seg->prev = tseg;
+      }
+   }
+
+/* Return the new head. */
+   return head;
+}
+
+static void Cache( AstPolygon *this, int *status ){
+/*
+*  Name:
+*     Cache
+
+*  Purpose:
+*     Calculate intermediate values and cache them in the Polygon structure.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void Cache( AstPolygon *this, int *status )
+
+*  Class Membership:
+*     Polygon 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 Polygon structure.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Local Variables: */
+   AstFrame *frm;       /* Pointer to base Frame in Polygon */
+   double **ptr;        /* Pointer to data in the encapsulated PointSet */
+   double end[ 2 ];     /* Start position for edge */
+   double maxwid;       /* Maximum polygon width found so far */
+   double polcen[ 2 ];  /* Polygon centre perpendicular to current edge */
+   double polwid;       /* Polygon width perpendicular to current edge */
+   double start[ 2 ];   /* Start position for edge */
+   int i;               /* Axis index */
+   int nv;              /* Number of vertices in Polygon */
+
+/* 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 );
+
+/* Get the number of vertices. */
+      nv = astGetNpoint( ((AstRegion *) this)->points );
+
+/* Get pointers to the coordinate data in the parent Region structure. */
+      ptr = astGetPoints( ((AstRegion *) this)->points );
+
+/* Free any existing edge information in the Polygon structure. */
+      if( this->edges ) {
+         for( i = 0; i < nv; i++ ) {
+            this->edges[ i ] = astFree( this->edges[ i ] );
+         }
+      }
+
+/* Ensure we have enough memory to store new edge information if necessary. */
+      this->edges = astGrow( this->edges, nv, sizeof( AstLineDef *) );
+      this->startsat = astGrow( this->startsat, nv, sizeof( double ) );
+
+/* Check pointers can be used safely. */
+      if( this->edges && this->startsat ) {
+
+/* Create and store a description of each edge. Also form the total
+   distance round the polygon, and the distance from the first vertex
+   at which each edge starts. */
+         this->totlen = 0.0;
+         start[ 0 ] = ptr[ 0 ][ nv - 1 ];
+         start[ 1 ] = ptr[ 1 ][ nv - 1 ];
+
+         for( i = 0; i < nv; i++ ) {
+            end[ 0 ] = ptr[ 0 ][ i ];
+            end[ 1 ] = ptr[ 1 ][ i ];
+            this->edges[ i ] = astLineDef( frm, start, end );
+            start[ 0 ] = end[ 0 ];
+            start[ 1 ] = end[ 1 ];
+
+            this->startsat[ i ] = this->totlen;
+            this->totlen += this->edges[ i ]->length;
+         }
+
+/* We now look for a point that is inside the polygon. We want a point
+   that is well within the polygon, since points that are only just inside
+   the polygon can give numerical problems. Loop round each edge with
+   non-zero length. */
+         maxwid = -1.0;
+         for( i = 0; i < nv; i++ ) {
+            if( this->edges[ i ]->length > 0.0 ) {
+
+/* We define another line perpendicular to the current edge, passing
+   through the mid point of the edge, extending towards the inside of the
+   polygon. The following function returns the distance we can travel
+   along this line before we hit any of the other polygon edges. It also
+   puts the position corresponding to half that distance into "polcen". */
+               polwid = Polywidth( frm, this->edges, i, nv, polcen, status );
+
+/* If the width of the polygon perpendicular to the current edge is
+   greater than the width perpdeicular to any other edge, record the
+   width and also store the current polygon centre. */
+               if( polwid > maxwid && polwid != AST__BAD ) {
+                  maxwid = polwid;
+                  (this->in)[ 0 ] = polcen[ 0 ];
+                  (this->in)[ 1 ] = polcen[ 1 ];
+               }
+            }
+         }
+
+/* If no width was found it probably means that the polygon vertices were
+   given in clockwise order, resulting in the above process probing the
+   infinite extent outside the polygonal hole. In this case any point
+   outside the hole will do, so we use the current contents of the
+   "polcen" array. Set a flag indicating if the vertices are stored in
+   anti-clockwise order. */
+         if( maxwid < 0.0 ) {
+            (this->in)[ 0 ] = polcen[ 0 ];
+            (this->in)[ 1 ] = polcen[ 1 ];
+            this->acw = 0;
+         } else {
+            this->acw = 1;
+         }
+      }
+
+/* Free resources */
+      frm = astAnnul( frm );
+
+/* Indicate cached information is up to date. */
+      this->stale = 0;
+   }
+}
+
+static void ClearAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     ClearAttrib
+
+*  Purpose:
+*     Clear an attribute value for a Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void ClearAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     Polygon member function (over-rides the astClearAttrib protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function clears the value of a specified attribute for a
+*     Polygon, so that the default value will subsequently be used.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon.
+*     attrib
+*        Pointer to a null terminated string specifying the attribute
+*        name.  This should be in lower case with no surrounding white
+*        space.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstPolygon *this;             /* Pointer to the Polygon structure */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the Polygon structure. */
+   this = (AstPolygon *) this_object;
+
+/* Check the attribute name and clear the appropriate attribute. */
+
+/* SimpVertices. */
+/* ------------- */
+   if ( !strcmp( attrib, "simpvertices" ) ) {
+      astClearSimpVertices( this );
+
+/* If the attribute is not recognised, pass it on to the parent method
+   for further interpretation. */
+   } else {
+      (*parent_clearattrib)( this_object, attrib, status );
+   }
+}
+
+/*
+*++
+*  Name:
+c     astConvex<X>
+f     AST_CONVEX<X>
+
+*  Purpose:
+*     Create a new Polygon representing the convex hull of a 2D data grid.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "polygon.h"
+c     AstPolygon *astConvex<X>( <Xtype> value, int oper, const <Xtype> array[],
+c                                const int lbnd[2], const int ubnd[2], int starpix )
+f     RESULT = AST_CONVEX<X>( VALUE, OPER, ARRAY, LBND, UBND, STARPIX, STATUS )
+
+*  Class Membership:
+*     Polygon method.
+
+*  Description:
+*     This is a set of functions that create the shortest Polygon that
+*     encloses all pixels with a specified value within a gridded
+*     2-dimensional data array (e.g. an image).
+*
+*     A basic 2-dimensional Frame is used to represent the pixel coordinate
+*     system in the returned Polygon. The Domain attribute is set to
+*     "PIXEL", the Title attribute is set to "Pixel coordinates", and the
+*     Unit attribute for each axis is set to "pixel". All other
+*     attributes are left unset. The nature of the pixel coordinate system
+*     is determined by parameter
+c     "starpix".
+f     STARPIX.
+*
+*     You should use a function which matches the numerical type of the
+*     data you are processing by replacing <X> in the generic function
+*     name
+c     astConvex<X>
+f     AST_CONVEX<X>
+c     by an appropriate 1- or 2-character type code. For example, if you
+*     are procesing data with type
+c     "float", you should use the function astConvexF
+f     REAL, you should use the function AST_CONVEXR
+*     (see the "Data Type Codes" section below for the codes appropriate to
+*     other numerical types).
+
+*  Parameters:
+c     value
+f     VALUE = <Xtype> (Given)
+*        A data value that specifies the pixels to be included within the
+*        convex hull.
+c     oper
+f     OPER = INTEGER (Given)
+*        Indicates how the
+c        "value"
+f        VALUE
+*        parameter is used to select the required pixels. It can
+*        have any of the following values:
+c        - AST__LT: include pixels with value less than "value".
+c        - AST__LE: include pixels with value less than or equal to "value".
+c        - AST__EQ: include pixels with value equal to "value".
+c        - AST__NE: include pixels with value not equal to "value".
+c        - AST__GE: include pixels with value greater than or equal to "value".
+c        - AST__GT: include pixels with value greater than "value".
+f        - AST__LT: include pixels with value less than VALUE.
+f        - AST__LE: include pixels with value less than or equal to VALUE.
+f        - AST__EQ: include pixels with value equal to VALUE.
+f        - AST__NE: include pixels with value not equal to VALUE.
+f        - AST__GE: include pixels with value greater than or equal to VALUE.
+f        - AST__GT: include pixels with value greater than VALUE.
+c     array
+f     ARRAY( * ) = <Xtype> (Given)
+c        Pointer to a
+f        A
+*        2-dimensional array containing the data to be processed.  The
+*        numerical type of this array should match the 1- or
+*        2-character type code appended to the function name (e.g. if
+c        you are using astConvexF, the type of each array element
+c        should be "float").
+f        you are using AST_CONVEXR, the type of each array element
+f        should be REAL).
+*
+*        The storage order of data within this array should be such
+*        that the index of the first grid dimension varies most
+*        rapidly and that of the second dimension least rapidly
+c        (i.e. Fortran array indexing is used).
+f        (i.e. normal Fortran array storage order).
+c     lbnd
+f     LBND( 2 ) = INTEGER (Given)
+c        Pointer to an array of two integers
+f        An array
+*        containing the coordinates of the centre of the first pixel
+*        in the input grid along each dimension.
+c     ubnd
+f     UBND( 2) = INTEGER (Given)
+c        Pointer to an array of two integers
+f        An array
+*        containing the coordinates of the centre of the last pixel in
+*        the input grid along each dimension.
+*
+c        Note that "lbnd" and "ubnd" together define the shape
+f        Note that LBND and UBND together define the shape
+*        and size of the input grid, its extent along a particular
+c        (j'th) dimension being ubnd[j]-lbnd[j]+1 (assuming the
+c        index "j" to be zero-based). They also define
+f        (J'th) dimension being UBND(J)-LBND(J)+1. They also define
+*        the input grid's coordinate system, each pixel having unit
+*        extent along each dimension with integral coordinate values
+*        at its centre or upper corner, as selected by parameter
+c        "starpix".
+f        STARPIX.
+c     starpix
+f     STARPIX = LOGICAL (Given)
+*        A flag indicating the nature of the pixel coordinate system used
+*        to describe the vertex positions in the returned Polygon. If
+c        non-zero,
+f        .TRUE.,
+*        the standard Starlink definition of pixel coordinate is used in
+*        which a pixel with integer index I spans a range of pixel coordinate
+*        from (I-1) to I (i.e. pixel corners have integral pixel coordinates).
+c        If zero,
+f        If .FALSE.,
+*        the definition of pixel coordinate used by other AST functions
+c        such as astResample, astMask,
+f        such as AST_RESAMPLE, AST_MASK,
+*        etc., is used. In this definition, a pixel with integer index I
+*        spans a range of pixel coordinate from (I-0.5) to (I+0.5) (i.e.
+*        pixel centres have integral pixel coordinates).
+f     STATUS = INTEGER (Given and Returned)
+f        The global status.
+
+*  Returned Value:
+c     astConvex<X>()
+f     AST_CONVEX<X> = INTEGER
+*        A pointer to the required Polygon.
+c        NULL
+f        AST__NULL
+*        is returned without error if the array contains no pixels that
+*        satisfy the criterion specified by
+c        "value" and "oper".
+f        VALUE and OPER.
+
+*  Notes:
+c     - NULL
+f     - AST__NULL
+*     will be returned if this function is invoked with the global
+*     error status set, or if it should fail for any reason.
+
+*  Data Type Codes:
+*     To select the appropriate masking function, you should
+c     replace <X> in the generic function name astConvex<X> with a
+f     replace <X> in the generic function name AST_CONVEX<X> with a
+*     1- or 2-character data type code, so as to match the numerical
+*     type <Xtype> of the data you are processing, as follows:
+c     - D: double
+c     - F: float
+c     - L: long int
+c     - UL: unsigned long int
+c     - I: int
+c     - UI: unsigned int
+c     - S: short int
+c     - US: unsigned short int
+c     - B: byte (signed char)
+c     - UB: unsigned byte (unsigned char)
+f     - D: DOUBLE PRECISION
+f     - R: REAL
+f     - I: INTEGER
+f     - UI: INTEGER (treated as unsigned)
+f     - S: INTEGER*2 (short integer)
+f     - US: INTEGER*2 (short integer, treated as unsigned)
+f     - B: BYTE (treated as signed)
+f     - UB: BYTE (treated as unsigned)
+*
+c     For example, astConvexD would be used to process "double"
+c     data, while astConvexS would be used to process "short int"
+c     data, etc.
+f     For example, AST_CONVEXD would be used to process DOUBLE
+f     PRECISION data, while AST_CONVEXS would be used to process
+f     short integer data (stored in an INTEGER*2 array), etc.
+f
+f     For compatibility with other Starlink facilities, the codes W
+f     and UW are provided as synonyms for S and US respectively (but
+f     only in the Fortran interface to AST).
+
+*--
+*/
+/* Define a macro to implement the function for a specific data
+   type. Note, this function cannot be a virtual function since the
+   argument list does not include a Polygon, and so no virtual function
+   table is available. */
+#define MAKE_CONVEX(X,Xtype) \
+AstPolygon *astConvex##X##_( Xtype value, int oper, const Xtype array[], \
+                             const int lbnd[2], const int ubnd[2], \
+                             int starpix, int *status ) { \
+\
+/* Local Variables: */ \
+   AstFrame *frm;            /* Frame in which to define the Polygon */ \
+   AstPointSet *candidate;   /* Candidate polygon vertices */ \
+   AstPolygon *result;       /* Result value to return */ \
+   int xdim;                 /* Number of pixels per row */ \
+   int ydim;                 /* Number of rows */ \
+   static double junk[ 6 ] = {0.0, 0.0, 1.0, 1.0, 0.0, 1.0 }; /* Junk poly */ \
+\
+/* Initialise. */ \
+   result = NULL; \
+   candidate = NULL; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return result; \
+\
+/* Get the array dimensions. */ \
+   xdim = ubnd[ 0 ] - lbnd[ 0 ] + 1; \
+   ydim = ubnd[ 1 ] - lbnd[ 1 ] + 1; \
+\
+/* Get the basic concvex hull. */ \
+   if( oper == AST__LT ) { \
+      candidate = ConvexHullLT##X( value, array, lbnd, starpix, xdim, ydim, status ); \
+\
+   } else if( oper == AST__LE ) { \
+      candidate = ConvexHullLE##X( value, array, lbnd, starpix, xdim, ydim, status ); \
+\
+   } else if( oper == AST__EQ ) { \
+      candidate = ConvexHullEQ##X( value, array, lbnd, starpix, xdim, ydim, status ); \
+\
+   } else if( oper == AST__NE ) { \
+      candidate = ConvexHullNE##X( value, array, lbnd, starpix, xdim, ydim, status ); \
+\
+   } else if( oper == AST__GE ) { \
+      candidate = ConvexHullGE##X( value, array, lbnd, starpix, xdim, ydim, status ); \
+\
+   } else if( oper == AST__GT ) { \
+      candidate = ConvexHullGT##X( value, array, lbnd, starpix, xdim, ydim, status ); \
+\
+   } else if( astOK ){ \
+      astError( AST__OPRIN, "astConvex"#X": Invalid operation code " \
+                "(%d) supplied (programming error).", status, oper ); \
+   } \
+\
+/* Check some good selected values were found. */ \
+   if( candidate ) { \
+\
+/* Create a default Polygon with 3 junk vertices. */ \
+      frm = astFrame( 2, "Domain=PIXEL,Unit(1)=pixel,Unit(2)=pixel," \
+                      "Title=Pixel coordinates", status ); \
+      result = astPolygon( frm, 3, 3, junk, NULL, " ", status ); \
+\
+/* Change the PointSet within the Polygon to the one created above. */ \
+      SetPointSet( result, candidate, status ); \
+\
+/* Free resources. */ \
+      frm = astAnnul( frm ); \
+      candidate = astAnnul( candidate ); \
+   } \
+\
+/* If an error occurred, clear the returned result. */ \
+   if ( !astOK ) result = astAnnul( result ); \
+\
+/* Return the result. */ \
+   return result; \
+}
+
+
+/* Expand the above macro to generate a function for each required
+   data type. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKE_CONVEX(LD,long double)
+#endif
+MAKE_CONVEX(D,double)
+MAKE_CONVEX(L,long int)
+MAKE_CONVEX(UL,unsigned long int)
+MAKE_CONVEX(I,int)
+MAKE_CONVEX(UI,unsigned int)
+MAKE_CONVEX(S,short int)
+MAKE_CONVEX(US,unsigned short int)
+MAKE_CONVEX(B,signed char)
+MAKE_CONVEX(UB,unsigned char)
+MAKE_CONVEX(F,float)
+
+/* Undefine the macros. */
+#undef MAKE_CONVEX
+
+/*
+*  Name:
+*     ConvexHull
+
+*  Purpose:
+*     Find the convex hull enclosing selected pixels in a 2D array.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     AstPointSet *ConvexHull<Oper><X>( <Xtype> value, const <Xtype> array[],
+*                                       const int lbnd[2], int starpix,
+*                                       int xdim, int ydim, int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     This function uses an algorithm similar to "Andrew's Monotone Chain
+*     Algorithm" to create a list of vertices describing the convex hull
+*     enclosing the selected pixels in the supplied array. The vertices
+*     are returned in a PointSet.
+
+*  Parameters:
+*     value
+*        A data value that specifies the pixels to be selected.
+*     array
+*        Pointer to a 2-dimensional array containing the data to be
+*        processed. The numerical type of this array should match the 1-
+*        or 2-character type code appended to the function name.
+*     lbnd
+*        The lower pixel index bounds of the array.
+*     starpix
+*        If non-zero, the usual Starlink definition of pixel coordinate
+*        is used (integral values at pixel corners). Otherwise, the
+*        system used by other AST functions such as astResample is used
+*        (integral values at pixel centres).
+*     xdim
+*        The number of pixels along each row of the array.
+*     ydim
+*        The number of rows in the array.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     A PointSet holding the vertices of the convex hull, or NULL if an
+*     error occurs.
+
+*  Notes:
+*     - The following code has been designed with a view to it being
+*     multi-threaded at some point.
+
+*/
+
+/* Define a macro to implement the function for a specific data
+   type and operation. */
+#define MAKE_CONVEXHULL(X,Xtype,Oper,OperI) \
+static AstPointSet *ConvexHull##Oper##X( Xtype value, const Xtype array[], \
+                                         const int lbnd[2], int starpix, \
+                                         int xdim, int ydim, int *status ) { \
+\
+/* Local Variables: */ \
+   AstPointSet *result; \
+   double **ptr; \
+   double *xv1; \
+   double *xv2; \
+   double *xv3; \
+   double *xv4; \
+   double *xvert; \
+   double *yv1; \
+   double *yv2; \
+   double *yv3; \
+   double *yv4; \
+   double *yvert; \
+   int nv1; \
+   int nv2; \
+   int nv3; \
+   int nv4; \
+   int nv; \
+   int xhi; \
+   int xhiymax; \
+   int xhiymin; \
+   int xlo; \
+   int xloymax; \
+   int xloymin; \
+   int yhi; \
+   int yhixmax; \
+   int yhixmin; \
+   int ylo; \
+   int yloxmax; \
+   int yloxmin; \
+\
+/* Initialise */ \
+   result = NULL; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return result; \
+\
+/* Find the lowest Y value at any selected pixel, and find the max and \
+   min X value of the selected pixels at that lowest Y value. */ \
+   FindBoxEdge##Oper##X( value, array, xdim, ydim, 1, 1, &ylo, &yloxmax,  \
+                         &yloxmin, status ); \
+\
+/* Skip if there are no selected values in the array. */ \
+   if( ylo > 0 ) { \
+\
+/* Find the highest Y value at any selected pixel, and find the max and \
+   min X value of the selected pixels at that highest Y value. */ \
+      FindBoxEdge##Oper##X( value, array, xdim, ydim, 1, 0, &yhi, &yhixmax,  \
+                            &yhixmin, status ); \
+\
+/* Find the lowest X value at any selected pixel, and find the max and \
+   min Y value of the selected pixels at that lowest X value. */ \
+      FindBoxEdge##Oper##X( value, array, xdim, ydim, 0, 1, &xlo, &xloymax,  \
+                            &xloymin, status ); \
+\
+/* Find the highest X value at any selected pixel, and find the max and \
+   min Y value of the selected pixels at that highest X value. */ \
+      FindBoxEdge##Oper##X( value, array, xdim, ydim, 0, 0, &xhi, &xhiymax,  \
+                            &xhiymin, status ); \
+\
+/* Create a list of vertices for the bottom right corner of the bounding \
+   box of the selected pixels. */ \
+      PartHull##Oper##X( value, array, xdim, ydim, yloxmax, ylo, xhi, xhiymin, \
+                         starpix, lbnd, &xv1, &yv1, &nv1, status ); \
+\
+/* Create a list of vertices for the top right corner of the bounding \
+   box of the selected pixels. */ \
+      PartHull##Oper##X( value, array, xdim, ydim, xhi, xhiymax, yhixmax, yhi, \
+                         starpix, lbnd, &xv2, &yv2, &nv2, status ); \
+\
+/* Create a list of vertices for the top left corner of the bounding \
+   box of the selected pixels. */ \
+      PartHull##Oper##X( value, array, xdim, ydim, yhixmin, yhi, xlo, xloymax, \
+                         starpix, lbnd, &xv3, &yv3, &nv3, status ); \
+\
+/* Create a list of vertices for the bottom left corner of the bounding \
+   box of the selected pixels. */ \
+      PartHull##Oper##X( value, array, xdim, ydim, xlo, xloymin, yloxmin, ylo, \
+                         starpix, lbnd, &xv4, &yv4, &nv4, status ); \
+\
+/* Concatenate the four vertex lists and store them in the returned \
+   PointSet. */ \
+      nv =  nv1 + nv2 + nv3 + nv4; \
+      result = astPointSet( nv, 2, " ", status ); \
+      ptr = astGetPoints( result ); \
+      if( astOK ) { \
+         xvert = ptr[ 0 ]; \
+         yvert = ptr[ 1 ]; \
+\
+         memcpy( xvert, xv1, nv1*sizeof( double ) ); \
+         memcpy( yvert, yv1, nv1*sizeof( double ) ); \
+         xvert += nv1; \
+         yvert += nv1; \
+\
+         memcpy( xvert, xv2, nv2*sizeof( double ) ); \
+         memcpy( yvert, yv2, nv2*sizeof( double ) ); \
+         xvert += nv2; \
+         yvert += nv2; \
+\
+         memcpy( xvert, xv3, nv3*sizeof( double ) ); \
+         memcpy( yvert, yv3, nv3*sizeof( double ) ); \
+         xvert += nv3; \
+         yvert += nv3; \
+\
+         memcpy( xvert, xv4, nv4*sizeof( double ) ); \
+         memcpy( yvert, yv4, nv4*sizeof( double ) ); \
+      } \
+\
+/* Free resources. */ \
+      xv1 = astFree( xv1 ); \
+      xv2 = astFree( xv2 ); \
+      xv3 = astFree( xv3 ); \
+      xv4 = astFree( xv4 ); \
+      yv1 = astFree( yv1 ); \
+      yv2 = astFree( yv2 ); \
+      yv3 = astFree( yv3 ); \
+      yv4 = astFree( yv4 ); \
+   } \
+\
+/* Free the returned PointSet if an error occurred. */ \
+   if( result && !astOK ) result = astAnnul( result ); \
+\
+/* Return the result. */ \
+   return result; \
+}
+
+/* Define a macro that uses the above macro to to create implementations
+   of ConvexHull for all operations. */
+#define MAKEALL_CONVEXHULL(X,Xtype) \
+MAKE_CONVEXHULL(X,Xtype,LT,AST__LT) \
+MAKE_CONVEXHULL(X,Xtype,LE,AST__LE) \
+MAKE_CONVEXHULL(X,Xtype,EQ,AST__EQ) \
+MAKE_CONVEXHULL(X,Xtype,NE,AST__NE) \
+MAKE_CONVEXHULL(X,Xtype,GE,AST__GE) \
+MAKE_CONVEXHULL(X,Xtype,GT,AST__GT)
+
+/* Expand the above macro to generate a function for each required
+   data type and operation. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKEALL_CONVEXHULL(LD,long double)
+#endif
+MAKEALL_CONVEXHULL(D,double)
+MAKEALL_CONVEXHULL(L,long int)
+MAKEALL_CONVEXHULL(UL,unsigned long int)
+MAKEALL_CONVEXHULL(I,int)
+MAKEALL_CONVEXHULL(UI,unsigned int)
+MAKEALL_CONVEXHULL(S,short int)
+MAKEALL_CONVEXHULL(US,unsigned short int)
+MAKEALL_CONVEXHULL(B,signed char)
+MAKEALL_CONVEXHULL(UB,unsigned char)
+MAKEALL_CONVEXHULL(F,float)
+
+/* Undefine the macros. */
+#undef MAKE_CONVEXHULL
+#undef MAKEALL_CONVEXHULL
+
+static AstPolygon *Downsize( AstPolygon *this, double maxerr, int maxvert,
+                             int *status ) {
+/*
+*++
+*  Name:
+c     astDownsize
+f     AST_DOWNSIZE
+
+*  Purpose:
+*     Reduce the number of vertices in a Polygon.
+
+*  Type:
+*     Public virtual function.
+
+*  Synopsis:
+c     #include "polygon.h"
+c     AstPolygon *astDownsize( AstPolygon *this, double maxerr, int maxvert )
+f     RESULT = AST_DOWNSIZE( THIS, MAXERR, MAXVERT, STATUS )
+
+*  Class Membership:
+*     Polygon method.
+
+*  Description:
+*     This function returns a pointer to a new Polygon that contains a
+*     subset of the vertices in the supplied Polygon. The subset is
+*     chosen so that the returned Polygon is a good approximation to
+*     the supplied Polygon, within the limits specified by the supplied
+*     parameter values. That is, the density of points in the returned
+*     Polygon is greater at points where the curvature of the boundary of
+*     the supplied Polygon is greater.
+
+*  Parameters:
+c     this
+f     THIS = INTEGER (Given)
+*        Pointer to the Polygon.
+c     maxerr
+f     MAXERR = DOUBLE PRECISION (Given)
+*        The maximum allowed discrepancy between the supplied and
+*        returned Polygons, expressed as a geodesic distance within the
+*        Polygon's coordinate frame. If this is zero or less, the
+*        returned Polygon will have the number of vertices specified by
+c        maxvert.
+f        MAXVERT.
+c     maxvert
+f     MAXVERT = INTEGER (Given)
+*        The maximum allowed number of vertices in the returned Polygon.
+*        If this is less than 3, the number of vertices in the returned
+*        Polygon will be the minimum needed to achieve the maximum
+*        discrepancy specified by
+c        maxerr.
+f        MAXERR.
+f     STATUS = INTEGER (Given and Returned)
+f        The global status.
+
+*  Returned Value:
+c     astDownsize()
+f     AST_DOWNSIZE = INTEGER
+*        Pointer to the new Polygon.
+
+*  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: */
+   AstFrame *frm;         /* Base Frame from the Polygon */
+   AstPointSet *pset;     /* PointSet holding vertices of downsized polygon */
+   AstPolygon *result;    /* Returned pointer to new Polygon */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the base Frame of the Polygon. */
+   frm = astGetFrame( ((AstRegion *) this)->frameset, AST__BASE );
+
+/* Create a PointSet holding the vertices of the downsized polygon. */
+   pset = DownsizePoly( ((AstRegion *) this)->points, maxerr, maxvert,
+                        frm, status );
+
+/* Take a deep copy of the supplied Polygon. */
+   result = astCopy( this );
+
+/* Change the PointSet within the result Polygon to the one created above. */ \
+   SetPointSet( result, pset, status ); \
+
+/* Free resources. */
+   frm = astAnnul( frm );
+   pset = astAnnul( pset );
+
+/* If an error occurred, annul the returned Polygon. */
+   if ( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static AstPointSet *DownsizePoly( AstPointSet *pset, double maxerr,
+                                  int maxvert, AstFrame *frm, int *status ) {
+/*
+*  Name:
+*     DownsizePoly
+
+*  Purpose:
+*     Reduce the number of vertices in a Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*    #include "polygon.h"
+*    AstPointSet *DownsizePoly( AstPointSet *pset, double maxerr, int maxvert,
+*                               AstFrame *frm, int *status )
+
+*  Class Membership:
+*     Polygon member function.
+
+*  Description:
+*     This function returns a pointer to a new PointSet that contains a
+*     subset of the vertices in the supplied PointSet. The subset is
+*     chosen so that the returned polygon is a good approximation to
+*     the supplied polygon, within the limits specified by the supplied
+*     parameter values. That is, the density of points in the returned
+*     polygon is greater at points where the curvature of the boundary of
+*     the supplied polygon is greater.
+
+*  Parameters:
+*     pset
+*        Pointer to the PointSet holding the polygon vertices.
+*     maxerr
+*        The maximum allowed discrepancy between the supplied and
+*        returned Polygons, expressed as a geodesic distance within the
+*        Polygon's coordinate frame. If this is zero or less, the
+*        returned Polygon will have the number of vertices specified by
+*        maxvert.
+*     maxvert
+*        The maximum allowed number of vertices in the returned Polygon.
+*        If this is less than 3, the number of vertices in the returned
+*        Polygon will be the minimum needed to achieve the maximum
+*        discrepancy specified by
+*        maxerr.
+*     frm
+*        Pointer to the Frame in which the polygon is defined.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*        Pointer to the new PointSet.
+
+*  Notes:
+*     - A null Object pointer (AST__NULL) will be returned if this
+*     function is invoked with the AST error status set, or if it
+*     should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstPointSet *result;   /* Returned pointer to new PointSet */
+   Segment *head;         /* Pointer to new polygon edge with highest error */
+   Segment *seg1;         /* Pointer to new polygon edge */
+   Segment *seg2;         /* Pointer to new polygon edge */
+   Segment *seg3;         /* Pointer to new polygon edge */
+   double **ptr;          /* Pointer to arrays of axis values */
+   double *x;             /* Pointer to array of X values for old Polygon */
+   double *xnew;          /* Pointer to array of X values for new Polygon */
+   double *y;             /* Pointer to array of Y values for old Polygon */
+   double *ynew;          /* Pointer to array of Y values for new Polygon */
+   double x1;             /* Lowest X value at any vertex */
+   double x2;             /* Highest X value at any vertex */
+   double y1;             /* Lowest Y value at any vertex */
+   double y2;             /* Highest Y value at any vertex */
+   int *newpoly;          /* Holds indices of retained input vertices */
+   int i1;                /* Index of first vertex added to output polygon */
+   int i1x;               /* Index of vertex with lowest X */
+   int i1y;               /* Index of vertex with lowest Y */
+   int i2;                /* Index of second vertex added to output polygon */
+   int i2x;               /* Index of vertex with highest X */
+   int i2y;               /* Index of vertex with highest Y */
+   int i3;                /* Index of third vertex added to output polygon */
+   int iadd;              /* Normalised vertex index */
+   int iat;               /* Index at which to store new vertex index */
+   int newlen;            /* Number of vertices currently in new Polygon */
+   int nv;                /* Number of vertices in old Polygon */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get the number of vertices in the supplied polygon. */
+   nv = astGetNpoint( pset );
+
+/* If the maximum error allowed is zero, and the maximum number of
+   vertices is equal to or greater than the number in the supplied
+   polygon, just return a deep copy of the supplied PointSet. */
+   if( maxerr <= 0.0 && ( maxvert < 3 || maxvert >= nv ) ) {
+      result = astCopy( pset );
+
+/* Otherwise... */
+   } else {
+
+/* Get pointers to the X and Y arrays holding the vertex coordinates in
+   the supplied polygon. */
+      ptr = astGetPoints( pset );
+      x = ptr[ 0 ];
+      y = ptr[ 1 ];
+
+/* Allocate memory for an array to hold the original indices of the vertices
+   to be used to create the returned Polygon. This array is expanded as
+   needed. */
+      newpoly = astMalloc( 10*sizeof( int ) );
+
+/* Check the pointers can be used safely. */
+      if( astOK ) {
+
+/* We first need to decide on three widely spaced vertices which form a
+   reasonable triangular approximation to the whole polygon. First find
+   the vertices with the highest and lowest Y values, and the highest and
+   lowest X values. */
+         x1 = DBL_MAX;
+         x2 = -DBL_MAX;
+         y1 = DBL_MAX;
+         y2 = -DBL_MAX;
+
+         i1y = i1x = 0;
+         i2y = i2x = nv/2;
+
+         for( i3 = 0; i3 < nv; i3++ ) {
+            if( y[ i3 ] < y1 ) {
+               y1 = y[ i3 ];
+               i1y = i3;
+            } else if( y[ i3 ] > y2 ) {
+               y2 = y[ i3 ];
+               i2y = i3;
+            }
+
+            if( x[ i3 ] < x1 ) {
+               x1 = x[ i3 ];
+               i1x = i3;
+            } else if( x[ i3 ] > x2 ) {
+               x2 = x[ i3 ];
+               i2x = i3;
+            }
+         }
+
+/* Use the axis which spans the greater range. */
+         if( y2 - y1 > x2 - x1 ) {
+            i1 = i1y;
+            i2 = i2y;
+         } else {
+            i1 = i1x;
+            i2 = i2x;
+         }
+
+/* The index with vertex i1 is definitely going to be one of our three
+   vertices. We are going to use the line from i1 to i2 to choose the two
+   other vertices to use. Create a structure describing the segment of the
+   Polygon from the lowest value on the selected axis (X or Y) to the
+   highest value. As always, the polygons is traversed in an anti-clockwise
+   direction. */
+         seg1 = NewSegment( NULL, i1, i2, nv, status );
+
+/* Find the vertex within this segment which is furthest away from the
+   line on the right hand side (as moving from vertex i1 to vertex i2). */
+         FindMax( seg1, frm, x, y, nv, 0, status );
+
+/* Likewise, create a structure describing the remained of the Polygon
+   (i.e. the segment from the highest value on the selected axis to the
+   lowest value). Then find the vertex within this segment which is
+   furthest away from the line on the right hand side. */
+         seg2 = NewSegment( NULL, i2, i1, nv, status );
+         FindMax( seg2, frm, x, y, nv, 0, status );
+
+/* Select the segment for which the found vertex is furthest from the
+   line. */
+         if( seg2->error > seg1->error ) {
+
+/* If the second segment, we will use the vertex that is farthest from
+   the line as one of our threee vertices. To ensure that movement from
+   vertex i1 to i2 to i3 is anti-clockwise, we must use this new vertex
+   as vertex i3, not i2. */
+            i3 = seg2->imax;
+
+/* Create a description of the polygon segment from vertex i1 to i3, and
+   find the vertex which is furthest to the right of the line joining the
+   two vertices. We use this as the middle vertex (i2). */
+            seg1 = NewSegment( seg1, i1, i3, nv, status );
+            FindMax( seg1, frm, x, y, nv, 0, status );
+            i2 = seg1->imax;
+
+/* Do the same if we are choosing the other segment, ordering the
+   vertices to retain anti-clockwise movement from i1 to i2 to i3. */
+         } else {
+            i2 = seg1->imax;
+            seg1 = NewSegment( seg1, i2, i1, nv, status );
+            FindMax( seg1, frm, x, y, nv, 0, status );
+            i3 = seg1->imax;
+         }
+
+/* Ensure the vertex indices are in the first cycle. */
+         if( i2 >= nv ) i2 -= nv;
+         if( i3 >= nv ) i3 -= nv;
+
+/* Create Segment structures to describe each of these three edges. */
+         seg1 = NewSegment( seg1, i1, i2, nv, status );
+         seg2 = NewSegment( seg2, i2, i3, nv, status );
+         seg3 = NewSegment( NULL, i3, i1, nv, status );
+
+/* Record these 3 vertices in an array holding the original indices of
+   the vertices to be used to create the returned Polygon. */
+         newpoly[ 0 ] = i1;
+         newpoly[ 1 ] = i2;
+         newpoly[ 2 ] = i3;
+
+/* Indicate the new polygon currently has 3 vertices. */
+         newlen = 3;
+
+/* Search the old vertices between the start and end of segment 3, looking
+   for the vertex which lies furthest from the line of segment 3. The
+   residual between this point and the line is stored in the Segment
+   structure, as is the index of the vertex at which this maximum residual
+   occurred. */
+         FindMax( seg3, frm, x, y, nv, 1, status );
+
+/* The "head" variable points to the head of a double linked list of
+   Segment structures. This list is ordered by residual, so that the
+   Segment with the maximum residual is at the head, and the Segment
+   with the minimum residual is at the tail. Initially "seg3" is at the
+   head. */
+         head = seg3;
+
+/* Search the old vertices between the start and end of segment 1, looking
+   for the vertex which lies furthest from the line of segment 1. The
+   residual between this point and the line is stored in the Segment
+   structure, as is the index of the vertex at which this maximum residual
+   occurred. */
+         FindMax( seg1, frm, x, y, nv, 1, status );
+
+/* Insert segment 1 into the linked list of Segments, at a position that
+   maintains the ordering of the segments by error. Thus the head of the
+   list will still have the max error. */
+         head = AddToChain( head, seg1, status );
+
+/* Do the same for segment 2. */
+         FindMax( seg2, frm, x, y, nv, 1, status );
+         head = AddToChain( head, seg2, status );
+
+/* If the maximum allowed number of vertices in the output Polygon is
+   less than 3, allow any number of vertices up to the number in the
+   input Polygon (termination will then be determined just by "maxerr"). */
+         if( maxvert < 3 ) maxvert = nv;
+
+/* Loop round adding an extra vertex to the returned Polygon until the
+   maximum residual between the new and old polygons is no more than
+   "maxerr". Abort early if the specified maximum number of vertices is
+   reached. */
+         while( head->error > maxerr && newlen < maxvert ) {
+
+/* The segment at the head of the list has the max error (that is, it is
+   the segment that departs most from the supplied Polygon). To make the
+   new polygon a better fit to the old polygon, we add the vertex that is
+   furthest away from this segment to the new polygon. Remember that a
+   polygon is cyclic so if the vertex has an index that is greater than the
+   number of vertices in the old polygon, reduce the index by the number
+   of vertices in the old polygon. */
+            iadd = head->imax;
+            if( iadd >= nv ) iadd -= nv;
+            iat = newlen++;
+            newpoly = astGrow( newpoly, newlen, sizeof( int ) );
+            if( !astOK ) break;
+            newpoly[ iat ] = iadd;
+
+/* We now split the segment that had the highest error into two segments.
+   The split occurs at the vertex that had the highest error. */
+            seg1 = NewSegment( NULL, head->imax, head->i2, nv, status );
+            seg2 = head;
+            seg2->i2 = head->imax;
+
+/* We do not know where these two new segments should be in the ordered
+   linked list, so remove them from the list. */
+            head = RemoveFromChain( head, seg1, status );
+            head = RemoveFromChain( head, seg2, status );
+
+/* Find the vertex that deviates most from the first of these two new
+   segments, and then add the segment into the list of vertices, using
+   the maximum deviation to determine the position of the segment within
+   the list. */
+            FindMax( seg1, frm, x, y, nv, 1, status );
+            head = AddToChain( head, seg1, status );
+
+/* Do the same for the second new segment. */
+            FindMax( seg2, frm, x, y, nv, 1, status );
+            head = AddToChain( head, seg2, status );
+         }
+
+/* Now we have reached the required accuracy, free resources. */
+         while( head ) {
+            seg1 = head;
+            head = head->next;
+            seg1 = astFree( seg1 );
+         }
+
+/* If no vertices have been left out, return a deep copy of the supplied
+   PointSet. */
+         if( newlen == nv ) {
+            result = astCopy( pset );
+
+/* Otherwise, sort the indices of the vertices to be retained so that they
+   are in the same order as they were in the supplied Polygon. */
+         } else if( astOK ){
+            qsort( newpoly, newlen, sizeof( int ), IntCmp );
+
+/* Create a new PointSet and get pointers to its axis values. */
+            result = astPointSet( newlen, 2, " ", status );
+            ptr = astGetPoints( result );
+            xnew = ptr[ 0 ];
+            ynew = ptr[ 1 ];
+
+/* Copy the axis values for the retained vertices from the old to the new
+   PointSet. */
+            if( astOK ) {
+               for( iat = 0; iat < newlen; iat++ ) {
+                  *(xnew++) = x[ newpoly[ iat ] ];
+                  *(ynew++) = y[ newpoly[ iat ] ];
+               }
+            }
+         }
+      }
+
+/* Free resources. */
+      newpoly = astFree( newpoly );
+   }
+
+/* If an error occurred, annul the returned PointSet. */
+   if ( !astOK ) result = astAnnul( result );
+
+/* Return the result. */
+   return result;
+}
+
+static void EnsureInside( AstPolygon *this, int *status ){
+/*
+*  Name:
+*     EnsureInside
+
+*  Purpose:
+*     Ensure the unnegated Polygon represents the inside of the polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void EnsureInside( AstPolygon *this, int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     Reversing the order of the vertices of a Polygon is like negating
+*     the Polygon. But the parent Region class assumes that an unnegated
+*     region bounded by closed curves (e.g. boxes, circles, ellipses, etc)
+*     is bounded. So we need to have a way to ensure that a Polygon also
+*     follows this convention. So this function reverses the order of the
+*     vertices in the Polygon, if necessary, to ensure that the unnegated
+*     Polygon is bounded.
+
+*  Parameters:
+*     this
+*        The Polygon.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Local Variables: */
+   AstRegion *this_region;
+   double **ptr;
+   double *p;
+   double *q;
+   double tmp;
+   int bounded;
+   int i;
+   int j;
+   int jmid;
+   int negated;
+   int np;
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Is the unnegated Polygon unbounded? If so, we need to reverse the
+   vertices. */
+   bounded = astGetBounded( this );
+   negated = astGetNegated( this );
+   if( ( bounded && negated ) || ( !bounded && !negated ) ) {
+      this_region = (AstRegion *) this;
+
+/* Get a pointer to the arrays holding the coordinates at the Polygon
+   vertices. */
+      ptr = astGetPoints( this_region->points );
+
+/* Get the number of vertices. */
+      np = astGetNpoint( this_region->points );
+
+/* Store the index of the last vertex to swap. For odd "np" the central
+   vertex does not need to be swapped. */
+      jmid = np/2;
+
+/* Loop round the two axes spanned by the Polygon. */
+      for( i = 0; i < 2; i++ ) {
+
+/* Get pointers to the first pair of axis values to be swapped - i.e. the
+   first and last axis values. */
+         p = ptr[ i ];
+         q = p + np - 1;
+
+/* Loop round all pairs of axis values. */
+         for( j = 0; j < jmid; j++ ) {
+
+/* Swap the pair. */
+            tmp = *p;
+            *(p++) = *q;
+            *(q--) = tmp;
+         }
+      }
+
+/* Invert the value of the "Negated" attribute to cancel out the effect
+   of the above vertex reversal. */
+      astNegate( this );
+
+/* Indicate the cached information in the Polygon structure is stale. */
+      this->stale = 1;
+   }
+}
+
+/*
+*  Name:
+*     FindBoxEdge
+
+*  Purpose:
+*     Find an edge of the bounding box containing the selected pixels.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void FindBoxEdge<Oper><X>( <Xtype> value, const <Xtype> array[],
+*                                int xdim, int ydim, int axis, int low,
+*                                int *val, int *valmax, int *valmin,
+*                                int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     This function search for an edge of the bounding box containing the
+*     selected pixels in the supplied array.
+
+*  Parameters:
+*     value
+*        A data value that specifies the pixels to be selected.
+*     array
+*        Pointer to a 2-dimensional array containing the data to be
+*        processed. The numerical type of this array should match the 1-
+*        or 2-character type code appended to the function name.
+*     xdim
+*        The number of pixels along each row of the array.
+*     ydim
+*        The number of rows in the array.
+*     axis
+*        The index (0 or 1) of the pixel axis perpendicular to the edge of the
+*        bounding box being found.
+*     low
+*        If non-zero, the lower edge of the bounding box on the axis
+*        specified by "axis" is found and returned. Otherwise, the higher
+*        edge of the bounding box on the axis specified by "axis" is
+*        found and returned.
+*     val
+*        Address of an int in which to return the value on axis "axis" of
+*        the higher or lower (as specified by "low") edge of the bounding
+*        box.
+*     valmax
+*        Address of an int in which to return the highest value on axis
+*        "1-axis" of the selected pixels on the returned edge.
+*     valmin
+*        Address of an int in which to return the lowest value on axis
+*        "1-axis" of the selected pixels on the returned edge.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes;
+*     - Zero is returned for "*val" if no good  values are found, or if
+*     an error occurs.
+
+*/
+
+/* Define a macro to implement the function for a specific data
+   type and operation. */
+#define MAKE_FINDBOXEDGE(X,Xtype,Oper,OperI) \
+static void FindBoxEdge##Oper##X( Xtype value, const Xtype array[], int xdim, \
+                                  int ydim, int axis, int low, int *val, \
+                                  int *valmax, int *valmin, int *status ) { \
+\
+/* Local Variables: */ \
+   int astep; \
+   int bstep; \
+   int a0; \
+   int a1; \
+   int b0; \
+   int b1; \
+   int inc; \
+   int a; \
+   int b; \
+   const Xtype *pc; \
+\
+/* Initialise. */ \
+   *val = 0; \
+   *valmin = 0; \
+   *valmax = 0; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return; \
+\
+/* If we are finding an edge that is parallel to the X axis... */ \
+   if(  axis ) { \
+\
+/* Get the vector step between adjacent pixels on the selected axis, and \
+   on the other axis. */ \
+      astep = xdim; \
+      bstep = 1; \
+\
+/* Get the first and last value to check on the selected axis, and the  \
+   increment between checks. */ \
+      if( low ) { \
+         a0 = 1; \
+         a1 = ydim; \
+         inc = 1; \
+      } else { \
+         a0 = ydim; \
+         a1 = 1; \
+         inc = -1; \
+      } \
+\
+/* The first and last value to check on the other axis. */ \
+      b0 = 1; \
+      b1 = xdim; \
+\
+/* Do the same if we are finding an edge that is parallel to the Y axis. */ \
+   } else {  \
+      astep = 1; \
+      bstep = xdim; \
+\
+      if( low ) { \
+         a0 = 1; \
+         a1 = xdim; \
+         inc = 1; \
+      } else { \
+         a0 = xdim; \
+         a1 = 1; \
+         inc = -1; \
+      } \
+\
+      b0 = 1; \
+      b1 = ydim; \
+   }  \
+\
+/* Loop round the axis values. */ \
+   a = a0; \
+   while( 1 ) { \
+\
+/* Get a pointer to the first value to be checked at this axis value. */ \
+      pc = array + (a - 1)*astep + (b0 - 1)*bstep; \
+\
+/* Scan the other axis to find the first and last selected pixel. */ \
+      for( b = b0; b <= b1; b++ ) { \
+         if( ISVALID(*pc,OperI,value) ) {  \
+            if( *valmin == 0 ) *valmin = b; \
+            *valmax = b; \
+         } \
+         pc += bstep; \
+      } \
+\
+/* If any selected pixels were found, store the axis value and exit. */ \
+      if( *valmax ) { \
+         *val = a; \
+         break; \
+      } \
+\
+/* Move on to the next axis value. */ \
+      if( a != a1 ) { \
+         a += inc; \
+      } else { \
+         break; \
+      } \
+\
+   } \
+}
+
+/* Define a macro that uses the above macro to to create implementations
+   of FindBoxEdge for all operations. */
+#define MAKEALL_FINDBOXEDGE(X,Xtype) \
+MAKE_FINDBOXEDGE(X,Xtype,LT,AST__LT) \
+MAKE_FINDBOXEDGE(X,Xtype,LE,AST__LE) \
+MAKE_FINDBOXEDGE(X,Xtype,EQ,AST__EQ) \
+MAKE_FINDBOXEDGE(X,Xtype,NE,AST__NE) \
+MAKE_FINDBOXEDGE(X,Xtype,GE,AST__GE) \
+MAKE_FINDBOXEDGE(X,Xtype,GT,AST__GT)
+
+/* Expand the above macro to generate a function for each required
+   data type and operation. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKEALL_FINDBOXEDGE(LD,long double)
+#endif
+MAKEALL_FINDBOXEDGE(D,double)
+MAKEALL_FINDBOXEDGE(L,long int)
+MAKEALL_FINDBOXEDGE(UL,unsigned long int)
+MAKEALL_FINDBOXEDGE(I,int)
+MAKEALL_FINDBOXEDGE(UI,unsigned int)
+MAKEALL_FINDBOXEDGE(S,short int)
+MAKEALL_FINDBOXEDGE(US,unsigned short int)
+MAKEALL_FINDBOXEDGE(B,signed char)
+MAKEALL_FINDBOXEDGE(UB,unsigned char)
+MAKEALL_FINDBOXEDGE(F,float)
+
+/* Undefine the macros. */
+#undef MAKE_FINDBOXEDGE
+#undef MAKEALL_FINDBOXEDGE
+
+/*
+*  Name:
+*     FindInsidePoint
+
+*  Purpose:
+*     Find a point that is inside the required outline.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void FindInsidePoint<Oper><X>( <Xtype> value, const <Xtype> array[],
+*                                    const int lbnd[ 2 ], const int ubnd[ 2 ],
+*                                    int *inx, int *iny, int *iv,
+*                                    int *status );
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     The central pixel in the array is checked to see if its value meets
+*     the requirements implied by <Oper> and "value". If so, its pixel
+*     indices and vector index are returned> if not, a spiral search is
+*     made until such a pixel value is found.
