path: root/ast/region.c

/*
*class++
*  Name:
*     Region

*  Purpose:
*     Represents a region within a coordinate system.

*  Constructor Function:
*     None.

*  Description:
*     This class provides the basic facilities for describing a region within
*     a specified coordinate system. However, the Region class does not
*     have a constructor function of its own, as it is simply a container
*     class for a family of specialised sub-classes such as Circle, Box, etc,
*     which implement Regions with particular shapes.
*
*     All sub-classes of Region require a Frame to be supplied when the Region
*     is created. This Frame describes the coordinate system in which the
*     Region is defined, and is referred to as the "encapsulated Frame" below.
*     Constructors will also typically required one or more positions to be
*     supplied which define the location and extent of the region. These
*     positions must be supplied within the encapsulated Frame.
*
*     The Region class inherits from the Frame class, and so a Region can be
*     supplied where-ever a Frame is expected. In these cases, supplying a
*     Region is equivalent to supplying a reference to its encapsulated Frame.
*     Thus all the methods of the Frame class can be used on the Region class.
*     For instance, the
c     astFormat function
f     AST_FORMAT routine
*     may be used on a Region to format an axis value.
*
*     In addition, since Frame inherits from Mapping, a Region is also a sort
*     of Mapping. Transforming positions by supplying a Region to one of the
c     astTran<X> functions
f     AST_TRAN<X> routines
*     is the way to determine if a given position is inside or outside the
*     Region. When used as a Mapping, most classes of Frame are equivalent to
*     a UnitMap. However, the Region class modifies this behaviour so that a
*     Region acts like a UnitMap only for input positions which are within the
*     area represented by the Region. Input positions which are outside the
*     area produce bad output values (i.e. the output values are equal to
*     AST__BAD). This behaviour is the same for both the forward and the
*     inverse transformation. In this sense the "inverse transformation"
*     is not a true inverse of the forward transformation, since applying
*     the forward transformation to a point outside the Region, and then
*     applying the inverse transformation results, in a set of AST__BAD axis
*     values rather than the original axis values. If required, the
c     astRemoveRegions
f     AST_REMOVEREGIONS
*     function can be used to remove the "masking" effect of any Regions
*     contained within a compound Mapping or FrameSet. It does this by
*     replacing each Region with a UnitMap or equivalent Frame (depending
*     on the context in which the Region is used).
*
*     If the coordinate system represented by the Region is changed (by
*     changing the values of one or more of the attribute which the Region
*     inherits from its encapsulated Frame), the area represented by
*     the Region is mapped into the new coordinate system. For instance, let's
*     say a Circle (a subclass of Region) is created, a SkyFrame being
*     supplied to the constructor so that the Circle describes a circular
*     area on the sky in FK4 equatorial coordinates. Since Region inherits
*     from Frame, the Circle will have a System attribute and this attribute
*     will be set to "FK4". If the System attribute of the Region is then
*     changed from FK4 to FK5, the circular area represented by the Region
*     will automatically be mapped from the FK4 system into the FK5 system.
*     In general, changing the coordinate system in this way may result in the
*     region changing shape - for instance, a circle may change into an
*     ellipse if the transformation from the old to the new coordinate system
*     is linear but with different scales on each axis. Thus the specific
*     class of a Region cannot be used as a guarantee of the shape in any
*     particular coordinate system. If the
c     astSimplify function
f     AST_SIMPLIFY routine
*     is used on a Region, it will endeavour to return a new Region of
*     a sub-class which accurately describes the shape in the current
*     coordinate system of the Region (but this may not always be possible).
*
*     It is possible to negate an existing Region so that it represents all
*     areas of the encapsulated Frame except for the area specified when
*     the Region was created.

*  Inheritance:
*     The Region class inherits from the Frame class.

*  Attributes:
*     In addition to those attributes common to all Frames, every
*     Region also has the following attributes:
*
*     - Adaptive: Should the area adapt to changes in the coordinate system?
*     - Negated: Has the original region been negated?
*     - Closed: Should the boundary be considered to be inside the region?
*     - MeshSize: Number of points used to create a mesh covering the Region
*     - FillFactor: Fraction of the Region which is of interest
*     - Bounded: Is the Region bounded?
*
*     Every Region also inherits any further attributes that belong
*     to the encapsulated Frame, regardless of that Frame's class. (For
*     example, the Equinox attribute, defined by the SkyFrame class, is
*     inherited by any Region which represents a SkyFrame.)

*  Functions:
c     In addition to those functions applicable to all Frames, the
c     following functions may also be applied to all Regions:
f     In addition to those routines applicable to all Frames, the
f     following routines may also be applied to all Regions:
*
c     - astGetRegionBounds: Get the bounds of a box containing a Region
f     - AST_GETREGIONBOUNDS: Get the bounds of a box containing a Region
c     - astGetRegionFrame: Get a copy of the Frame represent by a Region
f     - AST_GETREGIONFRAME: Get a copy of the Frame represent by a Region
c     - astGetRegionFrameSet: Get a copy of the Frameset encapsulated by a Region
f     - AST_GETREGIONFRAMESET: Get a copy of the Frameset encapsulated by a Region
c     - astGetRegionMesh: Get a mesh of points covering a Region
f     - AST_GETREGIONMESH: Get a mesh of points covering a Region
c     - astGetRegionPoints: Get the positions that define a Region
f     - AST_GETREGIONPOINTS: Get the positions that define a Region
c     - astGetUnc: Obtain uncertainty information from a Region
c     - astGetRegionDisc: Get the bounds of disc containing a Region
f     - AST_GETREGIONDISC: Get the bounds of disc containing a Region
f     - AST_GETUNC: Obtain uncertainty information from a Region
c     - astMapRegion: Transform a Region into a new coordinate system
f     - AST_MAPREGION: Transform a Region into a new coordinate system
c     - astNegate: Toggle the value of the Negated attribute
f     - AST_NEGATE: Toggle the value of the Negated attribute
c     - astOverlap: Determines the nature of the overlap between two Regions
f     - AST_OVERLAP: Determines the nature of the overlap between two Regions
c     - astMask<X>: Mask a region of a data grid
f     - AST_MASK<X>: Mask a region of a data grid
c     - astSetUnc: Associate a new uncertainty with a Region
f     - AST_SETUNC: Associate a new uncertainty with a Region
c     - astShowMesh: Display a mesh of points on the surface of a Region
f     - AST_SHOWMESH: Display a mesh of points on the surface of a Region

*  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:
*     3-DEC-2003 (DSB):
*        Original version.
*     12-MAY-2005 (DSB):
*        Override astNormBox method.
*     12-AUG-2005 (DSB):
*        Override ObsLat and ObsLon accessor methods.
*     14-FEB-2006 (DSB):
*        Override astGetObjSize.
*     2-MAR-2006 (DSB):
*        Changed AST_LONG_DOUBLE to HAVE_LONG_DOUBLE.
*     14-MAR-2006 (DSB):
*        Added astGetRefFS.
*     28-MAY-2007 (DSB):
*        - Added protected function astBndMesh.
*     14-JAN-2009 (DSB):
*        Override the astIntersect method.
*     20-JAN-2009 (DSB):
*        Change astPickAxes so that it returns a Region rather than a
*        Frame if possible. This included adding method astRegBasePick.
*     9-FEB-2009 (DSB):
*        Move PointList methods astGetEnclosure and astSetEnclosure to
*        Region.
*     18-FEB-2009 (DSB):
*        Remove methods astGetEnclosure and astSetEnclosure.
*     15-JUN-2009 (DSB):
*        Modify MapRegion to use FrameSets properly.
*     18-JUN-2009 (DSB):
*        Override ObsAlt accessor methods.
*     7-SEP-2009 (DSB):
*        Fix astMask to avoid reading variance values from the data array.
*     8-SEP-2009 (DSB):
*        Fix bugs in astOverlap that could result in wrong results if
*        either region is unbounded.
*     4-JAN-2010 (DSB):
*        Fix bug in GetRegionBounds (it was assumed implicitly that the base
*        Frame had the same number of axes as the current Frame).
*     18-MAR-2011 (DSB):
*        Added astGetRegionMesh public method.
*     22-MAR-2011 (DSB):
*        Improve uniformity of points produced by astRegBaseGrid method.
*     29-APR-2011 (DSB):
*        Prevent astFindFrame from matching a subclass template against a
*        superclass target.
*     17-MAY-2011 (DSB):
*        In RegBaseGrid, accept the final try even if it is not within 5%
*        of the required meshsize.
*     27-APR-2012 (DSB):
*        Store a negated copy of itself with each Region. Changing the Negated
*        attribute of a Region causes the cached information to be reset, and
*        re-calculating it can be an expensive operation. So instead of changing
*        "Negatated" in "this", access the negated copy of "this" using the
*        new protected method astGetNegation.
*     7-JUN-2012 (DSB):
*        Added protected astRegSplit method to split a Region into disjoint
*        component regions.
*     15-JUN-2012 (DSB):
*        Guard against division by zero in RegBase Grid if "ipr" is zero.
*     7-NOV-2013 (DSB):
*        Added method astGetRegionFrameSet.
*     3-FEB-2014 (DSB):
*        Fix bug masking regions that have no overlap with the supplied array.
*     17-APR-2015 (DSB):
*        Added Centre.
*     26-OCT-2016 (DSB):
*        - Override the astAxNorm method.
*        - Use astAxNorm to fix a bug in astGetRegionBounds for cases where
*        the Region cross a longitude=0 singularity.
*     11-NOV-2016 (DSB):
*        When loading a Region, use the dimensionality of the base Frame
*        of the FrameSet (rather than the current Frame as it used to be)
*        to define the number of axes required in the PointSet.
*     1-DEC-2016 (DSB):
*        Changed MapRegion to remove any unnecessary base frame axes in
*        the returned Region.
*     15-NOV-2018 (DSB):
*        Use error code AST__NOIMP instead of AST__INTER when reporting
*        an error about an abstract method not being implemented.
*     4-DEC-2018 (DSB):
*        Change GetBounded so that Regions defined within SkyFrames are
*        always bounded, whether negated or not.
*     11-DEC-2018 (DSB):
*        Add astGetRegionDisc.
*     16-JAN-2019 (DSB):
*        Change Conv() so that it aligns in the current Frame of "to". Without this, 
*        it is possible for uncertainty regions to be mapped incorrectly into the 
*        frame of the new region when creating new regions.
*class--

*  Implementation Notes:
*     - All sub-classes must over-ride the following abstract methods
*     declared in this class: astRegBaseBox, astRegBaseMesh, astRegPins,
*     astRegTrace. They must also extend the astTransform method. In addition
*     they should usually extend astSimplify and astRegCentre.

*/

/* 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 Region

/* Value for Ident attribute of of an encapsulated FrameSet which
   indicates that it is a dummy FrameSet (see astRegDummy). */
#define DUMMY_FS "ASTREGION-DUMMY"

/*
*  Name:
*     MAKE_CLEAR

*  Purpose:
*     Define a function to clear an attribute value for a Region.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_CLEAR(attribute)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static void Clear<Attribute>( AstFrame *this )
*
*     that clears the value of a specified attribute for the encapsulated
*     FrameSet within a Region (this). This function is intended to over-ride
*     the astClear<Attribute> method inherited from the Frame class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*/

/* Define the macro. */
#define MAKE_CLEAR(attribute) \
static void Clear##attribute( AstFrame *this_frame, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to the Region structure */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Obtain a pointer to the encapsulated FrameSet and invoke its \
   astClear method. The protected astClear##attribute method is not used \
   because we want the current Frame of the FrameSet tp be re-mapped if \
   necessary. */ \
   astClear( this->frameset, #attribute ); \
}

/*
*  Name:
*     MAKE_CLEAR_AXIS

*  Purpose:
*     Define a function to clear an attribute value for a Region axis.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_CLEAR_AXIS(attribute)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static void Clear<Attribute>( AstFrame *this, int axis )
*
*     that clears the value of a specified attribute for an axis of
*     the encapsulated FrameSet within a Region (this). This function is
*     intended to over-ride the astClear<Attribute> method inherited
*     from the Frame class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*/

/* Define the macro. */
#define MAKE_CLEAR_AXIS(attribute) \
static void Clear##attribute( AstFrame *this_frame, int axis, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to the Region structure */ \
   char buf[100];              /* Buffer for attribute name */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Validate the axis index supplied. */ \
   (void) astValidateAxis( this, axis, 1, "astClear" #attribute ); \
\
/* We use the public astSetx method rather than the protected \
   astSet#attribute method so that the current Frame in the encapsulated \
   FrameSet will be re-mapped if necessary. Construct the attribute name. */ \
   sprintf( buf, "%s(%d)", #attribute, axis + 1 ); \
\
/* Obtain a pointer to the Region's encapsulated FrameSet and invoke its \
   astClear method. The protected astClear#attribute method is notused \
   since we want the current Frame of the encapsulated FrameSet to be \
   remapped if required. */ \
   astClear( this->frameset, buf ); \
}

/*
*  Name:
*     MAKE_GET

*  Purpose:
*     Define a function to get an attribute value for a Region.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_GET(attribute,type)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static <type> Get<Attribute>( AstFrame *this )
*
*     that gets the value of a specified attribute for the encapsulated
*     FrameSet of a Region (this). This function is intended to over-ride
*     the astGet<Attribute> method inherited from the Frame class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*     type
*        The C type of the attribute.
*/

/* Define the macro. */
#define MAKE_GET(attribute,type) \
static type Get##attribute( AstFrame *this_frame, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to the Region structure */ \
   type result;                /* Value to return */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return (type) 0; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Obtain a pointer to the encapsulated FrameSet and invoke its \
   astGet<Attribute> method.  */ \
   result = astGet##attribute( this->frameset ); \
\
/* If an error occurred, clear the result value. */ \
   if ( !astOK ) result = (type) 0; \
\
/* Return the result. */ \
   return result; \
}

/*
*  Name:
*     MAKE_GET_AXIS

*  Purpose:
*     Define a function to get an attribute value for a Region axis.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_GET_AXIS(attribute,type)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static <type> Get<Attribute>( AstFrame *this, int axis )
*
*     that gets the value of a specified attribute for an axis of the
*     encapsulated FrameSet within a Region (this). This function is intended
*     to over-ride the astGet<Attribute> method inherited from the Frame
*     class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*     type
*        The C type of the attribute.
*/

/* Define the macro. */
#define MAKE_GET_AXIS(attribute,type) \
static type Get##attribute( AstFrame *this_frame, int axis, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to the Region structure */ \
   type result;                /* Value to return */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return (type) 0; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Validate the axis index supplied. */ \
   (void) astValidateAxis( this, axis, 1, "astGet" #attribute ); \
\
/* Obtain a pointer to the Region's encapsulated FrameSet and invoke its \
   astGet<Attribute> method.  */ \
   result = astGet##attribute( this->frameset, axis ); \
\
/* If an error occurred, clear the result value. */ \
   if ( !astOK ) result = (type) 0; \
\
/* Return the result. */ \
   return result; \
}

/*
*  Name:
*     MAKE_SET_SYSTEM

*  Purpose:
*     Define a function to set a System attribute value for a Region.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_SET_SYSTEM(attribute)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static void Set<Attribute>( AstFrame *this, AstSystemType value )
*
*     that sets the value of a specified attribute for the encapsulated
*     FrameSet of a Region (this). This function is intended to over-ride the
*     astSet<Attribute> method inherited from the Frame class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*/

/* Define the macro. */
#define MAKE_SET_SYSTEM(attribute) \
static void Set##attribute( AstFrame *this_frame, AstSystemType value, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to the Region structure */ \
   const char *text;           /* Pointer to system string */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Convert the supplied value to a string using the astSystemString
   method of the current Frame in the encapsulated FrameSet. */ \
   text = astSystemString( this->frameset, value ); \
\
/* Set the value by invoking the public astSetC method on the encapusulated \
   FrameSet. This ensures that the current Frame of the encapsulated \
   FrameSet is re-mapped if necessary. */ \
   astSetC( this->frameset, #attribute, text ); \
}

/*
*  Name:
*     MAKE_SET

*  Purpose:
*     Define a function to set an attribute value for a Region.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_SET(attribute,type,x)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static void Set<Attribute>( AstFrame *this, <type> value )
*
*     that sets the value of a specified attribute for the encapsulated
*     FrameSet of a Region (this). This function is intended to over-ride the
*     astSet<Attribute> method inherited from the Frame class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*     type
*        The C type of the attribute.
*     x
*        The single character code for the astSetx function for the given C
*        type.
*/

/* Define the macro. */
#define MAKE_SET(attribute,type,x) \
static void Set##attribute( AstFrame *this_frame, type value, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to the Region structure */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Set the value by invoking the public astSetx method on the encapusulated \
   FrameSet. This ensures that the current Frame of the encapsulated \
   FrameSet is re-mapped if necessary. */ \
   astSet##x( this->frameset, #attribute, value ); \
}

/*
*  Name:
*     MAKE_SET_AXIS

*  Purpose:
*     Define a function to set an attribute value for a Region axis.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_SET_AXIS(attribute,type,x)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static void Set<Attribute>( AstFrame *this, int axis, <type> value )
*
*     that sets the value of a specified attribute for an axis of the
*     encapsulated FrameSet within a Region (this). This function is intended
*     to over-ride the astSet<Attribute> method inherited from the Frame
*     class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*     type
*        The C type of the attribute.
*     x
*        The single character code for the astSetx function for the given C
*        type.
*/

/* Define the macro. */
#define MAKE_SET_AXIS(attribute,type,x) \
static void Set##attribute( AstFrame *this_frame, int axis, type value, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to the Region structure */ \
   char buf[100];              /* Buffer for attribute name */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Validate the axis index supplied. */ \
   (void) astValidateAxis( this, axis, 1, "astSet" #attribute ); \
\
/* We use the public astSetx method rather than the protected \
   astSet#attribute method so that the current Frame in the encapsulated \
   FrameSet will be re-mapped if necessary. Construct the attribute name. */ \
   sprintf( buf, "%s(%d)", #attribute, axis + 1 ); \
\
/* Obtain a pointer to the Region's encapsulated FrameSet and invoke its \
   astSet<x> method.  */ \
   astSet##x( this->frameset, buf, value ); \
}

/*
*  Name:
*     MAKE_TEST

*  Purpose:
*     Define a function to test if an attribute value is set for a Region.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_TEST(attribute)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static int Test<Attribute>( AstFrame *this )
*
*     that returns a boolean result (0 or 1) to indicate if the value
*     of a specified attribute for the encapsulated FrameSet within a
*     Region (this) is set. This function is intended to over-ride the
*     astTest<Attribute> method inherited from the Frame class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*/

/* Define the macro. */
#define MAKE_TEST(attribute) \
static int Test##attribute( AstFrame *this_frame, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;            /* Pointer to Region structure */ \
   int result;                 /* Result to return */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return 0; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Obtain a pointer to the Region's encapsulated FrameSet and invoke its \
   astTest<Attribute> method.  */ \
   result = astTest##attribute( this->frameset ); \
\
/* If an error occurred, clear the result value. */ \
   if ( !astOK ) result = 0; \
\
/* Return the result. */ \
   return result; \
}

/*
*  Name:
*     MAKE_TEST_AXIS

*  Purpose:
*     Define a function to test if an attribute value is set for a Region
*     axis.

*  Type:
*     Private macro.

*  Synopsis:
*     #include "region.h"
*     MAKE_TEST_AXIS(attribute)

*  Class Membership:
*     Defined by the Region class.

*  Description:
*     This macro expands to an implementation of a private member function
*     of the form:
*
*        static int Test<Attribute>( AstFrame *this, int axis )
*
*     that returns a boolean result (0 or 1) to indicate if the value
*     of a specified attribute for an axis of the encapsulated FrameSet
*     within a Region (this) is set. This function is intended to over-ride
*     the astTest<Attribute> method inherited from the Frame class.

*  Parameters:
*     attribute
*        Name of the attribute, as it appears in the function name.
*/

/* Define the macro. */
#define MAKE_TEST_AXIS(attribute) \
static int Test##attribute( AstFrame *this_frame, int axis, int *status ) { \
\
/* Local Variables: */ \
   AstRegion *this;              /* Pointer to the Region structure */ \
   int result;                   /* Value to return */ \
\
/* Check the global error status. */ \
   if ( !astOK ) return 0; \
\
/* Obtain a pointer to the Region structure. */ \
   this = (AstRegion *) this_frame; \
\
/* Validate the axis index supplied. */ \
   (void) astValidateAxis( this, axis, 1, "astTest" #attribute ); \
\
/* Obtain a pointer to the Region's encapsulated FrameSet and invoke its \
   astTest<Attribute> method.  */ \
   result = astTest##attribute( this->frameset, axis ); \
\
/* If an error occurred, clear the result value. */ \
   if ( !astOK ) result = 0; \
\
/* Return the result. */ \
   return result; \
}

/* Header 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 "mapping.h"             /* Coordinate Mappings */
#include "unitmap.h"             /* Unit Mappings */
#include "permmap.h"             /* Coordinate permutation Mappings */
#include "cmpmap.h"              /* Compound Mappings */
#include "frame.h"               /* Parent Frame class */
#include "skyframe.h"            /* Celestial coordinate frames */
#include "frameset.h"            /* Interconnected coordinate systems */
#include "region.h"              /* Interface definition for this class */
#include "circle.h"              /* Circular regions */
#include "box.h"                 /* Box regions */
#include "cmpregion.h"           /* Compound regions */
#include "wcsmap.h"              /* For AST__DPI */
#include "ellipse.h"             /* Elliptical regions */
#include "pointset.h"            /* Sets of points */
#include "globals.h"             /* Thread-safe global data access */

/* Error code definitions. */
/* ----------------------- */
#include "ast_err.h"             /* AST error codes */

/* C header files. */
/* --------------- */
#include <ctype.h>
#include <limits.h>
#include <stdarg.h>
#include <stddef.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>

/* Module Variables. */
/* ================= */

/* Address of this static variable is used as a unique identifier for
   member of this class. */
static int class_check;

/* Pointers to parent class methods which are extended by this class. */
static int (* parent_getobjsize)( AstObject *, int * );
static int (* parent_getusedefs)( AstObject *, int * );

#if defined(THREAD_SAFE)
static int (* parent_managelock)( AstObject *, int, int, AstObject **, int * );
#endif

/* Define macros for accessing each item of thread specific global data. */
#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(Region)

/* Define macros for accessing each item of thread specific global data. */
#define class_init astGLOBAL(Region,Class_Init)
#define class_vtab astGLOBAL(Region,Class_Vtab)
#define getattrib_buff astGLOBAL(Region,GetAttrib_Buff)



/* If thread safety is not needed, declare and initialise globals at static
   variables. */
#else

static char getattrib_buff[ 101 ];


/* Define the class virtual function table and its initialisation flag
   as static variables. */
static AstRegionVtab class_vtab;   /* Virtual function table */
static int class_init = 0;       /* Virtual function table initialised? */

#endif

/* Prototypes for Private Member Functions. */
/* ======================================== */
#if HAVE_LONG_DOUBLE     /* Not normally implemented */
static int MaskLD( AstRegion *, AstMapping *, int, int, const int[], const int ubnd[], long double [], long double, int * );
#endif
static int MaskB( AstRegion *, AstMapping *, int, int, const int[], const int[], signed char[], signed char, int * );
static int MaskD( AstRegion *, AstMapping *, int, int, const int[], const int[], double[], double, int * );
static int MaskF( AstRegion *, AstMapping *, int, int, const int[], const int[], float[], float, int * );
static int MaskI( AstRegion *, AstMapping *, int, int, const int[], const int[], int[], int, int * );
static int MaskL( AstRegion *, AstMapping *, int, int, const int[], const int[], long int[], long int, int * );
static int MaskS( AstRegion *, AstMapping *, int, int, const int[], const int[], short int[], short int, int * );
static int MaskUB( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned char[], unsigned char, int * );
static int MaskUI( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned int[], unsigned int, int * );
static int MaskUL( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned long int[], unsigned long int, int * );
static int MaskUS( AstRegion *, AstMapping *, int, int, const int[], const int[], unsigned short int[], unsigned short int, int * );

static AstAxis *GetAxis( AstFrame *, int, int * );
static AstFrame *GetRegionFrame( AstRegion *, int * );
static AstFrameSet *GetRegionFrameSet( AstRegion *, int * );
static AstFrame *PickAxes( AstFrame *, int, const int[], AstMapping **, int * );
static AstFrame *RegFrame( AstRegion *, int * );
static AstFrameSet *Conv( AstFrameSet *, AstFrameSet *, int * );
static AstFrameSet *Convert( AstFrame *, AstFrame *, const char *, int * );
static AstFrameSet *ConvertX( AstFrame *, AstFrame *, const char *, int * );
static AstFrameSet *FindFrame( AstFrame *, AstFrame *, const char *, int * );
static AstFrameSet *GetRegFS( AstRegion *, int * );
static AstLineDef *LineDef( AstFrame *, const double[2], const double[2], int * );
static AstMapping *RegMapping( AstRegion *, int * );
static AstMapping *RemoveRegions( AstMapping *, int * );
static AstMapping *Simplify( AstMapping *, int * );
static AstObject *Cast( AstObject *, AstObject *, int * );
static AstPointSet *BTransform( AstRegion *, AstPointSet *, int, AstPointSet *, int * );
static AstPointSet *BndBaseMesh( AstRegion *, double *, double *, int * );
static AstPointSet *BndMesh( AstRegion *, double *, double *, int * );
static AstPointSet *GetSubMesh( int *, AstPointSet *, int * );
static AstPointSet *RegBaseGrid( AstRegion *, int * );
static AstPointSet *RegBaseMesh( AstRegion *, int * );
static AstPointSet *RegGrid( AstRegion *, int * );
static AstPointSet *RegMesh( AstRegion *, int * );
static AstPointSet *RegTransform( AstRegion *, AstPointSet *, int, AstPointSet *, AstFrame **, int * );
static AstPointSet *ResolvePoints( AstFrame *, const double [], const double [], AstPointSet *, AstPointSet *, int * );
static AstRegion *MapRegion( AstRegion *, AstMapping *, AstFrame *, int * );
static AstRegion *RegBasePick( AstRegion *, int, const int *, int * );
static AstRegion **RegSplit( AstRegion *, int *, int * );
static AstSystemType SystemCode( AstFrame *, const char *, int * );
static AstSystemType ValidateSystem( AstFrame *, AstSystemType, const char *, int * );
static const char *Abbrev( AstFrame *, int, const char *, const char *, const char *, int * );
static const char *Format( AstFrame *, int, double, int * );
static const char *SystemString( AstFrame *, AstSystemType, int * );
static const int *GetPerm( AstFrame *, int * );
static double *RegCentre( AstRegion *, double *, double **, int, int, int * );
static double Angle( AstFrame *, const double[], const double[], const double[], int * );
static double AxAngle( AstFrame *, const double[], const double[], int, int * );
static double AxDistance( AstFrame *, int, double, double, int * );
static double AxOffset( AstFrame *, int, double, double, int * );
static double Distance( AstFrame *, const double[], const double[], int * );
static double Centre( AstFrame *, int, double, double, int * );
static double Gap( AstFrame *, int, double, int *, int * );
static double Offset2( AstFrame *, const double[2], double, double, double[2], int * );
static int Equal( AstObject *, AstObject *, int * );
static int GetNaxes( AstFrame *, int * );
static int GetObjSize( AstObject *, int * );
static int GetUseDefs( AstObject *, int * );
static int IsUnitFrame( AstFrame *, int * );
static int LineContains( AstFrame *, AstLineDef *, int, double *, int * );
static int LineCrossing( AstFrame *, AstLineDef *, AstLineDef *, double **, int * );
static int Match( AstFrame *, AstFrame *, int, int **, int **, AstMapping **, AstFrame **, int * );
static int Overlap( AstRegion *, AstRegion *, int * );
static int OverlapX( AstRegion *, AstRegion *, int * );
static int RegDummyFS( AstRegion *, int * );
static int RegPins( AstRegion *, AstPointSet *, AstRegion *, int **, int * );
static int SubFrame( AstFrame *, AstFrame *, int, const int *, const int *, AstMapping **, AstFrame **, int * );
static int RegTrace( AstRegion *, int, double *, double **, int * );
static int Unformat( AstFrame *, int, const char *, double *, int * );
static int ValidateAxis( AstFrame *, int, int, const char *, int * );
static void AxNorm( AstFrame *, int, int, int, double *, int * );
static void CheckPerm( AstFrame *, const int *, const char *, int * );
static void Copy( const AstObject *, AstObject *, int * );
static void Delete( AstObject *, int * );
static void Dump( AstObject *, AstChannel *, int * );
static void GetRegionBounds( AstRegion *, double *, double *, int * );
static void GetRegionBounds2( AstRegion *, double *, double *, int * );
static void GetRegionMesh( AstRegion *, int, int, int, int *, double *, int * );
static void GetRegionPoints( AstRegion *, int, int, int *, double *, int * );
static void GetRegionDisc( AstRegion *, double[2], double *, int * );
static void Intersect( AstFrame *, const double[2], const double[2], const double[2], const double[2], double[2], int * );
static void LineOffset( AstFrame *, AstLineDef *, double, double, double[2], int * );
static void MatchAxes( AstFrame *, AstFrame *, int *, int * );
static void MatchAxesX( AstFrame *, AstFrame *, int *, int * );
static void Negate( AstRegion *, int * );
static void Norm( AstFrame *, double[], int * );
static void NormBox( AstFrame *, double[], double[], AstMapping *, int * );
static void Offset( AstFrame *, const double[], const double[], double, double[], int * );
static void Overlay( AstFrame *, const int *, AstFrame *, int * );
static void PermAxes( AstFrame *, const int[], int * );
static void RegBaseBox( AstRegion *, double *, double *, int * );
static void RegBaseBox2( AstRegion *, double *, double *, int * );
static void RegClearAttrib( AstRegion *, const char *, char **, int * );
static void RegOverlay( AstRegion *, AstRegion *, int, int * );
static void RegSetAttrib( AstRegion *, const char *, char **, int * );
static void ReportPoints( AstMapping *, int, AstPointSet *, AstPointSet *, int * );
static void ResetCache( AstRegion *, int * );
static void Resolve( AstFrame *, const double [], const double [], const double [], double [], double *, double *, int * );
static void SetAxis( AstFrame *, int, AstAxis *, int * );
static void SetRegFS( AstRegion *, AstFrame *, int * );
static void ShowMesh( AstRegion *, int, const char *, int * );
static void ValidateAxisSelection( AstFrame *, int, const int *, const char *, int * );
static AstRegion *GetNegation( AstRegion *, int * );

static int GetBounded( AstRegion *, int * );
static AstRegion *GetDefUnc( AstRegion *, int * );

static AstRegion *GetUncFrm( AstRegion *, int, int * );
static AstRegion *GetUnc( AstRegion *, int, int * );
static int TestUnc( AstRegion *, int * );
static void ClearUnc( AstRegion *, int * );
static void SetUnc( AstRegion *, AstRegion *, int * );

static const char *GetDomain( AstFrame *, int * );
static int TestDomain( AstFrame *, int * );
static void ClearDomain( AstFrame *, int * );
static void SetDomain( AstFrame *, const char *, int * );

static const char *GetFormat( AstFrame *, int, int * );
static int TestFormat( AstFrame *, int, int * );
static void ClearFormat( AstFrame *, int, int * );
static void SetFormat( AstFrame *, int, const char *, int * );

static const char *GetLabel( AstFrame *, int, int * );
static int TestLabel( AstFrame *, int, int * );
static void ClearLabel( AstFrame *, int, int * );
static void SetLabel( AstFrame *, int, const char *, int * );

static const char *GetSymbol( AstFrame *, int, int * );
static int TestSymbol( AstFrame *, int, int * );
static void ClearSymbol( AstFrame *, int, int * );
static void SetSymbol( AstFrame *, int, const char *, int * );

static const char *GetTitle( AstFrame *, int * );
static void SetTitle( AstFrame *, const char *, int * );
static void ClearTitle( AstFrame *, int * );
static int TestTitle( AstFrame *, int * );

static const char *GetUnit( AstFrame *, int, int * );
static int TestUnit( AstFrame *, int, int * );
static void ClearUnit( AstFrame *, int, int * );
static void SetUnit( AstFrame *, int, const char *, int * );

static int GetDigits( AstFrame *, int * );
static int TestDigits( AstFrame *, int * );
static void ClearDigits( AstFrame *, int * );
static void SetDigits( AstFrame *, int, int * );

static int GetDirection( AstFrame *, int, int * );
static int TestDirection( AstFrame *, int, int * );
static void ClearDirection( AstFrame *, int, int * );
static void SetDirection( AstFrame *, int, int, int * );

static int GetActiveUnit( AstFrame *, int * );
static int TestActiveUnit( AstFrame *, int * );
static void SetActiveUnit( AstFrame *, int, int * );

static int GetMatchEnd( AstFrame *, int * );
static int TestMatchEnd( AstFrame *, int * );
static void ClearMatchEnd( AstFrame *, int * );
static void SetMatchEnd( AstFrame *, int, int * );

static int GetMaxAxes( AstFrame *, int * );
static int TestMaxAxes( AstFrame *, int * );
static void ClearMaxAxes( AstFrame *, int * );
static void SetMaxAxes( AstFrame *, int, int * );

static int GetMinAxes( AstFrame *, int * );
static int TestMinAxes( AstFrame *, int * );
static void ClearMinAxes( AstFrame *, int * );
static void SetMinAxes( AstFrame *, int, int * );

static int GetPermute( AstFrame *, int * );
static int TestPermute( AstFrame *, int * );
static void ClearPermute( AstFrame *, int * );
static void SetPermute( AstFrame *, int, int * );

static int GetPreserveAxes( AstFrame *, int * );
static int TestPreserveAxes( AstFrame *, int * );
static void ClearPreserveAxes( AstFrame *, int * );
static void SetPreserveAxes( AstFrame *, int, int * );

static double GetBottom( AstFrame *, int, int * );
static int TestBottom( AstFrame *, int, int * );
static void ClearBottom( AstFrame *, int, int * );
static void SetBottom( AstFrame *, int, double, int * );

static double GetTop( AstFrame *, int, int * );
static int TestTop( AstFrame *, int, int * );
static void ClearTop( AstFrame *, int, int * );
static void SetTop( AstFrame *, int, double, int * );

static double GetEpoch( AstFrame *, int * );
static int TestEpoch( AstFrame *, int * );
static void ClearEpoch( AstFrame *, int * );
static void SetEpoch( AstFrame *, double, int * );

static double GetObsAlt( AstFrame *, int * );
static int TestObsAlt( AstFrame *, int * );
static void ClearObsAlt( AstFrame *, int * );
static void SetObsAlt( AstFrame *, double, int * );

static double GetObsLat( AstFrame *, int * );
static int TestObsLat( AstFrame *, int * );
static void ClearObsLat( AstFrame *, int * );
static void SetObsLat( AstFrame *, double, int * );

static double GetObsLon( AstFrame *, int * );
static int TestObsLon( AstFrame *, int * );
static void ClearObsLon( AstFrame *, int * );
static void SetObsLon( AstFrame *, double, int * );

static AstSystemType GetSystem( AstFrame *, int * );
static int TestSystem( AstFrame *, int * );
static void ClearSystem( AstFrame *, int * );
static void SetSystem( AstFrame *, AstSystemType, int * );

static AstSystemType GetAlignSystem( AstFrame *, int * );
static int TestAlignSystem( AstFrame *, int * );
static void ClearAlignSystem( AstFrame *, int * );
static void SetAlignSystem( AstFrame *, AstSystemType, int * );

static const char *GetAttrib( AstObject *, const char *, int * );
static int TestAttrib( AstObject *, const char *, int * );
static void ClearAttrib( AstObject *, const char *, int * );
static void SetAttrib( AstObject *, const char *, int * );

static int GetNegated( AstRegion *, int * );
static int TestNegated( AstRegion *, int * );
static void ClearNegated( AstRegion *, int * );
static void SetNegated( AstRegion *, int, int * );

static int GetClosed( AstRegion *, int * );
static int TestClosed( AstRegion *, int * );
static void ClearClosed( AstRegion *, int * );
static void SetClosed( AstRegion *, int, int * );

static int GetMeshSize( AstRegion *, int * );
static int TestMeshSize( AstRegion *, int * );
static void ClearMeshSize( AstRegion *, int * );
static void SetMeshSize( AstRegion *, int, int * );

static double GetFillFactor( AstRegion *, int * );
static int TestFillFactor( AstRegion *, int * );
static void ClearFillFactor( AstRegion *, int * );
static void SetFillFactor( AstRegion *, double, int * );

static int GetRegionFS( AstRegion *, int * );
static int TestRegionFS( AstRegion *, int * );
static void ClearRegionFS( AstRegion *, int * );
static void SetRegionFS( AstRegion *, int, int * );

static int GetAdaptive( AstRegion *, int * );
static int TestAdaptive( AstRegion *, int * );
static void ClearAdaptive( AstRegion *, int * );
static void SetAdaptive( AstRegion *, int, int * );

#if defined(THREAD_SAFE)
static int ManageLock( AstObject *, int, int, AstObject **, int * );
#endif


/* Member functions. */
/* ================= */

static const char *Abbrev( AstFrame *this_frame, int axis, const char *fmt,
                           const char *str1, const char *str2, int *status ) {
/*
*  Name:
*     Abbrev

*  Purpose:
*     Abbreviate a formatted Region axis value by skipping leading fields.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     const char *Abbrev( AstFrame *this, int axis, const char *fmt,
*                         const char *str1, const char *str2, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astAbbrev
*     method inherited from the Frame class).

*  Description:
*     This function compares two Region axis values that have been
*     formatted (using astFormat) and determines if they have any
*     redundant leading fields (i.e. leading fields in common which
*     can be suppressed when tabulating the values or plotting them on
*     the axis of a graph).

*  Parameters:
*     this
*        Pointer to the Region
*     axis
*        The number of the Region axis for which the values have
*        been formatted (axis numbering starts at zero for the first
*        axis).
*     fmt
*        Pointer to a constant null-terminated string containing the
*        format specification used to format the two values.
*     str1
*        Pointer to a constant null-terminated string containing the
*        first formatted value.
*     str1
*        Pointer to a constant null-terminated string containing the
*        second formatted value.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer into the "str2" string which locates the first
*     character in the first field that differs between the two
*     formatted values.
*
*     If the two values have no leading fields in common, the returned
*     value will point at the start of string "str2". If the two
*     values are equal, it will point at the terminating null at the
*     end of this string.

*  Notes:
*     - This function assumes that the format specification used was
*     the same when both values were formatted and that they both
*     apply to the same Region axis.
*     - A pointer to the start of "str2" will be returned if this
*     function is invoked with the global error status set, or if it
*     should fail for any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   const char *result;           /* Pointer value to return */

/* Check the global error status. */
   if ( !astOK ) return str2;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astAbbrev" );

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astAbbrev method to perform the processing. Annul the Frame
   pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astAbbrev( fr, axis, fmt, str1, str2 );
   fr = astAnnul( fr );

/* If an error occurred, clear the result. */
   if ( !astOK ) result = str2;

/* Return the result. */
   return result;
}

static double Angle( AstFrame *this_frame, const double a[],
                     const double b[], const double c[], int *status ) {
/*
*  Name:
*     Angle

*  Purpose:
*     Calculate the angle subtended by two points at a third point.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double Angle( AstFrame *this, const double a[], const double b[],
*                   const double c[], int *status )

*  Class Membership:
*     Region member function (over-rides the protected astAngle
*     method inherited from the Frame class).

*  Description:
*     This function finds the angle at point B between the line joining points
*     A and B, and the line joining points C and B. These lines will in fact be
*     geodesic curves appropriate to the Frame in use. For instance, in
*     SkyFrame, they will be great circles.

*  Parameters:
*     this
*        Pointer to the Frame.
*     a
*        An array of double, with one element for each Frame axis
*        (Naxes attribute) containing the coordinates of the first point.
*     b
*        An array of double, with one element for each Frame axis
*        (Naxes attribute) containing the coordinates of the second point.
*     c
*        An array of double, with one element for each Frame axis
*        (Naxes attribute) containing the coordinates of the third point.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     astAngle
*        The angle in radians, from the line AB to the line CB. If the
*        Frame is 2-dimensional, it will be in the range $\pm \pi$,
*        and positive rotation is in the same sense as rotation from
*        the positive direction of axis 2 to the positive direction of
*        axis 1. If the Frame has more than 2 axes, a positive value will
*        always be returned in the range zero to $\pi$.

*  Notes:
*     - A value of AST__BAD will also be returned if points A and B are
*     co-incident, or if points B and C are co-incident.
*     - A value of AST__BAD will also be returned if this function is
*     invoked with the AST error status set, or if it should fail for
*     any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Value to return */

/* Check the global error status. */
   if ( !astOK ) return AST__BAD;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke this
   Frame's astAngle method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astAngle( fr, a, b, c );
   fr = astAnnul( fr );

/* If an error occurred, clear the result. */
   if ( !astOK ) result = AST__BAD;

/* Return the result. */
   return result;
}

static double AxAngle( AstFrame *this_frame, const double a[], const double b[], int axis, int *status ) {
/*
*  Name:
*     AxAngle

*  Purpose:
*     Returns the angle from an axis, to a line through two points.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double AxAngle( AstFrame *this, const double a[], const double b[], int axis, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astAxAngle
*     method inherited from the Frame class).

*  Description:
*     This function finds the angle, as seen from point A, between the positive
*     direction of a specified axis, and the geodesic curve joining point
*     A to point B.

*  Parameters:
*     this
*        Pointer to the Frame.
*     a
*        An array of double, with one element for each Frame axis
*        (Naxes attribute) containing the coordinates of the first point.
*     b
*        An array of double, with one element for each Frame axis
*        (Naxes attribute) containing the coordinates of the second point.
*     axis
*        The number of the Frame axis from which the angle is to be
*        measured (one-based)
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*        The angle in radians, from the positive direction of the
*        specified axis, to the line AB. If the Frame is 2-dimensional,
*        it will be in the range $\pm \pi$, and positive rotation is in
*        the same sense as rotation from the positive direction of axis 2
*        to the positive direction of axis 1. If the Frame has more than 2
*        axes, a positive value will always be returned in the range zero
*        to $\pi$.

*  Notes:
*     - The geodesic curve used by this function is the path of
*     shortest distance between two points, as defined by the
*     astDistance function.
*     - This function will return "bad" coordinate values (AST__BAD)
*     if any of the input coordinates has this value, or if the require
*     position angle is undefined.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Value to return */

/* Check the global error status. */
   if ( !astOK ) return AST__BAD;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis - 1, 1, "astAxAngle" );

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astAxAngle method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astAxAngle( fr, a, b, axis );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = AST__BAD;

/* Return the result. */
   return result;
}

static double AxDistance( AstFrame *this_frame, int axis, double v1, double v2, int *status ) {
/*
*  Name:
*     AxDistance

*  Purpose:
*     Find the distance between two axis values.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double AxDistance( AstFrame *this, int axis, double v1, double v2, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astAxDistance
*     method inherited from the Frame class).

*  Description:
*     This function returns a signed value representing the axis increment
*     from axis value v1 to axis value v2.
*
*     For a simple Frame, this is a trivial operation returning the
*     difference between the two axis values. But for other derived classes
*     of Frame (such as a SkyFrame) this is not the case.

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The index of the axis to which the supplied values refer. The
*        first axis has index 1.
*     v1
*        The first axis value.
*     v2
*        The second axis value.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The distance between the two axis values.

*  Notes:
*     - This function will return a "bad" result value (AST__BAD) if
*     any of the input vaues has this value.
*     - A "bad" value will also be returned if this function is
*     invoked with the AST error status set, or if it should fail for
*     any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Value to return */

/* Check the global error status. */
   if ( !astOK ) return AST__BAD;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis - 1, 1, "astAxDistance" );

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astAxDistance method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astAxDistance( fr, axis, v1, v2 );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = AST__BAD;

/* Return the result. */
   return result;
}

static void AxNorm( AstFrame *this_frame, int axis, int oper, int nval,
                    double *values, int *status ){
/*
*  Name:
*     AxNorm

*  Purpose:
*     Normalise an array of axis values.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void AxNorm( AstFrame *this, int axis, int oper, int nval,
*                  double *values, int *status )

*  Class Membership:
*     FrameSet member function (over-rides the protected astAxNorm
*     method inherited from the Frame class).

*  Description:
*     This function modifies a supplied array of axis values so that
*     they are normalised in the manner indicated by parameter "oper".
*
*     No normalisation is possible for a simple Frame and so the supplied
*     values are returned unchanged. However, this may not be the case for
*     specialised sub-classes of Frame. For instance, a SkyFrame has a
*     discontinuity at zero longitude and so a longitude value can be
*     expressed in the range [-Pi,+PI] or the range [0,2*PI].

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The index of the axis to which the supplied values refer. The
*        first axis has index 1.
*     oper
*        Indicates the type of normalisation to be applied. If zero is
*        supplied, the normalisation will be the same as that performed by
*        function astNorm. If 1 is supplied, the normalisation will be
*        chosen automatically so that the resulting list has the smallest
*        range.
*     nval
*        The number of points in the values array.
*     values
*        On entry, the axis values to be normalised. Modified on exit to
*        hold the normalised values.
*     status
*        Pointer to the inherited status variable.

*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis - 1, 1, "astAxNorm" );

/* Obtain a pointer to the Region's encapsulated Frame and invoke
   the astAxNorm method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astAxNorm( fr, axis, oper, nval, values );
   fr = astAnnul( fr );
}

static double AxOffset( AstFrame *this_frame, int axis, double v1, double dist, int *status ) {
/*
*  Name:
*     AxOffset

*  Purpose:
*     Add an increment onto a supplied axis value.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double AxOffset( AstFrame *this, int axis, double v1, double dist, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astAxOffset
*     method inherited from the Frame class).

*  Description:
*     This function returns an axis value formed by adding a signed axis
*     increment onto a supplied axis value.
*
*     For a simple Frame, this is a trivial operation returning the
*     sum of the two supplied values. But for other derived classes
*     of Frame (such as a SkyFrame) this is not the case.

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The index of the axis to which the supplied values refer. The
*        first axis has index 1.
*     v1
*        The original axis value.
*     dist
*        The axis increment to add to the original axis value.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The incremented axis value.

