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1 | // Boost.Geometry | |
2 | ||
3 | // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands. | |
4 | ||
5 | // This file was modified by Oracle on 2014. | |
6 | // Modifications copyright (c) 2014 Oracle and/or its affiliates. | |
7 | ||
8 | // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle | |
9 | ||
10 | // Use, modification and distribution is subject to the Boost Software License, | |
11 | // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at | |
12 | // http://www.boost.org/LICENSE_1_0.txt) | |
13 | ||
14 | #ifndef BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP | |
15 | #define BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP | |
16 | ||
17 | ||
18 | #include <boost/math/constants/constants.hpp> | |
19 | ||
20 | #include <boost/geometry/core/radius.hpp> | |
21 | #include <boost/geometry/core/srs.hpp> | |
22 | ||
23 | #include <boost/geometry/util/condition.hpp> | |
24 | #include <boost/geometry/util/math.hpp> | |
25 | ||
26 | #include <boost/geometry/algorithms/detail/flattening.hpp> | |
27 | #include <boost/geometry/algorithms/detail/result_inverse.hpp> | |
28 | ||
29 | ||
30 | #ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS | |
31 | #define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000 | |
32 | #endif | |
33 | ||
34 | ||
35 | namespace boost { namespace geometry { namespace detail | |
36 | { | |
37 | ||
38 | /*! | |
39 | \brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975 | |
40 | \author See | |
41 | - http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf | |
42 | - http://www.icsm.gov.au/gda/gdav2.3.pdf | |
43 | \author Adapted from various implementations to get it close to the original document | |
44 | - http://www.movable-type.co.uk/scripts/LatLongVincenty.html | |
45 | - http://exogen.case.edu/projects/geopy/source/geopy.distance.html | |
46 | - http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink | |
47 | ||
48 | */ | |
49 | template <typename CT, bool EnableDistance, bool EnableAzimuth> | |
50 | struct vincenty_inverse | |
51 | { | |
52 | typedef result_inverse<CT> result_type; | |
53 | ||
54 | public: | |
55 | template <typename T1, typename T2, typename Spheroid> | |
56 | static inline result_type apply(T1 const& lon1, | |
57 | T1 const& lat1, | |
58 | T2 const& lon2, | |
59 | T2 const& lat2, | |
60 | Spheroid const& spheroid) | |
61 | { | |
62 | result_type result; | |
63 | ||
64 | if (math::equals(lat1, lat2) && math::equals(lon1, lon2)) | |
65 | { | |
66 | result.set(CT(0), CT(0)); | |
67 | return result; | |
68 | } | |
69 | ||
70 | CT const c1 = 1; | |
71 | CT const c2 = 2; | |
72 | CT const c3 = 3; | |
73 | CT const c4 = 4; | |
74 | CT const c16 = 16; | |
75 | CT const c_e_12 = CT(1e-12); | |
76 | ||
77 | CT const pi = geometry::math::pi<CT>(); | |
78 | CT const two_pi = c2 * pi; | |
79 | ||
80 | // lambda: difference in longitude on an auxiliary sphere | |
81 | CT L = lon2 - lon1; | |
82 | CT lambda = L; | |
83 | ||
84 | if (L < -pi) L += two_pi; | |
85 | if (L > pi) L -= two_pi; | |
86 | ||
87 | CT const radius_a = CT(get_radius<0>(spheroid)); | |
88 | CT const radius_b = CT(get_radius<2>(spheroid)); | |
89 | CT const flattening = geometry::detail::flattening<CT>(spheroid); | |
90 | ||
91 | // U: reduced latitude, defined by tan U = (1-f) tan phi | |
92 | CT const one_min_f = c1 - flattening; | |
93 | CT const tan_U1 = one_min_f * tan(lat1); // above (1) | |
94 | CT const tan_U2 = one_min_f * tan(lat2); // above (1) | |
95 | ||
96 | // calculate sin U and cos U using trigonometric identities | |
97 | CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1)); | |
98 | CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2)); | |
99 | // cos = 1 / sqrt(1 + tan^2) | |
100 | CT const cos_U1 = c1 / temp_den_U1; | |