+
+*  Parameters:
+*     value
+*        The data value defining valid pixels.
+*     array
+*        The data array.
+*     lbnd
+*        The lower pixel index bounds of the array.
+*     ubnd
+*        The upper pixel index bounds of the array.
+*     inx
+*        Pointer to an int in which to return the X pixel index of the
+*        first point that meets the requirements implied by <oper> and
+*        "value".
+*     iny
+*        Pointer to an int in which to return the Y pixel index of the
+*        first point that meets the requirements implied by <oper> and
+*        "value".
+*     iv
+*        Pointer to an int in which to return the vector index of the
+*        first point that meets the requirements implied by <oper> and
+*        "value".
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*     - <Oper> must be one of LT, LE, EQ, NE, GE, GT.
+
+
+*/
+
+/* Define a macro to implement the function for a specific data
+   type and operation. */
+#define MAKE_FINDINSIDEPOINT(X,Xtype,Oper,OperI) \
+static void FindInsidePoint##Oper##X( Xtype value, const Xtype array[], \
+                                      const int lbnd[ 2 ], const int ubnd[ 2 ], \
+                                      int *inx, int *iny, int *iv, \
+                                      int *status ){ \
+\
+/* Local Variables: */ \
+   const Xtype *pv;  /* Pointer to next data value to test */ \
+   const char *text; /* Pointer to text describing oper */ \
+   int cy;           /* Central row index */ \
+   int iskin;        /* Index of spiral layer being searched */ \
+   int nskin;        /* Number of spiral layers to search */ \
+   int nx;           /* Pixel per row */ \
+   int tmp;          /* Temporary storage */ \
+   int xhi;          /* High X pixel index bound of current skin */ \
+   int xlo;          /* Low X pixel index bound of current skin */ \
+   int yhi;          /* High X pixel index bound of current skin */ \
+   int ylo;          /* Low X pixel index bound of current skin */ \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return; \
+\
+/* Find number of pixels in one row of the array. */ \
+   nx = ( ubnd[ 0 ] - lbnd[ 0 ] + 1 ); \
+\
+/* Find the pixel indices of the central pixel */ \
+   *inx = ( ubnd[ 0 ] + lbnd[ 0 ] )/2; \
+   *iny = ( ubnd[ 1 ] + lbnd[ 1 ] )/2; \
+\
+/* Initialise the vector index and pointer to refer to the central pixel. */ \
+   *iv = ( *inx - lbnd[ 0 ] ) + nx*( *iny - lbnd[ 1 ] ) ; \
+   pv = array + (*iv); \
+\
+/* Test the pixel value, returning if it is valid. This \
+   relies on the compiler optimisation to remove the "if" statements \
+   for all but the operation appropriate to the function being defined. */ \
+   if( OperI == AST__LT ) { \
+      if( *pv < value ) return; \
+\
+   } else if( OperI == AST__LE ) { \
+      if( *pv <= value ) return; \
+\
+   } else if( OperI == AST__EQ ) { \
+      if( *pv == value ) return; \
+\
+   } else if( OperI == AST__NE ) { \
+      if( *pv != value ) return; \
+\
+   } else if( OperI == AST__GE ) { \
+      if( *pv >= value ) return; \
+\
+   } else { \
+      if( *pv > value ) return; \
+   } \
+\
+/* The central pixel is invalid if we arrive here. So we need to do a \
+   spiral search out from the centre looking for a valid pixel. Record \
+   the central row index (this is the row at which we jump to the next \
+   outer skin when doing the spiral search below). */ \
+   cy = *iny; \
+\
+/* Find how many skins can be searched as part of the spiral search \
+   before the edge of the array is encountered. */ \
+   nskin = ubnd[ 0 ] - *inx; \
+   tmp = *inx - lbnd[ 0 ]; \
+   if( tmp < nskin ) nskin = tmp; \
+   tmp = ubnd[ 1 ] - *iny; \
+   if( tmp < nskin ) nskin = tmp; \
+   tmp = *iny - lbnd[ 1 ]; \
+   if( tmp < nskin ) nskin = tmp; \
+\
+/* Initialise the skin box bounds to be just the central pixel. */ \
+   xlo = xhi = *inx; \
+   ylo = yhi = *iny; \
+\
+/* Loop round each skin looking for a valid test pixel. */ \
+   for( iskin = 0; iskin < nskin; iskin++ ) { \
+\
+/* Increment the upper and lower bounds of the box forming the next \
+   skin. */ \
+      xhi++; \
+      xlo--; \
+      yhi++; \
+      ylo--; \
+\
+/* Initialise things for the first pixel in the new skin by moving one \
+   pixel to the right. */ \
+      pv++; \
+      (*iv)++; \
+      (*inx)++; \
+\
+/* Move up the right hand edge of the box corresponding to the current \
+   skin. We start at the middle of the right hand edge. */ \
+      for( *iny = cy; *iny <= yhi; (*iny)++ ) { \
+\
+/* Test the pixel value, returning if it is valid. This relies on the \
+   compiler optimisation to remove the "if" statements for all but the \
+   operation appropriate to the function being defined. */ \
+         if( OperI == AST__LT ) { \
+            if( *pv < value ) return; \
+\
+         } else if( OperI == AST__LE ) { \
+            if( *pv <= value ) return; \
+\
+         } else if( OperI == AST__EQ ) { \
+            if( *pv == value ) return; \
+\
+         } else if( OperI == AST__NE ) { \
+            if( *pv != value ) return; \
+\
+         } else if( OperI == AST__GE ) { \
+            if( *pv >= value ) return; \
+\
+         } else { \
+            if( *pv > value ) return; \
+         } \
+\
+/* Move up a pixel. */ \
+         pv += nx; \
+         *iv += nx; \
+      } \
+\
+/* Move down a pixel so that *iny == yhi. */ \
+      pv -= nx; \
+      *iv -= nx; \
+      (*iny)--; \
+\
+/* Move left along the top edge of the box corresponding to the current \
+   skin. */ \
+      for( *inx = xhi; *inx >= xlo; (*inx)-- ) { \
+\
+/* Test the pixel value, returning if it is valid. */ \
+         if( OperI == AST__LT ) { \
+            if( *pv < value ) return; \
+\
+         } else if( OperI == AST__LE ) { \
+            if( *pv <= value ) return; \
+\
+         } else if( OperI == AST__EQ ) { \
+            if( *pv == value ) return; \
+\
+         } else if( OperI == AST__NE ) { \
+            if( *pv != value ) return; \
+\
+         } else if( OperI == AST__GE ) { \
+            if( *pv >= value ) return; \
+\
+         } else { \
+            if( *pv > value ) return; \
+         } \
+\
+/* Move left a pixel. */ \
+         pv--; \
+         (*iv)--; \
+      } \
+\
+/* Move right a pixel so that *inx == xlo. */ \
+      pv++; \
+      (*iv)++; \
+      (*inx)++; \
+\
+/* Move down along the left hand edge of the box corresponding to the current \
+   skin. */ \
+      for( *iny = yhi; *iny >= ylo; (*iny)-- ) { \
+\
+/* Test the pixel value, returning if it is valid. */ \
+         if( OperI == AST__LT ) { \
+            if( *pv < value ) return; \
+\
+         } else if( OperI == AST__LE ) { \
+            if( *pv <= value ) return; \
+\
+         } else if( OperI == AST__EQ ) { \
+            if( *pv == value ) return; \
+\
+         } else if( OperI == AST__NE ) { \
+            if( *pv != value ) return; \
+\
+         } else if( OperI == AST__GE ) { \
+            if( *pv >= value ) return; \
+\
+         } else { \
+            if( *pv > value ) return; \
+         } \
+\
+/* Move down a pixel. */ \
+         pv -= nx; \
+         *iv -= nx; \
+      } \
+\
+/* Move up a pixel so that *iny == ylo. */ \
+      pv += nx; \
+      *iv += nx; \
+      (*iny)++; \
+\
+/* Move right along the bottom edge of the box corresponding to the current \
+   skin. */ \
+      for( *inx = xlo; *inx <= xhi; (*inx)++ ) { \
+\
+/* Test the pixel value, returning if it is valid. */ \
+         if( OperI == AST__LT ) { \
+            if( *pv < value ) return; \
+\
+         } else if( OperI == AST__LE ) { \
+            if( *pv <= value ) return; \
+\
+         } else if( OperI == AST__EQ ) { \
+            if( *pv == value ) return; \
+\
+         } else if( OperI == AST__NE ) { \
+            if( *pv != value ) return; \
+\
+         } else if( OperI == AST__GE ) { \
+            if( *pv >= value ) return; \
+\
+         } else { \
+            if( *pv > value ) return; \
+         } \
+\
+/* Move right a pixel. */ \
+         pv++; \
+         (*iv)++; \
+      } \
+\
+/* Move left a pixel so that *inx == xhi. */ \
+      pv--; \
+      (*iv)--; \
+      (*inx)--; \
+\
+/* Move up the right hand edge of the box correspionding to the current \
+   skin. We stop just below the middle of the right hand edge. */ \
+      for( *iny = ylo; *iny < cy; (*iny)++ ) { \
+\
+/* Test the pixel value, returning if it is valid. This relies on the \
+   compiler optimisation to remove the "if" statements for all but the \
+   operation appropriate to the function being defined. */ \
+         if( OperI == AST__LT ) { \
+            if( *pv < value ) return; \
+\
+         } else if( OperI == AST__LE ) { \
+            if( *pv <= value ) return; \
+\
+         } else if( OperI == AST__EQ ) { \
+            if( *pv == value ) return; \
+\
+         } else if( OperI == AST__NE ) { \
+            if( *pv != value ) return; \
+\
+         } else if( OperI == AST__GE ) { \
+            if( *pv >= value ) return; \
+\
+         } else { \
+            if( *pv > value ) return; \
+         } \
+\
+/* Move up a pixel. */ \
+         pv += nx; \
+         *iv += nx; \
+      } \
+   } \
+\
+/* Report an error if no inside pooint could be found. */ \
+   if( OperI == AST__LT ) { \
+      text = "less than"; \
+   } else if( OperI == AST__LE ) { \
+      text = "less than or equal to"; \
+   } else if( OperI == AST__EQ ) { \
+      text = "equal to"; \
+   } else if( OperI == AST__NE ) { \
+      text = "not equal to"; \
+   } else if( OperI == AST__GE ) { \
+      text = "greater than or equal to"; \
+   } else { \
+      text = "greater than"; \
+   } \
+   astError( AST__NONIN, "astOutline"#X": Could not find a pixel value %s " \
+             "%g in the supplied array.", status, text, (double) value ); \
+}
+
+/* Define a macro that uses the above macro to to create implementations
+   of FindInsidePoint for all operations. */
+#define MAKEALL_FINDINSIDEPOINT(X,Xtype) \
+MAKE_FINDINSIDEPOINT(X,Xtype,LT,AST__LT) \
+MAKE_FINDINSIDEPOINT(X,Xtype,LE,AST__LE) \
+MAKE_FINDINSIDEPOINT(X,Xtype,EQ,AST__EQ) \
+MAKE_FINDINSIDEPOINT(X,Xtype,GE,AST__GE) \
+MAKE_FINDINSIDEPOINT(X,Xtype,GT,AST__GT) \
+MAKE_FINDINSIDEPOINT(X,Xtype,NE,AST__NE)
+
+/* Expand the above macro to generate a function for each required
+   data type and operation. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKEALL_FINDINSIDEPOINT(LD,long double)
+#endif
+MAKEALL_FINDINSIDEPOINT(D,double)
+MAKEALL_FINDINSIDEPOINT(L,long int)
+MAKEALL_FINDINSIDEPOINT(UL,unsigned long int)
+MAKEALL_FINDINSIDEPOINT(I,int)
+MAKEALL_FINDINSIDEPOINT(UI,unsigned int)
+MAKEALL_FINDINSIDEPOINT(S,short int)
+MAKEALL_FINDINSIDEPOINT(US,unsigned short int)
+MAKEALL_FINDINSIDEPOINT(B,signed char)
+MAKEALL_FINDINSIDEPOINT(UB,unsigned char)
+MAKEALL_FINDINSIDEPOINT(F,float)
+
+/* Undefine the macros. */
+#undef MAKE_FINDINSIDEPOINT
+#undef MAKEALL_FINDINSIDEPOINT
+
+static void FindMax( Segment *seg, AstFrame *frm, double *x, double *y,
+                     int nv, int abs, int *status ){
+/*
+*  Name:
+*     FindMax
+
+*  Purpose:
+*     Find the maximum discrepancy between a given line segment and the
+*     Polygon being downsized.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void FindMax( Segment *seg, AstFrame *frm, double *x, double *y,
+*                   int nv, int abs, int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     The supplied Segment structure describes a range of vertices in
+*     the polygon being downsized. This function checks each of these
+*     vertices to find the one that lies furthest from the line joining the
+*     first and last vertices in the segment. The maximum error, and the
+*     vertex index at which this maximum error is found, is stored in the
+*     Segment structure.
+
+*  Parameters:
+*     seg
+*        The structure describing the range of vertices to check. It
+*        corresponds to a candidate edge in the downsized polygon.
+*     frm
+*        The Frame in which the positions are defined.
+*     x
+*        Pointer to the X axis values in the original Polygon.
+*     y
+*        Pointer to the Y axis values in the original Polygon.
+*     nv
+*        Total number of vertics in the old Polygon..
+*     abs
+*        If non-zero, then the stored maximum is the position with
+*        maximum absolute error. Otherwise, the stored maximum is the
+*        position with maximum positive error (positive errors are to the
+*        right when travelling from start to end of the segment).
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Local Variables: */
+   AstPointSet *pset1; /* PointSet holding vertex positions */
+   AstPointSet *pset2; /* PointSet holding offset par/perp components */
+   double **ptr1;      /* Pointers to "pset1" data arrays */
+   double **ptr2;      /* Pointers to "pset2" data arrays */
+   double *px;         /* Pointer to next X value */
+   double *py;         /* Pointer to next Y value */
+   double ax;          /* X value at start */
+   double ay;          /* Y value at start */
+   double ba;          /* Distance between a and b */
+   double bax;         /* X increment from a to b */
+   double bay;         /* Y increment from a to b */
+   double cax;         /* X increment from a to c */
+   double cay;         /* Y increment from a to c */
+   double end[ 2 ];    /* Position of starting vertex */
+   double error;       /* Error value for current vertex */
+   double start[ 2 ];  /* Position of starting vertex */
+   int i1;             /* Starting index (always in first cycle) */
+   int i2;             /* Ending index converted to first cycle */
+   int i2b;            /* Upper vertex limit in first cycle */
+   int i;              /* Loop count */
+   int n;              /* Number of vertices to check */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Stuff needed for handling cyclic redundancy of vertex indices. */
+   i1 = seg->i1;
+   i2 = seg->i2;
+   n = i2 - i1 - 1;
+   i2b = i2;
+   if( i2 >= nv ) {
+      i2 -= nv;
+      i2b = nv;
+   }
+
+/* If the segment has no intermediate vertices, set the segment error to
+   zero and return. */
+   if( n < 1 ) {
+      seg->error = 0.0;
+      seg->imax = i1;
+
+/* For speed, we use simple plane geometry if the Polygon is defined in a
+   simple Frame. */
+   } else if( !strcmp( astGetClass( frm ), "Frame" ) ) {
+
+/* Point "a" is the vertex that marks the start of the segment. Point "b"
+   is the vertex that marks the end of the segment. */
+      ax = x[ i1 ];
+      ay = y[ i1 ];
+      bax = x[ i2 ] - ax;
+      bay = y[ i2 ] - ay;
+      ba = sqrt( bax*bax + bay*bay );
+
+/* Initialise the largest error found so far. */
+      seg->error = -1.0;
+
+/* Check the vertices from the start (plus one) up to the end (minus one)
+   or the last vertex (which ever comes first). */
+      for( i = i1 + 1; i < i2b; i++ ) {
+
+/* Position "c" is the vertex being tested. Find the squared distance from
+   "c" to the line joining "a" and "b". */
+         cax = x[ i ] - ax;
+         cay = y[ i ] - ay;
+         error = ( bay*cax - cay*bax )/ba;
+         if( abs ) error = fabs( error );
+
+/* If this is the largest value found so far, record it. Note the error
+   here is a squared distance. */
+         if( error > seg->error ) {
+            seg->error = error;
+            seg->imax = i;
+         }
+      }
+
+/* If the end vertex is in the next cycle, check the remaining vertex
+   posI would have thought a telentitions in the same way. */
+      if( i2b != i2 ) {
+
+         for( i = 0; i < i2; i++ ) {
+
+            cax = x[ i ] - ax;
+            cay = y[ i ] - ay;
+            error = ( bay*cax - cay*bax )/ba;
+            if( abs ) error = fabs( error );
+
+            if( error > seg->error ) {
+               seg->error = error;
+               seg->imax = i + i2b;
+            }
+
+         }
+      }
+
+/* If the polygon is not defined in a simple Frame, we use the overloaded
+   Frame methods to do the geometry. */
+   } else {
+
+/* Create a PointSet to hold the positions of the vertices to test. We do
+   not need to test the start or end vertex. */
+      pset1 = astPointSet( n, 2, " ", status );
+      ptr1 = astGetPoints( pset1 );
+      if( astOK ) {
+
+/* Copy the vertex axis values form the start (plus one) up to the end
+   (minus one) vertex or the last vertex (which ever comes first). */
+         px = ptr1[ 0 ];
+         py = ptr1[ 1 ];
+
+         for( i = i1 + 1; i < i2b; i++ ){
+            *(px++) = x[ i ];
+            *(py++) = y[ i ];
+         }
+
+/* If the end vertex is in the next cycle, copy the remaining vertex
+   positions into the PointSet. */
+         if( i2b != i2 ) {
+            for( i = 0; i < i2; i++ ) {
+               *(px++) = x[ i ];
+               *(py++) = y[ i ];
+            }
+         }
+
+/* Record the start and end vertex positions. */
+         start[ 0 ] = x[ i1 ];
+         start[ 1 ] = y[ i1 ];
+         end[ 0 ] = x[ i2 ];
+         end[ 1 ] = y[ i2 ];
+
+/* Resolve the vector from the start to each vertex into two components,
+   parallel and perpendicular to the start->end vector. */
+         pset2 = astResolvePoints( frm, start, end, pset1, NULL );
+         ptr2 = astGetPoints( pset2 );
+         if( astOK ) {
+
+/* Find the vertex with largest perpendicular component. */
+            seg->error = -1.0;
+            py = ptr2[ 1 ];
+            for( i = 1; i <= n; i++ ) {
+
+               error = *(py++);
+               if( abs ) error = fabs( error );
+
+               if( error > seg->error ) {
+                  seg->error = error;
+                  seg->imax = i + i1;
+               }
+
+            }
+         }
+
+/* Free resources. */
+         pset2 = astAnnul( pset2 );
+      }
+      pset1 = astAnnul( pset1 );
+   }
+}
+
+static const char *GetAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     GetAttrib
+
+*  Purpose:
+*     Get the value of a specified attribute for a Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     const char *GetAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     Polygon member function (over-rides the protected astGetAttrib
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a pointer to the value of a specified
+*     attribute for a Polygon, formatted as a character string.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon.
+*     attrib
+*        Pointer to a null-terminated string containing the name of
+*        the attribute whose value is required. This name should be in
+*        lower case, with all white space removed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     - Pointer to a null-terminated string containing the attribute
+*     value.
+
+*  Notes:
+*     - The returned string pointer may point at memory allocated
+*     within the Polygon, or at static memory. The contents of the
+*     string may be over-written or the pointer may become invalid
+*     following a further invocation of the same function or any
+*     modification of the Polygon. A copy of the string should
+*     therefore be made if necessary.
+*     - A NULL pointer will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstPolygon *this;             /* Pointer to the Polygon structure */
+   const char *result;           /* Pointer value to return */
+   int ival;                     /* Integer attribute value */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(this_object);
+
+/* Obtain a pointer to the Polygon structure. */
+   this = (AstPolygon *) this_object;
+
+/* Compare "attrib" with each recognised attribute name in turn,
+   obtaining the value of the required attribute. If necessary, write
+   the value into "getattrib_buff" as a null-terminated string in an appropriate
+   format.  Set "result" to point at the result string. */
+
+/* SimpVertices. */
+/* ------------- */
+   if ( !strcmp( attrib, "simpvertices" ) ) {
+      ival = astGetSimpVertices( this );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%d", ival );
+         result = getattrib_buff;
+      }
+
+/* If the attribute name was not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      result = (*parent_getattrib)( this_object, attrib, status );
+   }
+
+/* Return the result. */
+   return result;
+
+}
+
+static int GetBounded( AstRegion *this, int *status ) {
+/*
+*  Name:
+*     GetBounded
+
+*  Purpose:
+*     Is the Region bounded?
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     int GetBounded( AstRegion *this, int *status )
+
+*  Class Membership:
+*     Polygon method (over-rides the astGetBounded method inherited from
+*     the Region class).
+
+*  Description:
+*     This function returns a flag indicating if the Region is bounded.
+*     The implementation provided by the base Region class is suitable
+*     for Region sub-classes representing the inside of a single closed
+*     curve (e.g. Circle, Interval, Box, etc). Other sub-classes (such as
+*     CmpRegion, PointList, etc ) may need to provide their own
+*     implementations.
+
+*  Parameters:
+*     this
+*        Pointer to the Region.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Non-zero if the Region is bounded. Zero otherwise.
+
+*/
+
+/* Local Variables: */
+   int neg;                  /* Has the Polygon been negated? */
+   int result;               /* Returned result */
+
+/* Initialise */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Ensure cached information is available. */
+   Cache( (AstPolygon *) this, status );
+
+/* See if the Polygon has been negated. */
+   neg = astGetNegated( this );
+
+/* If the polygon vertices are stored in anti-clockwise order, then the
+   polygon is bounded if it has not been negated. */
+   if( ( (AstPolygon *) this)->acw ) {
+      result = (! neg );
+
+/* If the polygon vertices are stored in clockwise order, then the
+   polygon is bounded if it has been negated. */
+   } else {
+      result = neg;
+   }
+
+/* Return the result. */
+   return result;
+}
+
+void astInitPolygonVtab_(  AstPolygonVtab *vtab, const char *name, int *status ) {
+/*
+*+
+*  Name:
+*     astInitPolygonVtab
+
+*  Purpose:
+*     Initialise a virtual function table for a Polygon.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void astInitPolygonVtab( AstPolygonVtab *vtab, const char *name )
+
+*  Class Membership:
+*     Polygon vtab initialiser.
