1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
|
// Boost.Geometry (aka GGL, Generic Geometry Library)
// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
// This file was modified by Oracle on 2014.
// Modifications copyright (c) 2014 Oracle and/or its affiliates.
// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
// 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_GEOGRAPHIC_ANDOYER_HPP
#define BOOST_GEOMETRY_STRATEGIES_GEOGRAPHIC_ANDOYER_HPP
#include <boost/geometry/core/coordinate_type.hpp>
#include <boost/geometry/core/radian_access.hpp>
#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/core/srs.hpp>
#include <boost/geometry/algorithms/detail/flattening.hpp>
#include <boost/geometry/strategies/distance.hpp>
#include <boost/geometry/util/math.hpp>
#include <boost/geometry/util/promote_floating_point.hpp>
#include <boost/geometry/util/select_calculation_type.hpp>
namespace boost { namespace geometry
{
namespace strategy { namespace distance
{
/*!
\brief Point-point distance approximation taking flattening into account
\ingroup distance
\tparam Spheroid The reference spheroid model
\tparam CalculationType \tparam_calculation
\author After Andoyer, 19xx, republished 1950, republished by Meeus, 1999
\note Although not so well-known, the approximation is very good: in all cases the results
are about the same as Vincenty. In my (Barend's) testcases the results didn't differ more than 6 m
\see http://nacc.upc.es/tierra/node16.html
\see http://sci.tech-archive.net/Archive/sci.geo.satellite-nav/2004-12/2724.html
\see http://home.att.net/~srschmitt/great_circle_route.html (implementation)
\see http://www.codeguru.com/Cpp/Cpp/algorithms/article.php/c5115 (implementation)
\see http://futureboy.homeip.net/frinksamp/navigation.frink (implementation)
\see http://www.voidware.com/earthdist.htm (implementation)
*/
template
<
typename Spheroid,
typename CalculationType = void
>
class andoyer
{
public :
template <typename Point1, typename Point2>
struct calculation_type
: promote_floating_point
<
typename select_calculation_type
<
Point1,
Point2,
CalculationType
>::type
>
{};
typedef Spheroid model_type;
inline andoyer()
: m_spheroid()
{}
explicit inline andoyer(Spheroid const& spheroid)
: m_spheroid(spheroid)
{}
template <typename Point1, typename Point2>
inline typename calculation_type<Point1, Point2>::type
apply(Point1 const& point1, Point2 const& point2) const
{
return calc<typename calculation_type<Point1, Point2>::type>
(
get_as_radian<0>(point1), get_as_radian<1>(point1),
get_as_radian<0>(point2), get_as_radian<1>(point2)
);
}
inline Spheroid const& model() const
{
return m_spheroid;
}
private :
template <typename CT, typename T>
inline CT calc(T const& lon1,
T const& lat1,
T const& lon2,
T const& lat2) const
{
CT const G = (lat1 - lat2) / 2.0;
CT const lambda = (lon1 - lon2) / 2.0;
if (geometry::math::equals(lambda, 0.0)
&& geometry::math::equals(G, 0.0))
{
return 0.0;
}
CT const F = (lat1 + lat2) / 2.0;
CT const sinG2 = math::sqr(sin(G));
CT const cosG2 = math::sqr(cos(G));
CT const sinF2 = math::sqr(sin(F));
CT const cosF2 = math::sqr(cos(F));
CT const sinL2 = math::sqr(sin(lambda));
CT const cosL2 = math::sqr(cos(lambda));
CT const S = sinG2 * cosL2 + cosF2 * sinL2;
CT const C = cosG2 * cosL2 + sinF2 * sinL2;
CT const c0 = 0;
CT const c1 = 1;
CT const c2 = 2;
CT const c3 = 3;
if (geometry::math::equals(S, c0) || geometry::math::equals(C, c0))
{
return c0;
}
CT const radius_a = CT(get_radius<0>(m_spheroid));
CT const flattening = geometry::detail::flattening<CT>(m_spheroid);
CT const omega = atan(math::sqrt(S / C));
CT const r3 = c3 * math::sqrt(S * C) / omega; // not sure if this is r or greek nu
CT const D = c2 * omega * radius_a;
CT const H1 = (r3 - c1) / (c2 * C);
CT const H2 = (r3 + c1) / (c2 * S);
return D * (c1 + flattening * (H1 * sinF2 * cosG2 - H2 * cosF2 * sinG2) );
}
Spheroid m_spheroid;
};
#ifndef DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
namespace services
{
template <typename Spheroid, typename CalculationType>
struct tag<andoyer<Spheroid, CalculationType> >
{
typedef strategy_tag_distance_point_point type;
};
template <typename Spheroid, typename CalculationType, typename P1, typename P2>
struct return_type<andoyer<Spheroid, CalculationType>, P1, P2>
: andoyer<Spheroid, CalculationType>::template calculation_type<P1, P2>
{};
template <typename Spheroid, typename CalculationType>
struct comparable_type<andoyer<Spheroid, CalculationType> >
{
typedef andoyer<Spheroid, CalculationType> type;
};
template <typename Spheroid, typename CalculationType>
struct get_comparable<andoyer<Spheroid, CalculationType> >
{
static inline andoyer<Spheroid, CalculationType> apply(andoyer<Spheroid, CalculationType> const& input)
{
return input;
}
};
template <typename Spheroid, typename CalculationType, typename P1, typename P2>
struct result_from_distance<andoyer<Spheroid, CalculationType>, P1, P2>
{
template <typename T>
static inline typename return_type<andoyer<Spheroid, CalculationType>, P1, P2>::type
apply(andoyer<Spheroid, CalculationType> const& , T const& value)
{
return value;
}
};
template <typename Point1, typename Point2>
struct default_strategy<point_tag, point_tag, Point1, Point2, geographic_tag, geographic_tag>
{
typedef strategy::distance::andoyer
<
srs::spheroid
<
typename select_coordinate_type<Point1, Point2>::type
>
> type;
};
} // namespace services
#endif // DOXYGEN_NO_STRATEGY_SPECIALIZATIONS
}} // namespace strategy::distance
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_STRATEGIES_GEOGRAPHIC_ANDOYER_HPP
|