*  Notes:
*     - This function will return a "bad" result value (AST__BAD) if
*     any of the input vaues has this value.
*     - A "bad" value will also be returned if this function is
*     invoked with the AST error status set, or if it should fail for
*     any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Value to return */

/* Check the global error status. */
   if ( !astOK ) return AST__BAD;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis - 1, 1, "astAxOffset" );

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astAxOffset method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astAxOffset( fr, axis, v1, dist );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = AST__BAD;

/* Return the result. */
   return result;
}

static AstPointSet *BndBaseMesh( AstRegion *this, double *lbnd, double *ubnd, int *status ){
/*
*+
*  Name:
*     astBndBaseMesh

*  Purpose:
*     Return a PointSet containing points spread around part of the boundary
*     of a Region, in the base Frame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *astBndBaseMesh( AstRegion *this, double *lbnd, double *ubnd )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a PointSet containing a set of points on the
*     boundary of the intersection between the supplied Region and the
*     supplied (current Frame) box. The mesh points refer to the base
*     Frame. If the boundary of the supplied Region does not intersect the
*     supplied box, then a PointSet containing a single bad point is
*     returned.

*  Parameters:
*     this
*        Pointer to the Region.
*     lbnd
*        Pointer to an array holding the lower limits of the axis values
*        within the required box. Defined in the current Frame of the Region.
*     ubnd
*        Pointer to an array holding the upper limits of the axis values
*        within the required box. Defined in the current Frame of the Region.

*  Returned Value:
*     Pointer to the PointSet holding the base Frame mesh. The axis values
*     in this PointSet will have associated accuracies derived from the
*     uncertainties which were supplied when the Region was created.
*
*     If the Region does not intersect the supplied box, the returned
*     PointSet will contain a single point with a value of AST__BAD on
*     every axis.

*  Notes:
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/

/* Local Variables: */
   AstBox *box;
   AstCmpRegion *cmpreg;
   AstPointSet *result;
   double **ptr;
   int ic;
   int nc;

/* Check the local error status. */
   if ( !astOK ) return NULL;

/* Form a Box describing the required box. */
   box = astBox( this, 1, lbnd, ubnd, NULL, "", status );

/* Check there is partial overlap between the Regions.*/
   if( astOverlap( this, box ) > 3 ) {

/* Form a CmpRegion representing the intersection between the supplied
   Region and the above box. */
      cmpreg = astCmpRegion( this, box, AST__AND, "", status );

/* Get the boundary mesh. */
      result = astRegBaseMesh( cmpreg );

/* Free resources. */
      cmpreg = astAnnul( cmpreg );

/* If the boundary of the supplied Region does not intersect the box,
   return a PointSet containing a single bad position. */
   } else {
      nc = astGetNin( this->frameset );
      result = astPointSet( 1, nc, "", status );
      ptr = astGetPoints( result );
      if( ptr ) {
         for( ic = 0; ic < nc; ic++ ) ptr[ ic ][ 0 ] = AST__BAD;
      }
   }

/* Free resources. */
   box = astAnnul( box );

/* Return NULL if an error occurred. */
   if( !astOK ) result = astAnnul( result );

/* Return the required pointer. */
   return result;
}

static AstPointSet *BndMesh( AstRegion *this, double *lbnd, double *ubnd, int *status ){
/*
*+
*  Name:
*     astBndMesh

*  Purpose:
*     Return a PointSet containing points spread around part of the boundary
*     of a Region, in the current Frame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *astBndMesh( AstRegion *this, double *lbnd, double *ubnd )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a PointSet containing a set of points on the
*     boundary of the intersection between the supplied Region and the
*     supplied box. The points refer to the current Frame of the
*     encapsulated FrameSet. If the boundary of the supplied Region does
*     not intersect the supplied box, then a PointSet containing a single
*     bad point is returned.

*  Parameters:
*     this
*        Pointer to the Region.
*     lbnd
*        Pointer to an array holding the lower limits of the axis values
*        within the required box. Defined in the current Frame of the Region.
*     ubnd
*        Pointer to an array holding the upper limits of the axis values
*        within the required box. Defined in the current base Frame of the
*        Region.

*  Returned Value:
*     Pointer to the PointSet. The axis values in this PointSet will have
*     associated accuracies derived from the uncertainties which were
*     supplied when the Region was created.
*
*    If the Region does not intersect the supplied box, the returned
*    PointSet will contain a single point with a value of AST__BAD on
*    every axis.

*  Notes:
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/

/* Local Variables: */
   AstMapping *map;
   AstPointSet *ps1;
   AstPointSet *result;

/* Initialise */
   result = NULL;

/* Check the local error status. */
   if ( !astOK ) return result;

/* Get the current->base Mapping from the Region. */
   map = astGetMapping( this->frameset, AST__CURRENT, AST__BASE );

/* Use astBndBaseMesh to get a mesh of base Frame points within this base
   Frame bounding box. */
   ps1 = astBndBaseMesh( this, lbnd, ubnd );

/* Transform it into the current Frame. */
   if( ps1 ) result = astTransform( map, ps1, 0, NULL );

/* Free resources. */
   map = astAnnul( map );
   ps1 = astAnnul( ps1 );

/* Return NULL if an error occurred. */
   if( !astOK ) result = astAnnul( result );

/* Return the required pointer. */
   return result;
}

static AstPointSet *BTransform( AstRegion *this, AstPointSet *in,
                                int forward, AstPointSet *out, int *status ) {
/*
*+
*  Name:
*     astBTransform

*  Purpose:
*     Use a Region to transform a set of points in the base Frame.

*  Type:
*     Protected virtual function.

*  Synopsis:
*     #include "circle.h"
*     AstPointSet *astBTransform( AstRegion *this, AstPointSet *in,
                                  int forward, AstPointSet *out )

*  Class Membership:
*     Region member function

*  Description:
*     This function takes a Region and a set of points within the base
*     Frame of the Region, 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 Region.
*     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.

*  Returned Value:
*     Pointer to the output (possibly new) PointSet.

*  Notes:
*     -  This is identical to the astTransform method for a Region except
*     that the supplied and returned points refer to the base Frame of
*     the Region, rather than the current Frame.
*-
*/

/* Local Variables: */
   AstPointSet *result;          /* Pointer to output PointSet */
   int old;                      /* Origial value of "nomap" flag */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Save the current value of the "nomap" flag for this Region,and then
   set it. Doing this tells the astRegMapping function (called by
   astRegTransform) to assume a unit map connects base and current Frame. */
   old = this->nomap;
   this->nomap = 1;

/* Invoke the usual astTransform method. The above setting of the "nomap"
   flag will cause the astTransform method to treat the base Frame as the
   current Frame. */
   result = astTransform( this, in, forward, out );

/* Reset the "nomap" flag. */
   this->nomap = old;

/* Return a pointer to the output PointSet. */
   return result;
}

static AstObject *Cast( AstObject *this_object, AstObject *obj, int *status ) {
/*
*  Name:
*     Cast

*  Purpose:
*     Cast an Object into an instance of a sub-class.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstObject *Cast( AstObject *this, AstObject *obj, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astCast
*     method inherited from the Frame class).

*  Description:
*     This function returns a deep copy of an ancestral component of the
*     supplied object. The required class of the ancestral component is
*     specified by another object. Specifically, if "this" and "new" are
*     of the same class, a copy of "this" is returned. If "this" is an
*     instance of a subclass of "obj", then a copy of the component
*     of "this" that matches the class of "obj" is returned. Otherwise,
*     a NULL pointer is returned without error.

*  Parameters:
*     this
*        Pointer to the Object to be cast.
*     obj
*        Pointer to an Object that defines the class of the returned Object.
*        The returned Object will be of the same class as "obj".

*  Returned Value:
*     A pointer to the new Object. NULL if "this" is not a sub-class of
*     "obj", or if an error occurs.

*  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; */
   AstFrame *cfrm;
   AstObject *new;
   astDECLARE_GLOBALS
   int generation_gap;

/* Initialise */
   new = NULL;

/* Check inherited status */
   if( !astOK ) return new;

/* Get a pointer to the thread specific global data structure. */
   astGET_GLOBALS(NULL);

/* See how many steps up the class inheritance ladder it is from "obj"
   to this class (Region). A positive value is returned if Region is
   a sub-class of "obj". A negative value is returned if "obj" is a
   sub-class of Region. Zero is returned if "obj" is a Region.
   AST__COUSIN is returned if "obj" is not on the same line of descent
   as Region. */
   generation_gap = astClassCompare( (AstObjectVtab *) &class_vtab,
                                     astVTAB( obj ) );

/* If "obj" is a Region or a sub-class of Region, we can cast by
   truncating the vtab for "this" so that it matches the vtab of "obJ",
   and then taking a deep copy of "this". */
   if( generation_gap <= 0 && generation_gap != AST__COUSIN ) {
      new = astCastCopy( this_object, obj );

/* If "obj" is not a Region or a sub-class of Region (e.g. a Frame or
   some sub-class of Frame), we attempt to cast the current Frame of the
   encapsulated FrameSet into the class indicated by "obj". */
   } else {
      cfrm = astGetFrame( ((AstRegion *) this_object)->frameset, AST__CURRENT );
      new = astCast( cfrm, obj );
      cfrm = astAnnul( cfrm );
   }

/* Return the new pointer. */
   return new;
}

static double Centre( AstFrame *this_frame, int axis, double value, double gap, int *status ) {
/*
*  Name:
*     Centre

*  Purpose:
*     Find a "nice" central value for tabulating Frame axis values.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double  Centre( AstFrame *this_frame, int axis, double value,
*                     double gap, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astCentre method
*     inherited from the Frame class).

*  Description:
*     This function returns an axis value which produces a nice formatted
*     value suitable for a major tick mark on a plot axis, close to the
*     supplied axis value.

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The number of the axis (zero-based) for which a central value
*        is to be found.
*     value
*        An arbitrary axis value in the section that is being plotted.
*     gap
*        The gap size.

*  Returned Value:
*     The nice central axis value.

*  Notes:
*     - A value of zero is returned if the supplied gap size is zero.
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Value to return */

/* Check the global error status. */
   if ( !astOK ) return 0.0;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astCentre" );

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astCentre method to obtain the required value. Annul the
   Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astCentre( fr, axis, value, gap );
   fr = astAnnul( fr );

/* If an error occurred, clear the result. */
   if ( !astOK ) result = 0.0;

/* Return the result. */
   return result;
}

static void CheckPerm( AstFrame *this_frame, const int *perm, const char *method, int *status ) {
/*
*  Name:
*     CheckPerm

*  Purpose:
*     Check that an array contains a valid permutation.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void CheckPerm( AstFrame *this, const int *perm, const char *method, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astCheckPerm
*     method inherited from the Frame class).

*  Description:
*     This function checks the validity of a permutation array that
*     will be used to permute the order of a Frame's axes. If the
*     permutation specified by the array is not valid, an error is
*     reported and the global error status is set. Otherwise, the
*     function returns without further action.

*  Parameters:
*     this
*        Pointer to the Frame.
*     perm
*        Pointer to an array of integers with the same number of
*        elements as there are axes in the Frame. For each axis, the
*        corresponding integer gives the (zero based) axis index to be
*        used to identify the information for that axis (using the
*        un-permuted axis numbering). To be valid, the integers in
*        this array should therefore all lie in the range zero to
*        (naxes-1) inclusive, where "naxes" is the number of Frame
*        axes, and each value should occur exactly once.
*     method
*        Pointer to a constant null-terminated character string
*        containing the name of the method that invoked this function
*        to validate a permutation array. This method name is used
*        solely for constructing error messages.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - Error messages issued by this function refer to the external
*     (public) numbering system used for axes (which is one-based),
*     whereas zero-based axis indices are used internally.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke this
   Frame's astCheckPerm method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astCheckPerm( fr, perm, method );
   fr = astAnnul( fr );

}

static void ClearAttrib( AstObject *this_object, const char *attrib, int *status ) {
/*
*  Name:
*     ClearAttrib

*  Purpose:
*     Clear an attribute value for a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void ClearAttrib( AstObject *this, const char *attrib, int *status )

*  Class Membership:
*     Region member function (over-rides the astClearAttrib protected
*     method inherited from the Frame class).

*  Description:
*     This function clears the value of a specified attribute for a
*     Region, so that the default value will subsequently be used.

*  Parameters:
*     this
*        Pointer to the Region.
*     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: */
   AstRegion *this;            /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_object;

/* Check the attribute name and clear the appropriate attribute. */

/* We first handle attributes that apply to the Region as a whole
   (rather than to the encapsulated FrameSet). */

/* Negated */
/* ------- */
   if ( !strcmp( attrib, "negated" ) ) {
      astClearNegated( this );

/* Closed */
/* ------ */
   } else if ( !strcmp( attrib, "closed" ) ) {
      astClearClosed( this );

/* FillFactor */
/* ---------- */
   } else if ( !strcmp( attrib, "fillfactor" ) ) {
      astClearFillFactor( this );

/* MeshSize */
/* -------- */
   } else if ( !strcmp( attrib, "meshsize" ) ) {
      astClearMeshSize( this );

/* Adaptive */
/* -------- */
   } else if ( !strcmp( attrib, "adaptive" ) ) {
      astClearAdaptive( this );


/* We now check for atttributes of superclasses which apply to the Region
   as a whole. We do not want to pass these on to the encapsulated FrameSet. */

/* ID. */
/* --- */
   } else if ( !strcmp( attrib, "id" ) ) {
      astClearID( this );

/* Ident. */
/* ------ */
   } else if ( !strcmp( attrib, "ident" ) ) {
      astClearIdent( this );

/* Invert. */
/* ------- */
   } else if ( !strcmp( attrib, "invert" ) ) {
      astClearInvert( this );

/* Report. */
/* ------- */
   } else if ( !strcmp( attrib, "report" ) ) {
      astClearReport( this );


/* If the name was not recognised, test if it matches any of the
   read-only attributes of this class (including those of all superclasses).
   If it does, then report an error. */
   } else if ( !strcmp( attrib, "class" ) ||
               !strcmp( attrib, "nin" ) ||
               !strcmp( attrib, "nobject" ) ||
               !strcmp( attrib, "nout" ) ||
               !strcmp( attrib, "bounded" ) ||
               !strcmp( attrib, "refcount" ) ||
               !strcmp( attrib, "tranforward" ) ||
               !strcmp( attrib, "traninverse" ) ) {
      astError( AST__NOWRT, "astClear: Invalid attempt to clear the \"%s\" "
                "value for a %s.", status, attrib, astGetClass( this ) );
      astError( AST__NOWRT, "This is a read-only attribute." , status);

/* Pass unrecognised attributes on to the Region's encapsulated FrameSet for
   further interpretation. Do not pass on FrameSet attributes since we
   pretend to the outside world that the encapsulated FrameSet is actually a
   Frame. */
   } else if ( strcmp( attrib, "base" ) &&
               strcmp( attrib, "current" ) &&
               strcmp( attrib, "nframe" ) ) {

/* If the Region is to adapt to coordinate system chanmges, use the public
   astClear method so that the current Frame in the encapsulated FrameSet will
   be re-mapped if the attribute changes require it. */
      if( astGetAdaptive( this ) ) {
         astClear( this->frameset, attrib );

/* If the Region is not to adapt to coordinate system chanmges, use the
   astRegSetAttrib method which assigns the attribute setting to both
   current and base Frames in the FrameSet without causing any remapping to
   be performed. */
      } else {
         astRegClearAttrib( this, attrib, NULL );
      }
   }
}

static AstFrameSet *Conv( AstFrameSet *from, AstFrameSet *to, int *status ){
/*
*  Name:
*     Conv

*  Purpose:
*     Find Mapping between Frames

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstFrameSet *Conv( AstFrameSet *from, AstFrameSet *to, int *status );

*  Class Membership:
*     Region member function

*  Description:
*     This function provides a convenient interface for astConvert.
*     It is like astConvert except it does not alter the base Frames of
*     the supplied FrameSets and does not require a Domain list.
*
*     It aligns in the current Frame of "to".

*  Parameters:
*     from
*        Pointer to the source FrameSet.
*     to
*        Pointer to the source FrameSet.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*        The conversion FrameSet (see astConvert).

*/

/* Local Variables: */
   AstFrameSet *result;        /* FrameSet to return */
   const char *dom;            /* Domain in which to align */
   int from_base;              /* Index of original base Frame in "from" */
   int to_base;                /* Index of original base Frame in "to" */

/* Check the global error status. */
   if( !astOK ) return NULL;

/* Note the indices of the base Frames in the FrameSets. */
   to_base = astGetBase( to );
   from_base = astGetBase( from );

/* Get the domain of the currentFrame of "to". */
   dom = astGetDomain( to );

/* Invoke astConvert. */
   result = astConvert( from, to, dom );

/* Re-instate original base Frames. */
   astSetBase( to, to_base );
   astSetBase( from, from_base );

/* Return the result. */
   return result;
}

static AstFrameSet *Convert( AstFrame *from, AstFrame *to,
                             const char *domainlist, int *status ) {
/*
*  Name:
*     Convert

*  Purpose:
*     Determine how to convert between two coordinate systems.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstFrameSet *Convert( AstFrame *from, AstFrame *to,
*                           const char *domainlist, int *status )

*  Class Membership:
*     Region member function (over-rides the public astConvert
*     method inherited fromm the Frame class).

*  Description:
*     This function compares two Regions and determines whether it
*     is possible to convert between the coordinate systems which
*     their current Frames represent. If conversion is possible, it
*     returns a FrameSet which describes the conversion and which may
*     be used (as a Mapping) to transform coordinate values in either
*     direction.

*  Parameters:
*     from
*        Pointer to a Region whose current Frame represents the
*        "source" coordinate system.  Note that the Base attribute of
*        the Region may be modified by this function.
*     to
*        Pointer to a Region whose current Frame represents the
*        "destination" coordinate system.  Note that the Base
*        attribute of the Region may be modified by this function.
*     domainlist
*        Pointer to a null-terminated character string containing a
*        comma-separated list of Frame domains. This may be used to
*        define a priority order for the different intermediate
*        coordinate systems that might be used to perform the
*        conversion.
*
*        The function will first try to obtain a conversion by making
*        use only of intermediate Frames whose Domain attribute
*        matches the first domain in this list. If this fails, the
*        second domain in the list will be used, and so on, until
*        conversion is achieved. A blank domain (e.g. two consecutive
*        commas) indicates that all Frames should be considered,
*        regardless of their Domain attributes. The list is
*        case-insensitive and all white space is ignored.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*        If the requested coordinate conversion is possible, the
*        function returns a pointer to a FrameSet which describes the
*        conversion. Otherwise, a null Object pointer (AST__NULL) is
*        returned without error.
*
*        If a FrameSet is returned, it will contain two Frames. Frame
*        number 1 (its base Frame) will describe the source coordinate
*        system, corresponding to the "from" parameter. Frame number 2
*        (its current Frame) will describe the destination coordinate
*        system, corresponding to the "to" parameter. The Mapping
*        which inter-relates these Frames will perform the required
*        conversion between the two coordinate systems.

*  Notes:
*     - The returned FrameSet will not contain any Regions. If one or
*     more of the supplied Frames are in fact Regions, the corresponding
*     Frames in any returned FrameSet will described the encapsulated
*     Frame, without any region information.
*     - 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: */
   AstFrameSet *result;       /* Returned FrameSet */

/* Check the inherited status. */
   if ( !astOK ) return NULL;

/* If the "from" pointer is a Region, get a pointer to the current Frame of
   the encapsulated FrameSet and use it instead of the supplied pointer. */
   if( astIsARegion( from ) ) {
      from = astGetFrame( ((AstRegion *) from)->frameset, AST__CURRENT );
   } else {
      from = astClone( from );
   }

/* If the "to" pointer is a Region, get a pointer to the current Frame of
   the encapsulated FrameSet and use it instead of the supplied pointer. */
   if( astIsARegion( to ) ) {
      to = astGetFrame( ((AstRegion *) to)->frameset, AST__CURRENT );
   } else {
      to = astClone( to );
   }

/* Now invoke astConvert on the above Frames. */
   result = astConvert( from, to, domainlist );

/* Annul the pointers used above. */
   from = astAnnul( from );
   to = astAnnul( to );

/* Return the result */
   return result;
}

static AstFrameSet *ConvertX( AstFrame *to, AstFrame *from,
                              const char *domainlist, int *status ) {
/*
*  Name:
*     ConvertX

*  Purpose:
*     Determine how to convert between two coordinate systems.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstFrameSet *astConvertX( AstFrame *to, AstFrame *from,
*                               const char *domainlist )

*  Class Membership:
*     Region member function (over-rides the protected astConvertX
*     method inherited from the Frame class).

*  Description:
*     This function performs the processing for the public astConvert
*     method and has exactly the same interface except that the order
*     of the first two arguments is swapped. This is a trick to allow
*     the astConvert method to be over-ridden by derived classes on
*     the basis of the class of either of its first two arguments.
*
*     See the astConvert method for details of the interface.
*-
*/

/* Local Variables: */
   AstFrameSet *result;       /* Returned FrameSet */

/* Check the inherited status. */
   if ( !astOK ) return NULL;

/* If the "to" pointer is a Region, get a pointer to the current Frame of
   the encapsulated FrameSet and use it instead of the supplied pointer. */
   if( astIsARegion( to ) ) {
      to = astGetFrame( ((AstRegion *) to)->frameset, AST__CURRENT );
   } else {
      to = astClone( to );
   }

/* If the "from" pointer is a Region, get a pointer to the current Frame of
   the encapsulated FrameSet and use it instead of the supplied pointer. */
   if( astIsARegion( from ) ) {
      from = astGetFrame( ((AstRegion *) from)->frameset, AST__CURRENT );
   } else {
      from = astClone( from );
   }

/* Now invoke astConvertX on the above Frames. */
   result = astConvertX( to, from, domainlist );

/* Annul the pointers used above. */
   from = astAnnul( from );
   to = astAnnul( to );

/* Return the result */
   return result;
}

static double Distance( AstFrame *this_frame, const double point1[],
                        const double point2[], int *status ) {
/*
*  Name:
*     Distance

*  Purpose:
*     Calculate the distance between two points.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double Distance( AstFrame *this, const double point1[],
*                      const double point2[], int *status )

*  Class Membership:
*     Region member function (over-rides the protected astDistance
*     method inherited from the Frame class).

*  Description:
*     This function finds the distance between two points whose
*     Region coordinates are given. The distance calculated is that
*     along the geodesic curve that joins the two points.

*  Parameters:
*     this
*        Pointer to the Region.
*     point1
*        An array of double, with one element for each Region axis
*        containing the coordinates of the first point.
*     point2
*        An array of double, with one element for each Region axis
*        containing the coordinates of the second point.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The distance between the two points.

*  Notes:
*     - This function will return a "bad" result value (AST__BAD) if
*     any of the input coordinates has this value.
*     - A "bad" value will also be returned if this function is
*     invoked with the AST error status set or if it should fail for
*     any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Value to return */

/* Check the global error status. */
   if ( !astOK ) return AST__BAD;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astDistance method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astDistance( fr, point1, point2 );
   fr = astAnnul( fr );

/* If an error occurred, clear the result. */
   if ( !astOK ) result = AST__BAD;

/* Return the result. */
   return result;
}

static int Equal( AstObject *this_object, AstObject *that_object, int *status ) {
/*
*  Name:
*     Equal

*  Purpose:
*     Test if two Objects are equivalent.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int Equal( AstObject *this_object, AstObject *that_object, int *status )

*  Class Membership:
*     Region member function (over-rides the astEqual protected
*     method inherited from the Frame class).

*  Description:
*     This function returns a boolean result (0 or 1) to indicate whether
*     two Regions are equivalent.

*  Parameters:
*     this
*        Pointer to the first Region.
*     that
*        Pointer to the second Region.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     One if the Regions are equivalent, zero otherwise.

*  Notes:
*     - The Regions are equivalent if they are of the same class, have
*     equal PointSets, have equal base Frames, have equal current Frames,
*     and if the Mapping between base Frames is a UnitMap. In addition, the
*     Negated attribute must have the same value in both Regions, as must
*     the Closed attribute.
*     - 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: */
   AstFrame *bf1;
   AstFrame *bf2;
   AstFrame *cf1;
   AstFrame *cf2;
   AstMapping *m1;
   AstMapping *m2;
   AstRegion *that;
   AstRegion *this;
   const char *class1;
   const char *class2;
   int result;

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Check that the two objects have the same class. */
   class1 = astGetClass( this_object );
   class2 = astGetClass( that_object );
   if( astOK && !strcmp( class1, class2 ) ) {

/* Obtain pointers to the two Region structures. */
      this = (AstRegion *) this_object;
      that = (AstRegion *) that_object;

/* Test their PointSets for equality. */
      if( astEqual( this->points, that->points ) ){

/* Test their base Frames for equality. */
         bf1 = astGetFrame( this->frameset, AST__BASE );
         bf2 = astGetFrame( that->frameset, AST__BASE );
         if( astEqual( bf1, bf2 ) ){

/* Test their current Frames for equality. */
            cf1 = astGetFrame( this->frameset, AST__CURRENT );
            cf2 = astGetFrame( that->frameset, AST__CURRENT );
            if( astEqual( cf1, cf2 ) ){

/* Get the two Mappings and check that they are equal */
               m1 = astGetMapping( this->frameset, AST__BASE, AST__CURRENT );
               m2 = astGetMapping( that->frameset, AST__BASE, AST__CURRENT );
               if( astEqual( m1, m2 ) ) {

/* Test the Negated and Closed flags are equal */
                  if( astGetNegated( this ) == astGetNegated( that ) &&
                       astGetClosed( this ) == astGetClosed( that ) ) {
                     result = 1;
                  }
               }

/* Free resources. */
               m1 = astAnnul( m1 );
               m2 = astAnnul( m2 );
            }

            cf1 = astAnnul( cf1 );
            cf2 = astAnnul( cf2 );
         }

         bf1 = astAnnul( bf1 );
         bf2 = astAnnul( bf2 );
      }
   }

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = 0;

/* Return the result, */
   return result;
}

static void ClearUnc( AstRegion *this, int *status ){
/*
*+
*  Name:
*     astClearUnc

*  Purpose:
*     Erase any uncertainty information in a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astClearUnc( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function erases all uncertainty information, whether default
*     or not, from a Region.

*  Parameters:
*     this
*        Pointer to the Region.

*-
*/

/* Check the inherited status. */
   if( !astOK ) return;

/* Annul any user-supplied uncertainty. Also indicate that cached
   information may now be out of date. */
   if( this->unc ) {
      this->unc = astAnnul( this->unc );
      astResetCache( this );
   }

/* Annul any default uncertainty. */
   if( this->defunc ) this->defunc = astAnnul( this->defunc );

}

static AstFrameSet *FindFrame( AstFrame *target_frame, AstFrame *template,
                               const char *domainlist, int *status ) {
/*
*  Name:
*     FindFrame

*  Purpose:
*     Find a coordinate system with specified characteristics.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstFrameSet *FindFrame( AstFrame *target, AstFrame *template,
*                             const char *domainlist, int *status )

*  Class Membership:
*     Region member function (over-rides the astFindFrame method
*     inherited from the Frame class).

*  Description:
*     This function uses a "template" Frame to search a Region to
*     identify a coordinate system which has a specified set of
*     characteristics. If a suitable coordinate system can be found,
*     the function returns a pointer to a FrameSet which describes the
*     required coordinate system and how to convert coordinates to and
*     from it.

*  Parameters:
*     target
*        Pointer to the target Region.
*     template
*        Pointer to the template Frame, which should be an instance of
*        the type of Frame you wish to find.
*     domainlist
*        Pointer to a null-terminated character string containing a
*        comma-separated list of Frame domains. This may be used to
*        establish a priority order for the different types of
*        coordinate system that might be found.
*
*        The function will first try to find a suitable coordinate
*        system whose Domain attribute equals the first domain in this
*        list. If this fails, the second domain in the list will be
*        used, and so on, until a result is obtained. A blank domain
*        (e.g. two consecutive commas) indicates that any coordinate
*        system is acceptable (subject to the template) regardless of
*        its domain.
*
*        This list is case-insensitive and all white space is ignored.
*        If you do not wish to restrict the domain in this way, you
*        should supply an empty string.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     If the search is successful, the function returns a pointer to a
*     FrameSet which contains the Frame found and a description of how
*     to convert to (and from) the coordinate system it
*     represents. Otherwise, a null Object pointer (AST__NULL) is
*     returned without error.
*
*     If a FrameSet is returned, it will contain two Frames. Frame
*     number 1 (its base Frame) represents the target coordinate
*     system and will be the same as the target. Frame number 2 (its
*     current Frame) will be a Frame representing the coordinate system
*     which the function found. The Mapping which inter-relates these two
*     Frames will describe how to convert between their respective coordinate
*     systems. Note, the Frames in this FrameSet will not be Regions -
*     that is, they will be simple Frames or other derived classes.

*  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: */
   AstFrameSet *result;          /* Pointer to result FrameSet */
   AstFrame *fr;                 /* Pointer to encapsulated Frame */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Invoke the astFindFrame method on the current Frame of the
   encapsulated FrameSet within the target Region. */
   fr = astGetFrame( ((AstRegion *) target_frame)->frameset, AST__CURRENT );
   result = astFindFrame( fr, template, domainlist );
   fr = astAnnul( fr );

/* Return the result. */
   return result;
}

static const char *Format( AstFrame *this_frame, int axis, double value, int *status ) {
/*
*  Name:
*     Format

*  Purpose:
*     Format a coordinate value for a Region axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     const char *Format( AstFrame *this, int axis, double value, int *status )

*  Class Membership:
*     Region member function (over-rides the astFormat method
*     inherited from the Frame class).

*  Description:
*     This function returns a pointer to a string containing the
*     formatted (character) version of a coordinate value for a
*     Region axis. The formatting applied is that specified by a
*     previous invocation of the astSetFormat method. A suitable
*     default format is applied if necessary.

*  Parameters:
*     this
*        Pointer to the Region.
*     axis
*        The number of the axis (zero-based) for which formatting is
*        to be performed.
*     value
*        The coordinate value to be formatted.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer to a null-terminated string containing the formatted
*     value.

*  Notes:
*     - The returned string pointer may point at memory allocated
*     within the Region object, 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 deletion
*     of the Region. 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: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   const char *result;           /* Pointer value to return */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astFormat" );

/* Obtain a pointer to the Region's current Frame and invoke the
   astFormat method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astFormat( fr, axis, value );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = NULL;

/* Return the result. */
   return result;
}

static double Gap( AstFrame *this_frame, int axis, double gap, int *ntick, int *status ) {
/*
*  Name:
*     Gap

*  Purpose:
*     Find a "nice" gap for tabulating Region axis values.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double Gap( AstFrame *this, int axis, double gap, int *ntick, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astGap method
*     inherited from the Frame class).

*  Description:
*     This function returns a gap size which produces a nicely spaced
*     series of formatted values for a Region axis, the returned gap
*     size being as close as possible to the supplied target gap
*     size. It also returns a convenient number of divisions into
*     which the gap can be divided.

*  Parameters:
*     this
*        Pointer to the Region.
*     axis
*        The number of the axis (zero-based) for which a gap is to be found.
*     gap
*        The target gap size.
*     ntick
*        Address of an int in which to return a convenient number of
*        divisions into which the gap can be divided.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The nice gap size.

*  Notes:
*     - A value of zero is returned if the target gap size is zero.
*     - A negative gap size is returned if the supplied gap size is negative.
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Gap value to return */

/* Check the global error status. */
   if ( !astOK ) return 0.0;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astGap" );

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astGap method to obtain the required gap value. Annul the
   Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astGap( fr, axis, gap, ntick );
   fr = astAnnul( fr );

/* If an error occurred, clear the result. */
   if ( !astOK ) result = 0.0;

/* Return the result. */
   return result;
}

static int GetObjSize( AstObject *this_object, int *status ) {
/*
*  Name:
*     GetObjSize

*  Purpose:
*     Return the in-memory size of an Object.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int GetObjSize( AstObject *this, int *status )

*  Class Membership:
*     Region member function (over-rides the astGetObjSize protected
*     method inherited from the parent class).

*  Description:
*     This function returns the in-memory size of the supplied Region,
*     in bytes.

*  Parameters:
*     this
*        Pointer to the Region.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The Object size, in bytes.

*  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: */
   AstRegion *this;         /* Pointer to Region structure */
   int result;                /* Result value to return */

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointers to the Region structure. */
   this = (AstRegion *) this_object;

/* Invoke the GetObjSize method inherited from the parent class, and then
   add on any components of the class structure defined by thsi class
   which are stored in dynamically allocated memory. */
   result = (*parent_getobjsize)( this_object, status );

   result += astGetObjSize( this->frameset );
   result += astGetObjSize( this->points );
   result += astGetObjSize( this->basemesh );
   result += astGetObjSize( this->basegrid );
   result += astGetObjSize( this->unc );
   result += astGetObjSize( this->negation );
   result += astGetObjSize( this->defunc );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = 0;

/* Return the result, */
   return result;
}

static const char *GetAttrib( AstObject *this_object, const char *attrib, int *status ) {
/*
*  Name:
*     GetAttrib

*  Purpose:
*     Get the value of a specified attribute for a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     const char *GetAttrib( AstObject *this, const char *attrib, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astGetAttrib
*     method inherited from the Frame class).

*  Description:
*     This function returns a pointer to the value of a specified
*     attribute for a Region, formatted as a character string.

*  Parameters:
*     this
*        Pointer to the Region.
*     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 Region, 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 Region. 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 */
   AstRegion *this;              /* Pointer to the Region structure */
   const char *result;           /* Pointer value to return */
   double dval;                  /* Floating point attribute value */
   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 Region structure. */
   this = (AstRegion *) 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. */

/* We first handle attributes that apply to the Region as a whole
   (rather than to the encapsulated FrameSet). */

/* Negated */
/* ------- */
   if ( !strcmp( attrib, "negated" ) ) {
      ival = astGetNegated( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Closed */
/* ------ */
   } else if ( !strcmp( attrib, "closed" ) ) {
      ival = astGetClosed( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Adaptive */
/* -------- */
   } else if ( !strcmp( attrib, "adaptive" ) ) {
      ival = astGetAdaptive( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* FillFactor */
/* ---------- */
   } else if ( !strcmp( attrib, "fillfactor" ) ) {
      dval = astGetFillFactor( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%.*g", AST__DBL_DIG, dval );
         result = getattrib_buff;
      }

/* MeshSize */
/* -------- */
   } else if ( !strcmp( attrib, "meshsize" ) ) {
      ival = astGetMeshSize( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Bounded */
/* ------- */
   } else if ( !strcmp( attrib, "bounded" ) ) {
      ival = astGetBounded( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Now get the values of attributes inherited from parent classes. We do
   this to avoid the request being passed on to the encapsulated FrameSet
   below. */

/* Class. */
/* ------ */
   } else if ( !strcmp( attrib, "class" ) ) {
      result = astGetClass( this );

/* ID. */
/* --- */
   } else if ( !strcmp( attrib, "id" ) ) {
      result = astGetID( this );

/* Ident. */
/* ------ */
   } else if ( !strcmp( attrib, "ident" ) ) {
      result = astGetIdent( this );

/* Invert. */
/* ------- */
   } else if ( !strcmp( attrib, "invert" ) ) {
      ival = astGetInvert( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Nin. */
/* ---- */
   } else if ( !strcmp( attrib, "nin" ) ) {
      ival = astGetNin( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Nobject. */
/* -------- */
   } else if ( !strcmp( attrib, "nobject" ) ) {
      ival = astGetNobject( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Nout. */
/* ----- */
   } else if ( !strcmp( attrib, "nout" ) ) {
      ival = astGetNout( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* RefCount. */
/* --------- */
   } else if ( !strcmp( attrib, "refcount" ) ) {
      ival = astGetRefCount( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Report. */
/* ------- */
   } else if ( !strcmp( attrib, "report" ) ) {
      ival = astGetReport( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* TranForward. */
/* ------------ */
   } else if ( !strcmp( attrib, "tranforward" ) ) {
      ival = astGetTranForward( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* TranInverse. */
/* ------------ */
   } else if ( !strcmp( attrib, "traninverse" ) ) {
      ival = astGetTranInverse( this );
      if ( astOK ) {
         (void) sprintf( getattrib_buff, "%d", ival );
         result = getattrib_buff;
      }

/* Pass unrecognised attributes on to the Region's encapsulated FrameSet for
   further interpretation. Do not pass on FrameSet attributes since we
   pretend to the outside world that the encapsulated FrameSet is actually a
   Frame. */
   } else if ( strcmp( attrib, "base" ) &&
               strcmp( attrib, "current" ) &&
               strcmp( attrib, "nframe" ) ) {
      result = astGetAttrib( this->frameset, attrib );
   }

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = NULL;

/* Return the result. */
   return result;
}

static int GetBounded( AstRegion *this, int *status ) {
/*
*+
*  Name:
*     astGetBounded

*  Purpose:
*     Is the Region bounded?

*  Type:
*     Protected function.

*  Synopsis:
*     int astGetBounded( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  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, Ellipse, Box, etc). Other sub-classes (such as
*     CmpRegion, PointList, etc ) may need to provide their own
*     implementations.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     Non-zero if the Region is bounded. Zero otherwise.

*-
*/

/* Local Variables: */
   int result;
   AstFrame *bfrm;

/* Check inherited status */
   if( !astOK ) return 0;

/* For Regions which are defined by one or more closed curves such as Circles,
   Boxes, etc, the Region is bounded so long as it has not been negated.
   Classes for which this is not true should over-ride this implementation.
   Note, Regions defined within SkyFrames (i.e. on a sphere) are always
   bounded, since a finite region has a finite negation. */
   bfrm = astGetFrame( this->frameset, AST__BASE );
   if( astIsASkyFrame( bfrm ) ) {
      result = 1;
   } else {
      result = !astGetNegated( this );
   }
   bfrm = astAnnul( bfrm );

   return result;
}

static AstAxis *GetAxis( AstFrame *this_frame, int axis, int *status ) {
/*
*  Name:
*     GetAxis

*  Purpose:
*     Obtain a pointer to a specified Axis from a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstAxis *GetAxis( AstFrame *this, int axis, int *status )

*  Class Membership:
*     Region member function (over-rides the astGetAxis method
*     inherited from the Frame class).

*  Description:
*     This function returns a pointer to the Axis object associated
*     with one of the axes of the current Frame of a Region. This
*     object describes the quantity which is represented along that
*     axis.

*  Parameters:
*     this
*        Pointer to the Region.
*     axis
*        The number of the axis (zero-based) for which an Axis pointer
*        is required.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer to the requested Axis object.

*  Notes:
*     - The reference count of the requested Axis object will be
*     incremented by one to reflect the additional pointer returned by
*     this function.
*     - 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: */
   AstAxis *result;              /* Pointer to Axis */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astGetAxis" );

/* Obtain a pointer to the Region's encapsulated FrameSet and invoke
   this FrameSet's astGetAxis method to obtain the required Axis
   pointer. */
   result = astGetAxis( this->frameset, axis );

/* If an error occurred, annul the result. */
   if ( !astOK ) result = astAnnul( result );

/* Return the result. */
   return result;
}

static AstRegion *GetDefUnc( AstRegion *this, int *status ) {
/*
*+
*  Name:
*     astGetDefUnc

*  Purpose:
*     Obtain a pointer to the default uncertainty Region for a given Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstRegion *astGetDefUnc( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a pointer to a Region which represents the
*     default uncertainty associated with a position on the boundary of the
*     given  Region. The returned Region refers to the base Frame within the
*     FrameSet encapsulated by the supplied Region.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     A pointer to the Region. This should be annulled (using astAnnul)
*     when no longer needed.

*  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: */
   AstFrame *bfrm;            /* Base Frame of supplied Region */
   AstRegion *result;         /* Returned pointer */
   double *lbnd;              /* Ptr. to array holding axis lower bounds */
   double *ubnd;              /* Ptr. to array holding axis upper bounds */
   double c;                  /* Central axis value */
   double hw;                 /* Half width of uncertainty interval */
   int i;                     /* Axis index */
   int nax;                   /* Number of base Frame axes */

/* Initialise */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get a pointer to the base Frame in the supplied Region. */
   bfrm = astGetFrame( this->frameset, AST__BASE );

/* Get the number of base Frame axes. */
   nax = astGetNaxes( bfrm );

/* Get the base frame bounding box of the supplied Region. The astRegBaseBox
   assumes the supplied Region has not been inverted. But if the Region
   contains other Regions (e.g. a Prism or CmpRegion, etc) then this
   assumption needs to be propagated to the component Regions, which
   astRegBaseBox does not do. For this reason we use astRegBaseBox2
   instead. */
   lbnd = astMalloc( sizeof( double)*(size_t) nax );
   ubnd = astMalloc( sizeof( double)*(size_t) nax );
   astRegBaseBox2( this, lbnd, ubnd );

/* Create a Box covering 1.0E-6 of this bounding box, centred on the
   centre of the box. */
   if( astOK ) {
      for( i = 0; i < nax; i++ ) {
         if( ubnd[ i ] != DBL_MAX && lbnd[ i ] != -DBL_MAX ) {
            hw = fabs( 0.5E-6*(  ubnd[ i ] - lbnd[ i ] ) );
            c = 0.5*(  ubnd[ i ] + lbnd[ i ] );
            if( hw == 0.0 ) hw = c*0.5E-6;
            ubnd[ i ] = c + hw;
            lbnd[ i ] = c - hw;
         } else {
            ubnd[ i ] = 0.0;
            lbnd[ i ] = 0.0;
         }
      }
      result = (AstRegion *) astBox( bfrm, 1, lbnd, ubnd, NULL, "", status );
   }

/* Free resources. */
   lbnd = astFree( lbnd );
   ubnd = astFree( ubnd );
   bfrm = astAnnul( bfrm );

/* Return NULL if an error occurred. */
   if( !astOK ) result = astAnnul( result );

/* Return the required pointer. */
   return result;
}

static AstRegion *GetNegation( AstRegion *this, int *status ) {
/*
*+
*  Name:
*     astGetNegation

*  Purpose:
*     Obtain a pointer to a negated copy of the supplied Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstRegion *GetNegation( AstRegion *this, int *status )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a pointer to a Region which is a negated
*     copy of "this". The copy is cached in the Region structure for
*     future use.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     A pointer to the Region. This should be annulled (using astAnnul)
*     when no longer needed.

*  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.
*-
*/

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* If the Region struture does not contain a pointer to a negated copy of
   itself, create one now. */
   if( ! this->negation ) {
      this->negation = astCopy( this );
      astNegate( this->negation );
   }

/* Return a clone of the negation pointer. */
   return astClone( this->negation );
}

static AstFrameSet *GetRegFS( AstRegion *this, int *status ) {
/*
*+
*  Name:
*     astGetRegFS

*  Purpose:
*     Obtain a pointer to the FrameSet encapsulated within a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstFrameSet *astGetRegFS( AstRegion *this )

*  Class Membership:
*     Region virtual function

*  Description:
*     This function returns a pointer to the FrameSet encapsulated by the
*     Region. This is a clone, not a deep copy, of the pointer stored
*     in the Region.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     A pointer to the FrameSet.

*  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.
*-
*/

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Return the required pointer. */
   return astClone( this->frameset );
}

static AstPointSet *GetSubMesh( int *mask, AstPointSet *in, int *status ) {
/*
*  Name:
*     GetSubMesh

*  Purpose:
*     Extract a selection of points from a PointSet.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *GetSubMesh( int *mask, AstPointSet *in, int *status )

*  Class Membership:
*     Region member function

*  Description:
*     This function creates a new PointSet holding points selected from a
*     supplied PointSet. An integer mask is supplied to indicate which
*     points should be selected.

*  Parameters:
*     mask
*        Pointer to a mask array, Its size should be equal to the number
*        of points in the supplied PointSet. Each corresponding point will
*        be copied if the mask value is zero.
*     in
*        Pointer to the PointSet holding the input positions.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to the output PointSet.

*  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: */
   AstPointSet *result;          /* Pointer to output PointSet */
   double **ptr_in;              /* Pointers to input axis values */
   double **ptr_out;             /* Pointers to output axis values */
   double *pin;                  /* Pointer to next input axis value */
   double *pout;                 /* Pointer to next output axis value */
   int *m;                       /* Pointer to next mask element */
   int ic;                       /* Axis index */
   int ip;                       /* Point index */
   int nc;                       /* Number of axes in both PointSets */
   int npin;                     /* Number of points in input PointSet */
   int npout;                    /* Number of points in output PointSet */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get the length of the mask. */
   npin = astGetNpoint( in );

/* Count the number of zeros in the mask. */
   npout = 0;
   m = mask;
   for( ip = 0; ip < npin; ip++ ) {
      if( *(m++) == 0 ) npout++;
   }

/* Create the output PointSet and get pointers to its data arrays. */
   nc = astGetNcoord( in );
   result = astPointSet( npout, nc, "", status );
   ptr_in = astGetPoints( in );
   ptr_out = astGetPoints( result );

/* Check pointers can be dereferenced safely. */
   if( astOK ) {

/* Copy the required axis values from the input to the output. */
      for( ic = 0; ic < nc; ic++ ) {
         pin = ptr_in[ ic ];
         pout = ptr_out[ ic ];
         m = mask;
         for( ip = 0; ip < npin; ip++, pin++, m++ ) {
            if( *m == 0 ) *(pout++) = *pin;
         }
      }
   }

/* Return a pointer to the output PointSet. */
   return result;

}

static AstRegion *GetUnc( AstRegion *this, int def, int *status ){
/*
*++
*  Name:
c     astGetUnc
f     AST_GETUNC

*  Purpose:
*     Obtain uncertainty information from a Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     AstRegion *astGetUnc( AstRegion *this, int def )
f     RESULT = AST_GETUNC( THIS, DEF, STATUS )

*  Class Membership:
*     Region method.

*  Description:
*     This function returns a Region which represents the uncertainty
*     associated with positions within the supplied Region. See
c     astSetUnc
f     AST_SETUNC
*     for more information about Region uncertainties and their use.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
c     def
f     DEF = LOGICAL (Given)
*        Controls what is returned if no uncertainty information has been
*        associated explicitly with the supplied Region. If
c        a non-zero value
f        .TRUE.
*        is supplied, then the default uncertainty Region used internally
*        within AST is returned (see "Applicability" below). If
c        zero is supplied, then NULL
f        .FALSE. is supplied, then AST__NULL
*        will be returned (without error).
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astGetUnc()
f     AST_GETUNC = INTEGER
*        A pointer to a Region describing the uncertainty in the supplied
*        Region.

