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1 | // Boost.Geometry |
2 | ||
3 | // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands. | |
4 | ||
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5 | // This file was modified by Oracle on 2014, 2016, 2017. |
6 | // Modifications copyright (c) 2014-2017 Oracle and/or its affiliates. | |
7c673cae FG |
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 | ||
b32b8144 FG |
14 | #ifndef BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP |
15 | #define BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP | |
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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 | ||
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26 | #include <boost/geometry/formulas/differential_quantities.hpp> |
27 | #include <boost/geometry/formulas/flattening.hpp> | |
28 | #include <boost/geometry/formulas/result_inverse.hpp> | |
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29 | |
30 | ||
31 | #ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS | |
32 | #define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000 | |
33 | #endif | |
34 | ||
35 | ||
b32b8144 | 36 | namespace boost { namespace geometry { namespace formula |
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37 | { |
38 | ||
39 | /*! | |
40 | \brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975 | |
41 | \author See | |
42 | - http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf | |
b32b8144 | 43 | - http://www.icsm.gov.au/gda/gda-v_2.4.pdf |
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44 | \author Adapted from various implementations to get it close to the original document |
45 | - http://www.movable-type.co.uk/scripts/LatLongVincenty.html | |
46 | - http://exogen.case.edu/projects/geopy/source/geopy.distance.html | |
47 | - http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink | |
48 | ||
49 | */ | |
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50 | template < |
51 | typename CT, | |
52 | bool EnableDistance, | |
53 | bool EnableAzimuth, | |
54 | bool EnableReverseAzimuth = false, | |
55 | bool EnableReducedLength = false, | |
56 | bool EnableGeodesicScale = false | |
57 | > | |
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58 | struct vincenty_inverse |
59 | { | |
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60 | static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale; |
61 | static const bool CalcAzimuths = EnableAzimuth || EnableReverseAzimuth || CalcQuantities; | |
62 | static const bool CalcFwdAzimuth = EnableAzimuth || CalcQuantities; | |
63 | static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities; | |
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64 | |
65 | public: | |
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66 | typedef result_inverse<CT> result_type; |
67 | ||
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68 | template <typename T1, typename T2, typename Spheroid> |
69 | static inline result_type apply(T1 const& lon1, | |
70 | T1 const& lat1, | |
71 | T2 const& lon2, | |
72 | T2 const& lat2, | |
73 | Spheroid const& spheroid) | |
74 | { | |
75 | result_type result; | |
76 | ||
77 | if (math::equals(lat1, lat2) && math::equals(lon1, lon2)) | |
78 | { | |
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79 | return result; |
80 | } | |
81 | ||
82 | CT const c1 = 1; | |
83 | CT const c2 = 2; | |
84 | CT const c3 = 3; | |
85 | CT const c4 = 4; | |
86 | CT const c16 = 16; | |
87 | CT const c_e_12 = CT(1e-12); | |
88 | ||
89 | CT const pi = geometry::math::pi<CT>(); | |
90 | CT const two_pi = c2 * pi; | |
91 | ||
92 | // lambda: difference in longitude on an auxiliary sphere | |
93 | CT L = lon2 - lon1; | |
94 | CT lambda = L; | |
95 | ||
96 | if (L < -pi) L += two_pi; | |
97 | if (L > pi) L -= two_pi; | |
98 | ||
99 | CT const radius_a = CT(get_radius<0>(spheroid)); | |
100 | CT const radius_b = CT(get_radius<2>(spheroid)); | |
b32b8144 | 101 | CT const f = formula::flattening<CT>(spheroid); |
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102 | |
103 | // U: reduced latitude, defined by tan U = (1-f) tan phi | |
b32b8144 | 104 | CT const one_min_f = c1 - f; |
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105 | CT const tan_U1 = one_min_f * tan(lat1); // above (1) |
106 | CT const tan_U2 = one_min_f * tan(lat2); // above (1) | |
107 | ||
108 | // calculate sin U and cos U using trigonometric identities | |
109 | CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1)); | |
110 | CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2)); | |
111 | // cos = 1 / sqrt(1 + tan^2) | |
112 | CT const cos_U1 = c1 / temp_den_U1; | |
113 | CT const cos_U2 = c1 / temp_den_U2; | |
114 | // sin = tan / sqrt(1 + tan^2) | |
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115 | // sin = tan * cos |
116 | CT const sin_U1 = tan_U1 * cos_U1; | |
