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// Boost.Geometry (aka GGL, Generic Geometry Library)
// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
// Copyright (c) 2008-2012 Bruno Lalande, Paris, France.
// Copyright (c) 2009-2012 Mateusz Loskot, London, UK.
// Parts of Boost.Geometry are redesigned from Geodan's Geographic Library
// (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands.
// Use, modification and distribution is subject to the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_GEOMETRY_STRATEGIES_CARTESIAN_CENTROID_BASHEIN_DETMER_HPP
#define BOOST_GEOMETRY_STRATEGIES_CARTESIAN_CENTROID_BASHEIN_DETMER_HPP
#include <boost/mpl/if.hpp>
#include <boost/numeric/conversion/cast.hpp>
#include <boost/type_traits.hpp>
#include <boost/geometry/arithmetic/determinant.hpp>
#include <boost/geometry/core/coordinate_type.hpp>
#include <boost/geometry/core/point_type.hpp>
#include <boost/geometry/strategies/centroid.hpp>
#include <boost/geometry/util/select_coordinate_type.hpp>
namespace boost { namespace geometry
{
// Note: when calling the namespace "centroid", it sometimes,
// somehow, in gcc, gives compilation problems (confusion with function centroid).
namespace strategy { namespace centroid
{
/*!
\brief Centroid calculation using algorithm Bashein / Detmer
\ingroup strategies
\details Calculates centroid using triangulation method published by
Bashein / Detmer
\tparam Point point type of centroid to calculate
\tparam PointOfSegment point type of segments, defaults to Point
\tparam CalculationType \tparam_calculation
\author Adapted from "Centroid of a Polygon" by
Gerard Bashein and Paul R. Detmer<em>,
in "Graphics Gems IV", Academic Press, 1994</em>
\qbk{
[heading See also]
[link geometry.reference.algorithms.centroid.centroid_3_with_strategy centroid (with strategy)]
}
*/
/*
\par Research notes
The algorithm gives the same results as Oracle and PostGIS but
differs from MySQL
(tried 5.0.21 / 5.0.45 / 5.0.51a / 5.1.23).
Without holes:
- this: POINT(4.06923363095238 1.65055803571429)
- geolib: POINT(4.07254 1.66819)
- MySQL: POINT(3.6636363636364 1.6272727272727)'
- PostGIS: POINT(4.06923363095238 1.65055803571429)
- Oracle: 4.06923363095238 1.65055803571429
- SQL Server: POINT(4.06923362245959 1.65055804168294)
Statements:
- \b MySQL/PostGIS: select AsText(Centroid(GeomFromText(
'POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2,3.7 1.6,3.4 2,4.1 3,5.3 2.6
,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3))')))
- \b Oracle: select sdo_geom.sdo_centroid(sdo_geometry(2003, null, null,
sdo_elem_info_array(1, 1003, 1), sdo_ordinate_array(
2,1.3,2.4,1.7,2.8,1.8,3.4,1.2,3.7,1.6,3.4,2,4.1,3,5.3,2.6
,5.4,1.2,4.9,0.8,2.9,0.7,2,1.3))
, mdsys.sdo_dim_array(mdsys.sdo_dim_element('x',0,10,.00000005)
,mdsys.sdo_dim_element('y',0,10,.00000005)))
from dual
- \b SQL Server 2008: select geometry::STGeomFromText(
'POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2,3.7 1.6,3.4 2,4.1 3,5.3 2.6
,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3))',0)
.STCentroid()
.STAsText()
With holes:
- this: POINT(4.04663 1.6349)
- geolib: POINT(4.04675 1.65735)
- MySQL: POINT(3.6090580503834 1.607573932092)
- PostGIS: POINT(4.0466265060241 1.63489959839357)
- Oracle: 4.0466265060241 1.63489959839357
- SQL Server: POINT(4.0466264962959677 1.6348996057331333)
Statements:
- \b MySQL/PostGIS: select AsText(Centroid(GeomFromText(
'POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2
,3.7 1.6,3.4 2,4.1 3,5.3 2.6,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3)
,(4 2,4.2 1.4,4.8 1.9,4.4 2.2,4 2))')));
- \b Oracle: select sdo_geom.sdo_centroid(sdo_geometry(2003, null, null
, sdo_elem_info_array(1, 1003, 1, 25, 2003, 1)
, sdo_ordinate_array(2,1.3,2.4,1.7,2.8,1.8,3.4,1.2,3.7,1.6,3.4,
2,4.1,3,5.3,2.6,5.4,1.2,4.9,0.8,2.9,0.7,2,1.3,4,2, 4.2,1.4,
4.8,1.9, 4.4,2.2, 4,2))
, mdsys.sdo_dim_array(mdsys.sdo_dim_element('x',0,10,.00000005)
,mdsys.sdo_dim_element('y',0,10,.00000005)))
from dual
*/
template
<
typename Point,
typename PointOfSegment = Point,
typename CalculationType = void
>
class bashein_detmer
{
private :
// If user specified a calculation type, use that type,
// whatever it is and whatever the point-type(s) are.
// Else, use the most appropriate coordinate type
// of the two points, but at least double
typedef typename
boost::mpl::if_c
<
boost::is_void<CalculationType>::type::value,
typename select_most_precise
<
typename select_coordinate_type
<
Point,
PointOfSegment
>::type,
double
>::type,
CalculationType
>::type calculation_type;
/*! subclass to keep state */
class sums
{
friend class bashein_detmer;
int count;
calculation_type sum_a2;
calculation_type sum_x;
calculation_type sum_y;
public :
inline sums()
: count(0)
, sum_a2(calculation_type())
, sum_x(calculation_type())
, sum_y(calculation_type())
{}
};
public :
typedef sums state_type;
static inline void apply(PointOfSegment const& p1,
PointOfSegment const& p2, sums& state)
{
/* Algorithm:
For each segment:
begin
ai = x1 * y2 - x2 * y1;
sum_a2 += ai;
sum_x += ai * (x1 + x2);
sum_y += ai * (y1 + y2);
end
return POINT(sum_x / (3 * sum_a2), sum_y / (3 * sum_a2) )
*/
// Get coordinates and promote them to calculation_type
calculation_type const x1 = boost::numeric_cast<calculation_type>(get<0>(p1));
calculation_type const y1 = boost::numeric_cast<calculation_type>(get<1>(p1));
calculation_type const x2 = boost::numeric_cast<calculation_type>(get<0>(p2));
calculation_type const y2 = boost::numeric_cast<calculation_type>(get<1>(p2));
calculation_type const ai = geometry::detail::determinant<calculation_type>(p1, p2);
state.count++;
state.sum_a2 += ai;
state.sum_x += ai * (x1 + x2);
state.sum_y += ai * (y1 + y2);
}
static inline bool result(sums const& state, Point& centroid)
{
calculation_type const zero = calculation_type();
if (state.count > 0 && ! math::equals(state.sum_a2, zero))
{
calculation_type const v3 = 3;
calculation_type const a3 = v3 * state.sum_a2;
typedef typename geometry::coordinate_type
<
Point
>::type coordinate_type;
set<0>(centroid,
boost::numeric_cast<coordinate_type>(state.sum_x / a3));
set<1>(centroid,
boost::numeric_cast<coordinate_type>(state.sum_y / a3));
return true;
}
return false;
}
};
#ifndef DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
namespace services
{
// Register this strategy for rings and (multi)polygons, in two dimensions
template <typename Point, typename Geometry>
struct default_strategy<cartesian_tag, areal_tag, 2, Point, Geometry>
{
typedef bashein_detmer
<
Point,
typename point_type<Geometry>::type
> type;
};
} // namespace services
#endif // DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
}} // namespace strategy::centroid
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_STRATEGIES_CARTESIAN_CENTROID_BASHEIN_DETMER_HPP
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