*  Applicability:
*     CmpRegion
*        The default uncertainty for a CmpRegion is taken from one of the
*        two component Regions. If the first component Region has a
*        non-default uncertainty, then it is used as the default uncertainty
*        for the parent CmpRegion. Otherwise, if the second component Region
*        has a non-default uncertainty, then it is used as the default
*        uncertainty for the parent CmpRegion. If neither of the
*        component Regions has non-default uncertainty, then the default
*        uncertainty for the CmpRegion is 1.0E-6 of the bounding box of
*        the CmpRegion.
*     Prism
*        The default uncertainty for a Prism is formed by combining the
*        uncertainties from the two component Regions. If a component
*        Region does not have a non-default uncertainty, then its default
*        uncertainty will be used to form the default uncertainty of the
*        parent Prism.
*     Region
*        For other classes of Region, the default uncertainty is 1.0E-6
*        of the bounding box of the Region. If the bounding box has zero
*        width on any axis, then the uncertainty will be 1.0E-6 of the
*        axis value.

*  Notes:
*     - If uncertainty information is associated with a Region, and the
*     coordinate system described by the Region is subsequently changed
*     (e.g. by changing the value of its System attribute, or using the
c     astMapRegion
f     AST_MAPREGION
*     function), then the uncertainty information returned by this function
*     will be modified so that it refers to the coordinate system currently
*     described by the supplied Region.
f     - A null Object pointer (AST__NULL) will be returned if this
f     function is invoked with STATUS set to an error value, or if it
c     - A null Object pointer (NULL) will be returned if this
c     function is invoked with the AST error status set, or if it
*     should fail for any reason.

*--
*/

/* Local Variables: */
   AstRegion *result;       /* Pointer to returned uncertainty Region */
   AstRegion *unc;          /* Pointer to original uncertainty Region */

/* Initialise */
   result = NULL;

/* Check inherited status */
   if( !astOK ) return result;

/* Check that we have an uncertainty Region to return (either assigned or
   default). */
   if( def || astTestUnc( this ) ) {

/* Obtain the uncertainty Region and take a copy so that we can modify it
   without affecting the supplied Region. */
      unc = astGetUncFrm( this, AST__CURRENT );
      result = astCopy( unc );
      unc = astAnnul( unc );

/* In its current context, the uncertainty region is known to refer to
   the Frame of the supplied Region and so its RegionFS attribute will be
   set to zero, indicating that the uncertainty FrameSet need not be
   dumped. However, outside of AST this information cannot be implied, so
   clear the RegionFS attribute so that the returned pointer will include
   Frame information if it is dumped to a Channel. */
      astClearRegionFS( result );

   }

/* Return the result. */
   return result;

}

static AstRegion *GetUncFrm( AstRegion *this, int ifrm, int *status ) {
/*
*+
*  Name:
*     astGetUncFrm

*  Purpose:
*     Obtain a pointer to the uncertainty Region for a given Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstRegion *astGetUncFrm( AstRegion *this, int ifrm )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a pointer to a Region which represents the
*     uncertainty associated with a position on the boundary of the given
*     Region. The returned Region can refer to the either the base or
*     the current Frame within the FrameSet encapsulated by the supplied
*     Region as specified by the "ifrm" parameter. If the returned Region is
*     re-centred at some point on the boundary of the supplied Region, then
*     the re-centred Region will represent the region in which the true
*     boundary position could be.

*  Parameters:
*     this
*        Pointer to the Region.
*     ifrm
*        The index of a Frame within the FrameSet encapsulated by "this".
*        The returned Region will refer to the requested Frame. It should
*        be either AST__CURRENT or AST__BASE.

*  Returned Value:
*     A pointer to the Region. This should be annulled (using astAnnul)
*     when no longer needed.

*  Notes:
*     - A default uncertainty Region will be created if the supplied Region
*     does not have an uncertainty 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.
*-
*/

/* Local Variables: */
   AstFrame *frm;             /* Current Frame from supplied Region */
   AstMapping *map;           /* Supplied to uncertainty Mapping */
   AstRegion *result;         /* Returned pointer */
   AstRegion *unc;            /* Base frame uncertainty Region to use */

/* Initialise */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* If the Region has an explicitly assigned base-frame uncertainty Region,
   use it. */
   if( this->unc ) {
      unc = this->unc;

/* If not, use the default base-frame uncertainty Region, creating it if
   necessary. */
   } else {
      if( !this->defunc ) this->defunc = astGetDefUnc( this );
      unc = this->defunc;
   }

/* If the uncertainty Region is the base Frame is required, just return a
   clone of the uncertainty Region pointer. The Frame represented by an
   uncertainty Region will always (barring bugs!) be the base Frame of
   its parent Region. */
   if( ifrm == AST__BASE ) {
      result = astClone( unc );

/* If the uncertainty Region is the current Frame is required... */
   } else {

/* Get a Mapping from the Frame represented by the uncertainty Region
   (the Region base Frame) to the Region current Frame. */
      map = astGetMapping( this->frameset, AST__BASE, AST__CURRENT );

/* If this is a UnitMap, the uncertainty Region is already in the correct
   Frame, so just return the stored pointer. */
      if( astIsAUnitMap( map ) ) {
         result = astClone( unc );

/* Otherwise, use this Mapping to map the uncertainty Region into the current
   Frame. */
      } else {
         frm = astGetFrame( this->frameset, AST__CURRENT );
         result = astMapRegion( unc, map, frm );

/* Free resources. */
         frm = astAnnul( frm );
      }

      map = astAnnul( map );
   }

/* Return NULL if an error occurred. */
   if( !astOK ) result = astAnnul( result );

/* Return the required pointer. */
   return result;
}

static int GetUseDefs( AstObject *this_object, int *status ) {
/*
*  Name:
*     GetUseDefs

*  Purpose:
*     Get the value of the UseDefs attribute for a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int GetUseDefs( AstObject *this_object, int *status ) {

*  Class Membership:
*     Region member function (over-rides the protected astGetUseDefs
*     method inherited from the Frame class).

*  Description:
*     This function returns the value of the UseDefs attribute for a
*     Region. supplying a suitable default.

*  Parameters:
*     this
*        Pointer to the Region.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     - The USeDefs value.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   int result;                   /* Value to return */

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_object;

/* If the UseDefs value for the Region has been set explicitly, use the
   Get method inherited from the parent Frame class to get its value. */
   if( astTestUseDefs( this ) ) {
      result = (*parent_getusedefs)( this_object, status );

/* Otherwise, supply a default value equal to the UseDefs value of the
   encapsulated Frame. */
   } else {
      fr = astGetFrame( this->frameset, AST__CURRENT );
      result = astGetUseDefs( fr );
      fr = astAnnul( fr );
   }

/* Return the result. */
   return result;
}

static int TestUnc( AstRegion *this, int *status ) {
/*
*+
*  Name:
*     astTestUnc

*  Purpose:
*     Does the Region contain non-default uncertainty information?

*  Type:
*     Protected function.

*  Synopsis:
*     int astTestUnc( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a flag indicating if the uncertainty Region in
*     the supplied Region was supplied explicit (i.e. is not a default
*     uncertainty Region).

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     Non-zero if the uncertainty Region was supplied explicitly.
*     Zero otherwise.

*  Notes:
*     - Classes of Region that encapsulate two or more other Regions
*     inherit their default uncertainty from the encapsulated Regions.
*     Non-default uncertainty in the component Regions does not imply
*     that the parent Region has non-default uncertainty.
*-
*/

/* Check the global error status. */
   if ( !astOK ) return 0;

   return ( this->unc != NULL );
}

static AstFrame *RegFrame( AstRegion *this, int *status ) {
/*
*+
*  Name:
*     astRegFrame

*  Purpose:
*     Obtain a pointer to the current Frame for a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstFrame *astRegFrame( AstRegion *this )

*  Class Membership:
*     Region virtual function

*  Description:
*     This function returns a pointer to the current Frame in the encapsulated
*     FrameSet. This is a clone, not a deep copy, of the pointer stored
*     in the FrameSet. For a deep copy, use astGetRegionFrame.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     A pointer to the Frame.

*  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.
*-
*/

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Return the required pointer. */
   return astGetFrame( this->frameset, AST__CURRENT );
}

static AstMapping *RegMapping( AstRegion *this, int *status ) {
/*
*+
*  Name:
*     astRegMapping

*  Purpose:
*     Obtain a pointer to the simplified base->current Mapping for a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstMapping *astRegMapping( AstRegion *this )

*  Class Membership:
*     Region member function

*  Description:
*     This function returns a pointer to the Mapping from the base to the
*     current Frame int he encapsulated FrameSet. The returned Mapping is
*     simplified before being returned.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     A pointer to the Mapping.

*  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: */
   AstMapping *map;           /* Unsimplified Mapping */
   AstMapping *result;        /* Simplified Mapping */

/* Initialise */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* If the "nomap" flag is set in the Region structure, re return a
   UnitMap. */
   if( this->nomap ) {
      result = (AstMapping *) astUnitMap( astGetNin( this->frameset ), "", status );

/* Otherwise use the Mapping from the Region's FrameSet. */
   } else {

/* Get the Mapping */
      map = astGetMapping( this->frameset, AST__BASE, AST__CURRENT );

/* Simplify it. */
      result = astSimplify( map );

/* Annul the pointer to the unsimplified Mapping */
      map = astAnnul( map );
   }

/* Return the required pointer. */
   return result;
}

static int GetNaxes( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetNaxes

*  Purpose:
*     Determine how many axes a Region has.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int GetNaxes( AstFrame *this, int *status )

*  Class Membership:
*     Region member function (over-rides the astGetNaxes method
*     inherited from the Frame class).

*  Description:
*     This function returns the number of axes for a Region. This is equal
*     to the number of axes in its current Frame.

*  Parameters:
*     this
*        Pointer to the Region.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The number of Region axes (zero or more).

*  Notes:
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   int result;                   /* Result to be returned */

/* Check the global error status. */
   if ( !astOK ) return 0;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's current Frame. */
   fr = astGetFrame( this->frameset, AST__CURRENT );

/* Obtain the number of axes in this Frame. */
   result = astGetNaxes( fr );

/* Annul the current Frame pointer. */
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = 0;

/* Return the result. */
   return result;
}

static const int *GetPerm( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetPerm

*  Purpose:
*     Access the axis permutation array for the current Frame of a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     const int *GetPerm( AstFrame *this, int *status )

*  Class Membership:
*     Region member function (over-rides the astGetPerm protected
*     method inherited from the Frame class).

*  Description:
*     This function returns a pointer to the axis permutation array
*     for the current Frame of a Region. This array constitutes a
*     lookup-table that converts between an axis number supplied
*     externally and the corresponding index in the Frame's internal
*     axis arrays.

*  Parameters:
*     this
*        Pointer to the Region.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to the current Frame's axis permutation array (a
*     constant array of int).  Each element of this contains the
*     (zero-based) internal axis index to be used in place of the
*     external index which is used to address the permutation
*     array. If the current Frame has zero axes, this pointer will be
*     NULL.

*  Notes:
*     - The pointer returned by this function gives direct access to
*     data internal to the Frame object. It remains valid only so long
*     as the Frame exists. The permutation array contents may be
*     modified by other functions which operate on the Frame and this
*     may render the returned pointer invalid.
*     - 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: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to Region structure */
   const int *result;            /* Result pointer value */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's current Frame and then obtain a
   pointer to its axis permutation array. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astGetPerm( fr );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = NULL;

/* Return the result. */
   return result;
}

static AstFrame *GetRegionFrame( AstRegion *this, int *status ) {
/*
*++
*  Name:
c     astGetRegionFrame
f     AST_GETREGIONFRAME

*  Purpose:
*     Obtain a pointer to the encapsulated Frame within a Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     AstFrame *astGetRegionFrame( AstRegion *this )
f     RESULT = AST_GETREGIONFRAME( THIS, STATUS )

*  Class Membership:
*     Region method.

*  Description:
*     This function returns a pointer to the Frame represented by a
*     Region.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astGetRegionFrame()
f     AST_GETREGIONFRAME = INTEGER
*        A pointer to a deep copy of the Frame represented by the Region.
*        Using this pointer to modify the Frame will have no effect on
*        the Region. To modify the Region, use the Region pointer directly.

*  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 *fr;                 /* Pointer to current Frame */
   AstFrame *result;             /* Pointer value to return */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get a pointer to the current Frame of the encapsulated FrameSet. */
   fr = astGetFrame( this->frameset, AST__CURRENT );

/* Take a deep copy of it, and then annul the original pointer. */
   result = astCopy( fr );
   fr = astAnnul( fr );

/* If not OK, annul the returned pointer. */
   if( !astOK ) result = astAnnul( result );

/* Return the result. */
   return result;
}

static AstFrameSet *GetRegionFrameSet( AstRegion *this, int *status ) {
/*
*++
*  Name:
c     astGetRegionFrameSet
f     AST_GETREGIONFRAMESET

*  Purpose:
*     Obtain a pointer to the encapsulated FrameSet within a Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     AstFrame *astGetRegionFrameSet( AstRegion *this )
f     RESULT = AST_GETREGIONFRAMESET( THIS, STATUS )

*  Class Membership:
*     Region method.

*  Description:
*     This function returns a pointer to the FrameSet encapsulated by a
*     Region. The base Frame is the Frame in which the box was originally
*     defined, and the current Frame is the Frame into which the Region
*     is currently mapped (i.e. it will be the same as the Frame returned
c     by astGetRegionFrame).
f     by AST_GETREGIONFRAME).

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astGetRegionFrameSet()
f     AST_GETREGIONFRAMESET = INTEGER
*        A pointer to a deep copy of the FrameSet represented by the Region.
*        Using this pointer to modify the FrameSet will have no effect on
*        the Region.

*  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.
*--
*/

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Return a deep copy of the encapsulated FrameSet. */
   return astCopy( this->frameset );
}

void astInitRegionVtab_(  AstRegionVtab *vtab, const char *name, int *status ) {
/*
*+
*  Name:
*     astInitRegionVtab

*  Purpose:
*     Initialise a virtual function table for a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astInitRegionVtab( AstRegionVtab *vtab, const char *name )

*  Class Membership:
*     Region vtab initialiser.

*  Description:
*     This function initialises the component of a virtual function
*     table which is used by the Region 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 */
   AstFrameVtab *frame;          /* Pointer to Frame component of Vtab */
   AstMappingVtab *mapping;      /* Pointer to Mapping 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. */
   astInitFrameVtab( (AstFrameVtab *) vtab, name );

/* Store a unique "magic" value in the virtual function table. This
   will be used (by astIsARegion) 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 = &(((AstFrameVtab *) vtab)->id);

/* Initialise member function pointers. */
/* ------------------------------------ */

/* Store pointers to the member functions (implemented here) that
   provide virtual methods for this class. */
   vtab->ClearNegated = ClearNegated;
   vtab->GetNegated = GetNegated;
   vtab->SetNegated = SetNegated;
   vtab->TestNegated = TestNegated;

   vtab->ClearRegionFS = ClearRegionFS;
   vtab->GetRegionFS = GetRegionFS;
   vtab->SetRegionFS = SetRegionFS;
   vtab->TestRegionFS = TestRegionFS;

   vtab->ClearClosed = ClearClosed;
   vtab->GetClosed = GetClosed;
   vtab->SetClosed = SetClosed;
   vtab->TestClosed = TestClosed;

   vtab->ClearMeshSize = ClearMeshSize;
   vtab->GetMeshSize = GetMeshSize;
   vtab->SetMeshSize = SetMeshSize;
   vtab->TestMeshSize = TestMeshSize;

   vtab->ClearAdaptive = ClearAdaptive;
   vtab->GetAdaptive = GetAdaptive;
   vtab->SetAdaptive = SetAdaptive;
   vtab->TestAdaptive = TestAdaptive;

   vtab->ClearFillFactor = ClearFillFactor;
   vtab->GetFillFactor = GetFillFactor;
   vtab->SetFillFactor = SetFillFactor;
   vtab->TestFillFactor = TestFillFactor;

   vtab->ResetCache = ResetCache;
   vtab->RegTrace = RegTrace;
   vtab->GetBounded = GetBounded;
   vtab->TestUnc = TestUnc;
   vtab->ClearUnc = ClearUnc;
   vtab->GetRegionFrame = GetRegionFrame;
   vtab->GetRegionFrameSet = GetRegionFrameSet;
   vtab->MapRegion = MapRegion;
   vtab->Overlap = Overlap;
   vtab->OverlapX = OverlapX;
   vtab->Negate = Negate;
   vtab->BndMesh = BndMesh;
   vtab->BndBaseMesh = BndBaseMesh;
   vtab->RegBaseGrid = RegBaseGrid;
   vtab->RegBaseMesh = RegBaseMesh;
   vtab->RegSplit = RegSplit;
   vtab->RegBaseBox = RegBaseBox;
   vtab->RegBaseBox2 = RegBaseBox2;
   vtab->RegBasePick = RegBasePick;
   vtab->RegCentre = RegCentre;
   vtab->RegGrid = RegGrid;
   vtab->RegMesh = RegMesh;
   vtab->RegClearAttrib = RegClearAttrib;
   vtab->RegSetAttrib = RegSetAttrib;
   vtab->GetDefUnc = GetDefUnc;
   vtab->GetNegation = GetNegation;
   vtab->GetUncFrm = GetUncFrm;
   vtab->SetUnc = SetUnc;
   vtab->GetUnc = GetUnc;
   vtab->ShowMesh = ShowMesh;
   vtab->GetRegionBounds = GetRegionBounds;
   vtab->GetRegionBounds2 = GetRegionBounds2;
   vtab->GetRegionMesh = GetRegionMesh;
   vtab->GetRegionPoints = GetRegionPoints;
   vtab->GetRegionDisc = GetRegionDisc;
   vtab->RegOverlay = RegOverlay;
   vtab->RegFrame = RegFrame;
   vtab->RegDummyFS = RegDummyFS;
   vtab->RegMapping = RegMapping;
   vtab->RegPins = RegPins;
   vtab->RegTransform = RegTransform;
   vtab->BTransform = BTransform;
   vtab->GetRegFS = GetRegFS;
   vtab->SetRegFS = SetRegFS;
   vtab->MaskB = MaskB;
   vtab->MaskD = MaskD;
   vtab->MaskF = MaskF;
   vtab->MaskI = MaskI;
   vtab->MaskL = MaskL;
   vtab->MaskS = MaskS;
   vtab->MaskUB = MaskUB;
   vtab->MaskUI = MaskUI;
   vtab->MaskUL = MaskUL;
   vtab->MaskUS = MaskUS;
#if HAVE_LONG_DOUBLE     /* Not normally implemented */
   vtab->MaskLD = MaskLD;
#endif

/* Save the inherited pointers to methods that will be extended, and store
   replacement pointers for methods which will be over-ridden by new member
   functions implemented here. */
   object = (AstObjectVtab *) vtab;
   mapping = (AstMappingVtab *) vtab;
   frame = (AstFrameVtab *) vtab;

   parent_getobjsize = object->GetObjSize;
   object->GetObjSize = GetObjSize;

   parent_getusedefs = object->GetUseDefs;
   object->GetUseDefs = GetUseDefs;

#if defined(THREAD_SAFE)
   parent_managelock = object->ManageLock;
   object->ManageLock = ManageLock;
#endif

   object->Cast = Cast;
   object->Equal = Equal;
   object->ClearAttrib = ClearAttrib;
   object->GetAttrib = GetAttrib;
   object->SetAttrib = SetAttrib;
   object->TestAttrib = TestAttrib;

   mapping->ReportPoints = ReportPoints;
   mapping->RemoveRegions = RemoveRegions;
   mapping->Simplify = Simplify;

   frame->Abbrev = Abbrev;
   frame->Angle = Angle;
   frame->AxAngle = AxAngle;
   frame->AxDistance = AxDistance;
   frame->AxNorm = AxNorm;
   frame->AxOffset = AxOffset;
   frame->CheckPerm = CheckPerm;
   frame->ClearDigits = ClearDigits;
   frame->ClearDirection = ClearDirection;
   frame->ClearDomain = ClearDomain;
   frame->ClearFormat = ClearFormat;
   frame->ClearLabel = ClearLabel;
   frame->ClearMatchEnd = ClearMatchEnd;
   frame->ClearMaxAxes = ClearMaxAxes;
   frame->ClearMinAxes = ClearMinAxes;
   frame->ClearPermute = ClearPermute;
   frame->ClearPreserveAxes = ClearPreserveAxes;
   frame->ClearSymbol = ClearSymbol;
   frame->ClearTitle = ClearTitle;
   frame->ClearUnit = ClearUnit;
   frame->Convert = Convert;
   frame->ConvertX = ConvertX;
   frame->Distance = Distance;
   frame->FindFrame = FindFrame;
   frame->Format = Format;
   frame->Centre = Centre;
   frame->Gap = Gap;
   frame->GetAxis = GetAxis;
   frame->GetDigits = GetDigits;
   frame->GetDirection = GetDirection;
   frame->GetDomain = GetDomain;
   frame->GetFormat = GetFormat;
   frame->GetLabel = GetLabel;
   frame->GetMatchEnd = GetMatchEnd;
   frame->GetMaxAxes = GetMaxAxes;
   frame->GetMinAxes = GetMinAxes;
   frame->GetNaxes = GetNaxes;
   frame->GetPerm = GetPerm;
   frame->GetPermute = GetPermute;
   frame->GetPreserveAxes = GetPreserveAxes;
   frame->GetSymbol = GetSymbol;
   frame->GetTitle = GetTitle;
   frame->GetUnit = GetUnit;
   frame->Intersect = Intersect;
   frame->IsUnitFrame = IsUnitFrame;
   frame->Match = Match;
   frame->Norm = Norm;
   frame->NormBox = NormBox;
   frame->Offset = Offset;
   frame->Offset2 = Offset2;
   frame->Overlay = Overlay;
   frame->PermAxes = PermAxes;
   frame->PickAxes = PickAxes;
   frame->Resolve = Resolve;
   frame->ResolvePoints = ResolvePoints;
   frame->SetAxis = SetAxis;
   frame->SetDigits = SetDigits;
   frame->SetDirection = SetDirection;
   frame->SetDomain = SetDomain;
   frame->SetFormat = SetFormat;
   frame->SetLabel = SetLabel;
   frame->SetMatchEnd = SetMatchEnd;
   frame->SetMaxAxes = SetMaxAxes;
   frame->SetMinAxes = SetMinAxes;
   frame->SetPermute = SetPermute;
   frame->SetPreserveAxes = SetPreserveAxes;
   frame->SetSymbol = SetSymbol;
   frame->SetTitle = SetTitle;
   frame->SetUnit = SetUnit;
   frame->SubFrame = SubFrame;
   frame->SystemCode = SystemCode;
   frame->SystemString = SystemString;
   frame->TestDigits = TestDigits;
   frame->TestDirection = TestDirection;
   frame->TestDomain = TestDomain;
   frame->TestFormat = TestFormat;
   frame->TestLabel = TestLabel;
   frame->TestMatchEnd = TestMatchEnd;
   frame->TestMaxAxes = TestMaxAxes;
   frame->TestMinAxes = TestMinAxes;
   frame->TestPermute = TestPermute;
   frame->TestPreserveAxes = TestPreserveAxes;
   frame->TestSymbol = TestSymbol;
   frame->TestTitle = TestTitle;
   frame->TestUnit = TestUnit;
   frame->Unformat = Unformat;
   frame->ValidateAxis = ValidateAxis;
   frame->ValidateAxisSelection = ValidateAxisSelection;
   frame->ValidateSystem = ValidateSystem;
   frame->LineDef = LineDef;
   frame->LineContains = LineContains;
   frame->LineCrossing = LineCrossing;
   frame->LineOffset = LineOffset;
   frame->MatchAxes = MatchAxes;
   frame->MatchAxesX = MatchAxesX;

   frame->GetActiveUnit = GetActiveUnit;
   frame->SetActiveUnit = SetActiveUnit;
   frame->TestActiveUnit = TestActiveUnit;

   frame->GetTop = GetTop;
   frame->SetTop = SetTop;
   frame->TestTop = TestTop;
   frame->ClearTop = ClearTop;

   frame->GetBottom = GetBottom;
   frame->SetBottom = SetBottom;
   frame->TestBottom = TestBottom;
   frame->ClearBottom = ClearBottom;

   frame->GetEpoch = GetEpoch;
   frame->SetEpoch = SetEpoch;
   frame->TestEpoch = TestEpoch;
   frame->ClearEpoch = ClearEpoch;

   frame->ClearObsAlt = ClearObsAlt;
   frame->TestObsAlt = TestObsAlt;
   frame->GetObsAlt = GetObsAlt;
   frame->SetObsAlt = SetObsAlt;

   frame->ClearObsLat = ClearObsLat;
   frame->TestObsLat = TestObsLat;
   frame->GetObsLat = GetObsLat;
   frame->SetObsLat = SetObsLat;

   frame->ClearObsLon = ClearObsLon;
   frame->TestObsLon = TestObsLon;
   frame->GetObsLon = GetObsLon;
   frame->SetObsLon = SetObsLon;

   frame->GetSystem = GetSystem;
   frame->SetSystem = SetSystem;
   frame->TestSystem = TestSystem;
   frame->ClearSystem = ClearSystem;

   frame->GetAlignSystem = GetAlignSystem;
   frame->SetAlignSystem = SetAlignSystem;
   frame->TestAlignSystem = TestAlignSystem;
   frame->ClearAlignSystem = ClearAlignSystem;

/* Declare the copy constructor, destructor and class dump
   functions. */
   astSetDelete( vtab, Delete );
   astSetCopy( vtab, Copy );
   astSetDump( vtab, Dump, "Region",
               "An area within a coordinate system" );

/* If we have just initialised the vtab for the current class, indicate
   that the vtab is now initialised, and store a pointer to the class
   identifier in the base "object" level of the vtab. */
   if( vtab == &class_vtab ) {
      class_init = 1;
      astSetVtabClassIdentifier( vtab, &(vtab->id) );
   }
}

static void Intersect( AstFrame *this_frame, const double a1[2],
                       const double a2[2], const double b1[2],
                       const double b2[2], double cross[2],
                       int *status ) {
/*
*  Name:
*     Intersect

*  Purpose:
*     Find the point of intersection between two geodesic curves.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void Intersect( AstFrame *this_frame, const double a1[2],
*                      const double a2[2], const double b1[2],
*                      const double b2[2], double cross[2],
*                      int *status )

*  Class Membership:
*     Region member function (over-rides the astIntersect method
*     inherited from the Frame class).

*  Description:
*     This function finds the coordinate values at the point of
*     intersection between two geodesic curves. Each curve is specified
*     by two points on the curve.

*  Parameters:
*     this
*        Pointer to the SkyFrame.
*     a1
*        An array of double, with one element for each Frame axis.
*        This should contain the coordinates of a point on the first
*        geodesic curve.
*     a2
*        An array of double, with one element for each Frame axis.
*        This should contain the coordinates of a second point on the
*        first geodesic curve.
*     b1
*        An array of double, with one element for each Frame axis.
*        This should contain the coordinates of a point on the second
*        geodesic curve.
*     b2
*        An array of double, with one element for each Frame axis.
*        This should contain the coordinates of a second point on
*        the second geodesic curve.
*     cross
*        An array of double, with one element for each Frame axis
*        in which the coordinates of the required intersection
*        point will be returned. These will be AST__BAD if the curves do
*        not intersect.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - The geodesic curve used by this function is the path of
*     shortest distance between two points, as defined by the
*     astDistance function.
*     - This function will return "bad" coordinate values (AST__BAD)
*     if any of the input coordinates has this value.
*     - For SkyFrames each curve will be a great circle, and in general
*     each pair of curves will intersect at two diametrically opposite
*     points on the sky. The returned position is the one which is
*     closest to point "a1".
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astIntersect method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astIntersect( fr, a1, a2, b1, b2, cross );
   fr = astAnnul( fr );
}

static int IsUnitFrame( AstFrame *this, int *status ){
/*
*  Name:
*     IsUnitFrame

*  Purpose:
*     Is this Frame equivalent to a UnitMap?

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int IsUnitFrame( AstFrame *this, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astIsUnitFrame
*     method inherited from the Frame class).

*  Description:
*     This function returns a flag indicating if the supplied Frame is
*     equivalent to a UnitMap when treated as a Mapping (note, the Frame
*     class inherits from Mapping and therefore every Frame is also a Mapping).

*  Parameters:
*     this
*        Pointer to the Frame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A non-zero value is returned if the supplied Frame is equivalent to
*     a UnitMap when treated as a Mapping.

*-
*/

/* Check the global error status. */
   if( !astOK ) return 0;

/* The Region class is never equivalent to a UnitMap. */
   return 0;
}

static int LineContains( AstFrame *this_frame, AstLineDef *l, int def, double *point, int *status ) {
/*
*  Name:
*     LineContains

*  Purpose:
*     Determine if a line contains a point.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int LineContains( AstFrame *this, AstLineDef *l, int def, double *point, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astLineContains
*     method inherited from the Frame class).

*  Description:
*     This function determines if the supplied point is on the supplied
*     line within the supplied Frame. The start point of the line is
*     considered to be within the line, but the end point is not. The tests
*     are that the point of closest approach of the line to the point should
*     be between the start and end, and that the distance from the point to
*     the point of closest aproach should be less than 1.0E-7 of the length
*     of the line.

*  Parameters:
*     this
*        Pointer to the Frame.
*     l
*        Pointer to the structure defining the line.
*     def
*        Should be set non-zero if the "point" array was created by a
*        call to astLineCrossing (in which case it may contain extra
*        information following the axis values),and zero otherwise.
*     point
*        Point to an array containing the axis values of the point to be
*        tested, possibly followed by extra cached information (see "def").
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A non-zero value is returned if the line contains the point.

*  Notes:
*     - The pointer supplied for "l" should have been created using the
*     astLineDef method. These structures contained cached information about
*     the lines which improve the efficiency of this method when many
*     repeated calls are made. An error will be reported if the structure
*     does not refer to the Frame specified by "this".
*     - Zero will be returned if this function is invoked with the global
*     error status set, or if it should fail for any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   int result;                   /* Returned value */

/* Initialise */
   result =0;

/* Obtain a pointer to the Region's current Frame and then invoke the
   method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( ((AstRegion *) this_frame)->frameset, AST__CURRENT );
   result = astLineContains( fr, l, def, point );
   fr = astAnnul( fr );

/* Return the result. */
   return result;
}

static int LineCrossing( AstFrame *this_frame, AstLineDef *l1, AstLineDef *l2,
                         double **cross, int *status ) {
/*
*  Name:
*     LineCrossing

*  Purpose:
*     Determine if two lines cross.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int LineCrossing( AstFrame *this, AstLineDef *l1, AstLineDef *l2,
*                       double **cross, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astLineCrossing
*     method inherited from the Frame class).

*  Description:
*     This function determines if the two suplied line segments cross,
*     and if so returns the axis values at the point where they cross.
*     A flag is also returned indicating if the crossing point occurs
*     within the length of both line segments, or outside one or both of
*     the line segments.

*  Parameters:
*     this
*        Pointer to the Frame.
*     l1
*        Pointer to the structure defining the first line.
*     l2
*        Pointer to the structure defining the second line.
*     cross
*        Pointer to a location at which to put a pointer to a dynamically
*        alocated array containing the axis values at the crossing. If
*        NULL is supplied no such array is returned. Otherwise, the returned
*        array should be freed using astFree when no longer needed. If the
*        lines are parallel (i.e. do not cross) then AST__BAD is returned for
*        all axis values. Note usable axis values are returned even if the
*        lines cross outside the segment defined by the start and end points
*        of the lines. The order of axes in the returned array will take
*        account of the current axis permutation array if appropriate. Note,
*        sub-classes such as SkyFrame may append extra values to the end
*        of the basic frame axis values. A NULL pointer is returned if an
*        error occurs.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A non-zero value is returned if the lines cross at a point which is
*     within the [start,end) segment of both lines. If the crossing point
*     is outside this segment on either line, or if the lines are parallel,
*     zero is returned. Note, the start point is considered to be inside
*     the length of the segment, but the end point is outside.

*  Notes:
*     - The pointers supplied for "l1" and "l2" should have been created
*     using the astLineDef method. These structures contained cached
*     information about the lines which improve the efficiency of this method
*     when many repeated calls are made. An error will be reported if
*     either structure does not refer to the Frame specified by "this".
*     - Zero will be returned if this function is invoked with the global
*     error status set, or if it should fail for any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   int result;                   /* Returned value */

/* Initialise */
   result =0;

/* Obtain a pointer to the Region's current Frame and then invoke the
   method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( ((AstRegion *) this_frame)->frameset, AST__CURRENT );
   result = astLineCrossing( fr, l1, l2, cross );
   fr = astAnnul( fr );

/* Return the result. */
   return result;
}

static AstLineDef *LineDef( AstFrame *this_frame, const double start[2],
                            const double end[2], int *status ) {
/*
*  Name:
*     LineDef

*  Purpose:
*     Creates a structure describing a line segment in a 2D Frame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstLineDef *LineDef( AstFrame *this, const double start[2],
*                             const double end[2], int *status )

*  Class Membership:
*     Region member function (over-rides the protected astLineDef
*     method inherited from the Frame class).

*  Description:
*     This function creates a structure containing information describing a
*     given line segment within the supplied 2D Frame. This may include
*     information which allows other methods such as astLineCrossing to
*     function more efficiently. Thus the returned structure acts as a
*     cache to store intermediate values used by these other methods.

*  Parameters:
*     this
*        Pointer to the Frame. Must have 2 axes.
*     start
*        An array of 2 doubles marking the start of the line segment.
*     end
*        An array of 2 doubles marking the end of the line segment.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to the memory structure containing the description of the
*     line. This structure should be freed using astFree when no longer
*     needed. A NULL pointer is returned (without error) if any of the
*     supplied axis values are AST__BAD.

*  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: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstLineDef *result;           /* Returned value */

/* Initialise */
   result = NULL;

/* Obtain a pointer to the Region's current Frame and then invoke the
   method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( ((AstRegion *) this_frame)->frameset, AST__CURRENT );
   result = astLineDef( fr, start, end );
   fr = astAnnul( fr );

/* Return the result. */
   return result;
}

static void LineOffset( AstFrame *this_frame, AstLineDef *line, double par,
                        double prp, double point[2], int *status ){
/*
*  Name:
*     LineOffset

*  Purpose:
*     Find a position close to a line.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void LineOffset( AstFrame *this, AstLineDef *line, double par,
*                      double prp, double point[2], int *status )

*  Class Membership:
*     Region member function (over-rides the protected astLineOffset
*     method inherited from the Frame class).

*  Description:
*     This function returns a position formed by moving a given distance along
*     the supplied line, and then a given distance away from the supplied line.

*  Parameters:
*     this
*        Pointer to the Frame.
*     line
*        Pointer to the structure defining the line.
*     par
*        The distance to move along the line from the start towards the end.
*     prp
*        The distance to move at right angles to the line. Positive
*        values result in movement to the left of the line, as seen from
*        the observer, when moving from start towards the end.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - The pointer supplied for "line" should have been created using the
*     astLineDef method. This structure contains cached information about the
*     line which improves the efficiency of this method when many repeated
*     calls are made. An error will be reported if the structure does not
*     refer to the Frame specified by "this".
*/


/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */

/* Obtain a pointer to the Region's current Frame and then invoke the
   method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( ((AstRegion *) this_frame)->frameset, AST__CURRENT );
   astLineOffset( fr, line, par, prp, point );
   fr = astAnnul( fr );
}


#if defined(THREAD_SAFE)
static int ManageLock( AstObject *this_object, int mode, int extra,
                       AstObject **fail, int *status ) {
/*
*  Name:
*     ManageLock

*  Purpose:
*     Manage the thread lock on an Object.

*  Type:
*     Private function.

*  Synopsis:
*     #include "object.h"
*     AstObject *ManageLock( AstObject *this, int mode, int extra,
*                            AstObject **fail, int *status )

*  Class Membership:
*     Region member function (over-rides the astManageLock protected
*     method inherited from the parent class).

*  Description:
*     This function manages the thread lock on the supplied Object. The
*     lock can be locked, unlocked or checked by this function as
*     deteremined by parameter "mode". See astLock for details of the way
*     these locks are used.

*  Parameters:
*     this
*        Pointer to the Object.
*     mode
*        An integer flag indicating what the function should do:
*
*        AST__LOCK: Lock the Object for exclusive use by the calling
*        thread. The "extra" value indicates what should be done if the
*        Object is already locked (wait or report an error - see astLock).
*
*        AST__UNLOCK: Unlock the Object for use by other threads.
*
*        AST__CHECKLOCK: Check that the object is locked for use by the
*        calling thread (report an error if not).
*     extra
*        Extra mode-specific information.
*     fail
*        If a non-zero function value is returned, a pointer to the
*        Object that caused the failure is returned at "*fail". This may
*        be "this" or it may be an Object contained within "this". Note,
*        the Object's reference count is not incremented, and so the
*        returned pointer should not be annulled. A NULL pointer is
*        returned if this function returns a value of zero.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*    A local status value:
*        0 - Success
*        1 - Could not lock or unlock the object because it was already
*            locked by another thread.
*        2 - Failed to lock a POSIX mutex
*        3 - Failed to unlock a POSIX mutex
*        4 - Bad "mode" value supplied.

*  Notes:
*     - This function attempts to execute even if an error has already
*     occurred.
*/

/* Local Variables: */
   AstRegion *this;       /* Pointer to Region structure */
   int result;            /* Returned status value */

/* Initialise */
   result = 0;

/* Check the supplied pointer is not NULL. */
   if( !this_object ) return result;

/* Obtain a pointers to the Region structure. */
   this = (AstRegion *) this_object;

/* Invoke the ManageLock method inherited from the parent class. */
   if( !result ) result = (*parent_managelock)( this_object, mode, extra,
                                                fail, status );

/* Invoke the astManageLock method on any Objects contained within
   the supplied Object. */
   if( !result ) result = astManageLock( this->frameset, mode, extra, fail );
   if( !result ) result = astManageLock( this->points, mode, extra, fail );
   if( !result ) result = astManageLock( this->unc, mode, extra, fail );
   if( !result ) result = astManageLock( this->negation, mode, extra, fail );
   if( !result ) result = astManageLock( this->defunc, mode, extra, fail );
   if( !result ) result = astManageLock( this->basemesh, mode, extra, fail );
   if( !result ) result = astManageLock( this->basegrid, mode, extra, fail );

   return result;

}
#endif

static AstRegion *MapRegion( AstRegion *this, AstMapping *map0,
                             AstFrame *frame0, int *status ) {
/*
*+
*  Name:
*     astMapRegion

*  Purpose:
*     Transform a Region into a new Frame using a given Mapping.

*  Type:
*     Protected virtual function.

*  Synopsis:
*     #include "region.h"
*     AstRegion *astMapRegion( AstRegion *this, AstMapping *map,
*                              AstFrame *frame )

*  Class Membership:
*     Region method.

*  Description:
*     This function returns a pointer to a new Region which corresponds to
*     supplied Region in some other specified coordinate system. A
*     Mapping is supplied which transforms positions between the old and new
*     coordinate systems. The new Region may not be of the same class as
*     the original region.

*  Parameters:
*     this
*        Pointer to the Region.
*     map
*        Pointer to a Mapping which transforms positions from the
*        coordinate system represented by the supplied Region to the
*        coordinate system specified by "frame". The supplied Mapping should
*        define both forward and inverse transformations, and these
*        transformations should form a genuine inverse pair. That is,
*        transforming a position using the forward transformation and then
*        using the inverse transformation should produce the original input
*        position. Some Mapping classes (such as PermMap, MathMap, SphMap)
*        can result in Mappings for which this is not true.
*     frame
*        Pointer to a Frame describing the coordinate system in which
*        the new Region is required.

*  Returned Value:
*     astMapRegion()
*        A pointer to a new Region. This Region will represent the area
*        within the coordinate system specified by "frame" which corresponds
*        to the supplied Region.

*  Notes:
*     - This is the protected implementation of this function - it does
*     not simplify the returned Region. The public implementation is
*     astMapRegionID, which simplifies the returned Region.
*     - 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: */
   AstFrame *frame;
   AstFrameSet *fs;
   AstMapping *tmap;
   AstMapping *usemap;
   AstMapping *map;
   AstPointSet *ps1;
   AstPointSet *pst;
   AstPointSet *ps2;
   AstRegion *usethis;
   AstRegion *result;
   double **ptr1;
   double **ptr2;
   int *axflags;
   int *inax;
   int *keep;
   int *outax;
   int i;
   int icurr;
   int j;
   int nax1;
   int nkept;
   int nnew;
   int nold;
   int np;
   int ntotal;
   int ok;

/* Initialise returned value. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Initialise local variables */
   axflags = NULL;

/* If a FrameSet was supplied for the Mapping, use the base->current
   Mapping */
   if( astIsAFrameSet( map0 ) ) {
      map = astGetMapping( (AstFrameSet *) map0, AST__BASE, AST__CURRENT );
   } else {
      map = astClone( map0 );
   }

/* If a FrameSet was supplied for the Frame, use the current Frame. */
   if( astIsAFrameSet( frame0 ) ) {
      frame = astGetFrame( (AstFrameSet *) frame0, AST__CURRENT );
   } else {
      frame = astClone( frame0 );
   }

/* First check the Mapping is suitable. It must defined both a forward
   and an inverse Mapping. */
   if( !astGetTranInverse( map ) ) {
      astError( AST__NODEF, "astMapRegion(%s): The supplied %s does not "
                "define an inverse transformation.", status, astGetClass( this ),
                astGetClass( map ) );
   } else if( !astGetTranForward( map ) ) {
      astError( AST__NODEF, "astMapRegion(%s): The supplied %s does not "
                "define a forward transformation.", status, astGetClass( this ),
                astGetClass( map ) );
   }


/* Get the number of axes in the supplied Region. */
   nold = astGetNaxes( this );

/* Get the number of axes in the returned Region. */
   nnew = astGetNaxes( frame );

/* The forward transformation must not introduce any bad axis values. We
   can only perform this test reliably if the supplied Region has no bad
   axis values. */
   ps1 = this->points;
   if( ps1 ) {
      nax1 = astGetNcoord( ps1 );
      np = astGetNpoint( ps1 );
      ptr1 = astGetPoints( ps1 );
      if( ptr1 ) {

/* Check the axis values defining the Region are good. */
         ok = 1;
         for( i = 0; i < nax1 && ok; i++ ){
            for( j = 0; j < np; j++ ) {
               if( ptr1[ i ][ j ] == AST__BAD ){
                  ok = 0;
                  break;
               }
            }
         }
         if( ok ) {

/* Transform the points defining the supplied Region into the current Frame
   of the Region. */
            pst = astRegTransform( this, ps1, 1, NULL, NULL );

/* The use the supplied Mapping to transfom them into the new Frame. */
            ps2 = astTransform( map, pst, 1, NULL );

/* Test if any of these axis values are bad. */
            ptr2 = astGetPoints( ps2 );
            if( ptr2 ) {
               for( i = 0; i < nnew && ok; i++ ){
                  for( j = 0; j < np; j++ ) {
                     if( ptr2[ i ][ j ] == AST__BAD ){
                        ok = 0;
                        break;
                     }
                  }
               }
               if( !ok ) {
                  astError( AST__NODEF, "astMapRegion(%s): The region which "
                            "results from using the supplied %s to transform "
                            "the supplied %s is undefined.", status, astGetClass( this ),
                            astGetClass( map ), astGetClass( this ) );

/* If all axis values are good, use the inverse transformation of the
   supplied Mapping to transform them back to the Frame of the supplied
   Region. */
               } else {
                  pst = astAnnul( pst );
                  pst = astTransform( map, ps2, 0, NULL );

/* Get a flag for each input of the supplied Mapping (i.e. each axis of
   the supplied Region) which is non-zero if the inverse transformation
   of the Mapping has produced any good axis values. */
                  ptr1 = astGetPoints( pst );
                  axflags = astCalloc( nold, sizeof(int) );
                  if( astOK ) {
                     for( i = 0; i < nold; i++ ){
                        for( j = 0; j < np; j++ ) {
                           if( ptr1[ i ][ j ] != AST__BAD ){
                              axflags[ i ] = 1;
                              break;
                           }
                        }
                     }
                  }
               }
            }
            ps2 = astAnnul( ps2 );
            pst = astAnnul( pst );
         }
      }
   }

/* Assume we will be using the supplied Region (this) and Mapping (map). */
   usethis = astClone( this );
   usemap = astClone( map );

/* If the new Frame for the Region has fewer axes than the old Frame, see
   if we can discard some base-frame axes. We only do this if the inverse
   transformation would otherwise supply bad values for the unused axes.
   Using bad axis values is not a good idea as some operations cannot be
   performed if any bad values are supplied. Also having more axes than
   needed is bad as it results in fewer mesh points per axis. */
   if( nnew < nold ) {

/* First invert the Mapping since astMapSplit only allows selection of
   inputs, and we want to select outputs. */
      astInvert( map );

/* Create an array holding the indices of the required inputs. */
      inax = astMalloc( nnew*sizeof(int) );
      if( astOK ) for( i = 0; i < nnew; i++ ) inax[i] = i;

/* Attempt to split the mapping to extract a new mapping that omits any
   unnecessary outputs (i.e. outputs that are indepenent of the selected
   inputs). Check the Mapping was split successfully. */
      outax = astMapSplit( map, nnew, inax, &tmap );
      if( outax ) {

/* Get the number of old axes that have been retained in the Mapping. */
         nkept = astGetNout( tmap );

/* Now we need to ensure that any unused axes for which the Mapping
   creates non-bad values are retained (such values are significant
   since they may determine whether the new Region is null or not).
   We only need to do this if any of the outputs that were split off
   above have been found to generate good values, as indicated by the
   "axflags" array. Count the number of extra axes that need to be kept,
   over and above those that are kept by the Mapping returned by
   astMapSplit above. */
         ntotal = 0;
         keep = NULL;
         if( axflags ) {
            keep = astMalloc( nold*sizeof(int) );
            if( astOK ) {

/* Loop round each axis in the supplied Region. */
               for( i = 0; i < nold; i++ ) {

/* Search the "outax" array to see if this axis was retained by astMapSplit.
   If it was, append its index to the total list of axes to keep. */
                  ok = 0;
                  for( j = 0; j < nkept; j++ ) {
                     if( outax[ j ] == i ) {
                        keep[ ntotal++ ] = i;
                        ok = 1;
                        break;
                     }
                  }

/* If the axis was not retained by astMapSplit, but generates good axis
   values, also append its index to the total list of axes to keep. */
                  if( !ok && axflags[ i ] ) {
                     keep[ ntotal++ ] = i;
                  }
               }
            }
         }

/* If there are no extra axes to keep, then the Mapping returned by
   astMapSplit above can be used as it is. */
         if( ntotal == nkept ) {

/* The values in the "outax" array will hold the zero-based indices of
   the original old axes that are retained by the new Mapping. We need to
   create a copy of the supplied Region that includes only these axes. */
            usethis = astAnnul( usethis );
            usethis = astPickAxes( this, nkept, outax, NULL );

/* Use the temportary Mapping returned by astMapSplit in place of the
   supplied Mapping (remember to invert to undo the inversion performed
   above). */
            usemap = astAnnul( usemap );
            usemap = astClone( tmap );
            astInvert( usemap );

/* Free temporary resources. */
            tmap = astAnnul( tmap );
            outax = astFree( outax );

/* If we need to retain some extra axes because they generate good values
   (even though they are independent of the new Frame axes)... */
         } else if( ntotal > nkept ){

/* We know the old Frame axes that we want to keep, so use astMapSplit
   in the opposite direction - i.e. use it on the Mapping form old to
   new.  */
            astInvert( map );

            tmap = astAnnul( tmap );
            outax = astFree( outax );

            outax = astMapSplit( map, ntotal, keep, &tmap );
            if( outax ) {
               usethis = astAnnul( usethis );
               usethis = astPickAxes( this, ntotal, keep, NULL );

               usemap = astAnnul( usemap );
               usemap = astClone( tmap );
            }

            astInvert( map );
         }
         keep = astFree( keep );
         outax = astFree( outax );
         tmap = astAnnul( tmap );
      }
      inax = astFree( inax );

/* Invert the Mapping again to bring it back to its original state. */
      astInvert( map );
   }

/* Take a deep copy of the supplied Region. */
   result = astCopy( usethis );

/* Get a pointer to the encapsulated FrameSet. */
   if( astOK ) {
      fs = result->frameset;

/* Add in the new Frame and Mapping. First note the index of the original
   current Frame. */
      icurr = astGetCurrent( fs );
      astAddFrame( fs, AST__CURRENT, usemap, frame );

/* Remove the original current Frame. */
      astRemoveFrame( fs, icurr );

/* The base and current Frames of the resulting FrameSet are now (in
   general) different and so the Region should include its FrameSet in any
   Dump. */
      astSetRegionFS( result, 1 );
   }

/* Since the Mapping has been changed, any cached information calculated
   on the basis of the Mapping properties may no longer be up to date. */
   astResetCache( result );

/* Free resources */
   usemap = astAnnul( usemap );
   usethis = astAnnul( usethis );
   map = astAnnul( map );
   frame = astAnnul( frame );
   axflags = astFree( axflags );

/* If not OK, annul the returned pointer. */
   if( !astOK ) result = astAnnul( result );

/* Return the result. */
   return result;
}

/*
*++
*  Name:
c     astMask<X>
f     AST_MASK<X>

*  Purpose:
*     Mask a region of a data grid.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     int astMask<X>( AstRegion *this, AstMapping *map, int inside, int ndim,
c                     const int lbnd[], const int ubnd[], <Xtype> in[],
c                     <Xtype> val )
f     RESULT = AST_MASK<X>( THIS, MAP, INSIDE, NDIM, LBND, UBND, IN, VAL,
f                           STATUS )

*  Class Membership:
*     Mapping method.

