[ceph.git] / ceph / src / boost / boost / geometry / util / normalize_spheroidal_coordinates.hpp

// Boost.Geometry (aka GGL, Generic Geometry Library)

// Copyright (c) 2017 Adam Wulkiewicz, Lodz, Poland.

// Copyright (c) 2015-2017, Oracle and/or its affiliates.

// Contributed and/or modified by Menelaos Karavelas, on behalf of Oracle
// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle

// Licensed under the Boost Software License version 1.0.
// http://www.boost.org/users/license.html

#ifndef BOOST_GEOMETRY_UTIL_NORMALIZE_SPHEROIDAL_COORDINATES_HPP
#define BOOST_GEOMETRY_UTIL_NORMALIZE_SPHEROIDAL_COORDINATES_HPP

#include <boost/geometry/core/assert.hpp>
#include <boost/geometry/core/cs.hpp>
#include <boost/geometry/util/math.hpp>


namespace boost { namespace geometry
{

namespace math 
{

#ifndef DOXYGEN_NO_DETAIL
namespace detail
{

// CoordinateType, radian, true
template <typename CoordinateType, typename Units, bool IsEquatorial = true>
struct constants_on_spheroid
{
    static inline CoordinateType period()
    {
        return math::two_pi<CoordinateType>();
    }

    static inline CoordinateType half_period()
    {
        return math::pi<CoordinateType>();
    }

    static inline CoordinateType quarter_period()
    {
        static CoordinateType const
            pi_half = math::pi<CoordinateType>() / CoordinateType(2);
        return pi_half;
    }

    static inline CoordinateType min_longitude()
    {
        static CoordinateType const minus_pi = -math::pi<CoordinateType>();
        return minus_pi;
    }

    static inline CoordinateType max_longitude()
    {
        return math::pi<CoordinateType>();
    }

    static inline CoordinateType min_latitude()
    {
        static CoordinateType const minus_half_pi
            = -math::half_pi<CoordinateType>();
        return minus_half_pi;
    }

    static inline CoordinateType max_latitude()
    {
        return math::half_pi<CoordinateType>();
    }
};

template <typename CoordinateType>
struct constants_on_spheroid<CoordinateType, radian, false>
    : constants_on_spheroid<CoordinateType, radian, true>
{
    static inline CoordinateType min_latitude()
    {
        return CoordinateType(0);
    }

    static inline CoordinateType max_latitude()
    {
        return math::pi<CoordinateType>();
    }
};

template <typename CoordinateType>
struct constants_on_spheroid<CoordinateType, degree, true>
{
    static inline CoordinateType period()
    {
        return CoordinateType(360.0);
    }

    static inline CoordinateType half_period()
    {
        return CoordinateType(180.0);
    }

    static inline CoordinateType quarter_period()
    {
        return CoordinateType(90.0);
    }

    static inline CoordinateType min_longitude()
    {
        return CoordinateType(-180.0);
    }

    static inline CoordinateType max_longitude()
    {
        return CoordinateType(180.0);
    }

    static inline CoordinateType min_latitude()
    {
        return CoordinateType(-90.0);
    }

    static inline CoordinateType max_latitude()
    {
        return CoordinateType(90.0);
    }
};

template <typename CoordinateType>
struct constants_on_spheroid<CoordinateType, degree, false>
    : constants_on_spheroid<CoordinateType, degree, true>
{
    static inline CoordinateType min_latitude()
    {
        return CoordinateType(0);
    }

    static inline CoordinateType max_latitude()
    {
        return CoordinateType(180.0);
    }
};


} // namespace detail
#endif // DOXYGEN_NO_DETAIL


template <typename Units, typename CoordinateType>
inline CoordinateType latitude_convert_ep(CoordinateType const& lat)
{
    typedef math::detail::constants_on_spheroid
            <
                CoordinateType,
                Units
            > constants;

    return constants::quarter_period() - lat;
}


template <typename Units, bool IsEquatorial, typename T>
static bool is_latitude_pole(T const& lat)
{
    typedef math::detail::constants_on_spheroid
        <
            T,
            Units
        > constants;

    return math::equals(math::abs(IsEquatorial
                                    ? lat
                                    : math::latitude_convert_ep<Units>(lat)),
                        constants::quarter_period());

}


template <typename Units, typename T>
static bool is_longitude_antimeridian(T const& lon)
{
    typedef math::detail::constants_on_spheroid
        <
            T,
            Units
        > constants;

    return math::equals(math::abs(lon), constants::half_period());

}


#ifndef DOXYGEN_NO_DETAIL
namespace detail
{


template <typename Units, bool IsEquatorial>
struct latitude_convert_if_polar
{
    template <typename T>
    static inline void apply(T & /*lat*/) {}
};

template <typename Units>
struct latitude_convert_if_polar<Units, false>
{
    template <typename T>
    static inline void apply(T & lat)
    {
        lat = latitude_convert_ep<Units>(lat);
    }
};


template <typename Units, typename CoordinateType, bool IsEquatorial = true>
class normalize_spheroidal_coordinates
{
    typedef constants_on_spheroid<CoordinateType, Units> constants;

protected:
    static inline CoordinateType normalize_up(CoordinateType const& value)
    {
        return
            math::mod(value + constants::half_period(), constants::period())
            - constants::half_period();            
    }

    static inline CoordinateType normalize_down(CoordinateType const& value)
    {
        return
            math::mod(value - constants::half_period(), constants::period())
            + constants::half_period();            
    }

public:
    static inline void apply(CoordinateType& longitude)
    {
        // normalize longitude
        if (math::equals(math::abs(longitude), constants::half_period()))
        {
            longitude = constants::half_period();
        }
        else if (longitude > constants::half_period())
        {
            longitude = normalize_up(longitude);
            if (math::equals(longitude, -constants::half_period()))
            {
                longitude = constants::half_period();
            }
        }
        else if (longitude < -constants::half_period())
        {
            longitude = normalize_down(longitude);
        }
    }

    static inline void apply(CoordinateType& longitude,
                             CoordinateType& latitude,
                             bool normalize_poles = true)
    {
        latitude_convert_if_polar<Units, IsEquatorial>::apply(latitude);

#ifdef BOOST_GEOMETRY_NORMALIZE_LATITUDE
        // normalize latitude
        if (math::larger(latitude, constants::half_period()))
        {
            latitude = normalize_up(latitude);
        }
        else if (math::smaller(latitude, -constants::half_period()))
        {
            latitude = normalize_down(latitude);
        }

        // fix latitude range
        if (latitude < constants::min_latitude())
        {
            latitude = -constants::half_period() - latitude;
            longitude -= constants::half_period();
        }
        else if (latitude > constants::max_latitude())
        {
            latitude = constants::half_period() - latitude;
            longitude -= constants::half_period();
        }
#endif // BOOST_GEOMETRY_NORMALIZE_LATITUDE

        // normalize longitude
        apply(longitude);

        // finally normalize poles
        if (normalize_poles)
        {
            if (math::equals(math::abs(latitude), constants::max_latitude()))
            {
                // for the north and south pole we set the longitude to 0
                // (works for both radians and degrees)
                longitude = CoordinateType(0);
            }
        }

        latitude_convert_if_polar<Units, IsEquatorial>::apply(latitude);

#ifdef BOOST_GEOMETRY_NORMALIZE_LATITUDE
        BOOST_GEOMETRY_ASSERT(! math::larger(constants::min_latitude(), latitude));
        BOOST_GEOMETRY_ASSERT(! math::larger(latitude, constants::max_latitude()));
#endif // BOOST_GEOMETRY_NORMALIZE_LATITUDE

        BOOST_GEOMETRY_ASSERT(math::smaller(constants::min_longitude(), longitude));
        BOOST_GEOMETRY_ASSERT(! math::larger(longitude, constants::max_longitude()));
    }
};


