ceph/src/boost/boost/geometry/srs/projections/impl/pj_mlfn.hpp

   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 /* meridional distance for ellipsoid and inverse
  40 **      8th degree - accurate to < 1e-5 meters when used in conjunction
  41 **              with typical major axis values.
  42 **      Inverse determines phi to EPS (1e-11) radians, about 1e-6 seconds.
  43 */
  44
  45 #ifndef BOOST_GEOMETRY_PROJECTIONS_PJ_MLFN_HPP
  46 #define BOOST_GEOMETRY_PROJECTIONS_PJ_MLFN_HPP
  47
  48
  49 #include <cstdlib>
  50
  51 #include <boost/geometry/srs/projections/exception.hpp>
  52 #include <boost/geometry/srs/projections/impl/pj_strerrno.hpp>
  53 #include <boost/geometry/util/math.hpp>
  54
  55
  56 namespace boost { namespace geometry { namespace projections {
  57
  58 namespace detail {
  59
  60 template <typename T>
  61 struct en
  62 {
  63     static const std::size_t size = 5;
  64
  65     T const& operator[](size_t i) const { return data[i]; }
  66     T & operator[](size_t i) { return data[i]; }
  67
  68 private:
  69     T data[5];
  70 };
  71
  72 template <typename T>
  73 inline en<T> pj_enfn(T const& es)
  74 {
  75     static const T C00 = 1.;
  76     static const T C02 = .25;
  77     static const T C04 = .046875;
  78     static const T C06 = .01953125;
  79     static const T C08 = .01068115234375;
  80     static const T C22 = .75;
  81     static const T C44 = .46875;
  82     static const T C46 = .01302083333333333333;
  83     static const T C48 = .00712076822916666666;
  84     static const T C66 = .36458333333333333333;
  85     static const T C68 = .00569661458333333333;
  86     static const T C88 = .3076171875;
  87
  88     T t;
  89     detail::en<T> en;
  90
  91     {
  92         en[0] = C00 - es * (C02 + es * (C04 + es * (C06 + es * C08)));
  93         en[1] = es * (C22 - es * (C04 + es * (C06 + es * C08)));
  94         en[2] = (t = es * es) * (C44 - es * (C46 + es * C48));
  95         en[3] = (t *= es) * (C66 - es * C68);
  96         en[4] = t * es * C88;
  97     }
  98
  99     return en;
 100 }
 101
 102 template <typename T>
 103 inline T pj_mlfn(T const& phi, T sphi, T cphi, detail::en<T> const& en)
 104 {
 105     cphi *= sphi;
 106     sphi *= sphi;
 107     return(en[0] * phi - cphi * (en[1] + sphi*(en[2]
 108         + sphi*(en[3] + sphi*en[4]))));
 109 }
 110
 111 template <typename T>
 112 inline T pj_inv_mlfn(T const& arg, T const& es, detail::en<T> const& en)
 113 {
 114     static const T EPS = 1e-11;
 115     static const int MAX_ITER = 10;
 116
 117     T s, t, phi, k = 1./(1.-es);
 118     int i;
 119
 120     phi = arg;
 121     for (i = MAX_ITER; i ; --i) { /* rarely goes over 2 iterations */
 122         s = sin(phi);
 123         t = 1. - es * s * s;
 124         phi -= t = (pj_mlfn(phi, s, cos(phi), en) - arg) * (t * sqrt(t)) * k;
 125         if (geometry::math::abs(t) < EPS)
 126             return phi;
 127     }
 128     BOOST_THROW_EXCEPTION( projection_exception(error_non_conv_inv_meri_dist) );
 129     return phi;
 130 }
 131
 132 } // namespace detail
 133 }}} // namespace boost::geometry::projections
 134
 135 #endif