*  Description:
*     This is a set of functions for masking out regions within gridded data
*     (e.g. an image). The functions modifies a given data grid by
*     assigning a specified value to all samples which are inside (or outside
c     if "inside" is zero)
f     if INSIDE is .FALSE.)
*     the specified Region.
*
*     You should use a masking function which matches the numerical
*     type of the data you are processing by replacing <X> in
c     the generic function name astMask<X> by an appropriate 1- or
f     the generic function name AST_MASK<X> by an appropriate 1- or
*     2-character type code. For example, if you are masking data
c     with type "float", you should use the function astMaskF (see
f     with type REAL, you should use the function AST_MASKR (see
*     the "Data Type Codes" section below for the codes appropriate to
*     other numerical types).

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to a Region.
c     map
f     MAP = INTEGER (Given)
*        Pointer to a Mapping. The forward transformation should map
*        positions in the coordinate system of the supplied Region
*        into pixel coordinates as defined by the
c        "lbnd" and "ubnd" parameters. A NULL pointer
f        LBND and UBND arguments. A value of AST__NULL
*        can be supplied if the coordinate system of the supplied Region
*        corresponds to pixel coordinates. This is equivalent to
*        supplying a UnitMap.
*
*        The number of inputs for this Mapping (as given by its Nin attribute)
*        should match the number of axes in the supplied Region (as given
*        by the Naxes attribute of the Region).
*        The number of outputs for the Mapping (as given by its Nout attribute)
*        should match the number of
c        grid dimensions given by the value of "ndim"
f        grid dimensions given by the value of NDIM
*        below.
c     inside
f     INSIDE = INTEGER (Given)
*        A boolean value which indicates which pixel are to be masked. If
c        a non-zero value
f        .TRUE.
*        is supplied, then all grid pixels with centres inside the supplied
*        Region are assigned the value given by
c        "val",
f        VAL,
*        and all other pixels are left unchanged. If
c        zero
f        .FALSE.
*        is supplied, then all grid pixels with centres not inside the supplied
*        Region are assigned the value given by
c        "val",
f        VAL,
*        and all other pixels are left unchanged. Note, the Negated
*        attribute of the Region is used to determine which pixel are
*        inside the Region and which are outside. So the inside of a Region
*        which has not been negated is the same as the outside of the
*        corresponding negated Region.
*
*        For types of Region such as PointList which have zero volume,
*        pixel centres will rarely fall exactly within the Region. For
*        this reason, the inclusion criterion is changed for zero-volume
*        Regions so that pixels are included (or excluded) if any part of
*        the Region passes through the pixel. For a PointList, this means
*        that pixels are included (or excluded) if they contain at least
*        one of the points listed in the PointList.
c     ndim
f     NDIM = INTEGER (Given)
*        The number of dimensions in the input grid. This should be at
*        least one.
c     lbnd
f     LBND( NDIM ) = INTEGER (Given)
c        Pointer to an array of integers, with "ndim" elements,
f        An array
*        containing the coordinates of the centre of the first pixel
*        in the input grid along each dimension.
c     ubnd
f     UBND( NDIM ) = INTEGER (Given)
c        Pointer to an array of integers, with "ndim" elements,
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.
c     in
f     IN( * ) = <Xtype> (Given and Returned)
c        Pointer to an array, with one element for each pixel in the
f        An array, with one element for each pixel in the
*        input grid, containing the data to be masked.  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 astMaskF, the type of each array element
c        should be "float").
f        you are using AST_MASKR, 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 final dimension least rapidly
c        (i.e. Fortran array indexing is used).
f        (i.e. normal Fortran array storage order).
*
*        On exit, the samples specified by
c        "inside" are set to the value of "val".
f        INSIDE are set to the value of VAL.
*        All other samples are left unchanged.
c     val
f     VAL = <Xtype> (Given)
*        This argument should have the same type as the elements of
c        the "in" array. It specifies the value used to flag the
f        the IN array. It specifies the value used to flag the
*        masked data (see
c        "inside").
f        INSIDE).
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astMask<X>()
f     AST_MASK<X> = INTEGER
*        The number of pixels to which a value of
c        "badval"
f        BADVAL
*        has been assigned.

*  Notes:
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*     - An error will be reported if the overlap of the Region and
*     the array cannot be determined.

*  Data Type Codes:
*     To select the appropriate masking function, you should
c     replace <X> in the generic function name astMask<X> with a
f     replace <X> in the generic function name AST_MASK<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, astMaskD would be used to process "double"
c     data, while astMaskS would be used to process "short int"
c     data, etc.
f     For example, AST_MASKD would be used to process DOUBLE
f     PRECISION data, while AST_MASKS 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. */
#define MAKE_MASK(X,Xtype) \
static int Mask##X( AstRegion *this, AstMapping *map, int inside, int ndim, \
                    const int lbnd[], const int ubnd[], \
                    Xtype in[], Xtype val, int *status ) { \
\
/* Local Variables: */ \
   AstFrame *grid_frame;         /* Pointer to Frame describing grid coords */ \
   AstRegion *used_region;       /* Pointer to Region to be used by astResample */ \
   Xtype *c;                     /* Pointer to next array element */ \
   Xtype *d;                     /* Pointer to next array element */ \
   Xtype *out;                   /* Pointer to the array used for resample output */ \
   Xtype *tmp_out;               /* Pointer to temporary output array */ \
   double *lbndgd;               /* Pointer to array holding lower grid bounds */ \
   double *ubndgd;               /* Pointer to array holding upper grid bounds */ \
   int *lbndg;                   /* Pointer to array holding lower grid bounds */ \
   int *ubndg;                   /* Pointer to array holding upper grid bounds */ \
   int idim;                     /* Loop counter for coordinate dimensions */ \
   int ipix;                     /* Loop counter for pixel index */ \
   int nax;                      /* Number of Region axes */ \
   int nin;                      /* Number of Mapping input coordinates */ \
   int nout;                     /* Number of Mapping output coordinates */ \
   int npix;                     /* Number of pixels in supplied array */ \
   int npixg;                    /* Number of pixels in bounding box */ \
   int result;                   /* Result value to return */ \
\
/* Initialise. */ \
   result = 0; \
\
/* Check the global error status. */ \
   if ( !astOK ) return result; \
\
/* Obtain value for the Naxes attribute of the Region. */ \
   nax = astGetNaxes( this ); \
\
/* If supplied, obtain values for the Nin and Nout attributes of the Mapping. */ \
   if( map ) { \
      nin = astGetNin( map ); \
      nout = astGetNout( map ); \
\
/* If OK, check that the number of mapping inputs matches the \
   number of axes in the Region. Report an error if necessary. */ \
      if ( astOK && ( nax != nin ) ) { \
         astError( AST__NGDIN, "astMask"#X"(%s): Bad number of mapping " \
                   "inputs (%d).", status, astGetClass( this ), nin ); \
         astError( AST__NGDIN, "The %s given requires %d coordinate value%s " \
                   "to specify a position.", status, \
                   astGetClass( this ), nax, ( nax == 1 ) ? "" : "s" ); \
      } \
\
/* If OK, check that the number of mapping outputs matches the \
   number of grid dimensions. Report an error if necessary. */ \
      if ( astOK && ( ndim != nout ) ) { \
         astError( AST__NGDIN, "astMask"#X"(%s): Bad number of mapping " \
                   "outputs (%d).", status, astGetClass( this ), nout ); \
         astError( AST__NGDIN, "The pixel grid requires %d coordinate value%s " \
                   "to specify a position.", status, \
                   ndim, ( ndim == 1 ) ? "" : "s" ); \
      } \
\
/* Create a new Region by mapping the supplied Region with the supplied \
   Mapping. The resulting Region represents a region in grid coordinates. */ \
      grid_frame = astFrame( ndim, "Domain=grid", status ); \
      used_region = astMapRegion( this, map, grid_frame ); \
      grid_frame = astAnnul( grid_frame ); \
\
/* If no Mapping was supplied check that the number of grid dimensions \
   matches the number of axes in the Region.*/ \
   } else if ( astOK && ( ( ndim != nax ) || ( ndim < 1 ) ) ) { \
      used_region = NULL; \
      astError( AST__NGDIN, "astMask"#X"(%s): Bad number of input grid " \
                "dimensions (%d).", status, astGetClass( this ), ndim ); \
      if ( ndim != nax ) { \
         astError( AST__NGDIN, "The %s given requires %d coordinate value%s " \
                   "to specify an input position.", status, \
                   astGetClass( this ), nax, ( nax == 1 ) ? "" : "s" ); \
      } \
\
/* If no Mapping was supplied and the parameters look OK, clone the \
   supplied Region pointer for use later on. */ \
   } else { \
      used_region = astClone( this ); \
   } \
\
/* Check that the lower and upper bounds of the input grid are \
   consistent. Report an error if any pair is not. */ \
   if ( astOK ) { \
      for ( idim = 0; idim < ndim; idim++ ) { \
         if ( lbnd[ idim ] > ubnd[ idim ] ) { \
            astError( AST__GBDIN, "astMask"#X"(%s): Lower bound of " \
                      "input grid (%d) exceeds corresponding upper bound " \
                      "(%d).", status, astGetClass( this ), \
                      lbnd[ idim ], ubnd[ idim ] ); \
            astError( AST__GBDIN, "Error in input dimension %d.", status, \
                      idim + 1 ); \
            break; \
         } \
      } \
   } \
\
/* Allocate memory, and then get the bounding box of this new Region in its \
   current Frame (grid coordinates). This bounding box assumes the region \
   has not been negated. */ \
   lbndg = astMalloc( sizeof( int )*(size_t) ndim ); \
   ubndg = astMalloc( sizeof( int )*(size_t) ndim ); \
   lbndgd = astMalloc( sizeof( double )*(size_t) ndim ); \
   ubndgd = astMalloc( sizeof( double )*(size_t) ndim ); \
   if( astOK ) { \
      astGetRegionBounds( used_region, lbndgd, ubndgd ); \
\
/* We convert the floating point bounds to integer pixel bounds, and at \
   the same time expand the box by 2 pixels at each edge to ensure that \
   rounding errors etc do not cause any of the Region to fall outside (or \
   on) the box. Do not let the expanded box extend outside the supplied \
   array bounds. Also note the total number of pixels in the supplied \
   array, and in the bounding box. */ \
      npix = 1; \
      npixg = 1; \
      for ( idim = 0; idim < ndim; idim++ ) { \
         if( lbndgd[ idim ] != AST__BAD && ubndgd[ idim ] != AST__BAD ) { \
            lbndg[ idim ] = astMAX( lbnd[ idim ], (int)( lbndgd[ idim ] + 0.5 ) - 2 ); \
            ubndg[ idim ] = astMIN( ubnd[ idim ], (int)( ubndgd[ idim ] + 0.5 ) + 2 ); \
         } else { \
            lbndg[ idim ] = lbnd[ idim ]; \
            ubndg[ idim ] = ubnd[ idim ]; \
         } \
         npix *= ( ubnd[ idim ] - lbnd[ idim ] + 1 ); \
         if( npixg >= 0 ) npixg *= ( ubndg[ idim ] - lbndg[ idim ] + 1 ); \
      } \
\
/* If the bounding box is null, fill the mask with the supplied value if \
   we assigning the value to the outside of the region (do the opposite if \
   the Region has been negated). */ \
      if( npixg <= 0 && astOK ) { \
         if( ( inside != 0 ) == ( astGetNegated( used_region ) != 0 ) ) { \
            c = in; \
            for( ipix = 0; ipix < npix; ipix++ ) *(c++) = val; \
            result = npix; \
         } \
\
/* If the bounding box is null, return without action. */ \
      } else if( npixg > 0 && astOK ) { \
\
/* All points outside this box are either all inside, or all outside, the \
   Region. So we can speed up processing by setting all the points which are \
   outside the box to the supplied data value (if required). This is \
   faster than checking each point individually using the Transform method \
   of the Region. We do this by supplying an alternative output array to \
   the resampling function below, which has been pre-filled with "val" at \
   every pixel. */ \
         if( ( inside != 0 ) == ( astGetNegated( used_region ) != 0 ) ) { \
\
/* Allocate memory for the alternative output array, and fill it with \
   "val". */ \
            tmp_out = astMalloc( sizeof( Xtype )*(size_t) npix ); \
            if( tmp_out ) { \
               c = tmp_out; \
               for( ipix = 0; ipix < npix; ipix++ ) *(c++) = val; \
               result = npix - npixg; \
            } \
\
/* Indicate that we will use this temporary array rather than the \
   supplied array. */ \
            out = tmp_out; \
\
/* If the outside of the grid box is outside the region of interest it \
   will be unchanged in the resturned array. Therefore we can use the \
   supplied array as the output array below. */ \
         } else { \
            tmp_out = NULL; \
            out = in; \
         } \
\
/* Temporarily invert the Region if required. The Region Transform methods \
   leave interior points unchanged and assign AST__BAD to exterior points. \
   This is the opposite of what we want (which is to leave exterior \
   points unchanged and assign VAL to interior points), so we negate the \
   region if the inside is to be assigned the value VAL.*/ \
         if( inside ) astNegate( used_region ); \
\
/* Invoke astResample to mask just the region inside the bounding box found \
   above (specified by lbndg and ubndg), since all the points outside this \
   box will already contain their required value. */ \
         result += astResample##X( used_region, ndim, lbnd, ubnd, in, NULL, AST__NEAREST, \
                                   NULL, NULL, 0, 0.0, 100, val, ndim, \
                                   lbnd, ubnd, lbndg, ubndg, out, NULL ); \
\
/* Revert to the original setting of the Negated attribute. */ \
         if( inside ) astNegate( used_region ); \
\
/* If required, copy the output data from the temporary output array to \
   the supplied array, and then free the temporary output array. */ \
         if( tmp_out ) { \
            c = tmp_out; \
            d = in; \
            for( ipix = 0; ipix < npix; ipix++ ) *(d++) = *(c++); \
            tmp_out = astFree( tmp_out ); \
         }\
      }\
   } \
\
/* Free resources */ \
   ubndg = astFree( ubndg ); \
   lbndg = astFree( lbndg ); \
   ubndgd = astFree( ubndgd ); \
   lbndgd = astFree( lbndgd ); \
   used_region = astAnnul( used_region ); \
\
/* If an error occurred, clear the returned result. */ \
   if ( !astOK ) result = 0; \
\
/* 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_MASK(LD,long double)
#endif
MAKE_MASK(D,double)
MAKE_MASK(L,long int)
MAKE_MASK(UL,unsigned long int)
MAKE_MASK(I,int)
MAKE_MASK(UI,unsigned int)
MAKE_MASK(S,short int)
MAKE_MASK(US,unsigned short int)
MAKE_MASK(B,signed char)
MAKE_MASK(UB,unsigned char)
MAKE_MASK(F,float)

/* Undefine the macro. */
#undef MAKE_MASK



static int Match( AstFrame *this_frame, AstFrame *target, int matchsub,
                  int **template_axes, int **target_axes,
                  AstMapping **map, AstFrame **result, int *status ) {
/*
*  Name:
*     Match

*  Purpose:
*     Determine if conversion is possible between two coordinate systems.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int Match( AstFrame *template, AstFrame *target, int matchsub,
*                int **template_axes, int **target_axes,
*                AstMapping **map, AstFrame **result, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astMatch
*     method inherited from the Frame class).

*  Description:
*     This function matches the current Frame of a "template" Region
*     to a "target" frame and determines whether it is possible to
*     convert coordinates between them.  If it is, a Mapping that
*     performs the transformation is returned along with a new Frame
*     that describes the coordinate system that results when this
*     Mapping is applied to the current Frame of the target
*     Region. In addition, information is returned to allow the axes
*     in this "result" Frame to be associated with the corresponding
*     axes in the target and template Frames from which they are
*     derived.

*  Parameters:
*     template
*        Pointer to the template Region, whose current Frame
*        describes the coordinate system (or set of possible
*        coordinate systems) into which we wish to convert our
*        coordinates.
*     target
*        Pointer to the target Frame. This describes the coordinate
*        system in which we already have coordinates.
*     matchsub
*        If zero then a match only occurs if the template is of the same
*        class as the target, or of a more specialised class. If non-zero
*        then a match can occur even if this is not the case.
*     template_axes
*        Address of a location where a pointer to int will be returned
*        if the requested coordinate conversion is possible. This
*        pointer will point at a dynamically allocated array of
*        integers with one element for each axis of the "result" Frame
*        (see below). It must be freed by the caller (using astFree)
*        when no longer required.
*
*        For each axis in the result Frame, the corresponding element
*        of this array will return the index of the axis in the
*        template Region's current Frame from which it is
*        derived. If it is not derived from any template Region
*        axis, a value of -1 will be returned instead.
*     target_axes
*        Address of a location where a pointer to int will be returned
*        if the requested coordinate conversion is possible. This
*        pointer will point at a dynamically allocated array of
*        integers with one element for each axis of the "result" Frame
*        (see below). It must be freed by the caller (using astFree)
*        when no longer required.
*
*        For each axis in the result Frame, the corresponding element
*        of this array will return the index of the target Frame axis
*        from which it is derived. If it is not derived from any
*        target Frame axis, a value of -1 will be returned instead.
*     map
*        Address of a location where a pointer to a new Mapping will
*        be returned if the requested coordinate conversion is
*        possible. If returned, the forward transformation of this
*        Mapping may be used to convert coordinates between the target
*        Frame and the result Frame (see below) and the inverse
*        transformation will convert in the opposite direction.
*     result
*        Address of a location where a pointer to a new Frame will be
*        returned if the requested coordinate conversion is
*        possible. If returned, this Frame describes the coordinate
*        system that results from applying the returned Mapping
*        (above) to the "target" coordinate system. In general, this
*        Frame will combine attributes from (and will therefore be
*        more specific than) both the target Frame and the current
*        Frame of the template Region. In particular, when the
*        template allows the possibility of transformaing to any one
*        of a set of alternative coordinate systems, the "result"
*        Frame will indicate which of the alternatives was used.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A non-zero value is returned if the requested coordinate
*     conversion is possible. Otherwise zero is returned (this will
*     not in itself result in an error condition).

*  Notes:
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to Region's current Frame */
   int match;                    /* Result to be returned */

/* Initialise the returned values. */
   *template_axes = NULL;
   *target_axes = NULL;
   *map = NULL;
   *result = NULL;
   match = 0;

/* Check the global error status. */
   if ( !astOK ) return match;

/* Invoke the parent astMatch method on the current Frame within the
   encapsulated FrameSet within the Region. */
   fr = astGetFrame( ((AstRegion *) this_frame)->frameset, AST__CURRENT );
   match = astMatch( fr, target, matchsub, template_axes, target_axes, map, result );
   fr = astAnnul( fr );

/* Return the result. */
   return match;
}

static void MatchAxes( AstFrame *frm1_frame, AstFrame *frm2, int *axes,
                       int *status ) {
/*
*  Name:
*     MatchAxes

*  Purpose:
*     Find any corresponding axes in two Frames.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void MatchAxes( AstFrame *frm1, AstFrame *frm2, int *axes )
*                     int *status )

*  Class Membership:
*     Region member function (over-rides the protected astMatchAxes
*     method inherited from the Frame class).

*  Description:
*     This function looks for corresponding axes within two supplied
*     Frames. An array of integers is returned that contains an element
*     for each axis in the second supplied Frame. An element in this array
*     will be set to zero if the associated axis within the second Frame
*     has no corresponding axis within the first Frame. Otherwise, it
*     will be set to the index (a non-zero positive integer) of the
*     corresponding axis within the first supplied Frame.

*  Parameters:
*     frm1
*        Pointer to the first Frame.
*     frm2
*        Pointer to the second Frame.
*     axes
*        Pointer to an
*        integer array in which to return the indices of the axes (within
*        the second Frame) that correspond to each axis within the first
*        Frame. Axis indices start at 1. A value of zero will be stored
*        in the returned array for each axis in the first Frame that has
*        no corresponding axis in the second Frame.
*
*        The number of elements in this array must be greater than or
*        equal to the number of axes in the first Frame.
*     status
*        Pointer to inherited status value.

*  Notes:
*     -  Corresponding axes are identified by the fact that a Mapping
*     can be found between them using astFindFrame or astConvert. Thus,
*     "corresponding axes" are not necessarily identical. For instance,
*     SkyFrame axes in two Frames will match even if they describe
*     different celestial coordinate systems
*/

/* Local Variables: */
   AstFrame *frm1;               /* Pointer to Region's current Frame */

/* Check the global error status. */
   if ( !astOK ) return;

/* Invoke the astMatchAxesX method on frm2, passing it the current Frame
   within the encapsulated FrameSet within the Region as "frm1". */
   frm1 = astGetFrame( ((AstRegion *) frm1_frame)->frameset, AST__CURRENT );
   astMatchAxesX( frm2, frm1, axes );
   frm1 = astAnnul( frm1 );
}

static void MatchAxesX( AstFrame *frm2_frame, AstFrame *frm1, int *axes,
                        int *status ) {
/*
*  Name:
*     MatchAxesX

*  Purpose:
*     Find any corresponding axes in two Frames.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void MatchAxesX( AstFrame *frm2, AstFrame *frm1, int *axes )
*                      int *status )

*  Class Membership:
*     Region member function (over-rides the protected astMatchAxesX
*     method inherited from the Frame class).

*     This function looks for corresponding axes within two supplied
*     Frames. An array of integers is returned that contains an element
*     for each axis in the second supplied Frame. An element in this array
*     will be set to zero if the associated axis within the second Frame
*     has no corresponding axis within the first Frame. Otherwise, it
*     will be set to the index (a non-zero positive integer) of the
*     corresponding axis within the first supplied Frame.

*  Parameters:
*     frm2
*        Pointer to the second Frame.
*     frm1
*        Pointer to the first Frame.
*     axes
*        Pointer to an integer array in which to return the indices of
*        the axes (within the first Frame) that correspond to each axis
*        within the second Frame. Axis indices start at 1. A value of zero
*        will be stored in the returned array for each axis in the second
*        Frame that has no corresponding axis in the first Frame.
*
*        The number of elements in this array must be greater than or
*        equal to the number of axes in the second Frame.
*     status
*        Pointer to inherited status value.

*  Notes:
*     -  Corresponding axes are identified by the fact that a Mapping
*     can be found between them using astFindFrame or astConvert. Thus,
*     "corresponding axes" are not necessarily identical. For instance,
*     SkyFrame axes in two Frames will match even if they describe
*     different celestial coordinate systems
*/

/* Local Variables: */
   AstFrame *frm2;

/* Check the global error status. */
   if ( !astOK ) return;

/* Get a pointer to the current Frame in the FrameSet. */
   frm2 = astGetFrame( ((AstRegion *) frm2_frame)->frameset, AST__CURRENT );

/* Invoke the astMatchAxesX on the current Frame. */
   astMatchAxesX( frm2, frm1, axes );

/* Free resources */
   frm2 = astAnnul( frm2 );
}

static void Negate( AstRegion *this, int *status ) {
/*
*++
*  Name:
c     astNegate
f     AST_NEGATE

*  Purpose:
*     Negate the area represented by a Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     void astNegate( AstRegion *this )
f     CALL AST_NEGATE( THIS, STATUS )

*  Class Membership:
*     Region method.

*  Description:
*     This function negates the area represented by a Region. That is,
*     points which were previously inside the region will then be
*     outside, and points which were outside will be inside. This is
*     acomplished by toggling the state of the Negated attribute for
*     the supplied region.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*--
*/

/* Check the global error status. */
   if ( !astOK ) return;

/* Toggle the Negated attribute. */
   astSetNegated( this, astGetNegated( this ) ? 0 : 1 );

}

static void Norm( AstFrame *this_frame, double value[], int *status ) {
/*
*  Name:
*     Norm

*  Purpose:
*     Normalise a set of Region coordinates.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void Norm( AstAxis *this, double value[], int *status )

*  Class Membership:
*     Region member function (over-rides the astNorm method
*     inherited from the Frame class).

*  Description:
*     This function converts a set of coordinate values for the
*     current Frame of a Region, which might potentially be
*     unsuitable for display to a user (for instance, may lie outside
*     the expected range of values) into a set of acceptable
*     alternative values suitable for display.
*
*     Typically, for Frames whose axes represent cyclic values (such
*     as angles or positions on the sky), this function wraps an
*     arbitrary set of coordinates, so that they lie within the first
*     cycle (say zero to 2*pi or -pi/2 to +pi/2). For Frames with
*     ordinary linear axes, without constraints, this function will
*     typically return the original coordinate values unchanged.

*  Parameters:
*     this
*        Pointer to the Region.
*     value
*        An array of double, with one element for each Region axis.
*        This should contain the initial set of coordinate values,
*        which will be modified in place.
*     status
*        Pointer to the inherited status variable.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to the current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astNorm method to obtain the new values. Annul the Frame
   pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astNorm( fr, value );
   fr = astAnnul( fr );
}

static void NormBox( AstFrame *this_frame, double lbnd[], double ubnd[],
                     AstMapping *reg, int *status ) {
/*
*  Name:
*     NormBox

*  Purpose:
*     Extend a box to include effect of any singularities in the Frame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void astNormBox( AstFrame *this, double lbnd[], double ubnd[],
*                      AstMapping *reg, int *status )

*  Class Membership:
*     Region member function (over-rides the astNormBox method inherited
*     from the Frame class).

*  Description:
*     This function modifies a supplied box to include the effect of any
*     singularities in the co-ordinate system represented by the Frame.
*     For a normal Cartesian coordinate system, the box will be returned
*     unchanged. Other classes of Frame may do other things. For instance,
*     a SkyFrame will check to see if the box contains either the north
*     or south pole and extend the box appropriately.

*  Parameters:
*     this
*        Pointer to the Frame.
*     lbnd
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). Initially, this should contain a set of
*        lower axis bounds for the box. They will be modified on exit
*        to include the effect of any singularities within the box.
*     ubnd
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). Initially, this should contain a set of
*        upper axis bounds for the box. They will be modified on exit
*        to include the effect of any singularities within the box.
*     reg
*        A Mapping which should be used to test if any singular points are
*        inside or outside the box. The Mapping should leave an input
*        position unchanged if the point is inside the box, and should
*        set all bad if the point is outside the box.
*     status
*        Pointer to the inherited status variable.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to the current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astNormBox method to obtain the new values. Annul the Frame
   pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astNormBox( fr, lbnd, ubnd, reg );
   fr = astAnnul( fr );
}

static void Offset( AstFrame *this_frame, const double point1[],
                    const double point2[], double offset, double point3[], int *status ) {
/*
*  Name:
*     Offset

*  Purpose:
*     Calculate an offset along a geodesic curve.

*  Type:
*     Public virtual function.

*  Synopsis:
*     #include "region.h"
*     void Offset( AstFrame *this,
*                  const double point1[], const double point2[],
*                  double offset, double point3[], int *status )

*  Class Membership:
*     Region member function (over-rides the protected astOffset
*     method inherited from the Frame class).

*  Description:
*     This function finds the Region coordinate values of a point
*     which is offset a specified distance along the geodesic curve
*     between two other points.

*  Parameters:
*     this
*        Pointer to the Region.
*     point1
*        An array of double, with one element for each Region axis.
*        This should contain the coordinates of the point marking the
*        start of the geodesic curve.
*     point2
*        An array of double, with one element for each Region axis
*        This should contain the coordinates of the point marking the
*        end of the geodesic curve.
*     offset
*        The required offset from the first point along the geodesic
*        curve. If this is positive, it will be towards the second
*        point. If it is negative, it will be in the opposite
*        direction. This offset need not imply a position lying
*        between the two points given, as the curve will be
*        extrapolated if necessary.
*     point3
*        An array of double, with one element for each Region axis
*        in which the coordinates of the required point will be
*        returned.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - The geodesic curve used by this function is the path of
*     shortest distance between two points, as defined by the
*     astDistance function.
*     - This function will return "bad" coordinate values (AST__BAD)
*     if any of the input coordinates has this value.
*     - "Bad" coordinate values will also be returned if the two
*     points supplied are coincident (or otherwise fail to uniquely
*     specify a geodesic curve) but the requested offset is non-zero.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astOffset method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astOffset( fr, point1, point2, offset, point3 );
   fr = astAnnul( fr );
}

static double Offset2( AstFrame *this_frame, const double point1[2],
                       double angle, double offset, double point2[2], int *status ){
/*
*  Name:
*     Offset2

*  Purpose:
*     Calculate an offset along a geodesic curve in a 2D Frame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     double Offset2( AstFrame *this, const double point1[2], double angle,
*                     double offset, double point2[2], int *status );

*  Class Membership:
*     Region member function (over-rides the protected astOffset2
*     method inherited from the Frame class).

*  Description:
*     This function finds the Frame coordinate values of a point which
*     is offset a specified distance along the geodesic curve at a
*     given angle from a specified starting point. It can only be
*     used with 2-dimensional Frames.
*
*     For example, in a basic Frame, this offset will be along the
*     straight line joining two points. For a more specialised Frame
*     describing a sky coordinate system, however, it would be along
*     the great circle passing through two sky positions.

*  Parameters:
*     this
*        Pointer to the Frame.
*     point1
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). This should contain the coordinates of the
*        point marking the start of the geodesic curve.
*     angle
*        The angle (in radians) from the positive direction of the second
*        axis, to the direction of the required position, as seen from
*        the starting position. Positive rotation is in the sense of
*        rotation from the positive direction of axis 2 to the positive
*        direction of axis 1.
*     offset
*        The required offset from the first point along the geodesic
*        curve. If this is positive, it will be in the direction of the
*        given angle. If it is negative, it will be in the opposite
*        direction.
*     point2
*        An array of double, with one element for each Frame axis
*        in which the coordinates of the required point will be returned.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The direction of the geodesic curve at the end point. That is, the
*     angle (in radians) between the positive direction of the second
*     axis and the continuation of the geodesic curve at the requested
*     end point. Positive rotation is in the sense of rotation from
*     the positive direction of axis 2 to the positive direction of axis 1.

*  Notes:
*     - The geodesic curve used by this function is the path of
*     shortest distance between two points, as defined by the
*     astDistance function.
*     - An error will be reported if the Frame is not 2-dimensional.
*     - This function will return "bad" coordinate values (AST__BAD)
*     if any of the input coordinates has this value.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double result;                /* Value to return */

/* Check the global error status. */
   if ( !astOK ) return AST__BAD;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astOffset2 method for this Frame. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astOffset2( fr, point1, angle, offset, point2 );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = AST__BAD;

/* Return the result. */
   return result;
}

static int Overlap( AstRegion *this, AstRegion *that, int *status ){
/*
*++
*  Name:
c     astOverlap
f     AST_OVERLAP

*  Purpose:
*     Test if two regions overlap each other.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     int astOverlap( AstRegion *this, AstRegion *that )
f     RESULT = AST_OVERLAP( THIS, THAT, STATUS )

*  Class Membership:
*     Region method.

*  Description:
*     This function returns an integer value indicating if the two
*     supplied Regions overlap. The two Regions are converted to a commnon
*     coordinate system before performing the check. If this conversion is
*     not possible (for instance because the two Regions represent areas in
*     different domains), then the check cannot be performed and a zero value
*     is returned to indicate this.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the first Region.
c     that
f     THAT = INTEGER (Given)
*        Pointer to the second Region.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astOverlap()
f     AST_OVERLAP = INTEGER
*        A value indicating if there is any overlap between the two Regions.
*        Possible values are:
*
*        0 - The check could not be performed because the second Region
*            could not be mapped into the coordinate system of the first
*            Region.
*
*        1 - There is no overlap between the two Regions.
*
*        2 - The first Region is completely inside the second Region.
*
*        3 - The second Region is completely inside the first Region.
*
*        4 - There is partial overlap between the two Regions.
*
*        5 - The Regions are identical to within their uncertainties.
*
*        6 - The second Region is the exact negation of the first Region
*            to within their uncertainties.

*  Notes:
*     - The returned values 5 and 6 do not check the value of the Closed
*     attribute in the two Regions.
*     - A value of zero will be returned if this function is invoked with the
*     AST error status set, or if it should fail for any reason.
*--

* Implementation Notes:
*    This function is simply a wrap-up for the protected astOverlapX
*    method which performs the required processing but swaps the order
*    of the two arguments. This is a trick to allow the astOverlap method
*    to be over-ridden by derived classes on the basis of the class of either
*    of the two arguments.
*/

/* Check the global error status. */
   if ( !astOK ) return 0;

/* Invoke the "astOverlapX" method with the two arguments swapped. */
   return astOverlapX( that, this );
}

static int OverlapX( AstRegion *that, AstRegion *this, int *status ){
/*
*+
*  Name:
*     astOverlapX

*  Purpose:
*     Test if two regions overlap each other.

*  Type:
*     Protected virtual function.

*  Synopsis:
*     #include "region.h"
*     int astOverlapX( AstRegion *that, AstRegion *this )

*  Class Membership:
*     Region method.

*  Description:
*     This function performs the processing for the public astOverlap
*     method and has exactly the same interface except that the order
*     of the two arguments is swapped. This is a trick to allow
*     the astOverlap method to be over-ridden by derived classes on
*     the basis of the class of either of its two arguments.
*
*     See the astOverlap method for details of the interface.
*-
*/

/* Local Variables: */
   AstFrame *bfrm_reg1;           /* Pointer to base Frame in "reg1" Frame */
   AstFrame *frm_reg1;            /* Pointer to current Frame in "reg1" Frame */
   AstFrameSet *fs0;              /* FrameSet connecting Region Frames */
   AstFrameSet *fs;               /* FrameSet connecting Region Frames */
   AstMapping *cmap;              /* Mapping connecting Region Frames */
   AstMapping *map;               /* Mapping form "reg2" current to "reg1" base */
   AstMapping *map_reg1;          /* Pointer to current->base Mapping in "reg1" */
   AstPointSet *ps1;              /* Mesh covering second Region */
   AstPointSet *ps2;              /* Mesh covering second Region */
   AstPointSet *ps3;              /* Mesh covering first Region */
   AstPointSet *ps4;              /* Mesh covering first Region */
   AstPointSet *ps5;              /* Another PointSet */
   AstPointSet *reg1_mesh;        /* Mesh covering first Region */
   AstPointSet *reg2_mesh;        /* Mesh covering second Region */
   AstPointSet *reg2_submesh;     /* Second Region mesh minus boundary points */
   AstRegion *reg1;               /* Region to use as the first Region */
   AstRegion *reg2;               /* Region to use as the second Region */
   AstRegion *unc1;               /* "unc" mapped into Frame of first Region */
   AstRegion *unc;                /* Uncertainty in second Region */
   double **ptr1;                 /* Pointer to mesh axis values */
   double **ptr;                  /* Pointer to pointset data */
   double *p;                     /* Pointer to next axis value */
   double axsum;                  /* Sum of axis values */
   int *mask;                     /* Mask identifying common boundary points */
   int allbad;                    /* Were all axis values bad? */
   int allgood;                   /* Were all axis values good? */
   int bnd1;                      /* Does reg1 have a finite boundary */
   int bnd2;                      /* Does reg2 have a finite boundary */
   int bnd_that;                  /* Does "that" have a finite boundary */
   int bnd_this;                  /* Does "this" have a finite boundary */
   int case1;                     /* First region inside second region? */
   int first;                     /* First pass? */
   int good;                      /* Any good axis values found? */
   int i;                         /* Mesh axis index */
   int iax;                       /* Axis index */
   int inv0;                      /* Original FrameSet Invert flag */
   int inside1;                   /* The position is inside reg1? */
   int inside2;                   /* The position is inside reg2? */
   int ip;                        /* Index of point */
   int j;                         /* Mesh point index */
   int nc;                        /* Number of axis values per point */
   int np;                        /* Number of points in mesh */
   int reg1_neg;                  /* Was "reg1" negated to make it bounded? */
   int reg2_neg;                  /* Was "reg2" negated to make it bounded? */
   int result;                    /* Value to return */
   int that_neg;                  /* Was "that" negated to make it bounded? */
   int this_neg;                  /* Was "this" negated to make it bounded? */
   int touch;                     /* Do the Regions touch? */

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Return 5 if the two Regions are equal using the astEqual method. */
   if( astEqual( this, that ) ) {
      return 5;

/* Return 6 if the two Regions are equal using the Equal method after
   temporarily negating the first. */
   } else {
      astNegate( this );
      result = astEqual( this, that );
      astNegate( this );
      if( result ) return 6;
   }

/* Get a FrameSet which connects the Frame represented by the second Region
   to the Frame represented by the first Region. Check that the conection is
   defined. */
   fs0 = astConvert( that, this, "" );
   if( !fs0 ) return 0;
   inv0 = astGetInvert( fs0 );

/* The rest of this function tests for overlap by representing one of the
   Regions as a mesh of points along its boundary, and then checking to see
   if any of the points in this mesh fall inside or outside the other Region.
   This can only be done if the Region has a boundary of finite length (e.g.
   Circles, Boxes, etc). Other Regions (e.g. some Intervals) do not have
   finite boundaries and consequently report an error if an attempt is made
   to represent them using a boundary mesh. We now therefore check to see if
   either of the two Regions has a finite boundary length. This will be the
   case if the region is bounded, or if it can be made bounded simply by
   negating it. If a Region is unbounded regardless of the setting of its
   Negated flag, then it does not have a finite boundary. We leave the
   Negated attributes (temporaily) set to the values that cause the
   Regions to be bounded. Set flags to indicate if the Regions have been
   negated. */
   bnd_this = astGetBounded( this );
   if( !bnd_this ) {
      astNegate( this );
      bnd_this = astGetBounded( this );
      if( ! bnd_this ) {
         astNegate( this );
         this_neg = 0;
      } else {
         this_neg = 1;
      }
   } else {
      this_neg = 0;
   }

   bnd_that = astGetBounded( that );
   if( !bnd_that ) {
      astNegate( that );
      bnd_that = astGetBounded( that );
      if( ! bnd_that ) {
         astNegate( that );
         that_neg = 0;
      } else {
         that_neg = 1;
      }
   } else {
      that_neg = 0;
   }

/* If neither Regions has a finite boundary, then we cannot currently
   determine any overlap, so report an error. Given more time, it
   is probably possible to think of some way of determining overlap
   between two unbounded Regions, but it will probably not be a common
   requirement and so is currently put off to a rainy day. */
   if( !bnd_this && !bnd_that && astOK ) {
      astError( AST__INTER, "astOverlap(Region): Neither of the two "
                "supplied Regions (classes %s and %s) has a finite "
                "boundary.", status, astGetClass(this), astGetClass(that) );
      astError( AST__INTER, "The current implementation of astOverlap "
                "cannot determine the overlap between two Regions "
                "unless at least one of them has a finite boundary." , status);
   }

/* If only one of the two Regions has a finite boundary, we must use its
   mesh first. Choose the finite boundary Region as the "second" region.
   Also store a flag indicating if the first Region has a finite boundary. */
   if( bnd_that ) {
      reg1 = this;
      reg2 = that;
      bnd1 = bnd_this;
      bnd2 = bnd_that;
      reg1_neg = this_neg;
      reg2_neg = that_neg;
   } else {
      reg1 = that;
      reg2 = this;
      bnd1 = bnd_that;
      bnd2 = bnd_this;
      reg1_neg = that_neg;
      reg2_neg = this_neg;
   }

/* We may need to try again with the above selections swapped. We only do
   this once though. Set a flag to indicate that we are about to start the
   first pass. */
   first = 1;
L1:

/* Get a FrameSet which connects the Frame represented by the second Region
   to the Frame represented by the first Region. Check that the conection is
   defined. */
   fs = astClone( fs0 );
   astSetInvert( fs, (reg2 == that ) ? inv0 : 1 - inv0 );
   if( fs ) {

/* Get a pointer to the Frame represented by the first Region. */
      frm_reg1 = astGetFrame( reg1->frameset, AST__CURRENT );

/* Get a pointer to the Mapping from current to base Frame in the first
   Region. */
      map_reg1 = astGetMapping( reg1->frameset, AST__CURRENT, AST__BASE );

/* Get the Mapping from the current Frame of the second Region to the
   current Frame of the first Region. */
      cmap = astGetMapping( fs, AST__BASE, AST__CURRENT );

/* Combine these Mappings to get the Mapping from current Frame of the
   second region to the base Frame of the first Region. */
      map = (AstMapping *) astCmpMap( cmap, map_reg1, 1, "", status );

/* Get a mesh of points covering the second Region. These points are
   within the current Frame of the second Region. */
      reg2_mesh = astRegMesh( reg2 );

/* Transform this mesh into the base Frame of the first Region. */
      ps1 = astTransform( map, reg2_mesh, 1, NULL );

/* Check there are some good points in the transformed pointset. */
      good = 0;
      np = astGetNpoint( ps1 );
      nc = astGetNcoord( ps1 );
      ptr1 = astGetPoints( ps1 );
      if( ptr1 ) {
         for( i = 0; i < nc && !good; i++ ) {
            for( j = 0; j < np; j++ ) {
               if( ptr1[ i ][ j ] != AST__BAD ) {
                  good = 1;
                  break;
               }
            }
         }
      }

/* If the transformed mesh contains no good points, swap the regions and
   try again. */
      if( !good ) {
         fs = astAnnul( fs );
         frm_reg1 = astAnnul( frm_reg1 );
         map_reg1 = astAnnul( map_reg1 );
         cmap = astAnnul( cmap );
         map = astAnnul( map );
         reg2_mesh = astAnnul( reg2_mesh );
         ps1 = astAnnul( ps1 );

         if( first ) {
            first = 0;

            if( !bnd_that ) {
               reg1 = this;
               reg2 = that;
               bnd1 = bnd_this;
               bnd2 = bnd_that;
               reg1_neg = this_neg;
               reg2_neg = that_neg;
            } else {
               reg1 = that;
               reg2 = this;
               bnd1 = bnd_that;
               bnd2 = bnd_this;
               reg1_neg = that_neg;
               reg2_neg = this_neg;
            }
            goto L1;

         } else {
            return 0;
         }
      }

/* Also transform the Region describing the positional uncertainty within
   the second supplied Region into the base Frame of the first supplied
   Region. */
      unc = astGetUncFrm( reg2, AST__CURRENT );
      bfrm_reg1 = astGetFrame( reg1->frameset, AST__BASE );
      unc1 = astMapRegion( unc, map, bfrm_reg1 );

/* See if all points within this transformed mesh fall on the boundary of
   the first Region, to within the joint uncertainty of the two Regions. If
   so the two Regions have equivalent boundaries. We can only do this is
   the first region is bounded. */
      if( astRegPins( reg1, ps1, unc1, &mask ) && good ) {

/* If the boundaries are equivalent, the Regions are either identical
   or are mutually exclusive. To distinguish between these cases, we
   transform an aritrary position (the mean of the pin positions) using
   both Regions - if it's inside both or outside both, then the Regions are
   identical, otherwise they are mutually exclusive. Note, we cannot just
   check the value of the Bounded attribute since both the region and its
   negation will be bounded if the region is defined on the sky. */
         ps4 = astPointSet( 1, nc, " ", status );
         ptr = astGetPoints( ps4 );
         if( astOK ) {