+
+*  Description:
+*     This function initialises the component of a virtual function
+*     table which is used by the Polygon 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 */
+   AstObjectVtab *object;        /* Pointer to Object 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 astIsAPolygon) 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->Downsize = Downsize;
+
+/* Save the inherited pointers to methods that will be extended, and
+   replace them with pointers to the new member functions. */
+   object = (AstObjectVtab *) vtab;
+   mapping = (AstMappingVtab *) vtab;
+   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;
+
+   parent_clearattrib = object->ClearAttrib;
+   object->ClearAttrib = ClearAttrib;
+   parent_getattrib = object->GetAttrib;
+   object->GetAttrib = GetAttrib;
+   parent_setattrib = object->SetAttrib;
+   object->SetAttrib = SetAttrib;
+   parent_testattrib = object->TestAttrib;
+   object->TestAttrib = TestAttrib;
+
+   region->RegPins = RegPins;
+   region->RegBaseMesh = RegBaseMesh;
+   region->RegBaseBox = RegBaseBox;
+   region->RegTrace = RegTrace;
+   region->GetBounded = GetBounded;
+
+   vtab->ClearSimpVertices = ClearSimpVertices;
+   vtab->GetSimpVertices = GetSimpVertices;
+   vtab->SetSimpVertices = SetSimpVertices;
+   vtab->TestSimpVertices = TestSimpVertices;
+
+/* 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. */
+   astSetDump( vtab, Dump, "Polygon", "Polygonal region" );
+   astSetDelete( vtab, Delete );
+   astSetCopy( vtab, Copy );
+
+/* If we have just initialised the vtab for the current class, indicate
+   that the vtab is now initialised, and store a pointer to the class
+   identifier in the base "object" level of the vtab. */
+   if( vtab == &class_vtab ) {
+      class_init = 1;
+      astSetVtabClassIdentifier( vtab, &(vtab->id) );
+   }
+}
+
+static int IntCmp( const void *a, const void *b ){
+/*
+*  Name:
+*     IntCmp
+
+*  Purpose:
+*     An integer comparison function for the "qsort" function.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     int IntCmp( const void *a, const void *b )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     See the docs for "qsort".
+
+*  Parameters:
+*     a
+*        Pointer to the first int
+*     b
+*        Pointer to the second int
+
+*  Returnd Value:
+*     Positive, negative or zero, depending on whether a is larger than,
+*     equal to, or less than b.
+
+*/
+
+   return *((int*)a) - *((int*)b);
+}
+
+static Segment *NewSegment( Segment *seg, int i1, int i2, int nvert,
+                            int *status ){
+/*
+*  Name:
+*     NewSegment
+
+*  Purpose:
+*     Initialise a structure describing a segment of the new Polygon
+*     created by astDownsize.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     Segment *NewSegment( Segment *seg, int i1, int i2, int nvert,
+*                          int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     This function initialises the contents of a structure describing
+*     the specified range of vertices within a Polygon. The cyclic nature
+*     of vertex indices is taken into account.
+*
+*     If no structure is supplied, memory is allocated to hold a new
+*     structure.
+
+*  Parameters:
+*     seg
+*        Pointer to a structure to initialise, or NULL if a new structure
+*        is to be allocated.
+*     i1
+*        The index of a vertex within the old Polygon (supplied to
+*        astDownsize) that marks the start of the new line segment in
+*        the downsized polygon.
+*     i2
+*        The index of a vertex within the old Polygon (supplied to
+*        astDownsize) that marks the end of the new line segment in
+*        the downsized polygon.
+*     nvert
+*        Total number of vertics in the old Polygon..
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returnd Value:
+*     Pointer to the initialised Segment structure. It should be freed using
+*     astFree when no longer needed.
+
+*/
+
+/* Local Variables: */
+   Segment *result;
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Get a pointer to the structure to be initialised, allocating memory
+   for a new structure if none was supplied. */
+   result = seg ? seg : astMalloc( sizeof( Segment ) );
+
+/* Check the pointer can be used safely. */
+   if( result ) {
+
+/* If the supplied ending index is less than the starting index, the
+   ending index must have gone all the way round the polygon and started
+   round again. Increase the ending index by the number of vertices to
+   put it in the same cycle as the starting index. */
+      if( i2 < i1 ) i2 += nvert;
+
+/* If the supplied starting index is within the first cycle (i.e. zero ->
+   nvert-1 ), use the indices as they are (which may mean that the ending
+   index is greater than nvert, but this is handled correctly by other
+   functions). */
+      if( i1 < nvert ) {
+         result->i1 = i1;
+         result->i2 = i2;
+
+/* If the supplied starting index is within the second cycle (i.e. nvert
+   or greater) the ending index will be even greater, so we can reduce
+   both by "nvert" to put them both in the first cycle. The goal is that
+   the starting index should always be in the first cycle, but the ending
+   index may possibly be in the second cycle. */
+      } else {
+         result->i1 = i1 - nvert;
+         result->i2 = i2 - nvert;
+      }
+
+/* Nullify the links to other Segments */
+      result->next = NULL;
+      result->prev = NULL;
+   }
+
+/* Return the pointer to the new Segment structure. */
+   return result;
+}
+
+/*
+*++
+*  Name:
+c     astOutline<X>
+f     AST_OUTLINE<X>
+
+*  Purpose:
+*     Create a new Polygon outling values in a 2D data grid.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "polygon.h"
+c     AstPolygon *astOutline<X>( <Xtype> value, int oper, const <Xtype> array[],
+c                                const int lbnd[2], const int ubnd[2], double maxerr,
+c                                int maxvert, const int inside[2], int starpix )
+f     RESULT = AST_OUTLINE<X>( VALUE, OPER, ARRAY, LBND, UBND, MAXERR,
+f                              MAXVERT, INSIDE, STARPIX, STATUS )
+
+*  Class Membership:
+*     Polygon method.
+
+*  Description:
+*     This is a set of functions that create a Polygon enclosing a single
+*     contiguous set of pixels that have a specified value within a gridded
+*     2-dimensional data array (e.g. an image).
+*
+*     A basic 2-dimensional Frame is used to represent the pixel coordinate
+*     system in the returned Polygon. The Domain attribute is set to
+*     "PIXEL", the Title attribute is set to "Pixel coordinates", and the
+*     Unit attribute for each axis is set to "pixel". All other
+*     attributes are left unset. The nature of the pixel coordinate system
+*     is determined by parameter
+c     "starpix".
+f     STARPIX.
+*
+*     The
+c     "maxerr" and "maxvert"
+f     MAXERR and MAXVERT
+*     parameters can be used to control how accurately the returned
+*     Polygon represents the required region in the data array. The
+*     number of vertices in the returned Polygon will be the minimum
+*     needed to achieve the required accuracy.
+*
+*     You should use a function which matches the numerical type of the
+*     data you are processing by replacing <X> in the generic function
+*     name
+c     astOutline<X>
+f     AST_OUTLINE<X>
+c     by an appropriate 1- or 2-character type code. For example, if you
+*     are procesing data with type
+c     "float", you should use the function astOutlineF
+f     REAL, you should use the function AST_OUTLINER
+*     (see the "Data Type Codes" section below for the codes appropriate to
+*     other numerical types).
+
+*  Parameters:
+c     value
+f     VALUE = <Xtype> (Given)
+*        A data value that specifies the pixels to be outlined.
+c     oper
+f     OPER = INTEGER (Given)
+*        Indicates how the
+c        "value"
+f        VALUE
+*        parameter is used to select the outlined pixels. It can
+*        have any of the following values:
+c        - AST__LT: outline pixels with value less than "value".
+c        - AST__LE: outline pixels with value less than or equal to "value".
+c        - AST__EQ: outline pixels with value equal to "value".
+c        - AST__NE: outline pixels with value not equal to "value".
+c        - AST__GE: outline pixels with value greater than or equal to "value".
+c        - AST__GT: outline pixels with value greater than "value".
+f        - AST__LT: outline pixels with value less than VALUE.
+f        - AST__LE: outline pixels with value less than or equal to VALUE.
+f        - AST__EQ: outline pixels with value equal to VALUE.
+f        - AST__NE: outline pixels with value not equal to VALUE.
+f        - AST__GE: outline pixels with value greater than or equal to VALUE.
+f        - AST__GT: outline pixels with value greater than VALUE.
+c     array
+f     ARRAY( * ) = <Xtype> (Given)
+c        Pointer to a
+f        A
+*        2-dimensional array containing the data to be processed.  The
+*        numerical type of this array should match the 1- or
+*        2-character type code appended to the function name (e.g. if
+c        you are using astOutlineF, the type of each array element
+c        should be "float").
+f        you are using AST_OUTLINER, the type of each array element
+f        should be REAL).
+*
+*        The storage order of data within this array should be such
+*        that the index of the first grid dimension varies most
+*        rapidly and that of the second dimension least rapidly
+c        (i.e. Fortran array indexing is used).
+f        (i.e. normal Fortran array storage order).
+c     lbnd
+f     LBND( 2 ) = INTEGER (Given)
+c        Pointer to an array of two integers
+f        An array
+*        containing the pixel index of the first pixel in the input grid
+*        along each dimension.
+c     ubnd
+f     UBND( 2) = INTEGER (Given)
+c        Pointer to an array of two integers
+f        An array
+*        containing the pixel index of the last pixel in the input grid
+*        along each dimension.
+*
+c        Note that "lbnd" and "ubnd" together define the shape
+f        Note that LBND and UBND together define the shape
+*        and size of the input pixel grid, its extent along a particular
+c        (j'th) dimension being ubnd[j]-lbnd[j]+1 pixels.
+f        (J'th) dimension being UBND(J)-LBND(J)+1 pixels.
+*        For FITS images,
+c        the lbnd values will be 1 and the ubnd
+f        the LBND values will be 1 and the UBND
+*        values will be equal to the NAXISi header values. Other
+*        data systems, such as the Starlink NDF system, allow an
+c        arbitrary pixel origin to be used (i.e. lbnd
+f        arbitrary pixel origin to be used (i.e. LBND
+*        is not necessarily 1).
+*
+*        These bounds also define the input grid's floating point coordinate
+*        system, each pixel having unit extent along each dimension with
+*        integral coordinate values at its centre or upper corner, as selected
+*        by parameter
+c        "starpix".
+f        STARPIX.
+c     maxerr
+f     MAXERR = DOUBLE PRECISION (Given)
+*        Together with
+c        "maxvert",
+f        MAXVERT,
+*        this determines how accurately the returned Polygon represents
+*        the required region of the data array. It gives the target
+*        discrepancy between the returned Polygon and the accurate outline
+*        in the data array, expressed as a number of pixels. Insignificant
+*        vertices are removed from the accurate outline, one by one, until
+*        the number of vertices remaining in the returned Polygon equals
+c        "maxvert",
+f        MAXVERT,
+*        or the largest discrepancy between the accurate outline and the
+*        returned Polygon is greater than
+c        "maxerr". If "maxerr"
+f        MAXERR. If MAXERR
+*        is zero or less, its value is ignored and the returned Polygon will
+*        have the number of vertices specified by
+c        "maxvert".
+f        MAXVERT.
+c     maxvert
+f     MAXVERT = INTEGER (Given)
+*        Together with
+c        "maxerr",
+f        MAXERR,
+*        this determines how accurately the returned Polygon represents
+*        the required region of the data array. It gives the maximum
+*        allowed number of vertices in the returned Polygon. Insignificant
+*        vertices are removed from the accurate outline, one by one, until
+*        the number of vertices remaining in the returned Polygon equals
+c        "maxvert",
+f        MAXVERT,
+*        or the largest discrepancy between the accurate outline and the
+*        returned Polygon is greater than
+c        "maxerr". If "maxvert"
+f        MAXERR. If MAXVERT
+*        is less than 3, its value is ignored and the number of vertices in
+*        the returned Polygon will be the minimum needed to ensure that the
+*        discrepancy between the accurate outline and the returned
+*        Polygon is less than
+c        "maxerr".
+f        MAXERR.
+c     inside
+f     INSIDE( 2 ) = INTEGER (Given)
+c        Pointer to an array of two integers
+f        An array
+*        containing the pixel indices of a pixel known to be inside the
+*        required region. This is needed because the supplied data
+*        array may contain several disjoint areas of pixels that satisfy
+*        the criterion specified by
+c        "value" and "oper".
+f        VALUE and OPER.
+*        In such cases, the area described by the returned Polygon will
+*        be the one that contains the pixel specified by
+c        "inside".
+f        INSIDE.
+*        If the specified pixel is outside the bounds given by
+c        "lbnd" and "ubnd",
+f        LBND and UBND,
+*        or has a value that does not meet the criterion specified by
+c        "value" and "oper",
+f        VALUE and OPER,
+*        then this function will search for a suitable pixel. The search
+*        starts at the central pixel and proceeds in a spiral manner until
+*        a pixel is found that meets the specified crierion.
+c     starpix
+f     STARPIX = LOGICAL (Given)
+*        A flag indicating the nature of the pixel coordinate system used
+*        to describe the vertex positions in the returned Polygon. If
+c        non-zero,
+f        .TRUE.,
+*        the standard Starlink definition of pixel coordinate is used in
+*        which a pixel with integer index I spans a range of pixel coordinate
+*        from (I-1) to I (i.e. pixel corners have integral pixel coordinates).
+c        If zero,
+f        If .FALSE.,
+*        the definition of pixel coordinate used by other AST functions
+c        such as astResample, astMask,
+f        such as AST_RESAMPLE, AST_MASK,
+*        etc., is used. In this definition, a pixel with integer index I
+*        spans a range of pixel coordinate from (I-0.5) to (I+0.5) (i.e.
+*        pixel centres have integral pixel coordinates).
+f     STATUS = INTEGER (Given and Returned)
+f        The global status.
+
+*  Returned Value:
+c     astOutline<X>()
+f     AST_OUTLINE<X> = INTEGER
+*        A pointer to the required Polygon.
+
+*  Notes:
+*     - This function proceeds by first finding a very accurate polygon,
+*     and then removing insignificant vertices from this fine polygon
+*     using
+c     astDownsize.
+f     AST_DOWNSIZE.
+*     - The returned Polygon is the outer boundary of the contiguous set
+*     of pixels that includes ths specified "inside" point, and satisfy
+*     the specified value requirement. This set of pixels may potentially
+*     include "holes" where the pixel values fail to meet the specified
+*     value requirement. Such holes will be ignored by this function.
+c     - NULL
+f     - AST__NULL
+*     will be returned if this function is invoked with the global
+*     error status set, or if it should fail for any reason.
+
+*  Data Type Codes:
+*     To select the appropriate masking function, you should
+c     replace <X> in the generic function name astOutline<X> with a
+f     replace <X> in the generic function name AST_OUTLINE<X> with a
+*     1- or 2-character data type code, so as to match the numerical
+*     type <Xtype> of the data you are processing, as follows:
+c     - D: double
+c     - F: float
+c     - L: long int
+c     - UL: unsigned long int
+c     - I: int
+c     - UI: unsigned int
+c     - S: short int
+c     - US: unsigned short int
+c     - B: byte (signed char)
+c     - UB: unsigned byte (unsigned char)
+f     - D: DOUBLE PRECISION
+f     - R: REAL
+f     - I: INTEGER
+f     - UI: INTEGER (treated as unsigned)
+f     - S: INTEGER*2 (short integer)
+f     - US: INTEGER*2 (short integer, treated as unsigned)
+f     - B: BYTE (treated as signed)
+f     - UB: BYTE (treated as unsigned)
+*
+c     For example, astOutlineD would be used to process "double"
+c     data, while astOutlineS would be used to process "short int"
+c     data, etc.
+f     For example, AST_OUTLINED would be used to process DOUBLE
+f     PRECISION data, while AST_OUTLINES would be used to process
+f     short integer data (stored in an INTEGER*2 array), etc.
+f
+f     For compatibility with other Starlink facilities, the codes W
+f     and UW are provided as synonyms for S and US respectively (but
+f     only in the Fortran interface to AST).
+
+*--
+*/
+/* Define a macro to implement the function for a specific data
+   type. Note, this function cannot be a virtual function since the
+   argument list does not include a Polygon, and so no virtual function
+   table is available. */
+#define MAKE_OUTLINE(X,Xtype) \
+AstPolygon *astOutline##X##_( Xtype value, int oper, const Xtype array[], \
+                              const int lbnd[2], const int ubnd[2], double maxerr, \
+                              int maxvert, const int inside[2], int starpix, \
+                              int *status ) { \
+\
+/* Local Variables: */ \
+   AstFrame *frm;            /* Frame in which to define the Polygon */ \
+   AstPointSet *candidate;   /* Candidate polygon vertices */ \
+   AstPointSet *pset;        /* PointSet holding downsized polygon vertices */ \
+   AstPolygon *result;       /* Result value to return */ \
+   const Xtype *pv;          /* Pointer to next test point */ \
+   Xtype v;                  /* Value of current pixel */ \
+   double **ptr;             /* Pointers to PointSet arrays */ \
+   int boxsize;              /* Half width of smoothign box in vertices */ \
+   int inx;                  /* X index of inside point */ \
+   int iny;                  /* Y index of inside point */ \
+   int iv;                   /* Vector index of next test pixel */ \
+   int ixv;                  /* X pixel index of next test point */ \
+   int nv0;                  /* Number of vertices in accurate outline */ \
+   int nx;                   /* Length of array x axis */ \
+   int smooth;               /* Do we need to smooth the polygon? */ \
+   int stop_at_invalid;      /* Indicates when to stop rightwards search */ \
+   int tmp;                  /* Alternative boxsize */ \
+   int valid;                /* Does current pixel meet requirements? */ \
+   static double junk[ 6 ] = {0.0, 0.0, 1.0, 1.0, 0.0, 1.0 }; /* Junk poly */ \
+\
+/* Initialise. */ \
+   result = NULL; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return result; \
+\
+/* Avoid compiler warnings. */ \
+   iv = 0; \
+\
+/* If we are going to be smoothing the polygon before downsizing it, we \
+   need to ensure that the full polygon is retained within TraceEdge. if \
+   this is not the case, TraceEdge can remove all vertices from straight \
+   lines, except for the vertices that mark the beinning and end of the \
+   straight line. */ \
+   smooth = ( maxerr > 0.0 || maxvert > 2 ); \
+\
+/* Store the X dimension of the array. */ \
+   nx = ubnd[ 0 ] - lbnd[ 0 ] + 1; \
+\
+/* See if a valid inside point was supplied. It must be inside the bounds \
+   of the array, and must have a pixel value that meets the specified \
+   requirement. */ \
+   inx = inside[ 0 ]; \
+   iny = inside[ 1 ]; \
+   valid = ( inx >= lbnd[ 0 ] && inx <= ubnd[ 0 ] && \
+             iny >= lbnd[ 1 ] && iny <= ubnd[ 1 ] ); \
+\
+   if( valid  ) { \
+      iv = ( inx - lbnd[ 0 ] ) + (iny - lbnd[ 1 ] )*nx; \
+      v = array[ iv ]; \
+\
+      if( oper == AST__LT ) { \
+         valid = ( v < value ); \
+\
+      } else if( oper == AST__LE ) { \
+         valid = ( v <= value ); \
+\
+      } else if( oper == AST__EQ ) { \
+         valid = ( v == value ); \
+\
+      } else if( oper == AST__NE ) { \
+         valid = ( v != value ); \
+\
+      } else if( oper == AST__GE ) { \
+         valid = ( v >= value ); \
+\
+      } else if( oper == AST__GT ) { \
+         valid = ( v > value ); \
+\
+      } else if( astOK ){ \
+         astError( AST__OPRIN, "astOutline"#X": Invalid operation code " \
+                   "(%d) supplied (programming error).", status, oper ); \
+      } \
+   } \
+\
+/* If no valid inside point was supplied, find one now. */ \
+   if( !valid ) { \
+\
+      if( oper == AST__LT ) { \
+         FindInsidePointLT##X( value, array, lbnd, ubnd, &inx, &iny, &iv, status ); \
+\
+      } else if( oper == AST__LE ) { \
+         FindInsidePointLE##X( value, array, lbnd, ubnd, &inx, &iny, &iv, status ); \
+\
+      } else if( oper == AST__EQ ) { \
+         FindInsidePointEQ##X( value, array, lbnd, ubnd, &inx, &iny, &iv, status ); \
+\
+      } else if( oper == AST__NE ) { \
+         FindInsidePointNE##X( value, array, lbnd, ubnd, &inx, &iny, &iv, status ); \
+\
+      } else if( oper == AST__GE ) { \
+         FindInsidePointGE##X( value, array, lbnd, ubnd, &inx, &iny, &iv, status ); \
+\
+      } else if( oper == AST__GT ) { \
+         FindInsidePointGT##X( value, array, lbnd, ubnd, &inx, &iny, &iv, status ); \
+\
+      } else if( astOK ){ \
+         astError( AST__OPRIN, "astOutline"#X": Invalid operation code " \
+                   "(%d) supplied (programming error).", status, oper ); \
+      } \
+   } \
+\
+/* We now need to find a point on the boundary of the region containing \
+   the inside point. Starting at the inside point, move to the right \
+   through the array until a pixel is found which fails to meet the value \
+   requirement or the edge of the array is reached. */ \
+\
+   candidate = NULL; \
+   pv = array + iv; \
+   ixv = inx; \
+   stop_at_invalid = 1; \
+\
+   while( ++ixv <= ubnd[ 0 ] ) { \
+\
+/* Get the next pixel value. */ \
+      v = *(++pv); \
+\
+/* See if it meets the value requirement. */ \
+      if( oper == AST__LT ) { \
+         valid = ( v < value ); \
+\
+      } else if( oper == AST__LE ) { \
+         valid = ( v <= value ); \
+\
+      } else if( oper == AST__EQ ) { \
+         valid = ( v == value ); \
+\
+      } else if( oper == AST__NE ) { \
+         valid = ( v != value ); \
+\
+      } else if( oper == AST__GE ) { \
+         valid = ( v >= value ); \
+\
+      } else if( oper == AST__GT ) { \
+         valid = ( v > value ); \
+\
+      } else if( astOK ){ \
+         astError( AST__OPRIN, "astOutline"#X": Invalid operation code " \
+                   "(%d) supplied (programming error).", status, oper ); \
+         break; \
+      } \
+\
+/* If we are currently looking for the next invalid pixel, and this pixel \
+   is invalid... */ \
+      if( stop_at_invalid ) { \
+         if( ! valid ) { \
+\
+/* The current pixel may be on the required polygon, or it may be on the  \
+   edge of a hole contained within the region being outlined. We would  \
+   like to jump over such holes so that we can continue to look for the  \
+   real edge of the region being outlined. In order to determine if we  \
+   have reached a hole, we trace the edge that passes through the current  \
+   pixel, forming a candidate polygon in the process. In the process, We  \
+   see if the inside point falls within this candidate polygon. If it does  \
+   then the polygon is accepted as the required polygon. Otherwise, it is  \
+   rejected as a mere hole, and we continue moving away from the inside  \
+   point, looking for a new edge. */ \
+            if( oper == AST__LT ) { \
+               candidate = TraceEdgeLT##X( value, array, lbnd, ubnd, iv - 1, \
+                                           ixv - 1, iny, starpix, smooth, status ); \
+\
+            } else if( oper == AST__LE ) { \
+               candidate = TraceEdgeLE##X( value, array, lbnd, ubnd, iv - 1, \
+                                           ixv - 1, iny, starpix, smooth, status ); \
+\
+            } else if( oper == AST__EQ ) { \
+               candidate = TraceEdgeEQ##X( value, array, lbnd, ubnd, iv - 1, \
+                                           ixv - 1, iny, starpix, smooth, status ); \
+\
+            } else if( oper == AST__NE ) { \
+               candidate = TraceEdgeNE##X( value, array, lbnd, ubnd, iv - 1, \
+                                           ixv - 1, iny, starpix, smooth, status ); \
+\
+            } else if( oper == AST__GE ) { \
+               candidate = TraceEdgeGE##X( value, array, lbnd, ubnd, iv - 1, \
+                                           ixv - 1, iny, starpix, smooth, status ); \
+\
+            } else if( oper == AST__GT ) { \
+               candidate = TraceEdgeGT##X( value, array, lbnd, ubnd, iv - 1, \
+                                           ixv - 1, iny, starpix, smooth, status ); \
+\
+            } else if( astOK ){ \
+               astError( AST__OPRIN, "astOutline"#X": Invalid operation code " \
+                         "(%d) supplied (programming error).", status, oper ); \
+            } \
+\
+/* If the candidate polygon is the required polygon, break out of the \
+   loop. Otherwise, indicate that we want to continue moving right, \
+   across the hole, until we reach the far side of the hole (i.e. find \
+   the next valid pixel). */ \
+            if( candidate ) { \
+               break; \
+            } else { \
+               stop_at_invalid = 0; \
+            } \
+         } \
+\
+/* If we are currently looking for the next valid pixel, and the current \
+   pixel is valid... */ \
+      } else if( valid ) { \
+\
+/* We have reached the far side of a hole. Continue moving right, looking \
+   now for the next invalid pixel (which may be on the required polygon). */ \
+         stop_at_invalid = 1; \
+      } \
+   } \
+\
+/* If we have not yet found the required polygon, we must have reached \
+   the right hand edge of the array. So we now follow the edge of the \
+   array round until we meet the boundary of the required region. */ \
+   if( !candidate ) { \
+      if( oper == AST__LT ) { \
+         candidate = TraceEdgeLT##X( value, array, lbnd, ubnd, iv - 1, \
+                                     ixv - 1, iny, starpix, smooth, status ); \
+\
+      } else if( oper == AST__LE ) { \
+         candidate = TraceEdgeLE##X( value, array, lbnd, ubnd, iv - 1, \
+                                     ixv - 1, iny, starpix, smooth, status ); \
+\
+      } else if( oper == AST__EQ ) { \
+         candidate = TraceEdgeEQ##X( value, array, lbnd, ubnd, iv - 1, \
+                                     ixv - 1, iny, starpix, smooth, status ); \
+\
+      } else if( oper == AST__NE ) { \
+         candidate = TraceEdgeNE##X( value, array, lbnd, ubnd, iv - 1, \
+                                     ixv - 1, iny, starpix, smooth, status ); \
+\
+      } else if( oper == AST__GE ) { \
+         candidate = TraceEdgeGE##X( value, array, lbnd, ubnd, iv - 1, \
+                                     ixv - 1, iny, starpix, smooth, status ); \
+\
+      } else if( oper == AST__GT ) { \
+         candidate = TraceEdgeGT##X( value, array, lbnd, ubnd, iv - 1, \
+                                     ixv - 1, iny, starpix, smooth, status ); \
+\
+      } else if( astOK ){ \
+         astError( AST__OPRIN, "astOutline"#X": Invalid operation code " \
+                   "(%d) supplied (programming error).", status, oper ); \
+      } \
+   } \
+\
+/* If required smooth the full resolution polygon before downsizing it. */ \
+   if( smooth ) { \
+\
+/* Initially, set the boxsize to be equal to the required accouracy. */ \
+      if( maxerr > 0 ) { \
+         boxsize = (int) maxerr; \
+      } else { \
+         boxsize = INT_MAX; \
+      } \
+\
+/* Determine a second box size equal to the average number of vertices in \
+   the accurate outline, per vertex in the returned Polygon. */ \
+      nv0 = astGetNpoint( candidate ); \
+      if( maxvert > 2 ) { \
+         tmp = nv0/(2*maxvert); \
+      } else { \
+         tmp = INT_MAX; \
+      } \
+\
+/* Use the minimum of the two box sizes. */ \
+      if( tmp < boxsize ) boxsize = tmp; \
+\
+/* Ensure the box is sufficiently small to allow at least 10 full boxes \
+   (=20 half boxes) around the polygon. */ \
+      tmp = nv0/20; \
+      if( tmp < boxsize ) boxsize = tmp; \
+      if( boxsize == 0 ) boxsize = 1; \
+\
+/* Smooth the polygon. */ \
+      SmoothPoly( candidate, boxsize, 1.0, status ); \
+   } \
+\
+/* Reduce the number of vertices in the outline. */ \
+   frm = astFrame( 2, "Domain=PIXEL,Unit(1)=pixel,Unit(2)=pixel," \
+                   "Title=Pixel coordinates", status ); \
+   pset = DownsizePoly( candidate, maxerr, maxvert, frm, status ); \
+\
+/* Create a default Polygon with 3 junk vertices. */ \
+   result = astPolygon( frm, 3, 3, junk, NULL, " ", status ); \
+\
+/* Change the PointSet within the Polygon to the one created above. */ \
+   SetPointSet( result, pset, status ); \
+\
+/* Free resources. Note, we need to free the arrays within the candidate \
+   PointSet explicitly, since they were not created as part of the \
+   construction of the PointSet (see TraceEdge). */ \
+   pset = astAnnul( pset ); \
+   frm = astAnnul( frm ); \
+   ptr = astGetPoints( candidate ); \
+   if( astOK ) { \
+      astFree( ptr[ 0 ] ); \
+      astFree( ptr[ 1 ] ); \
+   } \
+   candidate = astAnnul( candidate ); \
+\
+/* If an error occurred, clear the returned result. */ \
+   if ( !astOK ) result = astAnnul( result ); \
+\
+/* Return the result. */ \
+   return result; \
+}
+
+
+/* Expand the above macro to generate a function for each required
+   data type. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKE_OUTLINE(LD,long double)
+#endif
+MAKE_OUTLINE(D,double)
+MAKE_OUTLINE(L,long int)
+MAKE_OUTLINE(UL,unsigned long int)
+MAKE_OUTLINE(I,int)
+MAKE_OUTLINE(UI,unsigned int)
+MAKE_OUTLINE(S,short int)
+MAKE_OUTLINE(US,unsigned short int)
+MAKE_OUTLINE(B,signed char)
+MAKE_OUTLINE(UB,unsigned char)
+MAKE_OUTLINE(F,float)
+
+/* Undefine the macros. */
+#undef MAKE_OUTLINE
+
+/*
+*  Name:
+*     PartHull
+
+*  Purpose:
+*     Find the convex hull enclosing selected pixels in one corner of a 2D array.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void PartHull<Oper><X>( <Xtype> value, const <Xtype> array[], int xdim,
+*                             int ydim, int xs, int ys, int xe, int ye,
+*                             int starpix, const int lbnd[2], double **xvert,
+*                             double **yvert, int *nvert, int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     This function uses an algorithm similar to "Andrew's Monotone Chain
+*     Algorithm" to create a list of vertices describing one corner of the
+*     convex hull enclosing the selected pixels in the supplied array.