} // namespace detail
#endif // DOXYGEN_NO_DETAIL


/*!
\brief Short utility to normalize the coordinates on a spheroid
\tparam Units The units of the coordindate system in the spheroid
\tparam CoordinateType The type of the coordinates
\param longitude Longitude
\param latitude Latitude
\ingroup utility
*/
template <typename Units, typename CoordinateType>
inline void normalize_spheroidal_coordinates(CoordinateType& longitude,
                                             CoordinateType& latitude)
{
    detail::normalize_spheroidal_coordinates
        <
            Units, CoordinateType
        >::apply(longitude, latitude);
}

template <typename Units, bool IsEquatorial, typename CoordinateType>
inline void normalize_spheroidal_coordinates(CoordinateType& longitude,
                                             CoordinateType& latitude)
{
    detail::normalize_spheroidal_coordinates
        <
            Units, CoordinateType, IsEquatorial
        >::apply(longitude, latitude);
}

/*!
\brief Short utility to normalize the longitude on a spheroid.
       Note that in general both coordinates should be normalized at once.
       This utility is suitable e.g. for normalization of the difference of longitudes.
\tparam Units The units of the coordindate system in the spheroid
\tparam CoordinateType The type of the coordinates
\param longitude Longitude
\ingroup utility
*/
template <typename Units, typename CoordinateType>
inline void normalize_longitude(CoordinateType& longitude)
{
    detail::normalize_spheroidal_coordinates
        <
            Units, CoordinateType
        >::apply(longitude);
}


/*!
\brief Short utility to calculate difference between two longitudes
       normalized in range (-180, 180].
\tparam Units The units of the coordindate system in the spheroid
\tparam CoordinateType The type of the coordinates
\param longitude1 Longitude 1
\param longitude2 Longitude 2
\ingroup utility
*/
template <typename Units, typename CoordinateType>
inline CoordinateType longitude_distance_signed(CoordinateType const& longitude1,
                                                CoordinateType const& longitude2)
{
    CoordinateType diff = longitude2 - longitude1;
    math::normalize_longitude<Units, CoordinateType>(diff);
    return diff;
}


/*!
\brief Short utility to calculate difference between two longitudes
       normalized in range [0, 360).
\tparam Units The units of the coordindate system in the spheroid
\tparam CoordinateType The type of the coordinates
\param longitude1 Longitude 1
\param longitude2 Longitude 2
\ingroup utility
*/
template <typename Units, typename CoordinateType>
inline CoordinateType longitude_distance_unsigned(CoordinateType const& longitude1,
                                                  CoordinateType const& longitude2)
{
    typedef math::detail::constants_on_spheroid
        <
            CoordinateType, Units
        > constants;

    CoordinateType const c0 = 0;
    CoordinateType diff = longitude_distance_signed<Units>(longitude1, longitude2);
    if (diff < c0) // (-180, 180] -> [0, 360)
    {
        diff += constants::period();
    }
    return diff;
}

/*!
\brief The abs difference between longitudes in range [0, 180].
\tparam Units The units of the coordindate system in the spheroid
\tparam CoordinateType The type of the coordinates
\param longitude1 Longitude 1
\param longitude2 Longitude 2
\ingroup utility
*/
template <typename Units, typename CoordinateType>
inline CoordinateType longitude_difference(CoordinateType const& longitude1,
                                           CoordinateType const& longitude2)
{
    return math::abs(math::longitude_distance_signed<Units>(longitude1, longitude2));
}

template <typename Units, typename CoordinateType>
inline CoordinateType longitude_interval_distance_signed(CoordinateType const& longitude_a1,
                                                         CoordinateType const& longitude_a2,
                                                         CoordinateType const& longitude_b)
{
    CoordinateType const c0 = 0;
    CoordinateType dist_a12 = longitude_distance_signed<Units>(longitude_a1, longitude_a2);
    CoordinateType dist_a1b = longitude_distance_signed<Units>(longitude_a1, longitude_b);
    if (dist_a12 < c0)
    {
        dist_a12 = -dist_a12;
        dist_a1b = -dist_a1b;
    }
    
    return dist_a1b < c0 ? dist_a1b
         : dist_a1b > dist_a12 ? dist_a1b - dist_a12
         : c0;
}


} // namespace math


}} // namespace boost::geometry

#endif // BOOST_GEOMETRY_UTIL_NORMALIZE_SPHEROIDAL_COORDINATES_HPP
Commit	Line	Data
7c673cae FG	1	// Boost.Geometry (aka GGL, Generic Geometry Library)
7c673cae FG	2
11fdf7f2 TL	3	// Copyright (c) 2017 Adam Wulkiewicz, Lodz, Poland.
11fdf7f2 TL	4
b32b8144	5	// Copyright (c) 2015-2017, Oracle and/or its affiliates.
7c673cae FG	6
	7	// Contributed and/or modified by Menelaos Karavelas, on behalf of Oracle
	8	// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
	9
	10	// Licensed under the Boost Software License version 1.0.
	11	// http://www.boost.org/users/license.html
	12
	13	#ifndef BOOST_GEOMETRY_UTIL_NORMALIZE_SPHEROIDAL_COORDINATES_HPP
	14	#define BOOST_GEOMETRY_UTIL_NORMALIZE_SPHEROIDAL_COORDINATES_HPP
	15
	16	#include <boost/geometry/core/assert.hpp>
	17	#include <boost/geometry/core/cs.hpp>
	18	#include <boost/geometry/util/math.hpp>
	19
	20
	21	namespace boost { namespace geometry
	22	{
	23
	24	namespace math
	25	{
	26
	27	#ifndef DOXYGEN_NO_DETAIL
	28	namespace detail
	29	{
	30
b32b8144 FG	31	// CoordinateType, radian, true
b32b8144 FG	32	template <typename CoordinateType, typename Units, bool IsEquatorial = true>
7c673cae FG	33	struct constants_on_spheroid
	34	{
	35	static inline CoordinateType period()
	36	{
	37	return math::two_pi<CoordinateType>();
	38	}
	39
	40	static inline CoordinateType half_period()
	41	{
	42	return math::pi<CoordinateType>();
	43	}
	44
b32b8144 FG	45	static inline CoordinateType quarter_period()
	46	{
	47	static CoordinateType const
	48	pi_half = math::pi<CoordinateType>() / CoordinateType(2);
	49	return pi_half;
	50	}
	51
7c673cae FG	52	static inline CoordinateType min_longitude()
	53	{
	54	static CoordinateType const minus_pi = -math::pi<CoordinateType>();
	55	return minus_pi;
	56	}
	57
	58	static inline CoordinateType max_longitude()
	59	{
	60	return math::pi<CoordinateType>();
	61	}
	62
	63	static inline CoordinateType min_latitude()
	64	{
	65	static CoordinateType const minus_half_pi
	66	= -math::half_pi<CoordinateType>();
	67	return minus_half_pi;
	68	}
	69
	70	static inline CoordinateType max_latitude()
	71	{
	72	return math::half_pi<CoordinateType>();
	73	}
	74	};
	75
	76	template <typename CoordinateType>
b32b8144 FG	77	struct constants_on_spheroid<CoordinateType, radian, false>
	78	: constants_on_spheroid<CoordinateType, radian, true>
	79	{
	80	static inline CoordinateType min_latitude()
	81	{
	82	return CoordinateType(0);
	83	}
	84
	85	static inline CoordinateType max_latitude()
	86	{
	87	return math::pi<CoordinateType>();
	88	}
	89	};
	90
	91	template <typename CoordinateType>
	92	struct constants_on_spheroid<CoordinateType, degree, true>
7c673cae FG	93	{
	94	static inline CoordinateType period()
	95	{
	96	return CoordinateType(360.0);
	97	}
	98
	99	static inline CoordinateType half_period()
	100	{
	101	return CoordinateType(180.0);
	102	}
	103
b32b8144 FG	104	static inline CoordinateType quarter_period()
	105	{
	106	return CoordinateType(90.0);
	107	}
	108
7c673cae FG	109	static inline CoordinateType min_longitude()
	110	{
	111	return CoordinateType(-180.0);
	112	}
	113
	114	static inline CoordinateType max_longitude()
	115	{
	116	return CoordinateType(180.0);
	117	}
	118
	119	static inline CoordinateType min_latitude()
	120	{
	121	return CoordinateType(-90.0);
	122	}
	123
	124	static inline CoordinateType max_latitude()
	125	{
	126	return CoordinateType(90.0);
	127	}
	128	};
	129
b32b8144 FG	130	template <typename CoordinateType>
	131	struct constants_on_spheroid<CoordinateType, degree, false>
	132	: constants_on_spheroid<CoordinateType, degree, true>
	133	{
	134	static inline CoordinateType min_latitude()
	135	{
	136	return CoordinateType(0);
	137	}
	138
	139	static inline CoordinateType max_latitude()
	140	{
	141	return CoordinateType(180.0);
	142	}
	143	};
	144
	145
	146	} // namespace detail
	147	#endif // DOXYGEN_NO_DETAIL
	148
7c673cae FG	149
7c673cae FG	150	template <typename Units, typename CoordinateType>
b32b8144 FG	151	inline CoordinateType latitude_convert_ep(CoordinateType const& lat)
	152	{
	153	typedef math::detail::constants_on_spheroid
	154	<
	155	CoordinateType,
	156	Units
	157	> constants;
	158
	159	return constants::quarter_period() - lat;
	160	}
	161
	162
	163	template <typename Units, bool IsEquatorial, typename T>
	164	static bool is_latitude_pole(T const& lat)
	165	{
	166	typedef math::detail::constants_on_spheroid
	167	<
	168	T,
	169	Units
	170	> constants;
	171
	172	return math::equals(math::abs(IsEquatorial
	173	? lat
	174	: math::latitude_convert_ep<Units>(lat)),
	175	constants::quarter_period());
	176
	177	}
	178
	179
	180	template <typename Units, typename T>
	181	static bool is_longitude_antimeridian(T const& lon)
	182	{
	183	typedef math::detail::constants_on_spheroid
	184	<
	185	T,
	186	Units
	187	> constants;
	188
	189	return math::equals(math::abs(lon), constants::half_period());
	190
	191	}
	192
	193
	194	#ifndef DOXYGEN_NO_DETAIL
	195	namespace detail
	196	{
	197
	198
	199	template <typename Units, bool IsEquatorial>
	200	struct latitude_convert_if_polar
	201	{
	202	template <typename T>
11fdf7f2	203	static inline void apply(T & /lat/) {}
b32b8144 FG	204	};
	205
	206	template <typename Units>
	207	struct latitude_convert_if_polar<Units, false>
	208	{
	209	template <typename T>
	210	static inline void apply(T & lat)
	211	{
	212	lat = latitude_convert_ep<Units>(lat);
	213	}
	214	};
	215
	216
	217	template <typename Units, typename CoordinateType, bool IsEquatorial = true>
7c673cae FG	218	class normalize_spheroidal_coordinates
	219	{
	220	typedef constants_on_spheroid<CoordinateType, Units> constants;
	221
	222	protected:
	223	static inline CoordinateType normalize_up(CoordinateType const& value)
	224	{
	225	return
	226	math::mod(value + constants::half_period(), constants::period())
	227	- constants::half_period();
	228	}
	229
	230	static inline CoordinateType normalize_down(CoordinateType const& value)
	231	{
	232	return
	233	math::mod(value - constants::half_period(), constants::period())
	234	+ constants::half_period();
	235	}
	236
	237	public:
	238	static inline void apply(CoordinateType& longitude)
	239	{
	240	// normalize longitude
	241	if (math::equals(math::abs(longitude), constants::half_period()))
	242	{
	243	longitude = constants::half_period();
	244	}
	245	else if (longitude > constants::half_period())
	246	{
	247	longitude = normalize_up(longitude);
	248	if (math::equals(longitude, -constants::half_period()))
	249	{
	250	longitude = constants::half_period();
	251	}
	252	}
	253	else if (longitude < -constants::half_period())
	254	{