/* Get the average of the pin positions. */
            for( i = 0; i < nc; i++ ) {
               good = 0;
               axsum = 0.0;
               for( j = 0; j < np; j++ ) {
                  if( ptr1[ i ][ j ] != AST__BAD ) {
                     good++;
                     axsum += ptr1[ i ][ j ];
                  }
               }
               if( good ) {
                  ptr[ i ][ 0 ] = axsum/good;
               } else {
                  ptr[ i ][ 0 ] = AST__BAD;
               }
            }
         }

/* Transform from the base frame of reg1 to the current frame of reg1,
   then transform using reg1 as a Mapping to determine if it is inside
   reg1. */
         ps3 = astTransform( map_reg1, ps4, 0, NULL );
         ps5 = astTransform( reg1, ps3, 0, NULL );
         ptr = astGetPoints( ps5 );
         inside1 = astOK ? ( ptr[ 0 ][ 0 ] != AST__BAD ) : 0;
         ps3 = astAnnul( ps3 );
         ps5 = astAnnul( ps5 );

/* Transform from the base frame of reg1 to the current frame of reg2,
   then transform using reg2 as a Mapping to determine if it is inside
   reg2. */
         ps3 = astTransform( map, ps4, 0, NULL );
         ps5 = astTransform( reg2, ps3, 0, NULL );
         ptr = astGetPoints( ps5 );
         inside2 = astOK ? ( ptr[ 0 ][ 0 ] != AST__BAD ) : 0;
         ps3 = astAnnul( ps3 );
         ps5 = astAnnul( ps5 );

/* Free the remaining PointSet. */
         ps4 = astAnnul( ps4 );

/* Swap the inside flags if the regions were negated. */
         if( reg1_neg ) inside1 = !inside1;
         if( reg2_neg ) inside2 = !inside2;

/* If both points are inside or both points are outside, reg1 and reg2
   are equivalent, otherwise they are mutually exclusive. */
         result = ( inside1 == inside2 ) ? 5 : 6;

/* If the boundaries of the two Regions are not equivalent. */
      } else {

/* Create a new PointSet containing those points from the mesh which are
   not on the boundary of the first Region. These points are identified by
   the mask array created by the astRegPins method above. */
         reg2_submesh = GetSubMesh( mask, reg2_mesh, status );

/* Transform the points in the submesh of the second Region into the
   current Frame of the first Region. */
         (void ) astAnnul( ps1 );
         ps1 = astTransform( cmap, reg2_submesh, 1, NULL );

/* Transform this submesh using the first Region as a Mapping. Any points
   outside the first region will be set bad in the output PointSet. */
         ps2 = astTransform( (AstMapping *) reg1, ps1, 1, NULL );

/* Get the number of axes and points in this PointSet. */
         nc = astGetNcoord( ps2 );
         np = astGetNpoint( ps2 );

/* Note if there were any common points (i.e. points on the boundary of
   both regions). */
         touch = ( astGetNpoint( reg2_mesh ) != np );

/* Get pointers to the axis data in this PointSet, and check they can be
   used safely. */
         ptr = astGetPoints( ps2 );
         if( astOK ) {

/* Loop round all points checking if the axis values are bad. We want a
   flag saying if there are any good axis values and another flag saying if
   there are any bad axis values. */
            allbad = 1;
            allgood = 1;
            for( iax = 0; iax < nc; iax++ ) {
               p = ptr[ iax ];
               for( ip = 0; ip < np; ip++,p++ ) {
                  if( *p == AST__BAD ) {
                     allgood = 0;
                     if( !allbad ) break;
                  } else {
                     allbad = 0;
                     if( !allgood ) break;
                  }
               }
            }

/* If the entire mesh of the (potentially negated) second Region was either
   on the boundary of, or inside, the (potentially negated) first region,
   determine the result depending on whether the regions have been
   negated and whether they are bounded. Check for impossible states (or
   maybe just errors in my logic). */
            if( allgood ) {

/* Second region has a mesh so it must be bounded. */
               if( !bnd2 && astOK ) {
                     astError( AST__INTER, "astOverlap(%s): Inconsistent "
                               "state 1 (internal AST programming error).",
                               status, astGetClass( this ) );

/* If the first region has been made bounded by negating it... */
               } else if( reg1_neg ) {
                  if( bnd1 ) {

/* If the second region has been made bounded by negating it, then the
   unnegated first region is completely inside the unnegated second region. */
                     if( reg2_neg ) {
                        result = 2;

/* If the second region was bounded without negating it, then there is
   no overlap between the unnegated first region and the second region. */
                     } else {
                        result = 1;
                     }

/* If the first region has been negated then it should not be unbounded.
   This is ensured by the nature of the code that sets the "this_neg" and
   "that_neg" flags above. */
                  } else if( astOK ) {
                     astError( AST__INTER, "astOverlap(%s): Inconsistent "
                               "state 2 (internal AST programming error).",
                               status, astGetClass( this ) );
                  }

/* If the first region was bounded without negating it, but the second
   region was made bounded by negating it, there is partial overlap. */
               } else if( reg2_neg ) {
                  result = 4;

/* If the first region was bounded without negating it, but the second
   region was also bounded without negating it, the second region is
   completely inside the first region. */
               } else {
                  result = 3;
               }

/* If part of the mesh of the second Region was inside the first region,
   and part was outside, then there is partial ocverlap. */
            } else if( !allbad ) {
               result = 4;

/* If no part of the mesh of the (possibly negated) second Region was inside
   the (possibly negated) first region ... */
            } else {

/* First deal with cases where the first region is unbounded. */
               if( !bnd1 ) {
                  if( reg1_neg && astOK ) {
                     astError( AST__INTER, "astOverlap(%s): Inconsistent "
                               "state 5 (internal AST programming error).",
                               status, astGetClass( this ) );
                  } else if( reg2_neg ){
                     result = 2;
                  } else {
                     result = 1;
                  }

/* The second region has a mesh so it must be bounded. */
               } else if( !bnd2 && astOK ) {
                     astError( AST__INTER, "astOverlap(%s): Inconsistent "
                               "state 6 (internal AST programming error).",
                               status, astGetClass( this ) );

/* So now we know both (possibly negated) regions are bounded. */
               } else {

/* We know that none of the reg2 mesh points are inside the bounded reg1.
   But this still leaves two cases: 1) reg1 could be contained completely
   within reg2, or 2) there is no overlap between reg2 and reg1. To
   distinguish between these two cases we use reg2 to transform a point
   on the boundary of reg1. First get a mesh on the boundary of reg1. */
                  reg1_mesh = astRegMesh( reg1 );

/* Transform this mesh into the coordinate system of the second Region. */
                  ps3 = astTransform( cmap, reg1_mesh, 0, NULL );

/* Transform the points in this mesh using the second Region as a Mapping.
   Any points outside the second region will be set bad in the output
   PointSet. */
                  ps4 = astTransform( (AstMapping *) reg2, ps3, 1, NULL );

/* Get pointers to the axis data in this PointSet,and check they can be
   used safely. */
                  ptr = astGetPoints( ps4 );
                  if( astOK ) {

/* Test the firts point and set a flag indicating if we are in case 1 (if
   not, we must be in case 2). */
                     case1 = ( ptr[ 0 ][ 0 ] != AST__BAD );

/* Apply logic similar to the other cases to determine the result. */
                     if( reg1_neg ) {
                        if( case1 == ( reg2_neg != 0 ) ) {
                           result = 3;
                        } else {
                           result = 4;
                        }
                     } else {
                        if( case1 == ( reg2_neg != 0 ) ) {
                           result = 1;
                        } else {
                           result = 2;
                        }
                     }
                  }

/* Free resources. */
                  reg1_mesh = astAnnul( reg1_mesh );
                  ps3 = astAnnul( ps3 );
                  ps4 = astAnnul( ps4 );
               }
	    }
        }

/* If there was no intersection or overlap, but the regions touch, then we
   consider there to be an intersection if either region is closed. */
	if( touch && result == 1 ) {
	   if( astGetClosed( this) || astGetClosed( that ) ) result = 4;
	}

/* Free resources.*/
         reg2_submesh = astAnnul( reg2_submesh );
         ps2 = astAnnul( ps2 );
      }

/* Free resources.*/
      fs = astAnnul( fs );
      bfrm_reg1 = astAnnul( bfrm_reg1 );
      frm_reg1 = astAnnul( frm_reg1 );
      map_reg1 = astAnnul( map_reg1 );
      cmap = astAnnul( cmap );
      map = astAnnul( map );
      ps1 = astAnnul( ps1 );
      reg2_mesh = astAnnul( reg2_mesh );
      unc = astAnnul( unc );
      unc1 = astAnnul( unc1 );
      if( mask) mask = astFree( mask );
   }
   fs0 = astAnnul( fs0 );

/* The returned value should take account of whether "this" or "that" is
   the first Region. If "this" was used as the first Region, then the
   result value calculated above is already correct. If "that" was used as
   the first Region, then we need to change the result to swap "this" and
   "that". */
   if( reg1 == that ) {
      if( result == 2 ) {
         result = 3;
      } else if( result == 3 ) {
         result = 2;
      }
   }

/* Re-instate the original Negated flags. */
   if( this_neg ) astNegate( this );
   if( that_neg ) astNegate( that );

/* If not OK, return zero. */
   if( !astOK ) result = 0;

/* Return the result. */
   return result;
}

static void Overlay( AstFrame *template_frame, const int *template_axes,
                     AstFrame *result, int *status ) {
/*
*  Name:
*     Overlay

*  Purpose:
*     Overlay the attributes of a template Region on to another Frame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void Overlay( AstFrame *template, const int *template_axes,
*                   AstFrame *result, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astOverlay
*     method inherited from the Frame class).

*  Description:
*     This function overlays attributes from the current Frame of a
*     Region on to another Frame, so as to over-ride selected
*     attributes of that second Frame. Normally only those attributes
*     which have been specifically set in the template will be
*     transferred. This implements a form of defaulting, in which a
*     Frame acquires attributes from the template, but retains its
*     original attributes (as the default) if new values have not
*     previously been explicitly set in the template.

*  Parameters:
*     template
*        Pointer to the template Region, for whose current Frame
*        values should have been explicitly set for any attribute
*        which is to be transferred.
*     template_axes
*        Pointer to an array of int, with one element for each axis of
*        the "result" Frame (see below). For each axis in the result
*        frame, the corresponding element of this array should contain
*        the (zero-based) index of the axis in the current Frame of
*        the template Region to which it corresponds. This array is
*        used to establish from which template Frame axis any
*        axis-dependent attributes should be obtained.
*
*        If any axis in the result Frame is not associated with a
*        template Frame axis, the corresponding element of this array
*        should be set to -1.
*
*        If a NULL pointer is supplied, the template and result axis
*        indices are assumed to be identical.
*     result
*        Pointer to the Frame which is to receive the new attribute values.
*     status
*        Pointer to the inherited status variable.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the current Frame in the Region and invoke its
   astOverlay method to overlay its attributes. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( ((AstRegion *) template_frame)->frameset, AST__CURRENT );
   astOverlay( fr, template_axes, result );
   fr = astAnnul( fr );
}

static void PermAxes( AstFrame *this_frame, const int perm[], int *status ) {
/*
*  Name:
*     PermAxes

*  Purpose:
*     Permute the order of a Region's axes.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void PermAxes( AstFrame *this, const int perm[], int *status )

*  Class Membership:
*     Region member function (over-rides the astPermAxes method
*     inherited from the Frame class).

*  Description:
*     This function permutes the order in which the axes in the
*     current Frame of a Region occur.

*  Parameters:
*     this
*        Pointer to the Region.
*     perm
*        An array of int (with one element for each axis of the
*        Region's current Frame) which lists the axes in their new
*        order. Each element of this array should be a (zero-based)
*        axis index identifying the axes according to their old
*        (un-permuted) order.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - Only genuine permutations of the axis order are permitted, so
*     each axis must be referenced exactly once in the "perm" array.
*     - If more than one axis permutation is applied to the same Frame
*     in a Region, the effects are cumulative.
*/

/* Local Variables: */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Invoke the astPermAxes method on the encapsulated FrameSet. */
   astPermAxes( this->frameset, perm );

}

static AstFrame *PickAxes( AstFrame *this_frame, int naxes, const int axes[],
                           AstMapping **map, int *status ) {
/*
*  Name:
*     PickAxes

*  Purpose:
*     Create a new Frame by picking axes from a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstFrame *PickAxes( AstFrame *this, int naxes, const int axes[],
*                         AstMapping **map, int *status )

*  Class Membership:
*     Region member function (over-rides the astPickAxes protected
*     method inherited from the Frame class).

*  Description:
*     This function creates a new Frame whose axes are copies of axes
*     picked from the encapsulated Frame of an existing Region. Other
*     Frame attributes are also copied from this existing Frame to the
*     new Frame. Zero or more of the original axes may be picked in
*     any order, but each can be used only once. Additional axes (with
*     default characteristics) may be included in the new Frame if
*     required.
*
*     Optionally, a Mapping that converts between the original Frame's
*     axes and those of the new Frame may also be returned.

*  Parameters:
*     this
*        Pointer to the Region.
*     naxes
*        The number of axes required in the new Frame.
*     axes
*        Pointer to an array of int with naxes elements. This should
*        contain (zero based) axis indices specifying the axes which
*        are to be included in the new Frame, in the order
*        required. Each axis index may occur only once.
*
*        If additional (default) axes are also to be included, the
*        corresponding elements of this array should be set to -1.
*     map
*        Address of a location to receive a pointer to a new
*        Mapping. This will be a PermMap (or a UnitMap as a special
*        case) that describes the axis permutation that has taken
*        place between the current Frame of the Region and the new
*        Frame.  The forward transformation will convert from the
*        original Region's axes to the new one's, and vice versa.
*
*        If this Mapping is not required, a NULL value may be supplied
*        for this parameter.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to the new Frame.

*  Notes:
*     - The class of object returned may differ from that of the
*     original current Frame, depending on which axes are
*     selected. For example, if a single axis is picked from a
*     SkyFrame (which always has two axes), the resulting Frame cannot
*     be a valid SkyFrame, so will revert to the parent class (Frame)
*     instead.
*     - The new Frame contains a deep copy of all the data selected
*     from the original current Frame. Modifying the new Frame will
*     therefore not affect the Region or the Frames it contains.
*     - 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: */
   AstFrame *cfrm;            /* Current Frame from input Region */
   AstFrame *frame;           /* Pointer to Frame to be returned */
   AstMapping *cbmap;         /* Base->current Mapping from input Region */
   AstMapping *fsmap;         /* Mapping from selected current to base axes */
   AstRegion *breg;           /* Region spanning selected base Frame axes */
   AstRegion *creg;           /* Region spanning selected current Frame axes */
   AstRegion *this;           /* Pointer to Region structure */
   int *base_axes;            /* Holds selected base frame axis indices */
   int def;                   /* Were any default axes requested? */
   int i;                     /* Axis index */
   int nbase;                 /* No. of selected base Frame axes */

/* Initialise the returned pointers. */
   if ( map ) *map = NULL;
   frame = NULL;

/* Check the global error status. */
   if ( !astOK ) return frame;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Check that a valid set of axes is being selected . */
   astValidateAxisSelection( this, naxes, axes, "astPickAxes" );

/* Pick the required axes from the current Frame of the encapsulated
   FrameSet. */
   cfrm = astGetFrame( this->frameset, AST__CURRENT );
   frame = astPickAxes( cfrm, naxes, axes, map );

/* See if any default axes are to be included in the returned Frame. */
   def = 0;
   for( i = 0; i < naxes; i++ ) {
      if( axes[ i ] < 0 ) def = 1;
   }

/* Regions cannot yet include extra default axes in the returned Frame
   so return a basic Frame if any default axes were requested. */
   if( ! def ) {

/* We now see if the requested set of current Frame axes correspond to a
   unique set of base Frame axes. If they do, we may be able to return a
   Region spanning the selected axes rather than just a Frame. The check
   is performed by attempting to split the current->base Mapping. */
      cbmap = astGetMapping( this->frameset, AST__CURRENT, AST__BASE );
      base_axes = astMapSplit( cbmap, naxes, axes, &fsmap );

/* Check the Mapping could be split. */
      if( base_axes ) {

/* Store the number of base Frame axes that correspond to the requested
   set of current Frame axes. */
         nbase = astGetNout( fsmap );

/* Attempt to create a new Region that spans the corresponding set of
   base Frame axes. */
         breg = astRegBasePick( this, nbase, base_axes );
         if( breg ) {

/* Use the split Mapping to map the base Frame region into the requested
   Frame. We invert the "fsmap" first so that it maps the selected base
   Frame axes into the selected current Frame axes. */
            astInvert( fsmap );
            creg = astMapRegion( breg, fsmap, frame );

/* Copy properties from the old Region to the new Region. */
            astRegOverlay( creg, this, 0 );

/* Return this new Region in place of the simple Frame found above. */
            (void) astAnnul( frame );
            frame = (AstFrame *) creg;

/* Free resources */
            breg = astAnnul( breg );
         }
         fsmap = astAnnul( fsmap );
         base_axes = astFree( base_axes );
      }
      cbmap = astAnnul( cbmap );
   }
   cfrm = astAnnul( cfrm );

/* If an error occurred, annul the Mapping pointer (if requested) and
   the new Frame pointer. */
   if ( !astOK ) {
      if ( map ) *map = astAnnul( *map );
      frame = astAnnul( frame );
   }

/* Return the pointer to the new Frame. */
   return frame;
}

static void RegBaseBox( AstRegion *this, double *lbnd, double *ubnd, int *status ){
/*
*+
*  Name:
*     astRegBaseBox

*  Purpose:
*     Returns the bounding box of an un-negated Region in the base Frame of
*     the encapsulated FrameSet.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astRegBaseBox( AstRegion *this, double *lbnd, double *ubnd )

*  Class Membership:
*     Region virtual function.

*  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.

*-
*/

/* Check the inherited status. */
   if( !astOK ) return;

/* This abstract implementation simply reports an error. All sub-classes of
   Region should over-ride this to return appropriate values. */
   astError( AST__NOIMP, "astRegBaseBox(%s): The %s class does not implement "
             "the astRegBaseBox method inherited from the Region class "
             "(internal AST programming error).", status, astGetClass( this ),
             astGetClass( this ) );
}

static void RegBaseBox2( AstRegion *this, double *lbnd, double *ubnd, int *status ){
/*
*+
*  Name:
*     astRegBaseBox2

*  Purpose:
*     Returns the bounding box of an un-negated Region in the base Frame of
*     the encapsulated FrameSet.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astRegBaseBox2( AstRegion *this, double *lbnd, double *ubnd )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function is similar to astRegBaseBox in that it returns the
*     upper and lower axis bounds of a Region in the base Frame of the
*     encapsulated FrameSet. But, in addition to assuming that the
*     supplied Region has not been negated, it also assumes that any
*     component Regions contained within the supplied Region have not been
*     negated.

*  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.

*-
*/

/* This base class implementation simply calls astRegBaseBox. Sub-classes
   which contain component Regions should override it. */
   astRegBaseBox( this, lbnd, ubnd );

}

static AstPointSet *RegBaseGrid( AstRegion *this, int *status ){
/*
*+
*  Name:
*     astRegBaseGrid

*  Purpose:
*     Return a PointSet containing points spread through the volume of a
*     Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *astRegBaseGrid( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a PointSet containing a set of points spread
*     through the volume of the Region. The points refer to the base Frame of
*     the encapsulated FrameSet.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     Pointer to the PointSet. If the Region is unbounded, a NULL pointer
*     will be returned.

*  Notes:
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/

/* Local Variables: */
   AstBox *box;
   AstFrame *frmb;
   AstPointSet *ps1;
   AstPointSet *ps2;
   AstPointSet *result;
   double **ptr2;
   double **ptr;
   double *lbnd;
   double *ubnd;
   int good;
   int ic;
   int ip;
   int ipr;
   int meshsize;
   int naxb;
   int np;
   int npnt2;
   int ntry;

/* Initialise */
   result= NULL;

/* Check the local error status. */
   if ( !astOK ) return NULL;

/* If the Region structure contains a pointer to a PointSet holding
   positions spread over the volume of the Region in the base Frame,
   return it. */
   if( this->basegrid ) {
      result = astClone( this->basegrid );

/* Otherwise, check the Region is bounded. */
   } else if( astGetBounded( this ) ) {

/* Get the original MeshSize attribute. */
      meshsize = astGetMeshSize( this );

/* Get the base Frame bounding box. */
      naxb = astGetNin( this->frameset );
      lbnd = astMalloc( sizeof( double )*(size_t)naxb );
      ubnd = astMalloc( sizeof( double )*(size_t)naxb );
      astRegBaseBox( this, lbnd, ubnd );

/* Create a Box covering this bounding box. */
      frmb = astGetFrame( this->frameset, AST__BASE );
      box = astBox( frmb, 1, lbnd, ubnd, NULL, "", status );

/* Loop until we have a grid of nearly the right size. Make at most three
   attempts. */
      ipr = 0;
      np = meshsize;
      ntry = 0;
      while( ntry++ < 3 ) {

/* Copy the MeshSize attribute to the new Box since this will be used by
   the invocation of astRegBaseGrid below. */
         astSetMeshSize( box, np );

/* Invoke the Box astRegGrid method. Note, the Box class overrides this
   implementation of astRegBaseGrid and does not (must not) invoke this
   implementation, in order to avoid an infinite loop. */
         ps1 = astRegBaseGrid( box );

/* Some of the base Frame points in the above bounding box will fall outside
   the supplied Region. Use the Region as a Mapping to determine which they
   are. Since the points are base Frame points, use astBTransform rather
   than astTransform. */
         ps2 = astBTransform( this, ps1, 1, NULL );

/* We now create a PointSet which is a copy of "ps2" but with all the bad
   points (i.e. the points in the bounding box grid which are not inside
   the supplied Region) removed. Create a result PointSet which is the same
   size as "ps2", then copy just the good points from "ps2" to the result
   PointSet, keeping a record of the number of points copied. */
         ptr2 = astGetPoints( ps2 );
         npnt2 = astGetNpoint( ps2 );
         result = astPointSet( npnt2, naxb, "", status );
         ptr = astGetPoints( result );
         if( astOK ) {

/* Initialise the index of the next point to be stored in "result". */
            ipr = 0;

/* Loop round all points in "ps2" */
            for( ip = 0; ip < npnt2; ip++ ) {

/* Copy each axis value for this point from "ps2" to "result". If a bad
   axis value is encountered, flag that the point is bad and break out of
   the axis loop. */
               good = 1;
               for( ic = 0; ic < naxb; ic++ ) {
                  if( ptr2[ ic ][ ip ] == AST__BAD ) {
                     good = 0;
                     break;
                  } else {
                     ptr[ ic ][ ipr ] = ptr2[ ic ][ ip ];
                  }
               }

/* If the current point has no bad axis values, increment the index of
   the next point to be stored in "result". */
               if( good ) ipr++;
            }
         }

/* Free resources */
         ps1 = astAnnul( ps1 );
         ps2 = astAnnul( ps2 );

/* Leave the loop if an error has occurred. */
         if( !astOK ) break;

/* If the number of points in the grid is within 5% of the target value,
   it is good enough, so break. */
         if( fabs( (double)( ipr - meshsize ) )/meshsize < 0.05 ) break;

/* Otherwise, adjust the target size of the grid by the ratio by which it
   is in error. Don't do this if we have reached the maximum number of
   re-tries. */
         if( ntry < 3 ) {
            if( ipr == 0 ) {
               np *= 10;
            } else {
               np *= (double)meshsize/(double)ipr;
            }
            result = astAnnul( result );
         }
      }

/* Truncate the "result" PointSet to exclude any unused space at the end
   of the axis values arrays. */
      if( astOK ) astSetNpoint( result, ipr );

/* Free resources */
      lbnd = astFree( lbnd );
      ubnd = astFree( ubnd );
      frmb = astAnnul( frmb );
      box = astAnnul( box );

/* Cache the new grid for future use. */
      if( astOK ) this->basegrid = astClone( result );
   }

/* Annul the result if an error occurred. */
   if( !astOK ) result = astAnnul( result );

/* Return the result */
   return result;
}

static AstRegion **RegSplit( AstRegion *this, int *nlist, int *status ){
/*
*+
*  Name:
*     astRegSplit

*  Purpose:
*     Split a Region into a list of disjoint component Regions.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstRegion **astRegSplit( AstRegion *this, int *nlist )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function splits the supplied Region into a set of disjoint
*     component Regions. If the Region cannot be split, then the returned
*     array contains only one pointer - a clone of the supplied Region
*     pointer.

*  Parameters:
*     this
*        Pointer to the Region.
*     nlist
*        Pointer to an int in which to return the number of elements in
*        the returned array.

*  Returned Value:
*     Pointer to dynamically alloctaed memory holding an array of Region
*     pointers. The length of this array is given by the value returned
*     in "*nlist". The pointers in the returned array should be annulled
*     using astAnnul when no longer needed, and the memory used to hold
*     the array should be freed using astFree.

*  Notes:
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/

/* Local Variables; */
   AstRegion **result;

/* Initialise. */
   result = NULL;
   *nlist = 0;

/* Check the local error status. */
   if ( !astOK ) return result;

/* The base class just returns an array containing a clone of the
   supplied Region pointer. */
   result = astMalloc( sizeof( *result ) );
   if( astOK ) {
      result[ 0 ] = astClone( this );
      *nlist = 1;
   }

   if( !astOK ) {
      result = astFree( result );
      *nlist = 0;
   }

   return result;
}

static AstPointSet *RegBaseMesh( AstRegion *this, int *status ){
/*
*+
*  Name:
*     astRegBaseMesh

*  Purpose:
*     Return a PointSet containing points spread around the boundary of a
*     Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *astRegBaseMesh( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a PointSet containing a set 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.

*  Returned Value:
*     Pointer to the PointSet. The axis values in this PointSet will have
*     associated accuracies derived from the uncertainties which were
*     supplied when the Region was created.
*
*    If the Region has no boundary (i.e. is equivalent to a NullRegion), the
*    returned PointSet will contain a single point with a value of AST__BAD
*    on every axis.

*  Notes:
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/

/* Check the local error status. */
   if ( !astOK ) return NULL;

/* This abstract method must be over-ridden by each concrete sub-class.
   Report an error if this null imlementation is called.*/
   astError( AST__NOIMP, "astRegBaseMesh(%s): The %s class does not implement "
             "the astRegBaseMesh method inherited from the Region class "
             "(internal AST programming error).", status, astGetClass( this ),
             astGetClass( this ) );
   return NULL;
}

static AstRegion *RegBasePick( AstRegion *this, int naxes, const int *axes,
                               int *status ){
/*
*+
*  Name:
*     astRegBasePick

*  Purpose:
*     Return a Region formed by picking selected base Frame axes from the
*     supplied Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstRegion *astRegBasePick( AstRegion *this, int naxes, const int *axes )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function attempts to return a Region that is spanned by selected
*     axes from the base Frame of the encapsulated FrameSet of the supplied
*     Region. This may or may not be possible, depending on the class of
*     Region. If it is not possible a NULL pointer is returned.

*  Parameters:
*     this
*        Pointer to the Region.
*     naxes
*        The number of base Frame axes to select.
*     axes
*        An array holding the zero-based indices of the base Frame axes
*        that are to be selected.

*  Returned Value:
*     Pointer to the Region, or NULL if no region can be formed.

*  Notes:
*    - This base implementation returns NULL unless all base Frame axes
*    are selected (possibly in a permuted order).
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/
/* Local Variables: */
   AstFrame *fr;        /* Pointer to the Region's base Frame */
   AstRegion *result;   /* The returned Region pointer */
   int found;           /* Has the current axis index been found yet? */
   int i;               /* Axis index */
   int j;               /* Index into the "axes" array */
   int nax;             /* No. of base Frame axes */
   int ok;              /* Are we doing a genuine axis permutation? */
   int unit;            /* Is the axis permutation a unit map? */

/* Initialise */
   result = NULL;

/* Check the local error status. */
   if ( !astOK ) return result;

/* Get a pointer to the base Frame int he encapsulated FrameSet. */
   fr = astGetFrame( this->frameset, AST__BASE );

/* See how many axes it has. We only proceed if we are selecting all axes
   in the base Frame. */
   nax = astGetNaxes( fr );
   if( nax == naxes ) {

/* We now check that the axes array is a genuine permutation of all axes.
   This means that all axis indices must occur once, and only once, within
   the "axes" array. Look for each axis index in turn. */
      unit = 1;
      ok = 1;
      for( i = 0; i < nax && ok; i++ ) {

/* Check each element of the axes array to see if it holds the axis index
   currently being looked for. */
         found = 0;
         for( j = 0; j < nax; j++ ) {

/* If so, if this axis index has already been found, break out of the
   loop. */
            if( axes[ j ] == i ) {
               if( found ) {
                  ok = 0;
                  break;
               }
               found = 1;

/* Note if we do not have a unit map (i.e. each axis is permuted onto itself). */
               if( i != j ) unit = 0;
            }
         }

/* If the axis index was not found, we do not have a genuine axis
   permutation. */
         if( !found ) ok = 0;
      }

/* If we have a genuine axis permutation, create a Region which is a copy
   of the supplied region and set it to represent its base Frame. */
      if( ok ) {
         result = astCopy( this );
         astSetRegFS( result, fr );

/* If the axis selection is not equivalent to a unit mapping, we now
   permute the axes. */
         if( !unit ) astPermAxes( result, axes );
      }
   }

/* Free resources. */
   fr = astAnnul( fr );

/* Returned the result. */
   return result;
}

static double *RegCentre( AstRegion *this, double *cen, double **ptr,
                          int index, int ifrm, int *status ){
/*
*+
*  Name:
*     astRegCentre

*  Purpose:
*     Re-centre a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     double *astRegCentre( AstRegion *this, double *cen, double **ptr,
*                           int index, int ifrm )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function shifts the centre of the supplied Region to a
*     specified position, or returns the current centre of the Region.

*  Parameters:
*     this
*        Pointer to the Region.
*     cen
*        Pointer to an array of axis values, giving the new centre.
*        Supply a NULL value for this in order to use "ptr" and "index" to
*        specify the new centre.
*     ptr
*        Pointer to an array of pointers, one for each axis in the Region.
*        Each pointer locates an array of axis values. This is the format
*        returned by the PointSet method astGetPoints. Only used if "cen"
*        is NULL.
*     index
*        The index of the point within the arrays identified by "ptr" at
*        which is stored the coords for the new centre position. Only used
*        if "cen" is NULL.
*     ifrm
*        Should be AST__BASE or AST__CURRENT. Indicates whether the centre
*        position is supplied and returned in the base or current Frame of
*        the FrameSet encapsulated within "this".

*  Returned Value:
*     If both "cen" and "ptr" are NULL then a pointer to a newly
*     allocated dynamic array is returned which contains the centre
*     coords of the Region. This array should be freed using astFree when
*     no longer needed. If either of "ptr" or "cen" is not NULL, then a
*     NULL pointer is returned.

*  Notes:
*    - Any bad (AST__BAD) centre axis values are ignored. That is, the
*    centre value on such axes is left unchanged.
*    - Some Region sub-classes do not have a centre. Such classes will report
*    an AST__NOIMP error code if this method is called with either "ptr" or
*    "cen" not NULL. If "ptr" and "cen" are both NULL, then no error is
*    reported if this method is invoked on a Region of an unsuitable class,
*    but NULL is always returned.

*-
*/

/* Local Variables: */
   double *result;

/* Initialise */
   result = NULL;

/* Check the local error status. */
   if ( !astOK ) return result;

/* This abstract method must be over-ridden by each concrete sub-class
   which allows the centre to be shifted. Report an error if this null
   imlementation is called to set a new centre. If it is called to
   enquire the current centre, then return a NULL pointer. */
   if( ptr || cen ) astError( AST__NOIMP, "astRegCentre(%s): The %s "
                       "class does not implement the astRegCentre method "
                       "inherited from the Region class (internal AST "
                       "programming error).", status, astGetClass( this ),
                       astGetClass( this ) );

   return NULL;
}

static void RegClearAttrib( AstRegion *this, const char *aattrib,
                            char **base_attrib, int *status ) {
/*
*+
*  Name:
*     astRegClearAttrib

*  Purpose:
*     Clear an attribute value for a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astRegClearAttrib( AstRegion *this, const char *aattrib,
*                             char **base_attrib )

*  Class Membership:
*     Region virtual function

*  Description:
*     This function clears the value of a named attribute in both the base
*     and current Frame in the FrameSet encapsulated within a Region, without
*     remapping either Frame.
*
*     No error is reported if the attribute is not recognised by the base
*     Frame.

*  Parameters:
*     this
*        Pointer to the Region.
*     aattrib
*        Pointer to a null terminated string holding the attribute name.
*     base_attrib
*        Address of a location at which to return a pointer to the null
*        terminated string holding the attribute name which was cleared in
*        the base Frame of the encapsulated FrameSet. This may differ from
*        the supplied attribute if the supplied attribute contains an axis
*        index and the current->base Mapping in the FrameSet produces an
*        axis permutation. The returned pointer should be freed using
*        astFree when no longer needed. A NULL pointer may be supplied in
*        which case no pointer is returned.
*-
*/

/* Local Variables: */
   AstFrame *frm;
   AstMapping *junkmap;
   AstMapping *map;
   AstRegion *unc;
   char *attrib;
   char *battrib;
   char buf1[ 100 ];
   int *outs;
   int axis;
   int baxis;
   int i;
   int len;
   int nc;
   int rep;

/* Check the global error status. */
   if ( !astOK ) return;

/* Produce a lower case version of the attribute name string */
   nc = strlen( aattrib );
   attrib = astMalloc( nc + 1 );
   for( i = 0; i < nc; i++ ) attrib[ i ] = tolower( aattrib[ i ] );
   attrib[ nc ] = 0;

/* Clear the attribute in the current Frame in the encapsulated FrameSet.
   Use the protected astClearAttrib method which does not cause the Frame
   to be remapped within the FrameSet. */
   frm = astGetFrame( this->frameset, AST__CURRENT );
   astClearAttrib( frm, attrib );
   frm = astAnnul( frm );

/* Indicate that we should use the supplied attribute name  with the base Frame. */
   battrib = NULL;

/* If the attribute name contains an axis number, we need to create a new
   attribute name which refers to the corresponding base Frame axis
   (since the base<->current Mapping may permute the axes). First parse the
   supplied attribute name to locate any axis index. */
   len = strlen( attrib );
   if( nc = 0, ( 2 == astSscanf( attrib, "%[^(](%d) %n", buf1, &axis,
                                 &nc ) ) && ( nc >= len ) ) {

/* If found, convert the axis index from one-based to zero-based. */
      axis--;

/* See if the specified current Frame axis is connected to one and only
   one base Frame axis. If so, get the index of the base Frame axis. */
      map = astGetMapping( this->frameset, AST__CURRENT, AST__BASE );
      outs = astMapSplit( map, 1, &axis, &junkmap );
      if( junkmap && astGetNout( junkmap ) == 1 ) {
         baxis = outs[ 0 ];

/* If the base Frame axis index is different to the current Frame axis
   index, create a new attribute name string using the base Frame axis index. */
         if( baxis != axis ) {
            battrib = astMalloc( strlen( attrib ) + 10 );
            if( battrib ) sprintf( battrib, "%s(%d)", buf1, baxis + 1 );
         }

/* If there is no one base Frame axis which corresponds to the supplied
   current Frame axis, report an error. */
      } else if( astOK ) {
         astError( AST__INTER, "astRegClearAttrib(%s): Unable to clear "
                   "attribute \"%s\" in the base Frame of the %s", status,
                   astGetClass( this ), attrib, astGetClass( this ) );
         astError( AST__INTER, "There is no base Frame axis corresponding "
                   "to current Frame axis %d\n", status, axis + 1 );
      }

/* Free resources */
      outs = astFree( outs );
      if( junkmap ) junkmap = astAnnul( junkmap );
      map = astAnnul( map );
   }

/* Clear the appropriate attribute name in the base Frame. This time ensure
   that any error caused by the attribute name is annulled. Also clear it in
   any uncertainty Region (the current Frame of the uncertainty Region is
   assumed to be equivalent to the base Frame of the parent Region). */
   frm = astGetFrame( this->frameset, AST__BASE );
   if( frm ) {
      rep = astReporting( 0 );
      astClearAttrib( frm, battrib ? battrib : attrib );
      if( astTestUnc( this ) ) {
         unc = astGetUncFrm( this, AST__BASE );
         astRegClearAttrib( unc, battrib ? battrib : attrib, NULL );
         unc = astAnnul( unc );
      }
      if( astStatus == AST__BADAT ) astClearStatus;
      astReporting( rep );
   }
   frm = astAnnul( frm );

/* If required return the modified base Frame attribute name. Otherwise,
   free it. */
   if( base_attrib ) {
      if( battrib ) {
         *base_attrib = battrib;
      } else {
         *base_attrib = astStore( NULL, attrib, strlen( attrib ) + 1 );
      }
   } else {
      battrib = astFree( battrib );
   }

/* Since the base Frame has been changed, any cached information calculated
   on the basis of the base Frame properties may no longer be up to date. */
   astResetCache( this );

/* Free resources. */
   attrib = astFree( attrib );

}

static AstPointSet *RegGrid( AstRegion *this, int *status ){
/*
*+
*  Name:
*     astRegGrid

*  Purpose:
*     Return a PointSet containing points spread through the volume of a
*     Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *astRegGrid( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a PointSet containing a mesh of points spread
*     throughout the volume of the Region. The points refer to the current
*     Frame of the encapsulated FrameSet.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     Pointer to the PointSet. The axis values in this PointSet will have
*     associated accuracies derived from the uncertainties which were
*     supplied when the Region was created. Annul the pointer using
*     astAnnul when it is no longer needed.

*  Notes:
*    - It should not be assumed that the returned points are evenly
*    spaced withint he volume.
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/

/* Local Variables; */
   AstMapping *map;          /* Base -> current Frame Mapping */
   AstPointSet *result;      /* Pointer to returned PointSet */

/* Initialise the returned pointer */
   result = NULL;

/* Check the local error status. */
   if ( !astOK ) return result;

/* If the Region structure does not contain a pointer to a PointSet holding
   positions evenly spread over the volume of the Region in the base
   Frame, create one now. Note, we cannot cache the grid in the current
   Frame in this way since the current Frame grid depends on the proprties
   of the current Frame (e.g. System) which can be changed at any time.
   astRegBaseGrid stores a pointer for the PointSet in this->basegrid,
   and returns a clone of the pointer, which we do not need so annul it. */
   if( !this->basegrid ) astAnnul( astRegBaseGrid( this ) );

/* Get the simplified base->current Mapping */
   map = astRegMapping( this );

/* If the Mapping is a UnitMap, just return a clone of the PointSet
   pointer stored in the Region structure. */
   if( astIsAUnitMap( map ) ){
      result = astClone( this->basegrid );

/* Otherwise, create a new PointSet holding the above points transformed
   into the current Frame. */
   } else {
      result = astTransform( map, this->basegrid, 1, NULL );
   }

/* Free resources.*/
   map = astAnnul( map );

/* If an error has occurred, annul the returned PointSet. */
   if( !astOK ) result = astAnnul( result );

/* Return the result. */
   return result;
}

static AstPointSet *RegMesh( AstRegion *this, int *status ){
/*
*+
*  Name:
*     astRegMesh

*  Purpose:
*     Return a PointSet containing points spread over the boundary of a
*     Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *astRegMesh( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a PointSet containing a mesh of points on the
*     boundary of the Region. The points refer to the current Frame of
*     the encapsulated FrameSet.

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     Pointer to the PointSet. The axis values in this PointSet will have
*     associated accuracies derived from the uncertainties which were
*     supplied when the Region was created. Annul the pointer using
*     astAnnul when it is no longer needed.

*  Notes:
*    - It should not be assumed that the returned points are evenly
*    spaced on the boundary.
*    - A NULL pointer is returned if an error has already occurred, or if
*    this function should fail for any reason.
*-
*/

/* Local Variables; */
   AstMapping *map;          /* Base -> current Frame Mapping */
   AstPointSet *bmesh;       /* Base Frame mesh */
   AstPointSet *result;      /* Pointer to returned PointSet */

/* Initialise the returned pointer */
   result = NULL;

/* Check the local error status. */
   if ( !astOK ) return result;

/* Get a pointer to a PointSet holding positions evenly spread over the
   boundary of the Region in the base Frame. */
   bmesh = astRegBaseMesh( this );

/* Get the simplified base->current Mapping */
   map = astRegMapping( this );

/* If the Mapping is a UnitMap, just return a clone of the mesh PointSet
   pointer. */
   if( astIsAUnitMap( map ) ){
      result = astClone( bmesh );

/* Otherwise, create a new PointSet holding the above points transformed
   into the current Frame. */
   } else {
      result = astTransform( map, bmesh, 1, NULL );
   }

/* Free resources.*/
   bmesh = astAnnul( bmesh );
   map = astAnnul( map );

/* If an error has occurred, annul the returned PointSet. */
   if( !astOK ) result = astAnnul( result );

/* Return the result. */
   return result;
}

static int RegDummyFS( AstRegion *this, int *status ){
/*
*+
*  Name:
*     astRegDummyFS

*  Purpose:
*     Check if a Region has a dummy FrameSet.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     int astRegDummyFS( AstRegion *this )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a flag indicating if the supplied Region has
*     a dummy FrameSet.
*
*     The astDump method for a Region may choose not to include the
*     Region's FrameSet in the dump, depending on the value of the
*     RegionFS attribute and the nature of the FrameSet. If the FrameSet
*     is omitted from the Dump, then special action has to be taken when
*     the dump is subsequently read in and used to re-create the Region.
*     On encounterting such a dump, the astLoadRegion function will create
*     a dummy FrameSet and associate it with the reconstructed  Region.
*     The new Region should not be used however until this dummy FrameSet
*     has been replaced by the correct FrameSet. Performing this replacement
*     is the responsibility of the parent class (i.e. the class which choose
*     to omit the FrameSet from the dump). These will usually be Region
*     classes which encapsulate other Regions, such as CmpRegion, Prism,
*     Stc, etc.
*
*     This function can be used by astLoad... methods in sub-classes to
*     determine if a newly loaded component Region has a dummy FrameSet. If
*     so the astLoad function should either use the astSetRegFS method to
*     store a new FrameSet in the component Region. If the parent Region
*     itself has a dummy FrameSet (i.e. is a component Region contained
*     within a higher level Region) then it cannot do this and should
*     ignore the presence of the dummy FrameSet (it then becomes the
*     responsibility of hte parent Region to load appropriate FrameSets
*     into all its components).

*  Parameters:
*     this
*        Pointer to the Region.

*  Returned Value:
*     Non-zero if the Region has a dummy FrameSet.

*-
*/

/* Check the inherited status. */
   if( !astOK ) return 0;

/* The Ident attribute of the FrameSet will be set to DUMMY_FS if the
   FrameSet is a dummy. */
   return !strcmp( astGetIdent( this->frameset ), DUMMY_FS );
}

static int RegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
                    int **mask, int *status ){
/*
*+
*  Name:
*     astRegPins

*  Purpose:
*     Check if a set of points fall on the boundary of a given Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     int astRegPins( AstRegion *this, AstPointSet *pset, AstRegion *unc,
*                     int **mask )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function returns a flag indicating if the supplied set of
*     points all fall on the boundary of the given Region.
*
*     Some tolerance is allowed, as specified by the uncertainty Region
*     stored in the supplied Region "this", and the supplied uncertainty
*     Region "unc" which describes the uncertainty of the supplied points.

*  Parameters:
*     this
*        Pointer to the Region.
*     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.

*  Returned Value:
*     Non-zero if the points all fall on the boundary of the given
*     Region, to within the tolerance specified. Zero otherwise.

*-
*/

/* Check the inherited status. */
   if( !astOK ) return 0;

/* This abstract implementation simply reports an error. All sub-classes of
   Region should over-ride this to return appropriate values. */
   astError( AST__NOIMP, "astRegPins(%s): The %s class does not implement "
             "the astRegPins method inherited from the Region class "
             "(internal AST programming error).", status, astGetClass( this ),
             astGetClass( this ) );
   return 0;
}

static void GetRegionBounds( AstRegion *this, double *lbnd, double *ubnd, int *status ){
/*
*++
*  Name:
c     astGetRegionBounds
f     AST_GETREGIONBOUNDS

*  Purpose:
*     Returns the bounding box of Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     void astGetRegionBounds( AstRegion *this, double *lbnd, double *ubnd )
f     CALL AST_GETREGIONBOUNDS( THIS, LBND, UBND, STATUS )

*  Class Membership:
*     Region method.

*  Description:
c     This function
f     This routine
*     returns the upper and lower limits of a box which just encompasses
*     the supplied Region. The limits are returned as axis values within
*     the Frame represented by the Region. The value of the Negated
*     attribute is ignored (i.e. it is assumed that the Region has not
*     been negated).