+*     The corner is defined to be the area of the array to the right of
+*     the line from (xs,ys) to (xe,ye).
+
+*  Parameters:
+*     value
+*        A data value that specifies the pixels to be selected.
+*     array
+*        Pointer to a 2-dimensional array containing the data to be
+*        processed. The numerical type of this array should match the 1-
+*        or 2-character type code appended to the function name.
+*     xdim
+*        The number of pixels along each row of the array.
+*     ydim
+*        The number of rows in the array.
+*     xs
+*        The X GRID index of the first pixel on the line to be checked.
+*     ys
+*        The Y GRID index of the first pixel on the line to be checked.
+*     xe
+*        The X GRID index of the last pixel on the line to be checked.
+*     ye
+*        The Y GRID index of the last pixel on the line to be checked.
+*     starpix
+*        If non-zero, the usual Starlink definition of pixel coordinate
+*        is used (integral values at pixel corners). Otherwise, the
+*        system used by other AST functions such as astResample is used
+*        (integral values at pixel centres).
+*     lbnd
+*        The lower pixel index bounds of the array.
+*     xvert
+*        Address of a pointer in which to return a pointer to the list
+*        of GRID x values on the hull.
+*     yvert
+*        Address of a pointer in which to return a pointer to the list
+*        of GRID y values on the hull.
+*     nvert
+*        Address of a pointer in which to return the number of points in
+*        the returned xvert and yvert arrays.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Define a macro to implement the function for a specific data
+   type and operation. */
+#define MAKE_PARTHULL(X,Xtype,Oper,OperI) \
+static void PartHull##Oper##X( Xtype value, const Xtype array[], int xdim, \
+                               int ydim, int xs, int ys, int xe, int ye, \
+                               int starpix, const int lbnd[2], \
+                               double **xvert, double **yvert, int *nvert, \
+                               int *status ) { \
+\
+/* Local Variables: */ \
+   const Xtype *pc; \
+   double *pxy; \
+   double dx2; \
+   double dx1; \
+   double dy1; \
+   double dy2; \
+   double off; \
+   double xdelta; \
+   int ivert; \
+   int ix; \
+   int iy; \
+   int x0; \
+   int x1; \
+   int xl; \
+   int xlim; \
+   int xr; \
+   int yinc; \
+\
+/* Initialise */ \
+   *yvert = NULL; \
+   *xvert = NULL; \
+   *nvert = 0; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return; \
+\
+/* If the line has zero length. just return a single vertex. */ \
+   if( xs == xe && ys == ye ) { \
+      *xvert = astMalloc( sizeof( double ) ); \
+      *yvert = astMalloc( sizeof( double ) ); \
+      if( astOK ) { \
+         if( starpix ) { \
+            (*xvert)[ 0 ] = xs + lbnd[ 0 ] - 1.5; \
+            (*yvert)[ 0 ] = ys + lbnd[ 1 ] - 1.5; \
+         } else { \
+            (*xvert)[ 0 ] = xs + lbnd[ 0 ] - 1.0; \
+            (*yvert)[ 0 ] = ys + lbnd[ 1 ] - 1.0; \
+         } \
+         *nvert = 1; \
+      } \
+      return; \
+   } \
+\
+/* Otherwise check the line is sloping. */ \
+   if( xs == xe ) { \
+      astError( AST__INTER, "astOutline(Polygon): Bounding box " \
+                "has zero width (internal AST programming error).", \
+                status ); \
+      return; \
+   } else if( ys == ye ) { \
+      astError( AST__INTER, "astOutline(Polygon): Bounding box " \
+                "has zero height (internal AST programming error).", \
+                status ); \
+      return; \
+   } \
+\
+/* Calculate the difference in length between adjacent rows of the area \
+   to be tested. */ \
+   xdelta = ((double)( xe - xs ))/((double)( ye - ys )); \
+\
+/* The left and right X limits */ \
+   if( xe > xs ) { \
+      xl = xs; \
+      xr = xe; \
+   } else { \
+      xl = xe; \
+      xr = xs; \
+   } \
+\
+/* Get the increment in row number as we move from the start to the end \
+   of the line. */ \
+   yinc = ( ye > ys ) ? 1 : -1; \
+\
+/* Loop round all rows that cross the region to be tested, from start to \
+   end of the supplied line. */ \
+   iy = ys; \
+   while( astOK ) { \
+\
+/* Get the GRID X coord where the line crosses this row. */ \
+      xlim = (int)( 0.5 + xs + xdelta*( iy - ys ) ); \
+\
+/* Get the index of the first and last columns to be tested on this row. */ \
+      if( yinc < 0 ) { \
+         x0 = xl; \
+         x1 = xlim; \
+      } else { \
+         x0 = xlim; \
+         x1 = xr; \
+      } \
+\
+/* Get a pointer to the first pixel to be tested at this row. */ \
+      pc = array + ( iy - 1 )*xdim + x0 - 1; \
+\
+/* Loop round all columns to be tested in this row. */ \
+      for( ix = x0; ix <= x1 && astOK; ix++,pc++ ) { \
+\
+/* Ignore pixels that are not selected. */ \
+         if( ISVALID(*pc,OperI,value) ) { \
+\
+/* If this is the very first pixel, initialise the hull to contain just \
+   the first pixel. */ \
+            if( *nvert == 0 ){ \
+               *xvert = astMalloc( 200*sizeof( double ) ); \
+               *yvert = astMalloc( 200*sizeof( double ) ); \
+               if( astOK ) { \
+                  (*xvert)[ 0 ] = ix; \
+                  (*yvert)[ 0 ] = iy; \
+                  *nvert = 1; \
+               } else { \
+                  break; \
+               } \
+\
+/* Otherwise.... */ \
+            } else { \
+\
+/* Loop until the hull has been corrected to include the current pixel. */ \
+               while( 1 ) { \
+\
+/* If the hull currently contains only one pixel, add the current pixel to \
+   the end of the hull. */ \
+                  if( *nvert == 1 ){ \
+                     (*xvert)[ 1 ] = ix; \
+                     (*yvert)[ 1 ] = iy; \
+                     *nvert = 2; \
+                     break; \
+\
+/* Otherwise... */ \
+                  } else { \
+\
+/* Extend the line from the last-but-one pixel on the hull to the last \
+   pixel on the hull, and see if the current pixel is to the left of \
+   this line. If it is, it too is on the hull and so push it onto the end \
+   of the list of vertices. */ \
+                     dx1 = (*xvert)[ *nvert - 1 ] - (*xvert)[ *nvert - 2 ]; \
+                     dy1 = (*yvert)[ *nvert - 1 ] - (*yvert)[ *nvert - 2 ]; \
+                     dx2 = ix - (*xvert)[ *nvert - 2 ]; \
+                     dy2 = iy - (*yvert)[ *nvert - 2 ]; \
+\
+                     if( dx1*dy2 > dx2*dy1 ) { \
+                        ivert = (*nvert)++; \
+                        *xvert = astGrow( *xvert, *nvert, sizeof( double ) );  \
+                        *yvert = astGrow( *yvert, *nvert, sizeof( double ) );  \
+                        if( astOK ) {  \
+                           (*xvert)[ ivert ] = ix; \
+                           (*yvert)[ ivert ] = iy; \
+                        }  \
+\
+/* Leave the loop now that the new point is on the hull. */ \
+                        break; \
+\
+/* If the new point is to the left of the line, then the last point \
+   previously thought to be on hull is in fact not on the hull, so remove \
+   it. We then loop again to compare the new pixel with modified hull. */ \
+                     } else { \
+                        (*nvert)--; \
+                     } \
+                  } \
+               } \
+            } \
+         } \
+      } \
+\
+      if( iy == ye ) { \
+         break; \
+      } else { \
+         iy += yinc; \
+      } \
+\
+   } \
+\
+/* Convert GRID coords to PIXEL coords. */ \
+   if( astOK ) { \
+      pxy = *xvert; \
+      off = starpix ? lbnd[ 0 ] - 1.5 : lbnd[ 0 ] - 1.0; \
+      for( ivert = 0; ivert < *nvert; ivert++ ) *(pxy++) += off; \
+\
+      pxy = *yvert; \
+      off = starpix ? lbnd[ 1 ] - 1.5 : lbnd[ 1 ] - 1.0; \
+      for( ivert = 0; ivert < *nvert; ivert++ ) *(pxy++) += off; \
+\
+/* Free lists if an error has occurred. */ \
+   } else { \
+      *xvert = astFree( *xvert ); \
+      *yvert = astFree( *yvert ); \
+      *nvert = 0; \
+   } \
+}
+
+/* Define a macro that uses the above macro to to create implementations
+   of PartHull for all operations. */
+#define MAKEALL_PARTHULL(X,Xtype) \
+MAKE_PARTHULL(X,Xtype,LT,AST__LT) \
+MAKE_PARTHULL(X,Xtype,LE,AST__LE) \
+MAKE_PARTHULL(X,Xtype,EQ,AST__EQ) \
+MAKE_PARTHULL(X,Xtype,NE,AST__NE) \
+MAKE_PARTHULL(X,Xtype,GE,AST__GE) \
+MAKE_PARTHULL(X,Xtype,GT,AST__GT)
+
+/* Expand the above macro to generate a function for each required
+   data type and operation. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKEALL_PARTHULL(LD,long double)
+#endif
+MAKEALL_PARTHULL(D,double)
+MAKEALL_PARTHULL(L,long int)
+MAKEALL_PARTHULL(UL,unsigned long int)
+MAKEALL_PARTHULL(I,int)
+MAKEALL_PARTHULL(UI,unsigned int)
+MAKEALL_PARTHULL(S,short int)
+MAKEALL_PARTHULL(US,unsigned short int)
+MAKEALL_PARTHULL(B,signed char)
+MAKEALL_PARTHULL(UB,unsigned char)
+MAKEALL_PARTHULL(F,float)
+
+/* Undefine the macros. */
+#undef MAKE_PARTHULL
+#undef MAKEALL_PARTHULL
+
+static double Polywidth( AstFrame *frm, AstLineDef **edges, int i, int nv,
+                         double cen[ 2 ], int *status ){
+/*
+*  Name:
+*     Polywidth
+
+*  Purpose:
+*     Find the width of a polygon perpendicular to a given edge.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     double Polywidth( AstFrame *frm, AstLineDef **edges, int i, int nv,
+*                       double cen[ 2 ], int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     This function defines a line perpendicular to a given polygon edge,
+*     passing through the mid point of the edge, extending towards the
+*     inside of the polygon. It returns the distance that can be travelled
+*     along this line before any of the other polygon edges are hit (the
+*     "width" of the polygon perpendicular to the given edge). It also
+*     puts the position corresponding to half that distance into "cen".
+
+*  Parameters:
+*     frm
+*        The Frame in which the lines are defined.
+*     edges
+*        Array of "nv" pointers to AstLineDef structures, each defining an
+*        edge of the polygon.
+*     i
+*        The index of the edge that is to define the polygon width.
+*     nv
+*        Total number of edges.
+*     cen
+*        An array into which are put the coords of the point half way
+*        along the polygon width line.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returnd Value:
+*     The width of the polygon perpendicular to the given edge, or
+*     AST__BAD if the width cannot be determined (usually because the
+*     vertices been supplied in a clockwise direction, effectively
+*     negating the Polygon).
+
+*/
+
+/* Local Variables: */
+   AstLineDef *line;
+   double *cross;
+   double d;
+   double end[ 2 ];
+   double l1;
+   double l2;
+   double result;
+   double start[ 2 ];
+   int j;
+
+/* Check the global error status. */
+   result = AST__BAD;
+   if ( !astOK ) return result;
+
+/* Create a Line description for a line perpendicular to the specified
+   edge, passing through the mid point of the edge, and extending towards
+   the inside of the polygon. First move away from the start along the
+   line to the mid point. This gives the start of the new line. */
+   l1 = 0.5*( edges[ i ]->length );
+   astLineOffset( frm, edges[ i ], l1, 0.0, start );
+
+/* We now move away from this position at right angles to the line. We
+   start off by moving 5 times the length of the specified edge. For
+   some Frames (e.g. SkyFrames) this may result in a position that is
+   much too close (i.e. if it goes all the way round the great circle
+   and comes back to the beginning). Therefore, we check that the end
+   point is the requested distance from the start point, and if not, we
+   halve the length of the line and try again. */
+   l2 = 10.0*l1;
+   while( 1 ) {
+      astLineOffset( frm, edges[ i ], l1, l2, end );
+      d = astDistance( frm, start, end );
+      if( d != AST__BAD && fabs( d - l2 ) < 1.0E-6*l2 ) break;
+      l2 *= 0.5;
+   }
+
+/* Create a description of the required line. */
+   line = astLineDef( frm, start, end );
+
+/* Loop round every edge, except for the supplied edge. */
+   for( j = 0; j < nv; j++ ) {
+      if( j != i ) {
+
+/* Find the position at which the line created above crosses the current
+   edge. Skip to the next edge if the line does not intersect the edge
+   within the length of the edge. */
+         if( astLineCrossing( frm, line, edges[ j ], &cross ) ) {
+
+/* Find the distance between the crossing point and the line start. */
+            d = astDistance( frm, start, cross );
+
+/* If this is less than the smallest found so far, record it. */
+            if( d != AST__BAD && ( d < result || result == AST__BAD ) ) {
+               result = d;
+            }
+         }
+
+/* Free resources */
+         cross = astFree( cross );
+      }
+   }
+   line = astFree( line );
+
+/* If a width was found, return the point half way across the polygon. */
+   if( result != AST__BAD ) {
+      astOffset( frm, start, end, 0.5*result, cen );
+
+/* The usual reason for not finding a width is if the polygon vertices
+   are supplied in clockwise order, effectively negating the polygon, and
+   resulting in the "inside" of the polygon being the infinite region
+   outside a polygonal hole. In this case, the end point of the line
+   perpendicular to the initial edge can be returned as a representative
+   "inside" point. */
+   } else {
+      cen[ 0 ] = end[ 0 ];
+      cen[ 1 ] = end[ 1 ];
+   }
+
+/* Return the width. */
+   return result;
+
+}
+
+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 "polygon.h"
+*     void RegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status )
+
+*  Class Membership:
+*     Polygon 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: */
+   AstFrame *frm;             /* Pointer to encapsulated Frame */
+   AstPointSet *pset;         /* Pointer to PointSet defining the Region */
+   AstPolygon *this;          /* Pointer to Polygon structure */
+   AstRegion *reg;            /* Base Frame equivalent of supplied Polygon */
+   double **ptr;              /* Pointer to PointSet data */
+   double *x;                 /* Pointer to next X axis value */
+   double *y;                 /* Pointer to next Y axis value */
+   double dist;               /* Offset along an axis */
+   double x0;                 /* The first X axis value */
+   double y0;                 /* The first Y axis value */
+   int ip;                    /* Point index */
+   int np;                    /* No. of points in PointSet */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get a pointer to the Polygon structure. */
+   this = (AstPolygon *) this_region;
+
+/* If the base Frame bounding box has already been found, return the
+   values stored in the Polygon structure. */
+   if( this->lbnd[ 0 ] != AST__BAD ) {
+      lbnd[ 0 ] = this->lbnd[ 0 ];
+      lbnd[ 1 ] = this->lbnd[ 1 ];
+      ubnd[ 0 ] = this->ubnd[ 0 ];
+      ubnd[ 1 ] = this->ubnd[ 1 ];
+
+/* If the base Frame bounding box has not yet been found, find it now and
+   store it in the Polygon structure. */
+   } else {
+
+/* Get the axis values for the PointSet which defines the location and
+   extent of the region in the base Frame of the encapsulated FrameSet. */
+      pset = this_region->points;
+      ptr = astGetPoints( pset );
+      np = astGetNpoint( pset );
+
+/* Get a pointer to the base Frame in the frameset encapsulated by the
+   parent Region structure. */
+      frm = astGetFrame( this_region->frameset, AST__BASE );
+
+/* Find the upper and lower bounds of the box enclosing all the vertices.