	255	longitude = normalize_down(longitude);
	256	}
	257	}
	258
	259	static inline void apply(CoordinateType& longitude,
	260	CoordinateType& latitude,
	261	bool normalize_poles = true)
	262	{
b32b8144 FG	263	latitude_convert_if_polar<Units, IsEquatorial>::apply(latitude);
b32b8144 FG	264
7c673cae FG	265	#ifdef BOOST_GEOMETRY_NORMALIZE_LATITUDE
	266	// normalize latitude
	267	if (math::larger(latitude, constants::half_period()))
	268	{
	269	latitude = normalize_up(latitude);
	270	}
	271	else if (math::smaller(latitude, -constants::half_period()))
	272	{
	273	latitude = normalize_down(latitude);
	274	}
	275
	276	// fix latitude range
	277	if (latitude < constants::min_latitude())
	278	{
	279	latitude = -constants::half_period() - latitude;
	280	longitude -= constants::half_period();
	281	}
	282	else if (latitude > constants::max_latitude())
	283	{
	284	latitude = constants::half_period() - latitude;
	285	longitude -= constants::half_period();
	286	}
	287	#endif // BOOST_GEOMETRY_NORMALIZE_LATITUDE
	288
	289	// normalize longitude
	290	apply(longitude);
	291
	292	// finally normalize poles
	293	if (normalize_poles)
	294	{
	295	if (math::equals(math::abs(latitude), constants::max_latitude()))
	296	{
	297	// for the north and south pole we set the longitude to 0
	298	// (works for both radians and degrees)
	299	longitude = CoordinateType(0);
	300	}
	301	}
	302
b32b8144 FG	303	latitude_convert_if_polar<Units, IsEquatorial>::apply(latitude);
b32b8144 FG	304
7c673cae FG	305	#ifdef BOOST_GEOMETRY_NORMALIZE_LATITUDE
	306	BOOST_GEOMETRY_ASSERT(! math::larger(constants::min_latitude(), latitude));
	307	BOOST_GEOMETRY_ASSERT(! math::larger(latitude, constants::max_latitude()));
	308	#endif // BOOST_GEOMETRY_NORMALIZE_LATITUDE
	309
	310	BOOST_GEOMETRY_ASSERT(math::smaller(constants::min_longitude(), longitude));
	311	BOOST_GEOMETRY_ASSERT(! math::larger(longitude, constants::max_longitude()));
	312	}
	313	};
	314
	315
	316	} // namespace detail
	317	#endif // DOXYGEN_NO_DETAIL
	318
	319
	320	/*!
	321	\brief Short utility to normalize the coordinates on a spheroid
	322	\tparam Units The units of the coordindate system in the spheroid
	323	\tparam CoordinateType The type of the coordinates
	324	\param longitude Longitude
	325	\param latitude Latitude
	326	\ingroup utility
	327	*/
	328	template <typename Units, typename CoordinateType>
	329	inline void normalize_spheroidal_coordinates(CoordinateType& longitude,
	330	CoordinateType& latitude)
	331	{
	332	detail::normalize_spheroidal_coordinates
	333	<
	334	Units, CoordinateType
	335	>::apply(longitude, latitude);
	336	}
	337
b32b8144 FG	338	template <typename Units, bool IsEquatorial, typename CoordinateType>
	339	inline void normalize_spheroidal_coordinates(CoordinateType& longitude,
	340	CoordinateType& latitude)
	341	{
	342	detail::normalize_spheroidal_coordinates
	343	<
	344	Units, CoordinateType, IsEquatorial
	345	>::apply(longitude, latitude);
	346	}
7c673cae FG	347
	348	/*!
	349	\brief Short utility to normalize the longitude on a spheroid.
	350	Note that in general both coordinates should be normalized at once.
	351	This utility is suitable e.g. for normalization of the difference of longitudes.
	352	\tparam Units The units of the coordindate system in the spheroid
	353	\tparam CoordinateType The type of the coordinates
