boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType > Class Template Reference

Area calculation by spherical excess / Huiller's formula. More...

#include <area_huiller.hpp>

Classes
struct	excess_sum

Public Types
typedef calculation_type	return_type
typedef PointOfSegment	segment_point_type
typedef excess_sum	state_type

Public Member Functions
	huiller (calculation_type radius=1.0)
void	apply (PointOfSegment const &p1, PointOfSegment const &p2, excess_sum &state) const
return_type	result (excess_sum const &state) const

Detailed Description

template<typename PointOfSegment, typename CalculationType = void>
class boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >

Area calculation by spherical excess / Huiller's formula.

Template Parameters

PointOfSegment	point type of segments of rings/polygons
CalculationType

Author

Barend Gehrels. Adapted from:

• http://www.soe.ucsc.edu/~pang/160/f98/Gems/GemsIV/sph_poly.c
• http://williams.best.vwh.net/avform.htm

Note

The version in Gems didn't account for polygons crossing the 180 meridian.

This version works for convex and non-convex polygons, for 180 meridian crossing polygons and for polygons with holes. However, some cases (especially 180 meridian cases) must still be checked.

The version which sums angles, which is often seen, doesn't handle non-convex polygons correctly.

The version which sums longitudes, see http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/40409/1/07-03.pdf, is simple and works well in most cases but not in 180 meridian crossing cases. This probably could be solved.

This version is made for spherical equatorial coordinate systems

{

[heading Example] [area_with_strategy] [area_with_strategy_output]

[heading See also] [link geometry.reference.algorithms.area.area_2_with_strategy area (with strategy)] }

Member Typedef Documentation

template<typename PointOfSegment , typename CalculationType = void>

typedef calculation_type boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::return_type

template<typename PointOfSegment , typename CalculationType = void>

typedef PointOfSegment boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::segment_point_type

template<typename PointOfSegment , typename CalculationType = void>

typedef excess_sum boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::state_type

Constructor & Destructor Documentation

template<typename PointOfSegment , typename CalculationType = void>

boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::huiller ( calculation_type  radius = 1.0 )

inline

Member Function Documentation

template<typename PointOfSegment , typename CalculationType = void>

void boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::apply ( PointOfSegment const &  p1, PointOfSegment const &  p2, excess_sum &  state  ) const

inline

References boost::a, boost::geometry::math::abs(), boost::math::ef::atan(), boost::asio::b, boost::multiprecision::backends::c, boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::excess_sum::distance_over_unit_sphere, boost::E, boost::geometry::math::equals(), boost::asio::s, boost::geometry::math::sqrt(), boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::excess_sum::sum, and boost::math::ef::tan().

template<typename PointOfSegment , typename CalculationType = void>

return_type boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::result ( excess_sum const &  state ) const

inline

References boost::geometry::strategy::area::huiller< PointOfSegment, CalculationType >::excess_sum::area().

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The documentation for this class was generated from the following file:

• boost_1_57_0/boost/geometry/strategies/spherical/area_huiller.hpp