+   The box is expressed in terms of axis offsets from the first vertex, in
+   order to avoid problems with boxes that cross RA=0 or RA=12h */
+      lbnd[ 0 ] = 0.0;
+      lbnd[ 1 ] = 0.0;
+      ubnd[ 0 ] = 0.0;
+      ubnd[ 1 ] = 0.0;
+
+      x = ptr[ 0 ];
+      y = ptr[ 1 ];
+
+      x0 = *x;
+      y0 = *y;
+
+      for( ip = 0; ip < np; ip++, x++, y++ ) {
+
+         dist =  astAxDistance( frm, 1, x0, *x );
+         if( dist < lbnd[ 0 ] ) {
+            lbnd[ 0 ] = dist;
+         } else if( dist > ubnd[ 0 ] ) {
+            ubnd[ 0 ] = dist;
+         }
+
+         dist =  astAxDistance( frm, 2, y0, *y );
+         if( dist < lbnd[ 1 ] ) {
+            lbnd[ 1 ] = dist;
+         } else if( dist > ubnd[ 1 ] ) {
+            ubnd[ 1 ] = dist;
+         }
+
+      }
+
+/* Convert the box bounds to absolute values, rather than values relative
+   to the first vertex. */
+      lbnd[ 0 ] += x0;
+      lbnd[ 1 ] += y0;
+      ubnd[ 0 ] += x0;
+      ubnd[ 1 ] += y0;
+
+/* The astNormBox requires a Mapping which can be used to test points in
+   this base Frame. Create a copy of the Polygon and then set its
+   FrameSet so that the current Frame in the copy is the same as the base
+   Frame in the original. */
+      reg = astCopy( this );
+      astSetRegFS( reg, frm );
+      astSetNegated( reg, 0 );
+
+/* Normalise this box. */
+      astNormBox( frm, lbnd, ubnd, reg );
+
+/* Free resources */
+      reg = astAnnul( reg );
+      frm = astAnnul( frm );
+
+/* Store it in the olygon structure for future use. */
+      this->lbnd[ 0 ] = lbnd[ 0 ];
+      this->lbnd[ 1 ] = lbnd[ 1 ];
+      this->ubnd[ 0 ] = ubnd[ 0 ];
+      this->ubnd[ 1 ] = ubnd[ 1 ];
+
+   }
+}
+
+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 "polygon.h"
+*     AstPointSet *astRegBaseMesh( AstRegion *this, int *status )
+
+*  Class Membership:
+*     Polygon 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 Variables: */
+   AstFrame *frm;                 /* Base Frame in encapsulated FrameSet */
+   AstPointSet *result;           /* Returned pointer */
+   AstPolygon *this;              /* The Polygon structure */
+   double **rptr;                 /* Pointers to returned mesh data */
+   double **vptr;                 /* Pointers to vertex data */
+   double *lens;                  /* Pointer to work space holding edge lengths */
+   double d;                      /* Length of this edge */
+   double delta;                  /* Angular separation of points */
+   double end[ 2 ];               /* End position */
+   double mp;                     /* No. of mesh points per unit distance */
+   double p[ 2 ];                 /* Position in 2D Frame */
+   double start[ 2 ];             /* Start position */
+   double total;                  /* Total length of polygon */
+   int ip;                        /* Point index */
+   int iv;                        /* Vertex index */
+   int n;                         /* No. of points on this edge */
+   int next;                      /* Index of next point in returned PointSet */
+   int np;                        /* No. of points in returned PointSet */
+   int nv;                        /* No. of polygon vertices */
+
+/* Initialise */
+   result= NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* If the Region structure contains a pointer to a PointSet holding
+   a previously created mesh, return it. */
+   if( this_region->basemesh ) {
+      result = astClone( this_region->basemesh );
+
+/* Otherwise, create a new mesh. */
+   } else {
+
+/* Get a pointer to the Polygon structure. */
+      this = (AstPolygon *) this_region;
+
+/* Get a pointer to the base Frame in the encapsulated FrameSet. */
+      frm = astGetFrame( this_region->frameset, AST__BASE );
+
+/* Get the number of vertices and pointers to the vertex axis values. */
+      nv = astGetNpoint( this_region->points );
+      vptr = astGetPoints( this_region->points );
+
+/* Allocate memory to hold the geodesic length of each edge. */
+      lens = astMalloc( sizeof( double )*(size_t) nv );
+
+      if( astOK ) {
+
+/* Find the total geodesic distance around the boundary. */
+         total = 0.0;
+
+         start[ 0 ] = vptr[ 0 ][ 0 ];
+         start[ 1 ] = vptr[ 1 ][ 0 ];
+
+         for( iv = 1; iv < nv; iv++ ) {
+            end[ 0 ] = vptr[ 0 ][ iv ];
+            end[ 1 ] = vptr[ 1 ][ iv ];
+
+            d = astDistance( frm, start, end );
+            if( d != AST__BAD ) total += fabs( d );
+            lens[ iv ] = d;
+            start[ 0 ] = end[ 0 ];
+            start[ 1 ] = end[ 1 ];
+         }
+
+         end[ 0 ] = vptr[ 0 ][ 0 ];
+         end[ 1 ] = vptr[ 1 ][ 0 ];
+
+         d = astDistance( frm, start, end );
+         if( d != AST__BAD ) total += fabs( d );
+         lens[ 0 ] = d;
+
+/* Find the number of mesh points per unit geodesic distance. */
+         if( total > 0.0 ){
+            mp = astGetMeshSize( this )/total;
+
+/* Find the total number of mesh points required. */
+            np = 0;
+            for( iv = 0; iv < nv; iv++ ) {
+               if( lens[ iv ] != AST__BAD ) np += 1 + (int)( lens[ iv ]*mp );
+            }
+
+/* Create a suitable PointSet to hold the returned positions. */
+            result = astPointSet( np, 2, "", status );
+            rptr = astGetPoints( result );
+            if( astOK ) {
+
+/* Initialise the index of the next point to be added to the returned
+   PointSet. */
+               next = 0;
+
+/* Loop round each good edge of the polygon. The edge ends at vertex "iv". */
+               start[ 0 ] = vptr[ 0 ][ 0 ];
+               start[ 1 ] = vptr[ 1 ][ 0 ];
+
+               for( iv = 1; iv < nv; iv++ ) {
+                  end[ 0 ] = vptr[ 0 ][ iv ];
+                  end[ 1 ] = vptr[ 1 ][ iv ];
+                  if( lens[ iv ] != AST__BAD ) {
+
+/* Add the position of the starting vertex to the returned mesh. */
+                     rptr[ 0 ][ next ] = start[ 0 ];
+                     rptr[ 1 ][ next ] = start[ 1 ];
+                     next++;
+
+/* Find the number of points on this edge, and the geodesic distance
+   between them. */
+                     n = 1 + (int) ( lens[ iv ]*mp );
+
+/* If more than one point, find the distance between points. */
+                     if( n > 1 ) {
+                        delta = lens[ iv ]/n;
+
+/* Loop round the extra points. */
+                        for( ip = 1; ip < n; ip++ ) {
+
+/* Find the position of the next mesh point. */
+                           astOffset( frm, start, end, delta*ip, p );
+
+/* Add it to the mesh. */
+                           rptr[ 0 ][ next ] = p[ 0 ];
+                           rptr[ 1 ][ next ] = p[ 1 ];
+                           next++;
+
+                        }
+                     }
+                  }
+
+/* The end of this edge becomes the start of the next. */
+                  start[ 0 ] = end[ 0 ];
+                  start[ 1 ] = end[ 1 ];
+               }
+
+/* Now do the edge which ends at the first vertex. */
+               end[ 0 ] = vptr[ 0 ][ 0 ];
+               end[ 1 ] = vptr[ 1 ][ 0 ];
+               if( lens[ 0 ] != AST__BAD ) {
+                  rptr[ 0 ][ next ] = start[ 0 ];
+                  rptr[ 1 ][ next ] = start[ 1 ];
+                  next++;
+
+                  n = 1 + (int)( lens[ 0 ]*mp );
+                  if( n > 1 ) {
+                     delta = lens[ 0 ]/n;
+                     for( ip = 1; ip < n; ip++ ) {
+                        astOffset( frm, start, end, delta*ip, p );
+                        rptr[ 0 ][ next ] = p[ 0 ];
+                        rptr[ 1 ][ next ] = p[ 1 ];
+                        next++;
+                     }
+                  }
+               }
+
+/* Check the PointSet size was correct. */
+               if( next != np && astOK ) {
+                  astError( AST__INTER, "astRegBaseMesh(%s): Error in the "
+                            "allocated PointSet size (%d) - should have "
+                            "been %d (internal AST programming error).", status,
+                            astGetClass( this ), np, next );
+               }
+
+/* Save the returned pointer in the Region structure so that it does not
+   need to be created again next time this function is called. */
+               if( astOK ) this_region->basemesh = astClone( result );
+
+            }
+
+         } else if( astOK ) {
+            astError( AST__BADIN, "astRegBaseMesh(%s): The boundary of "
+                      "the supplied %s has an undefined length.", status,
+                      astGetClass( this ), astGetClass( this ) );
+         }
+
+      }
+
+/* Free resources. */
+      frm = astAnnul( frm );
+      lens = astFree( lens );
+   }
+
+/* Annul the result if an error has occurred. */
+   if( !astOK ) result = astAnnul( result );
+
+/* Return a pointer to the output PointSet. */
+   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 Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     int RegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
+*                  int **mask, int *status )
+
+*  Class Membership:
+*     Polygon 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 Polygon.
+*
+*     Some tolerance is allowed, as specified by the uncertainty Region
+*     stored in the supplied Polygon "this", and the supplied uncertainty
+*     Region "unc" which describes the uncertainty of the supplied points.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon.
+*     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: */
+   AstFrame *frm;               /* Base Frame in supplied Polygon */
+   AstPointSet *pset1;          /* Pointer to copy of supplied PointSet */
+   AstPointSet *pset2;          /* Pointer to PointSet holding resolved components */
+   AstPolygon *this;            /* Pointer to the Polygon structure. */
+   AstRegion *tunc;             /* Uncertainity Region from "this" */
+   double **ptr1;               /* Pointer to axis values in "pset1" */
+   double **ptr2;               /* Pointer to axis values in "pset2" */
+   double **vptr;               /* Pointer to axis values at vertices */
+   double *safe;                /* An interior point in "this" */
+   double edge_len;             /* Length of current edge */
+   double end[2];               /* Position of end of current edge */
+   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 par;                  /* Parallel component */
+   double parmax;               /* Max acceptable parallel component */
+   double prp;                  /* Perpendicular component */
+   double start[2];             /* Position of start of current edge */
+   double ubnd_tunc[2];         /* Upper bounds of "this" uncertainty Region */
+   double ubnd_unc[2];          /* Upper bounds of supplied uncertainty Region */
+   double wid;                  /* Width of acceptable margin around polygon */
+   int *m;                      /* Pointer to next mask value */
+   int i;                       /* Edge index */
+   int ip;                      /* Point index */
+   int np;                      /* No. of supplied points */
+   int nv;                      /* No. of vertices */
+   int result;                  /* Returned flag */
+
+/* Initialise */
+   result = 0;
+   if( mask ) *mask = NULL;
+
+/* Check the inherited status. */
+   if( !astOK ) return result;
+
+/* Get a pointer to the Polygon structure. */
+   this = (AstPolygon *) 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 pointers to the axis values at the polygon vertices. */
+   vptr = astGetPoints( this_region->points );
+
+/* Get the number of vertices. */
+   nv = astGetNpoint( this_region->points );
+
+/* Take a copy of the supplied PointSet and get pointers to its axis
+   values,and its size */
+   pset1 = astCopy( pset );
+   ptr1 = astGetPoints( pset1 );
+   np = astGetNpoint( pset1 );
+
+/* Create a PointSet to hold the resolved components and get pointers to its
+   axis data. */
+   pset2 = astPointSet( np, 2, "", status );
+   ptr2 = astGetPoints( pset2 );
+
+/* Create a mask array if required. */
+   if( mask ) *mask = astMalloc( sizeof(int)*(size_t) np );
+
+/* 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 Polygon for it still to be considered to be on the boundary.
+   First get the Region which defines the uncertainty within the Polygon
+   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. The current Frame of the
+   uncertainty Region is the same as the base Frame of the Polygon. */
+   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;
+   }
+
+/* The required border width is half of the total diagonal of the two bounding
+   boxes. */
+   if( astOK ) {
+      wid = 0.5*( l1 + l2 );
+
+/* Loop round each edge of the polygon. Edge "i" starts at vertex "i-1"
+   and ends at vertex "i". Edge zero starts at vertex "nv-1" and ends at
+   vertex zero. */
+      start[ 0 ] = vptr[ 0 ][ nv - 1 ];
+      start[ 1 ] = vptr[ 1 ][ nv - 1 ];
+      for( i = 0; i < nv; i++ ) {
+         end[ 0 ] = vptr[ 0 ][ i ];
+         end[ 1 ] = vptr[ 1 ][ i ];
+
+/* Find the length of this edge. */
+         edge_len = astDistance( frm, start, end );
+
+/* Resolve all the supplied mesh points into components parallel and
+   perpendicular to this edge. */
+         (void) astResolvePoints( frm, start, end, pset1, pset2 );
+
+/* A point is effectively on this edge if the parallel component is
+   greater than (-wid) and less than (edge_len+wid) AND the perpendicular
+   component has an absolute value less than wid. Identify such positions
+   and set them bad in pset1. */
+         parmax = edge_len + wid;
+         for( ip = 0; ip < np; ip++ ) {
+            par = ptr2[ 0 ][ ip ];
+            prp = ptr2[ 1 ][ ip ];
+
+            if( par != AST__BAD && prp != AST__BAD ) {
+               if( par > -wid && par < parmax && prp > -wid && prp < wid ) {
+                  ptr1[ 0 ][ ip ] = AST__BAD;
+                  ptr1[ 1 ][ ip ] = AST__BAD;
+               }
+            }
+         }
+
+/* The end of the current edge becomes the start of the next. */
+         start[ 0 ] = end[ 0 ];
+         start[ 1 ] = end[ 1 ];
+      }
+
+/* See if any good points are left in pset1. If so, it means that those
+   points were not on any edge of hte Polygon. We use two alogorithms
+   here depending on whether we are creating a mask array, since we can
+   abort the check upon finding the first good point if we are not
+   producing a mask. */
+      result = 1;
+      if( mask ) {
+         m = *mask;
+         for( ip = 0; ip < np; ip++, m++ ) {
+            if( ptr1[ 0 ][ ip ] != AST__BAD &&
+                ptr1[ 1 ][ ip ] != AST__BAD ) {
+               *m = 0;
+               result = 0;
+            } else {
+               *m = 1;
+            }
+         }
+      } else {
+         for( ip = 0; ip < np; ip++ ) {
+            if( ptr1[ 0 ][ ip ] != AST__BAD &&
+                ptr1[ 1 ][ ip ] != AST__BAD ) {
+               result = 0;
+               break;
+            }
+         }
+      }
+   }
+
+/* Free resources. */
+   tunc = astAnnul( tunc );
+   frm = astAnnul( frm );
+   safe = astFree( safe );
+   pset1 = astAnnul( pset1 );
+   pset2 = astAnnul( pset2 );
+
+/* 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 "polygon.h"
+*     int astTraceRegion( AstRegion *this, int n, double *dist, double **ptr );
+
+*  Class Membership:
+*     Polygon 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; */
+   AstFrame *frm;
+   AstMapping *map;
+   AstPointSet *bpset;
+   AstPointSet *cpset;
+   AstPolygon *this;
+   double **bptr;
+   double d;
+   double p[ 2 ];
+   int i;
+   int j0;
+   int j;
+   int ncur;
+   int nv;
+   int monotonic;
+
+/* 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 Polygon structure. */
+   this = (AstPolygon *) 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 polygon). */
+   } else {
+      bpset = astPointSet( n, 2, " ", status );
+      bptr = astGetPoints( bpset );
+      ncur = astGetNout( map );
+   }
+
+/* Check the pointers can be used safely. */
+   if( astOK ) {
+
+/* Get the number of vertices. */
+      nv = astGetNpoint( this_region->points );
+
+/* If we have a reasonable number of pointsand there are a reasonable
+   number of vertices, we can be quicker if we know if the parameteric
+   distances are monotonic increasing. Find out now. */
+      if( n > 5 && nv > 5 ) {
+
+         monotonic = 1;
+         for( i = 1; i < n; i++ ) {
+            if( dist[ i ] < dist[ i - 1 ] ) {
+               monotonic = 0;
+               break;
+            }
+         }
+
+      } else {
+         monotonic = 0;
+      }
+
+/* Loop round each point. */
+      j0 = 1;
+      for( i = 0; i < n; i++ ) {
+
+/* Get the required round the polygon, starting from vertex zero. */
+         d = dist[ i ]*this->totlen;
+
+/* Loop round each vertex until we find one which is beyond the required
+   point. If the supplied distances are monotonic increasing, we can
+   start the checks at the same vertex that was used for the previous
+   since we know there will never be a backward step. */
+         for( j = j0; j < nv; j++ ) {
+            if( this->startsat[ j ] > d ) break;
+         }
+
+/* If the distances are monotonic increasing, record the vertex that we
+   have reached so far. */
+         if( monotonic ) j0 = j;
+
+/* Find the distance to travel beyond the previous vertex. */
+         d -= this->startsat[ j - 1 ];
+
+/* Find the position, that is the required distance from the previous
+   vertex towards the next vertex. */
+         astLineOffset( frm, this->edges[ j - 1 ], d, 0.0, p );
+
+/* Store the resulting axis values. */
+         bptr[ 0 ][ i ] = p[ 0 ];
+         bptr[ 1 ][ i ] = p[ 1 ];
+      }
+   }
+
+/* If required, transform the base frame positions into the current
+   Frame, storing them in the supplied array. Then free resources. */
+   if( bpset ) {
+      cpset = astPointSet( n, ncur, " ", status );
+      astSetPoints( cpset, ptr );
+
+      (void) astTransform( map, bpset, 1, cpset );
+
+      cpset = astAnnul( cpset );
+      bpset = astAnnul( bpset );
+   }
+
+/* Free remaining resources. */
+   map = astAnnul( map );
+   frm = astAnnul( frm );
+
+/* Return a non-zero value to indicate that this class supports the
+   astRegTrace method. */
+   return 1;
+}
+
+static Segment *RemoveFromChain( Segment *head, Segment *seg, int *status ){
+/*
+*  Name:
+*     RemoveFromChain
+
+*  Purpose:
+*     Remove a Segment from the link list maintained by astDownsize.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     Segment *RemoveFromChain( Segment *head, Segment *seg, int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     The supplied Segment is removed form the list, and the gap is
+*     closed up.
+
+*  Parameters:
+*     head
+*        The Segment structure at the head of the list.
+*     seg
+*        The Segment to be removed from the list.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the link head (which will have changed if "seg" was the
+*     original head).
+
+*/
+
+/* Check the global error status. */
+   if ( !astOK ) return head;
+
+/* If the Segment was the original head, make the next segment the new
+   head. */
+   if( head == seg ) head = seg->next;
+
+/* Close up the links between the Segments on either side of the segment
+   being removed. */
+   if( seg->prev ) seg->prev->next = seg->next;
+   if( seg->next ) seg->next->prev = seg->prev;
+
+/* Nullify the links in the segment being removed. */
+   seg->next = NULL;
+   seg->prev = NULL;
+
+/* Return the new head. */
+   return head;
+}
+
+static void ResetCache( AstRegion *this_region, int *status ){
+/*
+*  Name:
+*     ResetCache
+
+*  Purpose:
+*     Clear cached information within the supplied Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.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.
+*/
+
+/* Local Variables: */
+   AstPolygon *this;
+   int i;
+   int nv;
+
+/* Get a pointer to the Polygon structure. */
+   this = (AstPolygon *) this_region;
+
+/* If a Polygon was supplied, indicate cached information needs to be
+   recalculated. */
+   if( this ) {
+      this->stale = 1;
+      this->lbnd[ 0 ] = AST__BAD;
+
+/* Free any edge structures (number of vertices may be about to change so
+   this cannot be left until the next call to "Cache()". */
+      if( this->edges ) {
+         nv = astGetNpoint( this_region->points );
+         for( i = 0; i < nv; i++ ) {
+            this->edges[ i ] = astFree( this->edges[ i ] );
+         }
+         this->edges = astFree( this->edges );
+      }
+
+/* Clear the cache of the parent class. */
+      (*parent_resetcache)( this_region, status );
+   }
+}
+
+static void SetAttrib( AstObject *this_object, const char *setting, int *status ) {
+/*
+*  Name:
+*     SetAttrib
+
+*  Purpose:
+*     Set an attribute value for a Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void SetAttrib( AstObject *this, const char *setting, int *status )
+
+*  Class Membership:
+*     Polygon member function (extends the astSetAttrib method inherited from
+*     the Region class).
+
+*  Description:
+*     This function assigns an attribute value for a Polygon, the attribute
+*     and its value being specified by means of a string of the form:
+*
+*        "attribute= value "
+*
+*     Here, "attribute" specifies the attribute name and should be in lower
+*     case with no white space present. The value to the right of the "="
+*     should be a suitable textual representation of the value to be assigned
+*     and this will be interpreted according to the attribute's data type.
+*     White space surrounding the value is only significant for string
+*     attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon.
+*     setting
+*        Pointer to a null terminated string specifying the new attribute
+*        value.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     void
+*/
+
+/* Local Vaiables: */
+   AstPolygon *this;             /* Pointer to the Polygon structure */
+   int ival;                     /* Integer attribute value */
+   int len;                      /* Length of setting string */
+   int nc;                       /* Number of characters read by astSscanf */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the Polygon structure. */
+   this = (AstPolygon *) this_object;
+
+/* Obtain the length of the setting string. */
+   len = strlen( setting );
+
+/* Test for each recognised attribute in turn, using "astSscanf" to parse the
+   setting string and extract the attribute value (or an offset to it in the
+   case of string values). In each case, use the value set in "nc" to check
+   that the entire string was matched. Once a value has been obtained, use the
+   appropriate method to set it. */
+
+/* SimpVertices. */
+/* ------------- */
+   if ( nc = 0,
+               ( 1 == astSscanf( setting, "simpvertices= %d %n", &ival, &nc ) )
+               && ( nc >= len ) ) {
+      astSetSimpVertices( this, ival );
+
+/* Pass any unrecognised setting to the parent method for further
+   interpretation. */
+   } else {
+      (*parent_setattrib)( this_object, setting, status );
+   }
+}
+
+static void SetPointSet( AstPolygon *this, AstPointSet *pset, int *status ){
+/*
+*  Name:
+*     SetPointSet
+
+*  Purpose:
+*     Store a new set of vertices in an existing Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void SetPointSet( AstPolygon *this, AstPointSet *pset, int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     The PointSet in the supplied Polygon is annulled, and replaced by a
+*     clone of the supplied PointSet pointer.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon to be changed.
+*     pset
+*        The PointSet containing the new vertex information.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Indicate the cached information in the polygon will need to be
+   re-calculated when needed. */
+   astResetCache( this );
+
+/* Annul the pointer to the PointSet already in the supplied Polygon. */
+   (void) astAnnul( ((AstRegion *) this)->points );
+
+/* Store a clone of the supplied new PointSet pointer. */
+   ((AstRegion *) this)->points = astClone( pset );
+
+}
+
+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 "polygon.h"
+*     void SetRegFS( AstRegion *this_region, AstFrame *frm, int *status )
+
+*  Class Membership:
+*     Polygon 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;
+
+/* Indicate cached information eeds re-calculating. */
+   astResetCache( this_region );
+
+/* Invoke the parent method to store the FrameSet in the parent Region
+   structure. */
+   (* parent_setregfs)( this_region, frm, status );
+
+}
+
+static AstMapping *Simplify( AstMapping *this_mapping, int *status ) {
+/*
+*  Name:
+*     Simplify
+
+*  Purpose:
+*     Simplify the Mapping represented by a Region.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     AstMapping *Simplify( AstMapping *this, int *status )
+
+*  Class Membership:
+*     Polygon 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: */
+   AstFrame *frm;             /* Current Frame */
+   AstMapping *map;           /* Base -> current Mapping */
+   AstMapping *result;        /* Result pointer to return */
+   AstPointSet *mesh;         /* Mesh of current Frame positions */
+   AstPointSet *ps2;          /* Polygon PointSet in current Frame */
+   AstPolygon *newpol;        /* New Polygon */
+   AstRegion *new;            /* Pointer to simplified Region */
+   AstRegion *this;           /* Pointer to supplied Region structure */
+   AstRegion *unc;            /* Pointer to uncertainty Region */
+   double **ptr2;             /* Pointer axis values in "ps2" */
+   double *mem;               /* Pointer to array holding new vertex coords */
+   double *p;                 /* Pointer to next vertex coords */
+   double *q;                 /* Pointer to next vertex coords */
+   int iv;                    /* Vertex index */
+   int nv;                    /* Number of vertices in polygon */
+   int ok;                    /* Are the new polygon vertices good? */
+   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 Polygon by re-defining it within its current
+   Frame. Transforming the Polygon from its base to its current Frame may
+   result in the region no having the same edges. If required, we test this
+   by transforming a set of bounds on the Polygon boundary. This can only
+   be done if the current Frame is 2-dimensional. Also, there is only any
+   point in doing it if the Mapping from base to current Frame in the
+   Polygon is not a UnitMap. */
+   map = astGetMapping(  new->frameset, AST__BASE, AST__CURRENT );
+   if( !astIsAUnitMap( map ) && astGetNout( map ) == 2 ) {
+
+/* Get a pointer to the Frame represented by the Polgon. */
+      frm = astGetFrame( new->frameset, AST__CURRENT );
+
+/* Get the Region describing the positional uncertainty in this Frame. */
+      unc = astGetUncFrm( new, AST__CURRENT );
+
+/* Get the positions of the vertices within this Frame. */
+      ps2 = astRegTransform( this, this->points, 1, NULL, NULL );
+      ptr2 = astGetPoints( ps2 );
+
+/* Get the number of vertices. */
+      nv = astGetNpoint( ps2 );
+
+/* Re-organise the vertex axis values into the form required by the
+   Polygon constructor function. */
+      mem = astMalloc( sizeof( double)*(size_t)( 2*nv ) );
+      if( astOK ) {
+         ok = 1;
+         p = mem;
+         q = ptr2[ 0 ];
+         for( iv = 0; iv < nv; iv++ ) {
+            if( ( *(p++) = *(q++) ) == AST__BAD ) ok = 0;
+         }
+         q = ptr2[ 1 ];
+         for( iv = 0; iv < nv; iv++ ) *(p++) = *(q++);
+
+/* Create a new Polygon using these transformed vertices. */
+         if( ok ) {
+            newpol = astPolygon( frm, nv, nv, mem, unc, "", status );
+
+/* If the SimpVertices attribute is zero, we now check that the
+   transformation has not bent the edges of the polygon significantly.