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
c     lbnd
f     LBND() = DOUBLE PRECISION (Returned)
c        Pointer to an
f        An
*        array in which to return the lower axis bounds covered by the Region.
*        It should have at least as many elements as there are axes in the
*        Region. If an axis has no lower limit, the returned value will
*        be the largest possible negative value.
c     ubnd
f     UBND() = DOUBLE PRECISION (Returned)
c        Pointer to an
f        An
*        array in which to return the upper axis bounds covered by the Region.
*        It should have at least as many elements as there are axes in the
*        Region. If an axis has no upper limit, the returned value will
*        be the largest possible positive value.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Notes:
*    - The value of the Negated attribute is ignored (i.e. it is assumed that
*    the Region has not been negated).
*    - If an axis has no extent on an axis then the lower limit will be
*    returned larger than the upper limit. Note, this is different to an
*    axis which has a constant value (in which case both lower and upper
*    limit will be returned set to the constant value).
*    - If the bounds on an axis cannot be determined, AST__BAD is returned for
*    both upper and lower bounds

*--
*/

/* Local Variables: */
   AstFrame *frm;             /* Current Frame */
   AstMapping *smap;          /* Simplified base -> current Mapping */
   AstPointSet *bmesh;        /* PointSet holding base Frame mesh */
   AstPointSet *cmesh;        /* PointSet holding current Frame mesh */
   double **bptr;             /* Pointer to PointSet coord arrays */
   double **cptr;             /* Pointer to PointSet coord arrays */
   double *blbnd;             /* Lower bounds in base Frame */
   double *bubnd;             /* Upper bounds in base Frame */
   double *p;                 /* Array of values for current axis */
   double width;              /* Width of bounding box on i'th axis */
   int i;                     /* Axis count */
   int ip;                    /* Index of current corner */
   int j;                     /* Timer for low/high swaps */
   int jmax;                  /* Increment between low/high swaps */
   int lo;                    /* Assign low bound to next corner? */
   int nbase;                 /* Number of base Frame axes */
   int ncur;                  /* Number of current Frame axes */
   int npos;                  /* Number of box corners */

/* Check the inherited status. */
   if( !astOK ) return;

/* Get the simplified base to current Mapping. */
   smap = astRegMapping( this );

/* If the simplified Mapping is a UnitMap, just store the base box bounds
   in the returned arrays */
   if( astIsAUnitMap( smap ) ) {
      astRegBaseBox( this, lbnd, ubnd );

/* Otherwise, we get a mesh of points over the boundary of the Region within
   the base Frame, transform them into the current Frame, and find their bounds. */
   } else {

/* If the Region is bounded, we can get a genuine mesh of points on the
   boundary of the Region. */
      if( astGetBounded( this ) ) {
         bmesh = astRegBaseMesh( this );

/* If the Region is not bounded, no mesh can be created so we use the
   corners of the base frame bounding box instead. */
      } else {

/* Get workspace to hold the bounds of the region within the base Frame. */
         nbase = astGetNin( smap );
         blbnd = astMalloc( sizeof( double )*nbase );
         bubnd = astMalloc( sizeof( double )*nbase );

/* Get the base Frame bounding box. */
         astRegBaseBox( this, blbnd, bubnd );

/* Get the number of corners in the base Frame bounding box. */
         npos = pow( 2, nbase );

/* Create a PointSet to hold the positions at the corners in the base
   frame box. */
         bmesh = astPointSet( npos, nbase, " ", status );
         bptr = astGetPoints( bmesh );
         if( bptr ) {

/* Store the coordinates of the box corners in the PointSet. */
            jmax = 1;
            for( i = 0; i < nbase; i++ ) {
               p = bptr[ i ];

               lo = 1;
               j = 0;
               for( ip = 0; ip < npos; ip++,j++ ) {
                  if( j == jmax ) {
                     lo = 1 - lo;
                     j = 0;
                  }
                  p[ ip ] = lo ? blbnd[ i ] : bubnd[ i ];
               }

               jmax *= 2;
            }
         }

/* Release resources. */
         blbnd = astFree( blbnd );
         bubnd = astFree( bubnd );
      }

/* Create a new PointSet holding the above points transformed into the
   current Frame. */
      cmesh = astTransform( smap, bmesh, 1, NULL );

/* There is a possibility that these points may span a singularity in the
   coordinate system such as the RA=0 line in a SkyFrame. So ensure the
   axis values are normalised into the shortest possible range. */
      frm = astGetFrame( this->frameset, AST__CURRENT );
      ncur = astGetNaxes( frm );

      cptr = astGetPoints( cmesh );
      npos = astGetNpoint( cmesh );
      for( i = 0; i < ncur; i++ ) {
         astAxNorm( frm, i+1, 1, npos, cptr[i] );
      }

/* Get the axis bounds of this PointSet. */
      astBndPoints( cmesh, lbnd, ubnd );

/* There is again a possibility that these bounds may span a singularity in
   the coordinate system such as the RA=0 line in a SkyFrame. So for each
   axis we ensure the width (i.e. "ubnd-lbnd" ) is correct. */
      for( i = 0; i < ncur; i++ ) {
         width = astAxDistance( frm, i + 1, lbnd[ i ], ubnd[ i ] );
         if( width != AST__BAD ) {
            ubnd[ i ] = lbnd[ i ] + width;
         } else {
            ubnd[ i ] = AST__BAD;
            lbnd[ i ] = AST__BAD;
         }
      }

/* Release resources. */
      frm = astAnnul( frm );
      bmesh = astAnnul( bmesh );
      cmesh = astAnnul( cmesh );
   }
   smap = astAnnul( smap );
}

static void GetRegionBounds2( AstRegion *this, double *lbnd, double *ubnd, int *status ){
/*
*+
*  Name:
*     astGetRegionBounds

*  Purpose:
*     Returns the bounding box of Region.

*  Type:
*     Protected virtual function.

*  Synopsis:
*     #include "region.h"
*     void astGetRegionBounds2( AstRegion *this, double *lbnd, double *ubnd )

*  Class Membership:
*     Region method.

*  Description:
*     This function is like astGetRegionBounds, in that it returns the upper
*     and lower limits of a box which just encompasses the supplied Region,
*     as axis values within the Frame represented by the Region. But, in
*     addition to assuming that the supplied Region has not been negated, it
*     also assumes that any component Regions contained within the supplied
*     Region have not been negated.

*  Parameters:
*     this
*        Pointer to the Region.
*     lbnd
*        Pointer to an array in which to return the lower axis bounds
*        covered by the Region. It should have at least as many elements
*        as there are axes in the Region.
*     ubnd
*        Pointer to an array in which to return the upper axis bounds
*        covered by the Region. It should have at least as many elements
*        as there are axes in the Region.

*  Notes:
*    - The value of the Negated attribute is ignored (i.e. it is assumed that
*    the Region has not been negated). The Nagated attributes of any
*    component Regions are also ignored.

*-
*/

/* Local Variables: */
   AstMapping *smap;          /* Simplified base -> current Mapping */
   double *lbndb;             /* Pointer to lower bounds on base box */
   double *ubndb;             /* Pointer to upper bounds on base box */
   int i;                     /* Axis count */
   int nbase;                 /* Number of base Frame axes */
   int ncur;                  /* Number of current Frame axes */

/* Check the inherited status. */
   if( !astOK ) return;

/* Find the number of axes in the base and current Frames of the
   encapsulated FrameSet. */
   nbase = astGetNin( this->frameset );
   ncur = astGetNout( this->frameset );

/* Get the bounding box in the base Frame of the encapsulated FrameSet. */
   lbndb = astMalloc( sizeof( double )*(size_t) nbase );
   ubndb = astMalloc( sizeof( double )*(size_t) nbase );
   astRegBaseBox2( this, lbndb, ubndb );

/* Get the simplified base to current Mapping. */
   smap = astRegMapping( this );

/* Check pointers can be used safely. */
   if( smap ) {

/* If the simplified Mapping is a UnitMap, just copy the base box bounds
   to the returned arrays */
      if( astIsAUnitMap( smap ) ) {
         for( i = 0; i < ncur; i++ ) {
            lbnd[ i ] = lbndb[ i ];
            ubnd[ i ] = ubndb[ i ];
         }

/* Otherwise, use astMapBox to find the corresponding current Frame
   limits. */
      } else {
         for( i = 0; i < ncur; i++ ) {
            astMapBox( smap, lbndb, ubndb, 1, i, lbnd + i, ubnd + i,
                       NULL, NULL );
         }
      }
   }

/* Release resources. */
   smap = astAnnul( smap );
   lbndb = astFree( lbndb );
   ubndb = astFree( ubndb );
}

static void GetRegionMesh( AstRegion *this, int surface, int maxpoint,
                           int maxcoord, int *npoint, double *points,
                           int *status ){
/*
*++
*  Name:
c     astGetRegionMesh
f     AST_GETREGIONMESH

*  Purpose:
*     Return a mesh of points covering the surface or volume of a Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     void astGetRegionMesh( AstRegion *this, int surface, int maxpoint,
c                            int maxcoord, int *npoint, double *points )
f     CALL AST_GETREGIONMESH( THIS, SURFACE, MAXPOINT, MAXCOORD, NPOINT,
f                             POINTS, STATUS )

*  Class Membership:
*     Region method.

*  Description:
c     This function
f     This routine
*     returns the axis values at a mesh of points either covering the
*     surface (i.e. boundary) of the supplied Region, or filling the
*     interior (i.e. volume) of the Region. The number of points in
*     the mesh is determined by the MeshSize attribute.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
c     surface
f     SURFACE = LOGICAL (Given)
c        If non-zero,
f        If .TRUE.,
*        the returned points will cover the surface or the Region.
*        Otherwise, they will fill the interior of the Region.
c     maxpoint
f     MAXPOINT = INTEGER (Given)
*        If zero, the number of points in the mesh is returned in
c        "*npoint",
f        NPOINT,
*        but no axis values are returned and all other parameters are ignored.
*        If not zero, the supplied value should be the length of the
c        second dimension of the "points"
f        first dimension of the POINTS
*        array. An error is reported if the number of points in the mesh
*        exceeds this number.
c     maxcoord
f     MAXCOORD = INTEGER (Given)
*        The length of the
c        first dimension of the "points" array.
f        second dimension of the POINTS array.
*        An error is reported if the number of axes in the supplied Region
*        exceeds this number.
c     npoint
f     NPOINT = INTEGER (Returned)
c        A pointer to an integer in which to return the
f        The
*        number of points in the returned mesh.
c     points
f     POINTS( MAXPOINT, MAXCOORD ) = DOUBLE PRECISION (Returned)
c        The address of the first element in a 2-dimensional array of
c        shape "[maxcoord][maxpoint]", in which to return the coordinate
c        values at the mesh positions. These are stored such that the
c        value of coordinate number "coord" for point number "point" is
c        found in element "points[coord][point]".
f        An array in which to return the coordinates values at the mesh
f        positions. These are stored such that the value of coordinate
f        number COORD for point number POINT is found in element
f        POINTS(POINT,COORD).
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Notes:
*     - An error is reported if the Region is unbounded.
*     - If the coordinate system represented by the Region has been
*     changed since it was first created, the returned axis values refer
*     to the new (changed) coordinate system, rather than the original
*     coordinate system. Note however that if the transformation from
*     original to new coordinate system is non-linear, the shape within
*     the new coordinate system may be distorted, and so may not match
*     that implied by the name of the Region subclass (Circle, Box, etc).

*--
*/

/* Local Variables: */
   AstPointSet *pset;       /* PointSet holding mesh/grid axis values */
   double **ptr;            /* Pointer to mesh/grid axes values */
   double *p;               /* Pointer to next input axis value */
   double *q;               /* Pointer to next output axis value */
   int j;                   /* Axis index */
   int nc;                  /* No. of axes to copy */

/* Initialise */
   *npoint = 0;

/* Check the inherited status. */
   if( !astOK ) return;

/* Report an error if the Region is unbounded. */
   if( !astGetBounded( this ) ) {
      if( astOK ) astError( AST__MBBNF, "astGetRegionMesh(%s): The supplied %s"
                            " is unbounded so no mesh can be created to cover "
                            "it.", status, astGetClass( this ), astGetClass( this ) );
   } else {

/* Get the mesh or grid as required. If only the size of the mesh or grid
   is required, get it in the base Frame as there is no need to spend the
   extra time transforming it into the current Frame. */
      if( maxpoint == 0  ){
         if( surface ) {
            pset = astRegBaseMesh( this );
         } else {
            pset = astRegBaseGrid( this );
         }
      } else {
         if( surface ) {
            pset = astRegMesh( this );
         } else {
            pset = astRegGrid( this );
         }
      }

/* Return the number of points in the mesh or grid. */
      *npoint = astGetNpoint( pset );

/* Do nothing more unless a non-zero array size was supplied. */
      if( *npoint > 0 && maxpoint != 0 && astOK ) {

/* Check the supplied array is large enough. */
         if( *npoint > maxpoint ) {
            astError( AST__DIMIN, "astGetRegionMesh(%s): The supplied "
                      "array can hold up to %d points but the %s supplied "
                      "has %d points on its mesh (programming error).",
                      status, astGetClass( this ), maxpoint, astGetClass( this ),
                      *npoint );
         }

/* Get the dimensionality of the PointSet, and get a pointer to the axis
   values. */
         nc = astGetNcoord( pset );
         ptr = astGetPoints( pset );

/* Check pointers can be used safely. */
         if ( astOK ) {

/* Check the supplied array has room for all the axes. */
            if( nc > maxcoord ) {
               astError( AST__DIMIN, "astGetRegionMesh(%s): The supplied "
                         "array can hold up to %d axes but the %s supplied "
                         "has %d axes (programming error).", status,
                         astGetClass( this ), maxcoord, astGetClass( this ), nc );

/* If all is OK, copy the current Frame axis values into the supplied array. */
            } else {

/* Loop round the axes to be copied. */
               for( j = 0; j < nc; j++ ) {

/* Get points to the first element of the input and output arrays. */
                  p = ptr[ j ];
                  q = points + j*maxpoint;

/* Copying the axis values. */
                  (void) memcpy( q, p, sizeof( double )*( *npoint ) );
               }
            }
         }
      }

/* Free resources. */
      pset = astAnnul( pset );
   }
}

static void GetRegionPoints( AstRegion *this, int maxpoint, int maxcoord,
                             int *npoint, double *points, int *status ){
/*
*++
*  Name:
c     astGetRegionPoints
f     AST_GETREGIONPOINTS

*  Purpose:
*     Returns the positions that define the given Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     void astGetRegionPoints( AstRegion *this, int maxpoint, int maxcoord,
c                              int *npoint, double *points )
f     CALL AST_GETREGIONPOINTS( THIS, MAXPOINT, MAXCOORD, NPOINT, POINTS,
f                               STATUS )

*  Class Membership:
*     Region method.

*  Description:
c     This function
f     This routine
*     returns the axis values at the points that define the supplied
*     Region. The particular meaning of these points will depend on the
*     type of class supplied, as listed below under "Applicability:".

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
c     maxpoint
f     MAXPOINT = INTEGER (Given)
*        If zero, the number of points needed to define the Region is
*        returned in
c        "*npoint",
f        NPOINT,
*        but no axis values are returned and all other parameters are ignored.
*        If not zero, the supplied value should be the length of the
c        second dimension of the "points"
f        first dimension of the POINTS
*        array. An error is reported if the number of points needed to define
*        the Region exceeds this number.
c     maxcoord
f     MAXCOORD = INTEGER (Given)
*        The length of the
c        first dimension of the "points" array.
f        second dimension of the POINTS array.
*        An error is reported if the number of axes in the supplied Region
*        exceeds this number.
c     npoint
f     NPOINT = INTEGER (Returned)
c        A pointer to an integer in which to return the
f        The
*        number of points defining the Region.
c     points
f     POINTS( MAXPOINT, MAXCOORD ) = DOUBLE PRECISION (Returned)
c        The address of the first element in a 2-dimensional array of
c        shape "[maxcoord][maxpoint]", in which to return
c        the coordinate values at the positions that define the Region.
c        These are stored such that the value of coordinate number
c        "coord" for point number "point" is found in element
c        "points[coord][point]".
f        An array in which to return the coordinates values at the
f        positions that define the Region. These are stored such that the
f        value of coordinate number COORD for point number POINT
f        is found in element POINTS(POINT,COORD).
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Applicability:
*     Region
*        All Regions have this attribute.
*     Box
*        The first returned position is the Box centre, and the second is
*        a Box corner.
*     Circle
*        The first returned position is the Circle centre, and the second is
*        a point on the circumference.
*     CmpRegion
*        Returns a value of zero for
c        "*npoint"
f        NPOINT
*        and leaves the supplied array contents unchanged. To find the
*        points defining a CmpRegion, use this method on the component
*        Regions, which can be accessed by invoking
c        astDecompose
f        AST_DECOMPOSE
*        on the CmpRegion.
*     Ellipse
*        The first returned position is the Ellipse centre. The second is
*        the end of one of the axes of the ellipse. The third is some
*        other point on the circumference of the ellipse, distinct from
*        the second point.
*     Interval
*        The first point corresponds to the lower bounds position, and
*        the second point corresponds to the upper bounds position. These
*        are reversed to indicate an extcluded interval rather than an
*        included interval. See the Interval constructor for more
*        information.
*     NullRegion
*        Returns a value of zero for
c        "*npoint"
f        NPOINT
*        and leaves the supplied array contents unchanged.
*     PointList
*        The positions returned are those that were supplied when the
*        PointList was constructed.
*     Polygon
*        The positions returned are the vertex positions that were supplied
*        when the Polygon was constructed.
*     Prism
*        Returns a value of zero for
c        "*npoint"
f        NPOINT
*        and leaves the supplied array contents unchanged. To find the
*        points defining a Prism, use this method on the component
*        Regions, which can be accessed by invoking
c        astDecompose
f        AST_DECOMPOSE
*        on the CmpRegion.

*  Notes:
*     - If the coordinate system represented by the Region has been
*     changed since it was first created, the returned axis values refer
*     to the new (changed) coordinate system, rather than the original
*     coordinate system. Note however that if the transformation from
*     original to new coordinate system is non-linear, the shape within
*     the new coordinate system may be distorted, and so may not match
*     that implied by the name of the Region subclass (Circle, Box, etc).

*--
*/

/* Local Variables: */
   AstPointSet *pset;       /* PointSet holding PointList axis values */
   double **ptr;            /* Pointer to axes values in the PointList */
   double *p;               /* Pointer to next input axis value */
   double *q;               /* Pointer to next output axis value */
   int j;                   /* Axis index */
   int nc;                  /* No. of axes to copy */

/* Initialise */
   *npoint = 0;

/* Check the inherited status. */
   if( !astOK ) return;

/* Return the number of points used to define the Region, if any. */
   *npoint = this->points ? astGetNpoint( this->points ) : 0;

/* Do nothing more unless a non-zero array size was supplied. */
   if( *npoint > 0 && maxpoint != 0 ) {

/* Transform the base Frame axis values into the current Frame. */
      pset = astTransform( this->frameset, this->points, 1, NULL );

/* Get the dimensionality of this PointList, and get a pointer to the axis
   values. */
      nc = astGetNcoord( pset );
      ptr = astGetPoints( pset );

/* Check pointers can be used safely. */
      if ( astOK ) {

/* Check the supplied array has room for all the axis values. */
         if( nc > maxcoord ) {
            astError( AST__DIMIN, "astGetRegionPoints(%s): The supplied "
                      "array can hold up to %d axes but the %s supplied "
                      "has %d axes (programming error).", status,
                      astGetClass( this ), maxcoord, astGetClass( this ), nc );

         } else if( *npoint > maxpoint ) {
            astError( AST__DIMIN, "astGetRegionPoints(%s): The supplied "
                      "array can hold up to %d points but the %s supplied "
                      "requires %d points to describe it (programming "
                      "error).", status, astGetClass( this ), maxpoint,
                       astGetClass( this ), *npoint );

/* If all is OK, copy the transformed axis values into the supplied array. */
         } else {

/* Loop round the axes to be copied. */
            for( j = 0; j < nc; j++ ) {

/* Get points to the first element of the input and output arrays. */
               p = ptr[ j ];
               q = points + j*maxpoint;

/* Copying the axis values. */
               (void) memcpy( q, p, sizeof( double )*( *npoint ) );
            }
         }
      }

/* Free resources. */
      pset = astAnnul( pset );

   }
}

static void GetRegionDisc( AstRegion *this, double centre[2], double *radius,
                           int *status ){
/*
*++
*  Name:
c     astGetRegionDisc
f     AST_GETREGIONDisc

*  Purpose:
*     Returns the centre and radius of a disc containing a 2D Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     void GetRegionDisc( AstRegion *this, double centre[3],
c                         double *radius )
f     CALL AST_GETREGIONDISC( THIS, CENTRE, RADIUS, STATUS )

*  Class Membership:
*     Region method.

*  Description:
c     This function
f     This routine
*     returns the centre and radius of a disce that just encloses the
*     supplied 2-dimensional Region. The centre is returned as a pair
*     of axis values within the Frame represented by the Region. The
*     value of the Negated attribute is ignored (i.e. it is assumed
*     that the Region has not been negated).

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
c     centre
f     CENTRE( 2 ) = DOUBLE PRECISION (Returned)
c        Pointer to a
f        A
*        two-element array in which to return the axis values at the centre
*        of the bounding disc.
c     radius
f     RADIUS = DOUBLE PRECISION (Returned)
c        Pointer to a variable in which to return the
f        The
*        radius of the bounding disc, as a geodesic distance within the
*        Frame represented by the Region. It will be returned holding
*        AST__BAD If the Region is unbounded.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Notes:
*    - An error is reported if the Region is not 2-dimensional.
*    - The value of the Negated attribute is ignored (i.e. it is assumed that
*    the Region has not been negated).
*    - If the Region is unbounded, the radius will be returned set to
*    AST__BAD and the supplied centre axis values will be returned unchanged.

*--
*/

/* Local Variables: */
   AstPointSet *mesh;
   double **ptr;
   double angle;
   double dist;
   double dx;
   double dxmax;
   double dxmin;
   double dy;
   double dymax;
   double dymin;
   double point1[ 2 ];
   double point2[ 2 ];
   double point3[ 2 ];
   double point4[ 2 ];
   int ipoint;
   int nax;
   int npoint;
   int old_neg;
   int step;

/* Initialise the radius. */
   *radius = AST__BAD;

/* Check the inherited status. */
   if( !astOK ) return;

/* Validate */
   nax = astGetNaxes( this );
   if( nax != 2 ) {
      astError( AST__INVAR, "astGetRegionDisc(%s): Supplied %s is not "
                "2-dimensional.", status, astGetClass( this ),
                astGetClass( this ));
   }

/* Temporarily set the Negated flag to zero. */
   if( astTestNegated( this ) ) {
      old_neg = astGetNegated( this );
   } else {
      old_neg = -100;
   }
   astSetNegated( this, 0 );

/* If the Region is not bounded, return AST__BAD as the radius. */
   if( astGetBounded( this ) ){

/* Get a mesh of points over the boundary of the Region within the
   current Frame. */
      mesh = astRegMesh( this );
      ptr = astGetPoints( mesh );
      if( astOK ) {

/* Since the Region may be defined on the sky, we cannot just find the
   centroid of the mesh points since the axes may not have a flat
   geometry. Instead we form a local coordinate system by choosing an
   arbitrary mesh point as the origin, and then defining a basis vector
   joining this origin with another arbitrary mesh point. The local
   coordinate system is then distance from the origin parallel and
   perpendicular to the basis vector. This is not necessarily a flat
   system, but it should allow us to find the centre of the disk by
   taking the centroid of the mesh points (in the local coordinate
   system). First choose the origin of the local system - the first mesh
   point. */
         point1[ 0 ] = ptr[ 0 ][ 0 ];
         point1[ 1 ] = ptr[ 1 ][ 0 ];

/* Next choose the other end of the basis vector - a point about half way
   round the boundary */
         npoint = astGetNpoint( mesh );
         point2[ 0 ] = ptr[ 0 ][ npoint/2 ];
         point2[ 1 ] = ptr[ 1 ][ npoint/2 ];

/* Check all these axis values are good. */
         if( point1[ 0 ] != AST__BAD && point1[ 1 ] != AST__BAD &&
             point2[ 0 ] != AST__BAD && point2[ 1 ] != AST__BAD ) {

/* No need to use all mesh points (there can be thousands). Choose a step
   length that gives us about two hundred. */
            step = ( npoint > 200 ) ? npoint/200 : 1;

/* Loop over 200ish points in the mesh, maintaining the bounding box of
   the mesh points in the local system. No need to do point 0 since we
   know it is at (0,0) in the local system. */
            dxmax = 0.0;
            dxmin = 0.0;
            dymax = 0.0;
            dymin = 0.0;
            for( ipoint = step; ipoint < npoint; ipoint += step ) {

/* Check the mesh point is good. */
               point3[ 0 ] = ptr[ 0 ][ ipoint ];
               point3[ 1 ] = ptr[ 1 ][ ipoint ];
               if( point3[ 0 ] != AST__BAD && point3[ 1 ] != AST__BAD ) {

/* Resolve the vector from point1 to the current point into two
   components - parallel and perpendicular to the vector from point1 to
   point2. */
                  astResolve( this, point1, point2, point3, point4, &dx, &dy );

/* The dy value returned by astResolve is always positive. Assign it a
   sign depending on the sign of the angle at point4. */
                  if( astAngle( this, point1, point4, point3 ) < 0.0 ) dy = -dy;

/* Record the max and min values of the two components. */
                  dxmax = astMAX( dx, dxmax );
                  dxmin = astMIN( dx, dxmin );
                  dymax = astMAX( dy, dymax );
                  dymin = astMIN( dy, dymin );
               }
            }

/* The centre of the bounding box is a good enough approximation to the
   centre of the bounding disc. Get the centre in the local system. */
            dx = 0.5*( dxmax + dxmin );
            dy = 0.5*( dymax + dymin );

/* Convert to the system of the Region. First get the Region coords of a
   point slightly "north" of point1 (go "north" by a distance equal to
   0.001 of the distance along the basis vector used above). */
            dist = astDistance( this, point1, point2 );
            point3[ 0 ] = point1[ 0 ];
            point3[ 1 ] = point1[ 1 ] + 0.001*dist;

/* Find the angle from "north" to the basis vector. */
            angle = astAngle( this, point3, point1, point2 );

/* Offset away from point1 at the above angle by the local x value of the
   centre. */
            angle = astOffset2( this, point1, angle, dx, point3 );

/* Rotate by 90 degrees and offset away from the above point (point3)
   by the local y value of the centre. This gives us the centre in Region
   coordinates. */
            (void) astOffset2( this, point3, angle - AST__DPIBY2, dy, centre );

/* Now loop round all good points on the mesh and find the maximum distance
   from this centre to any mesh point. */
            *radius = 0.0;
            for( ipoint = 0; ipoint < npoint; ipoint++ ) {
               point3[ 0 ] = ptr[ 0 ][ ipoint ];
               point3[ 1 ] = ptr[ 1 ][ ipoint ];
               dist = astDistance( this, centre, point3 );
               if( dist != AST__BAD ) *radius = astMAX( *radius, dist );
            }

/* Increase the radius by a very small amount to account for possible
   rounding errors. */
            *radius *= 1.000001;
         }
      }

/* Free resources. */
      mesh = astAnnul( mesh );
   }

/* Re-instate the orignal value of the Negated flag. */
   if( old_neg == -100 ) {
      astClearNegated( this );
   } else {
      astSetNegated( this, old_neg );
   }
}

static void RegOverlay( AstRegion *this, AstRegion *that, int unc, int *status ){
/*
*+
*  Name:
*     astRegOverlay

*  Purpose:
*     Copy properties from one Region to another.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astRegOverlay( AstRegion *this, AstRegion *that, int unc )

*  Class Membership:
*     Region virtual function.

*  Description:
*     This function copies selected properties from "that" to "this".
*     It is intended to be called by sub-classes which need to create a
*     similar copy of an existing Region. For instance, subclass
*     implementations of the Simplify method will usually use this
*     function to ensure that the simplified Region loooks like the original
*     Region.

*  Parameters:
*     this
*        Pointer to the new Region.
*     that
*        Pointer to the old Region.
*     unc
*        If non-zero, any uncertainty in "this" is cleared if "that" has
*        no uncertainty. If zero, any uncertainty in "this" is left
*        unchanged.
*-
*/

/* Check the inherited status. */
   if( !astOK ) return;

/* Copy the required attribute values. */
   this->negated = that->negated;
   this->closed = that->closed;
   this->regionfs = that->regionfs;
   this->adaptive = that->adaptive;

/* Clear things that depend on the number of axes. */
   if( astGetNaxes( this ) == astGetNaxes( that ) ) {
      if( astTestMeshSize( that ) ) astSetMeshSize( this, astGetMeshSize( that ) );
      if( astTestFillFactor( that ) ) astSetFillFactor( this, astGetFillFactor( that ) );
   } else {
      astClearMeshSize( this );
      astClearFillFactor( this );
   }

/* If required, clear uncertainty in "this" if "that" has no uncertainty. */
   if( unc && !astTestUnc( that ) ) astClearUnc( this );

}

static void RegSetAttrib( AstRegion *this, const char *asetting,
                          char **base_setting, int *status ) {
/*
*+
*  Name:
*     astRegSetAttrib

*  Purpose:
*     Set an attribute value for a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astRegSetAttrib( AstRegion *this, const char *asetting,
*                           char **base_setting )

*  Class Membership:
*     Region virtual function

*  Description:
*     This function assigns an attribute value to both the base and
*     current Frame in the FrameSet encapsulated within a Region, without
*     remapping either Frame.
*
*     No error is reported if the attribute is not recognised by the base
*     Frame.

*  Parameters:
*     this
*        Pointer to the Region.
*     asetting
*        Pointer to a null terminated attribute setting string. The supplied
*        string will be interpreted using the public interpretation
*        implemented by astSetAttrib. This can be different to the
*        interpretation of the protected accessor functions. For instance,
*        the public interpretation of an unqualified floating point value for
*        the Epoch attribute is to interpet the value as a gregorian year,
*        but the protected interpretation is to interpret the value as an
*        MJD.
*     base_setting
*        Address of a location at which to return a pointer to the null
*        terminated attribute setting string which was applied to the
*        base Frame of the encapsulated FrameSet. This may differ from
*        the supplied setting if the supplied setting contains an axis
*        index and the current->base Mapping in the FrameSet produces an
*        axis permutation. The returned pointer should be freed using
*        astFree when no longer needed. A NULL pointer may be supplied in
*        which case no pointer is returned.
*-
*/

/* Local Variables: */
   AstFrame *frm;
   AstMapping *junkmap;
   AstMapping *map;
   AstRegion *unc;
   char *setting;
   char *bsetting;
   char buf1[ 100 ];
   int *outs;
   int axis;
   int baxis;
   int i;
   int len;
   int nc;
   int rep;
   int value;

/* Check the global error status. */
   if ( !astOK ) return;

/* Produce a lower case version of the setting string */
   nc = strlen( asetting );
   setting = astMalloc( nc + 1 );
   for( i = 0; i < nc; i++ ) setting[ i ] = tolower( asetting[ i ] );
   setting[ nc ] = 0;

/* Apply the setting to the current Frame in the encapsulated FrameSet.
   Use the protected astSetAttrib method which does not cause the Frame
   to be remapped within the FrameSet. */
   frm = astGetFrame( this->frameset, AST__CURRENT );
   astSetAttrib( frm, setting );
   frm = astAnnul( frm );

/* Indicate that we should use the supplied setting with the base Frame. */
   bsetting = NULL;

/* If the attribute name contains an axis number, we need to create a new
   attribute setting which refers to the corresponding base Frame axis
   (since the base<->current Mapping may permute the axes). First parse the
   supplied attribute setting to locate any axis index. */
   len = strlen( setting );
   if( nc = 0, ( 2 == astSscanf( setting, "%[^(](%d)= %n%*s %n", buf1, &axis,
                                 &value, &nc ) ) && ( nc >= len ) ) {

/* If found, convert the axis index from one-based to zero-based. */
      axis--;

/* See if the specified current Frame axis is connected to one and only
   one base Frame axis. If so, get the index of the base Frame axis. */
      map = astGetMapping( this->frameset, AST__CURRENT, AST__BASE );
      outs = astMapSplit( map, 1, &axis, &junkmap );
      if( junkmap && astGetNout( junkmap ) == 1 ) {
         baxis = outs[ 0 ];

/* If the base Frame axis index is different to the current Frame axis
   index, create a new setting string using the base Frame axis index. */
         if( baxis != axis ) {
            bsetting = astMalloc( strlen( setting ) + 10 );
            if( bsetting ) {
               sprintf( bsetting, "%s(%d)=%s", buf1, baxis + 1, setting + value );
            }
         }

/* If there is no one base Frame axis which corresponds to the supplied
   current Frame axis, report an error. */
      } else if( astOK ) {
         astError( AST__INTER, "astRegSetAttrib(%s): Unable to apply "
                   "attribute setting \"%s\" to the base Frame in the %s", status,
                   astGetClass( this ), setting, astGetClass( this ) );
         astError( AST__INTER, "There is no base Frame axis corresponding "
                   "to current Frame axis %d\n", status, axis + 1 );
      }

/* Free resources */
      outs = astFree( outs );
      if( junkmap ) junkmap = astAnnul( junkmap );
      map = astAnnul( map );
   }

/* Apply the appropriate attribute setting to the base Frame. This time
   ensure that any error caused by the attribute setting is annulled.
   Also apply it to any uncertainty Region (the current Frame of the
   uncertainty Region is assumed to be equivalent to the base Frame of the
   parent Region). */
   frm = astGetFrame( this->frameset, AST__BASE );
   if( frm ) {
      rep = astReporting( 0 );
      astSetAttrib( frm, bsetting ? bsetting : setting );
      if( astTestUnc( this ) ) {
         unc = astGetUncFrm( this, AST__BASE );
         astRegSetAttrib( unc, bsetting ? bsetting : setting, NULL );
         unc = astAnnul( unc );
      }
      if( astStatus == AST__BADAT ) astClearStatus;
      astReporting( rep );
   }
   frm = astAnnul( frm );

/* If required return the modified base Frame setting. Otherwise, free it. */
   if( base_setting ) {
      if( bsetting ) {
         *base_setting = bsetting;
      } else {
         *base_setting = astStore( NULL, setting, strlen( setting ) + 1 );
      }
   } else {
      bsetting = astFree( bsetting );
   }

/* Since the base Frame has been changed, any cached information calculated
   on the basis of the base Frame properties may no longer be up to date. */
   astResetCache( this );

/* Free resources. */
   setting = astFree( setting );

}

static AstMapping *RemoveRegions( AstMapping *this_mapping, int *status ) {
/*
*  Name:
*     RemoveRegions

*  Purpose:
*     Remove any Regions from a Mapping.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstMapping *RemoveRegions( AstMapping *this, int *status )

*  Class Membership:
*     Region method (over-rides the astRemoveRegions method inherited
*     from the Frame class).

*  Description:
*     This function searches the supplied Mapping (which may be a
*     compound Mapping such as a CmpMap) for any component Mappings
*     that are instances of the AST Region class. It then creates a new
*     Mapping from which all Regions have been removed. If a Region
*     cannot simply be removed (for instance, if it is a component of a
*     parallel CmpMap), then it is replaced with an equivalent UnitMap
*     in the returned Mapping.
*
*     The implementation provided by the Region class just returns the
*     equivalent Frame.

*  Parameters:
*     this
*        Pointer to the original Region.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer to the modified mapping.

*  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.
*/

/* The Region class just returns a pointer to a deep copy of the Region's
   equivalent Frame. */
   return astGetRegionFrame( (AstRegion *)this_mapping );
}

static void ReportPoints( AstMapping *this_mapping, int forward,
                          AstPointSet *in_points, AstPointSet *out_points, int *status ) {
/*
*  Name:
*     ReportPoints

*  Purpose:
*     Report the effect of transforming a set of points using a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void ReportPoints( AstMapping *this, int forward,
*                        AstPointSet *in_points, AstPointSet *out_points, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astReportPoints
*     method inherited from the Frame class).

*  Description:
*     This function reports the coordinates of a set of points before
*     and after being transformed by a Region, by writing them to
*     standard output.

*  Parameters:
*     this
*        Pointer to the Region.
*     forward
*        A non-zero value indicates that the Region's forward
*        coordinate transformation has been applied, while a zero
*        value indicates the inverse transformation.
*     in_points
*        Pointer to a PointSet which is associated with the
*        coordinates of a set of points before the Region was
*        applied.
*     out_points
*        Pointer to a PointSet which is associated with the
*        coordinates of the same set of points after the Region has
*        been applied.
*     status
*        Pointer to the inherited status variable.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_mapping;

/* Obtain a pointer to the Region's current Frame and invoke its
   astReportPoints method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astReportPoints( (AstMapping *) fr, forward, in_points, out_points );
   fr = astAnnul( fr );

}

static void ResetCache( AstRegion *this, int *status ){
/*
*+
*  Name:
*     astResetCache

*  Purpose:
*     Clear cached information within the supplied Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astResetCache( AstRegion *this )

*  Class Membership:
*     Region virtual function

*  Description:
*     This function clears cached information from the supplied Region
*     structure.

*  Parameters:
*     this
*        Pointer to the Region.
*-
*/
   if( this ) {
      if( this->basemesh ) this->basemesh = astAnnul( this->basemesh );
      if( this->basegrid ) this->basegrid = astAnnul( this->basegrid );
      if( this->negation ) this->negation = astAnnul( this->negation );
   }
}


static void Resolve( AstFrame *this_frame, const double point1[],
                     const double point2[], const double point3[],
                     double point4[], double *d1, double *d2, int *status ){
/*
*  Name:
*     Resolve

*  Purpose:
*     Resolve a vector into two orthogonal components

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void Resolve( AstFrame *this, const double point1[],
*                   const double point2[], const double point3[],
*                   double point4[], double *d1, double *d2, int *status );

*  Class Membership:
*     Region member function (over-rides the protected astResolve
*     method inherited from the Frame class).

*  Description:
*     This function resolves a vector into two perpendicular components.
*     The vector from point 1 to point 2 is used as the basis vector.
*     The vector from point 1 to point 3 is resolved into components
*     parallel and perpendicular to this basis vector. The lengths of the
*     two components are returned, together with the position of closest
*     aproach of the basis vector to point 3.

*  Parameters:
*     this
*        Pointer to the Frame.
*     point1
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). This marks the start of the basis vector,
*        and of the vector to be resolved.
*     point2
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). This marks the end of the basis vector.
*     point3
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). This marks the end of the vector to be
*        resolved.
*     point4
*        An array of double, with one element for each Frame axis
*        in which the coordinates of the point of closest approach of the
*        basis vector to point 3 will be returned.
*     d1
*        The address of a location at which to return the distance from
*        point 1 to point 4 (that is, the length of the component parallel
*        to the basis vector). Positive values are in the same sense as
*        movement from point 1 to point 2.
*     d2
*        The address of a location at which to return the distance from
*        point 4 to point 3 (that is, the length of the component
*        perpendicular to the basis vector). The value is always positive.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - Each vector used in this function is the path of
*     shortest distance between two points, as defined by the
*     astDistance function.
*     - This function will return "bad" coordinate values (AST__BAD)
*     if any of the input coordinates has this value, or if the required
*     output values are undefined.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke this
   Frame's astResolve method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astResolve( fr, point1, point2, point3, point4, d1, d2 );
   fr = astAnnul( fr );

}

static AstPointSet *ResolvePoints( AstFrame *this_frame, const double point1[],
                                   const double point2[], AstPointSet *in,
                                   AstPointSet *out, int *status ) {
/*
*  Name:
*     ResolvePoints

*  Purpose:
*     Resolve a set of vectors into orthogonal components

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *ResolvePoints( AstFrame *this, const double point1[],
*                                 const double point2[], AstPointSet *in,
*                                 AstPointSet *out )

*  Class Membership:
*     Region member function (over-rides the astResolvePoints method
*     inherited from the Frame class).

*  Description:
*     This function takes a Frame and a set of vectors encapsulated
*     in a PointSet, and resolves each one into two orthogonal components,
*     returning these two components in another PointSet.
*
*     This is exactly the same as the public astResolve method, except
*     that this method allows many vectors to be processed in a single call,
*     thus reducing the computational cost of overheads of many
*     individual calls to astResolve.

*  Parameters:
*     this
*        Pointer to the Frame.
*     point1
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). This marks the start of the basis vector,
*        and of the vectors to be resolved.
*     point2
*        An array of double, with one element for each Frame axis
*        (Naxes attribute). This marks the end of the basis vector.
*     in
*        Pointer to the PointSet holding the ends of the vectors to be
*        resolved.
*     out
*        Pointer to a PointSet which will hold the length of the two
*        resolved components. A NULL value may also be given, in which
*        case a new PointSet will be created by this function.

*  Returned Value:
*     Pointer to the output (possibly new) PointSet. The first axis will
*     hold the lengths of the vector components parallel to the basis vector.
*     These values will be signed (positive values are in the same sense as
*     movement from point 1 to point 2. The second axis will hold the lengths
*     of the vector components perpendicular to the basis vector. These
*     values will always be positive.

*  Notes:
*     - The number of coordinate values per point in the input
*     PointSet must match the number of axes in the supplied Frame.
*     - If an output PointSet is supplied, it must have space for
*     sufficient number of points and 2 coordinate values per point.
*     - 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: */
   AstPointSet *result;          /* Pointer to output PointSet */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke this
   Frame's astResolve method. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astResolvePoints( fr, point1, point2, in, out );
   fr = astAnnul( fr );

/* Return a pointer to the output PointSet. */
   return result;

}

static void SetAttrib( AstObject *this_object, const char *setting, int *status ) {
/*
*  Name:
*     SetAttrib

*  Purpose:
*     Set an attribute value for a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void SetAttrib( AstObject *this, const char *setting, int *status )

*  Class Membership:
*     Region member function (extends the astSetAttrib method
*     inherited from the Frame class).

*  Description:
*     This function assigns an attribute value for a Region, 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 Region.
*     setting
*        Pointer to a null terminated string specifying the new
*        attribute value.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - This protected method is intended to be invoked by the Object
*     astSet method and makes additional attributes accessible to it.
*/

/* Local Variables: */
   AstRegion *this;              /* Pointer to the Region structure */
   double dval;                  /* Floating point attribute value */
   int ival;                     /* Integer attribute value */
   int id;                       /* Offset of ID string */
   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 Region structure. */
   this = (AstRegion *) 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. */

/* We first handle attributes that apply to the Region as a whole
   (rather than to the encapsulated Frame). */

/* Negated */
/* ------- */
   if ( nc = 0,
        ( 1 == astSscanf( setting, "negated= %d %n", &ival, &nc ) )
          && ( nc >= len ) ) {
      astSetNegated( this, ival );

/* Closed */
/*------- */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "closed= %d %n", &ival, &nc ) )
          && ( nc >= len ) ) {
      astSetClosed( this, ival );

/* FillFactor */
/* ---------- */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "fillfactor= %lg %n", &dval, &nc ) )
        && ( nc >= len ) ) {
      astSetFillFactor( this, dval );

/* MeshSize */
/* -------- */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "meshsize= %d %n", &ival, &nc ) )
          && ( nc >= len ) ) {
      astSetMeshSize( this, ival );

/* Adaptive */
/* -------- */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "adaptive= %d %n", &ival, &nc ) )
          && ( nc >= len ) ) {
      astSetAdaptive( this, ival );

/* Now do attributes inherited from parent classes. We do these here to
   avoid the settings being passed on to the encapsulated FrameSet below. */

/* ID. */
/* --- */
   } else if ( nc = 0, ( 0 == astSscanf( setting, "id=%n%*[^\n]%n", &id, &nc ) )
                       && ( nc >= len ) ) {
      astSetID( this, setting + id );

/* Ident. */
/* ------ */
   } else if ( nc = 0, ( 0 == astSscanf( setting, "ident=%n%*[^\n]%n", &id, &nc ) )
                       && ( nc >= len ) ) {
      astSetIdent( this, setting + id );

/* Invert. */
/* ------- */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "invert= %d %n", &ival, &nc ) )
        && ( nc >= len ) ) {
      astSetInvert( this, ival );

/* Report. */
/* ------- */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "report= %d %n", &ival, &nc ) )
        && ( nc >= len ) ) {
      astSetReport( this, ival );

/* Define macros to see if the setting string matches any of the
   read-only attributes of this class. */
#define MATCH(attrib) \
        ( nc = 0, ( 0 == astSscanf( setting, attrib "=%*[^\n]%n", &nc ) ) && \
                  ( nc >= len ) )

#define AXISMATCH(attrib) \
        ( nc = 0, ( 0 == astSscanf( setting, attrib "(%*d)=%*[^\n]%n", &nc ) ) && \
                  ( nc >= len ) )

/* If the attribute was not recognised, use this macro to report an error
   if a read-only attribute has been specified. */
   } else if ( MATCH( "class" ) ||
               MATCH( "nin" ) ||
               MATCH( "nobject" ) ||
               MATCH( "bounded" ) ||
               MATCH( "nout" ) ||
               MATCH( "refcount" ) ||
               MATCH( "tranforward" ) ||
               MATCH( "traninverse" ) ) {
      astError( AST__NOWRT, "astSet: The setting \"%s\" is invalid for a %s.", status,
                setting, astGetClass( this ) );
      astError( AST__NOWRT, "This is a read-only attribute." , status);

/* Pass unrecognised attributes on to the Region's encapsulated FrameSet for
   further interpretation. Do not pass on FrameSet attributes since we
   pretend to the outside world that the encapsulated FrameSet is actually a
   Frame. */
   } else if ( !MATCH( "base" ) &&
               !MATCH( "current" ) &&
               !MATCH( "nframe" ) ) {

/* If the Region is to adapt to coordinate system chanmges, use the public
   astSet method so that the current Frame in the encapsulated FrameSet will
   be re-mapped if the attribute changes require it. */
      if( astGetAdaptive( this ) ) {
         astSet( this->frameset, setting, status );

/* If the Region is not to adapt to coordinate system chanmges, use the
   astRegSetAttrib method which assigns the attribute setting to both
   current and base Frames in the FrameSet without causing any remapping to
   be performed. */
      } else {
         astRegSetAttrib( this, setting, NULL );
      }
   }

/* Undefine macros local to this function. */
#undef MATCH
}

static void SetAxis( AstFrame *this_frame, int axis, AstAxis *newaxis, int *status ) {
/*
*  Name:
*     SetAxis

*  Purpose:
*     Set a new Axis for a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void SetAxis( AstFrame *this, int axis, AstAxis *newaxis, int *status )

*  Class Membership:
*     Region member function (over-rides the astSetAxis method
*     inherited from the Frame class).

*  Description:
*     This function allows a new Axis object to be associated with one
*     of the axes of the current Frame in a Region, replacing the
*     previous one. Each Axis object contains a description of the
*     quantity represented along one of the Frame's axes, so this
*     function allows this description to be exchanged for another
*     one.

*  Parameters:
*     this
*        Pointer to the Region.
*     axis
*        The index (zero-based) of the axis whose associated Axis
*        object is to be replaced.
*     newaxis
*        Pointer to the new Axis object.
*     status
*        Pointer to the inherited status variable.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index supplied. */
   (void) astValidateAxis( this, axis, 1, "astSetAxis" );

/* Obtain a pointer to the Region's current Frame and invoke this
   Frame's astSetAxis method to assign the new Axis object. Annul the
   Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astSetAxis( fr, axis, newaxis );
   fr = astAnnul( fr );
}

static void SetRegFS( AstRegion *this, AstFrame *frm, int *status ) {
/*
*+
*  Name:
*     astSetRegFS

*  Purpose:
*     Stores a new FrameSet in a Region

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     void astSetRegFS( AstRegion *this, AstFrame *frm )

*  Class Membership:
*     Region virtual function.

