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/usr/include/SFCGAL/algorithm/area.h is in libsfcgal-dev 1.2.2-1.

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/**
 *   SFCGAL
 *
 *   Copyright (C) 2012-2013 Oslandia <infos@oslandia.com>
 *   Copyright (C) 2012-2013 IGN (http://www.ign.fr)
 *
 *   This library is free software; you can redistribute it and/or
 *   modify it under the terms of the GNU Library General Public
 *   License as published by the Free Software Foundation; either
 *   version 2 of the License, or (at your option) any later version.
 *
 *   This library 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
 *   Library General Public License for more details.

 *   You should have received a copy of the GNU Library General Public
 *   License along with this library; if not, see <http://www.gnu.org/licenses/>.
 */

#ifndef _SFCGAL_ALGORITHM_AREA_H_
#define _SFCGAL_ALGORITHM_AREA_H_

#include <SFCGAL/Geometry.h>
#include <SFCGAL/Kernel.h>

namespace SFCGAL {
namespace algorithm {
struct NoValidityCheck;

/**
 * @brief Compute the 2D area for a Geometry
 * @ingroup public_api
 * @warning Z component is ignored, there is no 2D projection for 3D geometries
 * @ingroup public_api
 * @pre g is a valid geometry
 */
SFCGAL_API double     area( const Geometry& g ) ;

/**
 * @brief Compute the 2D area for a Geometry
 *
 * @warning Z component is ignored, there is no 2D projection for 3D geometries
 * @ingroup detail
 * @pre g is a valid geometry
 * @warning No actual validity check is done
 */
SFCGAL_API double     area( const Geometry& g, NoValidityCheck ) ;

/**
 * @brief Compute the 2D signed area for a Triangle
 * @ingroup detail
 */
SFCGAL_API Kernel::FT signedArea( const Triangle& g );
/**
 * @brief Compute the 2D signed area for a closed LineString
 * @ingroup detail
 */
SFCGAL_API Kernel::FT signedArea( const LineString& g );

/**
 * Returns Compute the 2D area for a Triangle
 * @ingroup detail
 */
SFCGAL_API double    area( const Triangle& g ) ;
/**
 * Returns Compute the 2D area for a Polygon
 * @ingroup detail
 */
SFCGAL_API double     area( const Polygon& g ) ;
/**
 * Returns the 2D area for a GeometryCollection
 * @ingroup detail
 */
SFCGAL_API double     area( const GeometryCollection& g ) ;
/**
 * Returns the 2D area for a TriangulatedSurface
 * @ingroup detail
 */
SFCGAL_API double     area( const TriangulatedSurface& g ) ;
/**
 * Returns the 2D area for a TriangulatedSurface
 * @ingroup detail
 */
SFCGAL_API double      area( const PolyhedralSurface& g ) ;


/**
 * Returns 3D area for a Geometry
 * @ingroup public_api
 * @warning Solid area is set to 0 (might be defined as the area of the surface)
 * @ingroup public_api
 * @pre g is a valid geometry
 */
SFCGAL_API double         area3D( const Geometry& g ) ;

/**
 * Returns 3D area for a Geometry
 *
 * @warning Solid area is set to 0 (might be defined as the area of the surface)
 * @ingroup detail
 * @pre g is a valid geometry
 * @warning No actual validity check is done
 */
SFCGAL_API double         area3D( const Geometry& g, NoValidityCheck ) ;

/**
 * Returns 3D area for a Polygon
 * @ingroup detail
 */
SFCGAL_API double         area3D( const Polygon& g ) ;
/**
 * Returns the 3D area for a MultiPolygon
 * @ingroup detail
 */
SFCGAL_API double         area3D( const GeometryCollection& g ) ;

/**
 * Returns the 3D area for a PolyhedralSurface
 * @ingroup detail
 */
SFCGAL_API double         area3D( const PolyhedralSurface& g ) ;

/**
 * Returns the 3D area for a Triangle
 * @ingroup detail
 */
SFCGAL_API double         area3D( const Triangle& g ) ;

/**
 * Returns the 3D area for a TriangulatedSurface
 * @ingroup detail
 */
SFCGAL_API double         area3D( const TriangulatedSurface& g ) ;



}//algorithm
}//SFCGAL


#endif