117 | CT const sin_U2 = tan_U2 * cos_U2; | |
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118 | |
119 | // calculate sin U and cos U directly | |
120 | //CT const U1 = atan(tan_U1); | |
121 | //CT const U2 = atan(tan_U2); | |
122 | //cos_U1 = cos(U1); | |
123 | //cos_U2 = cos(U2); | |
124 | //sin_U1 = tan_U1 * cos_U1; // sin(U1); | |
125 | //sin_U2 = tan_U2 * cos_U2; // sin(U2); | |
126 | ||
127 | CT previous_lambda; | |
128 | CT sin_lambda; | |
129 | CT cos_lambda; | |
130 | CT sin_sigma; | |
131 | CT sin_alpha; | |
132 | CT cos2_alpha; | |
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133 | CT cos_2sigma_m; |
134 | CT cos2_2sigma_m; | |
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135 | CT sigma; |
136 | ||
137 | int counter = 0; // robustness | |
138 | ||
139 | do | |
140 | { | |
141 | previous_lambda = lambda; // (13) | |
142 | sin_lambda = sin(lambda); | |
143 | cos_lambda = cos(lambda); | |
144 | sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14) | |
145 | CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15) | |
146 | sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17) | |
147 | cos2_alpha = c1 - math::sqr(sin_alpha); | |
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148 | cos_2sigma_m = math::equals(cos2_alpha, 0) ? 0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18) |
149 | cos2_2sigma_m = math::sqr(cos_2sigma_m); | |
7c673cae | 150 | |
b32b8144 | 151 | CT C = f/c16 * cos2_alpha * (c4 + f * (c4 - c3 * cos2_alpha)); // (10) |
7c673cae | 152 | sigma = atan2(sin_sigma, cos_sigma); // (16) |
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153 | lambda = L + (c1 - C) * f * sin_alpha * |
154 | (sigma + C * sin_sigma * (cos_2sigma_m + C * cos_sigma * (-c1 + c2 * cos2_2sigma_m))); // (11) | |
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155 | |
156 | ++counter; // robustness | |
157 | ||
158 | } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12 | |
159 | && geometry::math::abs(lambda) < pi | |
160 | && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness | |
161 | ||
162 | if ( BOOST_GEOMETRY_CONDITION(EnableDistance) ) | |
163 | { | |
164 | // Oops getting hard here | |
165 | // (again, problem is that ttmath cannot divide by doubles, which is OK) | |
166 | CT const c1 = 1; | |
167 | CT const c2 = 2; | |
168 | CT const c3 = 3; | |
169 | CT const c4 = 4; | |
170 | CT const c6 = 6; | |
171 | CT const c47 = 47; | |
172 | CT const c74 = 74; | |
173 | CT const c128 = 128; | |
174 | CT const c256 = 256; | |
175 | CT const c175 = 175; | |
176 | CT const c320 = 320; | |
177 | CT const c768 = 768; | |
178 | CT const c1024 = 1024; | |
179 | CT const c4096 = 4096; | |
180 | CT const c16384 = 16384; | |
181 | ||
182 | //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1) | |
183 | CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1) | |
184 | ||
185 | CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3) | |
186 | CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4) | |
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187 | CT const cos_sigma = cos(sigma); |
188 | CT const sin2_sigma = math::sqr(sin_sigma); | |
189 | CT delta_sigma = B * sin_sigma * (cos_2sigma_m + (B/c4) * (cos_sigma* (-c1 + c2 * cos2_2sigma_m) | |
190 | - (B/c6) * cos_2sigma_m * (-c3 + c4 * sin2_sigma) * (-c3 + c4 * cos2_2sigma_m))); // (6) | |
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191 | |
192 | result.distance = radius_b * A * (sigma - delta_sigma); // (19) | |
193 | } | |
7c673cae | 194 | |
b32b8144 | 195 | if ( BOOST_GEOMETRY_CONDITION(CalcAzimuths) ) |
7c673cae | 196 | { |
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197 | if (BOOST_GEOMETRY_CONDITION(CalcFwdAzimuth)) |
198 | { | |
199 | result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20) | |
200 | } | |
201 | ||
202 | if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth)) | |
203 | { | |
204 | result.reverse_azimuth = atan2(cos_U1 * sin_lambda, -sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda); // (21) | |
205 | } | |
7c673cae | 206 | } |
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207 | |
208 | if (BOOST_GEOMETRY_CONDITION(CalcQuantities)) | |
7c673cae | 209 | { |
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210 | typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities; |
211 | quantities::apply(lon1, lat1, lon2, lat2, | |
212 | result.azimuth, result.reverse_azimuth, | |
213 | radius_b, f, | |
214 | result.reduced_length, result.geodesic_scale); | |
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215 | } |
216 | ||
217 | return result; | |
218 | } | |
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219 | }; |
220 | ||
b32b8144 | 221 | }}} // namespace boost::geometry::formula |
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222 | |
223 | ||
b32b8144 | 224 | #endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP |