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// Boost.Geometry (aka GGL, Generic Geometry Library)
// This file is manually converted from PROJ4
// Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands.
// 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)
// This file is converted from PROJ4, http://trac.osgeo.org/proj
// PROJ4 is originally written by Gerald Evenden (then of the USGS)
// PROJ4 is maintained by Frank Warmerdam
// PROJ4 is converted to Geometry Library by Barend Gehrels (Geodan, Amsterdam)
// Original copyright notice:
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
#ifndef BOOST_GEOMETRY_PROJECTIONS_PROJ_MDIST_HPP
#define BOOST_GEOMETRY_PROJECTIONS_PROJ_MDIST_HPP
#include <boost/geometry/util/math.hpp>
namespace boost { namespace geometry { namespace projections
{
namespace detail
{
static const int MDIST_MAX_ITER = 20;
template <typename T>
struct MDIST
{
int nb;
T es;
T E;
T b[MDIST_MAX_ITER];
};
template <typename CT>
inline bool proj_mdist_ini(CT const& es, MDIST<CT>& b)
{
CT numf, numfi, twon1, denf, denfi, ens, T, twon;
CT den, El, Es;
CT E[MDIST_MAX_ITER];
int i, j;
/* generate E(e^2) and its terms E[] */
ens = es;
numf = twon1 = denfi = 1.;
denf = 1.;
twon = 4.;
Es = El = E[0] = 1.;
for (i = 1; i < MDIST_MAX_ITER ; ++i)
{
numf *= (twon1 * twon1);
den = twon * denf * denf * twon1;
T = numf/den;
Es -= (E[i] = T * ens);
ens *= es;
twon *= 4.;
denf *= ++denfi;
twon1 += 2.;
if (Es == El) /* jump out if no change */
break;
El = Es;
}
b.nb = i - 1;
b.es = es;
b.E = Es;
/* generate b_n coefficients--note: collapse with prefix ratios */
b.b[0] = Es = 1. - Es;
numf = denf = 1.;
numfi = 2.;
denfi = 3.;
for (j = 1; j < i; ++j)
{
Es -= E[j];
numf *= numfi;
denf *= denfi;
b.b[j] = Es * numf / denf;
numfi += 2.;
denfi += 2.;
}
return true;
}
template <typename T>
inline T proj_mdist(T const& phi, T const& sphi, T const& cphi, MDIST<T> const& b)
{
T sc, sum, sphi2, D;
int i;
sc = sphi * cphi;
sphi2 = sphi * sphi;
D = phi * b.E - b.es * sc / sqrt(1. - b.es * sphi2);
sum = b.b[i = b.nb];
while (i) sum = b.b[--i] + sphi2 * sum;
return(D + sc * sum);
}
template <typename T>
inline T proj_inv_mdist(T const& dist, MDIST<T> const& b)
{
static const T TOL = 1e-14;
T s, t, phi, k;
int i;
k = 1./(1.- b.es);
i = MDIST_MAX_ITER;
phi = dist;
while ( i-- ) {
s = sin(phi);
t = 1. - b.es * s * s;
phi -= t = (proj_mdist(phi, s, cos(phi), b) - dist) *
(t * sqrt(t)) * k;
if (geometry::math::abs(t) < TOL) /* that is no change */
return phi;
}
/* convergence failed */
BOOST_THROW_EXCEPTION( projection_exception(-17) );
}
} // namespace detail
}}} // namespace boost::geometry::projections
#endif
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