1 // Boost.Geometry (aka GGL, Generic Geometry Library)
2 // This file is manually converted from PROJ4
3
4 // Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands.
5
6 // This file was modified by Oracle on 2017, 2018.
7 // Modifications copyright (c) 2017-2018, Oracle and/or its affiliates.
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 // This file is converted from PROJ4, http://trac.osgeo.org/proj
15 // PROJ4 is originally written by Gerald Evenden (then of the USGS)
16 // PROJ4 is maintained by Frank Warmerdam
17 // PROJ4 is converted to Geometry Library by Barend Gehrels (Geodan, Amsterdam)
18
19 // Original copyright notice:
20
21 // Permission is hereby granted, free of charge, to any person obtaining a
22 // copy of this software and associated documentation files (the "Software"),
23 // to deal in the Software without restriction, including without limitation
24 // the rights to use, copy, modify, merge, publish, distribute, sublicense,
25 // and/or sell copies of the Software, and to permit persons to whom the
26 // Software is furnished to do so, subject to the following conditions:
27
28 // The above copyright notice and this permission notice shall be included
29 // in all copies or substantial portions of the Software.
30
31 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
32 // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
33 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
34 // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
35 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
36 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
37 // DEALINGS IN THE SOFTWARE.
38
39 #ifndef BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_AUTH_HPP
40 #define BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_AUTH_HPP
41
42 #include <cassert>
43 #include <cmath>
44
45 #include <boost/geometry/core/assert.hpp>
46
47 namespace boost { namespace geometry { namespace projections {
48
49 namespace detail {
50
51 template <typename T>
52 struct apa
53 {
54 static const std::size_t size = 3;
55
operator []boost::geometry::projections::detail::apa56 T const& operator[](size_t i) const { return data[i]; }
operator []boost::geometry::projections::detail::apa57 T & operator[](size_t i) { return data[i]; }
58
59 private:
60 T data[3];
61 };
62
63 /* determine latitude from authalic latitude */
64 template <typename T>
pj_authset(T const & es)65 inline detail::apa<T> pj_authset(T const& es)
66 {
67 static const T P00 = .33333333333333333333;
68 static const T P01 = .17222222222222222222;
69 static const T P02 = .10257936507936507936;
70 static const T P10 = .06388888888888888888;
71 static const T P11 = .06640211640211640211;
72 static const T P20 = .01641501294219154443;
73
74 T t = 0;
75 detail::apa<T> apa;
76
77 {
78 apa[0] = es * P00;
79 t = es * es;
80 apa[0] += t * P01;
81 apa[1] = t * P10;
82 t *= es;
83 apa[0] += t * P02;
84 apa[1] += t * P11;
85 apa[2] = t * P20;
86 }
87
88 return apa;
89 }
90
91 template <typename T>
pj_authlat(T const & beta,detail::apa<T> const & apa)92 inline T pj_authlat(T const& beta, detail::apa<T> const& apa)
93 {
94 T const t = beta + beta;
95
96 return(beta + apa[0] * sin(t) + apa[1] * sin(t + t) + apa[2] * sin(t + t + t));
97 }
98
99 } // namespace detail
100 }}} // namespace boost::geometry::projections
101
102 #endif // BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_AUTH_HPP
103