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libcarla/include/system/boost/geometry/srs/projections/proj/tmerc.hpp

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2024-10-18 13:19:59 +08:00
// Boost.Geometry - gis-projections (based on PROJ4)
// Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
// This file was modified by Oracle on 2017, 2018, 2019, 2022.
// Modifications copyright (c) 2017-2022, Oracle and/or its affiliates.
// Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle.
// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
// 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 Boost.Geometry by Barend Gehrels
// Last updated version of proj: 8.2.1
// 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_TMERC_HPP
#define BOOST_GEOMETRY_PROJECTIONS_TMERC_HPP
#include <boost/geometry/util/math.hpp>
#include <boost/geometry/srs/projections/impl/base_static.hpp>
#include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
#include <boost/geometry/srs/projections/impl/projects.hpp>
#include <boost/geometry/srs/projections/impl/factory_entry.hpp>
#include <boost/geometry/srs/projections/impl/function_overloads.hpp>
#include <boost/geometry/srs/projections/impl/pj_mlfn.hpp>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace tmerc
{
static const double epsilon10 = 1.e-10;
/* Constant for "exact" transverse mercator */
static const int proj_etmerc_order = 6;
template <typename T>
inline T FC1() { return 1.; }
template <typename T>
inline T FC2() { return .5; }
template <typename T>
inline T FC3() { return .16666666666666666666666666666666666666; }
template <typename T>
inline T FC4() { return .08333333333333333333333333333333333333; }
template <typename T>
inline T FC5() { return .05; }
template <typename T>
inline T FC6() { return .03333333333333333333333333333333333333; }
template <typename T>
inline T FC7() { return .02380952380952380952380952380952380952; }
template <typename T>
inline T FC8() { return .01785714285714285714285714285714285714; }
template <typename T>
struct par_tmerc
{
T esp;
T ml0;
detail::en<T> en;
};
// More exact: Poder/Engsager
template <typename T>
struct par_tmerc_exact
{
T Qn; /* Merid. quad., scaled to the projection */
T Zb; /* Radius vector in polar coord. systems */
T cgb[6]; /* Constants for Gauss -> Geo lat */
T cbg[6]; /* Constants for Geo lat -> Gauss */
T utg[6]; /* Constants for transv. merc. -> geo */
T gtu[6]; /* Constants for geo -> transv. merc. */
};
template <typename T, typename Parameters>
struct base_tmerc_ellipsoid
{
par_tmerc<T> m_proj_parm;
// FORWARD(e_forward) ellipse
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
{
static const T half_pi = detail::half_pi<T>();
static const T FC1 = tmerc::FC1<T>();
static const T FC2 = tmerc::FC2<T>();
static const T FC3 = tmerc::FC3<T>();
static const T FC4 = tmerc::FC4<T>();
static const T FC5 = tmerc::FC5<T>();
static const T FC6 = tmerc::FC6<T>();
static const T FC7 = tmerc::FC7<T>();
static const T FC8 = tmerc::FC8<T>();
T al, als, n, cosphi, sinphi, t;
/*
* Fail if our longitude is more than 90 degrees from the
* central meridian since the results are essentially garbage.
* Is error -20 really an appropriate return value?