	354	\param longitude Longitude
	355	\ingroup utility
	356	*/
	357	template <typename Units, typename CoordinateType>
	358	inline void normalize_longitude(CoordinateType& longitude)
	359	{
	360	detail::normalize_spheroidal_coordinates
	361	<
	362	Units, CoordinateType
	363	>::apply(longitude);
	364	}
	365
	366
	367	/*!
	368	\brief Short utility to calculate difference between two longitudes
	369	normalized in range (-180, 180].
	370	\tparam Units The units of the coordindate system in the spheroid
	371	\tparam CoordinateType The type of the coordinates
	372	\param longitude1 Longitude 1
	373	\param longitude2 Longitude 2
	374	\ingroup utility
	375	*/
	376	template <typename Units, typename CoordinateType>
	377	inline CoordinateType longitude_distance_signed(CoordinateType const& longitude1,
	378	CoordinateType const& longitude2)
	379	{
	380	CoordinateType diff = longitude2 - longitude1;
	381	math::normalize_longitude<Units, CoordinateType>(diff);
	382	return diff;
	383	}
	384
	385
	386	/*!
	387	\brief Short utility to calculate difference between two longitudes
	388	normalized in range [0, 360).
	389	\tparam Units The units of the coordindate system in the spheroid
	390	\tparam CoordinateType The type of the coordinates
	391	\param longitude1 Longitude 1
	392	\param longitude2 Longitude 2
	393	\ingroup utility
	394	*/
	395	template <typename Units, typename CoordinateType>
	396	inline CoordinateType longitude_distance_unsigned(CoordinateType const& longitude1,
	397	CoordinateType const& longitude2)
	398	{
	399	typedef math::detail::constants_on_spheroid
	400	<
	401	CoordinateType, Units
	402	> constants;
	403
	404	CoordinateType const c0 = 0;
	405	CoordinateType diff = longitude_distance_signed<Units>(longitude1, longitude2);
	406	if (diff < c0) // (-180, 180] -> [0, 360)
	407	{
	408	diff += constants::period();
	409	}
	410	return diff;
411	}
412
b32b8144 FG	413	/*!
	414	\brief The abs difference between longitudes in range [0, 180].
	415	\tparam Units The units of the coordindate system in the spheroid
	416	\tparam CoordinateType The type of the coordinates
	417	\param longitude1 Longitude 1
	418	\param longitude2 Longitude 2
	419	\ingroup utility
	420	*/
	421	template <typename Units, typename CoordinateType>
	422	inline CoordinateType longitude_difference(CoordinateType const& longitude1,
	423	CoordinateType const& longitude2)
	424	{
	425	return math::abs(math::longitude_distance_signed<Units>(longitude1, longitude2));
	426	}
	427
	428	template <typename Units, typename CoordinateType>
	429	inline CoordinateType longitude_interval_distance_signed(CoordinateType const& longitude_a1,
	430	CoordinateType const& longitude_a2,
	431	CoordinateType const& longitude_b)
	432	{
	433	CoordinateType const c0 = 0;
	434	CoordinateType dist_a12 = longitude_distance_signed<Units>(longitude_a1, longitude_a2);
	435	CoordinateType dist_a1b = longitude_distance_signed<Units>(longitude_a1, longitude_b);
	436	if (dist_a12 < c0)
	437	{
	438	dist_a12 = -dist_a12;
	439	dist_a1b = -dist_a1b;
	440	}
	441
	442	return dist_a1b < c0 ? dist_a1b
	443	: dist_a1b > dist_a12 ? dist_a1b - dist_a12
	444	: c0;
	445	}
	446
	447
7c673cae FG	448	} // namespace math
	449
	450
	451	}} // namespace boost::geometry
	452
	453	#endif // BOOST_GEOMETRY_UTIL_NORMALIZE_SPHEROIDAL_COORDINATES_HPP