+   If it has, we annul the new Polygon. */
+            if( !astGetSimpVertices( this ) ) {
+
+/* Get a mesh of points covering the Polygon in this Frame. */
+               mesh = astRegMesh( new );
+
+/* See if all points within the mesh created from the original Polygon fall
+   on the boundary of the new Polygon, to within the uncertainty of the
+   Region. If not, annul the new Polgon. */
+               if( !astRegPins( newpol, mesh, NULL, NULL ) ) {
+                  newpol = astAnnul( newpol );
+               }
+
+/* Free the mesh. */
+               mesh = astAnnul( mesh );
+            }
+
+/* If we still have a new polygon, use the new Polygon in place of the
+   original Region. */
+            if( newpol ) {
+               (void) astAnnul( new );
+               new = (AstRegion *) newpol;
+               simpler = 1;
+            }
+         }
+      }
+
+/* Free other resources. */
+      frm = astAnnul( frm );
+      unc = astAnnul( unc );
+      ps2 = astAnnul( ps2 );
+      mem = astFree( mem );
+   }
+   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 void SmoothPoly( AstPointSet *pset, int boxsize, double strength,
+                        int *status ) {
+/*
+*  Name:
+*     SmoothPoly
+
+*  Purpose:
+*     Smoooth a polygon assuming plane geometry.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void SmoothPoly( AstPointSet *pset, int boxsize, double strength,
+*                      int *status )
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     This function smooths a polygon, without changing the number of
+*     vertices. It assumes plane geometry, so should not be used to
+*     smooth polygons defined within a SkyFrame or CmpFrame.
+*
+*     Each vertex is replaced by a new vertex determined as follows: the
+*     mean X and Y axis value of the vertices in a section of the polygon
+*     centred on the vertex being replaced are found (the length of the
+*     section is given by parameter "boxsize"). The new vertex position
+*     is then the weighted mean of this mean (X,Y) position and the old
+*     vertex position. The weight for the mean (X,Y) position is given
+*     by parameter "strength", and the weight for the old vertex
+*     position is (1.0 - strength)
+
+*  Parameters:
+*     pset
+*        A PointSet holding the polygon vertices.
+*     boxsize
+*        Half width of the box filter, given as a number of vertices.
+*     strength
+*        The weight to use for the mean (X,Y) position when finding each
+*        new vertex position. Should be in the range 0.0 to 1.0. A value
+*        of zero results in no change being made to the polygon. A value
+*        of 1.0 results in the returned polygon being fully smoothed.
+*     status
+*        Pointer to the inherited status variable.
+
+*/
+
+/* Local Variables: */
+   double **ptr;
+   double *newx;
+   double *newy;
+   double *nx;
+   double *ny;
+   double *oldx;
+   double *oldy;
+   double *ox;
+   double *oy;
+   double *px;
+   double *py;
+   double *qx;
+   double *qy;
+   double a;
+   double b;
+   double sx;
+   double sy;
+   int half_width;
+   int i;
+   int nv;
+   int top;
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Get the number of vertices. */
+   nv = astGetNpoint( pset );
+
+/* Get pointers to arrays holding the supplied vertex positions. */
+   ptr = astGetPoints( pset );
+   oldx = ptr[ 0 ];
+   oldy = ptr[ 1 ];
+
+/* Allocate arrays to hold the returned vertex positions. */
+   newx = astMalloc( nv*sizeof( double ) );
+   newy = astMalloc( nv*sizeof( double ) );
+
+/* Check these pointers can be used safely. */
+   if( astOK ) {
+
+/* Get weighting factors for the fully smoothed and unsmoothed positions. */
+      a = strength;
+      b = 1.0 - a;
+
+/* Ensure the box size is sufficiently small for there to be room for
+   two boxes along the polygon. */
+      half_width = nv/4 - 1;
+      if( boxsize < half_width ) half_width = boxsize;
+      if( half_width < 1 ) half_width = 1;
+
+/* Modify the weight for the fully smoothed position to include the
+   normalisation factor needed to account for the box width. */
+      a /= 2*half_width + 1;
+
+/* Find the sum of the x and y coordinates within a box centred on the
+   first vertex. This includes vertices from the end of the polygon. */
+      px = oldx + 1;
+      qx = oldx + nv;
+      sx = (oldx)[ 0 ];
+
+      py = oldy + 1;
+      qy = oldy + nv;
+      sy = (oldy)[ 0 ];
+
+      for( i = 0; i < half_width; i++ ) {
+         sx += *(px++) + *(--qx);
+         sy += *(py++) + *(--qy);
+      }
+
+/* Replacing vertices within the first half box will include vertices at
+   both ends of the polygon. Set up the pointers accordingly, and then
+   find replacements for each vertex in the first half box.*/
+      ox = oldx;
+      oy = oldy;
+      nx = newx;
+      ny = newy;
+      for( i = 0; i < half_width; i++ ) {
+
+/* Form the new vertex (x,y) values as the weighted mean of the mean
+   (x,y) values in the box, and the old (x,y) values. */
+         *(nx++) = a*sx + b*( *(ox++) );
+         *(ny++) = a*sy + b*( *(oy++) );
+
+/* Add in the next vertex X and Y axis values to the running sums, and
+   remove the position that has now passed out of the box. */
+         sx += *(px++) - *(qx++);
+         sy += *(py++) - *(qy++);
+      }
+
+/* Adjust the pointer for the rest of the polygon, up to one half box away
+   from the end. In this section, the smoothing box does not touch either
+   end of the polygon. */
+      top = nv - half_width - 1;
+      qx = oldx;
+      qy = oldy;
+      for( ; i < top; i++ ){
+
+/* Form the new vertex (x,y) values as the weighted mean of the mean
+   (x,y) values in the box, and the old (x,y) values. */
+         *(nx++) = a*sx + b*( *(ox++) );
+         *(ny++) = a*sy + b*( *(oy++) );
+
+/* Add in the next vertex X and Y axis values to the running sums, and
+   remove the position that has now passed out of the box. */
+         sx += *(px++) - *(qx++);
+         sy += *(py++) - *(qy++);
+      }
+
+/* Now do the last half box (which includes vertices from the start of
+   the polygon). */
+      top = nv;
+      px = oldx;
+      py = oldy;
+      for( ; i < top; i++ ){
+         *(nx++) = a*sx + b*( *(ox++) );
+         *(ny++) = a*sy + b*( *(oy++) );
+         sx += *(px++) - *(qx++);
+         sy += *(py++) - *(qy++);
+      }
+
+/* Replace the data points in the PointSet. */
+      ptr[ 0 ] = newx;
+      ptr[ 1 ] = newy;
+      oldx = astFree( oldx );
+      oldy = astFree( oldy );
+   }
+}
+
+static int TestAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     TestAttrib
+
+*  Purpose:
+*     Test if a specified attribute value is set for a Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     int TestAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     Polygon member function (over-rides the astTestAttrib protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function returns a boolean result (0 or 1) to indicate whether
+*     a value has been set for one of a Polygon's attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon.
+*     attrib
+*        Pointer to a null terminated string specifying the attribute
+*        name.  This should be in lower case with no surrounding white
+*        space.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     One if a value has been set, otherwise zero.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global status set, or if it should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstPolygon *this;             /* Pointer to the Polygon structure */
+   int result;                   /* Result value to return */
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the Polygon structure. */
+   this = (AstPolygon *) this_object;
+
+/* Check the attribute name and test the appropriate attribute. */
+
+/* SimpVertices. */
+/* ------------- */
+   if ( !strcmp( attrib, "simpvertices" ) ) {
+      result = astTestSimpVertices( this );
+
+/* If the attribute is not recognised, pass it on to the parent method
+   for further interpretation. */
+   } else {
+      result = (*parent_testattrib)( this_object, attrib, status );
+   }
+
+/* Return the result, */
+   return result;
+}
+
+/*
+*  Name:
+*     TraceEdge
+
+*  Purpose:
+*     Find a point that is inside the required outline.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     void TraceEdge<Oper><X>( <Xtype> value, const <Xtype> array[],
+*                              const int lbnd[ 2 ], const int ubnd[ 2 ],
+*                              int iv0, int ix0, int iy0, int starpix,
+*                              int full, int *status );
+
+*  Class Membership:
+*     Polygon member function
+
+*  Description:
+*     This function forms a polygon enclosing the region of the data
+*     array specified by <Oper> and "value". If this polygon contains
+*     the point "(inx,iny)", then a PointSet is returned holding the
+*     pixel coordinates of the Polygon vertices. If the polygon
+*     does not contain "(inx,iny)", a NULL pointer is returned.
+*
+*     Each vertex in the polygon corresponds to a corner of a pixel in
+*     the data array.
+
+*  Parameters:
+*     value
+*        The data value defining valid pixels.
+*     array
+*        The data array.
+*     lbnd
+*        The lower pixel index bounds of the array.
+*     ubnd
+*        The upper pixel index bounds of the array.
+*     iv0
+*        The vector index of a pixel inside the region such that the
+*        pixel to the right is NOT inside the region. This defines the
+*        start of the polygon.
+*     ix0
+*        The X pixel index of the pixel specified by "iv0".
+*     inx
+*        The X pixel index of a point which must be inside the polygon
+*        for the polygon to be acceptable.
+*     iny
+*        The Y pixel index of a point which must be inside the polygon
+*        for the polygon to be acceptable.
+*     starpix
+*        If non-zero, the usual Starlink definition of pixel coordinate
+*        is used (integral values at pixel corners). Otherwise, the
+*        system used by other AST functions such as astResample is used
+*        (integral values at pixel centres).
+*     full
+*        If non-zero, the full polygon is stored. If zero, vertices in the
+*        middle of straight sections of the Polygon are omitted.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     A pointer to a PointSet holding the vertices of the polygon, or
+*     NULL if the polygon did not contain "(inx,iny)".
+
+*  Notes:
+*     - <Oper> must be one of LT, LE, EQ, GE, GT, NE.
+
+
+*/
+
+/* Define a macro to implement the function for a specific data
+   type and operation. */
+#define MAKE_TRACEEDGE(X,Xtype,Oper,OperI) \
+static AstPointSet *TraceEdge##Oper##X( Xtype value, const Xtype array[], \
+                                        const int lbnd[ 2 ], const int ubnd[ 2 ], \
+                                        int iv0, int ix0, int iy0, \
+                                        int starpix, int full, \
+                                        int *status ){ \
+\
+/* Local Variables: */ \
+   AstPointSet *result; /* Pointer to text describing oper */ \
+   const Xtype *pa;     /* Pointer to current valid pixel value */ \
+   const Xtype *pb;     /* Pointer to neigbouring valid pixel value */ \
+   const Xtype *pc;     /* Pointer to neigbouring valid pixel value */ \
+   double *ptr[ 2 ];    /* PointSet data pointers */ \
+   double *xvert;       /* Pointer to array holding vertex X axis values */ \
+   double *yvert;       /* Pointer to array holding vertex Y axis values */ \
+   double dx;           /* Pertubation in X (pixels) to avoid the pixel edge */ \
+   double dy;           /* Pertubation in Y (pixels) to avoid the pixel edge */ \
+   double xx;           /* Pixel X coord at corner */ \
+   double yy;           /* Pixel Y coord at corner */ \
+   int at;              /* The pixel corner to draw to */ \
+   int done;            /* Have we arrived back at the start of the polygon? */ \
+   int ii;              /* Index of new vertex */ \
+   int ix;              /* X pixel index of current valid pixel */ \
+   int iy;              /* Y pixel index of current valid pixel */ \
+   int nright;          /* Overall number of right hand turns along polygon */ \
+   int nvert;           /* Number of vertices */ \
+   int nx;              /* Pixels per row */ \
+\
+/* Initialise */ \
+   result = NULL; \
+\
+/* Check the global error status. */ \
+   if ( !astOK ) return result; \
+\
+\
+/* Initialise pointers to arrays holding the X and Y pixel coordinates at \
+   the vertices of the polygon. */ \
+   xvert = NULL; \
+   yvert = NULL; \
+   nvert = 0; \
+\
+/* Find number of pixels in one row of the array. */ \
+   nx = ( ubnd[ 0 ] - lbnd[ 0 ] + 1 ); \
+\
+/* The four corners of a pixel are numbered as follows: 0=bottom left, \
+   1=top left, 2=top right, 3=bottom right. The following algorithm moves \
+   along pixel edges, from corner to corner, using the above numbering \
+   scheme to identify the corners. We start the polygon by moving from the \
+   bottom right to the top right corner of pixel "(ix0,iy0)". */ \
+   ix = ix0; \
+   iy = iy0; \
+   at = 2; \
+\
+/* Store a pointer to the first good pixel value. */ \
+   pa = array + ( ix - lbnd[ 0 ] ) + nx*( iy - lbnd[ 1 ] ) ; \
+\
+/* We count the number of times the polygon turns to the right compared \
+   to the left. Initialise it to zero. */ \
+   nright = 0; \
+\
+/* Loop round tracing out the polygon until we arrive back at the \
+   beginning. The Polygon class requires that the inside of the polygon \
+   is to the left as we move round the polygon in an anti-clockwise \
+   direction. So at each corner, we attempt to move to the next \
+   anti-clockwise good pixel corner. */ \
+   done = 0; \
+   while( !done ) { \
+\
+/* If we have arrived at the bottom left corner of the good pixel, we must \
+   have come from the top left corner since all movements around a pixel \
+   must be anti-clockwise. */ \
+      if( at == 0 ) { \
+\
+/* Note the pixel coordinates at the bottom left corner of the current \
+   pixel. */ \
+         if( starpix ) { \
+            xx = ix - 1.0; \
+            yy = iy - 1.0; \
+         } else { \
+            xx = ix - 0.5; \
+            yy = iy - 0.5; \
+         } \
+\
+/* Get a pointer to lower left pixel value */ \
+         pb = pa - nx - 1; \
+\
+/* Get a pointer to lower mid pixel value. */ \
+         pc = pb + 1; \
+\
+/* If the lower left pixel is within the array and meets the validity \
+   requirements, move to the left along its top edge. */ \
+         if( iy > lbnd[ 1 ] && ix > lbnd[ 0 ] && ISVALID(*pb,OperI,value) ) { \
+            nright++; \
+            pa = pb; \
+            at = 1; \
+            ix--; \
+            iy--; \
+            dx = DELTA; \
+            dy = -DELTA; \
+\
+/* Otherwise, if lower mid pixel is good, move down its left edge. */ \
+         } else if( iy > lbnd[ 1 ] && ISVALID(*pc,OperI,value) ) { \
+            pa = pc; \
+            at = 0; \
+            iy--; \
+            dx = DELTA; \
+            dy = 0.0; \
+\
+/* Otherwise, move to the right along the bottom edge of the current pixel. */ \
+         } else { \
+            nright--; \
+            at = 3; \
+            dx = DELTA; \
+            dy = DELTA; \
+         } \
+\
+/* If the polygon bends at this point, or if we will be smoothing the \
+   polygon, append the pixel coordinates at this pixel corner to the \
+   polygon. */ \
+         if( full || pa != pc ) ADD( xx, yy ); \
+\
+/* If we have arrived at the top left corner of the good pixel, we must \
+   have come from the top right corner. */ \
+      } else if( at == 1 ) { \
+\
+/* Note the pixel coordinates at the top left corner of the current \
+   pixel. */ \
+         if( starpix ) { \
+            xx = ix - 1.0; \
+            yy = iy; \
+         } else { \
+            xx = ix - 0.5; \
+            yy = iy + 0.5; \
+         } \
+\
+/* Get a pointer to upper left pixel value */ \
+         pb = pa + nx - 1; \
+\
+/* Get a pointer to mid left pixel value. */ \
+         pc = pa - 1; \
+\
+/* If upper left pixel is good, move up its left edge. */ \
+         if( iy < ubnd[ 1 ] && ix > lbnd[ 0 ] && ISVALID(*pb,OperI,value) ) { \
+            nright++; \
+            pa = pb; \
+            at = 2; \
+            ix--; \
+            iy++; \
+            dx = -DELTA; \
+            dy = -DELTA; \
+\
+/* Otherwise, if left mid pixel is good, move left along its top edge. */ \
+         } else if( ix > lbnd[ 0 ] && ISVALID(*pc,OperI,value) ) { \
+            pa = pc; \
+            at = 1; \
+            ix--; \
+            dx = 0.0; \
+            dy = -DELTA; \
+\
+/* Otherwise, move down the left edge of the current pixel. */ \
+         } else { \
+            nright--; \
+            at = 0; \
+            dx = DELTA; \
+            dy = -DELTA; \
+         } \
+\
+/* If the polygon bends at this point, or if we will be smoothing the \
+   polygon, append the pixel coordinates at this pixel corner to the \
+   polygon. */ \
+         if( full || pa != pc ) ADD( xx, yy ); \
+\
+/* If we have arrived at the top right corner of the good pixel, we must \
+   have come from the bottom right corner. */ \
+      } else if( at == 2 ) { \
+\
+/* Note the pixel coordinates at the top right corner of the current \
+   pixel. */ \
+         if( starpix ) { \
+            xx = ix; \
+            yy = iy; \
+         } else { \
+            xx = ix + 0.5; \
+            yy = iy + 0.5; \
+         } \
+\
+/* Pointer to upper right pixel value */ \
+         pb = pa + nx + 1; \
+\
+/* Pointer to top mid pixel value. */ \
+         pc = pa + nx; \
+\
+/* If upper right pixel is good, move right along its bottom edge. */ \
+         if( iy < ubnd[ 1 ] && ix < ubnd[ 0 ] && ISVALID(*pb,OperI,value) ){ \
+            nright++; \
+            pa = pb; \
+            at = 3; \
+            ix++; \
+            iy++; \
+            dx = -DELTA; \
+            dy = DELTA; \
+\
+/* Otherwise, if upper mid pixel is good, move up its right edge. */ \
+         } else if( iy < ubnd[ 1 ] && ISVALID(*pc,OperI,value) ) { \
+            pa = pc; \
+            at = 2; \
+            iy++; \
+            dx = -DELTA; \
+            dy = 0.0; \
+\
+/* Otherwise, move left along the top edge of the current pixel. */ \
+         } else { \
+            nright--; \
+            at = 1; \
+            dx = -DELTA; \
+            dy = -DELTA; \
+         } \
+\
+/* If the polygon bends at this point, or if we will be smoothing the \
+   polygon, append the pixel coordinates at this pixel corner to the \
+   polygon. */ \
+         if( full || pa != pc ) ADD( xx, yy ); \
+\
+/* Arrived at bottom right corner of good pixel from lower left. */ \
+      } else { \
+\
+/* Note the pixel coordinates at the bottom right corner of the current \
+   pixel. */ \
+         if( starpix ) { \
+            xx = ix; \
+            yy = iy - 1.0; \
+         } else { \
+            xx = ix + 0.5; \
+            yy = iy - 0.5; \
+         } \
+\
+/* Pointer to lower right pixel value */ \
+         pb = pa - ( nx - 1 ); \
+\
+/* Pointer to mid right pixel value. */ \
+         pc = pa + 1; \
+\
+/* If lower right pixel is good, move down its left edge. */ \
+         if( iy > lbnd[ 1 ] && ix < ubnd[ 0 ] && ISVALID(*pb,OperI,value) ) { \
+            nright++; \
+            pa = pb; \
+            at = 0; \
+            ix++; \
+            iy--; \
+            dx = DELTA; \
+            dy = DELTA; \
+\
+/* Otherwise, if right mid pixel is good, move right along its lower edge. */ \
+         } else if( ix < ubnd[ 0 ] && ISVALID(*pc,OperI,value) ) { \
+            pa = pc; \
+            at = 3; \
+            ix++; \
+            dx = 0.0; \
+            dy = DELTA; \
+\
+/* Otherwise, move up the right edge of the current pixel. */ \
+         } else { \
+            nright--; \
+            at = 2; \
+            dx = -DELTA; \
+            dy = DELTA; \
+         } \
+\
+/* If the polygon bends at this point, or if we will be smoothing the \
+   polygon, append the pixel coordinates at this pixel corner to the \
+   polygon. */ \
+         if( full || pa != pc ) ADD( xx, yy ); \
+      } \
+\
+/* If we have arrived back at the start, break out of the loop. */ \
+      if( ix == ix0 && iy == iy0 && at == 2 ) done = 1; \
+   } \
+\
+/* If we have circled round to the right, the polygon will not enclosed \
+   the specified position, so free resources and return a NULL pointer. */ \
+   if( nright > 0 ) { \
+      xvert = astFree( xvert ); \
+      yvert = astFree( yvert ); \
+\
+/* If we have circled round to the left, the polygon will enclose \
+   the specified position, so create and return a PointSet. */ \
+   } else { \
+      result = astPointSet( nvert, 2, " ", status ); \
+      ptr[ 0 ] = xvert; \
+      ptr[ 1 ] = yvert; \
+      astSetPoints( result, ptr ); \
+   } \
+\
+/* Annul the returned PointSet if anythign went wrong. */ \
+   if( !astOK && result ) result = astAnnul( result ); \
+\
+/* Return the PointSet pointer. */ \
+   return result; \
+}
+
+/* Define a macro to add a vertex position to dynamically allocated
+   arrays of X and Y positions. We offset the supplied position by
+   a small fraction of a pixel towards the centre of hte polygon to
+   avoid placing vertices exactly on the edge, which may cause problems
+   later for pixels that are on the edge of an area of bad pixel. */
+#define ADD(X,Y) {\
+   ii = nvert++; \
+   xvert = (double *) astGrow( xvert, nvert, sizeof( double ) ); \
+   yvert = (double *) astGrow( yvert, nvert, sizeof( double ) ); \
+   if( astOK ) { \
+      xvert[ ii ] = (X+dx); \
+      yvert[ ii ] = (Y+dy); \
+   } \
+}
+
+/* Define a macro that uses the above macro to to create implementations
+   of TraceEdge for all operations. */
+#define MAKEALL_TRACEEDGE(X,Xtype) \
+MAKE_TRACEEDGE(X,Xtype,LT,AST__LT) \
+MAKE_TRACEEDGE(X,Xtype,LE,AST__LE) \
+MAKE_TRACEEDGE(X,Xtype,EQ,AST__EQ) \
+MAKE_TRACEEDGE(X,Xtype,NE,AST__NE) \
+MAKE_TRACEEDGE(X,Xtype,GE,AST__GE) \
+MAKE_TRACEEDGE(X,Xtype,GT,AST__GT)
+
+/* Expand the above macro to generate a function for each required
+   data type and operation. */
+#if HAVE_LONG_DOUBLE     /* Not normally implemented */
+MAKEALL_TRACEEDGE(LD,long double)
+#endif
+MAKEALL_TRACEEDGE(D,double)
+MAKEALL_TRACEEDGE(L,long int)
+MAKEALL_TRACEEDGE(UL,unsigned long int)
+MAKEALL_TRACEEDGE(I,int)
+MAKEALL_TRACEEDGE(UI,unsigned int)
+MAKEALL_TRACEEDGE(S,short int)
+MAKEALL_TRACEEDGE(US,unsigned short int)
+MAKEALL_TRACEEDGE(B,signed char)
+MAKEALL_TRACEEDGE(UB,unsigned char)
+MAKEALL_TRACEEDGE(F,float)
+
+/* Undefine the macros. */
+#undef MAKE_TRACEEDGE
+#undef MAKEALL_TRACEEDGE
+
+static AstPointSet *Transform( AstMapping *this_mapping, AstPointSet *in,
+                               int forward, AstPointSet *out, int *status ) {
+/*
+*  Name:
+*     Transform
+
+*  Purpose:
+*     Apply a Polygon to transform a set of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+*                             int forward, AstPointSet *out, int *status )
+
+*  Class Membership:
+*     Polygon member function (over-rides the astTransform protected
+*     method inherited from the Region class).
+
+*  Description:
+*     This function takes a Polygon 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 Polygon.
+*     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 Polygon.
+*     -  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: */
+   AstFrame *frm;                /* Pointer to base Frame in FrameSet */
+   AstLineDef *a;                /* Line from inside point to test point */
+   AstLineDef *b;                /* Polygon edge */
+   AstPointSet *in_base;         /* PointSet holding base Frame input positions*/
+   AstPointSet *result;          /* Pointer to output PointSet */
+   AstPolygon *this;             /* Pointer to Polygon */
+   double **ptr_in;              /* Pointer to input base Frame coordinate data */
+   double **ptr_out;             /* Pointer to output current Frame coordinate data */
+   double *px;                   /* Pointer to array of first axis values */
+   double *py;                   /* Pointer to array of second axis values */
+   double p[ 2 ];                /* Current test position */
+   int closed;                   /* Is the boundary part of the Region? */
+   int i;                        /* Edge index */
+   int icoord;                   /* Coordinate index */
+   int in_region;                /* Is the point inside the Region? */
+   int ncoord_out;               /* No. of current Frame axes */
+   int ncross;                   /* Number of crossings */
+   int neg;                      /* Has the Region been negated? */
+   int npoint;                   /* No. of input points */
+   int nv;                       /* No. of vertices */
+   int point;                    /* Loop counter for input points */
+   int pos;                      /* Is test position in, on, or outside boundary? */
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain a pointer to the Polygon structure. */
+   this = (AstPolygon *) 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 );
+
+/* Get the number of points to be transformed. */
+   npoint = astGetNpoint( result );
+
+/* Get a pointer to the output axis values. */
+   ptr_out = astGetPoints( result );
+
+/* Find the number of axes in the current Frame. This need not be 2 (the
+   number of axes in the *base* Frame must be 2 however). */
+   ncoord_out = astGetNcoord( result );
+
+/* 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. */
+   in_base = astRegTransform( this, in, 0, NULL, &frm );
+   ptr_in = astGetPoints( in_base );
+
+/* Get the number of vertices in the polygon. */
+   nv = astGetNpoint( ((AstRegion *) this)->points );
+
+/* See if the boundary is part of the Region. */
+   closed = astGetClosed( this );
+
+/* See if the Region has been negated. */
+   neg = astGetNegated( this );
+
+/* Perform coordinate arithmetic. */
+/* ------------------------------ */
+   if ( astOK ) {
+      px = ptr_in[ 0 ];
+      py = ptr_in[ 1 ];
+
+/* Loop round each supplied point in the base Frame of the polygon. */
+      for ( point = 0; point < npoint; point++, px++, py++ ) {
+
+/* If the input point is bad, indicate that bad output values should be
+   returned. */
+         if( *px == AST__BAD || *py == AST__BAD ) {
+            in_region = 0;
+
+/* Otherwise, we first determine if the point is inside, outside, or on,
+   the Polygon boundary. Initialially it is unknown. */
+         } else {
+
+/* Ensure cached information is available.*/
+            Cache( this, status );
+
+/* Create a definition of the line from a point which is inside the
+   polygon to the supplied point. This is a structure which includes
+   cached intermediate information which can be used to speed up
+   subsequent calculations. */
+            p[ 0 ] = *px;
+            p[ 1 ] = *py;
+            a = astLineDef( frm, this->in, p );
+
+/* We now determine the number of times this line crosses the polygon
+   boundary. Initialise the number of crossings to zero. */
+            ncross = 0;
+            pos = UNKNOWN;
+
+/* Loop rouind all edges of the polygon. */
+            for( i = 0; i < nv; i++ ) {
+               b = this->edges[ i ];
+
+/* If this point is on the current edge, then we need do no more checks
+   since we know it is either inside or outside the polygon (depending on
+   whether the polygon is closed or not). */
+               if( astLineContains( frm, b, 0, p ) ) {
+                  pos = ON;
+                  break;
+
+/* Otherwise, see if the two lines cross within their extent. If so,
+   increment the number of crossings. */
+               } else if( astLineCrossing( frm, b, a, NULL ) ) {
+                  ncross++;
+               }
+            }
+
+/* Free resources */
+            a = astFree( a );
+
+/* If the position is not on the boundary, it is inside the boundary if
+   the number of crossings is even, and outside otherwise. */
+            if( pos == UNKNOWN ) pos = ( ncross % 2 == 0 )? IN : OUT;
+
+/* Whether the point is in the Region depends on whether the point is
+   inside the polygon boundary, whether the Polygon has been negated, and
+   whether the polygon is closed. */
+            if( neg ) {
+               if( pos == IN ) {
+                  in_region = 0;
+               } else if( pos == OUT ) {
+                  in_region = 1;
+               } else if( closed ) {
+                  in_region = 1;
+               } else {
+                  in_region = 0;
+               }
+
+            } else {
+               if( pos == IN ) {
+                  in_region = 1;
+               } else if( pos == OUT ) {
+                  in_region = 0;
+               } else if( closed ) {
+                  in_region = 1;
+               } else {
+                  in_region = 0;
+               }
+            }
+         }
+
+/* If the point is not inside the Region, store bad output values. */
+         if( !in_region ) {
+            for ( icoord = 0; icoord < ncoord_out; icoord++ ) {
+               ptr_out[ icoord ][ point ] = AST__BAD;
+            }
+         }
+      }
+   }
+
+/* Free resources */
+   in_base = astAnnul( in_base );
+   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). */
+
+/*
+*att++
+*  Name:
+*     SimpVertices
+
+*  Purpose:
+*     Simplify a Polygon by transforming its vertices?
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Integer (boolean).
+
+*  Description:
+*     This attribute controls the behaviour of the
+c     astSimplify
+f     AST_SIMPLIFY
+*     method when applied to a Polygon. The simplified Polygon is created
+*     by transforming the vertices from the Frame in which the Polygon
+*     was originally defined into the Frame currently represented by the
+*     Polygon. If SimpVertices is non-zero (the default) then this
+*     simplified Polygon is returned without further checks. If SimpVertices
+*     is zero, a check is made that the edges of the new Polygon do not
+*     depart significantly from the edges of the original Polygon (as
+*     determined by the uncertainty associated with the Polygon). This
+*     could occur, for instance, if the Mapping frrm the original to the
+*     current Frame is highly non-linear. If this check fails, the
+*     original unsimplified Polygon is returned without change.
+
+*  Applicability:
+*     Polygon
+*        All Polygons have this attribute.
+
+*att--
+*/
+astMAKE_CLEAR(Polygon,SimpVertices,simp_vertices,-INT_MAX)
+astMAKE_GET(Polygon,SimpVertices,int,0,( ( this->simp_vertices != -INT_MAX ) ?
+                                   this->simp_vertices : 1 ))
+astMAKE_SET(Polygon,SimpVertices,int,simp_vertices,( value != 0 ))
+astMAKE_TEST(Polygon,SimpVertices,( this->simp_vertices != -INT_MAX ))
+
+/* Copy constructor. */
+/* ----------------- */
+static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
+/*
+*  Name:
+*     Copy
+
+*  Purpose:
+*     Copy constructor for Polygon objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Copy( const AstObject *objin, AstObject *objout, int *status )
+
+*  Description:
+*     This function implements the copy constructor for Polygon 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: */
+   AstPolygon *out;               /* Pointer to output Polygon  */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain pointers to the output Polygon. */
+   out = (AstPolygon *) objout;
+
+/* For safety, first clear any references to the input memory from
+   the output Polygon. */
+   out->edges = NULL;
+   out->startsat = NULL;
+
+/* Indicate cached information needs nre-calculating. */
+   astResetCache( (AstPolygon *) out );
+}
+
+
+/* Destructor. */
+/* ----------- */
+static void Delete( AstObject *obj, int *status ) {
+/*
+*  Name:
+*     Delete
+
+*  Purpose:
+*     Destructor for Polygon objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Delete( AstObject *obj, int *status )
+
+*  Description:
+*     This function implements the destructor for Polygon 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: */
+   AstPointSet *ps;                  /* Pointer to PointSet inside Region */
+   AstPolygon *this;                 /* Pointer to Polygon */
+   int i;                            /* Index of vertex */
+   int istat;                        /* Original AST error status */
+   int nv;                           /* Number of vertices */
+   int rep;                          /* Original error reporting state */
+
+/* Obtain a pointer to the Polygon structure. */
+   this = (AstPolygon *) obj;
+
+/* Annul all resources. */
+   ps = ((AstRegion *) this)->points;
+   if( this->edges && ps ) {
+
+/* Ensure we get a value for "nv" even if an error has occurred. */
+      istat = astStatus;
+      astClearStatus;
+      rep = astReporting( 0 );
+
+      nv = astGetNpoint( ps );
+
+      astSetStatus( istat );
+      astReporting( rep );
+
+/* Free the structures holding the edge information. */
+      for( i = 0; i < nv; i++ ) {
+         this->edges[ i ] = astFree( this->edges[ i ] );
+      }
+   }
+
+   this->edges = astFree( this->edges );
+   this->startsat = astFree( this->startsat );
+}
+
+/* Dump function. */
+/* -------------- */
+static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
+/*
+*  Name:
+*     Dump
+
+*  Purpose:
+*     Dump function for Polygon 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 Polygon class to an output Channel.
+
+*  Parameters:
+*     this
+*        Pointer to the Polygon 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: */
+   AstPolygon *this;             /* Pointer to the Polygon structure */
+   int ival;                     /* Integer attribute value */
+   int set;                      /* Attribute value set? */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the Polygon structure. */
+   this = (AstPolygon *) this_object;
+
+/* Write out values representing the instance variables for the
+   Polygon 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. */
+
+/* SimpVertices. */
+/* ------------ */
+/* Write out the forward-inverse simplification flag. */
+   set = TestSimpVertices( this, status );
+   ival = set ? GetSimpVertices( this, status ) : astGetSimpVertices( this );
+   astWriteInt( channel, "SimpVT", set, 0, ival, "Simplify by transforming vertices?" );
+
+/* A flag indicating the convention used for determining the interior of
+   the polygon. A zero value indicates that the old AST system is in
+   use (inside to the left when moving anti-clockwise round the vertices
+   as viewed from the outside of the celestial sphere). A non-zero value
+   indicates the STC system is in use (inside to the left when moving
+   anti-clockwise round the vertices as viewed from the inside of the
+   celestial sphere). AST currently uses the STC system. */
+   astWriteInt( channel, "Order", 1, 0, 1, "Polygon uses STC vertex order convention" );
+}
+
+/* Standard class functions. */
+/* ========================= */
+/* Implement the astIsAPolygon and astCheckPolygon functions using the macros
+   defined for this purpose in the "object.h" header file. */
+astMAKE_ISA(Polygon,Region)
+astMAKE_CHECK(Polygon)
+
+AstPolygon *astPolygon_( void *frame_void, int npnt, int dim,
+                         const double *points, AstRegion *unc,
+                         const char *options, int *status, ...) {
+/*
+*++
+*  Name:
+c     astPolygon
+f     AST_POLYGON
+
+*  Purpose:
+*     Create a Polygon.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "polygon.h"
+c     AstPolygon *astPolygon( AstFrame *frame, int npnt, int dim,
+c                             const double *points, AstRegion *unc,
+c                             const char *options, ... )
+f     RESULT = AST_POLYGON( FRAME, NPNT, DIM, POINTS, UNC, OPTIONS, STATUS )
+
+*  Class Membership:
+*     Polygon constructor.
+
+*  Description:
+*     This function creates a new Polygon object and optionally initialises
+*     its attributes.
+*
+*     The Polygon class implements a polygonal area, defined by a
+*     collection of vertices, within a 2-dimensional Frame. The vertices
+*     are connected together by geodesic curves within the encapsulated Frame.
+*     For instance, if the encapsulated Frame is a simple Frame then the
+*     geodesics will be straight lines, but if the Frame is a SkyFrame then
+*     the geodesics will be great circles. Note, the vertices must be
+*     supplied in an order such that the inside of the polygon is to the
+*     left of the boundary as the vertices are traversed. Supplying them
+*     in the reverse order will effectively negate the polygon.
+*
+*     Within a SkyFrame, neighbouring vertices are always joined using the
+*     shortest path. Thus if an edge of 180 degrees or more in length is
+*     required, it should be split into section each of which is less
+*     than 180 degrees. The closed path joining all the vertices in order
+*     will divide the celestial sphere into two disjoint regions. The
+*     inside of the polygon is the region which is circled in an
+*     anti-clockwise manner (when viewed from the inside of the celestial
+*     sphere) when moving through the list of vertices in the order in
+*     which they were supplied when the Polygon was created (i.e. the
+*     inside is to the left of the boundary when moving through the
+*     vertices in the order supplied).
+
+*  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     npnt
+f     NPNT = INTEGER (Given)
+*        The number of points in the Region.
+c     dim
+f     DIM = INTEGER (Given)
+c        The number of elements along the second dimension of the "points"
+f        The number of elements along the first dimension of the POINTS
+*        array (which contains the point coordinates). This value is
+*        required so that the coordinate values can be correctly
+*        located if they do not entirely fill this array. The value
+c        given should not be less than "npnt".
+f        given should not be less than NPNT.
+c     points
+f     POINTS( DIM, 2 ) = DOUBLE PRECISION (Given)
+c        The address of the first element of a 2-dimensional array of
+c        shape "[2][dim]" giving the physical coordinates of the vertices.
+c        These should be stored such that the value of coordinate
+c        number "coord" for point number "pnt" is found in element
+c        "in[coord][pnt]".
+f        A 2-dimensional array giving the physical coordinates of the
+f        vertices. These should be stored such that the value of coordinate
+f        number COORD for point number PNT is found in element IN(PNT,COORD).
+c     unc
+f     UNC = INTEGER (Given)
+*        An optional pointer to an existing Region which specifies the
+*        uncertainties associated with the boundary of the Polygon being created.
+*        The uncertainty in any point on the boundary of the Polygon 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 Polygon. 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 Polygon 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 Polygon. 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 Polygon. 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     astPolygon()
+f     AST_POLYGON = INTEGER
+*        A pointer to the new Polygon.
+
+*  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.
+
+*  Status Handling:
+*     The protected interface to this function includes an extra
+*     parameter at the end of the parameter list descirbed above. This
+*     parameter is a pointer to the integer inherited status
+*     variable: "int *status".
+
+*--
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstFrame *frame;              /* Pointer to Frame structure */
+   AstPolygon *new;            /* Pointer to new Polygon */
+   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 Polygon, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitPolygon( NULL, sizeof( AstPolygon ), !class_init,
+                         &class_vtab, "Polygon", frame, npnt,
+                         dim, points, 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 Polygon'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 Polygon. */
+   return new;
+}
+
+AstPolygon *astPolygonId_( void *frame_void, int npnt, int dim,
+                           const double *points, void *unc_void,
+                           const char *options, ... ) {
+/*
+*  Name:
+*     astPolygonId_
+
+*  Purpose:
+*     Create a Polygon.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     AstPolygon *astPolygonId_( void *frame_void, int npnt,
+*                                int dim, const double *points, void *unc_void,
+*                                const char *options, ... )
+
+*  Class Membership:
+*     Polygon constructor.
+
+*  Description:
+*     This function implements the external (public) interface to the
+*     astPolygon constructor function. It returns an ID value (instead
+*     of a true C pointer) to external users, and must be provided
+*     because astPolygon_ 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 astPolygon_ 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 astPolygon_.
+
+*  Returned Value:
+*     The ID value associated with the new Polygon.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstFrame *frame;              /* Pointer to Frame structure */
+   AstPolygon *new;              /* Pointer to new Polygon */
+   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);
+
+/* 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 Polygon, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitPolygon( NULL, sizeof( AstPolygon ), !class_init,
+                         &class_vtab, "Polygon", frame, npnt, dim,
+                         points, 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 Polygon'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 Polygon. */
+   return astMakeId( new );
+}
+
+
+AstPolygon *astInitPolygon_( void *mem, size_t size, int init, AstPolygonVtab *vtab,
+                             const char *name, AstFrame *frame, int npnt,
+                             int dim, const double *points, AstRegion *unc, int *status ) {
+/*
+*+
+*  Name:
+*     astInitPolygon
+
+*  Purpose:
+*     Initialise a Polygon.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     AstPolygon *astInitPolygon( void *mem, size_t size, int init, AstPolygonVtab *vtab,
+*                                 const char *name, AstFrame *frame, int npnt,
+*                                 int dim, const double *points, AstRegion *unc )
+
+*  Class Membership:
+*     Polygon initialiser.
+
+*  Description:
+*     This function is provided for use by class implementations to initialise
+*     a new Polygon object. It allocates memory (if necessary) to accommodate
+*     the Polygon plus any additional data associated with the derived class.
+*     It then initialises a Polygon 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 Polygon at the start of the memory passed via the
+*     "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory in which the Polygon is to be initialised.
+*        This must be of sufficient size to accommodate the Polygon data
+*        (sizeof(Polygon)) 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 Polygon (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 Polygon
+*        structure, so a valid value must be supplied even if not required for
+*        allocating memory.
+*     init
+*        A logical flag indicating if the Polygon'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 Polygon.
+*     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.
+*     npnt
+*        The number of points in the Region.
+*     dim
+*        The number of elements along the second dimension of the "points"
+*        array (which contains the point coordinates). This value is
+*        required so that the coordinate values can be correctly
+*        located if they do not entirely fill this array. The value
+*        given should not be less than "npnt".
+*     points
+*        The address of the first element of a 2-dimensional array of
+*        shape "[2][dim]" giving the physical coordinates of the
+*        points. These should be stored such that the value of coordinate
+*        number "coord" for point number "pnt" is found in element
+*        "in[coord][pnt]".
+*     unc
+*        A pointer to a Region which specifies the uncertainty in the
+*        supplied positions (all points in the new Polygon 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 Polygon'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 Polygon.
+
+*  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: */
+   AstPolygon *new;        /* Pointer to new Polygon */
+   AstPointSet *pset;        /* Pointer to PointSet holding points */
+   const double *q;          /* Pointer to next supplied axis value */
+   double **ptr;             /* Pointer to data in pset */
+   double *p;                /* Pointer to next PointSet axis value */
+   int i;                    /* Axis index */
+   int j;                    /* Point index */
+   int nin;                  /* No. of axes */
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* If necessary, initialise the virtual function table. */
+   if ( init ) astInitPolygonVtab( vtab, name );
+
+/* Initialise. */
+   new = NULL;
+
+/* Check the number of axis values per position is correct. */
+   nin = astGetNaxes( frame );
+   if( nin != 2 ) {
+      astError( AST__BADIN, "astInitPolygon(%s): The supplied %s has %d "
+                "axes - polygons must have exactly 2 axes.", status, name,
+                astGetClass( frame ), nin );
+
+/* If so create a PointSet and store the supplied points in it. Check
+   none are bad. */
+   } else {
+      pset = astPointSet( npnt, 2, "", status );
+      ptr = astGetPoints( pset );
+      for( i = 0; i < 2 && astOK; i++ ) {
+         p = ptr[ i ];
+         q = points + i*dim;
+         for( j = 0; j < npnt; j++ ) {
+            if( (*(p++) = *(q++)) == AST__BAD ) {
+               astError( AST__BADIN, "astInitPolygon(%s): One or more "
+                         "bad axis values supplied for the vertex "
+                         "number %d.", status, name, j + 1 );
+               break;
+            }
+         }
+      }
+
+/* Initialise a Region structure (the parent class) as the first component
+   within the Polygon structure, allocating memory if necessary. */
+      new = (AstPolygon *) astInitRegion( mem, size, 0, (AstRegionVtab *) vtab,
+                                          name, frame, pset, unc );
+      if ( astOK ) {
+
+/* Initialise the Polygon data. */
+/* ------------------------------ */
+         new->lbnd[ 0 ] = AST__BAD;
+         new->ubnd[ 0 ] = AST__BAD;
+         new->lbnd[ 1 ] = AST__BAD;
+         new->ubnd[ 1 ] = AST__BAD;
+         new->simp_vertices = -INT_MAX;
+         new->edges = NULL;
+         new->startsat = NULL;
+         new->totlen = 0.0;
+         new->acw = 1;
+         new->stale = 1;
+
+/* Ensure the vertices are stored such that the unnegated Polygon
+   represents the inside of the polygon. */
+         EnsureInside( new, status );
+
+/* If an error occurred, clean up by deleting the new Polygon. */
+         if ( !astOK ) new = astDelete( new );
+      }
+
+/* Free resources. */
+      pset = astAnnul( pset );
+
+   }
+
+/* Return a pointer to the new Polygon. */
+   return new;
+}
+
+AstPolygon *astLoadPolygon_( void *mem, size_t size, AstPolygonVtab *vtab,
+                             const char *name, AstChannel *channel, int *status ) {
+/*
+*+
+*  Name:
+*     astLoadPolygon
+
+*  Purpose:
+*     Load a Polygon.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "polygon.h"
+*     AstPolygon *astLoadPolygon( void *mem, size_t size, AstPolygonVtab *vtab,
+*                                 const char *name, AstChannel *channel )
+
+*  Class Membership:
+*     Polygon loader.
+
+*  Description:
+*     This function is provided to load a new Polygon 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
+*     Polygon 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 Polygon at the start of the memory
+*     passed via the "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory into which the Polygon is to be
+*        loaded.  This must be of sufficient size to accommodate the
+*        Polygon data (sizeof(Polygon)) 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 Polygon (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 Polygon 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(AstPolygon) is used instead.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new Polygon. If this is NULL, a pointer
+*        to the (static) virtual function table for the Polygon 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 "Polygon" is used instead.
+
+*  Returned Value:
+*     A pointer to the new Polygon.
+
+*  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 */
+   AstPolygon *new;              /* Pointer to the new Polygon */
+   int order;                    /* Is the new (STC) order convention used? */
+
+/* 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 Polygon. In this case the
+   Polygon belongs to this class, so supply appropriate values to be
+   passed to the parent class loader (and its parent, etc.). */
+   if ( !vtab ) {
+      size = sizeof( AstPolygon );
+      vtab = &class_vtab;
+      name = "Polygon";
+
+/* If required, initialise the virtual function table for this class. */
+      if ( !class_init ) {
+         astInitPolygonVtab( 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 Polygon. */
+   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, "Polygon" );
+
+/* 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. */
+
+   new->simp_vertices = astReadInt( channel, "simpvt", -INT_MAX );
+   if ( TestSimpVertices( new, status ) ) SetSimpVertices( new, new->simp_vertices, status );
+
+/* A flag indicating what order the vertices are stored in. See the Dump
+   function. */
+      order = astReadInt( channel, "order", 0 );
+
+/* Initialise other class properties. */
+      new->lbnd[ 0 ] = AST__BAD;
+      new->ubnd[ 0 ] = AST__BAD;
+      new->lbnd[ 1 ] = AST__BAD;
+      new->ubnd[ 1 ] = AST__BAD;
+      new->edges = NULL;
+      new->startsat = NULL;
+      new->totlen = 0.0;
+      new->acw = 1;
+      new->stale = 1;
+
+/* If the order in which the vertices were written used the old AST
+   convention, negate the Polygon so that it is consistent with the
+   current conevtion (based on STC). */
+      if( ! order ) astNegate( new );
+
+/* Ensure the vertices are stored such that the unnegated Polygon
+   represents the inside of the polygon. */
+      EnsureInside( new, status );
+
+/* If an error occurred, clean up by deleting the new Polygon. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return the new Polygon 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. */
+
+
+AstPolygon *astDownsize_( AstPolygon *this, double maxerr, int maxvert,
+                          int *status ) {
+   if ( !astOK ) return NULL;
+   return (**astMEMBER(this,Polygon,Downsize))( this, maxerr, maxvert, status );
+}
+
+