*  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.
*-
*/

/* Local Variables: */
   AstFrame *f1;         /* Copy of supplied Frame */
   AstFrame *f2;         /* Copy of supplied Frame */
   AstFrameSet *fs;      /* New FrameSet */
   AstRegion *unc;       /* Uncertainty Region */
   AstUnitMap *um;       /* UnitMap connecting base anc current Frames */

/* Check the global error status. */
   if ( !astOK ) return;

/* Take a copy of the supplied Frame. */
   f1 = astCopy( frm );

/* Create the new FrameSet. First take another copy of the supplied Frame
   so that modifications using the supplied pointer will not affect the new
   FrameSet. We create two copies (rather than 1) because the base and
   current Frames must be independant objects - otherwise attribute changes
   done to one will also appear in the other. Then construct the FrameSet
   containing the two Frame copies connected by a UnitMap. */
   f2 = astCopy( f1 );
   fs = astFrameSet( f1, "", status );
   um = astUnitMap( astGetNaxes( f1 ), "", status );
   astAddFrame( fs, AST__BASE, um, f2 );
   um = astAnnul( um );
   f2 = astAnnul( f2 );

/* Annul any existing FrameSet */
   if( this->frameset ) (void) astAnnul( this->frameset );

/* Use the new FrameSet */
   this->frameset = fs;

/* If any uncertainty Region has a zero value for its RegionFS attribute,
   it will currently contain a dummy FrameSet rather than the correct
   FrameSet. The correct FrameSet has copies of the base Frame of the new
   Region as both its current and base Frames, and these are connected by
   a UnitMap (this is equivalent to a FrameSet containing a single Frame). */
   if( astTestUnc( this ) ) {
      unc = astGetUncFrm( this, AST__BASE );
      if( unc && !astGetRegionFS( unc ) ) astSetRegFS( unc, f1 );
      unc = astAnnul( unc );
   }

/* Free remaining resourvces */
   f1 = astAnnul( f1 );

}

static void SetUnc( AstRegion *this, AstRegion *unc, int *status ){
/*
*++
*  Name:
c     astSetUnc
f     AST_SETUNC

*  Purpose:
*     Store uncertainty information in a Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     void astSetUnc( AstRegion *this, AstRegion *unc )
f     CALL AST_SETUNC( THIS, UNC, STATUS )

*  Class Membership:
*     Region method.

*  Description:
*     Each Region (of any class) can have an "uncertainty" which specifies
*     the uncertainties associated with the boundary of the Region. This
*     information is supplied in the form of a second Region. The uncertainty
*     in any point on the boundary of a Region is found by shifting the
*     associated "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.
*
*     The uncertainty is usually specified when the Region is created, but
*     this
c     function
f     routine
*     allows it to be changed at any time.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region which is to be assigned a new uncertainty.
c     unc
f     UNC = INTEGER (Given)
*        Pointer to the new uncertainty Region. This 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 Region
c        "this".
f        THIS.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*--
*/

/* Local Variables: */
   AstFrame *frm;           /* Current Frame from FrameSet */
   AstFrameSet *fs2;        /* FrameSet from "unc" current Frame to "this" base Frame */
   AstFrameSet *fs;         /* FrameSet in "this" supplied Region */
   AstMapping *map2;        /* Base->current Mapping from FrameSet */
   AstMapping *map;         /* Base->current Mapping from FrameSet */
   AstMapping *smap;        /* Simplified base->current Mapping */
   double *cen0;            /* Pointer to array holding original centre */
   double **ptr_reg;        /* Pointer to axis values for Region's Pointset */
   int changed;             /* Has the uncertainty been changed? */

/* Check the inherited status. */
   if( !astOK ) return;

/* Annul any existing uncertainty Region. */
   if( this->unc ) {
      this->unc = astIsAObject( this->unc ) ?
                                astAnnul( this->unc ) : NULL;
      changed = 1;
   } else {
      changed = 0;
   }

/* Check an uncertainty Region was supplied, and is of a usable class
   (i.e. a class which can be re-centred). */
   cen0 = unc ? astRegCentre( unc, NULL, NULL, 0, AST__CURRENT ) : NULL;
   if( cen0 ) {
      cen0 = astFree( cen0 );

/* Map it into the same Frame as that represented by the base Frame in
   the supplied Region. */
      fs = this->frameset;
      astInvert( fs );
      fs2 = Conv( unc->frameset, fs, status );
      astInvert( fs );

      if( fs2 ) {
         map = astGetMapping( fs2, AST__BASE, AST__CURRENT );
         frm = astGetFrame( fs2, AST__CURRENT );
         this->unc = astMapRegion( unc, map, frm );
         if( this->unc ) {

/* Ensure the Region is bounded. We know that negating an unbounded
   Region will make it bounded because we know that the Region consists of
   Circles, Boxes and/or Ellipses, all of which have this property. */
            if( !astGetBounded( this->unc ) ) astNegate( this->unc );

/* If the base Frame in the uncertainty Region is the same as the base
   Frame in the Region being dumped, then we do no need to include the
   FrameSet in the dump of the uncertainty Region. Since the current
   Frame in the uncertainty Region always corresponds to the base Frame of
   its parent Region, we only need to check if the base->current Mapping
   in the uncertainty Region's FrameSet is a UnitMap or not (after
   simplification). If it is, set the RegionFS attribute of the uncertainty
   Region to zero (i.e. false). This will cause the FrameSet to be omitted
   from the Dump. */
            map2 = astGetMapping( this->unc->frameset, AST__BASE, AST__CURRENT );
            smap = astSimplify( map2 );
            if( astIsAUnitMap( smap ) ) astSetRegionFS( this->unc, 0 );

/* Re-centre the uncertainty Region at the first position in the PointSet
   associated with the Region structure (if any). */
            if( this->points ) {
               ptr_reg = astGetPoints( this->points );
               astRegCentre( this->unc, NULL, ptr_reg, 0, AST__CURRENT );
            }

/* Set a flag indicating that the uncertainty in the Region has changed. */
            changed = 1;

/* Free resources */
            map2 = astAnnul( map2 );
            smap = astAnnul( smap );
         }
         frm = astAnnul( frm );
         fs2 = astAnnul( fs2 );
         map = astAnnul( map );

/* Report error if conversion between Frames is not possible. */
      } else if( astOK ) {
         astError( AST__BADIN, "astSetUnc(%s): Bad %d dimensional "
                   "uncertainty Frame (%s %s) supplied.", status, astGetClass(this),
                   astGetNaxes(unc), astGetDomain(unc), astGetTitle(unc) );
         astError( AST__NCPIN, "Cannot convert it to the Frame of the "
                   "new %s.", status, astGetClass( this ) );
      }

/* Report an error if it is not of a usable class. */
   } else if( unc && astOK ){
      astError( AST__BADIN, "astSetUnc(%s): Bad uncertainty shape "
                "(%s) supplied.", status, astGetClass( this ), astGetClass(unc) );
      astError( AST__NCPIN, "The uncertainty Region must be an instance of "
                "a centro-symetric subclass of Region (e.g. Box, Circle, "
                "Ellipse, etc)." , status);
   }

/* If the uncertainty in the Region has changed, indicate that any cached
   information in the Region is now out of date. */
   if( changed ) astResetCache( this );

}

static void ShowMesh( AstRegion *this, int format, const char *ttl, int *status ){
/*
*++
*  Name:
c     astShowMesh
f     AST_SHOWMESH

*  Purpose:
*     Display a mesh of points covering the surface of a Region.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     void astShowMesh( AstRegion *this, int format, const char *ttl )
f     CALL AST_SHOWMESH( THIS, FORMAT, TTL, STATUS )

*  Class Membership:
*     Region method.

*  Description:
c     This function
f     This routine
*     writes a table to standard output containing the axis values at a
*     mesh of points covering the surface of the supplied Region. Each row
*     of output contains a tab-separated list of axis values, one for
*     each axis in the Frame encapsulated by the Region. The number of
*     points in the mesh is determined by the MeshSize attribute.
*
*     The table is preceded by a given title string, and followed by a
*     single line containing the word "ENDMESH".

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
c     format
f     FORMAT = LOGICAL (Given)
*        A boolean value indicating if the displayed axis values should
*        be formatted according to the Format attribute associated with
*        the Frame's axis. Otherwise, they are displayed as simple
*        floating point values.
c     ttl
f     TTL = CHARACTER * ( * ) (Given)
*        A title to display before displaying the first position.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*--
*/

/* Local Variables: */
   AstPointSet *ps;           /* PointSet holding mesh */
   char *buffer = NULL;       /* Buffer for line output text */
   char buf[ 40 ];            /* Buffer for floating poitn value */
   double **ptr;              /* Pointers to the mesh data */
   int i;                     /* Axis index */
   int j;                     /* Position index */
   int nax;                   /* Number of axes */
   int nc;                    /* Number of characters in buffer */
   int np;                    /* Number of axis values per position */

/* Check the inherited status. */
   if( !astOK ) return;

/* Get a PointSet holding the mesh */
   ps = astRegMesh( this );
   if( ps ) {

/* Get the number of axis values per position, and the number of positions. */
      nax = astGetNcoord( ps );
      np = astGetNpoint( ps );

/* Get a pointer to the mesh data, and check it can be used. */
      ptr = astGetPoints( ps );
      if( ptr ) {

/* Display the title. */
         if( ttl ) printf( "\n%s\n\n", ttl );

/* Loop round all positions. */
         for( j = 0; j < np; j++ ) {

/* Reset the current buffer length to zero. */
            nc = 0;

/* Loop round all axes */
            for( i = 0; i < nax; i++ ){

/* If the axis value is bad, append "<bad> in the end of the output buffer. */
               if( ptr[ i ][ j ] == AST__BAD ){
                  buffer = astAppendString( buffer, &nc, "<bad>" );

/* Otherwise, if required, append the formatted value to the end of the
   buffer. */
               } else if( format ){
                  buffer = astAppendString( buffer, &nc,
                                         astFormat( this, i, ptr[ i ][ j ] ) );

/* Otherwise, append the floating point value to the end of the buffer. */
               } else {
                  sprintf( buf, "%g", ptr[ i ][ j ] );
                  buffer = astAppendString( buffer, &nc, buf );
               }
/* Add a separating tab to the end of the buffer. */
               buffer = astAppendString( buffer, &nc, "\t" );
            }

/* Display the line buffer. */
            printf( "%s\n", buffer );
         }
      }

/* Print out a marker for th eend of the list. */
      printf( "ENDMESH\n\n" );

/* Release resources. */
      ps = astAnnul( ps );
      buffer = astFree( buffer );
   }
}

static AstMapping *Simplify( AstMapping *this_mapping, int *status ) {
/*
*  Name:
*     Simplify

*  Purpose:
*     Simplify the Mapping represented by a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstMapping *Simplify( AstMapping *this, int *status )

*  Class Membership:
*     Region method (over-rides the astSimplify method inherited
*     from the Frame class).

*  Description:
*     This function simplifies the encapsulated FrameSet and any
*     uncertainty Region in the supplied Region. This is different to
*     the Simplify method in the parent Frame class which always returns
*     a UnitMap.

*  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:
*     - This implementation just simplifies the encapsulated FrameSet
*     and uncertainty Region. Sub-classes should usually provide their own
*     implementation which invokes this implemetation, and then continues to
*     check for further simplifications (such as fitting a new region to the
*     current Frame).
*     - 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 *bfrm;               /* Pointer to "this" baseFrame */
   AstFrameSet *fs;              /* Pointer to encapsulated FrameSet */
   AstMapping *map;              /* Base->current Mapping for "this" */
   AstMapping *result;           /* Result pointer to return */
   AstPointSet *pset1;           /* Base Frame centre position */
   AstPointSet *pset2;           /* Current Frame centre position */
   AstRegion *new;               /* Pointer to simplified Region */
   AstRegion *sunc;              /* Simplified uncertainty Region */
   AstRegion *this;              /* Pointer to original Region structure */
   AstRegion *unc;               /* Original uncertainty Region */
   double **ptr1;                /* Pointer to axis values in "pset1" */
   double *cen;                  /* Original centre of uncertainty Region */
   double *lbnd;                 /* Lower bounds of "this" bounding box */
   double *orig_cen;             /* Original centre for uncertainty Region */
   double *s1_lbnd;              /* Lower bounds of "unc" when centred at lbnd */
   double *s1_ubnd;              /* Upper bounds of "unc" when centred at lbnd */
   double *s2_lbnd;              /* Lower bounds of "unc" when centred at ubnd */
   double *s2_ubnd;              /* Upper bounds of "unc" when centred at ubnd */
   double *ubnd;                 /* Upper bounds of "this" bounding box */
   double delta;                 /* Half width of test box */
   double w1;                    /* Width of "s1" bounding box */
   double w2;                    /* Width of "s2" bounding box */
   int ic;                       /* Axis index */
   int naxb;                     /* No. of base Frame axes in "this" */
   int nin;                      /* Number of base Frame axes in "this" */
   int nout;                     /* Number of current Frame axes in "this" */
   int ok;                       /* Can we use the simplified uncertainty? */
   int simpler;                  /* Has some simplication taken place? */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_mapping;

/* Take a deep copy of the supplied Region. This is so that the returned
   pointer will have a diferent value to the supplied pointer if any
   simplication takes place. */
   new = astCopy( this );

/* Simplify the encapsulated FrameSet, and note if any simplification took
   place. */
   fs = astSimplify( new->frameset );
   simpler = ( fs != new->frameset );

/* If so, annull the existing FrameSet and use the simpler FrameSet. */
   if( simpler ) {
      (void) astAnnul( new->frameset );
      new->frameset = astClone( fs );
   }
   fs = astAnnul( fs );

/* If the Region has default uncertainty, we simplify the uncertainty
   Region simply by deleting it. It will be regenerated when needed,
   using the simplified Region. */
   if( new->defunc ) new->defunc = astAnnul( new->defunc );

/* If the Region's uncertainty was supplied explicitly, try simplifying
   the unncertainty Region. */
   if( astTestUnc( new ) ){

/* Obtain the Region's uncertainty. */
      unc = astGetUncFrm( new, AST__BASE );

/* Get the base->current Mapping from "this". */
      map = astGetMapping( this->frameset, AST__BASE, AST__CURRENT );

/* If it has different numbers of inputs and outputs (e.g. a PermMap used
   to take a slice through a Region), we need to ensure that the
   uncertainty Region is centred on the slice. */
      nin = astGetNin( map );
      nout = astGetNout( map );
      if( nin != nout ) {

/* Get the current centre of the uncertainty Region in its current Frame
   (the same as the base Frame of "this"). */
         cen = astRegCentre( unc, NULL, NULL, 0, AST__CURRENT );

/* Store it in a PointSet so it can be transformed. */
         pset1 = astPointSet( 1, nin, "", status );
         ptr1 = astGetPoints( pset1 );
         if( astOK ) for( ic = 0; ic < nin; ic++ ) ptr1[ ic ][ 0 ] = cen[ ic ];

/* Transform into the curent Frame of "this", and then back into the base
   Frame. */
         pset2 = astTransform( map, pset1, 1, NULL );
         (void) astTransform( map, pset2, 0, pset1 );

/* Re-centre the uncertainty Region at this position. */
         astRegCentre( unc, NULL, ptr1, 0, AST__CURRENT );

/* Free resources. */
         cen = astFree( cen );
         pset1 = astAnnul( pset1 );
         pset2 = astAnnul( pset2 );
      }

/* Free resources. */
      map = astAnnul( map );

/* Try simplifying the uncertainty. Only proceed if the uncertainty can
   be simplified. */
      sunc = astSimplify( unc );
      if( sunc != unc ) {

/* If the uncertainty can be simplified it means that the base->current
   Mapping in the uncertainty Region is sufficiently linear to allow the
   uncertainty shape to retain its form when transformed from the base to
   the current Frane. But this has only been tested at the current centre
   position in the uncertainty Region. The uncertainty Region should
   describe the whole of "this" Region, and so we need to check that the
   simplified uncertainty does not change as we move it around within "this"
   Region. To do this, we re-centre the uncertainty region at opposite
   corners of a large test box, and then we find the bounding box of the
   re-centred uncertainty Region. If this uncertainty bounding box changes
   from corner to corner of the test box, then we do not simplify the
   uncertainty Region. If "this" is bounded, we use the bounding box of
   "this" as the test box. Otherwise we use a box 100 times the size of the
   uncertainty Region. */

/* Note the original base Frame centre of the simplified uncertainty Region. */
         orig_cen = astRegCentre( sunc, NULL, NULL, 0, AST__BASE );

/* Allocate memory to hold the bounds of the test box. */
         naxb = astGetNin( this->frameset );
         lbnd = astMalloc( sizeof( double )*(size_t)naxb );
         ubnd = astMalloc( sizeof( double )*(size_t)naxb );

/* If possible, get the base Frame bounding box of "this" and use it as
   the test box. */
         if( astGetBounded( this ) ) {
            astRegBaseBox( this, lbnd, ubnd );

/* Otherwise, store the bounds of a box which is 100 times the size of
   the uncertainty region, centred on the current centre of the uncertainty
   region (we know all uncertainty regions are bounded). */
         } else {
            astGetRegionBounds( sunc, lbnd, ubnd );
            for( ic = 0; ic < naxb; ic++ ) {
               delta = 0.5*fabs( ubnd[ ic ] - lbnd[ ic ] );
               lbnd[ ic ] = orig_cen[ ic ] - delta;
               ubnd[ ic ] = orig_cen[ ic ] + delta;
            }
         }

/* Re-centre it at the lower bounds of the test box. This is in the base Frame
   of "this" which is the same as the current Frame of "sunc". */
         astRegCentre( sunc, lbnd, NULL, 0, AST__CURRENT );

/* Get the bounding box of the re-centred uncertainty Region, within its
   current Frame, which is the same as the base Frame of "this". */
         s1_lbnd = astMalloc( sizeof( double )*(size_t)naxb );
         s1_ubnd = astMalloc( sizeof( double )*(size_t)naxb );
         astGetRegionBounds( sunc, s1_lbnd, s1_ubnd );

/* Now re-centre the uncertainty Region at the upper bounds of the test
   box. */
         astRegCentre( sunc, ubnd, NULL, 0, AST__CURRENT );

/* Get the bounding box of the re-centred uncertainty Region. */
         s2_lbnd = astMalloc( sizeof( double )*(size_t)naxb );
         s2_ubnd = astMalloc( sizeof( double )*(size_t)naxb );
         astGetRegionBounds( sunc, s2_lbnd, s2_ubnd );

/* Get a pointer to the base Frame of "this". */
         bfrm = astGetFrame( this->frameset, AST__BASE );

/* The "ok" flag is initialised to indicate that the simplified uncertainty
   Region should not be used. */
         ok = 0;

/* Check pointers can be referenced safely */
         if( astOK ) {

/* Now indicate that the simplified uncertainty Region should be used. */
            ok = 1;

/* Loop round all axes of the base Frame of "this". */
            for( ic = 0; ic < naxb; ic++ ) {

/* Get the width of the two bounding boxes on this axis. */
               w1 = s1_ubnd[ ic ] - s1_lbnd[ ic ];
               w2 = s2_ubnd[ ic ] - s2_lbnd[ ic ];

/* If these differ by more than 0.1% then we determine that the simplified
   uncertainty Region varies in size across the bounding box of "this", and
   so we do not use the simplified uncertainty Region. The figure of 0.1%
   is arbitrary. */
               if( fabs( w1 - w2 ) > 0.005*( fabs( w1 ) + fabs( w2 ) ) ) {
                  ok = 0;
                  break;
               }
            }
         }

/* Reinstate the original base Frame centre of the simplified uncertainty Region. */
         astRegCentre( sunc, orig_cen, NULL, 0, AST__BASE );

/* Free resources. */
         orig_cen = astFree( orig_cen );
         lbnd = astFree( lbnd );
         ubnd = astFree( ubnd );
         s1_lbnd = astFree( s1_lbnd );
         s1_ubnd = astFree( s1_ubnd );
         s2_lbnd = astFree( s2_lbnd );
         s2_ubnd = astFree( s2_ubnd );
         bfrm = astAnnul( bfrm );

/* If we can use the simplified uncertainty Region, indicate that we have
   performed some simplification, and store the new uncertainty Region. */
         if( ok ) {
            simpler = 1;
            astSetUnc( new, sunc );
         }
      }

/* Free resources */
      unc = astAnnul( unc );
      sunc = astAnnul( sunc );
   }

/* If any simplification could be performed, return the new Region.
   Otherwise, return a clone of the supplied pointer. */
   if( simpler ){
      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 int SubFrame( AstFrame *this_frame, AstFrame *template,
                     int result_naxes,
                     const int *target_axes, const int *template_axes,
                     AstMapping **map, AstFrame **result, int *status ) {
/*
*  Name:
*     SubFrame

*  Purpose:
*     Select axes from a Region and convert to the new coordinate system.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int SubFrame( AstFrame *target, AstFrame *template, int result_naxes,
*                   const int *target_axes, const int *template_axes,
*                   AstMapping **map, AstFrame **result, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astSubFrame
*     method inherited from the Frame class).

*  Description:
*     This function selects a requested sub-set (or super-set) of the
*     axes from the current Frame of a "target" Region and creates a
*     new Frame with copies of the selected axes assembled in the
*     requested order. It then optionally overlays the attributes of a
*     "template" Frame on to the result. It returns both the resulting
*     Frame and a Mapping that describes how to convert between the
*     coordinate systems described by the current Frame of the target
*     Region and the result Frame. If necessary, this Mapping takes
*     account of any differences in the Frames' attributes due to the
*     influence of the template.

*  Parameters:
*     target
*        Pointer to the target Region, from whose current Frame the
*        axes are to be selected.
*     template
*        Pointer to the template Frame, from which new attributes for
*        the result Frame are to be obtained. Optionally, this may be
*        NULL, in which case no overlaying of template attributes will
*        be performed.
*     result_naxes
*        Number of axes to be selected from the target Region. This
*        number may be greater than or less than the number of axes in
*        the Region's current Frame (or equal).
*     target_axes
*        Pointer to an array of int with result_naxes elements, giving
*        a list of the (zero-based) axis indices of the axes to be
*        selected from the current Frame of the target Region. The
*        order in which these are given determines the order in which
*        the axes appear in the result Frame. If any of the values in
*        this array is set to -1, the corresponding result axis will
*        not be derived from the target Region, but will be assigned
*        default attributes instead.
*     template_axes
*        Pointer to an array of int with result_naxes elements. This
*        should contain a list of the template axes (given as
*        zero-based axis indices) with which the axes of the result
*        Frame are to be associated. This array determines which axes
*        are used when overlaying axis-dependent attributes of the
*        template on to the result. If any element of this array is
*        set to -1, the corresponding result axis will not receive any
*        template attributes.
*
*        If the template argument is given as NULL, this array is not
*        used and a NULL pointer may also be supplied here.
*     map
*        Address of a location to receive a pointer to the returned
*        Mapping.  The forward transformation of this Mapping will
*        describe how to convert coordinates from the coordinate
*        system described by the current Frame of the target Region
*        to that described by the result Frame. The inverse
*        transformation will convert in the opposite direction.
*     result
*        Address of a location to receive a pointer to the result Frame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A non-zero value is returned if coordinate conversion is
*     possible between the current Frame of the target Region and
*     the result Frame. Otherwise zero is returned and *map and
*     *result are returned as NULL (but this will not in itself result
*     in an error condition). In general, coordinate conversion should
*     always be possible if no template Frame is supplied but may not
*     always be possible otherwise.

*  Notes:
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to Region's current Frame */
   int match;                    /* Result to be returned */

/* Initialise. */
   *map = NULL;
   *result = NULL;
   match = 0;

/* Check the global error status. */
   if ( !astOK ) return match;

/* Invoke the parent astSubFrame method on the Frame represented by the
   region. */
   fr = astGetFrame( ((AstRegion *) this_frame)->frameset, AST__CURRENT );
   match = astSubFrame( fr, template, result_naxes, target_axes, template_axes,
                        map, result );
   fr = astAnnul( fr );

/* Return the result. */
   return match;
}

static AstSystemType SystemCode( AstFrame *this_frame, const char *system, int *status ) {
/*
*  Name:
*     SystemCode

*  Purpose:
*     Convert a string into a coordinate system type code.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     AstSystemType SystemCode( AstFrame *this, const char *system, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astSystemCode
*     method inherited from the Frame class).

*  Description:
*     This function converts a string used for the external description of
*     a coordinate system into a Frame coordinate system type code (System
*     attribute value). It is the inverse of the astSystemString function.

*  Parameters:
*     this
*        Pointer to the Frame.
*     system
*        Pointer to a constant null-terminated string containing the
*        external description of the coordinate system.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The System type code.

*  Notes:
*     - A value of AST__BADSYSTEM is returned if the coordinate system
*     description was not recognised. This does not produce an error.
*     - A value of AST__BADSYSTEM is also returned if this function
*     is invoked with the global error status set or if it should fail
*     for any reason.
*/

/* Local Variables: */
   AstSystemType result;      /* Result value to return */
   AstFrame *fr;              /* Pointer to FrameSet's current Frame */
   AstRegion *this;           /* Pointer to the Region structure */

/* Initialise. */
   result = AST__BADSYSTEM;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astSystemCode method for this Frame. Annul the Frame pointer afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astSystemCode( fr, system );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = AST__BADSYSTEM;

/* Return the result. */
   return result;
}

static const char *SystemString( AstFrame *this_frame, AstSystemType system, int *status ) {
/*
*  Name:
*     SystemString

*  Purpose:
*     Convert a coordinate system type code into a string.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     const char *SystemString( AstFrame *this, AstSystemType system, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astSystemString
*     method inherited from the Frame class).

*  Description:
*     This function converts a Frame coordinate system type code
*     (System attribute value) into a string suitable for use as an
*     external representation of the coordinate system type.

*  Parameters:
*     this
*        Pointer to the Frame.
*     system
*        The coordinate system type code.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to a constant null-terminated string containing the
*     textual equivalent of the type code supplied.

*  Notes:
*     - A NULL pointer value is returned if the coordinate system
*     code was not recognised. This does not produce an error.
*     - A NULL pointer value is also returned if this function is
*     invoked with the global error status set or if it should fail
*     for any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to FrameSet's current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   const char *result;           /* Pointer value to return */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astSystemString method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astSystemString( fr, system );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = NULL;

/* Return the result pointer. */
   return result;

}

static int RegTrace( AstRegion *this, int n, double *dist, double **ptr, int *status ){
/*
*+
*  Name:
*     astRegTrace

*  Purpose:
*     Return requested positions on the boundary of a 2D Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     int astRegTrace( AstRegion *this, int n, double *dist, double **ptr );

*  Class Membership:
*     Region virtual function

*  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 astRegTrace method is implemented by the class
*     of Region supplied, and zero if not.

*-
*/

/* Concrete sub-classes of Region must over-ride this method. */
   return 0;
}

static int TestAttrib( AstObject *this_object, const char *attrib, int *status ) {
/*
*  Name:
*     TestAttrib

*  Purpose:
*     Test if a specified attribute value is set for a Region.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int TestAttrib( AstObject *this, const char *attrib, int *status )

*  Class Membership:
*     Region member function (over-rides the astTestAttrib protected
*     method inherited from the Frame class).

*  Description:
*     This function returns a boolean result (0 or 1) to indicate whether
*     a value has been set for one of a Region's attributes.

*  Parameters:
*     this
*        Pointer to the Region.
*     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: */
   AstRegion *this;              /* Pointer to the Region structure */
   int result;                   /* Result value to return */

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_object;

/* Check the attribute name and test the appropriate attribute. */

/* We first handle attributes that apply to the Region as a whole
   (rather than to the encapsulated FrameSet). */

/* Negated. */
/* -------- */
   if ( !strcmp( attrib, "negated" ) ) {
      result = astTestNegated( this );

/* Closed. */
/* ------- */
   } else if ( !strcmp( attrib, "closed" ) ) {
      result = astTestClosed( this );

/* FillFactor */
/* ---------- */
   } else if ( !strcmp( attrib, "fillfactor" ) ) {
      result = astTestFillFactor( this );

/* MeshSize */
/* -------- */
   } else if ( !strcmp( attrib, "meshsize" ) ) {
      result = astTestMeshSize( this );

/* Adaptive */
/* -------- */
   } else if ( !strcmp( attrib, "adaptive" ) ) {
      result = astTestAdaptive( this );

/* Now do attributes inherited from parent classes. This is so that the
   attribute test will not be passed on to the encpasulated FrameSet below. */

/* ID. */
/* --- */
   } else if ( !strcmp( attrib, "id" ) ) {
      result = astTestID( this );

/* Ident. */
/* ------ */
   } else if ( !strcmp( attrib, "ident" ) ) {
      result = astTestIdent( this );

/* Invert. */
/* ------- */
   } else if ( !strcmp( attrib, "invert" ) ) {
      result = astTestInvert( this );

/* Report. */
/* ------- */
   } else if ( !strcmp( attrib, "report" ) ) {
      result = astTestReport( this );

/* If the name is not recognised, test if it matches any of the
   read-only attributes of this class. If it does, then return
   zero. */
   } else if ( !strcmp( attrib, "class" ) ||
               !strcmp( attrib, "nin" ) ||
               !strcmp( attrib, "nobject" ) ||
               !strcmp( attrib, "bounded" ) ||
               !strcmp( attrib, "nout" ) ||
               !strcmp( attrib, "refcount" ) ||
               !strcmp( attrib, "tranforward" ) ||
               !strcmp( attrib, "traninverse" ) ) {
      result = 0;

/* Pass unrecognised attributes on to the Region's encapsulated FrameSet for
   further interpretation. Do not pass on FrameSet attributes since we
   pretend to the outside world that the encapsulated FrameSet is actually a
   Frame. */
   } else if ( strcmp( attrib, "base" ) &&
               strcmp( attrib, "current" ) &&
               strcmp( attrib, "nframe" ) ) {
      result = astTestAttrib( this->frameset, attrib );
   }

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = 0;

/* Return the result, */
   return result;
}

double *astRegTranPoint_( AstRegion *this, double *in, int np, int forward, int *status ){
/*
*+
*  Name:
*     astRegTranPoint

*  Purpose:
*     Transform points between the base and current Frames in a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     double *astRegTranPoint( AstRegion *this, double *in, int np, int forward )

*  Class Membership:
*     Region member function

*  Description:
*     This function transforms one or more points between the base and
*     current Frames of the FrameSet encapsulated by the supplied Region.

*  Parameters:
*     this
*        The Region pointer.
*     in
*        Pointer to a 1-d array holding the axis values to be transformed.
*        If "forward" is non-zero, the number of axis values supplied for
*        each position should equal the number of axes in the base Frame
*        of the FrameSet encapsulated by "this". If "forward" is zero, the
*        number of axis values supplied for each position should equal the
*        number of axes in the current Frame of the FrameSet encapsulated by
*        "this". All the axis values for a position should be in adjacent
*        elements of the array.
*     np
*        The number of points supplied in "in".
*     forward
*        If non-zero, the supplied points are assumed to refer to the base
*        Frame of the encapsulated FrameSet, and they are transformed to the
*        current Frame. If zero, the supplied points are assumed to refer to
*        the current Frame of the encapsulated FrameSet, and they are
*        transformed to the base Frame.

*  Returned Value:
*     Pointer to a new dynamically allocated array holding the
*     transformed axis values. If "forward" is non-zero, the number of axis
*     values for each position will be equal the number of axes in the
*     current Frame of the FrameSet encapsulated by "this". If "forward" is
*     zero, the number of axis values for each position will be equal to the
*     number of axes in the base Frame of the FrameSet encapsulated by "this".
*     All the axis values for a position will be in adjacent elements of the
*     array. The array should be freed using astFree when 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: */
   AstMapping *map;
   AstPointSet *pset_in;
   AstPointSet *pset_out;
   double **ptr_in;
   double **ptr_out;
   double *p;
   double *result;
   int ic;
   int ip;
   int naxin;
   int naxout;

/* Initialise */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get a pointer to the required Mapping. */
   if( forward ) {
      map = astGetMapping( this->frameset, AST__BASE, AST__CURRENT );
   } else {
      map = astGetMapping( this->frameset, AST__CURRENT, AST__BASE );
   }

/* Get the number of axis values per input and per output point. */
   naxin = astGetNin( map );
   naxout = astGetNout( map );

/* Create a pointSet holding the supplied axis values. */
   pset_in = astPointSet( np, naxin, "", status );

/* Get pointers to the memory used to store axis values within this
   PointSet. */
   ptr_in = astGetPoints( pset_in );

/* Allocate the output array. */
   result = astMalloc( sizeof( double )*(size_t)( naxout*np ) );

/* Check the pointers can be used. */
   if( astOK ) {

/* Store the supplied axis values in the PointSet memory. */
      p = in;
      for( ip = 0; ip < np; ip++ ) {
         for( ic = 0; ic < naxin; ic++ ) ptr_in[ ic ][ ip ] = *(p++);
      }

/* Transform the PointSet. */
      pset_out = astTransform( map, pset_in, 1, NULL );

/* Get a pointer to the memory in the transformed PointSet. */
      ptr_out = astGetPoints( pset_out );

      if( pset_out && astStatus == AST__INTER ) {
         p = in;
         for( ip = 0; ip < np; ip++ ) {
            for( ic = 0; ic < naxin; ic++ ) printf("%.*g\n", AST__DBL_DIG, *(p++) );
         }
      }

      if( astOK ) {

/* Store the resulting axis values in the output array. */
         p = result;
         for( ip = 0; ip < np; ip++ ) {
            for( ic = 0; ic < naxout; ic++ ) *(p++) = ptr_out[ ic ][ ip ];
         }
      }

/* Free resources. */
      pset_out = astAnnul( pset_out );
   }
   pset_in = astAnnul( pset_in );
   map = astAnnul( map );

/* Return NULL if anything went wrong. */
   if( !astOK ) result = astAnnul( result );

/* Return the result.*/
   return result;
}

static AstPointSet *RegTransform( AstRegion *this, AstPointSet *in,
                                  int forward, AstPointSet *out, AstFrame **frm, int *status ) {
/*
*+
*  Name:
*     astRegTransform

*  Purpose:
*     Transform a set of points using the encapsulated FrameSet.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstPointSet *astRegTransform( AstRegion *this, AstPointSet *in,
*                                   int forward, AstPointSet *out,
*                                   AstFrameSet **frm )

*  Class Membership:
*     Region virtual function

*  Description:
*     This function takes a Region and a set of points encapsulated
*     in a PointSet, and applies either the forward or inverse
*     coordinate transformation represented by the encapsulated FrameSet.
*     It also returned a pointer to either the current or base Frame in
*     the FrameSet.

*  Parameters:
*     this
*        Pointer to the Region.
*     in
*        Pointer to the PointSet holding the input coordinate data. If
*        NULL then the "points" PointSet within the supplied Region
*        ("this") is used.
*     forward
*        A non-zero value indicates that the forward coordinate transformation
*        (from base to current) should be applied, while a zero value requests
*        the inverse transformation (from current to base).
*     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.
*     frm
*        Location at which to return a pointer to a Frame. If "forward"
*        is non-zero, the current Frame in the encapsulated FrameSet will
*        be returned. Otherwise, the base Frame is returned. The returned
*        pointer should be annulled when no longer needed. May be NULL if
*        no pointer is needed.

*  Returned Value:
*     Pointer to the output (possibly new) PointSet. If "out" is NULL,
*     the returned pointer will be a clone of "in" if the Mapping is a
*     UnitMap. If "out" is not NULL, then the supplied "out" PointSet will
*     be used and returned.

*  Notes:
*     - An error will result if the Region supplied does not define
*     the requested coordinate transformation (either forward or
*     inverse).
*     - The number of coordinate values per point in the input
*     PointSet must match the number of input coordinates for the
*     Region being applied (or number of output coordinates if the
*     inverse transformation is requested).  This will be equal to the
*     number of axes in the Region's base Frame (or the current
*     Frame for the inverse transformation).
*     - If an output PointSet is supplied, it must have space for
*     sufficient number of points and coordinate values per point to
*     accommodate the result (e.g. the number of Region output
*     coordinates, or number of input coordinates if the inverse
*     transformation is requested). Any excess space will be ignored.
*     - 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: */
   AstMapping *smap;           /* Pointer to simplified Mapping */
   AstPointSet *result;        /* Pointer value to return */

/* Initialise */
   if( frm ) *frm = NULL;

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* If no input PointSet was provided, use the PointSet in the Region. */
   if( !in ) {
      if( this->points ) {
         in = this->points;
      } else {
         astError( AST__INTER, "astRegTransform(%s): No PointSet supplied "
                   "and the supplied %s has no PointSet (internal AST "
                   "programming error)", status, astGetClass( this ),astGetClass( this ) );
      }
   }

/* Get the simplified Mapping from base to current Frame. */
   smap = astRegMapping( this );

/* If it is a UnitMap, return a clone of the input PointSet unless an
   explicit output PointSet has been supplied. */
   if( astIsAUnitMap( smap ) && !out ) {
      result = astClone( in );

/* Otherwise use the Mapping to transform the supplied positions. */
   } else {
      result = astTransform( smap, in, forward, out );
   }

/* Return a pointer to the appropriate Frame. */
   if( frm ) *frm = astGetFrame( this->frameset, forward ? AST__CURRENT : AST__BASE );

/* Release resources. */
   smap = astAnnul( smap );

/* Return a pointer to the output PointSet. */
   return result;
}

static int Unformat( AstFrame *this_frame, int axis, const char *string,
                     double *value, int *status ) {
/*
*  Name:
*     Unformat

*  Purpose:
*     Read a formatted coordinate value for a Region axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int Unformat( AstFrame *this, int axis, const char *string,
*                   double *value, int *status )

*  Class Membership:
*     Region member function (over-rides the public astUnformat
*     method inherited from the Frame class).

*  Description:
*     This function reads a formatted coordinate value for a Region
*     axis (supplied as a string) and returns the equivalent numerical
*     value as a double. It also returns the number of characters read
*     from the string.

*  Parameters:
*     this
*        Pointer to the Region.
*     axis
*        The number of the Region axis for which the coordinate
*        value is to be read (axis numbering starts at zero for the
*        first axis).
*     string
*        Pointer to a constant null-terminated string containing the
*        formatted coordinate value.
*     value
*        Pointer to a double in which the coordinate value read will be
*        returned.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The number of characters read from the string to obtain the
*     coordinate value.

*  Notes:
*     - Any white space at the beginning of the string will be
*     skipped, as also will any trailing white space following the
*     coordinate value read. The function's return value will reflect
*     this.
*     - A function value of zero (and no coordinate value) will be
*     returned, without error, if the string supplied does not contain
*     a suitably formatted value.
*     - The string "<bad>" is recognised as a special case and will
*     generate the value AST__BAD, without error. The test for this
*     string is case-insensitive and permits embedded white space.
*     - A function result of zero will be returned and no coordinate
*     value will be returned via the "value" pointer if this function
*     is invoked with the global error status set, or if it should
*     fail for any reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   double coord;                 /* Coordinate value read */
   int nc;                       /* Number of characters read */

/* Initialise. */
   nc = 0;

/* Check the global error status. */
   if ( !astOK ) return nc;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astUnformat" );

/* Obtain a pointer to the Region's current Frame and invoke the
   astUnformat method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   nc = astUnformat( fr, axis, string, &coord );
   fr = astAnnul( fr );

/* If an error occurred, clear the number of characters read. */
   if ( !astOK ) {
      nc = 0;

/* Otherwise, if characters were read, return the coordinate value. */
   } else if ( nc ) {
      *value = coord;
   }

/* Return the number of characters read. */
   return nc;
}

static int ValidateAxis( AstFrame *this_frame, int axis, int fwd,
                         const char *method, int *status ) {
/*
*  Name:
*     ValidateAxis

*  Purpose:
*     Validate and permute a Region's axis index.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int ValidateAxis( AstFrame *this, int axis, int fwd, const char *method,
*                       int *status )

*  Class Membership:
*     Region member function (over-rides the protected
*     astValidateAxis method inherited from the Frame class).

*  Description:
*     This function checks the validity of an index (zero-based) which
*     is to be used to address one of the coordinate axes of the
*     current Frame in a Region. If the index is valid, it is
*     permuted using the axis permutation array associated with the
*     Region's current Frame and the (zero-based) permuted axis
*     index is returned.  This gives the index the axis had when the
*     Frame was first created. If the axis index supplied is not
*     valid, an error is reported and the global error status is set.

*  Parameters:
*     this
*        Pointer to the Region.
*     axis
*        The axis index (zero-based) to be checked. To be valid, it
*        must lie between zero and (naxes-1) inclusive, where "naxes"
*        is the number of coordinate axes associated with the
*        Region's current Frame.
*     fwd
*        If non-zero, the suppplied axis index is assumed to be an
*        "external" axis index, and the corresponding "internal" axis index
*        is returned as the function value. Otherwise, the suppplied axis
*        index is assumed to be an "internal" axis index, and the
*        corresponding "external" axis index is returned as the function
*        value.
*     method
*        Pointer to a constant null-terminated character string
*        containing the name of the method that invoked this function
*        to validate an axis index. This method name is used solely
*        for constructing error messages.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The permuted axis index - either "internal" or "external" as
*     specified by "fwd".

*  Notes:
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */
   int naxes;                    /* Number of Region axes */
   int result;                   /* Permuted axis index */

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_frame;

/* Determine the number of Region axes. */
   naxes = astGetNaxes( this );
   if ( astOK ) {

/* If the Region has no axes, report an error (convert to 1-based
   axis numbering for the benefit of the public interface). */
      if ( naxes == 0 ) {
         astError( AST__AXIIN, "%s(%s): Invalid attempt to use an axis index "
                   "(%d) for a %s which has no axes.", status, method,
                   astGetClass( this ), axis + 1, astGetClass( this ) );

/* Otherwise, check the axis index for validity and report an error if
   it is not valid (again, convert to 1-based axis numbering). */
      } else if ( ( axis < 0 ) || ( axis >= naxes ) ) {
         astError( AST__AXIIN, "%s(%s): Axis index (%d) invalid - it should "
                   "be in the range 1 to %d.", status, method, astGetClass( this ),
                   axis + 1, naxes );

/* If the axis index was valid, obtain a pointer to the Region's
   current Frame and invoke this Frame's astValidateAxis method to
   obtain the permuted axis index. Annul the Frame pointer
   afterwards. */
      } else {
         fr = astGetFrame( this->frameset, AST__CURRENT );
         result = astValidateAxis( fr, axis, fwd, "astValidateAxis" );
         fr = astAnnul( fr );
      }
   }

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = 0;

/* Return the result. */
   return result;
}

static void ValidateAxisSelection( AstFrame *this_frame, int naxes,
                                   const int *axes, const char *method, int *status ) {
/*
*  Name:
*     ValidateAxisSelection

*  Purpose:
*     Check that a set of axes selected from a Frame is valid.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     void ValidateAxisSelection( AstFrame *this, int naxes,
*                                 const int *axes, const char *method, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astValidateAxisSelection
*     method inherited from the Frame class).

*  Description:
*     This function checks the validity of an array of (zero-based)
*     axis indices that specify a set of axes to be selected from a
*     Frame. To be valid, no axis should be selected more than
*     once. In assessing this, any axis indices that do not refer to
*     valid Frame axes (e.g. are set to -1) are ignored.
*
*     If the axis selection is valid, this function returns without further
*     action. Otherwise, an error is reported and the global error status is
*     set.

*  Parameters:
*     this
*        Pointer to the Frame.
*     naxes
*        The number of axes to be selected (may be zero).
*     axes
*        Pointer to an array of int with naxes elements that contains the
*        (zero based) axis indices to be checked.
*     method
*        Pointer to a constant null-terminated character string
*        containing the name of the method that invoked this function
*        to validate an axis selection. This method name is used
*        solely for constructing error messages.
*     status
*        Pointer to the inherited status variable.
*/

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to current Frame */
   AstRegion *this;              /* Pointer to the Region structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke this
   Frame's astValidateAxisSelection method. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   astValidateAxisSelection( fr, naxes, axes, method );
   fr = astAnnul( fr );

}

static int ValidateSystem( AstFrame *this_frame, AstSystemType system, const char *method, int *status ) {
/*
*  Name:
*     ValidateSystem

*  Purpose:
*     Validate a value for a Frame's System attribute.

*  Type:
*     Private function.

*  Synopsis:
*     #include "region.h"
*     int ValidateSystem( AstFrame *this, AstSystemType system,
*                         const char *method, int *status )

*  Class Membership:
*     Region member function (over-rides the protected astValidateSystem
*     method inherited from the Frame class).

*  Description:
*     This function checks the validity of the supplied system value.
*     If the value is valid, it is returned unchanged. Otherwise, an
*     error is reported and a value of AST__BADSYSTEM is returned.

*  Parameters:
*     this
*        Pointer to the Frame.
*     system
*        The system value to be checked.
*     method
*        Pointer to a constant null-terminated character string
*        containing the name of the method that invoked this function
*        to validate an axis index. This method name is used solely
*        for constructing error messages.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The validated system value.

*  Notes:
*     - A value of AST_BADSYSTEM will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*-
*/

/* Local Variables: */
   AstSystemType result;      /* Validated system value */
   AstFrame *fr;              /* Pointer to FrameSet's current Frame */
   AstRegion *this;           /* Pointer to the Region structure */

/* Initialise. */
   result = AST__BADSYSTEM;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the FrameSet structure. */
   this = (AstRegion *) this_frame;

/* Obtain a pointer to the Region's encapsulated Frame and invoke the
   astValidateSystem method for this Frame. Annul the Frame pointer
   afterwards. */
   fr = astGetFrame( this->frameset, AST__CURRENT );
   result = astValidateSystem( this, system, method );
   fr = astAnnul( fr );

/* If an error occurred, clear the result value. */
   if ( !astOK ) result = AST__BADSYSTEM;

/* Return the result. */
   return result;
}

/* Region Attributes. */
/* -------------------- */

/*
*att++
*  Name:
*     Adaptive

*  Purpose:
*     Should the area adapt to changes in the coordinate system?

*  Type:
*     Public attribute.

*  Synopsis:
*     Integer (boolean).

*  Description:
*     The coordinate system represented by a Region may be changed by
*     assigning new values to attributes such as System, Unit, etc.
*     For instance, a Region representing an area on the sky in ICRS
*     coordinates may have its System attribute changed so that it
*     represents (say) Galactic coordinates instead of ICRS. This
*     attribute controls what happens when the coordinate system
*     represented by a Region is changed in this way.
*
*     If Adaptive is non-zero (the default), then the area represented by
*     the Region adapts to the new coordinate system. That is, the numerical
*     values which define the area represented by the Region are changed
*     by mapping them from the old coordinate system into the new coordinate
*     system. Thus the Region continues to represent the same physical
*     area.
*
*     If Adaptive is zero, then area represented by the Region does not adapt
*     to the new coordinate system. That is, the numerical values which
*     define the area represented by the Region are left unchanged. Thus
*     the physical area represented by the Region will usually change.
*
*     As an example, consider a Region describe a range of wavelength from
*     2000 Angstrom to 4000 Angstrom. If the Unit attribute for the Region
*     is changed from Angstrom to "nm" (nanometre), what happens depends
*     on the setting of Adaptive. If Adaptive is non-zero, the Mapping
*     from the old to the new coordinate system is found. In this case it
*     is a simple scaling by a factor of 0.1 (since 1 Angstrom is 0.1 nm).
*     This Mapping is then used to modify the numerical values within the
*     Region, changing 2000 to 200 and 4000 to 400. Thus the modified
*     region represents 200 nm to 400 nm, the same physical space as
*     the original 2000 Angstrom to 4000 Angstrom. However, if Adaptive
*     had been zero, then the numerical values would not have been changed,
*     resulting in the final Region representing 2000 nm to 4000 nm.
*
*     Setting Adaptive to zero can be necessary if you need to correct
*     inaccurate attribute settings in an existing Region. For instance,
*     when creating a Region you may not know what Epoch value to use, so
*     you would leave Epoch unset resulting in some default value being used.
*     If at some later point in the application, the correct Epoch value
*     is determined, you could assign the correct value to the Epoch
*     attribute. However, you would first need to set Adaptive temporarily
*     to zero, because otherwise the area represented by the Region would
*     be Mapped from the spurious default Epoch to the new correct Epoch,
*     which is not what is required.

*  Applicability:
*     Region
*        All Regions have this attribute.
*att--
*/

/* This is a boolean value (0 or 1) with a value of -INT_MAX when
   undefined but yielding a default of 1. */
astMAKE_CLEAR(Region,Adaptive,adaptive,-INT_MAX)
astMAKE_GET(Region,Adaptive,int,1,( ( this->adaptive == -INT_MAX ) ?
                                   1 : this->adaptive ))
astMAKE_SET(Region,Adaptive,int,adaptive,( value != 0 ))
astMAKE_TEST(Region,Adaptive,( this->adaptive != -INT_MAX ))

/*
*att++
*  Name:
*     Negated

*  Purpose:
*     Region negation flag.

*  Type:
*     Public attribute.

*  Synopsis:
*     Integer (boolean).

*  Description:
*     This attribute controls whether a Region represents the "inside" or
*     the "outside" of the area which was supplied when the Region was
*     created. If the attribute value is zero (the default), the Region
*     represents the inside of the original area. However, if it is non-zero,
*     it represents the outside of the original area. The value of this
*     attribute may be toggled using the
c     astNegate function.
f     AST_NEGATE routine.

*     Note, whether the boundary is considered to be inside the Region or
*     not is controlled by the Closed attribute. Changing the value of
*     the Negated attribute does not change the value of the Closed attribute.
*     Thus, if Region is closed, then the boundary of the Region will be
*     inside the Region, whatever the setting of the Negated attribute.

*  Applicability:
*     Region
*        All Regions have this attribute.
*att--
*/

/* This is a boolean value (0 or 1) with a value of -INT_MAX when
   undefined but yielding a default of zero. */
astMAKE_CLEAR(Region,Negated,negated,(astResetCache(this),-INT_MAX))
astMAKE_GET(Region,Negated,int,0,( ( this->negated == -INT_MAX ) ?
                                   0 : this->negated ))
astMAKE_SET(Region,Negated,int,negated,(astResetCache(this),( value != 0 )))
astMAKE_TEST(Region,Negated,( this->negated != -INT_MAX ))

/*
*att++
*  Name:
*     Bounded

*  Purpose:
*     Is the Region bounded?

*  Type:
*     Public attribute.

*  Synopsis:
*     Integer (boolean), read-only.

*  Description:
*     This is a read-only attribute indicating if the Region is bounded.
*     A Region is bounded if it is contained entirely within some
*     finite-size bounding box.

*  Applicability:
*     Region
*        All Regions have this attribute.
*att--
*/

/*
*att+
*  Name:
*     RegionFS

*  Purpose:
*     Should Region FrameSet be dumped?

*  Type:
*     Protected attribute.

*  Synopsis:
*     Integer (boolean).

*  Description:
*     This attribute indicates whether the FrameSet encapsulated by the
*     Region should be included in the dump produced by the Dump function.
*
*     If set to a non-zero value (the default), the FrameSet in the Region
*     will always be included in the dump as usual. If set to zero, the
*     FrameSet will only be included in the dump if the Mapping from base
*     to current Frame is not a UnitMap. If the base->current Mapping is
*     a UnitMap, the FrameSet is omitted from the dump. If the dump is
*     subsequently used to re-create the Region, the new Region will have a
*     default FrameSet containing a single default Frame with the appropriate
*     number of axes.
*
*     This facility is indended to reduce the size of textual dumps of
*     Regions in situations where the Frame to which the Region refers can
*     be implied by the context in which the Region is used. This is
*     often the case when a Region is encapsulated within another Region.
*     In such cases the current Frame of the encapsulated Region will
*     usually be equivalent to the base Frame of the parent Region
*     structure, and so can be re-instated (by calling the astSetRegFS
*     method) even if the FrameSet is omitted from the dump of the
*     encapsulated Region. Note if the base->current Mapping in the FrameSet
*     in the encapsulated Region is not a UnitMap, then we should always
*     dump the FrameSet regardless of the setting of RegionFS. This is because
*     the parent Region structure will not know how to convert the PointSet
*     stored in the encapsulated Region into its own base Frame if the
*     FrameSet is not available.

*  Applicability:
*     Region
*        All Regions have this attribute.
*att-
*/

/* This is a boolean value (0 or 1) with a value of -INT_MAX when
   undefined but yielding a default of one. */
astMAKE_CLEAR(Region,RegionFS,regionfs,-INT_MAX)
astMAKE_TEST(Region,RegionFS,( this->regionfs != -INT_MAX ))
astMAKE_SET(Region,RegionFS,int,regionfs,( value != 0 ))
astMAKE_GET(Region,RegionFS,int,1,( ( this->regionfs == -INT_MAX ) ?
                                   1 : this->regionfs ))

/*
*att++
*  Name:
*     FillFactor

*  Purpose:
*     Fraction of the Region which is of interest.

*  Type:
*     Public attribute.

*  Synopsis:
*     Floating point.

*  Description:
*     This attribute indicates the fraction of the Region which is of
*     interest. AST does not use this attribute internally for any purpose.
*     Typically, it could be used to indicate the fraction of the Region for
*     which data is available.
*
*     The supplied value must be in the range 0.0 to 1.0, and the default
*     value is 1.0 (except as noted below).

*  Applicability:
*     Region
*        All Regions have this attribute.
*     CmpRegion
*        The default FillFactor for a CmpRegion is the FillFactor of its
*        first component Region.
*     Prism
*        The default FillFactor for a Prism is the product of the
*        FillFactors of its two component Regions.
*     Stc
*        The default FillFactor for an Stc is the FillFactor of its
*        encapsulated Region.
*att--
*/

astMAKE_CLEAR(Region,FillFactor,fillfactor,AST__BAD)
astMAKE_GET(Region,FillFactor,double,1.0,( ( this->fillfactor == AST__BAD ) ?
                                        1.0 : this->fillfactor ))
astMAKE_TEST(Region,FillFactor,( this->fillfactor != AST__BAD ))
astMAKE_SET(Region,FillFactor,double,fillfactor,((value<0.0||value>1.0)?(
       astError(AST__ATSER,"astSetFillFactor(%s): Invalid value (%g) supplied "
                "for attribute FillFactor.", status,astGetClass(this),value),
       astError(AST__ATSER,"FillFactor values should be in the range 0.0 to 1.0", status),
       this->fillfactor):value))

/*
*att++
*  Name:
*     MeshSize

*  Purpose:
*     Number of points used to represent the boundary of a Region.

*  Type:
*     Public attribute.

*  Synopsis:
*     Integer.

*  Description:
*     This attribute controls how many points are used when creating a
*     mesh of points covering the boundary or volume of a Region. Such a
*     mesh is returned by the
c     astGetRegionMesh
f     AST_GETREGIONMESH
*     method. The boundary mesh is also used when testing for overlap
*     between two Regions: each point in the bomdary mesh of the first
*     Region is checked to see if it is inside or outside the second Region.
*     Thus, the reliability of the overlap check depends on the value assigned
*     to this attribute. If the value used is very low, it is possible for
*     overlaps to go unnoticed. High values produce more reliable results, but
*     can result in the overlap test being very slow. The default value is 200
*     for two dimensional Regions and 2000 for three or more dimensional
*     Regions (this attribute is not used for 1-dimensional regions since the
*     boundary of a simple 1-d Region can only ever have two points). A
*     value of five is used if the supplied value is less than five.

*  Applicability:
*     Region
*        All Regions have this attribute.
*     CmpRegion
*        The default MeshSize for a CmpRegion is the MeshSize of its
*        first component Region.
*     Moc
*        The MeshSize attribute is ignored when forming a mesh covering
*        the boundary of a Moc. Instead, the mesh will include a point
*        for the exterior corners of every HEALPix cell (at the order
*        specified by attribute MaxOrder) that touches the boundary. Note,
*        this applies only to meshes covering the boundary of the Moc -
*        the MeshSize attribute is used as normal when forming a mesh
*        covering the area of the Moc.
*     Stc
*        The default MeshSize for an Stc is the MeshSize of its
*        encapsulated Region.
*att--
*/
/* If the value of MeshSize is set or cleared, annul the PointSet used to
   cache a mesh of base Frame boundary points. This will force a new
   PointSet to be created next time it is needed. See function RegMesh. */
astMAKE_CLEAR(Region,MeshSize,meshsize,(astResetCache(this),-INT_MAX))
astMAKE_SET(Region,MeshSize,int,meshsize,(astResetCache(this),( value > 5 ? value : 5 )))
astMAKE_TEST(Region,MeshSize,( this->meshsize != -INT_MAX ))
astMAKE_GET(Region,MeshSize,int,0,( ( this->meshsize == -INT_MAX)?((astGetNaxes(this)==1)?2:((astGetNaxes(this)==2)?200:2000)): this->meshsize ))

/*
*att++
*  Name:
*     Closed

*  Purpose:
*     Should the boundary be considered to be inside the region?

*  Type:
*     Public attribute.

*  Synopsis:
*     Integer (boolean).

*  Description:
*     This attribute controls whether points on the boundary of a Region
*     are considered to be inside or outside the region. If the attribute
*     value is non-zero (the default), points on the boundary are considered
*     to be inside the region (that is, the Region is "closed"). However,
*     if the attribute value is zero, points on the bounary are considered
*     to be outside the region.

*  Applicability:
*     Region
*        All Regions have this attribute.
*     PointList
*        The value of the Closed attribute is ignored by PointList regions.
*        If the PointList region has not been negated, then it is always
*        assumed to be closed. If the PointList region has been negated, then
*        it is always assumed to be open. This is required since points
*        have zero volume and therefore consist entirely of boundary.
*     CmpRegion
*        The default Closed value for a CmpRegion is the Closed value of its
*        first component Region.
*     Stc
*        The default Closed value for an Stc is the Closed value of its
*        encapsulated Region.
*     Moc
*        The Moc class ignored this attribute, and the behaviour for
*        boundary points is undefined (i.e. they may be inside or
*        outside the Region, depending on the position being tested and
*        the nature of the Moc).
*att--
*/
/* This is a boolean value (0 or 1) with a value of -INT_MAX when
   undefined but yielding a default of 1. */
astMAKE_CLEAR(Region,Closed,closed,(astResetCache(this),-INT_MAX))
astMAKE_GET(Region,Closed,int,1,( ( this->closed == -INT_MAX ) ?
                                   1 : this->closed ))
astMAKE_SET(Region,Closed,int,closed,(astResetCache(this),( value != 0 )))
astMAKE_TEST(Region,Closed,( this->closed != -INT_MAX ))

/* Access to attributes of the encapsulated Frame. */
/* ----------------------------------------------- */
/* Use the macros defined at the start of this file to implement
   private member functions that give access to the attributes of the
   encapsulated Frame of a Region and its axes. These functions over-ride
   the attribute access methods inherited from the Frame class. */

/* Clear, Get, Set and Test axis-independent Frame attributes. */
MAKE_CLEAR(Digits)
MAKE_CLEAR(Domain)
MAKE_CLEAR(MatchEnd)
MAKE_CLEAR(MaxAxes)
MAKE_CLEAR(MinAxes)
MAKE_CLEAR(Permute)
MAKE_CLEAR(PreserveAxes)
MAKE_CLEAR(Title)

MAKE_GET(Digits,int)
MAKE_GET(Domain,const char *)
MAKE_GET(MatchEnd,int)
MAKE_GET(MaxAxes,int)
MAKE_GET(MinAxes,int)
MAKE_GET(Permute,int)
MAKE_GET(PreserveAxes,int)
MAKE_GET(Title,const char *)
MAKE_SET(Digits,int,I)
MAKE_SET(Domain,const char *,C)
MAKE_SET(MatchEnd,int,I)
MAKE_SET(MaxAxes,int,I)
MAKE_SET(MinAxes,int,I)
MAKE_SET(Permute,int,I)
MAKE_SET(PreserveAxes,int,I)
MAKE_SET(Title,const char *,C)
MAKE_TEST(Digits)
MAKE_TEST(Domain)
MAKE_TEST(MatchEnd)
MAKE_TEST(MaxAxes)
MAKE_TEST(MinAxes)
MAKE_TEST(Permute)
MAKE_TEST(PreserveAxes)
MAKE_TEST(Title)

MAKE_GET(ActiveUnit,int)
MAKE_SET(ActiveUnit,int,I)
MAKE_TEST(ActiveUnit)

MAKE_GET(System,AstSystemType)
MAKE_SET_SYSTEM(System)
MAKE_TEST(System)
MAKE_CLEAR(System)

MAKE_GET(AlignSystem,AstSystemType)
MAKE_SET_SYSTEM(AlignSystem)
MAKE_TEST(AlignSystem)
MAKE_CLEAR(AlignSystem)

MAKE_GET(Epoch,double)
MAKE_SET(Epoch,double,D)
MAKE_TEST(Epoch)
MAKE_CLEAR(Epoch)

MAKE_GET(ObsLon,double)
MAKE_SET(ObsLon,double,D)
MAKE_TEST(ObsLon)
MAKE_CLEAR(ObsLon)

MAKE_GET(ObsLat,double)
MAKE_SET(ObsLat,double,D)
MAKE_TEST(ObsLat)
MAKE_CLEAR(ObsLat)

MAKE_GET(ObsAlt,double)
MAKE_SET(ObsAlt,double,D)
MAKE_TEST(ObsAlt)
MAKE_CLEAR(ObsAlt)

/* Clear, Get, Set and Test axis-dependent Frame attributes. */
MAKE_CLEAR_AXIS(Direction)
MAKE_CLEAR_AXIS(Format)
MAKE_CLEAR_AXIS(Label)
MAKE_CLEAR_AXIS(Symbol)
MAKE_CLEAR_AXIS(Unit)
MAKE_GET_AXIS(Direction,int)
MAKE_GET_AXIS(Format,const char *)
MAKE_GET_AXIS(Label,const char *)
MAKE_GET_AXIS(Symbol,const char *)
MAKE_GET_AXIS(Unit,const char *)
MAKE_SET_AXIS(Direction,int,I)
MAKE_SET_AXIS(Format,const char *,C)
MAKE_SET_AXIS(Label,const char *,C)
MAKE_SET_AXIS(Symbol,const char *,C)
MAKE_SET_AXIS(Unit,const char *,C)
MAKE_TEST_AXIS(Direction)
MAKE_TEST_AXIS(Format)
MAKE_TEST_AXIS(Label)
MAKE_TEST_AXIS(Symbol)
MAKE_TEST_AXIS(Unit)

MAKE_GET_AXIS(Bottom,double)
MAKE_SET_AXIS(Bottom,double,D)
MAKE_TEST_AXIS(Bottom)
MAKE_CLEAR_AXIS(Bottom)

MAKE_GET_AXIS(Top,double)
MAKE_SET_AXIS(Top,double,D)
MAKE_TEST_AXIS(Top)
MAKE_CLEAR_AXIS(Top)

/* Copy constructor. */
/* ----------------- */
static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
/*
*  Name:
*     Copy

*  Purpose:
*     Copy constructor for Region objects.

*  Type:
*     Private function.

*  Synopsis:
*     void Copy( const AstObject *objin, AstObject *objout, int *status )

*  Description:
*     This function implements the copy constructor for Region objects.

*  Parameters:
*     objin
*        Pointer to the object to be copied.
*     objout
*        Pointer to the object being constructed.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     -  This constructor makes a deep copy.
*/

/* Local Variables: */
   AstRegion *in;                /* Pointer to input Region */
   AstRegion *out;               /* Pointer to output Region */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain pointers to the input and output Regions. */
   in = (AstRegion *) objin;
   out = (AstRegion *) objout;

/* For safety, first clear any references to the input memory from
   the output Region. */
   out->basemesh = NULL;
   out->basegrid = NULL;
   out->frameset = NULL;
   out->points = NULL;
   out->unc = NULL;
   out->negation = NULL;
   out->defunc = NULL;

/* Now copy each of the above structures. */
   out->frameset = astCopy( in->frameset );
   if( in->points ) out->points = astCopy( in->points );
   if( in->basemesh ) out->basemesh = astCopy( in->basemesh );
   if( in->basegrid ) out->basegrid = astCopy( in->basegrid );
   if( in->unc ) out->unc = astCopy( in->unc );
   if( in->negation ) out->negation = astCopy( in->negation );
   if( in->defunc ) out->defunc = astCopy( in->defunc );
}


/* Destructor. */
/* ----------- */
static void Delete( AstObject *obj, int *status ) {
/*
*  Name:
*     Delete

*  Purpose:
*     Destructor for Region objects.

*  Type:
*     Private function.

*  Synopsis:
*     void Delete( AstObject *obj, int *status )

*  Description:
*     This function implements the destructor for Region 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: */
   AstRegion *this;                 /* Pointer to Region */

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) obj;

/* Annul all resources. */
   this->frameset = astAnnul( this->frameset );
   if( this->points ) this->points = astAnnul( this->points );
   if( this->basemesh ) this->basemesh = astAnnul( this->basemesh );
   if( this->basegrid ) this->basegrid = astAnnul( this->basegrid );
   if( this->unc ) this->unc = astAnnul( this->unc );
   if( this->negation ) this->negation = astAnnul( this->negation );
   if( this->defunc ) this->defunc = astAnnul( this->defunc );
}

/* Dump function. */
/* -------------- */
static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
/*
*  Name:
*     Dump

*  Purpose:
*     Dump function for Region 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 Region class to an output Channel.

*  Parameters:
*     this
*        Pointer to the Region 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 Constants: */
#define KEY_LEN 50               /* Maximum length of a keyword */
#define COM_LEN 50               /* Maximum length of a comment */

/* Local Variables: */
   AstFrame *fr;                 /* Pointer to the current Frame */
   AstMapping *smap;             /* Base->current Mapping */
   AstRegion *this;              /* Pointer to the Region structure */
   AstRegion *unc;               /* Pointer to the uncertainty Region */
   double dval;                  /* Floating point attribute value */
   int ival;                     /* Integer attribute value */
   int set;                      /* Attribute value set? */
   int unit;                     /* Base->current is unitmap? */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the Region structure. */
   this = (AstRegion *) this_object;

/* Write out values representing the instance variables for the
   Region 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. */

/* Negated. */
/* -------- */
   set = TestNegated( this, status );
   ival = set ? GetNegated( this, status ) : astGetNegated( this );
   astWriteInt( channel, "Negate", (ival != 0), 0, ival,
                ival ? "Region negated" : "Region not negated" );

/* FillFactor */
/* ---------- */
   set = TestFillFactor( this, status );
   dval = set ? GetFillFactor( this, status ) : astGetFillFactor( this );
   astWriteDouble( channel, "Fill", set, 0, dval,"Region fill factor" );

/* MeshSize. */
/* --------- */
   set = TestMeshSize( this, status );
   ival = set ? GetMeshSize( this, status ) : astGetMeshSize( this );
   astWriteInt( channel, "MeshSz", set, 0, ival,
                "No. of points used to represent boundary" );

/* Closed. */
/* ------- */
   set = TestClosed( this, status );
   ival = set ? GetClosed( this, status ) : astGetClosed( this );
   astWriteInt( channel, "Closed", set, 0, ival,
                ival ? "Boundary is inside" : "Boundary is outside" );

/* Adaptive */
/* -------- */
   set = TestAdaptive( this, status );
   ival = set ? GetAdaptive( this, status ) : astGetAdaptive( this );
   astWriteInt( channel, "Adapt", (ival != 0), 0, ival,
                ival ? "Region adapts to coord sys changes" : "Region does not adapt to coord sys changes" );

/* FrameSet */
/* -------- */

/* If the vertices are the same in both base and current Frames (i.e.
   if the Frames are connected by a UnitMap), then just dump the current
   Frame (unless the RegionFS attribute is zero, in which case the
   current Frame can be determined from the higher level context of the
   Region and so does not need to be dumped- e.g. if the Region is contained
   within another Region the parent Region will define the current Frame).
   Otherwise, dump the whole FrameSet. */
   ival = astGetRegionFS( this );
   smap = astRegMapping( this );
   if( ( unit = astIsAUnitMap( smap ) ) ){
      set = 0;
      if( ival ) {
         fr = astGetFrame( this->frameset, AST__CURRENT );
         astWriteObject( channel, "Frm", 1, 1, fr, "Coordinate system" );
         fr = astAnnul( fr );
      }
   } else {
      set = ( ival == 0 );
      astWriteObject( channel, "FrmSet", 1, 1, this->frameset,
                      "Original & current coordinate systems" );
   }

/* Annul the Mapping pointers */
   smap = astAnnul( smap );

/* RegionFS */
/* -------- */
   astWriteInt( channel, "RegFS", set, 0, ival,
                ival ? "Include Frame in dump" : "Do not include Frame in dump" );

/* Points */
/* ------ */
   if( this->points ) {
      astWriteObject( channel, "Points", 1, 1, this->points,
                      "Points defining the shape" );

/* If the FrameSet was not included in the dump, then the loader will use
   the PointSet to determine the number of axes in the frame spanned by
   the Region. If there is no PointSet, then we must explicitly include
   an item giving the number of axes.*/
   } else {
      astWriteInt( channel, "RegAxes", 1, 1, astGetNaxes( this ),
                   "Number of axes spanned by the Region" );
   }

/* Uncertainty */
/* ----------- */
/* Only dump the uncertinaty Region if required. */
   if( astTestUnc( this ) ) {
      unc = astGetUncFrm( this, AST__BASE );
      astWriteObject( channel, "Unc", 1, 1, unc,
                      "Region defining positional uncertainties." );
      unc = astAnnul( unc );
   }

/* Undefine macros local to this function. */
#undef KEY_LEN
}


/* Standard class functions. */
/* ========================= */
/* Implement the astIsARegion and astCheckRegion functions using
   the macros defined for this purpose in the "object.h" header
   file. */
astMAKE_ISA(Region,Frame)
astMAKE_CHECK(Region)

AstRegion *astInitRegion_( void *mem, size_t size, int init,
                           AstRegionVtab *vtab, const char *name,
                           AstFrame *frame, AstPointSet *pset,
                           AstRegion *unc, int *status ){
/*
*+
*  Name:
*     astInitRegion

*  Purpose:
*     Initialise a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstRegion *astInitRegion( void *mem, size_t size, int init,
*                               AstRegionVtab *vtab, const char *name,
*                               AstFrame *frame, AstpointSet *pset,
*                               AstRegion *unc )

*  Class Membership:
*     Region initialiser.

*  Description:
*     This function is provided for use by class implementations to
*     initialise a new Region object. It allocates memory (if
*     necessary) to accommodate the Region plus any additional data
*     associated with the derived class.  It then initialises a
*     Region 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 Region at the start of the memory passed
*     via the "vtab" parameter.

*  Parameters:
*     mem
*        A pointer to the memory in which the Region is to be
*        created. This must be of sufficient size to accommodate the
*        Region data (sizeof(Region)) 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 Region (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 Region structure, so a valid value must be
*        supplied even if not required for allocating memory.
*     init
*        A logical flag indicating if the Region'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 Region.
*     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
*        Pointer to the encapsulated Frame. A deep copy of this Frame is
*        taken. This means that subsequent changes to the supplied Frame
*        will have no effect on the new Region.
*     pset
*        A PointSet holding the points which define the Region. These
*        positions should refer to the given Frame. May be NULL.
*     unc
*        A pointer to a Region which specifies the uncertainty in the
*        supplied positions (all points on the boundary of the new Region
*        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 Region's bounding box are used.
*        If an uncertainty Region is supplied, it 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.
*        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 in 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 Region.

*  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: */
   AstFrame *f0;                  /* Frame to use */
   AstRegion *new;                /* Pointer to new Region */
   int nax;                       /* No. of axes in supplied Frame */
   int ncoord;                    /* Coords per point */

/* Check the global status. */
   if ( !astOK ) return NULL;

/* If necessary, initialise the virtual function table. */
   if( init ) astInitRegionVtab( vtab, name );

/* Note the number of axes in the supplied Frame. */
   nax = astGetNaxes( frame );

/* Check the pointset if supplied. */
   if( pset ) {

/* Note the number of axes per point in the supplied PointSet */
      ncoord = astGetNcoord( pset );

/* If OK, check that the number of coordinates per point matches the number
   of axes in the Frame. Report an error if these numbers do not match. */
      if ( astOK && ( ncoord != nax ) ) {
         astError( AST__NCPIN, "astInitRegion(%s): Bad number of coordinate "
                   "values per point (%d).", status, name, ncoord );
         astError( AST__NCPIN, "The %s given requires %d coordinate value(s) "
                   "for each point.", status, astGetClass( frame ), nax );
      }
   }

/* Initialise a Frame structure (the parent class) as the first
   component within the Region structure, allocating memory if
   necessary. Give this Frame zero axes as the Frame information will be
   specified by the encapsulated FrameSet. */
   new = (AstRegion *) astInitFrame( mem, size, 0, (AstFrameVtab *) vtab,
                                     name, 0 );
   if ( astOK ) {

/* Initialise the Region data. */
/* ----------------------------- */
      new->frameset = NULL;
      new->points = NULL;
      new->unc = NULL;
      new->meshsize = -INT_MAX;
      new->adaptive = -INT_MAX;
      new->basemesh = NULL;
      new->basegrid = NULL;
      new->negated = -INT_MAX;
      new->closed = -INT_MAX;
      new->regionfs = -INT_MAX;
      new->fillfactor = AST__BAD;
      new->defunc = NULL;
      new->nomap = 0;
      new->negation = NULL;

/* If the supplied Frame is a Region, gets its encapsulated Frame. If a
   FrameSet was supplied, use its current Frame, otherwise use the
   supplied Frame. */
      if( astIsARegion( frame ) ) {
         f0 = astGetFrame( ((AstRegion *) frame)->frameset, AST__CURRENT );

      } else if( astIsAFrameSet( frame ) ) {
         f0 = astGetFrame( (AstFrameSet *) frame, AST__CURRENT );

      } else {
         f0 = astClone( frame );
      }

/* Store a clone of the supplied PointSet pointer. */
      new->points = pset ? astClone( pset ) : NULL;


#ifdef DEBUG
      if( pset ) {
         double **ptr;
         double lim;
         int ii,jj, np;
         ptr = astGetPoints( pset );
         np = astGetNpoint( pset );
         lim = sqrt( DBL_MAX );
         for( ii = 0; astOK && ii < ncoord; ii++ ) {
            for( jj = 0; jj < np; jj++ ) {
               if( fabs( ptr[ ii ][ jj ] ) > lim ) {
                  if( !strcmp( name, "Interval" ) ) {
                     if( ptr[ ii ][ jj ] != AST__BAD &&
                         ptr[ ii ][ jj ] != DBL_MAX &&
                         ptr[ ii ][ jj ] != -DBL_MAX ) {
                        astError( AST__INTER, "astInitRegion(%s): suspicious "
                          "axis value (%g) supplied.", status, name, ptr[ ii ][ jj ] );
                        break;
                     }
                  } else {
                     astError( AST__INTER, "astInitRegion(%s): suspicious "
                            "axis value (%g) supplied.", status, name,
                            ptr[ ii ][ jj ] );
                     break;
                  }
               }
            }
         }
      }
#endif

/* Form a FrameSet consisting of two copies of the supplied Frame connected
   together by a UnitMap, and store in the Region structure. We use the
   private SetRegFS rather than the protected astSetRegFS because this
   initialiser may be being called from a subclass which over-rides
   astSetRegFS. If this were the case, then the implementation of
   astSetRegFS provided by the subclass may access information within the
   subclass structure which has not yet been initialised. */
      SetRegFS( new, f0, status );
      f0 = astAnnul( f0 );

/* Store any uncertainty Region. Use the private SetUnc rather than
   astSetUnc to avoid subclass implementations using subclass data which
   has not yet been initialised. */
      SetUnc( new, unc, status );

/* If an error occurred, clean up by deleting the new object. */
      if ( !astOK ) new = astDelete( new );
   }

/* Return a pointer to the new object. */
   return new;
}

AstRegion *astLoadRegion_( void *mem, size_t size,
                           AstRegionVtab *vtab, const char *name,
                           AstChannel *channel, int *status ) {
/*
*+
*  Name:
*     astLoadRegion

*  Purpose:
*     Load a Region.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "region.h"
*     AstRegion *astLoadRegion( void *mem, size_t size,
*                               AstRegionVtab *vtab, const char *name,
*                               AstChannel *channel )

*  Class Membership:
*     Region loader.

*  Description:
*     This function is provided to load a new Region 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
*     Region structure in this memory, using data read from the
*     input Channel.

*  Parameters:
*     mem
*        A pointer to the memory into which the Region is to be
*        loaded.  This must be of sufficient size to accommodate the
*        Region data (sizeof(Region)) 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 Region (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 Region 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(AstRegion) is used instead.
*     vtab
*        Pointer to the start of the virtual function table to be
*        associated with the new Region. If this is NULL, a pointer
*        to the (static) virtual function table for the Region 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 "Region" is used instead.

*  Returned Value:
*     A pointer to the new Region.

*  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 Constants: */
   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
#define KEY_LEN 50               /* Maximum length of a keyword */

/* Local Variables: */
   AstFrame *f1;                  /* Base Frame for encapsulated FrameSet */
   AstRegion *new;                /* Pointer to the new Region */
   int nax;                       /* No. of axes in Frame, or FrameSet base Frame */
   int naxpt;                     /* No. of axes in per point */

/* Get a pointer to the thread specific global data structure. */
   astGET_GLOBALS(channel);

/* Initialise. */
   new = NULL;

/* Check the global error status. */
   if ( !astOK ) return new;

/* If a NULL virtual function table has been supplied, then this is
   the first loader to be invoked for this Region. In this case the
   Region belongs to this class, so supply appropriate values to be
   passed to the parent class loader (and its parent, etc.). */
   if ( !vtab ) {
      size = sizeof( AstRegion );
      vtab = &class_vtab;
      name = "Region";

/* If required, initialise the virtual function table for this class. */
      if ( !class_init ) {
         astInitRegionVtab( 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 Region. */
   new = astLoadFrame( mem, size, (AstFrameVtab *) 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, "Region" );

/* 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. */

/* Negated */
/* ------- */
      new->negated = astReadInt( channel, "negate", -INT_MAX );
      if ( TestNegated( new, status ) ) SetNegated( new, new->negated, status );

/* FillFactor */
/* ---------- */
      new->fillfactor = astReadDouble( channel, "fill", AST__BAD );
      if ( TestFillFactor( new, status ) ) SetFillFactor( new, new->fillfactor, status );

/* MeshSize */
/* -------- */
      new->meshsize = astReadInt( channel, "meshsz", -INT_MAX );
      if ( TestMeshSize( new, status ) ) SetMeshSize( new, new->meshsize, status );

/* Closed */
/* ------ */
      new->closed = astReadInt( channel, "closed", -INT_MAX );
      if ( TestClosed( new, status ) ) SetClosed( new, new->closed, status );

/* Adaptive */
/* -------- */
      new->adaptive = astReadInt( channel, "adapt", -INT_MAX );
      if ( TestAdaptive( new, status ) ) SetAdaptive( new, new->adaptive, status );

/* Points */
/* ------ */
      new->points = astReadObject( channel, "points", NULL );

/* If some points were found, ensure that they are in a PointSet and get
   the number of axis values per point. */
      if( new->points ){
         if( astIsAPointSet( new->points) ) {
            naxpt = astGetNcoord( new->points );
         } else {
            naxpt = 0;
            astError( AST__REGIN, "astLoadRegion(%s): Corrupt %s specifies points "
                      "using a %s (should be a PointSet).", status, astGetClass( new ),
                      astGetClass( new ), astGetClass( new->points ) );
         }

/* If no PointSet was loaded, attempt to determine the number of axes
   spanned by the Region by reading the RegAxes value. */
      } else {
         naxpt = astReadInt( channel, "regaxes", 0 );
      }

/* Uncertainty */
/* ----------- */
      new->unc = astReadObject( channel, "unc", NULL );
      new->defunc = NULL;

/* FrameSet */
/* -------- */
/* First see if the dump contains a single Frame. If so, create a
   FrameSet from it and a copy of itself, using a UnitMap to connect the
   two. */
      new->nomap = 0;
      new->frameset = NULL;
      f1 = astReadObject( channel, "frm", NULL );
      if( f1 ) {
         new->regionfs = 1;
         nax = astGetNaxes( f1 );
         astSetRegFS( new, f1 );
         f1 = astAnnul( f1 );

/* If no Frame was found in the dump, look for a FrameSet. Get the number
   of axes spanning its base Frame ("Nin"). */
      } else {
         new->frameset = astReadObject( channel, "frmset", NULL );
         if( new->frameset ) {
            nax = astGetNin( new->frameset );

/* If a FrameSet was found, the value of the RegionFS attribute is still
   unknown and so we must read it from an attribute as normal. */
            new->regionfs = astReadInt( channel, "regfs", 1 );
            if ( TestRegionFS( new, status ) ) SetRegionFS( new, new->regionfs, status );

         } else {
            nax = 0;
         }
      }

/* If neither a Frame nor a FrameSet was found, create a default FrameSet
   and set the RegionFS attribute false, to indicate that the FrameSet
   should not be used. */
      if( !new->frameset ){
         nax = naxpt ? naxpt : 1;
         f1 = astFrame( nax, "", status );
         new->frameset = astFrameSet( f1, "", status );
         astSetIdent( new->frameset, DUMMY_FS );
         f1 = astAnnul( f1 );
         new->regionfs = 0;
      }

/* Report an error if the number of axis values per point in the pointset is
   incorrect. */
      if ( astOK && new->points && ( naxpt != nax ) ) {
         astError( AST__REGIN, "astLoadRegion(%s): Corrupt %s contains "
                   " incorrect number of coordinate values per point (%d).", status,
                   astGetClass( new ), astGetClass( new ), naxpt );
         astError( AST__REGIN, "The %s requires %d coordinate value(s) "
                   "for each point.", status, astGetClass( new ), nax );
      }

/* Initialise other fields which are used as caches for values derived
   from the attributes set above. */
      new->basemesh = NULL;
      new->basegrid = NULL;

/* If an error occurred, clean up by deleting the new Region. */
      if ( !astOK ) new = astDelete( new );
   }

/* Return the new Region pointer. */
   return new;

/* Undefine macros local to this function. */
#undef KEY_LEN
}

/* Virtual function interfaces. */
/* ============================ */
/* These provide the external interface to the virtual functions defined by
   this class. Each simply checks the global error status and then locates and
   executes the appropriate member function, using the function pointer stored
   in the object's virtual function table (this pointer is located using the
   astMEMBER macro defined in "object.h").

   Note that the member function may not be the one defined here, as it may
   have been over-ridden by a derived class. However, it should still have the
   same interface. */

void astRegClearAttrib_( AstRegion *this, const char *attrib, char **base_attrib, int *status ) {
   if ( !astOK ) return;
   (**astMEMBER(this,Region,RegClearAttrib))( this, attrib, base_attrib, status );
}
void astRegSetAttrib_( AstRegion *this, const char *setting, char **base_setting, int *status ) {
   if ( !astOK ) return;
   (**astMEMBER(this,Region,RegSetAttrib))( this, setting, base_setting, status );
}
void astNegate_( AstRegion *this, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,Negate))( this, status );
}
AstFrame *astGetRegionFrame_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,GetRegionFrame))( this, status );
}
AstFrameSet *astGetRegionFrameSet_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,GetRegionFrameSet))( this, status );
}
AstRegion *astMapRegion_( AstRegion *this, AstMapping *map, AstFrame *frame, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,MapRegion))( this, map, frame, status );
}
int astOverlap_( AstRegion *this, AstRegion *that, int *status ){
   if ( !astOK ) return 0;
   return (**astMEMBER(this,Region,Overlap))( this, that, status );
}
int astOverlapX_( AstRegion *that, AstRegion *this, int *status ){
   if ( !astOK ) return 0;
   return (**astMEMBER(that,Region,OverlapX))( that, this, status );
}
AstFrame *astRegFrame_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegFrame))( this, status );
}
AstRegion *astRegBasePick_( AstRegion *this, int naxes, const int *axes, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegBasePick))( this, naxes, axes, status );
}
AstPointSet *astBTransform_( AstRegion *this, AstPointSet *in,
                             int forward, AstPointSet *out, int *status ) {
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,BTransform))( this, in, forward, out, status );
}
AstPointSet *astRegTransform_( AstRegion *this, AstPointSet *in,
                               int forward, AstPointSet *out,
                               AstFrame **frm, int *status ) {
   if( frm ) *frm = NULL;
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegTransform))( this, in, forward, out, frm, status );
}
int astRegPins_( AstRegion *this, AstPointSet *pset, AstRegion *unc, int **mask, int *status ){
   if( mask ) *mask = NULL;
   if ( !astOK ) return 0;
   return (**astMEMBER(this,Region,RegPins))( this, pset, unc, mask, status );
}
AstMapping *astRegMapping_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegMapping))( this, status );
}
int astRegDummyFS_( AstRegion *this, int *status ){
   if ( !astOK ) return 0;
   return (**astMEMBER(this,Region,RegDummyFS))( this, status );
}
int astGetBounded_( AstRegion *this, int *status ){
   if ( !astOK ) return 0;
   return (**astMEMBER(this,Region,GetBounded))( this, status );
}
int astTestUnc_( AstRegion *this, int *status ){
   if ( !astOK ) return 0;
   return (**astMEMBER(this,Region,TestUnc))( this, status );
}
void astClearUnc_( AstRegion *this, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,ClearUnc))( this, status );
}
void astRegBaseBox_( AstRegion *this, double *lbnd, double *ubnd, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,RegBaseBox))( this, lbnd, ubnd, status );
}
void astRegBaseBox2_( AstRegion *this, double *lbnd, double *ubnd, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,RegBaseBox2))( this, lbnd, ubnd, status );
}
void astResetCache_( AstRegion *this, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,ResetCache))( this, status );
}
int astRegTrace_( AstRegion *this, int n, double *dist, double **ptr, int *status ){
   if ( !astOK ) return 0;
   return (**astMEMBER(this,Region,RegTrace))( this, n, dist, ptr, status );
}
void astGetRegionBounds_( AstRegion *this, double *lbnd, double *ubnd, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,GetRegionBounds))( this, lbnd, ubnd, status );
}
void astGetRegionMesh_( AstRegion *this, int surface, int maxpoint,
                        int maxcoord, int *npoint, double *points,
                        int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,GetRegionMesh))( this, surface, maxpoint, maxcoord,
                                             npoint, points, status );
}
void astGetRegionPoints_( AstRegion *this, int maxpoint, int maxcoord,
                          int *npoint, double *points, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,GetRegionPoints))( this, maxpoint, maxcoord,
                                               npoint, points, status );
}
void astGetRegionDisc_( AstRegion *this, double centre[2], double *radius, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,GetRegionDisc))( this, centre, radius, status );
}
void astShowMesh_( AstRegion *this, int format, const char *ttl, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,ShowMesh))( this, format,ttl, status );
}
void astGetRegionBounds2_( AstRegion *this, double *lbnd, double *ubnd, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,GetRegionBounds2))( this, lbnd, ubnd, status );
}
void astRegOverlay_( AstRegion *this, AstRegion *that, int unc, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,RegOverlay))( this, that, unc, status );
}
AstPointSet *astRegGrid_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegGrid))( this, status );
}
AstPointSet *astRegMesh_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegMesh))( this, status );
}
double *astRegCentre_( AstRegion *this, double *cen, double **ptr, int index,
                       int ifrm, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegCentre))( this, cen, ptr, index, ifrm, status );
}
AstRegion *astGetNegation_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,GetNegation))( this, status );
}
AstRegion *astGetUncFrm_( AstRegion *this, int ifrm, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,GetUncFrm))( this, ifrm, status );
}
AstRegion *astGetDefUnc_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,GetDefUnc))( this, status );
}
AstRegion *astGetUnc_( AstRegion *this, int def, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,GetUnc))( this, def, status );
}
void astSetUnc_( AstRegion *this, AstRegion *unc, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,SetUnc))( this, unc, status );
}
AstFrameSet *astGetRegFS_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,GetRegFS))( this, status );
}
void astSetRegFS_( AstRegion *this, AstFrame *frm, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,Region,SetRegFS))( this, frm, status );
}
AstPointSet *astRegBaseMesh_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegBaseMesh))( this, status );
}
AstRegion **astRegSplit_( AstRegion *this, int *nlist, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegSplit))( this, nlist, status );
}
AstPointSet *astRegBaseGrid_( AstRegion *this, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,RegBaseGrid))( this, status );
}
AstPointSet *astBndBaseMesh_( AstRegion *this, double *lbnd, double *ubnd, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,BndBaseMesh))( this, lbnd, ubnd, status );
}
AstPointSet *astBndMesh_( AstRegion *this, double *lbnd, double *ubnd, int *status ){
   if ( !astOK ) return NULL;
   return (**astMEMBER(this,Region,BndMesh))( this, lbnd, ubnd, status );
}

#define MAKE_MASK_(X,Xtype) \
int astMask##X##_( AstRegion *this, AstMapping *map, int inside, int ndim, \
                   const int lbnd[], const int ubnd[], Xtype in[], \
                   Xtype val, int *status ) { \
   if ( !astOK ) return 0; \
   return (**astMEMBER(this,Region,Mask##X))( this, map, inside, ndim, lbnd, \
                                              ubnd, in, val, status ); \
}
#if HAVE_LONG_DOUBLE     /* Not normally implemented */
MAKE_MASK_(LD,long double)
#endif
MAKE_MASK_(D,double)
MAKE_MASK_(F,float)
MAKE_MASK_(L,long int)
MAKE_MASK_(UL,unsigned long int)
MAKE_MASK_(I,int)
MAKE_MASK_(UI,unsigned int)
MAKE_MASK_(S,short int)
MAKE_MASK_(US,unsigned short int)
MAKE_MASK_(B,signed char)
MAKE_MASK_(UB,unsigned char)
#undef MAKE_MASK_

/* Special public interface functions. */
/* =================================== */
/* These provide the public interface to certain special functions
   whose public interface cannot be handled using macros (such as
   astINVOKE) alone. In general, they are named after the
   corresponding protected version of the function, but with "Id"
   appended to the name. */

/* Public 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. */

/* Special interface function implementations. */
/* ------------------------------------------- */


AstRegion *astMapRegionId_( AstRegion *this, AstMapping *map, AstFrame *frame, int *status ) {
/*
*++
*  Name:
c     astMapRegion
f     AST_MAPREGION

*  Purpose:
*     Transform a Region into a new Frame using a given Mapping.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "region.h"
c     AstRegion *astMapRegion( AstRegion *this, AstMapping *map,
c                              AstFrame *frame )
f     RESULT = AST_MAPREGION( THIS, MAP, FRAME, STATUS )

*  Class Membership:
*     Region method.

*  Description:
*     This function returns a pointer to a new Region which corresponds to
*     supplied Region described by some other specified coordinate system. A
*     Mapping is supplied which transforms positions between the old and new
*     coordinate systems. The new Region may not be of the same class as
*     the original region.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the Region.
c     map
f     MAP = INTEGER (Given)
*        Pointer to a Mapping which transforms positions from the
*        coordinate system represented by the supplied Region to the
*        coordinate system specified by
c        "frame".
f        FRAME.
*        The supplied Mapping should define both forward and inverse
*        transformations, and these transformations should form a genuine
*        inverse pair. That is, transforming a position using the forward
*        transformation and then using the inverse transformation should
*        produce the original input position. Some Mapping classes (such
*        as PermMap, MathMap, SphMap) can result in Mappings for which this
*        is not true.
c     frame
f     FRAME = INTEGER (Given)
*        Pointer to a Frame describing the coordinate system in which
*        the new Region is required.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astMapRegion()
f     AST_MAPREGION = INTEGER
*        A pointer to a new Region. This Region will represent the area
*        within the coordinate system specified by
c        "frame"
f        FRAME
*        which corresponds to the supplied Region.

*  Notes:
*     - The uncertainty associated with the supplied Region is modified
*     using the supplied Mapping.
*     - 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.
*--

*  Implementation Notes:
*     - The only difference between this public interface and the protected
*     astMapRegion interface is that this implementation additionally
*     simplifies the returned Region. The protected implementation does
*     not do this since doing so can lead to infinite recursion because
*     it is sometimes necessary for Simplify to call astMapRegion.

*/

/* Local Variables: */
   AstRegion *new;                /* Pointer to new Region */
   AstRegion *result;             /* Pointer value to return */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Invoke the protected astMapRegion function. */
   new = astMapRegion( this, map, frame );

/* Simplify the resulting Region. */
   result = astSimplify( new );

/* Free resources. */
   new = astAnnul( new );

/* If not OK, annul the returned pointer. */
   if( !astOK ) result = astAnnul( result );

/* Return the result. */
   return result;
}