101 | CT const cos_U2 = c1 / temp_den_U2; | |
102 | // sin = tan / sqrt(1 + tan^2) | |
103 | CT const sin_U1 = tan_U1 / temp_den_U1; | |
104 | CT const sin_U2 = tan_U2 / temp_den_U2; | |
105 | ||
106 | // calculate sin U and cos U directly | |
107 | //CT const U1 = atan(tan_U1); | |
108 | //CT const U2 = atan(tan_U2); | |
109 | //cos_U1 = cos(U1); | |
110 | //cos_U2 = cos(U2); | |
111 | //sin_U1 = tan_U1 * cos_U1; // sin(U1); | |
112 | //sin_U2 = tan_U2 * cos_U2; // sin(U2); | |
113 | ||
114 | CT previous_lambda; | |
115 | CT sin_lambda; | |
116 | CT cos_lambda; | |
117 | CT sin_sigma; | |
118 | CT sin_alpha; | |
119 | CT cos2_alpha; | |
120 | CT cos2_sigma_m; | |
121 | CT sigma; | |
122 | ||
123 | int counter = 0; // robustness | |
124 | ||
125 | do | |
126 | { | |
127 | previous_lambda = lambda; // (13) | |
128 | sin_lambda = sin(lambda); | |
129 | cos_lambda = cos(lambda); | |
130 | sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14) | |
131 | CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15) | |
132 | sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17) | |
133 | cos2_alpha = c1 - math::sqr(sin_alpha); | |
134 | cos2_sigma_m = math::equals(cos2_alpha, 0) ? 0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18) | |
135 | ||
136 | CT C = flattening/c16 * cos2_alpha * (c4 + flattening * (c4 - c3 * cos2_alpha)); // (10) | |
137 | sigma = atan2(sin_sigma, cos_sigma); // (16) | |
138 | lambda = L + (c1 - C) * flattening * sin_alpha * | |
139 | (sigma + C * sin_sigma * ( cos2_sigma_m + C * cos_sigma * (-c1 + c2 * math::sqr(cos2_sigma_m)))); // (11) | |
140 | ||
141 | ++counter; // robustness | |
142 | ||
143 | } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12 | |
144 | && geometry::math::abs(lambda) < pi | |
145 | && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness | |
146 | ||
147 | if ( BOOST_GEOMETRY_CONDITION(EnableDistance) ) | |
148 | { | |
149 | // Oops getting hard here | |
150 | // (again, problem is that ttmath cannot divide by doubles, which is OK) | |
151 | CT const c1 = 1; | |
152 | CT const c2 = 2; | |
153 | CT const c3 = 3; | |
154 | CT const c4 = 4; | |
155 | CT const c6 = 6; | |
156 | CT const c47 = 47; | |
157 | CT const c74 = 74; | |
158 | CT const c128 = 128; | |
159 | CT const c256 = 256; | |
160 | CT const c175 = 175; | |
161 | CT const c320 = 320; | |
162 | CT const c768 = 768; | |
163 | CT const c1024 = 1024; | |
164 | CT const c4096 = 4096; | |
165 | CT const c16384 = 16384; | |
166 | ||
167 | //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1) | |
168 | CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1) | |
169 | ||
170 | CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3) | |
171 | CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4) | |
172 | CT delta_sigma = B * sin_sigma * ( cos2_sigma_m + (B/c4) * (cos(sigma)* (-c1 + c2 * cos2_sigma_m) | |
173 | - (B/c6) * cos2_sigma_m * (-c3 + c4 * math::sqr(sin_sigma)) * (-c3 + c4 * cos2_sigma_m))); // (6) | |
174 | ||
175 | result.distance = radius_b * A * (sigma - delta_sigma); // (19) | |
176 | } | |
177 | else | |
178 | { | |
179 | result.distance = CT(0); | |
180 | } | |
181 | ||
182 | if ( BOOST_GEOMETRY_CONDITION(EnableAzimuth) ) | |
183 | { | |
184 | result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20) | |
185 | } | |
186 | else | |
187 | { | |
188 | result.azimuth = CT(0); | |
189 | } | |
190 | ||
191 | return result; | |
192 | } | |
193 | ||
194 | // inline CT azimuth21() const | |
195 | // { | |
196 | // // NOTE: signs of X and Y are different than in the original paper | |
197 | // atan2(-cos_U1 * sin_lambda, sin_U1 * cos_U2 - cos_U1 * sin_U2 * cos_lambda); // (21) | |
198 | // } | |
199 | }; | |
200 | ||
201 | }}} // namespace boost::geometry::detail | |
202 | ||
203 | ||
204 | #endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP |