upgrade AST

1 files changed, 0 insertions, 7087 deletions

diff --git a/ast/polygon.c b/ast/polygon.c
deleted file mode 100644
index 1dfae39..0000000
--- a/ast/polygon.c
+++ /dev/null
@@ -1,7087 +0,0 @@
-/*
-*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 ] );
-         }
-
-/* Allocate memory to store new edge information if necessary. */
-      } else {
-         this->edges = astMalloc( sizeof( AstLineDef *)*(size_t) nv );
-         this->startsat = astMalloc( sizeof( double )*(size_t) nv );
-      }
-
-/* Check pointers can be used safely. */
-      if( this->edges ) {
-
-/* 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 = astAnnul( *mask );
-   }
-
-/* Return the result. */
-   return result;
-}
-
-static int RegTrace( AstRegion *this_region, int n, double *dist, double **ptr,
-                     int *status ){
-/*
-*+
-*  Name:
-*     RegTrace
-
-*  Purpose:
-*     Return requested positions on the boundary of a 2D Region.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "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 ? astCheckRegion( 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 );
-}
-
-