*
* http://trac.osgeo.org/proj/ticket/5
*/
if( lp_lon < -half_pi || lp_lon > half_pi )
{
xy_x = HUGE_VAL;
xy_y = HUGE_VAL;
BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
return;
}
sinphi = sin(lp_lat);
cosphi = cos(lp_lat);
t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
t *= t;
al = cosphi * lp_lon;
als = al * al;
al /= sqrt(1. - par.es * sinphi * sinphi);
n = this->m_proj_parm.esp * cosphi * cosphi;
xy_x = par.k0 * al * (FC1 +
FC3 * als * (1. - t + n +
FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t)
+ FC7 * als * (61. + t * ( t * (179. - t) - 479. ) )
)));
xy_y = par.k0 * (pj_mlfn(lp_lat, sinphi, cosphi, this->m_proj_parm.en) - this->m_proj_parm.ml0 +
sinphi * al * lp_lon * FC2 * ( 1. +
FC4 * als * (5. - t + n * (9. + 4. * n) +
FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t)
+ FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) )
))));
}
// INVERSE(e_inverse) ellipsoid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
{
static const T half_pi = detail::half_pi<T>();
static const T FC1 = tmerc::FC1<T>();
static const T FC2 = tmerc::FC2<T>();
static const T FC3 = tmerc::FC3<T>();
static const T FC4 = tmerc::FC4<T>();
static const T FC5 = tmerc::FC5<T>();
static const T FC6 = tmerc::FC6<T>();
static const T FC7 = tmerc::FC7<T>();
static const T FC8 = tmerc::FC8<T>();
T n, con, cosphi, d, ds, sinphi, t;
lp_lat = pj_inv_mlfn(this->m_proj_parm.ml0 + xy_y / par.k0, par.es, this->m_proj_parm.en);
if (fabs(lp_lat) >= half_pi) {
lp_lat = xy_y < 0. ? -half_pi : half_pi;
lp_lon = 0.;
} else {
sinphi = sin(lp_lat);
cosphi = cos(lp_lat);
t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
n = this->m_proj_parm.esp * cosphi * cosphi;
d = xy_x * sqrt(con = 1. - par.es * sinphi * sinphi) / par.k0;
con *= t;
t *= t;
ds = d * d;
lp_lat -= (con * ds / (1.-par.es)) * FC2 * (1. -
ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) -
ds * FC6 * (61. + t * (90. - 252. * n +
45. * t) + 46. * n
- ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) )
)));
lp_lon = d*(FC1 -
ds*FC3*( 1. + 2.*t + n -
ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n
- ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) )
))) / cosphi;
}
}
static inline std::string get_name()
{
return "tmerc_ellipsoid";
}
};
template <typename T, typename Parameters>
struct base_tmerc_ellipsoid_exact
{
par_tmerc_exact<T> m_proj_parm;
static inline std::string get_name()
{
return "tmerc_ellipsoid";
}
/* Helper functions for "exact" transverse mercator */
inline
static T gatg(const T *p1, int len_p1, T B, T cos_2B, T sin_2B)
{
T h = 0, h1, h2 = 0;
const T two_cos_2B = 2*cos_2B;
const T* p = p1 + len_p1;
h1 = *--p;
while (p - p1) {
h = -h2 + two_cos_2B*h1 + *--p;
h2 = h1;
h1 = h;
}
return (B + h*sin_2B);
}
/* Complex Clenshaw summation */
inline
static T clenS(const T *a, int size,
T sin_arg_r, T cos_arg_r,
T sinh_arg_i, T cosh_arg_i,
T *R, T *I)
{
T r, i, hr, hr1, hr2, hi, hi1, hi2;
/* arguments */
const T* p = a + size;
r = 2*cos_arg_r*cosh_arg_i;
i = -2*sin_arg_r*sinh_arg_i;
/* summation loop */
hi1 = hr1 = hi = 0;
hr = *--p;
for (; a - p;) {
hr2 = hr1;
hi2 = hi1;
hr1 = hr;
hi1 = hi;
hr = -hr2 + r*hr1 - i*hi1 + *--p;
hi = -hi2 + i*hr1 + r*hi1;
}
r = sin_arg_r*cosh_arg_i;
i = cos_arg_r*sinh_arg_i;
*R = r*hr - i*hi;
*I = r*hi + i*hr;
return *R;
}
/* Real Clenshaw summation */
static T clens(const T *a, int size, T arg_r)
{
T r, hr, hr1, hr2, cos_arg_r;
const T* p = a + size;
cos_arg_r = cos(arg_r);
r = 2*cos_arg_r;
/* summation loop */
hr1 = 0;
hr = *--p;
for (; a - p;) {
hr2 = hr1;
hr1 = hr;
hr = -hr2 + r*hr1 + *--p;
}
return sin(arg_r)*hr;
}
/* Ellipsoidal, forward */
//static PJ_XY exact_e_fwd (PJ_LP lp, PJ *P)
inline void fwd(Parameters const& par,
T const& lp_lon,
T const& lp_lat,
T& xy_x, T& xy_y) const
{
//PJ_XY xy = {0.0,0.0};
//const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact);
/* ell. LAT, LNG -> Gaussian LAT, LNG */
T Cn = gatg (this->m_proj_parm.cbg, proj_etmerc_order, lp_lat,
cos(2*lp_lat), sin(2*lp_lat));
/* Gaussian LAT, LNG -> compl. sph. LAT */
const T sin_Cn = sin (Cn);
const T cos_Cn = cos (Cn);
const T sin_Ce = sin (lp_lon);
const T cos_Ce = cos (lp_lon);
const T cos_Cn_cos_Ce = cos_Cn*cos_Ce;
Cn = atan2 (sin_Cn, cos_Cn_cos_Ce);
const T inv_denom_tan_Ce = 1. / hypot (sin_Cn, cos_Cn_cos_Ce);
const T tan_Ce = sin_Ce*cos_Cn * inv_denom_tan_Ce;
#if 0
// Variant of the above: found not to be measurably faster
const T sin_Ce_cos_Cn = sin_Ce*cos_Cn;
const T denom = sqrt(1 - sin_Ce_cos_Cn * sin_Ce_cos_Cn);
const T tan_Ce = sin_Ce_cos_Cn / denom;
#endif
/* compl. sph. N, E -> ell. norm. N, E */
T Ce = asinh ( tan_Ce ); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */
/*
* Non-optimized version:
* const T sin_arg_r = sin(2*Cn);
* const T cos_arg_r = cos(2*Cn);
*
* Given:
* sin(2 * Cn) = 2 sin(Cn) cos(Cn)
* sin(atan(y)) = y / sqrt(1 + y^2)
* cos(atan(y)) = 1 / sqrt(1 + y^2)
* ==> sin(2 * Cn) = 2 tan_Cn / (1 + tan_Cn^2)
*
* cos(2 * Cn) = 2cos^2(Cn) - 1
* = 2 / (1 + tan_Cn^2) - 1
*/
const T two_inv_denom_tan_Ce = 2 * inv_denom_tan_Ce;
const T two_inv_denom_tan_Ce_square = two_inv_denom_tan_Ce * inv_denom_tan_Ce;
const T tmp_r = cos_Cn_cos_Ce * two_inv_denom_tan_Ce_square;
const T sin_arg_r = sin_Cn * tmp_r;
const T cos_arg_r = cos_Cn_cos_Ce * tmp_r - 1;
/*
* Non-optimized version:
* const T sinh_arg_i = sinh(2*Ce);
* const T cosh_arg_i = cosh(2*Ce);
*
* Given
* sinh(2 * Ce) = 2 sinh(Ce) cosh(Ce)
* sinh(asinh(y)) = y
* cosh(asinh(y)) = sqrt(1 + y^2)
* ==> sinh(2 * Ce) = 2 tan_Ce sqrt(1 + tan_Ce^2)
*
* cosh(2 * Ce) = 2cosh^2(Ce) - 1
* = 2 * (1 + tan_Ce^2) - 1
*
* and 1+tan_Ce^2 = 1 + sin_Ce^2 * cos_Cn^2 / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
* = (sin_Cn^2 + cos_Cn^2 * cos_Ce^2 + sin_Ce^2 * cos_Cn^2) / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
* = 1. / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
* = inv_denom_tan_Ce^2
*
*/
const T sinh_arg_i = tan_Ce * two_inv_denom_tan_Ce;
const T cosh_arg_i = two_inv_denom_tan_Ce_square - 1;
T dCn, dCe;
Cn += clenS (this->m_proj_parm.gtu, proj_etmerc_order,
sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i,
&dCn, &dCe);
Ce += dCe;
if (fabs (Ce) <= 2.623395162778) {
xy_y = this->m_proj_parm.Qn * Cn + this->m_proj_parm.Zb; /* Northing */
xy_x = this->m_proj_parm.Qn * Ce; /* Easting */
} else {
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
xy_x = xy_y = HUGE_VAL;
}
}
/* Ellipsoidal, inverse */
inline void inv(Parameters const& par,
T const& xy_x,
T const& xy_y,
T& lp_lon,
T& lp_lat) const
{
//PJ_LP lp = {0.0,0.0};
//const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact);
/* normalize N, E */
T Cn = (xy_y - this->m_proj_parm.Zb)/this->m_proj_parm.Qn;
T Ce = xy_x/this->m_proj_parm.Qn;
if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */
/* norm. N, E -> compl. sph. LAT, LNG */
const T sin_arg_r = sin(2*Cn);
const T cos_arg_r = cos(2*Cn);
//const T sinh_arg_i = sinh(2*Ce);
//const T cosh_arg_i = cosh(2*Ce);
const T exp_2_Ce = exp(2*Ce);
const T half_inv_exp_2_Ce = 0.5 / exp_2_Ce;
const T sinh_arg_i = 0.5 * exp_2_Ce - half_inv_exp_2_Ce;
const T cosh_arg_i = 0.5 * exp_2_Ce + half_inv_exp_2_Ce;
T dCn_ignored, dCe;
Cn += clenS(this->m_proj_parm.utg, proj_etmerc_order,
sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i,
&dCn_ignored, &dCe);
Ce += dCe;
/* compl. sph. LAT -> Gaussian LAT, LNG */
const T sin_Cn = sin (Cn);
const T cos_Cn = cos (Cn);
#if 0
// Non-optimized version:
T sin_Ce, cos_Ce;
Ce = atan (sinh (Ce)); // Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI);
sin_Ce = sin (Ce);
cos_Ce = cos (Ce);
Ce = atan2 (sin_Ce, cos_Ce*cos_Cn);
Cn = atan2 (sin_Cn*cos_Ce, hypot (sin_Ce, cos_Ce*cos_Cn));
#else
/*
* One can divide both member of Ce = atan2(...) by cos_Ce, which gives:
* Ce = atan2 (tan_Ce, cos_Cn) = atan2(sinh(Ce), cos_Cn)
*
* and the same for Cn = atan2(...)
* Cn = atan2 (sin_Cn, hypot (sin_Ce, cos_Ce*cos_Cn)/cos_Ce)
* = atan2 (sin_Cn, hypot (sin_Ce/cos_Ce, cos_Cn))
* = atan2 (sin_Cn, hypot (tan_Ce, cos_Cn))
* = atan2 (sin_Cn, hypot (sinhCe, cos_Cn))
*/
const T sinhCe = sinh (Ce);
Ce = atan2 (sinhCe, cos_Cn);
const T modulus_Ce = hypot (sinhCe, cos_Cn);
Cn = atan2 (sin_Cn, modulus_Ce);
#endif
/* Gaussian LAT, LNG -> ell. LAT, LNG */
// Optimization of the computation of cos(2*Cn) and sin(2*Cn)
const T tmp = 2 * modulus_Ce / (sinhCe * sinhCe + 1);
const T sin_2_Cn = sin_Cn * tmp;
const T cos_2_Cn = tmp * modulus_Ce - 1.;
//const T cos_2_Cn = cos(2 * Cn);
//const T sin_2_Cn = sin(2 * Cn);
lp_lat = gatg (this->m_proj_parm.cgb, proj_etmerc_order, Cn, cos_2_Cn, sin_2_Cn);
lp_lon = Ce;
}
else {
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
lp_lat = lp_lon = HUGE_VAL;
}
}
};
template <typename T, typename Parameters>
struct base_tmerc_spheroid
{
par_tmerc<T> m_proj_parm;
// FORWARD(s_forward) sphere
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
{
static const T half_pi = detail::half_pi<T>();
T b, cosphi;
/*
* Fail if our longitude is more than 90 degrees from the
* central meridian since the results are essentially garbage.
* Is error -20 really an appropriate return value?
*
* http://trac.osgeo.org/proj/ticket/5
*/
if( lp_lon < -half_pi || lp_lon > half_pi )
{
xy_x = HUGE_VAL;
xy_y = HUGE_VAL;
BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
return;
}
cosphi = cos(lp_lat);
b = cosphi * sin(lp_lon);
if (fabs(fabs(b) - 1.) <= epsilon10)
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
xy_x = this->m_proj_parm.ml0 * log((1. + b) / (1. - b));
xy_y = cosphi * cos(lp_lon) / sqrt(1. - b * b);
b = fabs( xy_y );
if (b >= 1.) {
if ((b - 1.) > epsilon10)
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
else xy_y = 0.;
} else
xy_y = acos(xy_y);
if (lp_lat < 0.)
xy_y = -xy_y;
xy_y = this->m_proj_parm.esp * (xy_y - par.phi0);
}
// INVERSE(s_inverse) sphere
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
{
T h, g;
h = exp(xy_x / this->m_proj_parm.esp);
g = .5 * (h - 1. / h);
h = cos(par.phi0 + xy_y / this->m_proj_parm.esp);
lp_lat = asin(sqrt((1. - h * h) / (1. + g * g)));
/* Make sure that phi is on the correct hemisphere when false northing is used */
if (xy_y < 0. && -lp_lat+par.phi0 < 0.0) lp_lat = -lp_lat;
lp_lon = (g != 0.0 || h != 0.0) ? atan2(g, h) : 0.;
}
static inline std::string get_name()
{
return "tmerc_spheroid";
}
};
template <typename Parameters, typename T>
inline void setup(Parameters const& par, par_tmerc<T>& proj_parm)
{
if (par.es != 0.0) {
proj_parm.en = pj_enfn<T>(par.es);
proj_parm.ml0 = pj_mlfn(par.phi0, sin(par.phi0), cos(par.phi0), proj_parm.en);
proj_parm.esp = par.es / (1. - par.es);
} else {
proj_parm.esp = par.k0;
proj_parm.ml0 = .5 * proj_parm.esp;
}
}
template <typename Parameters, typename T>
inline void setup_exact(Parameters const& par, par_tmerc_exact<T>& proj_parm)
{
assert( par.es > 0 );
/* third flattening n */
//since we do not keep n in parameters we compute it here;
const T n = pow(tan(asin(par.e)/2),2);
T np = n;
/* COEF. OF TRIG SERIES GEO <-> GAUSS */
/* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
/* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
/* PROJ_ETMERC_ORDER = 6th degree : Engsager and Poder: ICC2007 */
proj_parm.cgb[0] = n*( 2 + n*(-2/3.0 + n*(-2 + n*(116/45.0 + n*(26/45.0 +
n*(-2854/675.0 ))))));
proj_parm.cbg[0] = n*(-2 + n*( 2/3.0 + n*( 4/3.0 + n*(-82/45.0 + n*(32/45.0 +
n*( 4642/4725.0))))));
np *= n;
proj_parm.cgb[1] = np*(7/3.0 + n*( -8/5.0 + n*(-227/45.0 + n*(2704/315.0 +
n*( 2323/945.0)))));
proj_parm.cbg[1] = np*(5/3.0 + n*(-16/15.0 + n*( -13/9.0 + n*( 904/315.0 +
n*(-1522/945.0)))));
np *= n;
/* n^5 coeff corrected from 1262/105 -> -1262/105 */
proj_parm.cgb[2] = np*( 56/15.0 + n*(-136/35.0 + n*(-1262/105.0 +
n*( 73814/2835.0))));
proj_parm.cbg[2] = np*(-26/15.0 + n*( 34/21.0 + n*( 8/5.0 +
n*(-12686/2835.0))));
np *= n;
/* n^5 coeff corrected from 322/35 -> 332/35 */
proj_parm.cgb[3] = np*(4279/630.0 + n*(-332/35.0 + n*(-399572/14175.0)));
proj_parm.cbg[3] = np*(1237/630.0 + n*( -12/5.0 + n*( -24832/14175.0)));
np *= n;
proj_parm.cgb[4] = np*(4174/315.0 + n*(-144838/6237.0 ));
proj_parm.cbg[4] = np*(-734/315.0 + n*( 109598/31185.0));
np *= n;
proj_parm.cgb[5] = np*(601676/22275.0 );
proj_parm.cbg[5] = np*(444337/155925.0);
/* Constants of the projections */
/* Transverse Mercator (UTM, ITM, etc) */
np = n*n;
/* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */
proj_parm.Qn = par.k0/(1 + n) * (1 + np*(1/4.0 + np*(1/64.0 + np/256.0)));
/* coef of trig series */
/* utg := ell. N, E -> sph. N, E, KW p194 (65) */
/* gtu := sph. N, E -> ell. N, E, KW p196 (69) */
proj_parm.utg[0] = n*(-0.5 + n*( 2/3.0 + n*(-37/96.0 + n*( 1/360.0 +
n*( 81/512.0 + n*(-96199/604800.0))))));
proj_parm.gtu[0] = n*( 0.5 + n*(-2/3.0 + n*( 5/16.0 + n*(41/180.0 +
n*(-127/288.0 + n*( 7891/37800.0 ))))));
proj_parm.utg[1] = np*(-1/48.0 + n*(-1/15.0 + n*(437/1440.0 + n*(-46/105.0 +
n*( 1118711/3870720.0)))));
proj_parm.gtu[1] = np*(13/48.0 + n*(-3/5.0 + n*(557/1440.0 + n*(281/630.0 +
n*(-1983433/1935360.0)))));
np *= n;
proj_parm.utg[2] = np*(-17/480.0 + n*( 37/840.0 + n*( 209/4480.0 +
n*( -5569/90720.0 ))));
proj_parm.gtu[2] = np*( 61/240.0 + n*(-103/140.0 + n*(15061/26880.0 +
n*(167603/181440.0))));
np *= n;
proj_parm.utg[3] = np*(-4397/161280.0 + n*( 11/504.0 + n*( 830251/7257600.0)));
proj_parm.gtu[3] = np*(49561/161280.0 + n*(-179/168.0 + n*(6601661/7257600.0)));
np *= n;
proj_parm.utg[4] = np*(-4583/161280.0 + n*( 108847/3991680.0));
proj_parm.gtu[4] = np*(34729/80640.0 + n*(-3418889/1995840.0));
np *= n;
proj_parm.utg[5] = np*(-20648693/638668800.0);
proj_parm.gtu[5] = np*(212378941/319334400.0);
/* Gaussian latitude value of the origin latitude */
const T Z = base_tmerc_ellipsoid_exact<T, Parameters>::gatg (proj_parm.cbg, proj_etmerc_order, par.phi0, cos(2*par.phi0), sin(2*par.phi0));
/* Origin northing minus true northing at the origin latitude */
/* i.e. true northing = N - par.Zb */
proj_parm.Zb = - proj_parm.Qn*(Z + base_tmerc_ellipsoid_exact<T, Parameters>::clens(proj_parm.gtu, proj_etmerc_order, 2*Z));
}
}} // namespace detail::tmerc
#endif // doxygen
/*!
\brief Transverse Mercator projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Cylindrical
- Spheroid
- Ellipsoid
\par Example
\image html ex_tmerc.gif
*/
//approximate tmerc algorithm
/*
template <typename T, typename Parameters>
struct tmerc_ellipsoid : public detail::tmerc::base_tmerc_ellipsoid<T, Parameters>
{
template <typename Params>
inline tmerc_ellipsoid(Params const&, Parameters const& par)
{
detail::tmerc::setup(par, this->m_proj_parm);
}
};
*/
template <typename T, typename Parameters>
struct tmerc_ellipsoid : public detail::tmerc::base_tmerc_ellipsoid_exact<T, Parameters>
{
template <typename Params>
inline tmerc_ellipsoid(Params const&, Parameters const& par)
{
detail::tmerc::setup_exact(par, this->m_proj_parm);
}
};
/*!
\brief Transverse Mercator projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Cylindrical
- Spheroid
- Ellipsoid
\par Example
\image html ex_tmerc.gif
*/
template <typename T, typename Parameters>
struct tmerc_spheroid : public detail::tmerc::base_tmerc_spheroid<T, Parameters>
{
template <typename Params>
inline tmerc_spheroid(Params const&, Parameters const& par)
{
detail::tmerc::setup(par, this->m_proj_parm);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_tmerc, tmerc_spheroid, tmerc_ellipsoid)
// Factory entry(s) - dynamic projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(tmerc_entry, tmerc_spheroid, tmerc_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(tmerc_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(tmerc, tmerc_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_TMERC_HPP
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